Fundamental Medical and Engineering Investigations on Protective Artificial Respiration

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Notes on Numerical Fluid Mechanics and Multidisciplinary Design (NNFM)

Editors W. Schröder/Aachen B.J. Boersma/Delft K. Fujii/Kanagawa W. Haase/München M.A. Leschziner/London J. Periaux/Paris S. Pirozzoli/Rome A. Rizzi/Stockholm B. Roux/Marseille Y. Shokin/Novosibirsk

Fundamental Medical and Engineering Investigations on Protective Artificial Respiration A Collection of Papers from the DFG Funded Research Program PAR

Michael Klaas, Edmund Koch, and Wolfgang Schröder (Eds.)

ABC

Dr.-Ing. Michael Klaas Lehrstuhl für Strömungslehre und Aerodynamisches Institut RWTH Aachen Wüllnerstr. 5a 52062 Aachen Tel.: ++49 (0) 241/80-95412 Fax: ++49 (0) 241/80-92257 E-mail: [email protected]

Prof. Dr.-Ing. Wolfgang Schröder Lehrstuhl für Strömungslehre und Aerodynamisches Institut RWTH Aachen Wüllnerstr. 5a 52062 Aachen Tel.: ++49 (0) 241/80-95410 Fax: ++49 (0) 241/80-92257 E-mail: offi[email protected]

Prof. Dr. rer. nat. Edmund Koch Arbeitsgruppe Klinisches Sensoring und Monitoring Medizinische Fakultät Carl Gustav Carus TU Dresden Fetscherstr. 74 01307 Dresden Tel.: ++49 (0) 351/458-6131 Fax: ++49 (0) 351/458-6325 E-mail: [email protected]

ISBN 978-3-642-20325-1

e-ISBN 978-3-642-20326-8

DOI 10.1007/978-3-642-20326-8 Notes on Numerical Fluid Mechanics and Multidisciplinary Design

ISSN 1612-2909

Library of Congress Control Number: 2011925862 c 2011 

Springer-Verlag Berlin Heidelberg

This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable for prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typeset & Cover Design: Scientific Publishing Services Pvt. Ltd., Chennai, India. Printed on acid-free paper 543210 springer.com

NNFM Editor Addresses

Prof. Dr. Wolfgang Schröder (General Editor) RWTH Aachen Lehrstuhl für Strömungslehre und Aerodynamisches Institut Wüllnerstr. 5a 52062 Aachen Germany E-mail: offi[email protected] Prof. Dr. Kozo Fujii Space Transportation Research Division The Institute of Space and Astronautical Science 3-1-1, Yoshinodai, Sagamihara Kanagawa, 229-8510 Japan E-mail: fujii@flab.eng.isas.jaxa.jp Dr. Werner Haase Höhenkirchener Str. 19d D-85662 Hohenbrunn Germany E-mail: offi[email protected] Prof. Dr. Ernst Heinrich Hirschel (Former General Editor) Herzog-Heinrich-Weg 6 D-85604 Zorneding Germany E-mail: [email protected] Prof. Dr. Ir. Bendiks Jan Boersma Chair of Energytechnology Delft University of Technology Leeghwaterstraat 44 2628 CA Delft The Netherlands E-mail: [email protected] Prof. Dr. Michael A. Leschziner Imperial College of Science Technology and Medicine Aeronautics Department Prince Consort Road London SW7 2BY U.K. E-mail: [email protected]

Prof. Dr. Sergio Pirozzoli Università di Roma “La Sapienza” Dipartimento di Meccanica e Aeronautica Via Eudossiana 18 00184, Roma, Italy E-mail: [email protected] Prof. Dr. Jacques Periaux 38, Boulevard de Reuilly F-75012 Paris France E-mail: [email protected] Prof. Dr. Arthur Rizzi Department of Aeronautics KTH Royal Institute of Technology Teknikringen 8 S-10044 Stockholm Sweden E-mail: [email protected] Dr. Bernard Roux L3M – IMT La Jetée Technopole de Chateau-Gombert F-13451 Marseille Cedex 20 France E-mail: [email protected] Prof. Dr. Yurii I. Shokin Siberian Branch of the Russian Academy of Sciences Institute of Computational Technologies Ac. Lavrentyeva Ave. 6 630090 Novosibirsk Russia E-mail: [email protected]

Foreword

In 2005 the German Research Association DFG launched the research program “Protective Artificial Respiration” which is a joint initiative of medicine and fluid mechanics. The main long-term objective of this program is the development of a more protective artificial respiratory system to reduce the physical stress of patients undergoing artificial respiration. To satisfy this goal 11 projects have been defined. In each of these projects scientists from medicine and fluid mechanics do collaborate in several experimental and numerical investigations to improve the fundamental knowledge on respiration and to develop a more individual artificial breathing concept. This volume contains the papers presented at the “2nd Aachen Symposium on Natural and Artificial Respiration” held at the “Erholungs-Gesellschaft Aachen 1837” in Aachen, Germany on November, 23 – 24, 2009. The symposium was organized by the Institute of Aerodynamics, RWTH Aachen University, Germany. Numerous visiting scientist contributed to the success of this research program, namely Ben Fabry (University of Erlangen, Erlangen, Germany), Samir N. Ghadiali (The Ohio State University, Columbus/OH, USA), Göran Hedenstierna (University Hospital, Uppsala, Sweden), Rof Hubmayr (Mayo Clinic, Rochester/MN, USA), Oliver Jensen (The University of Nottingham, Nottingham, UK), Christian Kähler (Universität der Bundeswehr München, Neubiberg, Germany), ChingLong Lin (University of Iowa, Iowa City/IA, USA), Ralph Lindken (TU Delft, Delft, Netherlands), Young Moon (Korea University, Seoul, Korea), Paolo Pelosi (University of Insubria, Varese, Italy), Christian Putensen (University Hospital Bonn, Bonn, Germany), Michael Quintel (Georg-August-University of Göttingen, Göttingen, Germany), Peter Schmid (Ecole Polytechnique, Palaiseau, France), Arthur .S. Slutsky (St. Michael's Hospital, Toronto, Canada), Christian Stemmer (TU München, Munich, Germany), Bela Suki (Boston University College of Engineering, Boston/MA, USA), and Marcos F. Vidal Melo (Harvard Medical School, Boston/MA, USA). In the name of all scientists involved in the research program „Protective Artificial Respiration”, the speakers of the program, Edmund Koch (TU Dresden, Germany) and Wolfgang Schröder (RWTH Aachen University, Aachen Germany), would like to express gratitude to all the visiting scientists for their contributions. The present monograph is a snapshot of the state-of-the-art of the joint initiative of medicine and engineering to develop new ventilation systems. The volume gives a broad overview of the ongoing work in this field in Germany. The order of the papers in this book corresponds closely to that of the sessions of the Symposium.

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Foreword

The editors are grateful to Prof. Dr. W. Schröder as the General Editor of the "Notes on Numerical Fluid Mechanics and Multidisciplinary Design" and to the Springer-Verlag for the opportunity to publish the results of the Symposium. December 2010

M. Klaas, Aachen E. Koch, Dresden W. Schröder, Aachen

Contents

Advanced Multi-scale Modelling of the Respiratory System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lena Wiechert, Andrew Comerford, Sophie Rausch, Wolfgang A. Wall Analysis of the Flow in Dynamically Changing Central Airways . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E. Hylla, O. Frederich, F. Thiele, M. Puderbach, J. Ley-Zaporozhan, H.-U. Kauczor, X. Wang, H.-P. Meinzer, I. Wegner Cell Physiology and Fluid Mechanics in the Pulmonary Alveolus and Its Capillaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Kerstin Schirrmann, Michael Mertens, Ulrich Kertzscher, Klaus Affeld, Wolfgang M. Kuebler

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33

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Experimental and Numerical Investigation on the Flow-Induced Stresses on the Alveolar-Epithelial-Surfactant-Air Interface . . . . . . . . . . . . . . . . . . S. Meissner, L. Knels, T. Koch, E. Koch, S. Adami, X.Y. Hu, N.A. Adams

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Fluid Mechanical Equilibrium Processes in a Multi-bifurcation Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T. Soodt, A. Henze, D. Boenke, M. Klaas, W. Schr¨ oder

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In Vivo Microscopy and Analysis of Regional Ventilation in a Porcine Model of Acute Lung Injury . . . . . . . . . . . . . . . . . . . . Johannes Bickenbach, Michael Czaplik, Rolf Rossaint

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Contents

Magnetic Resonance Imaging and Computational Fluid Dynamics of High Frequency Oscillatory Ventilation (HFOV) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 Alexander-Wigbert K. Scholz, Lars Krenkel, Maxim Terekhov, Janet Friedrich, Julien Rivoire, Rainer K¨ obrich, Ursula Wolf, Daniel Kalthoff, Matthias David, Claus Wagner, Laura Maria Schreiber Mechanostimulation and Mechanics Analysis of Lung Cells, Lung Tissue and the Entire Lung Organ . . . . . . . . . . . . . . . . . . . . . 129 Stefan Schumann, Katharina Gamerdinger, Caroline Armbruster, Constanze Dassow, David Schwenninger, Josef Guttmann The Effect of Unsteadiness on Particle Deposition in Human Upper and Lung Airways . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 YuXuan Liu, Yang Liu, HaiYan Luo, Martin CM Wong Transport at Air-Liquid Bridges under High-Frequency Ventilation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 Katrin Bauer, Humberto Chaves, Christoph Br¨ ucker Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183

Advanced Multi-scale Modelling of the Respiratory System Lena Wiechert, Andrew Comerford, Sophie Rausch, and Wolfgang A. Wall

Abstract. This chapter is concerned with computational modelling of the respiratory system against the background of acute lung diseases and mechanical ventilation. Conceptually, we divide the lung into two major subsystems, namely the conducting airways and the respiratory zone. Due to their respective complexity, both parts are out of range for a simulation resolving all relevant length scales. Therefore, we develop novel multi-scale approaches taking into account the unresolved parts appropriately. In the respiratory zone, an alveolar ensemble is modelled considering not only tissue behaviour but also the influence of the covering surfactant film. On the global scale, a homogenised parenchyma model is derived from experiments on living lung tissue. At certain hotspots, novel nested multi-scale procedures are utilised to simulate the dynamic behaviour of lung parenchyma as a whole while still resolving alveolar scales locally. In the tracheo-bronchial region, CT-based geometries are employed in fluid-structure interaction simulations. Physiological outflow boundary conditions are derived by considering the impedance of the unresolved parts of the lung in a fully coupled 3D-0D procedure. Finally, a novel coupling approach enables the connection of 3D parenchyma and airway models into one overall lung model for the first time.

1 Introduction When compared to other areas in (computational) continuum biomechanics, like the circulatory or the muscosceletal system, research on the respiratory system is only in its infancy. This is quite astonishing especially when considering the huge impact a better understanding of respiratory mechanics can offer. A sound standing “virtual lung model” could be a valuable tool for Lena Wiechert · Andrew Comerford · Sophie Rausch · Wolfgang A. Wall Institute for Computational Mechanics e-mail: {wiechert,comerford,rausch,wall}@lnm.mw.tum.de

M. Klaas et al. (Eds.): Fundamental Medical and Engineering Invest. on PAR, NNFM 116, pp. 1–32. c Springer-Verlag Berlin Heidelberg 2011 springerlink.com 

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various applications ranging from the better understanding of lung diseases to progress on individual therapeutic approaches. Within the “Protective Artificial Respiration” program, we are interested in improving the treatment of patients suffering from the Acute Respiratory Distress Syndrome (ARDS). This severe diffuse lung disease is characterised by a number of symptoms such as reduced overall lung compliance, edema, severe hypoxemia and general inflammation of the lung parenchyma. Although many therapeutic approaches have been developed, the mortality associated with ARDS remains relatively high (Tsushima et al. 2009). An indispensable tool in the treatment for ARDS is mechanical ventilation. However, heterogeneity of the ARDS lung predisposes patients towards a number of associated complications which are collectively termed ventilator induced lung injuries (VILI) and deemed one of the most important factors in the pathogenesis of ARDS (Ranieri et al. 1999). VILI mainly occurs at the alveolar level of the lungs in terms of primary mechanical and secondary inflammatory injuries (DiRocco et al. 2005). Primary injuries are consequences of alveolar overexpansion or frequent recruitment and derecruitment inducing high shear stresses. Since mechanical stimulation of cells can result in the release of proinflammatory mediators – a phenomenon commonly called mechanotransduction – secondary inflammatory injuries often directly follow, possibly starting a cascade of events leading to sepsis or multi-organ failure. Understanding the reason why the lungs still become damaged or inflamed despite recent developments towards more “protective” ventilation protocols (Amato et al. 1998) is a key question sought by the medical community. Computational models of the respiratory system can provide essential insights into the involved phenomena and open up new vistas towards improved patient-specific ventilation protocols. However, the lung comprises 23 generations of dichotomously bifurcating airways ending in approximately 300 million alveoli. This complexity inhibits a direct numerical simulation resolving all levels of the respiratory system from the onset. Therefore, we first develop detailed models for distinct parts of the lung. However, for our models to be of clinical significance, the regions not modelled explicitly must also be taken into account. Therefore, we have established advanced multi-scale approaches, which connect the individual detailed models, allowing for the simulation of the entire lung. Since our methods are built up from “first principles”, the developed model will be applicable to a wide spectrum of problems and diseases. The work described in the following was realised in our in-house finite element (FE) software platform BACI covering a wide range of applications in computational mechanics, like e.g. multi-field and multi-scale problems, structural and fluid dynamics, material modelling and finite element technology.

2 Computational Model of Pulmonary Alveoli Since pulmonary alveoli are the main site of VILI, a detailed knowledge of all involved phenomena is crucial in order to obtain insights in the underlying

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mechanisms. To this end, it is not only necessary to investigate alveolar soft tissue characteristics but also the influence of the alveolar liquid lining on the overall mechanical behaviour. Previous models usually focused on only one of these two aspects. In Dale et al. (1980), an alveolus was modelled as a network of fibres without considering either the effect of interfacial phenomena or an underlying ground substance. Some subsequent approaches based on the work of Kowe et al. (1986) retained the idea of reducing alveolar soft tissue to a network of fibres while additionally considering surface stresses due to the liquid lining. Other attempts concentrated on the modelling of tissue mechanics whereas interfacial phenomena were treated in a simplified manner or even totally neglected as presented in Karakaplan et al. (1980) or Gefen et al. (2001), respectively. Contrary to the mentioned former approaches, our alveolar model introduced in the following combines a detailed constitutive law for alveolar soft tissue with an elaborate dynamic surface stress model.

2.1 Modelling of Alveolar Tissue Alveolar tissue consists of three layers, the epithelial monolayer of alveolar type I and type II cells, the basal layer comprising the fibre network and – depending on the location – the interstitium or endothelial layer of blood vessels. According to Suki et al. (2005), the fibre network itself is composed of mechanically dominant collagen I as well as collagen III, elastin and proteoglycans. It was shown in Yuan et al. (1997) that the contribution of interstitial cells to alveolar mechanics seems to be marginal and the macroscopic elastic and dissipative properties are dominated by both collagen and elastin. Experimental results presented e.g. in Toshima et al. (2004) suggest that lung tissue can be treated as a homogeneous, isotropic continuum. Assuming a hyperelastic material behaviour, the existence of a strainenergy function (SEF) can be postulated W := W (I¯1 , I3 ) = Wvol (I3 ) + Wiso (I¯1 )

(1)

with Wvol denoting the volumetric and Wiso representing the isochoric part. I3 and I¯1 denote the third and modified first invariant of the right CauchyGreen deformation tensor C given by I3 := detC,

−1/3 I¯1 := I3 trC.

(2)

Since the constituents of alveolar tissue exhibit different mechanical properties, a material model capable of distinguishing the corresponding contributions to the overall energy seems particularly suitable. Following the approach introduced for arterial tissue in Holzapfel et al. (2000), our isochoric part of the SEF therefore consists of two main parts related to the major stressbearing elements in alveolar walls. The first contribution representing mainly

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ground substance and the elastin fibre network is given as follows   W gs (I¯1 ) = c I¯1 − 3 iso

(3)

with c > 0 being a shear-modulus-like parameter. The second contribution to the isochoric SEF is related to the collagen fibre network. Assuming an isotropic distribution of fibre orientations, the corresponding part reads      2  k1 1¯ exp k I − 1 − 1 for I¯1 ≥ 3 2 1 fib ¯ 3 Wiso (I1 ) = 2k2 (4) 0 for I¯1 < 3 following Delfino et al. (1997) with k1 ≥ 0 as a stress-like parameter and k2 > 0 as a dimensionless parameter. Hence, collagen fibres contribute to the overall potential only in case of tension. Since soft biological tissues are commonly known to be quasi-incompressible, a penalty function enforcing this constraint locally is used for the volumetric part of the SEF. It is noteworthy that each part of the SEF fulfils the principles of objectivity and material symmetry as well as the requirements of polyconvexity and a stress-free reference state. More details on the employed constitutive models can be found in Wiechert et al. (2009). Unfortunately, reliable material parameters for single alveolar walls are currently unavailable. Therefore, we fitted our constitutive model to experimental data obtained for lung tissue strips in Al Jamal et al. (2001) as a first step. Consequently, the chosen parameters model a homogenised continuum of alveolar tissue and air rather than a single alveolar interseptum. However, we currently work on deriving parameters for the alveolar wall by resolving the micro-structure of the tested tissue strips in an inverse analysis as presented in section 3.

2.2 Modelling of Alveolar Liquid Lining Pulmonary alveoli are covered by a thin continuous aqueous film with a monomolecular layer of surface active agents – the so-called surfactant – on top of it (Bastacky et al. 1995). This surfactant layer contributes to alveolar stability at low lung volumes and reduces the work of breathing significantly. In general, molecules at an interface are in an energetically unfavourable state compared to those in the bulk due to reduced intermolecular attraction. As a consequence, surface stresses arise that tend to minimise surface area and, thus, interfacial energy. In case of ideal liquids such as water, these surface stresses are constant. By contrast, surface stresses of a surfactant layer depend on the local surfactant concentration. During breathing, the liquid lining periodically expands and contracts, resulting in a periodic variation of surfactant concentration and therefore also surface stresses.

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Fig. 1 Non-linear and time-dependent behaviour of surfactant model for sinusoidal change of interfacial area S. Left: Different amplitudes. Right: Different frequencies.

To capture this particular behaviour, we employ the surfactant constitutive model introduced in Otis et al. (1994). Briefly, current surfactant concentrations Γ are calculated by modelling transport between bulk fluid and interface. An isothermal relationship is then used to determine local surface stresses, which depend nonlinearly and dynamically on the current interfacial area. In the first regime, Γ is less than the maximum equilibrium concentration Γ ∗ and surfactant transport is governed by Langmuir kinetics. The temporal development of Γ depending on the interfacial area S is given by   dΓ  Γ  Γ  S = S k1 C 1 − ∗ − k2 ∗ ∗ dt Γ Γ Γ

(5)

with k1 and k2 being the adsorption and desorption coefficient, respectively, whereas C denotes the bulk concentration of surfactant molecules in the hypophase. The corresponding current surface stress is related to the surfactant concentration via the following linear isotherm γ = γ0 − m1

Γ Γ∗

(6)

where γ0 is the reference surface tension of water and m1 is the experimentally derived isotherm slope for the first regime. In the second regime (Γ ∗ ≤ Γ < Γmax ), the monolayer is modeled as insoluble. Consequently, no mass transport of surfactant takes place and the concentration changes merely due to variations of interfacial area. Again, surface stresses can be calculated with the help of a linear isotherm according to

Γ ∗ γ = γ − m2 −1 (7) Γ∗ with γ ∗ being the minimum equilibrium surface stress and m2 denoting the isotherm slope for the second regime.

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In the third regime, Γ equals the maximum surfactant concentration Γmax and accordingly minimum surface stress γmin is reached. Any further decrease in interfacial area results in a ‘squeeze-out’ of molecules. In Figure 1, plots are shown illustrating the course of γ for different frequencies and amplitudes if interfacial area is changed sinusoidally. Instead of modelling the thin liquid lining explicitly, we confine ourselves to considering the interfacial energy of the surfactant layer only. An isolated surface stress element as e.g. proposed in Kowe et al. (1986), however, degenerates to an ideal point without appropriate boundary conditions. It seems more sensible to establish a direct coupling between bulk and interface mechanics. Therefore, we incorporate the additional interfacial energy of the surfactant layer into the surfaces of standard structural finite elements representing the alveolar wall. Due to the small thickness of the liquid lining, the surface area of the surfactant-air interface and the alveolar wall are assumed to be identical. Consequently, we obtain for the overall work associated with a change in interfacial area  S

Wsurf =

γdS ∗

(8)

S0

with S0 and S denoting initial and current interfacial area, respectively. After discretising the interface in space, the variation of the overall work with respect to the nodal displacements D δWsurf = finally yields

∂ ∂S





δWsurf

S

γdS S0

∂S =γ ∂D

T

∗

∂S ∂D

T δD

T δD = fsurf δD

(9)

(10)

with the force vector

∂S . (11) ∂D The consistent tangent stiffness matrix is derived by linearisation of (11) fsurf = γ

Ksurf = γ



T

T ∂ ∂S ∂γ ∂S ∂S + . ∂D ∂D ∂S ∂D ∂D

(12)

The derivative of the current local surface stresses with respect to the interfacial area can be determined in a straightforward manner based on the constitutive equations introduced previously. In contrast to former approaches presented e.g. in Kowe et al. (1986) or Denny and Schroter (2000), our consistent continuum-mechanical formulation enables us to consider arbitrarily curved interfaces for the first time. More details can be found in Wiechert et al. (2009).

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Fig. 2 Single artificial alveoli with different interfacial configurations under sinusoidally varying hydrostatic pressure (pmax = 600Pa). (a) Undeformed geometry with mesh. (b) Section of undeformed geometry. (c)-(e) Sections of deformed geometries under maximum load in case of (c) tissue, (d) tissue coupled with surfactant and (e) tissue coupled with water film (each exaggerated 1.5 times).

Figure 2 shows first results of simulations combining interfacial effects with the presented material model for an artificial alveolar geometry. The observable differences in the overall deformation states affirm the importance of considering interfacial phenomena in alveolar mechanics. A comparison of the results for surfactant and water films demonstrates the efficiency of surfactant in decreasing the surface tension of the aqueous hypophase, hence reducing the overall stiffness of alveoli. Pathological changes in surfactant composition may thus result in severe alterations of alveolar mechanical behaviour. As illustrated by the exemplary simulations, this effect can inherently be taken into account in our model.

2.3 Geometric Representation Alveolar tissue can be characterised as an irregular open foam consisting of mainly polyhedral structures with average dimensions ranging from 90 to 200μm depending on the species. Recently, micro-CT data for isolated fixed rat lung tissue became available (Schittny et al. 2008), allowing us to investigate realistic alveolar assemblages in detail for the first time. Obviously, overstraining and inflammation of alveolar tissue is a highly local phenomenon. Hence, resolving the alveolar micro-structure and quantifying local stresses and strains in alveolar walls seems to be essential when investigating the effect of VILI. In preliminary studies presented in Rausch et al. (2010a), we studied the influence of local geometric features on the distribution of strains. A cube of lung tissue was segmented from CT data and meshed with recently developed tetrahedral elements (Gee et al. 2009) as shown in Figure 3(a). For our simulations, we prescribed simple global deformation states (Figure 3(b)) and calculated the local principal strains (Figure 3(c)). We found that local strains in alveolar walls are up to four times larger than the prescribed global ones. Consequently, resolving the realistic alveolar morphology is crucial when investigating local overstretching of lung tissue.

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Fig. 3 Simulated deformation of a CT-based alveolar geometry. (a) Detail view of utilised finite element mesh. (b) Uniaxial tension and simple shear as “global” deformation states prescribed in the simulations. (c) Distribution of local third principal strains in case of global uniaxial stretch. Colours from blue to red indicate increasing strains.

However, due to the persisting limited availability of CT-based geometries – particularly for species other than rats –, we are interested in finding ways to generate simplified artificial alveolar representations. Furthermore, realistic geometries require elaborate FE meshes due to their complex irregularity. The simulation using the relatively small alveolar ensemble shown in Figure 3(c) already involves 8.6 million FE. Hence, by analysing general phenomena using CT-based geometries, we want to provide a basis for validating our simpler artificial models later on. A well-established regular shape employed for the representation of artificial alveolar ducts and alveoli is the so-called tetrakaidecahedron or truncated octahedron, see e.g. Fung (1988) or Denny and Schroter (2000). We propose to connect these complex polyhedra to an artificial ventilatory unit by employing a modified version of the labyrinthine algorithm presented in Kitaoka et al. (2000) for cubic alveoli. Point of origin is an assemblage of identical space-filling and initially closed cells, in our case represented by tetrakaidecahedra. By successively opening faces, connections of all cells to an arbitrarily located starting cell are established. The employment of a set of geometry-dependent connection rules a priori guarantees minimal overall pathlength within the ensemble. Since this feature seems essential against the background of optimal gas exchange, the labyrinthine algorithm was deemed suitable to model the presumed physiological state. Examples of created random pathways through an assemblage of 35 tetrakaidecahedra are depicted on the left hand side of Figure 4. For the sake of lucidity, the surrounding tetrakaidecahedra are left out and only the pathways connecting the cell centres are displayed. On the right hand side of Figure 4, a calculated displacement distribution for an assemblage of 91 interconnected 3D alveoli under hydrostatic pressure is shown. Due to the regular shape, alveolar ensembles can be meshed with

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Fig. 4 (a) Random pathways through an assemblage of 35 tetrakaidecahedra. Colours indicate distances to the starting cell with blue denoting proximal and red meaning distal. (b) Ensemble of 91 interconnected alveoli under hydrostatic pressure. Colours from blue to red indicate increasing absolute displacements.

hexahedral elements exclusively. Overall, much less degrees of freedom are required for meshing a cube of the same size than the CT-based geometry presented before. However, the geometric representation is of course simplified here and the similarity of results – particularly the relation between global and local quantities – still needs to be shown. Although alternative concepts for creating interalveolar connections exist in the literature (Denny and Schroter 1996), so far only simplified configurations were used for computational simulations (confer e.g. Denny and Schroter (1997, 2006); Kowe et al. (1986)). Therefore, to the authors’ knowledge no other simulations based on advanced artificial acinar models – not to mention CT-based ones – have been done so far.

3 Computational Model of Lung Parenchyma As indicated in the previous section, the simulation of small alveolar ensembles already becomes computationally very expensive. Hence, modelling all 300 million alveoli in the human lung is obviously not feasible. Therefore, we propose to employ novel multi-scale techniques to resolve the alveolar micro-structure at certain hotspots only and model lung parenchyma as a homogenised continuum otherwise. In the following, both complementary approaches will be briefly presented.

3.1 Homogenised Parenchyma Model Although some experimental data on the mechanical behaviour of lung parenchyma can be found in literature, e.g. in Fukaya et al. (1968), Cavalcante et al. (2005) or Gao et al. (2006), the accuracy is often not adequate and detailed geometrical information, such as clamp location during testing, is missing. To feed our sophisticated models, therefore additional experimental studies are necessary. Hence, we have conducted uniaxial tension tests on living lung tissue prepared from isolated rat lungs as previously described (Martin et al. 1996). Briefly, rat lungs were dissected from the animal, filled with agarose solution und cut into 500μm thick tissue strips. After

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Fig. 5 Determination of material parameters for lung parenchyma. (a) Experimental set-up for uniaxial tension tests with the BoseElectroforce3100. (b) Experimentally determined stress curves. The first three plots show the distribution of different specimens dissected from one animal. The region characterised by the lighter colour is the confidence region of the percentile, the darker colour indicates the confidence region of the quartiles. The last plot compares the quartile confidence regions of three different rat lungs.

slicing, the agarose was washed out again. Previous tests have shown that these so-called precision-cut lung slices (PCLS) are viable for more than three days. Our experiments were performed within 48 hours after dissection of the lungs. As a testing device, the Bose ElectroForce3100 is employed (force transducer with a range of ± 0.5N and a resolution of under 2.5mN, displacement transducer with a range of ± 2.5mm and a resolution of under 12.5μm, see Figure 5(a)). In a first step, we focus on the elastic properties of lung parenchyma. Hence, all tissue strips are preconditioned before testing in order to eliminate viscoelastic effects inherent to all soft biological tissues. Subsequently, the PCLS are cyclically stretched to determine their elastic material behaviour. Interestingly, the experimentally derived stress curves are very similar for both different specimens of one rat and specimens of different animals. A representative selection of stress plots can be found in Figure 5(b). For the determination of a proper constitutive model and the corresponding material parameters, we perform a so-called inverse analysis based on the Levenberg-Marquardt Algorithm (Levenberg 1944; Marquardt 1963). Briefly, we simulate the experiment in silico for each chosen combination of SEF using varying material parameters until we obtain the optimal fit (see Figure 6). In this context, the experimentally derived stresses serve as input for the simulation whereas the displacements are chosen as target values. We did not only compare combinations of SEF found in the literature, but also recombinations of their summands. In order to find a global minimum, a good initial guess is needed. Therefore, material parameters are preconditioned based on their individual influence on the resulting stress-strain curve.

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Fig. 6 Flow chart showing the steps of the inverse analysis using a LevenbergMarquardt algorithm.

The optimal combination of SEF for the constitutive description of lung parenchyma turned out to be Wpar (I 1 , J) = c1 (I 1 − 3)2 + c2 (I 1 − 3)3 + κ (−2lnJ + J 2 − 1) with the fitted parameters c1 = 4.1 kPa, c2 = 20.7 kPa and κ = 4.1 kPa. For full details of the experimental studies, the inverse analysis and the examined material models see Rausch et al. (2010b).

3.2 Multi-scale Parenchyma Model At certain hotspots in our parenchyma model, we want to zoom in on the alveolar micro-structure in order to quantify local stresses and strains relevant for VILI. To bridge the gap between the global parenchyma and the local alveolar level, we have developed a novel computational multi-scale approach based on the nested solution of the boundary value problems (BVP) on both levels. The benefit of this strategy if twofold; firstly, improved homogenised parenchyma properties are derived based on a detailed modeling of the underlying complex micro-structure. Secondly, the global parenchyma model figuratively serves as an “embedding” of locally resolved acinar structures, thereby providing physiologically reasonable boundary conditions for alveolar simulations. Our approach extends existing methods (Feyel and Chaboche 2000; Kouznetsova et al. 2001; Miehe 2003) to coupled and dynamic scenarios inherent to (mechanical) ventilation. To account for the transient effects, we propose to couple a dynamic simulation on the parenchyma level locally with a quasi-static simulation of the discretised alveolar level. This procedure enables us to investigate the time-dependent behaviour of lung parenchyma as a whole and local alveolar ensembles simultaneously without necessitating to resolve the alveolar micro-structure completely.

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On the parenchymal level, a non-linear dynamic problem is discretised in time using the well-known generalised-α time integration scheme (Chung and Hulbert 1993). The corresponding equations of motion are evaluated at so-called generalised midpoints tn+1−αf and tn+1−αm , respectively. In this context, αf and αm are parameters of the time integration scheme and n refers to the time step. The discrete effective dynamic residual of linear momentum balance for a physically undamped system reads RM;effdyn (DM;n+1 ) = MM AM;n+1−αm + FM;Int (DM;n+1−αf ) − FM;Ext;n+1−αf (13) with DM;∗ and AM;∗ being discrete macro-scale displacements and accelerations at the time t∗ . M M , FM;Int and FM;Ext;∗ denote the system’s consistent mass matrix, internal and external force vector, respectively. These non-linear equations can be linearised consistently at tn+1 and solved with a NewtonRaphson iterative scheme. Introducing β and γ as parameters of Newmark’s method and i as macro-scale iteration index, the linearised form finally reads 1 − αm i MM + (1 − αf )KM;T (Din+1−αf )ΔDi+1 M;n+1 = −RM;effdyn (DM;n+1 ). βΔt2 (14) The evaluation of the mass and tangent stiffness matrices MM and KiM;T as well as the residual RiM;effdyn relies on the parenchymal reference density ρM;0 , second Piola-Kirchhoff stresses SiM;n+1−αf and the constitutive matrix i CM;n+1−α . Instead of employing a phenomenological constitutive law, these m quantities are directly computed from so-called representative volume elements (RVE) of the alveolar microstructure. While the reference density ρM;0 is simply calculated as the volume average of the micro-scale counterpart, the determination of the local parenchyma stress-strain relationship, i.e. SiM;n+1−αf and CiM;n+1−αm , is more elaborate involving a complete solution of the underlying micro-scale, i.e. alveolar, BVP. In this connection, the current global deformation state serves as a boundary condition for the alveolar RVE. As a first step, the deformation of the RVE is assumed to be homogeneous on the boundary Γ yielding the following so-called “displacement boundary conditions” T

i

Dim;n+1−αf ;Γ = D FM;n+1−αf .

(15)

In this context, D is a global reference coordinate matrix associated with i the RVE boundary nodes and FM;n+1−αf refers to the macro-scale deformation gradient. Apart from establishing a macro-micro scale transition, this constraining of the fine-scale boundary deformation also enables us to consider the influence of the surrounding structure not modeled explicitly on the alveolar level in an indirect way. The fine-scale problem itself is assumed to be quasi-static since inertial effects are already taken into account on the macro-scale. However, since

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Fig. 7 Schematic overview on nested dynamic multi-scale method for a given time step [tn , tn+1 ]. Nonlinearities on both scales are taken into account.

both scales are fully coupled, a pseudo time step as well as a generalised mid-point tn+1−αf need to be introduced also on the micro-level. By this means, equilibrium can be evaluated at the same physical point in time and information can be transferred between scales consistently. The linearised form of the micro-scale residual of linear momentum balance finally reduces to i;j+1 i;j Km;T (Di;j (16) m;n+1−αf )ΔDm;n+1−αf = −Fm;Int (Dm;n+1−αf ) with j denoting the micro-scale iteration index. After having solved the micro-scale BVP associated with the i-th macroscopic iteration at tn+1−αf , local stresses and strains are available. Global macro-scale stresses and constitutive tensors can then be determined by averaging over the associated RVE. Basic principle is the so-called Hill-Mandel or macro-homogeneity condition (Hill 1963) demanding that the volume average of the variational work on the fine-scale equals the local variational work on the coarse-scale. In this connection, the first Piola-Kirchhoff stresses P and the deformation gradient F are chosen as energy conjugated quantities whose macroscopic measures are obtained as the volume averages of the corresponding microscopic counterparts, i.e.  1 PM = Pm dV (17) V0 Bm;0

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FM

1 = V0

 Bm;0

Fm dV

(18)

where (18) was already used implicitly in the course of the macro-micro transition. It can be shown that for this specific choice – already recommended e.g. in Kouznetsova et al. (2001) and Miehe (2003) – all involved volume averages can be defined exclusively in terms of quantities of the undeformed RVE boundary. Particularly, a consistent constitutive matrix AiM;n+1−αf relating PiM;n+1−αf and FiM;n+1−αf can be determined based on the overall micro-scale stiffness matrix simply by static condensation of the inner degrees of freedom. Standard pull-back operations then allow the calculation i of material quantities SiM ;n+1−αf and CM;n+1−α required for the macro-level f formulation. A schematic representation of the dynamic multi-scale method is shown in Figure 7 (see Wiechert and Wall (2010a) for more details). Since a fully coupled multi-scale analysis – especially in case of large threedimensional problems – is computationally expensive, parallel computing and the employment of efficient solvers are of course indispensable and therefore realised in this work. We use a smoothed aggregation multigrid preconditioned

Fig. 8 Simple example illustrating the mutual coupling of parenchyma and alveolar levels in the multi-scale model. Right: heterogeneous deformation of simplified parenchyma strip due to different liquid lining compositions in local artificial alveolar assemblages. Left: deformation states for alveolar assemblages under surface tension load using traction-free (top) and multi-scale boundary conditions (bottom). Colours from blue to red indicate increasing displacements.

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conjugate gradient method as described in Gee et al. (2008). In Wiechert et al. (2007), we could already show that parallel solver times scale linearly with the number of degrees of freedom for our complex alveolar structures. In Figure 8, a simple numerical example is given. We simulated the behaviour of an idealised parenchyma strip with associated micro-structures consisting of nine artificial interconnected alveoli. A diseased state was modelled by assuming surfactant deficiency, i.e. a purely aqueous liquid lining, in some of the alveolar micro-structures, whereas the surfactant layer was intact in the others. On the right hand side of Figure 8, the impact of the local heterogeneities on the overall behaviour of the parenchyma strip is illustrated. Due to the fully coupled nature of the developed multi-scale approach, the alveolar micro-structure is of course in turn affected by the global parenchyma model. In order to investigate this effect, a comparative single-scale simulation of the chosen alveolar micro-structure with traction-free boundary conditions was conducted. On the left hand side of Figure 8, the deformation states under the surface tension load are depicted. In the comparative simulation, the influence of the surrounding unresolved alveoli is neglected completely. This corresponds to previous alveolar models presented e.g. in Denny and Schroter (2000). In the multi-scale simulation, however, the interdependence effect is inherently considered by means of the employed multi-scale boundary conditions.

4 Computational Model of the Tracheo-Bronchial Region Although VILI is known to occur primarily in the respiratory zone of the lung, obviously also the conducting part plays an essential role in its development. Modelling the tracheo-bronchial region is important for determining the distribution of flow and pressure into the peripheral regions of the lung. In literature, flow in this region has been studied extensively in both idealised geometries (Green 2004; Liu et al. 2003; Zhang and Kleinstreuer 2004) and – more recently – in CT-based geometries (Ma and Lutchen 2006; Kabilan et al. 2006; Wall and Rabczuk 2008). The effects of fluid structure interaction (FSI) in the tracheo-bronchial region, however, have received very little attention. To the authors’ knowledge, the only paper to address this issue was Wall and Rabczuk (2008). Specifically, this effect is important not only for a better reproduction of the in vivo fluid mechanics, but also for the determination of stresses and strains in the airway wall, which potentially are associated with the onset of inflammation and remodelling of the epithelium.

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Fig. 9 Segmented airways utilised in computational simulations.

The coupling of incompressible flows and soft tissue is a very challenging task. Many existing approaches are either unstable or very inefficient in such situations. Therefore, we have developed new robust and efficient coupling schemes for FSI simulations (see K¨ uttler and Wall (2008a,b, 2009)). In particular, we found that the best strategy for such complex biological problems are monolithic schemes (K¨ uttler et al. 2009; Gee et al. 2010). In our studies, we utilise CT-based patient-specific geometries up to a maximum of seven generations (Comerford et al. 2010a). These geometries are extracted from standard CT-images (with a resolution of 0.6mm) which are routinely performed in the hospital (see Figure 9). Following segmentation, high quality meshes are generated, typically containing approximately 2 million tetrahedral elements equating to about 1.6 million degrees of freedom. Compared with previous pure computational fluid dynamics (CFD) simulations, we found that the influence of FSI on normalised flow distributions and secondary flow intensities is moderate (Wall and Rabczuk 2008). However, airflow patterns, both axial and in-plane, were quite different although the changes in cross-sectional areas were only around 2%. Even more importantly, CFD simulations are not capable of capturing stresses in lung tissue. Hence, consideration of airway wall deformability is crucial for investigating mechanisms of VILI. Due to limitations on the number of vessels visible on the CT scan, only a part of the airway tree can be resolved in 3D. Therefore, realistic boundary conditions need to be applied at the outlets of the 3D domain in order to take the peripheral region into account. Recently, we have developed a reduceddimensional model of the non-imageable vessels (Comerford et al. 2010a). Briefly, the 3D airway model is supplemented by simplified 1D trees attached to every 3D outlet as shown schematically in Figure 10(a). By considering the unresolved peripheral impedances, reasonable outflow boundary conditions are derived for the resolved 3D domain. Our approach is based on the application of the linearised momentum equation for flow in flexible tubes which is considered suitable due to the high wave speed. For each individual peripheral airway (radius r, length L), we have the 1D fluid momentum equation given by

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∂u 1 ∂p ν ∂ + = ∂t ρ ∂x r ∂r



∂u r ∂r

17

(19)

where u is the velocity in the streamwise direction, t denotes the time, ρ the fluid density and ν refers to the kinematic viscosity. In addition to the momentum equation, we also have the 1D continuity equation C

∂p ∂q + =0 ∂t ∂x

(20)

where p is the pressure, q is the flow rate and C denotes the vessel compliance, which is given by the following linearised state equation (Suki et al. 1993) C=

2πr3 . Eh

(21)

In this context, E and h refer to the elastic modulus and the wall thickness, respectively. Equations (19) and (20) can then be transformed into an expression for the impedance in the frequency domain by utilising Womersley’s solution, which is an analytical solution for oscillatory flow in a circular tube (Zamir 2000). The derived equation expresses the impedance at the root of each airway segment (Z(0, ω)) as a function of the impedance in the downstream airway tree (Z(L, ω), and is given by Z(0, ω) =

ig −1 sin(ωL/c) + Z(L, ω)cos(ωL/c) cos(ωL/c) + igZ(L, ω)sin(ωL/c)

(22)

where g is the product of the wave speed c and the vessel compliance C and ω refers to the circular frequency. The wave speed c is given by  A0 (1 − Fj ) c= (23) ρC where A0 is the cross sectional area and Fj is a function of the zeroth and first order Bessel functions as calculated from Womersley’s solution. The tubes are continuously bifurcated down to the acinar region. The present implementation allows essentially any tree to be attached to the end of the 3D domain, for example an asymmetric structured tree based on Olufsen et al. (2000). However, we have also established an approach of employing spacefilling trees (see Figure 10(b)) based on previously introduced methods for growing artificial airways in patient-specific lobe geometries (Tawhai et al. 2000). The impedance of each individual branch is then summed in series and parallel in order to obtain the total impedance of a specific tree. At bifurcations, the impedance of the parent vessel is related to the daughter vessels using a standard bifurcation condition

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Fig. 10 (a) 3D airway geometry with a schematic of a reduced dimensional airway tree attached (exemplarily shown for one outlet). (b) Space filling tree in the right inferior lobe as an example of a reduced dimensional tree.

1 1 1 = + ZP ZL ZR

(24)

with subscripts P , L and R denoting parent, left and right daughter vessels, respectively. Recursively applying equations (22) and (24) from the root of the tree down to a critical radius provides the impedance of the lung tree in the frequency domain. To calculate the time varying pressure at the root of a specific tree, the impedance must be first transformed into the time domain via T /2 1  z(t) = Z(ωn)eiωn t . (25) T −T /2

The time varying pressure at the root of the tree is then obtained by convoluting the impedance in the time domain with the history of flow at the outlet, i.e.  τ ∗ p (t) = q(t)z(t − τ )dτ. (26) t−τ

Finally, this model is coupled to the 3D domain utilising a Dirichlet-Neumann approach, introduced originally for blood flow in Vignon-Clementel et al. (2006). This method was shown to be mathematically well posed and computationally efficient. In brief, given some analytical expression for the downstream domain pressure, p∗ (t), the time dependent pressure at the outflow of the 3D domain can be represented by

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 p(t) = Γs

w(p∗ I˜ − τ˜) · ndS = p∗ (t),

19

(27)

where the second term can be neglected if the flow is fully developed (˜ τ = 0). To satisfy this condition, the outlets of the 3D model were extruded until the observed profiles were parabolic and streamwise independent. We could verify that the pressure drop along these artificial pipes is insignificant. For a validation of the impedance based boundary conditions, we investigated the mean flow division ratio in a 3D seven generation airway model without considering FSI. The following distribution was obtained: right lobe (57%), left lobe (42%), right upper lobe (19%), right middle lobe (10%), right lower lobe (28%), upper left lobe (24%) and right lower lobe (18%). These flow divisions were deemed suitable compared with reported literature values (Horsfield et al. 1971). Furthermore, we observed a pressure drop around 33 Pa for a flowrate of 0.5l/s , in which the impedance in the downstream domain is dominated by resistance. This finding also agrees with the reported value in literature (Pedley 1977). In the seven generation airway model, we have also studied how these boundary conditions can be used to simulate hypothetical disease in the human lung which initiates in the peripheral regions. With the proposed coupling strategy, no a priori assumption about flow into the downstream region is made. This is a major advantage over previous impedance implementations. Here, we consider a lung of reduced functional residual capacity due to a light constriction of the left superior lobe. This could represent atelectasis or a derecruited region of the lung. The constriction of the airways is modelled by increasing the impedance on the outlet. The model responds by letting less flow into this lobe and naturally diverting flow to other regions of the lung. This shows that with our method we can simulate heterogeneous changes in the lung. Furthermore, the pressure flow relationship is only really affected in the vicinity of the occlusion. In Figure 11 (a) and (b) it is evident that there is a widening of the loop (hysteresis) indicating an increase in the phase difference between pressure and flow. In other parts of the lung, however, the relationship remains very similar. This suggests the response is quite local, meaning that although pressure and flow are increased throughout the lung, the dynamics between the two remain similar. The aforementioned methodologies have now been utilised for complex models of transient FSI coupled with impedance-based outflow boundary conditions. As a next step, we have considered a model from generation 3 to 7 of the central airways. In these simulations, the airway walls have been modelled as a Neo-Hookean material based on values reported in literature (Kamm 1999). Figures 12(a) and (b) show the differences in pressure and third principal stresses for traction-free and impedance conditions, respectively, demonstrating the influence of the downstream region on simulation results. The importance of the utilised volume structural elements is

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(a)

(b)

(c)

(d)

Fig. 11 Pressure flow relationship for light activity in different generations of the lung under healthy and diseased conditions (partial occlusion of the superior left lobe). (a) Second generation left lobe. (b) Third generation superior left lobe. (c) Third generation inferior left lobe. (d) Third generation inferior right lobe.

highlighted in Figure 12(c). Over the thickness of the wall, we see considerable changes in the stresses due to local bending effects. In order to investigate diseased state conditions in the FSI model, we have modelled an increase in impedance on some of the outlets which lead into the right middle lobe. The results (data not shown) indicate that if such a local occlusion occurs, stresses are elevated throughout the whole lung. In the airways leading into the occluded region, pressure is increased due to the higher impedance values at the outlets. Consequently, local stress levels are elevated and the flow is reduced by approximately 50% (at maximum inspiration). For continuity reasons, flow into the other regions is increased. Hence, stresses are also elevated in the other regions of the lung, albeit not to the same degree. In addition to the above mentioned models for the tracheo-bronchial region, we have also developed an approach to simulate the transport of nanoparticles. Nanoparticle deposition in the human lung is of considerable interest. In particular, they can be potentially utilised in pulmonary medicine for targeted drug delivery of pulmonary and non-pulmonary diseases (via alveolar to pulmonary capillary absorption). Further to drug delivery, the

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Fig. 12 Pressure and stress distribution in the tracheo-bronchial region at maximum inspiration. (a) Comparison of pressure for traction-free and impedance boundary conditions. Note that the impedance conditions essentially represent a model of the generations 7-17. (b) The corresponding stresses in the airway wall for the same simulations. (c) Cross-sectional slice through the airway wall highlighting the importance of true volume representations of the airway wall. (d) Vector plot of velocity distribution with airway wall stresses overlain.

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Fig. 13 Deposition of nanoparticles to the the epithelial surface at early inspiration (red: high deposition, blue: low deposition). (a) 1.5nm particles (b) 5nm particles. The complicated lung surface topology effects the local transport to the epithelial surface. In addition, the surface deposition for smaller sized particles is elevated compared with the larger particles. This phenomenon is directly related to the less convective nature of the transport for smaller particles.

lungs in every day life are exposed to various nanoparticulates, for example exhaust fumes and viruses. The exposure to such particles is interesting due to their highly potent nature, meaning they exhibit a high area to mass ratio (Oberd¨ orster 2001). We have recently undertaken a study in this area and found that the distribution to the epithelial surface is strongly affected by the geometry and prevailing airflow dynamics. Example surface depositions are shown in Figure 13. Further details on this topic can be found in Comerford et al. (2010b).

5 Coupling of Computational Models for Parenchyma and Conducting Airways Recently, we have been focusing on completing our “bridging of scales” via the development of a computationally efficient complete lung model based on the coupling of the aforementioned models in this paper. In this context, two different types of interactions of the models of the conducting and the respiratory zone need to be considered. Firstly, lung parenchyma surrounds the main part of the airway tree, thereby affecting airflow and inducing an interdependence of neighboring airways not present in the isolated airway tree. This effect can be considered by means of the FSI procedures employed so far. Secondly, the parenchyma is inflated by the air transported in the conducting part. Since we confine ourselves to resolving only parts of both the airway tree and the alveolar structures, the transport of gases down to the respiratory zone cannot be simulated explicitly but has to be modelled.

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For this purpose, the parenchyma model needs to be divided into subdomains associated with the outlets of the resolved 3D airway tree. Each subdomain can be thought of as an homogenised continuum consisting of smaller airways and alveoli that is provided with gases by the associated 3D airway. Consequently, we have to couple the volume of air flowing through the outlet with the change in volume of the corresponding parenchyma subdomain (confer Figure 14). In this connection, the determination of air volumes involves integrating the corresponding flowrates over time, e.g. using a one-step theta-scheme dV f = dt (θQn+1 + (1 − θ) Qn ) . The flowrate itself is defined as follows  Q= u da

(28)

(29)

ˆ B

with u being the the fluid velocity at the outlet and a denoting the corresponding area in the deformed configuration. The current volume of the surrounding parenchyma reads  Vs = dv. (30) Ωs

Using

∂xk ∂xk

= 1, (30) can be equivalently written as follows  1 ∇ · xdv 3 Ωs  1 = x · da 3 B∪B∪ ˆ B ˜

Vs =

(31)

where x = X + d denotes the current boundary position depending on the initial coordinates X and current displacements d. The change in parenchymal volume for a given timestep dt, i.e. during [tn , tn+1 ] finally simply equates to s dV s = Vn+1 − Vns .

(32)

Consequently, both air and parenchyma volume changes can be exclusively determined by integrating over the corresponding deforming domain boundaries. In order to ensure that the respective volume changes are equal, we employ a so-called Lagrange multiplier technique. For a single artificial outlet surrounded by homogenised parenchyma, the corresponding constraint potential can be stated as follows   W volco = λ dV s − dV f (33) where λ denotes the Lagrangian multiplier associated with the volume constraint. Obviously, simulation models with multiple outlets simply involve the consideration of multiple constraint potentials. The corresponding additional virtual work reads

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Fig. 14 Conception of coupled 3D models of lower airways and surrounding parenchyma. In addition to the coupling of deformations and velocities at the FSI ˆ is coupled to the change boundary B, the air volume flowing through the outlet B ˆ ∪ B. ˜ in volume of the surrounding parenchyma enclosed by B ∪ B

  ∂dV s ∂dV f δW volco = δλ dV s − dV f + λ δd − λ δu. ∂d ∂u

(34)

In combination with the FSI approach, a 3D overall lung model is established. This allows us to couple the transport of air and corresponding parenchyma deformation for both the inspiration and expiration phases. To the authors’ knowledge, this is the first model capable of simulating the expiration phase in a physiologically realistic manner. After linearisation of (34), the resulting monolithic linear problem including FSI and volume coupling can be solved using Block Gauß-Seidel preconditioned Newton Krylov techniques. For this purpose, methods presented in K¨ uttler et al. (2009) have been extended to the volume coupling case. More details on the associated numerical approaches can be found in Wiechert and Wall (2010b). A simple numerical example is given in Figure 15 and shall illustrate the novel volume-coupled FSI approach. A cuboidal parenchyma model is split into two parts consistent with the two outlets of the embedded deformable cylindrical airways. If both parenchyma blocks exhibit the same material properties, a perfectly symmetric distribution of parenchyma deformations and airflow develops for a prescribed inflow. However, if the Young’s modulus of the right block is doubled, most of the inflowing air is transported into the softer left parenchyma block resulting in a heterogeneous deformation state. In combination with the multi-scale approach of lung parenchyma, the developed models allow to simulate airflow in the airways and coupled local alveolar deformation realistically for the first time. Currently, we are working on simulating coupled airflow and parenchyma deformation using CT-based instead of simplified geometries. Such a CTbased geometry is shown in Figure 16(a), where a three generation airway model feeds the five segmented lobes representing the individual parenchyma blocks.

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Fig. 15 Deformation of parenchyma model and distribution of airflow velocities for a given prescribed inflow. Diagrams on the right visualise how air volumes split between the two outlets. (a) Tissue parameters are homogeneous throughout the parenchyma model. (b) Young’s modulus of the right half of the parenchyma model is twice as large as the one of the left half. (c) Combination of volume-coupling and multi-scale approach enabling the determination of local alveolar stresses and strains depending on the airflow in the associated airways.

In the future, more realistic predictions of the distribution of gases and local deformations involves a further subdivision of parenchymal volumes. For this purpose, we have developed several geometry editing tools. As already introduced in section 4, we implemented an algorithm to generate subjectspecific artificial airway trees for the non-imageable vessels beyond the 3D

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Fig. 16 (a) Segmented lung geometry with the five individual lung lobes. (b) Subdivision of lobes for generating volumes associated with the ends of the spacefilling tree. Here, two subvolumes are created corresponding to a single bifurcation with two daughter airways. This process is repeated continuously down to the desired level.

domain. These trees are grown in each of the segmented five lobes. For the volume coupling approach, each outlet of the resulting airway tree needs to be associated with a block representing homogenised lung parenchyma interspersed with smaller airways. Hence, we have developed an algorithm to subdivide the lobe geometry based on the growing pattern of the spacefilling tree. An illustrative subdivision is shown in Figure 16(b).

6 Summary and Outlook In this paper, substantial progress towards an overall computational lung model has been presented. Since pulmonary alveoli are the main site of VILI, we established a detailed model of alveolar ensembles considering the influence of the covering surfactant film as well as the soft tissue behaviour. Alveolar behaviour was simulated using both artificial as well as CT-based geometries for the first time. We found that resolving the alveolar morphology is important when investigating local overstretching of lung tissue. On the global level, a homogenised parenchyma model was derived from experimental studies on living lung tissue. An inverse analysis was performed to identify a suitable constitutive model and the corresponding optimal parameter set. Furthermore, we have developed a nested dynamic multi-scale approach to zoom in on local alveolar micro-structures at certain hotspots in the parenchyma model. This strategy enables us to formulate physiologically reasonable boundary conditions for local alveolar ensembles.

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For simulating airflow and airway wall deformation in the tracheo-bronchial region, CT-based geometries have been utilised. We have developed new robust FSI schemes enabling the efficient coupling of incompressible flows and soft tissue. Our 3D airway model was supplemented by simplified 1D trees attached to every 3D outlet. A fully coupled approach enabled the consideration of the downstream unresolved impedances, thereby deriving reasonable outflow boundary conditions for the resolved 3D domain. Our findings highlighted the importance of the small airways on pressure and stress levels in the lower generations. In order to establish an overall “virtual” lung model, a novel 3D coupling approach was developed. In combination with the presented FSI methods, the physically motivated coupling of air and parenchyma volumes offers the possibility to simulate airflow and parenchyma deformations realistically for the first time. In the future, the presented individual models as well as the corresponding coupling approaches will be improved further. Subsequently, only a few issues will be listed exemplarily. On the alveolar level, we currently work on characterising the material behaviour of single alveolar walls by combining inverse analysis and multiscale techniques, thereby resolving the local micro-geometry of the tested strips in our computational model. Besides, a comparison of CT-based and artificial geometric representations of alveoli will be drawn. This way, we want to clarify the level of complexity needed in order to simulate local behaviour, e.g. in terms of resulting stresses and strains, appropriately. In the tracheo-bronchial region, more realistic material models for airway walls – including smooth muscle and cartilage rings in the larger vessels as well as oriented elastin and collagen fibre directions – will be developed and supported with parameters derived from upcoming experimental studies on airway wall tissue from the first few generations. As already indicated in section 5, future work will also be concerned with combining our spacefilling algorithm and the volume coupling approach presented in this paper. For the modelling of flow in the resolved 3D and the generated spacefilling tree, we can apply the 3D-0D coupling presented in section 4. In combination with the volume coupling approach, a 3D-0D-3D coupling will be established that will provide detailed insight into respiratory mechanics. The partitioning of the parenchyma model into smaller subdomains by means of the spacefilling tree will enable us to determine the local deformations more realistically. Furthermore, 3D pressure and flow information throughout the lung is available depending on local tissue deformations in the acinar region. In order to validate our computational models, we plan to correlate simulation results with medical data obtained from e.g. PET-CT or EIT imaging for patient-specific disease conditions. The developed model of the respiratory system is a powerful tool as it can provide useful insights into lung ventilation, perfusion and recruitment

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procedures and may help identifying regions at risk from overdistension. With this model, our next step will be the investigation of the effect of different ventilation strategies on local stresses and strains in the lungs. Particularly, we are interested in so-called noisy ventilation, i.e. variable tidal volume ventilation. We believe that our model can provide useful data to aid the development and understanding of such ventilation protocols. Although developed against the background of VILI, our approaches are by no means restricted to this particular application. Hence, we believe that our models can promote further understanding of the lung under healthy and diseased conditions. Thus, they will be valuable for investigating a variety of interesting problems and answering a number of questions brought up by the medical and biological community.

Acknowledgement Support by the German Science Foundation/Deutsche Forschungsgemeinschaft (DFG) through projects WA1521/6-2, WA1521/8-1, WA1521/9-1 and WA1521/ 13-1 within the priority program “Protective Artificial Respiration” (PAR) is gratefully acknowledged. We also would like to thank our medical partners, i.e. the Guttmann workgroup at University Hospital Freiburg (Division of Clinical Respiratory Physiology) and the Uhlig workgroup at University Hospital Aachen (Institute for Pharmacology and Toxicology).

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Analysis of the Flow in Dynamically Changing Central Airways E. Hylla, O. Frederich, F. Thiele, M. Puderbach, J. Ley-Zaporozhan, H.-U. Kauczor, X. Wang, H.-P. Meinzer, and I. Wegner

Abstract. To analyse the dynamic flow in central airways, a workflow has been established which finally enables numerical simulation with simultaneous consideration of natural deformed geometries and inversion of flow direction. A comprehensive description of the radiologic experiments, the segmentation methods and the simulation procedure is given. Finally results gained from simulations in static and dynamic airways are presented and discussed.

1 Introduction In different medical emergencies (e.g. the case of an acute lung injury) artificial ventilation is the only life-saving therapy. Although this is a common procedure, it remains a critical situation often combined with serious side effects. Furthermore it is known, that the parameters used for the ventilation are primarily based on empirical models and studies but not on the understanding of the physiological and physical phenomena. These are some reasons, why the mortality of artificially ventilated patients is still high. Up to this point physics of the respiratory system are E. Hylla · O. Frederich · F. Thiele Berlin Institute of Technology, Institute of Fluid Mechanics and Engineering Acoustics, M¨uller-Breslau-Str. 12, 10623 Berlin, Germany e-mail: [email protected] M. Puderbach German Cancer Research Center, Department of Radiology, Im Neuenheimer Feld 280, 69120 Heidelberg, Germany J. Ley-Zaporozhan · H.-U. Kauczor University Hospital Heidelberg, Department of Diagnostic and Interventional Radiology, Im Neuenheimer Feld 430, 69120 Heidelberg, Germany X. Wang · H.-P. Meinzer · I. Wegner German Cancer Research Center, Department of Medical and Biological Informatics, Im Neuenheimer Feld 280, 69120 Heidelberg, Germany M. Klaas et al. (Eds.): Fundamental Medical and Engineering Invest. on PAR, NNFM 116, pp. 33–48. c Springer-Verlag Berlin Heidelberg 2011 springerlink.com 

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partly unknown. To improve this situation, several interdisciplinary projects funded by the German Research Foundation (DFG) have been launched in order to provide deepened understanding of the fluid and structural physics present in natural geometries of airways. The objectives of the present work are to predict the flow physics and to describe quantitatively the functional relevance of temporary and fixed deformations in the central airways. Therefore, numerical simulations of the unsteady flow in the upper airways have to be enabled, performed and analysed. The interdisciplinary workflow, which enables dynamic simulations in natural airways is given first. The detailed description of the different work packages is followed by the presentation and discussion of simulation results.

2 Workflow The present work is the result of an interdisciplinary cooperation between specialists in different research fields. The acquisition of natural dynamic airway geometries, their preparation and realistic boundary conditions require the abilities and methodic features of radiologists. Extracting the surfaces and their deformations from the medical experiments is performed by medical informatics whereas the flow predictions are an engineering task. In order to study the flow physics in several different human and animal geometries and to extract the functional relevance of the geometries motion, an automated workflow has been developed. An overview over the different work packages which are linked among each other is given in figure 1. The radiologic imaging method Four-Dimensional Computed Tomography (4D-CT) has been utilised for capturing dynamic geometries of the central airways, both human and animal. The output consists of several stacks of greyscale images over the time, in which each stack represents a volume. By means of image segmentation structures like the bronchial tree can be extracted from the images. A time-resolved description of the surface is gained the same way by processing temporal stacks. The anatomic volume is segmented by an adaptive region growing algorithm [1] with as many bifurcation levels as possible. The current method, depending on the image quality and the partial volume effect, reaches up to 7 levels, whereas the optical inspection allows even more levels. In the future with the aid of Bayesian Tracking [2] algorithmically unrecognisable tubular structures will be found based on likelihood estimations allowing to bridge stenosis.

RADIOLOGY

MED. INFORMATICS

FLUID MECHANICS

* 4D−CT−data

* Dynamic segmentation * Surface generation

* Discretisation * Unsteady bc’s * Unsteady flow physics

Fig. 1 Established interdisciplinary workflow.

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3 Radiology 3.1 Animals The animal experiment was performed after approval by the local animal experimental committee, and both care and handling of the animal were in accordance with German law for animal protection. A healthy domestic pig (33 kg) was anaesthetised using intravenous injection of sodium pentobarbital (Narcoren) and pancuronium bromide and intubated using a cuffed endotracheal tube. The examination was performed in supine position during continuous mechanical ventilation. No additional respiratory belt or direct contact breathing control material was used.

3.2 Ventilation Mechanical ventilation was performed using intermittent positive pressure ventilation (Evita 4, Draeger, Germany). The respiratory rate was 20 breaths per minute with an inspiratory/expiratory ratio of 1:2. A tidal volume (Vt ) of 450 mL using a PEEP level of 5 cm H2 O (≈ 490 Pa) was applied.

3.3 CT Scan Protocol Multislice CT was performed using a 16-detector CT (Aquilion-16, Toshiba, Japan). The scanner was calibrated regularly using a water phantom to allow for reliable quantitative measurements and comparison between examinations. A chargecoupled device camera was installed on the end of the CT table, 1.5 m from the animal’s subxiphoidal triangle. The charge-coupled device camera captures the motion picture, and the thoracic respiratory velocity is calculated by using the change of the intensity of pixels in each frame [3]. A larger change corresponds to higher velocity; when switching from inspiration to expiration, the change of the intensity will be small. The motion was detected by the camera and automatically analysed by dedicated software on a PC, resulting in a gating signal. The output signal of the gating device was connected to the scanner instead of the electrocardiogram gating unit. The retrospective respiratory acquisition protocol was adopted from cardiac imaging. Parameters for retrospective scans were collimation 1 mm, 120 kV, 300 mA, gantry rotation time 0.5 seconds, pitch 0.15 (helical pitch 2.4), which was adjusted to the breathing rate, small field of view (240 mm), matrix size 512 × 512, in-plane resolution 0.47 × 0.47mm. No dose modulation was used. All images were reconstructed using the soft tissue kernel (FC12) with a slice thickness of 1 mm and reconstruction interval of 0.8 mm. All volume datasets were reconstructed at 10% increment throughout the respiratory cycle (at 0, 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, and 90%) using half-scan reconstruction. The dose length product using this protocol was approximately 6280 mGy cm for the scan length of 25 cm. Using a standard helical acquisition with a pitch 0.94 (helical pitch 15) approximately 1000 mGy cm results.

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4 Segmentation Methods The segmentation of the tracheo-bronchial tree is an important preliminary step for the flow simulation of the airways. According to the complex structure of the bronchial tree with several branching levels, we present a hybrid segmentation method, which is composed of the following four modules: adaptive region growing, boosting, cropping and manual correction (see figure 2). The algorithm Region Growing is a frequently used technique for segmentation of airways. In this method voxels with grey values within a predefined threshold interval and connected to a seed point are included into the segmentation. Apart from various advantages such as fast runtime and easy usability the main drawback of this method is its sensitivity to leakage. On bronchial tree segmentation leaks occur in the airway wall due to the limited CT resolution and the partial volume effect. Because the airway lumen and the lung interior have similar intensities, the segmentation can be expanded into the lung parenchyma. To avoid this effect we propose an adaptive method [1] in the first module, which performs segmentation in a range of thresholds in a predefined interval simultaneously. After computation, leakages are detected automatically and the threshold before leakage is chosen to be confirmed or adapted by the user. Because the leakage often occurs in one bronchus only while the growing process could be expanded in all other bronchi, we propose a boosting method [4] in the second module which performs the adaptive region growing method at every leaf of the current bronchial tree. After boosting the segmentation may contain false positive voxels because in the images bronchi seem to end in the lung parenchyma which is due to partial volume effect. To remove such voxels a cropping method is presented in the third module. Finally the manual correction module offers the user the possibility to process the segmentation using several interactively selected points. All modules are implemented with the open source C++ library Medical Imaging Interaction Toolkit (MITK) [5].

4.1 Adaptive Region Growing In contrast to the classic region growing algorithm the adaptive method is not performed with fixed thresholds. Instead, the threshold interval is gradually increased during the segmentation process. For each voxel included into the segmentation the corresponding thresholds are noticed in a mask image. Within a given threshold interval, if the number of voxels to be added to segmentation suddenly enormously increases, a leakage is detected. Using the mask image the most complete segmentation without any leakage can be simply provided. If necessary, the user could correct the thresholds interactively. In this case, a 3D segmentation preview is visualised via volume rendering. Finally a tree representation is created from the segmentation using a skeletonisation algorithm.

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Fig. 2 Workflow of the segmentation modules.

4.2 Boosting Leaf nodes of the previously extracted tree serve as seed points for the boosting method. If a seed point has a grey value outside of the used threshold interval, it is substituted for a new point which is selected applying with a cost function. This function consists of an intensity- and a distance-based measure and ensures that the new point is near the original point and has a grey value within the threshold interval. Using the optimised seed points the adaptive region growing method is restarted at the ends of the initially provided bronchial tree. As soon as the number of the newly included voxels exceeds an image specific threshold the segmentation process is aborted. Using a mask image it is guaranteed that voxels which are already included in the initial segmentation are not reconsidered in the boosting method. Finally the result is added to the initial segmentation and the tree representation is recomputed by means of skeletonisation.

4.3 Cropping The cropping method enables the user to interactively select a branch of the tree representation and to remove the selection from both segmentation image and tree representation. For a fast correction the interactively picked position within the tree is analysed and the corresponding bronchus and all child bronchi are marked at once and visualised as selected.

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4.4 Manual Correction Once the size of a bronchial wall falls below image resolution the bronchus is not captured as tubular structure inside the image. Medical experts often still can distinguish between bronchus and parenchyma and thus add a manually segmented bronchus to the segmentation result. For manual segmentation the user sets at least a start and an end point inside the partially shown bronchus. Optionally a few way points can be defined on the way from start to end point. The way points support to extract a region of interest (ROI) around the bronchus which lowers the duration time of the following algorithms. A vesselness image is calculated from the image with the size of the ROI using a multiscale approach. The result serves as a cost image in a minimal cost path algorithm. This algorithm provides a curve between the start and the end point. Furthermore the curve is attracted by the way points. The resulting curve is then post processed to the centreline of the bronchus. Finally, the radius of the bronchus is estimated using the scale image in the multiscale approach.

4.5 Dynamic Segmentation By using the hybrid module based segmentation process, one bronchial tree can be extracted out of a stack of CT images. To segment the bronchial tree out of a time series of CT images one can either segment each time step independently or reuse the parameters found for the previous image stack to process the tree segmentation of the next image stack. As the image quality varies between different time steps due to motion artefacts and such, using optimal parameters per time step might result in a varying diameter of the same bronchus. And as the goal of this project is to simulate air flow within the bronchial tree, only changes due to respiratory motion are to be extracted. Thus using one set of parameters for all time steps is proposed here even though the optimal parameters per time step lead to the possibly deepest bronchial tree segmentation per time step.

5 Simulation Methodology The following flow predictions are based on the three-dimensional, incompressible Navier-Stokes equations (1) and the law of mass conservation for the incompressible case (2): ∂u 1 + (u · ∇) u + ∇p − ν ∇2 u = 0 (1) ∂t ρ ∇ · u = 0.

(2)

The properties of the Newtonian fluid are the kinematic viscosity ν , the density ρ , the velocity vector u and the pressure p. The employed flow solver [6] is based on a Finite-Volume discretisation of second order accuracy in space and time. Furthermore, the solver uses the SIMPLE algorithm [7] coupling pressure and velocity fields. Convective terms can be treated with upwind, central or flux-blending based

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difference schemes. The equation systems are solved using a BiCGSTAB solver [8] with ILU preconditioning techniques. To enable flow simulation in complex and moving geometries like those of a bronchial tree, the Immersed Boundary (IB) Method [9] was integrated into the above mentioned flow solver [10]. The simulation code is written in FORTRAN and MPI is used to parallelise large scale calculations.

5.1 Immersed Boundary Approach The IB Method is a numerical approach, which is best suited for simulating flows within complex and moving geometries [11]. Instead of one body-fitted grid, two grids are used (figure 3): a Cartesian computational grid (Ω ), often containing isotropically refined regions, and one grid (Γb ) to represent the surface envelope of the fluid region. The essential advantage of this method is the distinction between the computational grid and the surface description. Imposition of the boundary conditions at the surface grid, which is immersed into the Cartesian grid, is the main issue of the IB-Method. One way to impose the boundary conditions is the application of ghost-cells. These are cells of the computational domain lying outside but adjacent to the flow field. The values of these ghost-cells are modified in order to fulfil the boundary condition at the IB surface. By replacing the surface during the simulation it is possible to consider moving geometries.

Γb

Ωb

Ω

+

Ωf

Fig. 3 Principle of the IB-Method: Ω computational grid, Γb immersed surface grid, nonfluid region Ωb , fluid region Ω f .

Identification and Marking Identification and marking of the computational domain is necessary to distinguish between fluid (Ω f ) and non-fluid (Ωb ) regions. Therefore cell faces of the domain grid to be cut by the IB must be identified. After all intersected cells have been found, the fluid and non-fluid regions are gradually marked with a painter variable. This process has to be repeated each time, the surface grid changes. If all surface configurations are known before the simulation, e.g. in the case of a prescribed motion extracted from natural and dynamically changing geometries, the identification and marking can be realised as a preprocessing step.

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Boundary Conditions The general approach for each type of boundary condition is the same. The difference to other established ghost-cell methods [12] is that the ghost-cells are not calculated. Within the flow field discretisation for an arbitrary variable Φ leads to an equation for each cell p, including coefficient contributions anb from the neighbouring cells and a source term Sφ :

Φ p a p + ∑ Φnb anb = SΦ . As the calculation of Φ neglects all non-fluid cells, contributions from neighbouring ghost-cells (figure 4 a) are gained by interpolation with inner cells (superscript in) and shifted to the source term: ghost ghost in in Φ p a p + ∑ Φnb anb = SΦ − ∑ Φnb anb .

The no-slip wall is the most important boundary condition for complex geometries and its treatment is discussed in the following. Currently velocities of the ghost-cells ughost are interpolated linearly in one direction to gain the no-slip condition on the IB:     1 1 ughost = uin · 1 − + uib · . fib fib The interpolation (figure 4 b) contains velocity contributions of the adjacent inner cell (uin ) and the IB surface (uib ). The distance fib is measured from the centre of the inner cell (in) to the respective point on the immersed surface (ib). If the IB is located close ( fib < 0.5) to the inner cell, interpolated velocities at the ghost-cell can reach unphysical high values, which can cause numerical instability. Currently an alternative interpolation (figure 4 c) based on the next inner cell (i2n) is used for these special cases [10]. The contributions of the ghost-cells are then added to the source term. Thereafter the velocity gradient is recalculated, with respect to the appropriate interpolation. The pressure is extrapolated linearly to the IB and the pressure gradient is recalculated as well. The linear interpolation provides first order accuracy at the immersed boundary. To increase the accuracy the linear interpolation could be replaced by a higher order scheme.

IB outer cell fluid cell ghost cell

a)

ughost

ughost uin

b)

ui2n

c)

Fig. 4 Arrangement of outer-, fluid- and ghost-cells a), original interpolation b) and alternative interpolation c) for a non moving IB (uib = 0).

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Fig. 5 Flow in a steady human lung comparing the results from the IB code and StarCD. Pressure coefficient and velocity values along a stream trace [16].

5.2 Method Validation The simulation software presented has been validated using test cases with increasing complexity. One of them, the steady flow in a generic Weibel lung [13] is an appropriate case coming close to a natural lung flow. The results of the validation published in [14] show a very good agreement for the Weibel lung. In addition, predictions in a steady human lung have been obtained employing the IB code and the commercial solver StarCD [15]. Figure 5 shows an acceptable agreement comparing the two results.

6 Simulation Setup A well resolved dynamic geometry has been acquired via CT from artificially ventilated porcine airways (figure 6 left), which are known to be very similar to human airways. The natural deformations between 10 surfaces representing one respiration cycle were initially extracted employing a rigid registration with subsequent pointto-point mapping. The investigation of the dynamic flow behaviour has been started with approximately 650 000 fluid cells in the first instance. To increase the temporal resolution of a breathing cycle additional surfaces are interpolated linearly among each of the 10 given configurations. This leads to a total number of 160 stages resolving the whole breathing cycle appropriately. The required surface velocity uib at the IB can be determined by a central difference scheme of the deformed surface: uib =

dx x(t + Δ t) − x(t − Δ t) ≈ . dt 2Δ t

Due to the linear interpolation of the surface deformation these wall velocities are stepwise constant. Breathing under normal conditions (duration T = 3s per breathing cycle) at a Reynolds number of Red = 2 000 is assumed for the simulations. Air

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100

L

ΔL [%]

d

γ [%]

8

endotracheal tube

4

0 0

25

50 T [%]

75

100

inspiration 0

-100 0

expiration

25

50 T [%]

75

100

Fig. 6 Porcine bronchial tree (left) vertical change (middle) and generic inlet velocity amplification (right) during one breathing cycle.

is modelled as an incompressible fluid with its kinematic viscosity at 25 ◦ C. Fixed mass fluxes modulated with a sinusoidal signal (figure 6 right) are imposed on the inlet and outlet boundaries. Preliminary investigations [17] have shown that the flow behaviour in the bronchial tree is laminar, which makes turbulence modelling unnecessary. The simulation was parallelised by splitting the computational domain into 8 sub-domains using the open source library METIS [18].

7 Results In this section results of the transient process from a steady flow in a static geometry to an oscillatory flow in a dynamic geometry are presented and discussed. Parameters and simulation details are summarised in Table 1. Table 1 Summarised simulation parameters

Geometry

Vertical dimension of the surface (L) [mm] Diameter of the trachea (d) [mm] Diameter of the endotracheal tube [mm]

≈ 247 ≈ 13 ≈6

Grids

Number of triangles of surface grid Number of Cartesian domain cells Number of Cartesian fluid cells

277, 632 2, 060, 993 651, 549

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Number of total iterations Number CPU’s (AMD Opteron 2.2 GHz) Simulation time [h]

50, 000 8 ≈ 48

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Duration of breathing cycle [s] Time steps per breathing cycle Iterations per time step Number CPU’s used for computation Simulation time for 640 time steps [h]

3 160 and 320 400 8 ≈ 240

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7.1 Static Geometry Results of a steady inspiratory flow in the static geometry are shown in figure 7. Following a streamtrace from the inlet to the lowest outlet the absolute velocity, which is dominated by the vertical component w, is decreasing. The most intensive drop of momentum can be found in the upper part, where the fluid has to pass the thin endotracheal tube. This corresponds with the values of the pressure coefficient c p (figure 7 right). The orientation of the endotracheal tube is important. In the present configuration the tube has vaguely the same direction as the left branch, thus the flow tends towards this side. Slices containing velocity vectors reveal different zones of flow effects (figure 8). On the one hand there are core regions with relatively high velocities, and on the other hand there are bypass-like regions. The area close to the first branching is under a strong influence of a large recirculation region, indicated by the upward pointing velocity vectors. Focusing on the higher level branches the velocity distributions appear to be less disturbed and more like typical laminar profiles.

0 1

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Fig. 8 Scaled velocity distributions at selective slices.

7.2 Dynamic Geometry Results of an unsteady simulation considering the changes of the geometry and inversion of flow direction are shown in figure 9. During inspiration there are high local velocities, while the velocity distribution is more homogeneous at the expiration phase. Again this is an effect caused by the endotracheal tube, which generates a jet-like flow under inspiratory condition. This region also comprises secondary flow motions under inspiration. Figure 10 shows a set of images displaying velocity vectors at slices close to the first bifurcation. At the beginning of the second breathing cycle at t = 1.0 T (compare figure 6 right) the velocity profiles still show the behaviour of expiration and then change quickly to inspiration (t = 1.25 T ). Thereafter the velocities in the first branches increase further, although the point of maximum inlet velocity is already passed (t = 1.37 T ). On the other hand the change

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Fig. 9 Velocity distributions at a slice within the first right bifurcation. Maximum inspiration (left) and maximum expiration (right).

from inspiration back to expiration corresponds to the sinusoidal signal imposed at the in- and outlet boundaries (t = 1.5 T ). It is currently unclear, whether this kind of delayed change from expiration to inspiration is a physical or a numerical effect. In the latter case one reason for that could be a too coarse temporal resolution of the breathing cycle. The multiple inflows during expiration guarantee faster development of the solution than the single inflow could achieve during inspiration. Thus a delayed change can only be observed from the expiration to the inspiration. However the delayed flow behaviour remains at a higher resolution of 320 time steps per breathing cycle. In all probability the effect is caused by the constraint of the prescribed surface motion in connection with the fixed mass fluxes at the in- and outlets. The situation can be likely improved by modelling neglected lower airways. Values of the helicity (H = u · (∇ × u)) can be used to indicate rotational secondary flow motion, whereby the sign defines the direction of the rotation. As shown in figure 11 the rotatory influence during inspiration is more important than during the expiration phase. Depending on the flow direction the bifurcations are dividing or joining the mass fluxes, which certainly is reason for the different helicity intensities. Those counter rotating vortex pairs have also been found in human airways [17].

Fig. 10 Oscillating flow within the first branching in a dynamic geometry.

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Fig. 11 Iso surfaces displaying positive (green) and negative (purple) helicity values at maximum inspiration (left) and expiration (right).

8 Conclusions and Outlook To predict the flow physics in natural, dynamically changing airways an interdisciplinary workflow among different departments has been established. This workflow allows to extract geometries representing the anatomy of human and animal airways with dynamic changes during the respiration cycle. A self-developed methodology on the base of the Immersed Boundary Method enables dynamic flow simulations. This approach has been validated and applied to natural geometries gained in the aforementioned process. Steady simulations proved the necessity of a threedimensional dynamic method in order to gain the relevant flow physics. The analysis of the steady flow field in the static geometry also reveals the influence of the endotracheal tube. The oscillating flow field in the dynamic geometry shows some kind of delayed reaction to the change from ex- to inspiration, which has to be examined further. Thereafter different ventilation strategies can be discussed in the future. Although the workflow and the simulation code developed reached a robust state, a phase of improvements has been started. The presented enhanced segmentation

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method using adaptive region growing followed by the boost algorithm allows an increase of the segmentation depth and the accuracy of the extracted deformations. Flow simulations within these recently gained segmentation results will be realised. This more realistic description of the dynamic airways will offer extensive details of the flow physics especially in higher level branches. The generically modulated mass flow at the tubular inflow will be replaced by experimental data, gained during the CT scans. Furthermore the numerical solution procedure will be incorporated by an adaptive mesh algorithm and lung impedance modelling.

Acknowledgements The financial support of the German Research Foundation (DFG) within the scope of the research project “Protective Artificial Respiration” is gratefully acknowledged.

References 1. Wolber, P., Wegner, I., Heimann, T., Wolf, I., Meinzer, H.-P.: Tracking und Segmentierung baumf¨ormiger, tubul¨arer Strukturen mit einem hybriden Verfahren. Bildverarbeitung f¨ur die Medizin, pp. 242–246 (2008) 2. Schaap, M., Smal, I., Metz, C., van Walsum, T., Niessen, W.: Bayesian tracking of elongated structures in 3D images. In: Karssemeijer, N., Lelieveldt, B. (eds.) IPMI 2007. LNCS, vol. 4584, pp. 74–85. Springer, Heidelberg (2007) 3. Zaporozhan, J., Ley, S., Unterhinninghofen, R., Saito, Y., Fabel-Schulte, M., Keller, S., Szabo, G., Kauczor, H.-U.: Free-breathing threedimensional computed tomography of the lung using prospective respiratory gating: charge-coupled device camera and laser sensor device in an animal experiment. Invest. Radiol. 41, 468–475 4. Gergel, I., Wegner, I., Tetzlaff, R., Meinzer, H.-P.: Zweistufige Segmentierung des Tracheobronchialbaums mittels iterativen adaptiven Bereichswachstumsverfahren. Bildverarbeitung f¨ur die Medizin (2009) 5. Wolf, I., Vetter, M., Wegner, I., B¨ottger, T., Nolden, M., Sch¨obinger, M., Hastenteufel, M., Kunert, T., Meinzer, H.-P.: The Medical Imaging Interaction Toolkit. Medical Image Analysis 9, 594–604 (2005) 6. Xue, L.: Entwicklung eines effizienten parallelen L¨osungsalgorithmus zur dreidimensionalen Simulation komplexer turbulenter Str¨omungen. PhD thesis, TU Berlin (1998) 7. Patankar, S.V.: Numerical Heat Transfer and Fluid Flow. McGraw Hill, New York (1980) 8. Saad, Y.: Iterative Methods for Sparse Linear Systems, 2nd edn. SIAM, Philadelphia (2003) 9. Peskin, C.S.: The immersed boundary method. Acta Numerica, 479–512 (2002) 10. Hylla, E.: Validierung und Erweiterung eines numerischen Verfahrens zur Simulation von inkompressiblen Str¨omungen mittels der Immersed Boundary Methode. Diploma thesis, ISTA, TU Berlin (2008) 11. Tseng, Y.H., Ferziger, J.H.: A ghost-cell immersed boundary method for flow in complex geometry. Journal of Computational Physics 192, 593–623 (2003) 12. Mittal, R., Iaccarino, G.: Immersed boundary methods. Annual Review of Fluid Mechanics 37, 239–261 (2005) 13. Weibel, E.R.: Morphometry of the human lung. Springer, Berlin (1963)

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14. Hylla, E., Frederich, O., Mauß, J., Thiele, F.: Application of the immersed boundary method for the simulation of incompressible flows in complex and moving geometries. In: STAB 2008: Notes on Numerical Fluid Mechanics and Multidisciplinary Design (2008) ( in press) 15. CD-adapco, Star-CD version 3.26 - Methodology (2005) 16. Frederich, O., Amtsfeld, P., Hylla, E., Thiele, F., Puderbach, M., Kauczor, H.-U., Wegner, I., Meinzer, H.-P.: Numerically Predicted Flow in Central Airways: Modelling, Simulation and Initial Analysis. In: Proceedings of 6th International Symposium on Turbulence and Shear Flow Phenomena, Seoul (2009) 17. Frederich, O., Amtsfeld, P., Hylla, E., Thiele, F., Puderbach, M., Kauczor, H.-U., Wegner, I., Meinzer, H.-P.: Numerical Simulation and Analysis of the Flow in Central Airways. In: STAB 2008: Notes on Numerical Fluid Mechanics and Multidisciplinary Design (2008) (in press) 18. Karypis, G., Kumar, V.: METIS. A Software Package for Partitioning Unstructured Graphs, Partitioning Meshes, and Computing Fill-Reducing Orderings of Sparse Matrices, Version 4.0, University of Minnesota, Department of Computer Science (1998)

Cell Physiology and Fluid Mechanics in the Pulmonary Alveolus and Its Capillaries Kerstin Schirrmann, Michael Mertens, Ulrich Kertzscher, Klaus Affeld, and Wolfgang M. Kuebler

1 Introduction Depending on the applied ventilation strategy, mechanical ventilation leads to alveolar epithelial and capillary endothelial damage. Protective ventilatory approaches try to minimize this biotrauma while still ensuring sufficient gas exchange. However, the optimization of ventilation strategies is hampered by the lack of insights into the cellular and molecular mechanisms underlying ventilator-induced lung injury, and by the lack of morphological and biomechanical information pertinent to the development of suitable computational and experimental models for ventilation-dependent biofluid mechanics [13, 15, 30]. Here, we present our experimental and simulation studies at the level of the alveoli and their capillaries. Regarding capillary perfusion, we show the results concerning the mechanisms of hypoxic pulmonary vasoconstriction as well as an enlarged experimental model for studying the flow in pulmonary capillary networks. We studied alveolar mechanics, both in the mouse model and in a simulation model, providing insights into the effects of ventilation strategies with regard to the underlying lung injury and disease. Further, we present our results concerning the role of the mechanosensitive transient receptor potential channel TRPV4. Kerstin Schirrmann · Ulrich Kertzscher · Klaus Affeld Charit´e - Universit¨ atsmedizin Berlin, Biofluid Mechanics Lab e-mail: [email protected] Michael Mertens · Wolfgang M. Kuebler Charit´e - Universit¨ atsmedizin Berlin, Institute of Physiology e-mail: [email protected]

M. Klaas et al. (Eds.): Fundamental Medical and Engineering Invest. on PAR, NNFM 116, pp. 49–65. c Springer-Verlag Berlin Heidelberg 2011 springerlink.com 

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2 Intravital Microscopy of the Murine Lung To generate data of alveolar and capillary morphology changes during ventilation in vivo, we developed an intravital microscopy model to visualize subpleural alveoli and pulmonary microvessels in the ventilated mouse lung. Anesthetized mice were intubated and mechanically ventilated. A thoracic window was excised from the right chest wall, covered with a transparent membrane and tightly re-sealed with alpha-cyanoacrylate to provide visual access to the lung. Intrathoracic air was removed and negative intrapleural pressure re-established via a transdiaphragmal intrapleural catheter. Drugs and fluid were administered through a jugular vein catheter and arterial pressure assessed by a carotid artery catheter [29] (Fig. 1). This thoracic window preparation allows for the first time for microscopic visualization and digital recording of pulmonary capillary perfusion and alveolar dynamics in the intact lung of the ventilated, anesthetized mouse.

Fig. 1 Anesthetized mice are mechanically ventilated via a tracheal tube. Catheters are implanted into the right carotid artery and the jugular vein. A circular window of 7–10 mm diameter is excised out of the right thoracic wall, providing visual access to the lower margin of the upper lung lobe. The window is covered by a transparent polyvinylidene membrane and tightly sealed with alpha-cyanoacrylate glue

3 Pulmonary Capillary Perfusion 3.1 Microvascular Perfusion in the Ventilated Mouse Lung Previously, the analysis of larger vascular networks in the intact lung had been restricted to the arteriolar compartment [16]. Intravital microscopy of the murine lung allowed to visualize extensive capillary networks (Fig. 2), measure microvascular blood flow velocity and individual capillary segment length. This data can subsequently be used to simulate the flow in complex networks.

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Fig. 2 Exemplary picture of pulmonary microvessels in the ventilated mouse lung. Arteriolar branching into the dense alveolar capillary network can be seen. Blood vessels were visualized by plasma staining with FITC-Dextran

Fig. 3 Temporal and spatial profile of hypoxic pulmonary vasoconstriction. Bar graph gives relative diameter change in response to hypoxia (FiO2 = 0.11) in medium-sized (30–50 μm diameter) and small arterioles (20–30 μm) and venules (20–30 μm; 30–50 μm) determined 10, 30, and 60 min after FiO2 reduction. *P = 0.05 vs. baseline (FiO2 = 0.3). #P > 0.05 vs. 10 min of hypoxia. Data reproduced from Tabuchi A. et al. [29] with kind permission of Journal of Applied Physiology

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Use of high numerical aperture objective lenses and light-sensitive analog cameras allowed for visualization of pulmonary microvascular responses in mice. For example, we were able to show that hypoxic pulmonary vasoconstriction (HPV) was mainly prominent in medium-sized arterioles (> 50 μm), whereas small arterioles and venules did not constrict markedly in response to hypoxia (Fig. 3). This finding confirms the notion that marked vasoconstrictive response in the pulmonary microvasculature are primarily restricted to arteriolar vessel segments of more than 30 μm diameter [37]. Murine pulmonary arterioles of 30 μm or more stain positive for alpha-smooth muscle actin [22], and relevant HPV responses in pulmonary arterioles of 30–50 μm diameter have previously been demonstrated in isolated, perfused canine and feline lungs by video microscopy [12, 20]. While pulmonary arterioles with diameters of < 30 μm may contain pericytes, which show morphological features of smooth musclelike cells and are considered as contractile cells [5, 32], this mechanism does not seem to contribute to HPV in vivo in a relevant manner. Notably, a differential regulation of the acute and the sustained phase of hypoxic vasoconstriction has been proposed [33, 34]. Characteristically, isolated perfused mouse lungs show a biphasic response to hypoxia [33], that is not reflected by the continuous vasoconstriction response in small pulmonary arterioles of 30– 50 μm diameter as assessed by direct intravital microscopy. This seemingly discrepant findings may suggest a differential regulation of hypoxic vasoconstriction along the pulmonary vascular tree, a notion that is in line with the previous finding that there is a diversity in the distribution of K+ -channels along the pulmonary arteries [2].

3.2 Modeling the Pulmonary Microcirculation For a better understanding of the blood flow in pulmonary capillary networks we introduced a blood model and applied it to a capillary network model. Here, we studied the distributions of flow and hematocrit in the network. It is the basic work for later parameter studies on the effects of lung disease and ventilation strategies on capillary perfusion, gas exchange and mechanical stress in the capillary network. The blood model used consists of dyed water droplets in sunflower oil, representing the red blood cells and the plasma, respectively. The blood model is constantly produced with syringe pumps which are connected to a tube with cannulas where the water droplets form. Droplet size, flow rate and flow fraction of water (equivalent to the haematocrit in blood) can be adjusted. The apparent viscosity of the blood model is in the order of 0.2 Pa s (for flow fraction of water 0.5). The network model has an artificial geometry based on morphological data of a rabbit lung. These were acquired from two stacks of 2-photonmicroscopy images of a fixed rabbit lung by courtesy of Jens Lindert, Columbia University, New York. The basic model geometry is a uniform hexagon network.

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This is deformed in a way that the lengths and diameters of the model segments correspond to the statistics of the rabbit lung segments. Two semicircular representations of the network were milled into polymethyl metacrylate (mirror inverted). The two halves were connected and provided with inlets and outlets. The average diameter of the model segments is 1.6 mm (scale up 400 : 1). The flow in the network model was studied at Reynolds numbers (Re) smaller than one (pulmonary capillary network: Re = 0.01). The network flow was digitally recorded, the movies were analyzed offline. Preprocessing was done with ImageJ [24] and included binarization, gauss filtering and a watershed algorithm. For flow analysis we used self written matlab (The MathWorks, Inc.) code for particle tracking. With that we can study droplet velocity, flow rate and volume fraction of water in each segment as well as transit times of the droplets through the network. Here, we concentrate on the volume fraction of water which is proportional to the number of droplets in a segment. The blood model provides similarities to the capillary blood flow concerning the F˚ ahrraeus effect, flow resistance characteristics (F˚ ahrraeus Lindquist effect) and the existence of separation effects at bifurcations [26]. Figure 4 shows the whole network model (a) and four images of the blood flow in a part of the network at intervals of 1 second (b–e). Note the different number of water droplets within the segments of one image and within the same segment in the four images (for example the segment marked with *). In the segment marked with # flow rates were low and water droplets passed in both directions during the experiment. The main finding is that the flow in our model network is irregular, even though the inlet is steady. This is in accordance with experimental results by Wagner and colleagues, who observed flow switching among capillary segments in isolated, blood-perfused canine lungs [31]. The reason for the unsteadyness in our model lies in the two phase or particulate nature of the model fluid and the droplet induced increase of flow resistance: Segments with high flow rates gather many droplets. These droplets increase the segmental flow resistance and the flow rate decreases. Thus, the droplet number decreases again and the flow rate in parallel segments increases. Less droplets induce resistance decrease and again the flow rate increases. Thus, segments can be perfused with droplets whose geometry induced resistance is much higher than the average. Future studies should address, whether the flow variation in the model network is as self similar as in the canine experiments [31]. With a closer look at the flow in the network model we find two problems that need to be solved: 1) There are main paths between the inlets and outlets with high flow rates while perpendicular segments are hardly perfused. This seems not physiological and will be addressed with altered inlet-outlet combinations and an adjusted network geometry in the future. 2) We also find droplet coalescence at low flow regions. These bigger droplets increase the flow resistance and sometimes block the segment. Blocked segments change the network and are found mainly at regions with very low flow rates. They

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(a)

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therefore do not influence the irregularity of the flow. Moving large droplets increase the effect of droplet induced resistance change and enhance the effect of varying flow rate. However, the described effect was found also in parts of the network without large droplets. Nevertheless, coalescence is supposed to be reduced by emulsifying agents in the next experiments. Additionally, we want to study how the flow changes at varying pressure ratios between the inside and the outside of a flexible network model. With this we intend to model the influences of different ventilation scenarios on the flow in the capillary network.

4 Alveolar Mechanics 4.1 Measurements of Alveolar Mechanics in Healthy and Acid-Injured Lungs Knowledge of alveolar morphological changes during ventilation is essential for the development of lung protective ventilation modes. Until recently, the efficiency of many proposed ventilation strategies could not be assessed in vivo at the level of the distal airways. Previous research focused on lung tissue that had been fixed at static ventilation pressures/volumes [7, 8, 28],

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but could not reflect dynamic changes during the normal ventilation cycle. Nieman and coworkers first proposed an in vivo approach for the visualization of alveolar mechanics in which they opened the thorax and immobilized the lung parenchyma by use of a suction device [10, 23] to avoid displacement of the area of observation during the breathing cycle. These rather unphysiological limitations were overcome in the above mentioned model for contact-free intravital microscopy of the ventilated mouse lung under closed thorax conditions (Sect. 2). Based on their observations of alveolar dynamics in the mechanically fixed lung, Nieman and coworkers proposed that lung volume increase is caused by cyclic opening and collapse of alveoli. The theory of cyclic opening and collapse would suggest the clinical use of ventilation modes that differ significantly from the proposed low tidal volume ventilation in patients with acute lung injury [3]. Based on the Nieman theorem, high inspiration pressures or application of high positive end-expiratory pressures (PEEP) would be useful to recruit more alveoli and keep them open. Overdistension and subsequent mechanical damage of alveoli could be excluded over a large range of tidal volumes, because open alveoli would not undergo additional morphological changes pertinent to overdistension. By use of the described closed thorax model enabling contact free observation and analysis of alveolar dynamics we were able to visualize subpleural alveoli in vivo during the different phases of the respiratory cycle. Subpleural alveolar areas and alveolar number were measured at 0 cmH2 O end-expiratory pressure, and at 6, 12, 18 and 24 cmH2 O end-inspiratory pressure, respectively. In healthy, undamaged lungs the absolute alveolar number per observation field remained constant over the whole ventilatory cycle, whereas the surface area of each alveolus increased with increasing pressure following a sigmoid pressure-area relationship [18]. This finding demonstrates that lung volume increase is caused by inflation of open alveoli while cyclic alveolar recruitment and collapse do not contribute relevantly to the regular respiratory cycle. To address the occurrence of cyclic alveolar opening and collapse in injured lungs, we induced acid aspiration injury in ventilated mice [17]. Following tracheal instillation of HCl (pH 1.5), alveolar dynamics changed in a time-dependent manner, in that alveolar compliance decreased by 50% over the time course of two hours. Similar to the findings in intact lungs, the overall number of alveoli per observation field remained constant, demonstrating the absence of cyclic alveolar opening and collapse even under conditions of established lung injury [18] (Fig. 5). Interestingly, changes of alveolar dynamics in lung injury were heterogeneous, in that some alveoli were not affected by acid aspiration, while others showed a dramatic decrease in alveolar compliance. A relevant concern in the analysis of the intravital microscopic observations is pertinent to the fact that acid instillation may have caused severe alveolar edema, which may have affected alveolar dynamics, yet cannot be identified by conventional intravital microscopy. To rule out this

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Fig. 5 Group data show alveolar pressure-area relationships at baseline, 1 hour and 2 hours after acid instillation in injured lungs. Data reproduced from Mertens M. et al. [18] with kind permission of Critical Care Medicine

possibility, we combined intravital microscopy with optical coherence tomography (OCT). This method allows for discrimination between air and liquid filled structures. It is also suitable to reconstruct the 3-dimensional structure of air filled alveoli. Similar to our intravital microscopic findings, OCT imaging and subsequent 3-dimensional reconstruction demonstrated that alveoli increase in volume with increasing ventilation pressures and that neither healthy lungs nor lungs damaged by acid aspiration showed signs of alveolar flooding [18] (Fig. 6). Our results confirm the intuitive notion that lung volume increase is caused by alveolar volume increase. They refute the results of Nieman and coworkers in that they do not yield any signs for alveolar recruitment or collapse. We consider the marked discrepancy between these findings to result from the different applied experimental models, in that mechanical fixation of the area of observation may favor unphysiological alveolar dynamics such as repetitive opening and collapse. Our findings are clinically relevant with respect to the development and testing of existent and new ventilation strategies and maneuvers. While the opening and collapse hypothesis would favor high pressure ventilation modes and the application of high PEEP, our findings indicate that application of high tidal volume to acid-injured lungs will further amplify lung injury due to overdistension of alveoli. The fact that the alveolar population responds heterogeneously to lung injury further aggravates this scenario, in that high tidal volumes will preferentially cause overdistension of healthy alveoli with a high compliance.

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Fig. 6 An alveolar cluster was recorded at ventilation pressures of 0 cmH2 O (gray) and 24 cmH2 O (reticule) by optical coherence tomography and three-dimensionally reconstructed. Data reproduced from Mertens M. et al. [18] with kind permission of Critical Care Medicine

4.2 Modeling Alveolar Interaction The mechanisms of alveolar volume change are intensively discussed in the community [4, 13, 14, 18]. As described in Sect. 4.1, we found heterogeneous distension of alveoli rather than cyclic opening and collapse in acute lung injury [18]. Understanding the mechanisms of alveolar volume change and alveolar mechanics better may allow for improved evaluation of ventilation strategies such as the described recruitment maneuvers. Here, we use a theoretical model for studying alveolar interaction and stability that allows for simulating the effects of lungs injury and disease at the alveolar level [27]. We also use our model to further discuss the experimental results in mice (Sect. 4.1). The alveolar model is based on pressure volume curves of single alveoli which are derived theoretically. For this derivation only two main influences on the pressure volume relationship are taken into account: the surface tension of the alveolar wall fluid lining (pfl ) and a tissue term (pti ) which involves the tissue elasticity and the connection of the alveoli via collagen and elastin fibers. We simplify these two influences and use a spherical cap model with a ridgid entrance ring for morphology. This results in the following equation for the simplified pressure volume curve of single alveoli (1).  p(V ) = pfl (V ) + pti (V ) =

2γ r(V ) 2γ r(V )

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Fig. 7 Pressure volume curve of a single model alveolus (equation 1)

with γ = 0.02 N/m constant surface tension of the fluid lining, r(V ) volume dependent radius of curvature of the spherical cap, Vsf stress-free volume, a and b parameters defining the pti (see appendix). This pressure volume curve is visualized in Fig. 7. Connected alveoli share the same pressure and are in stable equilibrium in case of static pressure volume curves. Figure 7 shows, that several volumes result in the same pressure p1 (V1 ) = p2 (V2 ). Thus, coexistence of small and big alveoli is possible. We simulated the interaction of two alveoli as follows [27]: We calculated the volume distributions ([V1 , V2 ] in steps) between the alveoli that fulfill the equal pressure condition and tested the stability of the resulting system volumes graphically according to M¨ uller and Strehlow [21]. The result is the quasi-static pressure volume curve of systems of connected alveoli. The characteristics of the modeled alveoli can be varied to simulate dysfunction of the surfactant system (γ), stiffening (a, Vsf ) or size variation (r0 , Vsf ). We simulated the altered alveoli in interaction with a standard alveolus in order to study the secondary effects of lung injury and disease on intact alveoli. The quasi-static pressure volume curve of a system of two connected model alveoli is given in Fig. 8. Selected states are marked from a–k to illustrate the distribution of the overall system volume (x-axis) between the two alveoli. Below 300 Pa both alveoli are collapsed, in the pressure range of 300–800 Pa alveoli of different size can coexist, above 800 Pa both alveoli are open. Inflation and deflation processes differ slightly, a hysteresis occurs. The pressure volume curves of systems with one standard alveolus and one alveolus with altered parameters are given in Figs. 9a (γ1 = 0.072 N/m, surface tension of water) and 9b (a2 = 2a, Vsf,2 = Vsf /2). Note, that the alveolus with increased surface tenstion cannot be open at pressures between 500 and 700 Pa. However, the stiff alveolus can be open at 500 Pa. Further, inflating the connected alveoli to a surface area equivalent to that of a system with two standard alveoli at 700 Pa results in an increased volume of the standard alveoli, which is higher in the stiff-alveolus case.

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Fig. 8 Pressure volume curve of a system with two connected standard model alveoli, derived by combining the pressure volume curves of single alveoli (Fig. 7) and a stability analysis. Volume distributions between the two alveoli are illustrated in small sketches: (a) both alveoli collapsed; (b–f ) one alveolus collapsed, one open; (g–k ) both alveoli open; (f, h) opening of the second alveolus; (g, e) closing of one alveolus. The grey part of the curve is valid only at deflation (h, g, e)

(a)

(b)

Fig. 9 Pressure volume curves of systems with two connected model alveoli: one standard alveolus (left in the sketches) and one alveolus (right) with (a) increased surface tension in the fluid lining (γ1 = 0.72 N/m) and (b) with stiffer tissue properties (a1 = 2a), respectively. Sketches illustrate the volume distribution between the two alveoli. States with system surface areas equivalent to two standard alveoli at 700 Pa are marked with *

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It is known from soap bubbles that the smaller bubbles fill the connected larger soap bubbles since they are dominated by the surface tension of their fluid walls. In alveoli the additional influence of the tissue allows alveoli with identical properties to coexist both at equivalent and at different volumes in the intact lung. Which states of interacting alveoli are stable depends on the pressure and the filling state of the system. Heterogeneous tissue properties and morphology result in more heterogeneous alveolar sizes. Our model includes the assumption, that normal alveoli are open at 500 Pa and increase their volume with pressure increasing to 700 Pa. A transmural pressure of 500 Pa is already provided by the thorax. However, the simulation of surfactant irregularities showed that the injured alveoli were collapsed at 500 as well as at 700 Pa. At the same time, the model predicted that these alveoli can be opened by the application of high pressure (2880 Pa in the example, Fig. 9a) and kept open if the pressure does not decrease below a minimal PEEP (1100 Pa). The alveoli with high surface tension had a similar size as standard alveoli at 700 Pa with a PEEP of approximately 1000 Pa (corresponds to 1500 Pa transmural pressure in Fig. 9a). Thus, our model helps to understand, why recruitment maneuvers can be successfull regarding the re-establishment of alveolar surface area if an adequate PEEP is applied, as known from clinical observations [14, 19]. It is also considered, that healthy tissue might be overdistended during recruitment maneuvers [9, 13, 14]. This can be understood with our model as well since the undamaged standard alveolus is markedly distended even during PEEP application. Changes in tissue characteristics resulting in lower compliance and smaller stress free volume have different effects: Derecruitment is unlikely and re-establishment of the surface area requires high pressures, even higher than in the example with surfactant depletion. In this kind of lung injury recruitment maneuvers and PEEP will have small effects but high risk of overdistension of parallel existing unaffected alveoli. In the mouse experiments small alveoli in normal lungs had a higher compliance and were more affected by the acid injury than bigger alveoli [18]. The simulation model for alveolar interaction cannot explain which alveoli will be affected by lung injury, nor can it predict the compliance of small or large alveoli. Still, we can provide an explanation for an observation that seems odd. The experiments showed some alveoli becoming smaller with increasing pressure. Such a situation already occurs with identical alveoli in the simulation model: From sketch i in Fig. 8 to sketch g the pressure increases. The larger alveolus (right) increases the volume while the smaller alveolus (left) decreases in volume. This is in line with the observation that we found alveolar compliance < 1 mostly with smaller alveoli [18]. The model also might help to interpret the different observations in different animal models of lung injury. In experiments with lavage models derecruitment was observed [6]. This is in accordance with our simulations, assumed that this lung injury affects mainly the surfactant system. With acid induced lung injury the number of alveoli was constant and alveolar flooding could be excluded (Sect. 4.1, [18]).

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In our simulation we calculated similar behavior for alveoli with decreased compliance. Thus, our model suggests that this injury is mainly driven by stiffening of the tissue rather than surfactant inactivation. The results of both approaches, the animal experiments and the simulations, urge that a single protective ventilation strategy not exist. We need patient adjusted strategies that take into account the characteristics of the underlying lung injury and disease. Our presented work serves a better understanding of the alveolar mechanics, providing a first step to an individual protective ventilation. Appendix We calculate the volume dependent radius of curvature of the spherical cap r(V ) (2) with the help of the height of the cap h(V ) (3), an auxiliary quantity Z(V ) (4) and the opening diameter r0 = 0.05 mm: r02 h(V ) + 2h(V ) 2 r02 h(V ) = Z(V ) − Z(V )   13  3V r06 π 2 + 9V 2 Z(V ) = + π π r(V ) =

(2) (3)

(4)

We set the tissue component of the pressure volume relationship as linear as of a certain volume with zero pressure below the intersection with the volume axis, since the tissue is assumed not to bear compressive stress (5):  0 for V < Vsf = − ab pti (V ) = (5) aV + b else. From pressures and volumes at the end of inspiration and expiration we receive a = 1.29 × 1014 Pa/m3 , b = 1.11 × 103 Pa [27].

5 The Role of the Transient Receptor Potential Channel TRPV4 in Ventilator Induced Lung Injury Mechanical forces play an important role in the regulation, function and metabolism of cells [25]. Shear-stress or static distension trigger endothelial responses, in that they are sensed by cell-cell/cell-matrix interactions, caveolae, the endothelial surface layer, cilia, and ion channels [1]. Over recent years, the transient receptor potential (TRP) family of ion channels has been identified as a group of polymodal sensory channels. The TRP family consists of seven subfamilies, of which several members of the

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vanilloid-type (TRPV) subfamily have been implicated in mechanotransduction [35]. Patch clamp analysis identified TRPV4 as a Ca2+ -channel that is expressed and functional in lung microvascular endothelial cells. In isolated perfused rat lungs, we could show endothelial TRPV4 to be activated by increases in lung hydrostatic pressure and subsequent endothelial stretch. Activation of TRPV4 was identified to result in lung barrier deterioration and consequently lung edema formation, as demonstrated by the increase in lung vascular filtration coefficient (Kf ) in response to increased hydrostatic pressure or the specific TRPV4 activator 4αPDD, and the inhibition of the pressure-induced Kf increase by the TRPV channel blocker ruthenium red (RuR) [36].

Fig. 10 Kf was determined in isolated perfused rat lungs at baseline (left atrial pressure PLA = 5 cmH2 O) (left) and after 30 minutes of pressure elevation (PLA = 15 cmH2 O) (right). The TRPV4 inhibitor RuR (1 μmol/l) or the TRPV4 activator 4αPDD (10 μmol/l) was added to the perfusate 10 minutes before Kf measurements or PLA elevation, respectively. *P = 0.05 vs. control. Data reproduced from Yin J. et al. [36] with kind permission of Circulation research

Importantly, endothelial stretch does not only constitute a consequence of increased lung hydrostatic pressure, but is similarly a characteristic of alveolar overventilation. In line with this notion, high tidal volume ventilation in isolated perfused rat lungs was likewise shown to cause TRPV4 activation and lung edema formation [11]. This finding identifies TRPV4 antagonists as promising pharmaceutical intervention for the treatment of ventilatorinduced acute lung injury.

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References [1] Ali, M.H., Schumacker, P.T.: Endothelial responses to mechanical stress: where is the mechanosensor? Crit. Care Med. 30(suppl.5), 198–206 (2002) [2] Archer, S.L., Huang, J.M., Reeve, H.L., Hampl, V., Tolarov, S., Michelakis, E., Weir, E.K.: Differential distribution of electrophysiologically distinct myocytes in conduit and resistance arteries determines their response to nitric oxide and hypoxia. Circ. Res. 78(3), 431–442 (1996) [3] ARDSNetwork, Ventilation with lower Tidal Volumes as Compared with Traditional Tidal Volumes for Acute lung Injury and the Acute Respiratory Distress Syndrome. The Acute Respiratory Distress Syndrome Network. N. Engl. J. Med. 342(18):1301–1308 (2000) [4] Carney, D.E., DiRocco, J., Nieman, G.F.: Dynamic alveolar mechanics and ventilator-induced lung injury. Crit. Care Med. 33(suppl.3), 122–128 (2005) [5] Davies, P., Burke, G., Reid, L.: The structure of the wall of the rat intraacinar pulmonary artery: an electron microscopic study of microdissected preparations. Microvasc. Res. 32(1), 50–63 (1986) [6] DiRocco, J.D., et al.: Dynamic alveolar mechanics in four models of lung injury. Intensive Care Med. 32(1), 140–148 (2006), doi:10.1007/s00134-005-2854-3 [7] Dunnill, M.S.: Effect of lung inflation on alveolar surface area in the dog. Nature 214(5092), 1013–1014 (1967) [8] Forrest, J.B.: Lung tissue plasticity: morphometric analysis of anisotropic strain in liquid filled lungs. Respir. Physiol. 27(2), 223–239 (1976) [9] Gattinoni, L., Pesenti, A.: The concept of “baby lung”. Intensive Care Med. 31, 776–784 (2005) [10] Halter, J.M., et al.: Effect of positive end-expiratory pressure and tidal volume on lung injury induced by alveolar instability. Crit. Care 11(1), R20 (2007), doi:10.1186/cc5695 [11] Hamanaka, K., Jian, M.Y., Weber, D.S., Alvarez, D.F., Townsley, M.I., AlMehdi, A.B., King, J.A., Liedtke, W., Parker, J.C.: Trpv4 initiates the acute calcium-dependent permeability increase during ventilator-induced lung injury in isolated mouse lungs. Am. J. Physiol. Lung Cell Mol. Physiol. 293(4), 923 (2007) [12] Hillier, S.C., Graham, J.A., Hanger, C.C., Godbey, P.S., Glenny, R.W., Wagner, W.W.: Hypoxic vasoconstriction in pulmonary arterioles and venules. J. Appl. Physiol. 82(4), 1084–1090 (1997) [13] Hubmayr, R.D.: Perspective on lung injury and recruitment: a skeptical look at the opening and collapse story. Am. J. Respir. Crit. Care Med. 165(12), 1647–1653 (2002) [14] Kacmarek, R.M., Kallet, R.H.: Should recruitment maneuvers be used in the management of ali and ards? Respir. Care 52(5), 622–631 (2007) [15] Kuebler, W.M., Parthasarathi, K., Lindert, J., Bhattacharya, J.: Real-time lung microscopy. J. Appl. Physiol. 102(3), 1255–1264 (2007), doi:10.1152/japplphysiol.00786.2006 [16] Kuhnle, G.E., Groh, J., Leipfinger, F.H., Kuebler, W.M., Goetz, A.E.: Quantitative analysis of network architecture, and microhemodynamics in arteriolar vessel trees of the ventilated rabbit lung. Int. J. Microcirc. Clin. Exp. 12(3), 313–324 (1993)

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[17] Matute-Bello, G., Frevert, C.W., Martin, T.R.: Animal models of acute lung injury. Am. J. Physiol. Lung Cell Mol. Physiol. 295(3), L379–L399 (2008), doi:10.1152/ajplung.00010.2008 [18] Mertens, M., et al.: Alveolar dynamics in acute lung injury: heterogeneous distension rather than cyclic opening and collapse. Crit. Care Med. 37(9), 2604–2611 (2009), doi:10.1097/CCM.0b013e3181a5544d [19] Mols, G., Priebe, H.J., Guttmann, J.: Alveolar recruitment in acute lung injury. Br. J. Anaesth. 96(2), 156–166 (2006) [20] Moudgil, R., Michelakis, E.D., Archer, S.L.: Hypoxic pulmonary vasoconstriction. J. Appl. Physiol. 98(1), 390–403 (2005), doi:10.1152/japplphysiol.00733.2004 [21] M¨ uller, I., Strehlow, P.: Rubber and Rubber Balloons, Paradigms of Thermodynamics. LNP, vol. 637. Springer, Heidelberg (2004), doi:10.1007/b93853 [22] Paddenberg, R., Knig, P., Faulhammer, P., Goldenberg, A., Pfeil, U., Kummer, W.: Hypoxic vasoconstriction of partial muscular intra-acinar pulmonary arteries in murine precision cut lung slices. Respir. Res. 7, 93 (2006), doi:10.1186/1465-9921-7-93 [23] Pavone, L., et al.: Alveolar instability caused by mechanical ventilation initially damages the nondependent normal lung. Crit. Care 11(5), R104 (2007), doi:10.1186/cc6122 [24] Rasband, W.S.: Imagej (1997–2009), http://rsb.info.nih.gov/ij/ [25] Riley, D.J., Rannels, D.E., Low, R.B., Jensen, L., Jacobs, T.P.: Nhlbi workshop summary. effect of physical forces on lung structure, function, and metabolism. Am. Rev. Respir. Dis. 142(4), 910–914 (1990) [26] Schirrmann, K., Kertzscher, U., Goubergrits, L., Kubler, W.M., Affeld, K.: A liquid-liquid-system as a model for blood flow in capillaries. International Journal of Artificial Organs 30(8), 727–727 (2007) [27] Schirrmann, K., Mertens, M., Kertzscher, U., Kuebler, W.M., Affeld, K.: Theoretical modeling of the interaction between alveoli during inflation and deflation in normal and diseased lungs. J. Biomech. (2010), doi:10.1016/j.jbiomech.2009.11.025 (ahead of printing) [28] Staub, N.C., Storey, W.F.: Relation between morphological and physiological events in lung studied by rapid freezing. J. Appl. Physiol. 17, 381–390 (1962) [29] Tabuchi, A., Mertens, M., Kuppe, H., Pries, A.R., Kuebler, W.M.: Intravital microscopy of the murine pulmonary microcirculation. J. Appl. Physiol. 104(2), 338–346 (2008), doi:10.1152/japplphysiol.00348.2007 [30] Uhlig, S.: Ventilation-induced lung injury and mechanotransduction: stretching it too far? Am. J. Physiol. Lung Cell Mol. Physiol. 282(5), 892 (2002), doi:10.1152/ajplung.00124.2001 [31] Wagner, W.W., Todoran, T.M., Tanabe, N., Wagner, T.M., Tanner, J.A., Glenny, R.W., Presson, R.G.: Pulmonary capillary perfusion: intra-alveolar fractal patterns and interalveolar independence. J. Appl. Physiol. 86, 825–831 (1999)

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[32] Walker, D.C., Behzad, A.R., Chu, F.: Neutrophil migration through preexisting holes in the basal laminae of alveolar capillaries and epithelium during streptococcal pneumonia. Microvasc. Res. 50(3), 397–416 (1995), doi:10.1006/mvre.1995.1067 [33] Weissmann, N., Dietrich, A., Fuchs, B., Kalwa, H., Ay, M., Dumitrascu, R., Olschewski, A., Storch, U., Schnitzler, M.M., Ghofrani, H.A., Schermuly, R.T., Pinkenburg, O., Seeger, W., Grimminger, F., Gudermann, T.: Classical transient receptor potential channel 6 (trpc6) is essential for hypoxic pulmonary vasoconstriction and alveolar gas exchange. Proc. Natl. Acad. Sci. U S A 103(50), 19,093–19,098 (2006), doi:10.1073/pnas.0606728103 [34] Weissmann, N., Zeller, S., Schfer, R.U., Turowski, C., Ay, M., Quanz, K., Ghofrani, H.A., Schermuly, R.T., Fink, L., Seeger, W., Grimminger, F.: Impact of mitochondria and nadph oxidases on acute and sustained hypoxic pulmonary vasoconstriction. Am. J. Respir. Cell Mol. Biol. 34(4), 505–513 (2006), doi:10.1165/rcmb.2005-0337OC [35] Yin, J., Kuebler, W.M.: Mechanotransduction by trp channels: General concepts and specific role in the vasculature. Cell Biochem. Biophys. (2009), doi:10.1007/s12013-009-9067-2 [36] Yin, J., Hoffmann, J., Kaestle, S.M., Neye, N., Wang, L., Baeurle, J., Liedtke, W., Wu, S., Kuppe, H., Pries, A.R., Kuebler, W.M.: Negative-feedback loop attenuates hydrostatic lung edema via a cgmp-dependent regulation of transient receptor potential vanilloid 4. Circ. Res. 102(8), 966–974 (2008), doi:10.1161/CIRCRESAHA.107.168724 [37] Ying, X., Minamiya, Y., Fu, C., Bhattacharya, J.: Ca2+ waves in lung capillary endothelium. Circ. Res. 79(4), 898–908 (1996)

Experimental and Numerical Investigation on the Flow-Induced Stresses on the Alveolar-Epithelial-Surfactant-Air Interface S. Meissner, L. Knels, T. Koch, E. Koch, S. Adami, X.Y. Hu, and N.A. Adams

Abstract. To develop new protective artificial respiration strategies a profound knowledge of the lung functionality is required. Still unknown are the dominating effects on the alveolar level and the exact geometry of the alveolar structure itself. We try to fill this gap with our multi-disciplinary research, where on the one hand we are interested in visualization techniques to reconstruct the three-dimensional structure of the alveoli and on the other hand develop a numerical tool to simulate the complex physics at the surfactant enriched liquid-lining layer interface.

1 Introduction Artificial ventilation is an indispensable component in anaesthesiology, intensive care and emergency medicine. In times of a limited or failed spontaneous breathing, artificial ventilation systems can ensure a sufficient oxygenation of a patient in supporting or taking over the spontaneous breathing. But concurrently, as the mechanical ventilation is not physiological, artificial respiratory systems can cause so-called ventilator induced lung injury (VILI) [9] or worsen a pre-existing lung-injury. This problem is mainly caused by the different functionality of the lung during spontaneous breathing and artificial ventilation. Naturally, the diaphragm induces a negative pressure in the ribcage and air is sucked in the alveolar structures. The opposite way around current artificial ventilation concepts press air into the lung using a positive pressure. The hence resulting induced mechanical stresses and over distension of the alveoli as well as alveolar collapse and recruitment are believed to be the key S. Meissner · L. Knels · T. Koch · E. Koch Klinisches Sensoring und Monitoring, Medizinische Fakult¨at Carl Gustav Carus der Technischen Universit¨at Dresden, 01307 Dresden, Germany e-mail: [email protected] S. Adami · X.Y. Hu · N.A. Adams Lehrstuhl f¨ur Aerodynamik, Technische Universit¨at M¨unchen, 85748 Garching e-mail: [email protected]

M. Klaas et al. (Eds.): Fundamental Medical and Engineering Invest. on PAR, NNFM 116, pp. 67–80. c Springer-Verlag Berlin Heidelberg 2011 springerlink.com 

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problem of artificial respiration concepts. As a remedy, protective artificial ventilation strategies are required to spare patients during mechanical ventilation. Currently, protective ventilation concepts try to reduce the loads on the lung tissue while maintaining the oxygenation level of the patient. Different clinical studies have shown that e.g. ventilation with smaller tidal volumes can drastically decrease the mortality of patients with a lung injury. But all these approaches are deduced more from clinical experience rather than by theoretical and validated analysis [4, 5, 3]. With our multi-disciplinary research we want to give a more detailed insight in the functionality of human lungs, especially the phenomena occurring on the alveolar level. Combining experiments and numerical simulations, we want to study the flow-induced stresses on the alveolar-epithelial-surfactant-air interface to identify key parameters of the respiratory system. With the numerical simulations, we can analyze the flow in the alveolar structures quantitatively and correlate it with the phenomenological findings of the experiments. Furthermore, local quantities such as the surfactant concentration and shear stress can be monitored in the computational approach. These studies can then be used to develop new artificial respiratory concepts. To visualize the alveolar geometry and to generate input data for the numerical models, we use a three-dimensional optical coherence tomography (OCT) system, which enables us to reconstruct biological tissues in vivo with a higher resolution and penetration depth compared to established visualization techniques [17, 26, 19, 18]. Furthermore, we have developed a numerical model to simulate moving and deforming interfaces with incorporation of surfactant effects based on the smoothed particle hydrodynamics (SPH) method. Other tools based on finite-element methods or finite-volume methods can be found in literature, but they all lack either in the restriction to simple geometries or the conservation properties [22, 14, 27, 16].

2 Methods and Material 2.1 Alveolar Imaging by Optical Coherence Tomography 2.1.1

Optical Coherence Tomography

OCT is an innovative three-dimensional imaging modality based on interferometry [13]. A scheme of OCT setup is shown in Fig. 1. In our setup we used a Fourier domain OCT system [8], with a short coherent SLD light source, centered at a wavelength of 830 nm and a width (FWHM) of approximately 50 nm. The near infrared light emitted from the SLD is transmitted by an optical fibre to the scanner head, including all components of the required interferometer. The light is splitted by a beam splitter into reference and sample light. The sample beam is deflected by two galvanometer scanners and focused by an achromatic lens to the sample. The backscattered light is superimposed with the reference light and the interference signal is coupled by the collimator in the fibre again and sent to the spectrometer, where it is spectrally degraded and acquired by a CCD line detector.

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Fig. 1 Scheme of the used FD-OCT system. The scanner head (SH) integrates all components of the used interferometer. The SH is placed on a three axis translation stage to provide an optimal positioning of the SH above the sample. Additionally, a dichroic mirror (DM) is inserted in the course of beam to adapt optics for intra vital microscopy. The interference signal is acquired by a spectrometer and by using a Fourier transformation converted to the depth information of the sample.

Using a Fourier transformation, the spectrum is converted to the depth information. The used OCT system provides an axial resolution of 8 μm in air a lateral one of 8 μm and an A-scan rate of 12 kHz. 2.1.2

Isolated and Perfused Rabbit Lungs

In our experiments, we used isolated rabbit lungs [17] to acquire realistic alveolar geometries. Isolated and perfused rabbit lungs were applied with different levels of constant positive airway pressures (CPAP) to simulate the breathing cycle and the identical alveolar structures were documented by three-dimensional OCT image stacks. The CPAP levels were set to 5, 10, 15, 20, 25, 20, 15, 10, 5 cmH2 O. The acquired images have a size of 480 x 480 x 512 pixels3 resulting in a volume of approximately 2 x 2 x 2 mm3 [17]. Subsequently, the lungs were perfusion fixated. Fixation was carried out with a mixture of 1.5% glutaraldehyde (GA), 1.5% paraformaldehyde and 0.15 mol/L HEPES solution (300 mosmol/L, pH = 7.35). The lung was perfused with fixation solution for 30 min with an initial rate of 30 ml/min after changing the perfusion cycle. During fixation, a CPAP of 10 cmH2 O was applied. The fixed lung was perfused with increasing concentrations of ethanol in HEPES buffer (100 ml 20% ethanol, 100 ml 50%, 100 ml 70%, and 100 ml 95%) and finally recirculated with 100% ethanol. Ethanol dissolves the lipids in the membranes of the lung parenchyma leading to membrane porosity. The series of increasing ethanol concentrations was used to slow down this dissolving process, which results in slow streaming of ethanol into

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the air-filled parts of the lung. The ethanol-filling reduces artefacts caused by tissue air interface in the OCT images. Due to this the penetration depth into subpleural lung parenchyma is increased [18]. 2.1.3

Image Quantification

The acquired two-dimensional IVM images and the three-dimensional OCT data sets were used to quantify alveolar areas depending on the applied pulmonale pressure. The alveolar areas in the IVM images were segmented manually using a tablet computer. From the OCT image stacks, cross-sections parallel to the pleura (enface images) were extracted representing a depth of approximately 45 μm beneath the pleura vizeralis. The depth of 45 μm was chosen because OCT enface images from this depth show the best correlation with the IVM images. The alveolar areas in the OCT enface images were quantified using a self-developed algorithm [17].

2.2 Numerical Modeling of the Epithelial-Surfactant-Air Interface 2.2.1

Governing Equations

The numerical modelling of the epithelial-surfactant-air interface is a challenging task. First of all, different length-scales ranging from ∼ 1 μm of the thickness of the surfactant layer to ∼ 100 μm as characteristic size of an alveolar duct occur in the system. To capture all these details a very efficient numerical tool is required using a high spatial resolution. Furthermore, our geometry of interest contains three coupled phases and each of them has to be modelled in a different way. The air phase and the liquid-lining layer of an alveolus are treated as incompressible fluids as the expected Reynolds numbers are very small (Re  1). The surfactant model has to include surface diffusion, bulk diffusion, advection in the soluble phase and transport from the bulk phase to the interface. Finally, a structure model is needed to simulate the realistic behaviour of the alveolar tissue including a fluid-structure-interaction algorithm (FSI). Note, that here we only focus on the modelling of the surfactant-air interface and we will present the fully coupled problem in future works. Assuming incompressibility, the continuity of mass in the fluid phases follows from dρ = −ρ ∇ · u (1) dt where ρ , t and u are the density of the fluid, the time and the velocity vector, respectively. The change of momentum is calculated from the Navier-Stokes equation as du 1 1 = g − ∇p + ν ∇2 u + ∇ · [α (I − n ⊗ n) δΣ ] . (2) dt ρ ρ Here, the body force term g denotes the gravitational acceleration and ∇p is the gradient of the pressure. Together with the kinematic viscosity ν (which follows

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from the dynamic viscosity η as ν = η /ρ ) the Laplacian of the velocity gives the viscous term. The last term on the right-hand side of Eq. 2 describes the surface tension effect as the gradient of the stress tensor at an interface, where α is the surface tension coefficient, I the unit matrix, n the normal vector of the interface and δΣ is the surface delta-function. The evolution of the surfactant concentration on the interfaceis obtained by dΓ = ∇s · Ds ∇sΓ + S˙Γ , dt

(3)

where Ds is the diffusion coefficient matrix and S˙Γ describes the mass transport from the bulk phase to the interface and vice versa. We only consider the case of isotropic diffusion on the interface, thus the diffusion coefficient matrix reduces to Ds = Ds · I. The surface-gradient operator is ∇s = (I − n ⊗ n). The transport of bulk surfactant C in the soluble liquid lining layer follows from dC A = ∇ · D∞ ∇C − S˙Γ . dt V

(4)

Here, D∞ = D∞ ·I is the bulk diffusion coefficient matrix for the isotropic case and S˙Γ is the coupling term between the interfacial surfactant eq. (3) and the bulk surfactant eq. (4). Note, the pre-factor A/V of interfacial area A and volume V in eq. (4) to ensure conservation of the total surfactant mass in the system (in two dimensions A and V are the interfacial length and area, respectively). Following Langmuir kinetics [6], the surfactant is transported between the interface and the soluble bulk phase by adsorption and desorption via S˙Γ = k1Cs (Γ ∗ − Γ ) − k2Γ

(5)

where k1 is the adsorption coefficient and k2 is the desorption coefficient. The adsorption rate is proportional to the bulk concentration directly underlying the interface Cs , hence variable in time. Reaching the maximum surfactant concentration Γ ∗ , the interface is saturated with surfactant molecules and the adsorption rate is zero. Note that in literature there occur also more complex transport models, e.g. in Otis et al. [24], but here we only want to present our general model and describe all relevant phenomena. For more detailed information, we refer to a very interesting overview of different models by Chang and Franses [7]. To close our model, we relate the interfacial surfactant concentration Γ to the surface-tension coefficient α by a constitutive equation. In its very general form, this so-called equation of state is

α = f (Γ )

(6)

Very popular constitutive equations are the Frumkin isotherm or the Langmuir equation, see e.g. Pawar and Stebe [25] or Ghadiali and Gaver [10].

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Multi-phase Smoothed Particle Hydrodynamics (SPH)

We want to give a brief overview on the multi-phase SPH method used for the simulation of moving interfaces including the effect of surfactants. For the details of the method we refer to Adami et al. [1]. Introduced independently in 1977 by Gingold and Monaghan [11] and Lucy [15], SPH was originally intended to solve astro-physical problems. This Lagrangian framework enabled the simulation of star formations and interactions of different galaxies where grid-based methods failed mainly due to the problem of large computational domains. Over the years, SPH was applied to a lot of different problems ranging from structural analysis [2] to free-surface flows [20] or even microscopic multi-phase flows [12]. SPH is our method of choice, because it is advantageous especially for multi-phase problems with moving and deforming interfaces. The more, contrary to grid-based methods mass conservation on the interface can be achieved exactly and no interface capturing scheme is needed. The key step in SPH is the smoothing of a field quantitiy ψ (a scalar or a vector) in the domain with the smoothing kernel W

ψ (r) =



    ψ r W r − r , h dr ,

(7)

where h is the smoothing length. This kernel can be any function which satisfies the  properties W (r − r , h) = 1 and limh→0W (r − r , h) = δ (r − r ). Approximating the volume integration in eq. (7) with a sum, the quantity ψ (r) at the position r can be obtained from ψ (r) = ∑ ψ (r j )W (r − r j , h)V j , (8) j

where the summation is performed over all points r j in the domain. Hence, to reduce the computational cost the kernel function is chosen such that it has a compact support, i.e. the function is non-zero only in the range of the compact support. Typical kernel functions are spline functions with a compact support of 2–3 h [21] leading to about 50 neighbouring points in 3D. As an example, we show the resulting discretization of the pressure term in the momentum equation (2) following the multi-phase SPH model of Hu and Adams [12]   dui 1 = − ∑ Vi2 pi + V j2 p j ∇iW (ri − r j , h) (9) dt mi j Since the mass mi is the same for each particle, this form conserves momentum exactly due to the anti-symmetry of the gradient of the kernel function.

3 Results 3.1 Alveolar Imaging by Optical Coherence Tomography The image sequence shown in Fig. 2 demonstrates that OCT is a useful tool to investigate subpleural alveolar structures in isolated lung. Figure 2 shows the

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Fig. 2 This figure shows a comparison of IVM (right) and OCT enface (left) images for applied CPAP levels of 5 (top), 15 (middle) and 25 cmH2 O (down). Some alveoli (A-D) are indicated exemplarily in all four images. A correlation between both imaging modalities can be recognized.

identical alveolar structures imaged by OCT (left) and IVM (right). Identical alveoli can be detected in all six images. Four alveoli are denoted exemplarily by A-D in all images. A good correlation between the established IVM and OCT can be recognized. Furthermore, an increase in alveolar area is recognizable comparing the IVM and OCT images acquired by an applied CPAP of 5 and 25 cmH2 O. The graphs in Fig. 3 show the alveolar area at several CPAP levels for IVM as well as OCT. Both modalities result in increased alveolar areas with increased CPAP. Comparing the inspiratory and expiratory phase a hysteresis behavior can be recognized. The advantageous of OCT imaging of post-perfusion fixation ethanol-filled alveolar tissue is shown in Fig. 4. The image presents OCT cross-sections of subpleural air-filled (Fig. 4A) and ethanol-filled (Fig. 4B) alveolar tissue. The penetration depth is increased up to 800 μm in the ethanol-filled lungs compared to the air-filled lungs where only the first layer of subpleural alveoli can be acquired. The higher image quality of the images taken from the ethanol-filled lungs is caused by the elimination of the air-tissue interface, which leads to artifacts in the OCT images [18].

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Fig. 3 The graph represents the change of alveolar areas depending on the applied CPAP. The alveolar areas are normalized to the areas measured for an applied CPAP of 5 cmH2 O in the inspiratory phase. A correlation between these two modalities and a hysteresic behaviour is detectable.

Fig. 4 Cross-sections of subpleural alveolar tissue air-filled (A) and ethanol-filled (B) after post perfusion both images were taken at an applied pulmonary pressure of 10 cmH2 O. The increased penetration depth and quality of the ethanol-filled tissue is recognizable. The ethanol-filled lung allows imaging enclosed alveolar acini, denoted by a. The scale bar is 200 microns.

Due to OCT being a three-dimensional imaging modality, the acquired OCT data can be used to perform a three-dimensional segmentation and reconstruction of single alveolar structures. Figure 5 presents a 3D reconstruction of an alveolar structure. The reconstruction shown in Fig. 5 is based on a three-dimensional image stack taken from a post perfusion ethanol-filled lung and presents subpleural alveolar acini.

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Fig. 5 Three-dimensional reconstruction of subpleural alveolar acini taken from ethanolfilled OCT image stack.

3.2 SPH Simulations of Fluid-Air Interfaces with Surfactant In this section, we present some basic simulation results and validation cases to show the accuracy and capabilities of our numerical method. The first two examples demonstrate the correct treatment of surfactant at an air-liquid interface and in the presence of transport from/to the bulk phase. The last case shows the principle application of our simulation tool to a complex three-dimensional alveolar geometry, which was extracted from OCT scans. The detailed simulation and analysis of such a setup is currently the focus of our research and will be presented in the future. Due to the smoothing with the kernel function, the discontinuity at an interface is approximated in SPH with several layers of particles on each side of that interface. More precise, interface phenomena are numerically solved within a thin transition band of the thickness of the compact support. With increasing resolution the width of this smeared interface decreases and converges to the discontinuity in the limit of an infinite resolution. To validate the diffusion on an interface with numerically non-zero thickness, we compare the temporal evolution of the surfactant on a sphere with radius R. The initial condition follows from the analytical solution at time t = 0 with a surface diffusion coefficient Ds = 1

Γ (θ , φ ,t) = 2 + 0.5e−2t cosφ sinθ + e−6t cos2φ sin2 θ + e−12t cos3φ sin3 θ ,

(10)

see Novak et al. [23]. Fig. 6(a) shows the sphere particles at t = 0.1, colored with the actual surfactant concentration.

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(a)

(b)

Fig. 6 Diffusion on a sphere: a) numerical solution at T=0.1; b) convergence of error norm L1 over resolution R/h.

To show convergence of the method, we calculate the error norm   ∑ Γ (r j ) − Γanalyt (r j ) · A j L1 = ∑ Γanalyt (r j ) · A j

(11)

and plot it over the non-dimensional resolution R/h at t = 0.1 in Fig. 6(b). Note, in eq. (11) only particles near the interface contribute to the error since the interfacial area of particles in the bulk is zero. As a reference, the two lines with 1st and 2nd order convergence show the quality of our result. In our next case we show the diffusion of surfactant in the bulk phase coupled with adsorption to the interface. For simplicity, here we do neglect desorption rates and only consider transport by adsorption according to S˙Γ = k1C|r=R .

(12)

Initially, the volume surfactant concentration in the bulk phase is C∞ = 1 and the interface of the sphere with radius R = 1 is clean of surfactant. Due to the adsorption of surfactant molecules from the bulk phase to the interface, the interfacial concentration will increase with time in this example. Consequently, the concentration in the bulk phase directly underlying the interface decreases and diffusion tries to balance this consumption. In Fig. 7(a) a snapshot of a simulation with k1 = 0.5 shows the bulk-surfactant profile at T = 1 and the contour lines clearly show the diffusive profile near the interface. To safe computational time we used three symmetry boundary conditions. Exact conservation of surfactant material in the system is shown in Fig. 7(b). The three curves show the surfactant mass on the interface, in the bulk phase and the total mass. Note that for clarity two different y-axes are used in this plot. Nondimensionalized with the total mass of surfactant, the two fractions always sum up to one.

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(b)

Fig. 7 Bulk diffusion and adsorption to the interface. a) Colour plot with contours of bulk surfactant concentration at t=1.2; b) evolution of surfactant masses on the interface and in the bulk phase showing exact conservation.

(a)

(b)

Fig. 8 (a) Triangulated surface data from OCT-measurement. b) SPH-Discretization with particles of three different types (blue: air, white: liquid layer, red: epithelial cells)

Having demonstrated the validity of our model to simulate interfaces with surfactants including surface diffusion, adsorption/desorption and bulk diffusion, we now want to give an outlook of the application of this simulation tool to study realistic three-dimensional alveolar structures. Using the surface data extracted from the OCT scans as shown in Fig. 8(a), we can discretize the epithelial cell layer as the boundary of our computational domain with wall particles (see the red particles in Fig. 8(b)). Then, we create several layers

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of fluid particles to fill the liquid layer with computational nodes (see the white particles in Fig. 8(b)). The remaining volume represents the air in the alveoli and is discretized here with the blue particles. In a first step, we want to study the fluid motion and local distributions of different quantities like the shear stress at the epithelial surface and surfactant concentration when applying a given deformation to the boundary particles. In doing so, we hope to see the critical conditions which must have been present when forcing this deformation during ventilation. Furthermore, we plan to develop a monolithic fluid-structure interaction with a soft-tissue model for the epithelial cells to simulate a real ventilation cycle without prescribing the deformation of the boundaries.

4 Conclusion We have shown that optical coherence tomography can visualize alveoli with a depth of about 200 μm in three-dimensions in space when using isolated rabbit lungs. The main advantages of this technique are that it can be used in non-fixed tissue, no contact is needed and it allows three-dimensional in vivo imaging. Furthermore, we demonstrated that the OCT data sets acquired with an ethanol filled lung are suitable for segmentation and reconstruction of subpleural lung tissue. Certainly, the reconstructed structures do not represent an in vivo situation. However, we believe that the reconstructed structures represent the alveolar structure with applied CPAP because we have no evidence that the structure is changing during fixation and filling. With this method, we can avoid artifacts caused during the preparation process of the tissue for imaging modalities with a higher resolution. From the OCT data we can calculate a triangle mesh of the alveolar structure, which is required for the development of numerical models of the lung, representing a structure of CPAP conditions. Based on the SPH method, we have developed a numerical tool to simulate interfaces with surfactants including diffusion and transport processes. We have validated our model with analytic test cases and can now perform realistic simulations using the geometrical data from the OCT scans. Acknowledgements. The authors wish to acknowledge the support of the German Research Foundation (DFG Deutsche Forschungsgemeinschaft) for funding this work within the project Protective Artificial Ventilation (PAR) KO 1814/6-1, KO 1814/6-2 and AD 186/6-1.

References 1. Adami, S., Hu, X.Y., Adams, N.A.: A conservative SPH method for surfactant dynamics. J. Comput. Phys. 229(5), 1909–1926 (2010) 2. Antoci, C., Gallati, M., Sibilla, S.: Numerical simulation of fluid-structure interaction by SPH. Comput. & Structures 85(11–14), 879–890 (2007)

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3. ARDS Clinical Trials Network, Higher vs. Lower End-Expiratory Pressures in Patients with the Acute Respiratory Distress Syndrome. N. Engl. J. Med. 351(4), 327–336 (2004) 4. ARDS Network, Effect of a Protective-Ventilation Strategy on Mortality in the Acute Respiratory Distress Syndrome. N. Engl. J. Med. 338, 347–354 (1998) 5. ARDS Network, Ventilation with lower tidal volumes as compared with traditional tidal volumes for acute lung injury and the acute respiratory distress syndrome. N. Engl. J. Med. 342(18), 1301–1308 (2000) 6. Borwankar, R.P., Wasan, D.T.: The kinetics of adsorption of surface active agents at gasliquid surfaces. Chem. Engrg. Sci. 38(10), 1637–1649 (1983) 7. Chang, C., Franses, E.: Adsorption dynamics of surfactants at the air/water interface: a critical review of mathematical models, data, and mechanisms. Colloids Surf. A 100, 1–45 (1995) 8. Fercher, A.F., Drexler, W., Hitzenberger, C.K., Lasser, R.: Optical coherence tomography- principles and applications. Reports on Progress in Physics 66(2), 239–303 (2003) 9. Frank, J.A., Matthay, M.A.: Science review: mechanisms of ventilator induced injury. Crit. Care. 7, 233–241 (2003) 10. Ghadiali, S.N., Gaver, D.P.: The influence of non-equilibrium surfactant dynamics on the flow of a semi-infinite bubble in a rigid cylindrical capillary tube. J. Fluid Mech. 478, 165–196 (2003) 11. Gingold, R.A., Monaghan, J.J.: Smoothed particle hydrodynamics, Theory and application to non-spherical stars. Mon. Not R. Astron. Soc. 181, 375 (1977) 12. Hu, X.Y., Adams, N.A.: A multi-phase SPH method for macroscopic and mesoscopic flows. J. Comput. Phys. 213(2), 844–861 (2006) 13. Huang, D., Swanson, E.A., Lin, C.P., Schuman, J.S., Stinson, W.G., Chang, W., Hee, M.R., Flotte, T., Gregory, K., Puliafito, C.A., Fujimoto, J.G.: Optical coherence tomography. Science 254, 1178–1181 (1991) 14. James, A., Lowengrub, J.: A surfactant-conserving volume-of-fluid method for interfacial flows with surfactant. J. Comput. Phys. 212(2), 590–616 (2006) 15. Lucy, L.B.: A numerical approach to the testing of the fission hypothesis. Astron. J. 82, 1013 (1977) 16. McGough, P., Basaran, O.: Repeated formation of fluid threads in breakup of a surfactant-covered jet. Phys. Rev. Lett. 96(5) (2006) 17. Meissner, S., Knels, L., Krueger, A., Koch, T., Koch, E.: Simultaneous 3D Optical Coherence Tomography and intravital microscopy for imaging subpleural pulmonary alveoli in isolated rabbit lungs. J. Biomed. Opt. 14(5), 054020 (2009) 18. Meissner, S., Knels, L., Koch, E.: Improved 3D Fourier Domain Optical Coherence Tomography by index matching in alveolar structures. J. Biomed. Opt. 14(6), 064037 (2009) 19. Mertens, M., Tabuchi, A., Meissner, S., Krueger, A., Kertzscher, U., Pries, A.R., Affeld, K., Slutsky, A.S., Koch, E., Kuebler, W.M.: Alveolar dynamics in acute lung injury: heterogeneous distension rather than cyclic recruitment. Crit. Care. Med. 37(9), 2604–2611 (2009) 20. Monaghan, J.J.: Simulating free surface flows with SPH. J. Comput. Phys. 110, 399–399 (1994) 21. Morris, J.P., Fox, P.J., Zhu, Y.: Modeling low Reynolds number incompressible flows using SPH. J. Comput. Phys. 136(1), 214–226 (1997) 22. Muradoglu, M., Tryggvason, G.: A front-tracking method for computation of interfacial flows with soluble surfactants. J. Comput. Phys. 227(4), 2238–2262 (2008)

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23. Novak, I.I., Gao, F., Choi, Y., Resasco, D., Schaff, J.C., Slepchenko, B.M.: Diffusion on curved surface coupled to diffusion in the volume: Application to cell biology. J. Comput. Phys. 226, 1271–1290 (2007) 24. Otis, D.R., Ingenito, E.P., Kamm, R.D., Johnson, M.: Dynamic surface tension of surfactant TA: experiments and theory. J. Appl. Physiol. 77(6), 2681–2688 (1994) 25. Pawar, Y., Stebe, K.: Marangoni effects on drop deformation in an extensional flow: The role of surfactant physical chemistry. Phys. Fluids 8, 476–480 (1996) 26. Popp, A., Wendel, M., Knels, L., Koch, T., Koch, E.: Imaging of the Three-Dimensional Alveolar Structure and the Alveolar Mechanics of a Ventilated and Perfused Isolated Rabbit Lung with Fourier Transform Optical Coherence Tomography. J. Biomed. Opt. 11(1) (2006) 27. Yon, S., Pozrikidis, C.: A finite-volume/boundary-element method for flow past interfaces in the presence of surfactants, with application to shear flow past a viscous drop. Computers & Fluids 27(8), 879–902 (1998)

Fluid Mechanical Equilibrium Processes in a Multi-bifurcation Model T. Soodt, A. Henze, D. Boenke, M. Klaas, and W. Schr¨oder

Abstract. A comprehensive analysis of experimental and numerical results as to modeling the elastic behavior of a lung is presented. The main focus of this study is the dynamical distribution of the static pressure in a multiple branched network due to spontaneous volume change of its terminal units. The interaction between pressure and volume is the most essential feature in lung related science. Flow cases are performed in an idealized three-dimensional respiratory system under natural ventilation. The results demonstrate the dynamical spatial pressure expansion, the dominating oscillations, and a comparison of the compliance with high-frequency oscillation ventilation.

1 Introduction Studies show that in Europe approximately 100,000 patients per year are artificially ventilated due to the Respiratory Distress Syndrome (RDS) [17]. Following the predictions of the World Health Organization (WHO), the number of patients will double till 2020. Unfortunately, many details of the lung fluid mechanics are still unknown and therefore, a meaningful control mechanism for lung machines is not possible. The result is that the mortality rate of patients with Acute Lung Injury (ALI) is in the order of 40 – 50%. Therefore, adequate modeling and fundamental research is necessary. This article focuses on the investigations of fluid mechanics in a simplified symmetric lung model. To be more precise, the fluid dynamical equilibrium process in a threedimensional multi-bifurcation system under oscillating ventilation is investigated. T. Soodt Institute of Aerodynamics, RWTH Aachen University, W¨ullnerstr. 5a, D-52062, Germany e-mail: [email protected] A. Henze Institute of Aerodynamics, RWTH Aachen University, W¨ullnerstr. 5a, D-52062, Germany e-mail: [email protected] M. Klaas et al. (Eds.): Fundamental Medical and Engineering Invest. on PAR, NNFM 116, pp. 81–95. c Springer-Verlag Berlin Heidelberg 2011 springerlink.com 

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The geometry represents a generalized human lung up to the 6th generation with non-monotonic compliances at each exit. In-vitro experiments and numerical calculations are carried out and will support fundamental fluid dynamical understanding for such processes. Physiological relevance can be found when using this type of fluid-structure interaction as a model of biomechanical systems such as lungs. It could be used to describe the opening or closing mechanism for either balloonidealized alveoli or for collapsed airways. It is evident that differing geometry and particular varying compliances have to be accounted. However, the essential flow structures which occur in an inhomogeneous lung during respiration, like e.g. the intrapulmonary mass transport between areas with differing time constants, viz. pendelluft (Lee et al. [9]), are the same. First, a short discussion to determine the physiological location of the analogous compliant modules is given. The physiological applicability is intentionally left to the reader’s choice. The description of balloon-idealized alveoli is used since most publications picture the distal end of a lung lobule as a bunch of grapes (Miller [10]). For example, Neergaard [12] demonstrated in a fundamental paper the importance of surface tension in the lung in which the model of an alveolus as a spherical membrane at the end of a cylinder is introduced. On the other hand, Fung [6] stated that the conception of a balloon-like alveolus is incorrect citing the fact that these structures cannot be seen in morphological investigations. He claims that the origin of the misunderstanding lies in the method how the lung geometry was generated. A detailed and perspicuous representation of this misconception is discussed by Prange [14]. It is the author’s opinion that the presented balloon model should be rather used to model the opening and closing of collapsed airways. Perun and Gaver [13] studied in an in-vitro model the reopening behavior of a collapsed airway. The experimental data resulting from a planar configuration shows that the Laplace law can be adequately used by taking a different coefficient into account. Hence, opening a meniscus shaped collapsed airway or a balloon is mechanically identical. In the following some comprehensive reviews depicting the need to understand such equilibrium processes are referred to. For example, the results of Alencar et al. [1] indicate that inflating the lung from a state in which a considerable part of the gas-exchange region is collapsed is a non-equilibrium dynamical process characterized by a sequence of instabilities with negative elastance. Alencar continues the work that had previously done by Suki et al. [16], [15], who experimentally studied the process and the distribution of airway opening by using mammalian lungs in a vacuum chamber and analytical approaches based on symmetric binary tree models. One of his main experimental aims has been the measurement of global pressure-volume (p-V) relations of degassed lungs during inspiration and expiration. The focus was to achieve the differences between firstly and repeatedly inflated lungs. Based on the results he hypothesizes the existence of randomly distributed non-linear local compliances which are able to trigger avalanches. Avalanches are further defined as the consecutive opening of in-series connected closed airways. The current study focuses therefore on equilibrium processes initiated by non-linear compliances.

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The structure of this paper is as follows. First, a concise description of the lung model, the elastic units, the experimental setup, and the numerical method is given. Subsequently, numerical and experimental results are compared and discussed. Finally, the findings are summarized and some conclusions are drawn.

2 Description 2.1 Model Geometry and Manufacturing Process The dichometry of the model used for the experimental and numerical investigations is based on the proposal by Weibel [19] and the definitions by Kitaoka et al. [7]. The branching of the model is therefore symmetrical with an angular pitch of Θ = 34.88◦ , an angle of torsion of Φ = 90◦, and a scale factor of d1 /d0 = 0.78 (Fig. 2 (left)). The scale factor describes the diameter ratio between the daughter branches d1 to the mother branch d0 . The model contains the first six bifurcations such that the last generation contains 26 = 64 exit channels. The manufacture processes of the experimental model included computational design with AutoCAD 2002 (Autodesk GmbH), grid generation, rapid-prototyping with corn starch (CP GmbH, Aachen), coating the RP surface, casting with high transparent silicone (RTV615, Momentive, New York), embossing the exits of the model and wash-out. The coating material was a high viscous and water-soluble glue to smooth the surface roughness and to protect the model being affected by humidity during casting. The relatively high and non-physiological surface roughness is a result of the discrete RP printing technique. The water-solubility was a necessary prerequisite for a residue-free wash-out of the coating material. The cast material consists of two components which were mixed and degassed using a vacuum chamber. The mixing was processed to eliminate density variations such so that

Fig. 1 Left: branching definitions given by Weibel [19] und Kitaoka [7]; right: casted model with embedded corn starch prototype before wash-out.

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no optical refraction was manually detectable. The degassing was used to avoid air bubbles which would improperly alter the surface structure.

2.2 Nonlinear Compliance of Terminal Units The stress-strain relation of a Mooney-Rivlin type rubber is given by Mueller and Struchtrup [11].

Δ p∗i = 2 · ci · G ·

−w −x y d β · (D∗ − D∗ · (1 + ( )i · D∗ ), R0 G

(1)

The functional relation is extended by the authors. R D = α · (D − 1) + 1, D = = R0 ∗

z

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VB , i = 1, 2. V0 ∗1/D∗

Δ p = Δ p1 + Δ p∗2 Δp VB = Δ VS − (Vd +VS ) pu + Δ p

(2) (3) (4)

The values which are adapted to the mechanical properties of the experimental model and used for the computation are the shear modulus G = 0.67 MPa, the membrane thickness d = 0.25 mm, the reference volume V0 = 1 l, the form parameter (β /G)1 = 0.0009, (β /G)2 = 0.0014, the strain super-elevation α1 = 700, α2 = 500, constants c1 = 11.25, c2 = 5.25, and exponents w = 1, x = 2, y1 = 8.65, y2 = 5, z1 = 1.15, z2 = 1.05. The shear modulus G can be achieved, following the assumption G = E/2, by a tensile test according to DIN 50125-E2-16-33 where five equidistant loading points between F = 2 N and F = 6 N are taken for a linear regression. The assumption G = E/2, where E represents the Young’s modulus, is based on Hooke’s relation G = E/(2 + 2ν ) and the assumption of a small Poisson number for rubber ν = 0.0003 [4] which can be neglected. The volume-pressure relations of the membranes were measured by using a syringe which displaced a specific volume of fluid 10 ml ≤ VS ≤ 34 ml to inflate the membrane and by recording the static pressure simultaneously with a pressure sensor (XCS-062 SERIES, Kulite) located normal to the streamwise direction. The displacement of the syringe and the flow velocity was small such that quasi-steady conditions and constant total pressure could be assumed. The in- and deflation curves in Fig. 2 (right) show the mean experimental compliance results for 7 inflation volumes based on an arithmetic average of n = 10 samples. The various data is denoted by symbols and plotted for volume displacements of the syringe VS . Each sample uses newly equipped compliant material such that variations of elasticity due to relaxation can be neglected. The solid line represents the analytical result based on Eq. 1, 2, and 3 and Eq. 4 takes the isothermal compression for the volume calculation into account. Additional input for the volume correction is the dead space volume Vd = 5.17 ml, the ambient pressure pa = 1.01

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bar, and Δ p defined as the measured pressure against the ambient pressure pa . On the left to the diagram a set of pictures illustrates the various states of an opening balloon. The averaged hysteresis slope for a single balloon with a maximum volume of VB = 19 ml and the coefficient of variation CV are based on 10 newly equipped samples. The highest measurement deviation is found at the first local maximum which is called opening pressure pO . Due to the linear behavior at VB ≤ 1.28 ml the corresponding compliance can be determined by CM = Δ VB /Δ pO .

Fig. 2 Photos of an opening sequence (left) and the hysteresis slopes of the compliance of the balloon (right). The symbols denote the measured values and the solid line shows the result of the analytical equation for the compression phase. Several syringe volumes at 10 ml ≤ V S ≤ 34 ml illustrate the hysteresis behavior.

2.3 Experimental Setup In the following, the specifications of the experimental setup are discussed. Using the hollow lung model which has been described in the previous chapter pneumatic connectors are attached to the holes. Stiff pneumatic pipes connect these openings through the housing. Changeable swivels with clamped latex membranes are used as terminal units with non-linear compliance behavior. A high optical contrast is achieved by choosing white housing walls and black membranes. A binary numeration of the terminal units based on the orientation at the branches following the pathway of the inspiration flow is applied. The digit position in the six digit number represents the degree of linkage. In the following, the reversal of the bifurcation generation equivalent to the digit position is defined as linkage generation (LG). The inlet is connected to a straight pipe at a length of L = 1 m containing a flow straightener. The configuration of the inflow pipe suppresses secondary flow structures induced by the elbow piece which connects the inflow pipe and the engine (Fig. 3). Such secondary flow structures generated in curved pipes are described in detail in Berger et al. [2]. Intensive tests guarantee the absence of any leakage by

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Fig. 3 Left: Photo of the partially opened experimental model and the measuring system; right: Schematic of the complete experimental setup.

recording the pressure loss as a function of time for a pressure load of pL = 200 mbar. Pressure transducers are placed perpendicular to the streamwise direction to measure the static pressure. They are located at different degrees of linkage such that localization effects can be captured. Five MV-D1024-80-CL-8 CMOS cameras (Photonfocus AG, CH-8853 Lachen) are mounted perpendicular to each model side to record simultaneously the cross-section change of all balloons during ventilation. The pressure is generated by a spindle motor driven piston at sinusoidal volume change Δ V . The relation is given by Δ V = x · π · D/4, whereas x represents the amplitude and D the effective piston diameter D = 1.918 · 10−1 m. The amplitude x and the frequency f are the adjustable parameters in the experiments. The velocity u can be calculated by u = 2π · f · x = 8 · f · Δ V /D2 .

(5)

2.4 Mathematical Formulation Each bifurcation consists of three pipes at constant cross section. The velocity inside the pipes is computed by solving the mechanical energy equation for each pipe assuming a locally one-dimensional, unsteady, viscous flow field. The external forces acting onto a control element are the pressure and the friction forces. The latter are computed assuming a fully developed pipe flow. In each time step, the local Reynolds number is computed and depending on the result the friction coefficient λ for laminar or turbulent flows is determined. The volume forces are neglected due to the tiny height differences over the human lung. Since the cross section is constant for each pipe the convective acceleration is zero such that the resulting equation is written du 1 ρ l 2 = (p0 − pi − λ u ). (6) dt ρl 2d The pressure inside the nodes is computed depending on the assumption of the properties of the nodes. If the node is linearly elastic the pressure reads

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p = pa + C(V − Vre f )

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where C represents the compliance. Inside nodes with nonlinear elastic behavior, i.e., the limiting nodes representing the alveoli, Eq. 1 is used. The volumes are computed using the conservation of mass, i.e., the continuity equation for each node and the connecting pipes dV = − ∑ ui A i (8) dt If a node is assumed to be rigid the time derivative is zero. Hence, it is impossible to explicitly solve the resulting system of equations. In the six-fold generation the set of equations consists of 128 continuity equations and 127 mechanical energy equations. The system can be solved in two ways. To avoid inaccurate solutions due to round-off errors a preconditioned BiCGStab method as suggested by van der Vorst [18] is used to solve the system. The nodes and the pipe elements are numbered as sketched in Fig. 4. The parameters for the pipes such as length, diameter, shear modulus etc. are defined for each generation. The material thickness d in Eq. 1 is varied in a certain predefined margin to make sure that the characteristics of the simulated alveoli differ slightly from each other.

Fig. 4 The sketch shows the numbering of the nodes and pipes in the one-dimensional model.

3 Results and Discussion The structure of the discussion is as follows. First, the pressure and the volume distribution for the given setup at global and local position are described. Subsequently, the spatial pressure expansion due to balloon opening is experimental and computational analyzed. Next, spectral analyses for measured and numerical data are presented. Finally, numerical analysis at high respiratory frequency is performed.

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3.1 Global and Local Behavior The global and local pressure distributions due to single or multiple opening/ closing events of the terminal units are investigated. A cosine based pressure gradient starting with ambient pressure conditions is performed. The ventilation frequency in this study ranges from fV = 0.2 Hz to fV = 0.6 Hz. A general overview for one ventilation cycle at a period of TV = 2.5 s is given in Fig. 5. The left figure shows the static pressure distribution vs. time measured at the inlet of the model and the right figure illustrates the static pressure and the subsequent volume at a defined terminal unit. It is evident that the opening and closing events and even the balloon opening pressure po possess different oscillating behavior. It will be shown later that this oscillation is very regular for the opening events. The opening causes after the local pressure drop an overshoot of the pressure over the virtual pressure level which is shown in Fig. 6. This high pressure triggers the opening of the next balloon. Virtual means the condition without having an opening event. This oscillation of the static pressure can be qualitatively indentified at the inlet (Fig. 5 (left)) and at the distal end (Fig. 5 (right)). The occurrence at both locations can be explained by the fact that the pressure equilibrium mechanism is nearly undelayed due to the ideal stiff geometry of the model such that no significant transfer function exits. Figure 5 shows that differences of the global and the local pressure are found in time intervals of spontaneous volume change. The balloon expansion/ collapse directly cause a significant local pressure drop/ rise magnitude of which is significantly reduced at the inlet. When the balloon collapses this phenomenon is more distinct due to the lower mass flux. The pressure loss, indicated by the different pressure levels at the beginning and the end of the ventilation cycle is caused by the increase of the inner energy during the deformation of the rubber. This pressure loss does not impair the current investigation since it has no significant influence on the equilibrium processes. The pressure variation is not of perfect cosine shape since the total volume of the system changes at opening and collapsing.

Fig. 5 Left: Static pressure vs. time slope measured at the inlet; Right: Static pressure and the subsequent balloon volume of one terminal unit vs. time. The distributions show opening and closing sequences indicated by the pressure oscillation. The marked sections evidence significant global and local differences. The period of one cycle is TV = 2.5 s.

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3.2 Degree of Influence This section describes for the opening phase the pressure differences relative to the degree of linkage to derive an impact factor. The impact factor is defined as IF = (pk − pI )/(pO − pI ), where pO represents the pressure of the opening balloon and therefore with the maximum excitation. The index k of pressure pk indicates the degree of linkage and pI represents the pressure at the inlet. In Fig. 6 (left) the pressure at different linkage generations is illustrated. The ventilation frequency is fV = 0.2 Hz. The direct neighbor (LG = 1) is already open and the pressure pO occurs at the minimum of balloon 100111. The spatial extension of the associated pressure decrease can be determined, as explained before, by the differing digit in the binary number. Figure 6 (right) shows comparable numerical data computed by the one-dimensional model. The experimental and numerical results are qualitatively similar. Additional to the described spatial relationship a characteristic overshoot is observed. The analysis of this phenomenon reveals a positive dependence between the magnitude of the primary and the secondary excitation. Furthermore a decreasing magnitude of the second local extremum is observed at higher degree of linkage. A similar effect also occurs at the closing sequence, where both analyzed dependences significantly increase. In theoretical studies this overshooting is described as pendelluft. In the following, a quantitative analysis of this qualitative similarity is performed. Figure 7 shows the impact factor (IF) of closed (n = 1 − 27) and open direct neighbors (n = 29 − 43) based on measurements in comparison to the computational results (closed neighbor: n = 1 − 31; open neighbor: n = 34 − 58). The comparison of closed or open direct neighbors evidences a decreasing influence factor (IF) at increasing linkage generation (LG). The mean impact factors are IF1,c ≈ 0.4 for LG = 1, IF2,c ≈ 0.2 for LG = 2, IF4,c ≈ 0.065 for LG = 4, and IF5,c ≈ 0 (Fig. 8) for LG = 5. In fact, the measurements result in a zero-impact factor (IF) at generations (LG) greater than 4. Data of LG = 3 are not present in the measured results

Fig. 6 Temporal pressure distribution during the opening sequence of the balloon 100111 (o); left (experimental), right (numerical). The direct neighbor balloon 100110 (x), LG = 1, is already open. The ventilation frequency is fV = 0.2 Hz.

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due to the experimental setup. The comparison with an already open direct neighbor shows for the measured data a reduced impact factor. The difference decreases at higher generations of linkage. In this case the mean values are IF1,o ≈ 0.265 for LG = 1, IF2,o ≈ 0.13 for LG = 2, IF4,o ≈ 0.055 for LG = 4, and IF5,o ≈ 0 for LG = 5. The resulting impact factors IF illustrated in Fig. 7 (right) are based on the one-dimensional numerical model. The mean IF values at a closed direct neighbor are IF1,c ≈ 0.386 for LG = 1, IF2,c ≈ 0.173 for LG = 2, and IF3,c ≈ 0.101 for LG = 3. The averaged results with an already open direct neighbor are IF1,o ≈ 0.359 for LG = 1, IF2,o ≈ 0.158 for LG = 2, and IF3,o ≈ 0.100 for LG = 3. A quantitatively good agreement between experimental and numerical results for the data with a closed neighbor is achieved. The general tendency that IF is nearly divided by a factor of 2 at increasing LG, i.e., from IF1 , c ≈ 0.4 to IF2 , c ≈ 0.2 and IF3 , c ≈ 0.1 to IF4 , c ≈ 0.05 is valid for experimental and numerical data. However,

Fig. 7 Measured and computed relative pressure drops at increasing linkage generation (LG = 1, 2 and 4). The impact factor (IF) is shown for a set of closed (measurements: n = 1 − 27, computations: n = 1 − 31) and open (measurements: n = 29 − 43, computations: n = 34 − 58) direct neighbors. The solid line represents the average of one set.

Fig. 8 Measured pressure drop at linkage generation LG = 3 and computed relative pressure drop at LG = 5. The solid line represents the average of one set.

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the measurements and the computations differ when the neighbor balloon is already open. Unlike the experimental data the numerical findings show hardly any difference in the distribution of the impact factors at closed and open neighbor balloons. Nevertheless, the decreasing difference between closed and open neighbor balloons at higher linkage generation is qualitatively confirmed.

3.3 Frequency Analysis Spectral analyses for experimental and numerical data have been performed to determine and characterize the oscillations. The signals shown in Fig. 9 were high-pass filtered using a Chebyshev technique before a discrete Fast-Fourier method is used to transform the signals into the frequency domain. Through the filter of order three the time depended gradient is subtracted from the oscillation and removes the offset. The cut-off frequency is fC = 2 Hz for the experimental and fC = 5 Hz for the numerical data. The equilibrating frequencies, accounting only values greater than fE ≥ 10 Hz, are compared to the ventilation frequency fV = 0.4 Hz more than n ≥ 25 times higher. Thus, the pressure gradient can be assumed small and therefore any interference can be neglected. The comparison of the experimental and numerical frequency spectra evidences good qualitative and quantitative agreement for the frequency and the magnitude ratios. Figure 9 shows distinct power spectra in the frequency interval of fO = 18 − 28 Hz. A comparative analysis of the signal in the time-domain indicates that this frequency domain is dominated by the regular self-induced balloon openings. Furthermore, this regime is characterized by the system’s resonance frequency fR resulting from the relation between the resistance R and the compliance C fR =

1 1 = τ RC

(9)

Fig. 9 Left: Spectral analysis of measured pressure distributions in a terminal unit (top) and inlet (bottom); Right: Spectral analysis of computed pressure distributions. Number of sequences n = 8. Ventilation frequency is fV = 0.4 Hz.

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whereas τ represents the time constant. Another pronounced regime is given by a second power spectrum at a frequency range between fP = 35 − 58 Hz. This frequency spectrum is evident only for the terminal unit and not at the inlet. Thus, it can be concluded that these frequencies are stronger damped as the first spectrum. As mentioned before this high frequency spectrum defines the pendelluft phenomenon or the Y-bifurcation’s resonance frequency.

3.4 Numerical High-Frequency Analysis Next, the results of the one-dimensional numerical model at High-Frequency Oscillation Ventilation (HFOV) in contrast to ventilation frequencies at rest, i.e., Common Mandatory Ventilation (CMV), are discussed. Clinical studies evidence high-frequency oscillation ventilation as a proper method to recruit atelectasis. For example, Lee et al. [8] demonstrate on premature infants that the tidal volume doubles when the ventilation frequency is similar to the resonance frequency. At resonance frequency there is an interference of the inertance and elastance forces, such that only the friction forces remain. Therefore, the same pressure load at resonance frequency creates a higher tidal volume. Claris et al. [3] posted HFOV to probably lower the risk of barotrauma and unlike CMV to improve ventilation and oxygenation in many cases in. Fredberg et al. [5] show that by variance of the ventilation frequency the spatial distribution and the temporal synchronization of the alveolar pressure can be systematically manipulated. This technique, however, is rarely established in clinic life. One of the main reasons why it is hardly applied is the insufficient knowledge. Therefore the frequency adjustment is based purely on empirical success. For this reason, numerical investigations with respiratory rates which exceed the test parameters of the experimental model are performed to yield additional insight of the system’s equilibrium processes. In Figs. 10 – 12 the results are juxtaposed for a ventilation rate of fV = 0.2 Hz (left) and fV = 24 Hz (right). The frequency fV = 24 Hz is used since Lee et al. [8] showed that the tidal volume is significantly increased at ventilation near the resonance frequency. Figures 10 – 11 show the local temporal volume and pressure distributions of all 64 terminal units of the sixfold bifurcation model. At fV = 0.2 Hz (left) single or packet-wise opening and closing can be clearly indentified whereas at fV = 24 Hz (right) neither for inspiration nor for expiration such events can be observed. At this high frequency all balloons open or close simultaneously. Additionally, no pendelluft for the complete ventilation cycle occurs since the driving mechanism is due to resonance missing. Analyses of Fig. 10 (left) and Fig. 11 (left) show that the different inflection points of the single balloon compliance slope evidenced in Fig. 2 (right) lead to different pressure levels for the opening and the closing sequence at inspiration and expiration. This results in ventilatory energy consumption even without a numerical applied hysteresis (Fig. 12 (left)).

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Fig. 10 Volume vs. time at the corresponding 64 distal ends for a ventilation frequency of f v = 0.2 Hz (left) and of f v = 24 Hz (right).

Fig. 11 Pressure vs. time at the corresponding 64 distal ends for a ventilation frequency of f v = 0.2 Hz (left) and of f v = 24 Hz (right).

Figure 12 illustrates the volume vs. pressure distribution computed at node 1 for a complete ventilation cycle. Note that the breathing work, the physiological equivalent to energy, can be determined by integrating the p-V distributions for a complete ventilation cycle represented by the enclosed area. Figure 12 (left) indicates unlike Fig. 12 (right) low energy consumption since the pressure equilibrium between node 1 and one node of BF = 6 is possible. At fV = 24 Hz the breathing work and the global compliance differs significantly. Fig. 12 (right) shows after reversal from inspiration to expiration negative pressure values. These values are related to the ambient condition and occur due to the increased velocity and inertia. Additionally, the velocity dependent friction loss amplifies this effect and the supplementary increase of the ventilation energy. In other words, the negative pressure in the expiration phase sucks the mass out of the system.

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Fig. 12 Volume vs. pressure for a ventilation frequency of fv = 0.2 Hz (left) and of fv = 24 Hz (right). The area of the enclosed curves represents the breathing work.

4 Conclusion The objective of this study has been to model the elastic properties of the lung and to determine fluid mechanical mechanisms under physiological conditions such that atelectasis could be recruited. The findings show the setup to be interpreted as models for balloon idealized alveoli or collapsed airways. A description of the elastic units, the experimental setup, and the numerical formulation has been given, where the elastic characteristic has been experimentally determined, analytically described and numerically implemented. Investigations have been performed experimentally for CMV and numerically for CMV and HFOV conditions. The spatial pressure distributions, impact factor (IF), and the linkage generation (LG), have been used to describe the occurring phenomena. The numerical model has been qualitatively and quantitatively validated under the aspect of the IF and dominating frequency spectra. The comparison of the numerical and experimental CMV data has shown a convincing agreement. Thus, the numerical method has been applied to HFOV allowing comparison of CMV and HFOV data. Spatial dependences have been shown, a spectral characterization has been discussed, and ventilation frequency dependent compliances have been determined. The results show that the spatial dependence can be approximated by the relation IFi ≈ 0.4/LG. Furthermore, the spectral analyses evidence two significant frequency domains fO = 18 − 28 Hz and fP = 35 − 58 Hz. Theoretical considerations characterize these domains as self-induced opening frequency and pendelluft. Finally, HFOV results show the absence of pendelluft and the significant increase of breathing load.

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References 1. Alencar, A., Arold, S., Buldyrev, S., Majumdar, A., Stamenovi, D., Stanley, H., Suki, B.: Dynamic instabilities in the inflating lung. Nature 417, 809–811 (2002) 2. Berger, S., Talbot, L.: Flow in curved pipes. Ann. Rev. Fluid Mech. 15, 461–512 (1983) 3. Claris, O., Lapillonne, A., Picaud, J.C., Basson, E.: High-frequency oscillatory ventilation. Semin Neonatol 2, 129–137 (1997) 4. Dahl, C.N.C., Lardner, T.J.: An introduction to the mechanics of solids. Tech. rep., McGraw-Hill, New York (1959) 5. Fredberg, J., Keefe, D., Glass, G., Castile, R., Frantz, I.: Alveolar pressure nonhomogeneity during small amplitude high-frequency oscillation. J. Appl. Physiol. 57(3), 788–800 (1984) 6. Fung, Y.: The surface tension make the lung inherently unstable? Circulation Research 37 (October 1975) 7. Kitaoka, H., Takaki, R., Suki, B.: A three-dimensional model of the human airway tree. Journal of Applied Physiology 87(6), 2207–2217 (1999) 8. Lee, S., Alexander, J., Blowes, R., Ingram, D., Milner, A.D.: Determination of resonance frequency of the respiratory system in respiratory distress syndrome. Arch. Dis. Child Fetal Neonatal Ed. 80(3), 198–202 (1999) 9. Lee, W., Kawahashi, M., Hirahara, H.: Analysis of pendelluft flow generated by hfov in a human airway model. Physiol. Meas. 27, 661–674 (2006) 10. Miller, W.S.: The Lung. Charles C Thomas, Springfield (1947) 11. M¨uller, I., Struchtrup, H.: Inflating a rubber balloon. Mathematics and Mechanics of Solids 7, 569–577 (2002) 12. von Neergaard, K.: Neue Auffassungen u¨ ber einen Grundbegriff der Atemmechanik: Die Retraktionskraft der Lunge, abh¨angig von der Oberfl¨achenspannung in den Alveolen. Z. Ges. Exp. Med. 66, 373–394 (1929) 13. Perun, M.L., Gaver, D.P.: Experimental model investigation of the opening of a collapsed untethered pulmonary airway. J. Biomech. Eng. 117, 245–253 (1995) 14. Prange, H.D.: Laplace’s law and the alveolus: A misconception of anatomy and a misapplication of physics. Adv. Physiol. Educ. 27, 34–40 (2003) 15. Suki, B., Andrade, J.S., Coughlin, M.F., Stamenovic, D., Stanley, H.E., Sujeer, M., Zapperi, S.: Mathematical modeling of the first inflation of degassed lungs. Annals of Biomedical Engineering 26, 608–617 (1998) 16. Suki, B., Barab´asl, A., Hantos, Z., Pet´ak, F., Stanley, H.: Avalanches and power-law behavior in lung inflation. Nature 368, 615–618 (1994) 17. The Acute Respiratory Distress Syndrome Network: Ventilation with lower tidal volumes as compared with traditional tidal volumes for acute lung injury and the acute respiratory distress syndrome. N. Engl. J. Med. 342(18), 1301–1308 (2000) 18. van der Vorst, H.: Bi-cgstab: A fast and smoothly converging variant of bi-cg for the solution of nonsymmetric systems. SIAM J. Sci. Stat. Comput. 13(2), 631–644 (1992) 19. Weibel, E.: Morphometry of the human lung. Academic Press, New York (1963)

In Vivo Microscopy and Analysis of Regional Ventilation in a Porcine Model of Acute Lung Injury Johannes Bickenbach, Michael Czaplik, and Rolf Rossaint

Abstract. The beneficial role of lung protective ventilation in patients with Acute Lung Injury (ALI) or Acute Respiratory Distress Syndrome (ARDS) has become evident. However, knowledge about the effects of mechanical ventilation at the alveolar level is still limited. In vivo microscopy could help to understand alveolar mechanics. We tested a relatively new, less invasive method of in vivo microscopy not influencing the mechanical behaviour of alveoli and giving depth information about the tissue. The aim of this first observation was to demonstrate feasibility of a fibered confocal laser scanning microscopy (CLSM) used endoscopically and through a thoracic window in a rabbit model. Both endoscopic application and use through a thoracic window provided high-resolution images of alveolar structure. Within experimental ALI, relevant heterogeneity with collapsed adjacent to expanded regions was observable. Quantification measurements may help to further evaluate alveolar mechanics.

1 Background Despite a better understanding of pathophysiological processes as well as implementation of new treatment options, the Acute Lung Injury (ALI) the Acute Respiratory Distress Syndrome (ARDS) is still a life threatening disease with a high mortality [11, 2]. Although survival rates are improving during the past decade [18, 1], knowledge about lung protective ventilation is still not completed. Johannes Bickenbach Department of Intensive Care, University Hospital RWTH Aachen, Germany Michael Czaplik · Rolf Rossaint Department of Anaesthesiology, University Hospital RWTH Aachen, Germany

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We know that setting the ventilator in a protective manner means reducing plateau pressure and using small tidal volumes to avoid over-distension and setting adequate PEEP levels to recruit the lung [18]. By doing so, however, this protocol may not be sufficient in every individual patient [17]. There is lack of evidence how inspired gas allocates to alveoli. The ex-act mechanical processes of alveolar ventilation have not been fully elucidated yet. The technique of intravital microscopy enables us to directly visualize these processes of distinct alveolar regions. First examinations using this technique showed alveoli which could be identified according to their dif-ferent mechanical behaviour when changing ventilator settings and when using different experimental models of inducing lung injury [15, 8, 16, 14, 9, 13]. This two-dimensional in vivo video microscopy describing alveolar mechanics was performed in a porcine [15, 8, 16, 14, 9] and in a rat model [13]. Briefly this technique consists of a superficial view on alveoli after fixation by a glass plate and suction. Although extremely innovative and of high scientific value, this technique only gives limited information about only one regional parenchymal area. Besides, due to the surgical opening of the thorax transpulmonary pressures are modified, being part of the lung open to atmosphere, thus affecting regional lung mechanics at end expiration and inspiration. In acute lung injury, a ventilation-perfusion mismatch due to heterogeneous damage and coexistence of collapsed and recruited alveoli can be observed [14]. With regard to this pathophysiology, analysis of different lung regions and the potentially different dynamical behaviour of alveoli should be taken into account. An ideal investigative microscopy tool should be (1) applicable in real-time, (2) allow three-dimensional observation of different lung regions and (3) used in vivo, during mechanical ventilation. The fibered confocal laser scanning microscopy (CLSM) could be a meaningful alternative to conven-tional microscopy. This relatively new application device provides a clear, high resolution in-focus image of living sample [13, 19]. A microscope’s objective is replaced by a flexible fiberoptic miniprobe of less than 1 mm in diameter. It can be used non-invasively and enables real-time imaging of alveolar structure endoscopically [3, 20, 21] or through a thoracic window [3]. The feasibility of in vivo CLSM and its qualitative assessment was therefore examined endoscopically and through a thoracic window. Further, Alveolar dynamics were examined in normal lungs and in acid aspiration-induced ALI.

2 Materials and Methods Female rabbits were anesthetized after cannulation of an ear vein. Anesthetic depth was evaluated regularly by limb-withdrawal to paw pinch, and anesthesia was maintained by repetitive injections of half of the dose necessary for initial anesthesia induction every 30 - 60 min.

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Tracheotomy was performed with a custom made suction catheter. After skin preparation and removement, the medial and caudal ends of the underlying muscles were dissected to expose ribs and intercostal muscles of the right anterior-lateral thoracic wall. A 10-15 mm circular window was excised in the center of which the lower margin of the upper right lung lobe was exposed. After insertion of an interpleural catheter, the window was again covered with a transparent polyvinylidene membrane so that closed chest conditions could be simulated. For endoscopic imaging in the rabbit model, the probe was introduced under bronchoscopic sight control. For the imaging process, the probe was further advanced carefully until an adequate signalling could be recorded. Animals were ventilated volume controlled (8ml/kg body weight) with room air and a respiratory rate of 30 breaths/min. Inspiratory peak pressure was limited to 12 mbar (KTR-4 small animal ventilator, Harvard Appa-ratus, Holliston, United States). The laser scanning unit (LSU) provides both its illumination and detection capabilities. It performs a complete raster scanning of the entire fibre bundle and operates at 488nm excitation wavelength. The excitation strength can be readily adapted to the fluorophore concentration in order to make the most out of the available fluorescence signal. Images from a layer of 0 to 50 μm in axial resolution are produced enabling to gain depth information about the tissue observed. For confocal microscopy, an exogenous staining was used. Fluorescein 0.1% was applied into the central venous line right before the beginning of microscopy. Moreover, concerning the use through a thoracic window, CLSM was compared with another new method, namely Fourier domain optical coherence tomography (FD-OCT) in a mouse model. Both FD-OCT and CLSM allowed analysis of alveolar structure as well as an unambiguous comparison concerning the quality of images [13]. After baseline, ALI was induced by intratracheal instillation of HCl (2 μL/g bw) until a stable injury (paO2 60 s). Thus, we were able to provide evidence for one of these mechanisms of HFOV gas transport postulated by Chang [4], which he called Pendelluft. The redistribution time constant was short enough to be analyzed in the presence of oxygen. So, we were able to measure the redistribution time constants in a living animal model.

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7 Imaging and Simulation of Velocity Profiles in Larger Airways Phase contrast MRI can measure regional velocities. In an airway cast another study has shown that this is also feasible with hyperpolarized gas in larger airways simulated by an airway cast [20]. Since regional gas flow velocity is also a parameter which is available from CFD simulations a direct comparison of CFD with in-vitro or in-vivo measurements becomes feasible. In a first step we implemented phasecontrast MRI for measuring gas flow under continuous flow conditions because this enables a simple validation of the MRI measurements with a volume flow meter. For the Helium-3 experiments, a closed loop tube system was filled with nitrogen in order to avoid polarization losses by oxygen. For the measurements with fluorinated gases the whole system was filled with the gas. In both cases an air turbine generated a controllable and constant flow, the volume flow was measured with a volume flow meter. Within the loop, the gas was piped through the oval trachea phantom, which was positioned in the 1.5 T Magnet (Siemens Sonata, Siemens Medical Systems, Erlangen, Germany), and a flow sensitive GREsequence was performed. Fig. 9 shows that flow measurements in the trachea phantom were successfully implemented for both Helium-3 as well as fluorinated gases. To the best of our knowledge the measurements in fluorinated gases are the first of their kind, similar measurements have not been made by other groups. Because of the somewhat lower signal intensity with fluorinated gases the spatial resolution is somewhat lower than at the measurements with Helium-3, but still 9 pixels extend across the trachea diameter. Currently we are working on an optimization of the signal intensity and on improving the spatial resolution. Physical characteristics of the two contrast gases, however, are very different. Under identical volume flow conditions of 520 mL/s the Reynolds number for C4 F8 - and Helium-3 gas are 15862 and 2500, respectively. Thus, with fluorinated gases gas flow is usually in the turbulent flow regime which needs to be taken into account during the interpretation of the results. With all gases examined (Helium-3, SF6 , C4 F8 , C2 F6 ) the correlation between the MRI measurements and the volume flow measurements was very good. Thus, a validated technique for non-invasive measurement of regional gas flow is available at this point [13]. For comparison of the experimental 19 F-MRI results with numerical data, CFD simulations of a similar set-up were conducted. The computational domain consisted of a bended inflow duct and the trachea like pipe geometry. The bended inflow was a result of the space constraints in the MR examination room and was the reason for the development of secondary flow phenomena at the inlet of the trachea phantom. First comparisons between MRI and CFD showed stronger differences due to the fact that the bended inlet ducting was not modeled in the initial CFD-simulations and therefore the inlet velocity profiles differed strongly (skewed velocity distribution for bended inlet compared to straight inlet, De >>30). The occurrence of secondary flow phenomena as a result of a bending can be described with the dimensionless Dean number (De), which relates the pressure los due to bending of a pipe to the pressure loss in an according straight pipe.

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Fig. 9 MRI of gas flow velocity in trachea phantom. From [22]. Left: Axial cross section of Helium-3 (top) and C4 F8 - (bottom) gas flow velocity in the trachea phantom. Center and Right: Vertical flow profile as a function of position in a C4 F8 (center) and a Helium-3 (right) measurement obtained at equal volume flow of 520 mL/s.

 De = Re ·

a , 2·R

(2)

with Re : ‘Reynolds number‘ , a : ‘pipe diameter‘ , R : ‘radius‘ Secondary flow structures can be observed for a Dean number exceeding 30. Inflow conditions for the CFD simulations were adapted from volume flow measurements in the closed loop gas system during the MRI experiments. A preliminary result in terms of velocity distributions is depicted in Fig. 10 and a good agreement between MRI (right) and CFD (left) was observed. Fig. 11 shows a comparison of velocity profiles of fully developed flow at a Reynolds number of approx. 8500, based on the mean inflow velocity at approx. 298 K obtained with CFD, MRI and analytically. The black lines represent the numerical results, whereas the red lines stand for the MRI data. Solid lines represent results in a horizontal symmetry cut plane trough the trachea phantom and dashed lines through a vertical symmetry cut plane. The blue dotted line illustrates analytical results with regard to the 1/7-power law. However, the power law coefficient was adapted top the governing Reynolds number and reads as 1/6. For the comparison of the numerical/experimental data with analytical results, a normalization of the maximum velocity value was conducted. Therefore, the flow velocity was normalized with the maximum velocity in the core flow region. The power law gives a good approximation of a turbulent pipe flow velocity profile with limitations in the near wall and centre line region. Comparing the analytical/numerical with the experimental data it becomes obvious that the curves are in good agreement in terms of the general velocity profile but the MR based velocity encoding technique seems to cut off the peak velocities while gaining good results in the high gradient boundary region. More recent results revealed (not shown), that this phenomena only appears at low mean flow

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Fig. 10 Comparison between CFD simulations (left) and phase contrast MRI (right) for constant flow of 21.5 l/min.

velocities (less than 1.5 m/s) and is most likely related to necessary signal averaging and smoothing during evaluation as a result of signal inconsistency in the centre of the MR coil. The slight variations in the area with strong gradients probably related to a coarse resolution of the experimental data and inaccuracy due to a noisy signal. Most of these problems should be overcome with an optimized experimental set-up and improved evaluation algorithms.

Fig. 11 Comparison between CFD simulations (black), phase contrast MRI (red), and analytical solution for constant volume flow of 21.5 l/min.

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8 Numerical Flow Simulations Besides the experimental MRI investigations and the effort towards a successful cast model completion, parametric CFD studies of various flow scenarios for identifying governing transport mechanisms and their influencing parameters were conducted within the framework of this project. Initial investigations focused on the constant flow through a model of the upper central airways and included gas transport and distribution analysis as well as gas mixing effects. In a second approach, based on literature results and experiences from animal experiments, the focus was laid on the impact of endotracheal tubes on the overall flow regime in the trachea and the upper central airways[15]. Most recent investigations are concentrating on the investigation of oscillatory flow regimes in a 3rd to 4th generation model of a lung.

8.1 Continuous Flow Investigations 8.1.1

Gas Distribution in a 3rd Generation Airway Model with Constant Flow through

The influence of tube placing and orientation as well as Reynolds number effects R R , Solkane ) are studied numerion the distribution of gas mixtures (e.g. Heliox th cally on a 4 generation model of a lung. Figure 12 shows on the left hand side an example of the predicted flow in a 4th generation model of a lung for steady inflow conditions. The picture illustrates the flow field in terms of stream traces and color coded velocity magnitudes in the outlet plane of a single branch. The laminar flow characteristic at the outlet of the chosen branch can be clearly identified with the 2D velocity profile, which tends to be slightly asymmetric. The observed asymmetric profile is supposed to be a result of the 3 dimensional bending and branching of the geometry which is also illustrated in Fig. 12.

Fig. 12 Exemplary numerical result of a steady flow through a 4th generation model of the lung (left) and a typical geometry for the investigation of the endotracheal tube placing on the flow regime in the same 4th generation lung model (right).

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The picture on the right hand side depicts the geometrical set-up used for investigation of the impact of an endotracheal tube and its orientation on the resulting flow regime in the model of the lung. The endotracheal tubes size, the placement, and the orientation have been found to affect the general flow regime and therefore the gas distribution as described exemplary in the following section. 8.1.2

Impact of Endotracheal Tubes on the Flow Field in a Generic Trachea

Experimental data from HFOV animal experiments and experiments focusing on the flow field in a generic trachea with endotracheal tube in the magnetic resonance tomograph in Mainz, as well as results from other research groups, e.g. [19], revealed that the endotracheal tube (ETT) has a strong impact on the predicted flow field. One major reason for this is the ETT induced change of the cross section area. Due to different length scales and cross section changes in the airways including the airway management devices (tube, connector, etc.) the local Reynolds number based on the local diameter and mean velocity varies from below 1000 in the upper central airways to 4000 and more in the endotracheal tube (for physiological gas and R even higher for dense medical gases, e.g. Solkane ) under artificial ventilation, but strongly depending on the respirator settings. In addition, vortical structures develop at discontinuous changes in cross section area or at rough edges, i.e. at the connector or the Murphy eye of the tube. For higher Reynolds numbers, disturbances developing discontinuous area alterations as well as the free shear layer developing at the outlet of the ETT (free stream jet) may locally trigger transition from a laminar to a turbulent flow. Finally, secondary flow structures develop as a result from the tube bending in accordance with the Dean number (De >>30). Various CFD simulations were conducted to investigate the impact of the ETT geometry on the flow field in a generic trachea under different inflow conditions using three different simplified 9 mm ETT geometries. It can be concluded that the ETT definitely has a strong impact on the flow field in the trachea and that it is inevitable to model at least the typical bending of the endotracheal tube. Figure 13 illustrates the difference between three simplified ETT models of different

Fig. 13 Comparison of different simplified ETTs and their impact of the resulting flow field at identical inlet conditions. Left: generic trachea with simplified straight tube ending. Middle: simplified tube with bending. Right: simplified tube with bending and connector (change in cross section area).

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abstraction level for identical inflow conditions (uniform velocity profile, identical mass flow) and their impact on the flow regime in terms of normalized helicity. Shown are iso-surfaces of the same magnitude of the normalized helicity for all three cases, indicating the three-dimensionality of the flow. The asymmetric flow characteristics of the cases with bending are obvious and related to secondary flow structures caused by the bending. The strong structures observed for the simplest case with only a short straight tube ending (left) are most likely a result from an ETT jet flow regime together with an undeveloped inflow velocity profile. Therefore it is concluded, that modeling the tube with bending is essential for a accurate CFD simulation. The modeling of a connector is not as important as the modeling of the bending (only slight impact on the resulting flow regime), but is recommendable, since it does not severely effect the computational costs.

8.2 Oscillatory Flow Investigations With the newly implemented open pressure boundary conditions it is possible to conduct parametric numerical studies of oscillatory flow in a model of the lung. The main focus is laid on the understanding of the complex and multifaceted transport and mixing mechanisms. A first study with the new boundary conditions compared the effect of 2 different pressure amplitudes and 2 different frequencies on the overall flow field and the flow structures. Preliminary results reveal no unexpected behavior of the flow. As already described by other research groups, the velocity profile shows a skewed distribution between inspiration and expiration phase. This is most likely one important aspect for a convective net mass transport under low tidal volume oscillatory ventilation. One important finding is that the maximum flow velocity is not only determined by the pressure amplitude but also by the frequency. Identical amplitudes led to lower maximum velocities at higher frequencies. This was also observed in MRI experiments. Fig. 14 illustrates two snapshots during

Fig. 14 Comparison of the velocity distribution during expiration (left) and inspiration (right). Color coded is the fraction of the tracer gas for investigation of the gas distribution within the lung during various breathing cycles.

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inspiration and expiration phase. The local velocities and the flow direction within the cut plane are represented by vectors. Focus is laid on the dependence of the developing asymmetrical velocity profiles of inspiration and expiration cycle as a function of the ventilation parameters (pressure, frequency, and Reynolds number). Of further interest is also the characteristic of the oscillatory system including phenomena like “Pendelluft” and branch/segment recruitment. These topics are currently under investigation.

9 Conclusion and Outlook Our MRI studies of HFOV demonstrate that MRI of experimental HFOV is feasible. Hyperpolarized 3 He allowed for imaging the gas movement in high spatial and temporal resolution. 3 He-MRI provides evidence for intrapulmonary redistribution to be an efficient mechanism of gas transport in the periphery of the airways. We conclude that HFOV is rather limited in the central airways, which may be analyzed by imaging of flow profiles and by analytical methods of fluid mechanics. Contrary to 3 He-MRI, 19 F-MRI of fluorinated gases benefits from moderate costs. The technology is based on thermal polarization, which is stable and very reproducible. Changes of the physical gas properties, however, have to be taken into account, since the fluorinated gases have large molecular weights and high concentrations are needed to achieve a sufficient SNR. For continuous flow, good agreement of phase contrast MRI of fluorinated gases with CFD and volume flow measurements was observed in a simple straight pipe model. We are currently extending our MRI velocity measurements to oscillatory flow conditions, and we are in the process of data analysis of a pig study using 19 F-MRI wash-out measurements under HFOV. After final data analysis we will have available dynamic MRI methods for imaging of the intrapulmonary 19 F- or Helium-3 gas concentration as well as phase contrast gas flow measurements to be used in preclinical HFOV studies. With a new 2D laser Doppler anemometry (LDA) system, further experimental investigations on gas transport in a new 4th generation cast model will be conducted. One major object beside the detailed parametric investigation of different oscillatory flow regimes is the crossvalidation of MRI, CFD and LDA data obtained for the same geometry and identical inflow conditions. This allows for a final objective and quantitative evaluation of the accuracy of the velocity encoding MRI technique as well as for the numerical methods. The applications of the optical LDA measurement technique was the reason for the focus on the surface quality of the foundry core model, as it is sensitive to optical inadequateness and diffuse amorphous reflexion. First numerical calculations of an oscillatory flow in a 3rd generation lung model showed the ability of newly implemented open pressure boundary conditions for simulating flows in such complex systems. Further numerical together with experimental investigations will focus on the gas transport mechanisms in a model of the upper central airways with applied HFOV and the optimization of ventilation parameters.

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Acknowledgements. Financial support has been granted by the German Research Foundation (SCHR 687/2, SCHR 687/5, WA 1510/8) and the European Union (PheliNet). First of all, the authors would like to thank the German Research Foundation (DFG) for their funding and their support of the interdisciplinary ”PAR” (Protective Artificial Respiration) project. We would also like to thank all participating partners and colleagues who contributed to this work and to this research project.

References 1. Amor, N., Zanker, P.P., Blumler, P., Meise, F.M., Schreiber, L.M., Scholz, A., Schmiedeskamp, J., Spiess, H.W., Munnemann, K.: Magnetic resonance imaging of dissolved hyperpolarized 129Xe using a membrane-based continuous flow system. J. Magn. Reson 201, 93–99 (2009) 2. Chan, K.P., Stewart, T.E.: Clinical use of high-frequency oscillatory ventilation in adult patients with acute respiratory distress syndrome. Crit. Care Med. 33, S170–S174 (2005) 3. Chan, K.P., Stewart, T.E., Mehta, S.: High-frequency oscillatory ventilation for adult patients with ARDS. Chest 131, 1907–1916 (2007) 4. Chang, H.K.: Mechanisms of gas transport during ventilation by high-frequency oscillation. J. Appl. Physiol. 56, 553–563 (1984) 5. Downar, J., Mehta, S.: Bench-to-bedside review: high-frequency oscillatory ventilation in adults with acute respiratory distress syndrome. Crit. Care 10, 240 (2006) 6. Fain, S.B., Korosec, F.R., Holmes, J.H., O’Halloran, R., Sorkness, R.L., Grist, T.M.: Functional lung imaging using hyperpolarized gas MRI. J. Magn. Reson Imaging 25, 910–923 (2007) 7. Gast, K.K., Wolf, U.: Functional 3He-MRI of the lungs. Radiologe 49, 720–731 (2009) 8. Hager, D.N., Fessler, H.E., Kaczka, D.W., Shanholtz, C.B., Fuld, M.K., Simon, B.A., Brower, R.G.: Tidal volume delivery during high-frequency oscillatory ventilation in adults with acute respiratory distress syndrome. Crit. Care Med. 35, 1522–1529 (2007) 9. Heraty, K.B., Laffey, J.G., Quinlan, N.J.: Fluid dynamics of gas exchange in highfrequency oscillatory ventilation: in vitro investigations in idealized and anatomically realistic airway bifurcation models. Ann. Biomed. Eng. 36, 1856–1869 (2008) 10. Hopkins, S.R., Levin, D.L., Emami, K., Kadlecek, S., Yu, J., Ishii, M., Rizi, R.R.: Advances in magnetic resonance imaging of lung physiology. J. Appl. Physiol. 102, 1244– 1254 (2007) 11. Imai, Y., Nakagawa, S., Ito, Y., Kawano, T., Slutsky, A.S., Miyasaka, K.: Comparison of lung protection strategies using conventional and high-frequency oscillatory ventilation. J. Appl. Physiol. 91, 1836–1844 (2001) 12. Imai, Y., Slutsky, A.S.: High-frequency oscillatory ventilation and ventilator-induced lung injury. Crit. Care Med. 134, S129–S134 (2005) 13. Kalthoff, D.: Entwicklung von Methoden zur Untersuchung von Strmungsverhltnisse von Kontrastgasen mittels Magnetresonanz-Tomographie. Diploma Thesis, Department of Physics, Mainz University (2007) 14. Knopp, T., Zhang, X., Kessler, R., et al.: Enhancement of an industrial finite-volume code for large-eddy-type simulation of incompressible high Reynolds number flow using nearwall modelling. In: Comput.Methods Appl. Mech. Eng. (2009) (in Press) 15. Krenkel, L., Wagner, C., et al.: Protective artificial lung ventilation: investigation of the air flow in a generic model of the lung. Accepted for Notes on Numerical Fluid Mechanics and Multidisciplinary Design. Springer, Heidelberg (2009)

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16. Lenz, C.: Rekonstruktion von Luftwegen in der Lunge aus medizinischen Bilddaten. Master Thesis, Universitt Leipzig (2009) 17. Pennecot, J., Krenkel, L., Wagner, C.: An Automated Reconstruction of the Lungs for CFD Simulations, Venice, Italy. In: ECCOMAS 2008 (2008) 18. Pillow, J.J.: High-frequency oscillatory ventilation: mechanisms of gas exchange and lung mechanics. Crit. Care Med. 33, 135–141 (2005) 19. Rocco, P.R.M., Zin, W.A.: Modelling the mechanical effects of tracheal tubes in normal subjects. Eur. Respir. J. 8, 121–126 (1995) 20. Rochefort de, L., Vial, L., Fodil, R., Maitre, X., Louis, B., Isabey, D., Caillibotte, G., Thiriet, M., Bittoun, J., Durand, E., Sbirlea-Apiou, G.: In vitro validation of computational fluid dynamic simulation in human proximal airways with hyperpolarized 3He magnetic resonance phase-contrast velocimetry. J. Appl. Physiol. 102, 2012–2023 (2007) 21. Scholz, A.W., Wolf, U., Fabel, M., Weiler, N., Heussel, C.P., Eberle, B., David, M., Schreiber, W.G.: Comparison of magnetic resonance imaging of inhaled SF6 with respiratory gas analysis. Magn. Reson Imaging 27, 549–556 (2009) 22. Schreiber, W.G., Markstaller, K., Weiler, N., Eberle, B., Laukemper-Ostendorf, S., Scholz, A., Burger, K., Thelen, M., Kauczor, H.U.: 19F-MRT of pulmonary ventilation in the breath-hold technic using SF6 gas. Rofo 172, 500–503 (2000) 23. Schreiber, W.G., Eberle, B., Laukemper-Ostendorf, S., Markstaller, K., Weiler, N., Scholz, A., Burger, K., Heussel, C.P., Thelen, M., Kauczor, H.U.: Dynamic (19)F-MRI of pulmonary ventilation using sulfur hexafluoride (SF(6)) gas. Magn. Reson. Med. 45, 605–613 (2001) 24. Terekhov, M., Rivoire, J., Scholz, A., Wolf, U., Karpuk, S., Salhi, Z., Koebrich, R., David, M., Schreiber, L.M.: Measurement of gas transport kinetics in high-frequency oscillatory ventilation (HFOV) of the lung using hyperpolarized 3He MRI. J. Magn. Reson. Imaging (2009) (in review) 25. Wolf, U., Scholz, A., Heussel, C.P., Markstaller, K., Schreiber, W.G.: Subsecond fluorine-19 MRI of the lung. Magn. Reson. Med. 55, 948–951 (2006)

Mechanostimulation and Mechanics Analysis of Lung Cells, Lung Tissue and the Entire Lung Organ Stefan Schumann, Katharina Gamerdinger, Caroline Armbruster, Constanze Dassow, David Schwenninger, and Josef Guttmann

Abstract. Analysis of respiratory mechanics under mechanical ventilation is crucial for a lung-protective ventilation setting. However, under the conditions of mechanostimulation caused by mechanical ventilation, only the global components of mechanical impedance can be determined. These include the airflow resistance, compliance, and inertance. Whereas in the case of conventional mechanical ventilation, the organ integrity of the lung is certainly preserved, it is practically impossible to obtain quantitative information about the local pulmonary mechanics, for instance at the alveolar level. Analysis of pulmonary mechanics at a local level requires sophisticated experimental techniques for the mechanostimulation of anatomical subunits of the lung. In this chapter, we summarize our investigations in the field of experimental mechanostimulation and mechanics analysis of lung cells, lung tissue and entire lung organ. Stefan Schumann University Medical Center Freiburg e-mail: [email protected] Katharina Gamerdinger University Medical Center Freiburg e-mail: [email protected] Caroline Armbruster University Medical Center Freiburg e-mail: [email protected] Constanze Dassow University Medical Center Freiburg e-mail: [email protected] David Schwenninger University Medical Center Freiburg e-mail: [email protected] Josef Guttmann University Medical Center Freiburg e-mail: [email protected] M. Klaas et al. (Eds.): Fundamental Medical and Engineering Invest. on PAR, NNFM 116, pp. 129–154. c Springer-Verlag Berlin Heidelberg 2011 springerlink.com 

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1 Introduction Mechanical or artificial ventilation is the most important life-saving therapeutic instrument in modern intensive care medicine. The technical gas delivery system (ventilator) and the respiratory system (lungs and thorax) of a patient represent a connected pneumatic system of high complexity with the artificial airways (respiratory tubing system, gas humidifier, endotracheal tube) being the pneumatic interconnection [21]. The respiratory system produces mechanical impedance to the ventilator output, and the ventilator transfers mechanical energy to the biological system to overcome its impedance. The transfer of a level of mechanical energy that is too high from the technical subsystem towards the biological subsystem is the primary cause for ventilator-induced lung injury (VILI) [41], which has been attributed to barotrauma [27, 61], volutrauma [15], atelectrauma [23, 36], and finally to biotrauma [57]. Consequently, it is the ultimate goal of lung-protective ventilation [22] to individually titrate the ventilator setting to minimize the energy transfer on a breath-by-breath basis. Recently, the global pulmonary stress-strain relationship was identified to be the primary cause for ventilator-induced lung injury [10]. As such, the energy transfer related to mechanical ventilation implies a mechanostimulation of cells, in particular those lining the capillaries, airways and alveoli, which transform mechanostimulation into chemical signals: mechanotransduction [42]. Quantitative analysis of the relationship between energy transfer and cellular mechanotransduction requires new methods of experimental mechanostimulation and of analyzing structural mechanics at different levels of pulmonary organ integrity. The precision of both local mechanostimulation and local mechanics analysis is highest at a cellular level, but lowest if the structural integrity of the lung is preserved, i.e. under conditions where mechanostimulation is realized per mechanical ventilation (Fig. 1). Since this principle dilemma cannot be circumvented, investigation at different levels of lung integrity is required in order to support the development of effective lung-protective ventilation strategies. In this article, we summarize our investigation in the fields of experimental mechanostimulation and mechanics analysis on the three levels of (i) lung cells, (ii) lung tissue, and (iii) the entire lung in models of mechanically ventilated isolated lungs and animals.

2 Lung Cells Reasoned by the complex anatomy of alveolar tissue, the local mechanical stress that is exerted to a single cell depends predominantly on its position within an alveolus as well as on the physiological and functional conditions of the alveolus. Underinflation (atelectasis) or overinflation of alveoli or their surrounding parenchyma are crucial for the stress transmission. In the human lung, with its 300 million alveoli consisting of different cell types, there is a mix of considerably different cellular stress-strain relationships during mechanical ventilation. Hence, experimental mechanostimulation of isolated lung cells serves to understand fundamental processes in pulmonary mechanobiology.

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Fig. 1 Schematic representation of relationships between pulmonary organ integrity and the precision of local mechanostimulation (green curve) and mechanics analysis (blue curve). The level of pulmonary organ integrity increases from isolated cells to lung tissue samples (PCLS: precision-cut lung slice), to isolated lungs and right on up to the lung in the mechanically ventilated animal or in the patient. At a cellular level, the precision of both local mechanostimulation and local mechanics analysis is high, whereas in the case of full pulmonary organ integrity, mechanical ventilation means a global mechanostimulation. Consequently, mechanical ventilation is associated with a global analysis of lung mechanics with the consequence of low precision for local mechanostimulation and local mechanics analysis.

2.1 Experimental Mechanostimulation The consequences of mechanical stimulation on cell expression and cell development in cell cultures [33, 34, 44, 52, 60] as well as on biologic [16, 17] and artificial tissue samples [19] have been investigated by using different experimental mechanostimulation devices to simulate biologic mechanical stress and strain. Most experimental mechano-stimulators use elastic biocompatible carrier membranes to transfer mechanical stress to the biologic sample (Fig. 2). By determining membrane deformation [4, 43, 59] the applied strain can be translated into tissue elongation. Amongst the numerous custom-made mechanical devices, the most established one is the Flexercell toolkit (Flexcell, Flexcell Inc, Hillsborough, NC) [8, 28]. This system allows the application of cyclic strain to biological samples under direct vision. However, a more homogeneous stimulation can be achieved by biaxial mechanostimulation using the so-called ”bubble inflation technique” or ”membrane inflation technique” [53, 62]. We adopted the membrane inflation technique and developed a pressure-driven strain-applicator, which uses spherical deflection of a carrier membrane [45, 24] for transmitting a well-defined tensile strain to biologic samples placed on top of it.

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Our strain-applicator consists of two similar vertically arranged cylindrical rigid chambers (Fig. 3). Both chambers are gas-tight and fluid-tight separated by a circular elastic membrane which is fixed in a membrane holder. Mechanical energy (in the form of pressurized gas or liquid) is transmitted to the lower ”pressurechamber”. The upper ”supply-chamber” is designed for supply of tissue nutrition medium. Since the circulation of nutrition medium allows keeping cells or tissue alive under conditions of mechanostimulation, we call this experimental device a ”bioreactor”. The horizontally arranged membrane carries the biologic sample and transmits the mechanical energy to the sample. The deflection of the carrier membrane is actuated by static or cyclic application and withdrawal of gas or liquid to the pressure-chamber. This allows transmission of variable degrees of tensile strain to a cultivated biologic sample via the elastic carrier membrane. We use Polydimethylsiloxan (PDMS) to serve as a material for elastic membranes. It is used in a wide range of biomedical applications, thanks to its bioinertness, low toxicity, good thermal and oxidative stability, and its anti-adhesive properties. We described a method to produce thin circular PDMS-membranes with defined mechanical properties for use in the bioreactor via a spin-coating technique [3]. For cell growth on top of PDMS membranes, it is necessary to modify the hydrophobic surface to enable cell adhesion. Therefore, we exposed the membranes to R allowing us to label the surface UV-light and covered them with Sulfo-SANPAH, with RGD-peptides [29]. Consequently, the cells are evenly spread on modified membranes (Fig. 4) and kept under cell culture conditions (37 ◦ C, 5%CO2 ) in an incubator for 24 hours. After cultivation, cells adherent on membranes are deflected in the bioreactor. The maximum volume of deflection was varied between 0.5mL and 1.0mL. These

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Fig. 3 Bioreactor for experimental mechanostimulation of lung cells and tissue (exploded drawing). The bioreactor or experimental strain-applicator consists of a lower pressure chamber (1) and an upper supply chamber (2). Both chambers are separated by a specimen-carrying membrane (3), which is fixed in the membrane holder (4). Upwards- and downwards deflection of the specimen-carrying membrane (3) is controlled by volume input and output via an inlet (5).

Fig. 4 Adhesion of different cell types to modified PDMS surface. A: NIH3T3 (mouse fibroblast); B: RLE-6TN (rat alveolar type II cell); C: A549 (human lung carcinoma cell).

volumes reflect 8% to 20% distension. Cell adherence is controlled via microscopy. Larger deflections lead to cell detachment and cell death. During mechanostimulation, mechanical properties are measured. After stimulation, vitality of cells is determined.

2.2 Analysis of Mechanics - Pressure-Volume Relationship as a Substitute for Stress-Strain Relationship A primary limitation of most experimental mechanostimulators for biologic tissue is the lack of contact free techniques of enabling the analysis of mechanical forces that are transferred to the sample. In this context, ”contact free” means that special

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devices like indenters are not required to transmit deformation forces to the biological sample [25]. Whereas the primary goal of experimental mechanostimulators is the mere mechanostimulation of biological samples, we made further attempts to analyze mechanical properties of biological samples. Consequently, more elaborate experimental techniques are required to adequately investigate and analyze mechanical properties. One interesting method of analyzing cell mechanics and not just stimulating the cells, is the so-called Celldrum technique, presented by the Artmann group [58]. With this technique the authors measured the resonance frequency of fibroblast-populated collagen matrices as a response on sound stimulation. Alternatively, we determined the pressure-volume relationships inside the pressurized chamber of our strain applicator by measuring pressure changes following the volume changes under both static and dynamic conditions. We determined the volume distensibility, i.e. the ratio volume change divided by pressure change, which is called ”compliance” - in analogy to respiratory mechanics - of the carrier-membranes. To test the device, we placed a second test membrane on top of the carrier membrane to connect their compliances in series. Both membranes were clamped in the device. If the compliance CM1 of the carrier-membrane is known and Ccomb (= resulting compliance of carrier membrane and test membrane mechanically connected in series) is directly determined (which typically is the case when testing a biologic sample), the compliance of the test membrane CM2 can be calculated with: CM2 =

1 1 Ccomb − CM1 1

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The compliance of the compressible air volume inside the pressure-chamber needs to be considered as connected in parallel with the membrane’s compliance. Furthermore, under the assumption that the inflation of the pressure chamber (see position 1 in Fig. 3) causes a membrane deformation with a shape approximating a spherical cap [1], the stress-strain relationship, i.e. its slope, Young’s modulus E, can be determined from geometry of the bioreactor and compliance according to R2 V 2 (2) π C · t h4 where R is the radius of the undeflected membrane, t is the material’s thickness, V is the applied volume and h is the maximal height of the deflected membrane [45]. It must be noted that, depending on the geometry of the bioreactor compliance, a nonlinear profile follows if displayed against inserted volume V or deflection height h: E=2

2 R2 V 2 π d · E h4

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we get C=

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When assuming E as constant; examination of the limits results in lim C(h) = +∞

h→0

lim C(h) = +∞

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That means that C(h) underlies a specific concave profile. Furthermore it follows that deviations from this profile can be attributed to a nonlinear behavior of a material’s stress-strain relationship. It becomes obvious that the compliance of the carrier membrane plays an essential role in this analysis: The more pliant the carrier membrane the better the signal-to-noise ratio. We therefore developed a highly pliant PDMS membrane [3] (as mentioned above). After conducting the modification procedure for enabling cell growth on hydrophobic membranes we determined the mechanical properties of the modified membranes to get reference data without cells. To analyze mechanical properties of single cell layers during application of stress we established the cultivation of different human and rat cell lines, especially fibroblasts and alveolar cells on these PDMS membranes (see Section 2.1). Fig. 5 illustrates the results of a mechanics analysis obtained from mechanostimulation of A549 cells (see Fig. 2C). Mechanostimulation of the cell monolayer was realized by increasing the volume inflated into the pressure chamber of the bioreactor from 0.1mL to 0.5mL. It must be noted that the compliance curve shows the concave profile as predicted in theory.

Fig. 5 Mechanical property (compliance) as a function of carrier membrane deflection of A549 cell monolayers; mean values and standard deviation of n=4 measurements.

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3 Lung Tissue Alveolar parenchyma samples represent yet another step towards higher pulmonary organ integrity. By proceeding to pulmonary tissue samples, the organ is resembled closely featuring all cell types and connective tissues. This allows investigation and comparison of healthy or damaged structures amongst each other, as well as in relation to the surrounding tissue. As a major advantage this level of organ integrity enables visual access to alveolar structures during experimental mechanostimulation via direct observation under the microscope. Hence, tissue characteristics can be easily and directly characterized.

3.1 Experimental Mechanostimulation The prerequisite for experimental mechanostimulation of pulmonary parenchyma is an adequate method for preparation of tissue samples under preservation of the native alveolar structure, all of which can be kept viable for at least several hours. A technique for the preparation of alveolar tissue was developed by Stefaniak et al. [55]. They described a method to produce so-called precision-cut lung slices (PCLS), which was further improved upon by the Uhlig group [32]. The PCLS were also investigated in our mechanostimulator [13]. By cutting lung tissue into thin slices, the identical membrane inflation technique (as used for mechanostimulation of cells) can be used for mechanostimulation of lung parenchyma. PCLS are prepared by filling the lung with a low-melting point agarose with subsequent solidification. Treated in this manner, the tissue is suitable for the preparation of very thin, machine-cut slices that can be cultivated under cell culture conditions [32]. This combines an easy-handling of the sample with a relatively intact cell-matrix environment. PCLS are viable for at least 3 days [32], providing a multitude of defined slices from one organ. Using a specific clamping device, the PCLS can be mounted in the bioreactor on top of the flexible membrane and stretched biaxially. Aside from the mechanical characteristics measured directly in the bioreactor, the PCLS can be observed by microscopic techniques under conditions of static and dynamic mechanostimulation.

3.2 Mechanics Analysis The mechanics analysis of PCLS associated with mechanostimulation inside the bioreactor can be subdivided into two parts. First, the analysis of the pressurevolume relationship analogous to the method described for the investigation of cells. Second, the synchronous recording of microscopic images to identify both strain-dependent and time-dependent local changes in tissue morphology. For this second step, two methodological extensions have been developed; (i) dynamic video-sequencing and (ii) alveolar tracking which are presented in the following.

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Dynamic Video-Sequencing

Pressure-volume loops for breathing cycles characterize the global dynamic respiratory system mechanics during controlled mechanical ventilation [20]. To understand the mechanical properties of lung parenchyma is a prerequisite to improve our understanding of the pressure-volume relationship of the entire lung organ. In this context, it would be important to know to which extent local mechanical tissue properties affect total respiratory system mechanics. The PCLS can be considered as a viable low scale lung model where the tissue mechanics of alveolar parenchyma can be compared with local changes in alveolar morphology during mechanostimulation. However, simultaneous acquisition of morphological and mechanical information raises a dilemma. For optimal video imaging, the tissue being inspected should be mechanostimulated two-dimensionally in one horizontal plane in order to keep the video camera in focus. However, for analysis of mechanical tissue characteristics, the mechanostimulation - according to the bubble or membrane inflation technique - is achieved through homogeneous three-dimensional deflection, which is associated with a vertical displacement. This results in an in-focus and out-of-focus movement of the sample. To solve this dilemma, the dynamic video-sequencing technique was developed [46]. Inside the bioreactor we applied cyclic strain on PCLS from rat lungs. Pressure-volume loops and dynamic microscopy images were simultaneously recorded during sinusoidal mechanostimulation. To this end, a gas volume was insufflated sinusoidally into the pressure chamber of the bioreactor with a deflection rate of 15min−1 using a ventilator for small animals (Harvard Rodent Ventilator, Model 7025, Harvard Apparatus, Southnattick, MASS, USA). For estimation of the pressure-volume relationship inside the bioreactor, pressure and gas flow were measured, and gas volume was achieved by numerical integration of flow. Pressurevolume loops from the tissue were calculated by compensating for that fraction of pressure that was required to overcome the carrier membrane volume distensibility. For dynamic video-sequencing the bioreactor was centrally fixed under a microscope (AxioImager, Carl Zeiss AG, Oberkochen, Germany). The vertical focus position of the non-deflected tissue served as the height offset. After moving the offset position into focus, the microscope stage was moved downwards for 2mm. The deflection amplitude of the probe was then set such that one exactly focused image was represented in the microscope’s display. This is when the deflected probe was in its maximal position. The range of 0 to 2mm of stage displacement was subdivided into a number of vertical position steps. For each position a movie sequence of 20s was recorded thus including about 5 complete deflection cycles at a frame rate of 25s−1 . From each movie the respective image with the best visual definition was extracted. Since the selected images are in the focal plane of the microscope, their magnification is similar and as a consequence, comparable. The extracted images were rearranged corresponding to their respective temporal position inside the deflection/retraction cycle. The extracted images were synchronized with pressure-volume data and sizes to build a new video sequence (Fig. 6).

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From the rearranged video sequence, changes discovered in alveolar geometry during dynamic mechanostimulation can be analyzed and hence, tracking of alveolar structures is possible (Fig. 7).

Fig. 7 Images of alveolar tissue recorded and selected at different deflection and retraction ranges. Top: during deflection, time progressing from left to right. Bottom: during retraction, time progressing from right to left. Actual pressure is indicated inside the images. Orange markings indicate tracked structure analyzed for position and size (see Fig. 6).

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Alveolar Tracking

Based on the in-focus images of the rearranged video sequence (see Fig. 7) tracking of alveolar structures with respect to deflection and retraction pressure, structural geometry and displacement are performed (Fig. 8). Taken together, this dynamic video-sequencing allows visualization of dynamic changes in alveolar morphology on a microscopic scale during 3-dimensional mechanostimulation. Since the bioreactor allows determination of the pressure-volume relationships of a sample, an appropriate assignment of strain to morphologic conditions becomes available. In this way, comparison of tissue morphology with mechanical characteristics of the parenchyma at a microscopic level during dynamic mechanostimulation could improve the understanding of macroscopic mechanical characteristics of the lung.

Fig. 8 Exemplary courses of deflection pressure, structure size and structure position during cyclical deflection (black) and retraction (grey) A: pressure-course during a single deflection measured inside the pressure chamber of the bioreactor. Imaging positions could be assigned to the pressure time course of mechanostimulation (see Fig. 9). B: respective course of vertical diameter of the displayed alveolar structure. C: vertical and D horizontal displacement of the structure.

4 Complete Lung The principle of experimental mechanostimulation as outlined above, implies that the experimental device (strain-applicator; bioreactor) acts as an external source for mechanical energy that is transferred to the biological sample, it being either lung cells or lung tissue. The mechanical energy is transformed into mechanical stress leading to mechanical strain and thus, to deformation. From the analysis of the stress-strain relationship under experimental mechanostimulation, the mechanical

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properties of the biologic sample are derived. Translating these principles of experimental mechanostimulation to the whole lung under the condition of mechanical ventilation means that the ventilator now acts as an external source of mechanical energy (for this, we do not consider the situation of spontaneous breathing with the respiratory muscles being the internal source of mechanical energy). From the physical point of view, the lung is a three-dimensional pressure-volume system offering mechanical impedance, which the ventilator has to overcome. If mechanical ventilation is regarded as global mechanostimulation of the lung, the analysis of lung mechanics is usually restricted to the global analysis of the elastic, resistive, and inertive components of the mechanical impedance of the respiratory system.

4.1 Isolated Lung Investigations of isolated lungs can be performed either in a homogeneously or inhomogeneously injured organ under nutrition, perfusion and oxygenation control, and under the influence of the chest wall mechanics being eliminated. The experimental mechanostimulation, i.e. the mechanical ventilation as well as the methods of mechanics analysis, can be performed in the same manner in isolated lungs as in an animal model or in a patient. However, the isolated lung can be investigated free from influences of its natural surrounding boundary conditions predominantly caused by thorax and abdomen. 4.1.1

Isolated Porcine Lung Model

In an isolated porcine lung model we analyzed the influence of perfusion pressure during anterograde perfusion on the pulmonary edema formation under the guise of mechanical ventilation [48]. The lungs were ventilated in the volume control mode (SV 900 C; SiemensElema, Solna, Sweden) with a tidal volume of 3mL/kgBW on two different levels of positive end-expiratory pressure (PEEP) levels; 4cmH2 O and 8cmH2 O. After awaiting stationary ventilation conditions, perfusion with nutrition solution (PERFADEX; Vitrolife, Gothenburg, Sweden) was applied at different hydrostatic pressures that were achieved by height differences between the lung and fluid reservoir of 100cm (high level) or 55cm (low level), respectively. During high-level perfusion, the maximal fluidic pressure reached 50mmHg and lung mass increased by 130%. During low-level perfusion, the fluidic pressure reached 28mmHg and lung mass increased only by 91% at PEEP of 4cmH2 O. Histological examination of the lung tissue confirmed that this increase in lung mass corresponded to an increase of interstitial edema. Using a PEEP of 8cmH2 O at lowlevel perfusion reduced the relative increase in lung mass to 30%. Perfusion at high fluidic pressure amplitudes led to an increased lung mass compared with low fluidic pressure amplitudes. Edema formation in isolated lungs caused by flush perfusion was reduced using low perfusion pressures in combination with high PEEP. Low flush perfusion pressures might reduce edema formation

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and improve compliance of the isolated lungs. We concluded that an increase of PEEP can only prevent from edema formation at low levels of perfusion pressure. Therefore perfusion of isolated lungs (e.g. in a transplantation setting) should be performed at low perfusion pressure. 4.1.2

Isolated Rat Lung Model

Whereas perfusion-related mechanostimulation was investigated in a large animal’s lung, the effects of the combination of different PEEP levels and different tidal volume settings on peak pressure can be investigated advantageously in isolated normal and injured lungs of small animals. Lungs were isolated from 12 female wistar rats weighing in at 280 to 350g and freely suspended in a chamber that was continuously humidified by nebulized water to prevent the organ from drying. Airway pressure was measured using a piezo-resistive pressure transducer (SI-special instruments, N¨ordlingen, Germany). In eight animals lung injury was induced by instillation of a 5% solution of Tween20 in saline (4.5mL/kg) into the trachea. Control isolated normal lungs were treated in a similar fashion, but without Tween-20 instillation. The isolated lungs were mechanically ventilated via a cannula using a small animal ventilator (flexivent, SCIREQ Scientific Respiratory Equipment Inc., Canada). Three different levels of PEEP (5, 10, 20cmH2O) and of tidal volume (6, 10, 15mL/kg) were investigated. Tween-20 instillation caused a heterogeneous injury. There were different degrees to the injured areas on the lung surface. Control lungs had a homogeneous, normal-appearing lung surface. In the normal lung, the peak inspiratory pressure (PIP) clearly increased with increasing PEEP and tidal volume up to 74.9 ± 5.9cmH2O (Fig. 9). In contrast, in the injured lung, the PIP increased at the PEEP levels of 5 and 10cmH2 O; only at a PEEP of 20cmH2 O, the PIP increases again up to 68.3 ± 2.2cmH2O (Fig. 9). In the normal lungs, dynamic intratidal compliance decreased at the end of inspiration with increasing tidal volume (Vt) at a low PEEP of 5cmH2 O whereas it remained mostly constant at PEEP levels of 10 and 20cmH2 O (Fig. 10). In the injured lung, the dynamic intratidal compliance increased slightly at the end of inspiration with increasing Vt at PEEP levels of 5 and 10cmH2 O, whereas at a PEEP of 20cmH2O dynamic compliance is considerably lower and decreases with increasing Vt (Fig. 11).

4.2 Animal Model (rat) Long-term effects of mechanical ventilation settings on the respiratory system mechanics should be investigated in animal models and not in isolated lungs. 46 female anesthetized Wistar rats were tracheostomized and mechanically ventilated at a FiO2 of 1.0 using the flexivent animal research ventilator mentioned above. Ventilation was set to a frequency of 70min−1 and a tidal volume of 10mL/kg using a pressure limited constant inspiratory flow ventilatory pattern. After preparation the rats were randomized to be ventilated at a PEEP level between 0 and 10cmH2 O. The rats were divided into two groups. The lung injury

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Fig. 9 The relationship between tidal volume and peak inspiratory pressure at three different PEEP levels (in cmH2 O) obtained from normal (n=4) and from injured (n=8) isolated rat lungs.

Fig. 10 Intratidal compliance at peak inspiratory pressure (end of inspiration) in a normal lung is highest when it is ventilated with PEEP 5cmH2 O and Vt 6mL/kg. With other settings, the compliance is lower.

group received saline bronchoalveolar lavage, the other group served as the control group (sham). Lung injury was induced by repeated lavage with saline until ARDS-criteria were met (PaO2/FiO2 < 200mmHg). Measurement of respiratory mechanics and blood gas analysis were performed before and then hourly after lavage/sham. Two subsequent low-flow maneuvers (pressure amplitude of 40cmH2O) were performed for analysis of respiratory system mechanics. The shape of the inspiratory pressure-volume curves (PV loops) during low-flow maneuvers varied between the sham and lavage groups. In the sham group, during the first measurement, a pronounced concave deflection was visible in the first of the two consecutive pressure-volume curves (Fig. 12 left). This deflection was not visible in either of the curves during second measurement.

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Fig. 11 Intratidal compliance at peak inspiratory pressure (end of inspiration) in a normal lung is highest when it is ventilated with PEEP 5cmH2 O and Vt 6mL/kg. With other settings, the compliance is lower.

In the lavage group, the shapes of the two consecutive curves did not differ from each other (Fig. 12 right). First and second loops had concave shapes during all measurements. In the sham group, inspiratory dynamic compliance increased after the two lowflow maneuvers. After lung injury, inspiratory dynamic compliance did not differ noticeably after the low-flow maneuvers. Furthermore, in the lavage group, inspiratory dynamic compliance was well below compliance in the sham group. From these findings we conclude that healthy lungs have the capability to maintain alveolar stability after recruitment. This ability is lost in lung injury induced by saline lavage.

Fig. 12 Left: PV loops of two consecutive low-flow maneuvers in the sham group. Right: PV loops of two consecutive low-flow maneuvers in the lavage group. Respective left panel: first low-flow maneuver, respective right panel: second low-flow maneuver. Top: immediately before injury/sham, middle: immediately after injury/sham, and bottom: 4 hours after injury/sham.

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4.3 Analysis of Global Respiratory System Mechanics With respect to the analysis of respiratory mechanics, there is a change in the paradigm in as much as the technique of analyzing respiratory data when obtained from static or quasi-static respiratory maneuvers is increasingly dropped out. Instead, analysis of intratidal dynamic respiratory mechanics is favored. With the SLICE method [20], compliance and resistance of subsequent intratidal volume portions (”slices”) can be calculated from the pressure-volume (PV) loop of a breath via a multiple linear regression analysis. Based on the SLICE method, we have developed the new gliding-SLICE [47] method in order to receive detailed profiles of intratidal compliance and resistance. Fig. 13 illustrates the principle of the analysis of intratidal dynamic respiratory mechanics by means of a simulated breath assuming volume-controlled mechanical ventilation with constant inspiratory flow rate. To evaluate whether the nonlinear intratidal compliance profile hints at what level the lung’s protective PEEP and tidal volume (Vt) should be set at, we investigated the dynamic pressure-volume relationship in a mechanically ventilated animal model. In 12 piglets, atelectasis was induced by application of negative pressure. Pressure and flow signals were recorded during mechanical ventilation at different levels of PEEP at a tidal volume of 12mL/kgBW . Using the gliding-SLICE method, intratidal compliance profiles were investigated. In contrast to quasi-static compliance, the gliding-SLICE method revealed pronounced intratidal nonlinearity of the compliance profile under ongoing ventilation

Fig. 13 Left: Courses of flow, volume, airway pressure and tracheal pressure (grey) from a simulated breath assuming increasing intratidal compliance in the lower, and decreasing compliance in the upper, ranges of tidal volume. Right top: Pressure volume loop of the breath. Right bottom: Simulated compliance volume curve (solid line) and compliances calculated via different methods (dashed line: quasistatic compliance, +: original SLICE method, •: gliding SLICE method).

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(Fig. 14). At low levels of PEEP the shape of the intratidal compliance-volume curve was convex. With higher levels of PEEP intratidal compliance decreased nearly from the onset of inspiration. From our findings, we conclude that the gliding-SLICE method gives detailed insights into the intratidal course of respiratory mechanics during uninterrupted mechanical ventilation and allows one to identify intratidal recruitment and/or overdistension. This may help to titrate lung-protective ventilation settings on a breath-by-breath basis.

Fig. 14 Intratidal compliance profiles (CRS ) in atelectatic piglets at different PEEP levels. At a PEEP of 0 cmH2 O increasing compliance in the low volume range indicates atelectasis and decreasing compliance in the high volume range indicates overdistension. At a PEEP of 15cmH2 O, constant compliance in the low volume range indicates that neither atelectasis nor overdistension are present. Above a volume of 5mL/kgBW overdistension is indicated by decreasing compliance. Quasistatic compliance (Cqstat) cannot identify any intratidal compliance changes. Enveloping areas indicate confidence intervals.

5 Mechanics Analysis in Microscopic Scale Complementary to Macroscopic Mechanics Data The ultimate goal of experimental mechanostimulation and mechanics analysis is to bridge the initially introduced gap between organ integrity and the precision of local mechanostimulation and local mechanics analysis. A very promising approach to closing this gap would be the mechanics analysis of alveolar parenchyma at a microscopic level in the intact mechanically ventilated animal. This includes obtaining the global respiratory mechanics of the lung as a whole organ, simultaneously determining alveolar mechanics at a microscopic level, and comparing macroscopic and microscopic findings.

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To obtain the morphology data of alveoli in-vivo at a microscopic scale, intravital microscopy is most often made use. From the recorded microscope images changes in alveolar morphology are then processed. Applying the appropriate methods, it is possible to determine the mechanical properties of the locally observed lung parenchyma as well as the alveolar morphology. We developed a novel method to determine mechanic material properties of the locally observed lung parenchyma as illustrated below.

5.1 Alveolar Imaging Methods for imaging inner organs can be roughly divided into four groups: 1) Direct imaging, which requires isolated organs or thoracotomy [11, 40]. 2) Microscopic imaging of tissue slices for the formally fixated lung tissue [18]. 3) Imaging endoscopically through trachea and bronchi [7]. 4) Imaging through thorax windows, thus leaving the thoracic wall intact as much as possible [26, 54, 56, 38]. For method groups 1 and 4, it is possible to record either subpleural alveoli from the top, thus gaining two dimensional information of their boundaries [11, 40, 39], or recording subpleural alveoli using three dimensional (3D) imaging methods at a microscopic level. 3D data on the alveolar scale was obtained using e.g. optical coherence tomography (OCT) [37] and confocal microscopy [7]. Utilizing fiber optics, confocal microscopy has also been applied for method group 3 [7]. Method group 2 delivers 3D information if the tissue is continuously sliced and imaged [18]. In contrast to the described methods, we suggested a fifth means of alveolar imaging using an endoscope introduced through the intercostal space, thus allowing alveolar imaging in the intact animal (Fig. 15). This method reduces invasiveness in comparison to method group 1, but leaves the possibility to influence (e.g. fixate in the field of view) the lung via the application of a defined pressure at the endoscope’s tip [30, 50].

E R

A S

L Fig. 15 Example of alveolar microscopy using an endoscopic system (E) to visualize the subpleural alveoli of an animal lung (L) [54, 50, 30]. It is placed between two ribs (R) using an aperture (A) that is fixed by a screw nut (S).

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5.2 Alveolar Morphology The imaging methods mentioned above lead to two different representations of alveoli. Microscopy shows entire alveoli, thus delivering images where the alveoli’s outer boundaries can be determined. The OCT and confocal microscopy of sliced tissue deliver clear information about tissue and air distribution in a given spatial plane of 3D image data. Thus, analyzing alveolar mechanics while dependent upon the mechanostimulation (due to mechanical ventilation) requires image processing methods. Existing methods for alveolar image processing can basically be subdivided into two groups: I.) Alveolar geometry is derived from manually determined alveolar outlines [11, 40, 35, 30] and II.) Fully automated calculation of alveolar geometry that correlates with alveolar morphology [31, 2, 49, 6]. Manual determination of alveolar outlines is done using image processing software that allows users to set points along the border of an alveolus [50]. Using these points, an alveolar area (AA ) that represents a cross section area of a selected alveolus, can be determined by integrating the area within the user-created polygon (Fig. 16). Alternatively, maximal and minimal diameter of single alveoli can be determined by the user. This also represents the alveolar size, but comprises less manual work. The determined area has been used to calculate numerical values that represent a certain mechanical property of the observed alveolus. The most reported value [35, 14, 30], I − E Δ %, was introduced by McCann et al. [35] and is determined to give information about the mechanical stability of the alveolus. It is calculated by









 Fig. 16 Schematic diagram of a cross section through alveolar tissue. One alveolar border is marked as an example by six crosses (representing marks of a subject), which are interconnected by dashed lines. The corresponding alveolar area (AA ) is shaded. AT is the area of the connecting tissue. The arrows marked with CV and CH are examples of vertical and horizontal chord-length and AC depicts an example of an area, where there are no visible alveoli (typical for oedematous tissue).

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using the alveolus area at the end of inspiration (AA (EI)) and the area at the end of expiration (AA (EE)) as follows: I − E Δ % = 100% ·

(AA (EI) − AA(EE)) AA (EI)

(6)

The higher the value is, the more instable the alveolus. Thus, no size-change during ventilation expresses the highest stability. A different value for representing the alveolar mechanics of a single alveolus is alveolar compliance (CA ) [39]. CA is calculated similarly to lung compliance by dividing an increase in alveolar area (Δ A) by the difference in pressure (Δ P) that caused Δ A. A fully automated method to evaluating the physiological condition of the observed lung area is the ”number of black pixel” (%NBP) value as proposed by Allen et al. [2]. This value assumes that dark areas (AC ) in the recorded images represent collapsed alveolar tissue or general tissue in unphysiologic condition. It is not suitable for comparison, since the value is highly depending on the used imaging method and equipment as well as on the threshold, which divides the image into white and black pixels. A similar value, calculated via neural networks, was proposed by our group [49]. It uses information on changes in recorded alveolar videos as an input for a neural network. The network was, thereby, trained on target values that were obtained from experts who evaluated a set of videos in terms of alveolar stability. Fully automated methods of evaluating image data are especially possible for images of lung tissue slices, either obtained by actual slicing or by 3D imaging methods like OCT, which show clearly distinguishable alveolar tissue and alveolar air-spaces. Lum et al. [31] proposed measuring the chord-length, which is the distance of two alveolar walls that are separated by the alveolar cavity. Distances can easily be measured horizontally (CH ) or vertically (CV ), since tissue and airspaces can be distinguished automatically by binarization of the images (Fig. 16). The chord-length is, thus, a measure for a mean alveolar area. If tissue and airspaces are distinguishable due to their grey values, it is possible to relate the number of airspace-pixel to the number of tissue pixel. This was proposed under the name ”volume air index” [6], by utilizing the histogram of images from confocal microscopy. Since liquid within the lung will be identified as tissue, it delivers online information that is related to the ”wet-to-dry ratio” (division of the weight of wet lung tissue by its weight after drying) in the locally recorded area. A similar parameter, but one intended for microscopic images, is the area in the whole image that can be identified as the alveolar area (AA ) relative to the remaining area (AT + AC ) [14]. An exception from method groups I and II is a method to determine alveolar outlines semi-automatically and based on a given initialization in a video-sequence [50]. With that, an active contour [63] is used. An active contour consists of an arbitrary number of points that are iteratively moved to match the alveolar borders optimally. Therefore, at least two forces are moving the points: The internal and

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the external forces. The external force moves the points towards image features like edges that are present at the alveolar borders. The internal force moves the points such that the outside of the contour is as smooth as possible. If both forces are equal for all points, the algorithm stops. This equilibrium is, depending on the used weights for the forces, a good representation of the alveolar border, given that the points were initially placed around an alveolus. The result of one video-frame can then be used as the initialization in the next video-frame, automatically tracing the alveolus’ outline. Complementary to the measures that correspond with the alveolar size is the alveolar number [40, 14]. A changing alveolar number in a specific field of view is supposed to correspond with alveolar recruitment and derecruitment in the observed lung tissue area.

5.3 Local Tissue Mechanics Our novel technique to endoscopically determine local material properties is based on the fact that a tissue deformation caused by a defined stress can be used to determine said tissues material parameters [51]. In the case of our endoscopic method for alveolar imaging, the defined stress was applied by adjusting the pressure at the endoscopic tip, while it touches the lung-tissue (Fig. 15). The pressure was thereby adjusted by modifying the flow of flushing liquid through the system of two concentric trocars, in which the endoscope had been placed. The resulting deformation was determined by optical tracking of particles of known size, embedded in a thin silicon membrane and placed on the pleural surface. Based on the known size of the particles in the video, their axial position relative to the endoscope was determined. Thus, deformation of the tissue due to the applied suction pressure was analyzed. By creating a finite element model of the physical setting (Fig. 17), it was possible to determine the mechanical material properties by using the inverse finite element analysis. Therefore, the model was solved with different values for the parameters of the material properties, until the deformation from the model matched the measured deformation. While the Neo-Hookean material law for hyperelastic solids was used for our analysis, any model’s parameters could be determined by the inverse finite element analysis.

5.4 First Assessment of Value The advantage of the fully automated image processing algorithms is that they can easily be used while recording the images, thus delivering an online index during experiments. Manual and semi automated methods have to be used offline, after the experiments were conducted.

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Particlemembrane

dm

Lung-parenchyma

Fig. 17 Finite element model of the endoscopic system’s tip on the lung-parenchyma (with two symmetry planes, thus only a quarter of the setting needed to be modeled). The model was solved for a negative pressure applied to the tissue. The color depicts the resulting axial deformation of the tissue (from blue to red). dm is the maximal deformation.

Recently, the 2D microscopic imaging techniques were related to 3D imaging data (OCT). This showed that the alveolar borders in microscopic images can be related to a cross-sectional image taken at a depth of about half the alveolar diameter [39]. This supports the intuitive assumption that the visible borders in microscopic images correspond to the maximal diameter of the alveolus and are, as such, related to the alveolar volume. Hence, the locally observed pressure-dependent changes in the alveolar diameter can be compared to global parameters such as airway pressure and lung volume. Also, alveolar compliance can be compared to static or dynamic lung compliance. Furthermore, the stress-strain relationship of the local tissue can be compared to the global stress-strain relationship that is also present when analyzing the pressurevolume relationship of the organ. However, results for alveolar mechanics are not yet conclusive. While many studies report of opportunities abounding in alveolar size [18, 12, 39], others report just the opposite [5, 9]. Problems in comparing the different results include the different methods used for imaging with different degrees of invasiveness, the different representative values that are calculated, and the use of different animal models.

Acknowledgement Support provided by the German Science Foundation/Deutsche Forschungsgemeinschaft (DFG) through projects GU561/4-1, GU561/4-2, and GU561/6-1 within the priority program ”Protective Artificial Respiration” (PAR) is hereby gratefully acknowledged. We also would like to thank our partners from the fields of mechanical engineering and molecular

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and cellular biology, i.e. the Wall workgroup at Technical University of Munich (Institute of Computational Mechanics) and the Uhlig workgroup at University Hospital Aachen (Institute for Pharmacology and Toxicology).

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The Effect of Unsteadiness on Particle Deposition in Human Upper and Lung Airways YuXuan Liu, Yang Liu, HaiYan Luo, and Martin CM Wong*

Abstract. The particle deposition in human upper airway and lung airways were intensively studied. Most of the investigations considered the flow as steady, and the flow was either laminar or turbulent. However, the actually respiratory flow is strongly dependant on time, and the unsteadiness would affect the particle deposition significantly. In this study, we compared the respiratory flow and particle deposition in CT-scanned human upper airway with both steady and unsteady model in laminar regime. The result indicates that the unsteady effect has significant influence on flow and particle deposition in human upper airways.

1 Introduction Detailed knowledge of particle deposition in human lung airway is an important issue in assessing the efficacy of inhaled drug therapy. Performing a detailed particle deposition characterization in the upper and lung airway using experimental techniques is expensive and difficult to achieve due to the intrusive character of such methods. Numerical simulation of particle motion in airway is an effective approach to tackle this problem and the basic physics of this problem can be gleaned from the particle deposition patterns in human lung airways. Several studies were carried out [1, 4, 5, 9, 11, 12, 13, 18, 19, 26, 27] to investigate the air flow and particle deposition in bifurcation airway using Weibel model [24]. The Weible model takes the human lung as 23 generations regularly bifurcated airways, however, the actual human lung airways show distinct irregular features, and the regular airway models may not reflect the realistic flow characteristics in the human lung. The development of computational capability and computerized tomography (CT) makes it possible to generate a real lung model for CFD simulation. However, most of the numerical studies using CT-scan based airway geometries are restricted to a few generations of intrathoracic airways without the upper YuXuan Liu · Yang Liu · HaiYan Luo Department of Mechanical Engineering, The Hong Kong Polytechnic University, Hong Kong Martin CM Wong Industrial Centre, The Hong Kong Polytechnic University, Hong Kong M. Klaas et al. (Eds.): Fundamental Medical and Engineering Invest. on PAR, NNFM 116, pp. 155–166. springerlink.com © Springer-Verlag Berlin Heidelberg 2011

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airways [7, 14, 20, 21]. Recently, Lin et al. [15] carried out DNS simulation to study the effect of laryngeal jet on flow in lung airways, and pointed out that the inclusion of the upper airways is essential in generating the turbulent laryngeal jet that significantly affects mean turbulent flow structures and wall shear stress. Several studied were carried out to investigate the particle deposition in human upper airways. Xi and Longest [23] assessed the effects of geometric simplifications on diffusional transport and deposition characteristics of inhaled aerosols in models of the extrathoracic oral airway. Their results indicate that the geometric simplifications did not significantly affect the total deposition efficiency or maximum local efficiency, but they do affect the particle transport dynamics and the underlying flow characteristics such as separation, turbulence intensity, and secondary motions. Eitel et al. [6] used lattice Boltzmann method (LBM) to simulation both steady and unsteady inspiration and expiration flow in human lung. A model of a human lung ranging from the trachea down to the sixth generation of the bronchial tree is used for the simulation. The results for steady air flow at inspiration and expiration show secondary vortex structures and air exchange mechanisms. It is shown that the asymmetric geometry of the human lung plays a significant role for the development of the flow field in the respiratory system. The unsteady solutions show the secondary flow structures are much more time dependent at inspiration than at expiration. Choi et al. [3] studied the effects of intra- and inter-subject variabilities in airway geometry on airflow in the human lungs by large eddy simulation, and found that the upper airway had significant influence on the flow in lung airways. Most of the studied the effect of different parameters on time averaged quantities, and the effect of unsteadiness has been typically ignored. It has been found that the measurements at unsteady flow corroborate the flow characteristics to be completely different from the steady flow field [8]. Therefore, in this study we investigated the effect of steady and unsteady model on flow characteristics and particle depositions in human upper airway.

2 Numerical Method The CT-Scanned lung model is the same subject as used in our previous paper [19, 20] but is extended to upper airway, as shown in Fig. 1. To count properly the inlet boundary condition, an extended tube has been attached to the mouth which could simulate the fully developed velocity profile. To avoid any complexity and uncertainty due to turbulence, the flow is restricted to laminar regime, and it will serve as a vehicle to seek basic understanding of the effect of flow unsteadiness on flow field and particle deposition in upper airway. The computations were carried out at inlet velocity U = 0.5 ~ 0.6 m/s (corresponding to Reynolds number of 600 ~ 720). At the outlets, we followed the boundary condition of Ertbruggen et al. [7], i.e., used the flow percentages computed by Horsfield et al. [10] to impose mass flow in all of the outlets, except for one where the static pressure level was set, avoiding redundancy in the boundary conditions. At the surface of the whole bifurcation airway, no-slip boundary condition was invoked. The motion of the

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solid particles in air is governed by Newton's second law and dilute two-phase flow model [5, 19], and the Stokes number is defined as

St =

ρ p d p2U 18μDin

(1)

ρp

d μ is the dynamic is the particle density, p is the particle diameter, D viscosity, and in is the diameter of the extended inlet tube. St is referred to as the inertial parameter; it is an index of the impactability of a particle. It is assumed that deposition occurs as long as a particle touches the walls, i.e., when the particle's centre comes within one radius from the wall. This indicates that no rebound of the particle is allowed. The inlet particle distribution is uniform and the velocity is set equal to flow rate at the “extended” inlet and one-way coupling is adopted between the air and particle flow field. The integration time step is computed based on a characteristic time that is related to an estimate of the time required for the particle to traverse the current continuous phase control volume. where

Fig. 1 Upper and lung airway model

The governing equations are solved using a finite volume method by the commercial CFD solver FLUENT. The inlet particle number is 55396 which is uniformly distributed in the inlet. The cell number of the computational model is 1,318,309. These numbers are determined by using different meshes, from coarse to progressively fine,

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until the calculated velocity profile is mesh convergent to within a prescribed tolerance (~ 0.5%). A refined mesh has been employed near the walls where velocity gradient may be larger. These choices provide a balance between desired solution accuracy and reasonable computational time. The detailed numerical technique and its validation were discussed elsewhere [16, 17, 19].

3 Results and Discussion To compare the results of steady and unsteady models, the momentum equation (Navier-Stokes Equation) of steady model is solved by both the 1st-order upwind and the 2nd-order upwind methods; for unsteady model, the time step is 0.001s and the momentum equation is solved by implicit 2nd-order scheme. To investigate the unsteady effect, several virtual point sensors are placed in the airway to record the time/iteration histories of velocity components. Fig. 2 shows the time/iteration histories of velocity component at each sensor at U = 0.5 m/s (Re = 600). At sensor-1 which is located in the oral cavity, the velocity histories of both steady and unsteady model are flat and almost the same, indicating the unsteady effect in oral cavity can be neglected. At sensor-2 which is located before laryngeal jet, the time series of unsteady model shows regular oscillation pattern; the velocity series of the 1st-order steady model is still almost flat but the value is quite different from unsteady model; the velocity series of the 2nd-order steady model exhibits beating oscillation behavior but the value is close to the unsteady one. At sensor-3 which is located right after the laryngeal jet, even there exists laryngeal jet, the time series of unsteady model still shows the regular oscillation pattern; those of steady model exhibit quite larger oscillation and the direction and value are totally different from that of unsteady model, indicating that the flow structures are different. The 1st-order steady model shows regular pattern, but the 2nd-order steady model exhibits strongly irregular oscillations indicating some turbulent features. At sensor-4 which is located just before the lung bronchus, the time series of the unsteady model still shows the regular oscillating pattern; the velocity series of the 1st-order steady model exhibits regular but smaller oscillating amplitude, and the absolute value is much smaller than that of unsteady model; again, the 2nd-order steady model exhibits strong turbulent features. At Re = 600, from the analyses of unsteady model the flow is typically laminar even it starts to oscillate. The unsteadiness should be counted to accommodate the instabilities induced by momentum change. The steady model can not accommodate and suppress the momentum oscillations in upper airway, unless for very low Reynolds number. Fig. 3 shows the comparison of axial velocity contours and second flow vectors for both unsteady and steady models at each cross-section from oral cavity all the way down to the entrance of the lung bronchus. Generally, the maximum axial velocity occurs at section-5 where it is the narrowest part in larynx and forms the laryngeal jet. From Section-1 to section-5, the axial velocity contours of unsteady and the 2nd-order steady model are almost the same; but those of the 1st-order steady model exhibits different contour structures, and the velocity contours are

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more uniform and less skewed, indicating they are not sensitive to the centrifugal force. After the laryngeal jet section-5, the jet generates reversed flow in trachea, consequently the flow structures of unsteady modeling are different from those of steady modelings. Since the velocity profile of 1st-order steady modeling is less skewed, the jet effect is not as strong as those of unsteady and 2nd-order steady modelings. Generally, it is seemed that the reversed flow generated by unsteady model is stronger and longer than those by steady models, and the velocity profiles of unsteady model are more skewed than those of steady models. For unsteady model, the reserved flow seems free to develop in down stream of the laryngeal jet; but for steady models, the reversed flow seems to be restricted.

Fig. 2 Time/iteration histories of axial velocity component at virtual point sensors .

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Fig. 3 Axial velocity contours at each cross-sections.

An inspection of axial velocity contours at longitudinal-section in Fig. 4 further evidences the above discussion. There is no difference before the laryngeal jet between the unsteady and 2nd-order steady modelings. The steady model apparently suppresses the flow separation. In the highlighted circle-A, the reserved flow is almost no difference between the unsteady and the 2nd-order steady modeling, but it is very weak in the 1st-order modeling. In the highlighted circle-B, circle-C and circle-D, the reversed flow of unsteady modeling is much stronger than those of steady modelings, consequently it gives rise to totally different velocity profiles in trachea. The contour of unsteady modeling is more nature and smooth, but that of 2nd-steady modeling exhibits some irregularity and turbulent features.

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The velocity profiles in trachea, particularly at the entrance of lung bronchus, has significant influence on air flow in bifurcation airways [25]. The gas-exchange in pulmonary acinus and particle deposition in airways all strongly depend on the velocity profiles at the entrance of lung bronchus. Therefore, this velocity profiles would determine the accuracy and significance of the lung modeling. From the discussion of Fig. 2, the velocity profiles should oscillate with time. Fig. 5 shows the variation of axial velocity contours at the entrance of lung bronchus with different time/iteration. For unsteady model, the velocity contours are strongly skewed, but has very little variation with time. For 2nd-order steady model, the velocity contour seems more uniform but change significantly with iterations.

Fig. 4 Axial velocity contours at longitudinal-section.

The flow pattern and profiles would affect the particle deposition significantly. Here we compare the particle deposition with available measurement data and empirical results [2][22]. Fig. 6 shows the particle deposition efficiency at oral cavity. Both the unsteady and steady model could get the excellent results compare to the available measurements; with increasing St number, the present calculated deposition efficiencies increase and follow the similar trend as that of measurement. It is not surprised since there is almost no difference in flow structures in oral cavity for both unsteady and 2nd-order steady modeling. The deposition efficiency is strongly dependant on flow structures. The flow structures of unsteady and steady modeling are quite different in trachea due to the laryngeal effect, therefore it can be expected that the unsteadiness will give rise to significant variation of deposition efficiency. Fig. 7 shows the comparison of

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particle deposition efficiency at trachea. The results of unsteady model are close to the empirical model, but the results of the 2nd-steady model are scattered and a little far from the empirical curve due to the strong flow oscillation.

Fig. 5 Velocity contour at the entrance of lung bronchus at different time/iteration.

Fig. 6 Particle deposition efficiency at oral cavity.

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Fig. 7 Particle deposition efficiency at trachea.

4 Conclusion The effect of unsteadiness on air flow and particle deposition in human upper airway has been numerically studied suing a CFD solver Fluent. The air flow was restricted in laminar regime and solved by unsteady, 1st-order and 2nd-order steady models. The calculated results lead to following conclusions: 1.

2.

3.

In oral cavity, the unsteadiness does not have significant influence on particle deposition efficiency. But at high Stokes number, the unsteady and 2nd-order steady model could have closer results compare to measurement. The steady model restricts the reversed flow after laryngeal jet, consequently the 2nd-order solution is quite oscillating and makes the particle deposition efficiency much higher than the empirical model. Overall, the unsteady model could get better deposition results throughout the upper airway.

Acknowledgments. The support given by The Hong Kong Polytechnic University under grant numbers G-U690 and G-U377 is gratefully acknowledged.

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References [1] Balashazy, I., Hofmann, W., Heistracher, T.: Computation of local enhancement factors for the quantification of particle deposition patterns in airway dividers. Journal of Aerosol Science 30, 185–203 (1999) [2] Chan, T.L., Schreck, R.M., Lippmann, M.: Effect of the laryngeal jet on particle deposition in human trachea and upper bronchial airway. Journal of Aerosol 11, 447–459 (1980) [3] Choi, J.W., Tawhai, M.H., Hoffman, E.A., Lin, C.-L.: On intra- and inter-subject variabilities of airflow in the human lungs. Physics of Fluids 21, 101901 (2009) [4] Comer, J.K., Kleinstreuer, C., Hyun, S., Kim, C.S.: Aerosol transport and deposition in sequentially bifurcating airways. ASME Journal of Biomechanical Engineering 122, 152–158 (2000) [5] Comer, J.K., Kleinstreuer, C., Kim, C.: Flow structures and particle deposition patterns in double-bifurcation airway models. Part 2. Aerosol transport and deposition. Journal of Fluid Mechanics 435, 55–80 (2001) [6] Eitel, G., Schroder, W., Meinke, M.: Numerical investigation of the flow field in the upper human airways. Modeling in Medicine and Biology VIII 13, 103–114 (2009) [7] Ertbruggen, C.V., Hirsch, C., Paiva, M.: Anatomically based three-dimensional model of airways to simulate flow and particle transport using computational fluid dynamics. Journal of Applied Physiology 98, 970–980 (2005) [8] Grosse, S., Schroder, W., Klaas, M., Klockner, A., Roggenkamp, J.: Time resolved analysis of steady and oscillating flow in the upper human airways. Experiments in Fluids 42, 955–970 (2007) [9] Heistracher, T., Hofmman, W.: Flow and deposition patterns in successive airway dividers. Annals of Occupational Hygiene 41, 537–542 (1997) [10] Horsfield, K., Dart, G., Olson, D.E., Filley, G.F., Cumming, G.: Models of the human bronchial tree. J. Applied Physiology 31, 207–217 (1971) [11] Johnson, J.R., Schroter, R.C.: Deposition of particles in model airways. Journal of Applied Physiology 47, 947–953 (1979) [12] Kim, C.S., Iglesias, A.J.: Deposition of inhaled particles in bifurcating airway models. I. Inspiratory deposition. Journal of Aerosol Medicine 2, 1–14 (1989) [13] Lee, J.W., Goo, I.H., Chung, M.K.: Characteristics of inertial deposition in a double bifurcation. Journal of Aerosol Science 27, 119–138 (1996) [14] Li, Z., Kleinstreuer, C., Zhang, Z.: Simulation of airflow fields and microparticle deposition in realitic human lung airway models. Part I: Airflow Patterns, European Journal of Mechanics B/Fluids 26, 650–668 (2007) [15] Lin, C.L., Tawhai, M.H., McLennan, G., Hoffman, E.A.: Characteristics of the turbulent laryngeal jet and its effect on airflow in the human intra-thoracic airways. Respiratory Physiology & Neurobiology 157, 295–309 (2007) [16] Liu, Y., So, R.M.C., Zhang, C.H.: Modeling the bifurcating flow in a human lung airway. Journal of Biomechanics 35, 477–485 (2002) [17] Liu, Y., So, R.M.C., Zhang, C.H.: Modeling the bifurcating flow in an asymmetric human lung airway. Journal of Biomechanics 36, 951–959 (2003) [18] Longest, W.P., Vinchurkar, S.: Validating CFD predictions of respiratory aerosol deposition: Effects of upstream transition and turbulence. Journal of Biomechanics 40, 305–316 (2007)

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[19] Luo, H.Y., Liu, Y., Yang, X.L.: Particle deposition in obstructed airways. Journal of Biomechanics 40, 3096–3104 (2007) [20] Luo, H.Y., Liu, Y.: Modeling the Bifurcating Flow in an CT-Scanned Human Lung Airway. J. Biomechanics 41, 2681–2688 (2008) [21] Luo, H.Y., Liu, Y.: Particle deposition in a CT-scanned human lung airway. Journal of Biomechanics 42, 1869–1876 (2009) [22] Su, W.C., Cheng, Y.S.: Deposition of man-made fibers in human respiratory airway casts. Journal Aerosol Science 40, 270–284 (2009) [23] Xi, J.X., Longest, P.W.: Effects of oral airway geometry characteristics on the diffusional deposition of inhaled nanoparticles. J. of Biomechanical Engineering 130, 011008 (2008) [24] Weible, E.R.: Morphometry of the human lung. Academic, New York (1963) [25] Yang, X.L., Liu, Y., So, R.M.C., Yang, J.M.: The Effect of Inlet Velocity Profile on the Bifurcation COPD Airway Flow. Computers in Biology and Medicine 36, 181–194 (2006) [26] Zhang, Z., Kleinstreuer, C.: Effect of particle inlet distribution on deposition in a triple bifurcation lung airway model. Journal of Aerosol Medicine 14, 13–29 (2001) [27] Zhang, Z., Kleinstreuer, C., Kim, C.S.: Cyclic micron-size particle inhalation and deposition in a triple bifurcation lung airway model. Journal of Aerosol Science 33, 257–281 (2002)

Transport at Air-Liquid Bridges under High-Frequency Ventilation Katrin Bauer , Humberto Chaves, and Christoph Br¨ ucker

Abstract. In diseased lungs airway closure can occur due to the formation of liquid bridges. These can be caused e.g. by surface tension-driven instabilities. The airway closure leads to a blockage of gas exchange in the deeper part of the lung which in severe cases requires to apply mechanical ventilation and recruitment maneuvers. High-frequency ventilation is refered therein as a proper way to enhance mass transport and keep the lung open. The present paper discusses the transport near the air-liquid interface under oscillatory excitation. A rigid tube model partially filled with liquid representing the airway blockage is used. An oscillatory flow with varying frequencies and amplitudes is applied with the aim to investigate the conditions for liquid break up and drop formation at the interface. It was found in high-frequency oscillation that near the interface a convective mass transport is generated due to secondary streaming. Above a critical value of excitation amplitudes for constant frequencies, the interface becomes unstable and drop formation starts. It can be assumed that despite the physical blockage effect in the presence of liquid bridges, high-frequency ventilation induces enhanced mass exchange across the interface and may help to break-up the liquid bridges.

1 Introduction The human lung airways are typically coated by a thin viscous liquid film. In the case of a disease the film can form a meniscus and obstruct the airways. Especially in the case of neonates a deficiency of surfactant often Katrin Bauer · Humberto Chaves · Christoph Br¨ ucker Institute of Mechanics and Fluid Dynamics, TU Bergakademie Freiberg, Lampadiusstr. 4, 09599 Freiberg, Germany e-mail: [email protected] 

Corresponding author.

M. Klaas et al. (Eds.): Fundamental Medical and Engineering Invest. on PAR, NNFM 116, pp. 167–181. springerlink.com © Springer-Verlag Berlin Heidelberg 2011

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leads to airway closure due to higher surface tensions (Halpern and Grotberg [11]). Studies have shown that also asthma might be related with surfactant deficiency [14]. In more compliant lungs, higher surface tension can lead to a “compliant collapse” [5] at which the airway walls are buckled/deformed. In both cases the airways have to be recruited by mechanical ventilation which can again damage the airways as conventional mechanical ventilation is applied [19], [20]. Therefore, often lower tidal volumes at higher breathing frequencies, so called High Frequency Oscillatory Ventilation (HFOV) is used which leads to less overdistension in the lungs but still sufficient gas exchange [21]. The airway reopening often takes place spontaneously as the liquid column breaks up into droplets. This effect is known as Rayleigh instability (Halpern and Grotberg [11]). They have also shown that, if frequency and amplitude are sufficiently large, the lung can be kept open. However, in surfactant depleted airways even the event of airway reopening can further damage the airway walls. During reopening, a higher pressure against the high surface tension has to be created and airway closure can reoccur again. Frequent opening and closing can damage the airway tissue [15]. Surfactant reduces the potential to damage the airways and needs to be efficiently distributed within the human lung. If surfactant is added to a liquid, a net flow (Marangoni flow) will occur from regions of low to high surface tension leading to the distribution of surfactant [10]. Another mechanism to distribute surfactant within the airway might be steady streaming which is induced by oscillatory excitation of the flow. Oscillations within liquid bridges also may lead to streaming induced by tangential stress at an interface or boundary layer (Nicolas et al. [12]), (Lee at al [13]), (Goldberg et al [9]. This effect is observed in various applications such as oscillatory flows in tapered channels (Gaver and Grotberg [4]), curved or flexible tubes (Eckmann and Grotberg [6]), (Wang and Tarbell [7] Dragon and Grotberg [8]). The occurrence of this mean streaming motion overlayed on the oscillatory motion is forced by Reynolds stress gradients similar to turbulence (Lighthill [2]). By time averaging the Navier Stokes equations the streaming source appears as additional body force terms represented by the gradients of Reynolds stresses. Since these body force terms are proportional to the Reynolds number it can be assumed that the streaming increases with increasing Reynolds number. The effect of enhanced streaming at increasing Reynolds number could be confirmed by Haselton and Scherer [1] in the human lung airways. They found a linear dependency of the streaming velocity on the Reynolds number which is here based on the maximum flow velocity. According to Haselton and Scherer [1] the y-shaped bifurcating contributes to the streaming by imposing different velocity profiles in inspiration and expiration flow. Hence, after one oscillation period particles do not return to their initial position but are shifted. A mean flow is generated which transports mass along the pipe centre towards the lower generations and near the walls in the opposite direction leading to an effective mass exchange.

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In our case the oscillatory flow in a rigid tube with liquid-air interface representing an airway occlusion is investigated. Mass transport during steady streaming and liquid break up conditions for varying frequencies and amplitudes are analyzed in detail.

2 Experimental Model Oscillatory flow is investigated in a vertically oriented tube of 500mm length with an open end at the top at ambient pressure. Up to the height of y = 400mm the pipe is filled with oil (density ρ = 840kg/m3, kinematic viscosity ν = 31 · 10−6 m2 /s, surface tension σ = 23mN/m). The pipe diameter is D = 12mm. At the bottom entrance a piston connected to a magnetically driven shaker generates the vertical oscillation of the fluid in the pipe. The complete experimental set-up is shown in figure 1. For application of the results on the liquid bridges in human lungs, the characteristic flow parameters have to be discussed first. In the lung airway the liquid occlusion usually occurs in the lower airways where gravitational effects can be neglegted and the surface motion is dominated by capillary effects. A lower threshold of the wavelength can be defined where capillary

region of interest

oil

piston

shaker

Fig. 1 Experimental set-up, note the lengths ratios are not in true scale

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 effects become dominant, which is λmin = 2π σ/ρg. With the values given above, the critical wavelength in our experiment is λmin = 10.5mm. Since the characteristisc length scale in our experiment, i.e. the pipe diameter, is of the same order (D=12mm), we expect that the herein observed surface waves with typical wavelength 5 mm ¡ λmin represent capillary waves. Furthermore, an important characteric number is the Capillary number Ca which denotes the relation of viscous forces to surface tension Ca = νρu/σ. Here, u denotes the characteristic flow velocity. When Ca  1 the flow is dominated by viscous forces [5]. In our case, the maximum Capillary number is Ca = 0.2 based on the maximum flow velocity. Hence, surface tension dominated effects play a role near the interface. For free surface flow the Weber number is furthermore important denoting the relation of fluid’s inertia to surface tension with W e = ρu2 l/σ. For the variable l the oscillatory amplitude is set here as the characteristic length. Oscillatory tube flow is also characterized by the Womersley number α (Womersley [3]) which  is a ratio of inertia to viscous forces in ocsillatory flows with α = D/2 (ω/ν). For very small Womersley numbers (α < 3) quasistationary flow can be assumed with velocity profiles similar to a laminar parabolic profile with the flow maximum in the pipe centre. For increasing α the velocity maximum is shifted to the tube wall and the velocity profiles are characterized by an annular shape. The flow investigations were performed for different oscillatory amplitudes and frequencies. The amplitudes were varied between 0.3 and 1.75mm, the frequencies between 10 and 40Hz. For these parameters steady streaming flow at the interface was investigated in detail. For flow characterization DPIV (Digital Particle image Velocimetry) measurements have been carried out. Therefore small tracer particles (Fillite, hollow spheres) with a mean diameter of 20μm were added to the liquid and the center plane of the pipe was illuminated by a 10mJ Nd:YAG high speed laser (Pegasus, NewWave). Images were recorded using a high speed camera (Photron, Fastcam PCI 1024). In order to visualize the secondary streaming, phase locked images were taken. Hence, the image cross correlation was made between two subsequent periods at the same phase angle. For all settings 50 images were taken and averaged in order to receive statistically firm results. For the analysis of liquid break-up the maximum amplitudes and frequencies were measured for the threshold beyond the free surface becomes unstable.

3 Results 3.1 Streaming Motion Near Stable Interface Fig. 2 (left) shows exemplarily the results of steady streaming flow as velocity vectors beneath the free surface at a frequency of 10Hz and excitation

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Fig. 2 Velocity vectors below the free surface for f = 10Hz and smax = 1.00mm, a) averaged result of the steady mean flow, b) superposed particle images for 35 subsequent periods, c) sketch of streaming topology (schematically)

amplitude of 1mm. The velocity vector lengths indicate regions of higher and lower streaming velocity amplitudes whereas the maximum streaming velocity occurs along the tube axis. It can be seen that streaming structures have been generated in form of an inner vortex-like streaming pattern around the tube center - a toroidal structure if considered as axisymmetric flow - and a smaller vortex-like structure near the wall with opposite rotation. The streaming velocity is more than one order of magnitude smaller than the maximum piston velocity. Both vortexlike structures are stretched in direction of oscillation. The existence of these streaming motion patterns suggests the existence of a double boundary layer as described by Gaver and Grotberg for a tapered channel. A good qualitative visualization of the streaming motion provides the superposition of particle images from subsequent cylces shown here for 35 periods in Fig.2b). The resulting pictures represent path-lines of solely the streaming component of the particle motion. It can be seen that the streaming flow extends about one diameter in the liquid collumn. Deeper in the collumn the influence of the free surface has vanished and streaming has disappeared. The typical flow pattern which applies to the majority of characteristic parameters is shown schematically in Fig.2c). Such a type of streaming pattern can be found also for other boundary conditions in oscillatation fluid collumns, i.e. near a solid wall (see e.g. [12] or [9]). In the following the variations of streaming patterns and velocities are analyzed for different variations of characteristic parameters. First, results are discussed for the case of a constant Womersley-number of α = 8.5 with change of the Weber-number. The streaming patterns are visualized in Fig. 3 by particle path-lines of the streaming motion. The formation of two counter rotating vortex-like streaming patterns can be best identified in this illustration. The path lines suggest only small changes of the characteristic streaming patterns. For increasing amplitude we observe a deeper penetration of streaming into the liquid collumn. For small amplitude (smax = 0.5mm (Fig. 3a) the axial

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Fig. 3 Superposed particle images for 35 subsequent periods at α = 8.5 , a) We=0.018, b) We = 0.049, c) We=0.14, d) We=0.28, e) We = 0.49, f) W e = 0.77

extension of the vortex-like streaming pattern is only about 0.5D . As the amplitude increases up to smax = 1.75mm (Fig. 3f) the axial extension of the inner vortex-like streaming pattern has almost doubled. The axial extension of the outer structure, however, has remained constant. A quantitative comparison of the streaming velocities for different Webernumbers is given by means of the radial profiles of the axial velocity component in direction of oscillation, plotted for the axial position of the maximum streaming velocity, see Fig. 4. The location of maximum streaming velocity was found at a dimensionless distance of y/D = 0.3 away from the interface. Here, bidirectional streaming can be observed, with the maximum streaming velocity in the pipe centre directed to the bottom entrance (negative y-direction). The shape of the velocity profiles is similar for all amplitudes. However, it can be seen that for increasing Weber numbers the streaming velocity in the pipe center has strongly increased. A doubling of the Weber number leads approximately to a three fold larger maximum of the axial streaming velocity in the pipe center. Nevertheless, the overall streaming velocity is still one order of magnitude lower than the maximum oscillatory velocity (piston velocity).

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Fig. 4 Axial velocity profiles at the location of the maximum streaming velocity at α = 8.5 for different amplitudes.

As the results for constant Womersley number have shown, the streaming velocity increases with the Weber number. In the other set of experiments, we kept the Weber number constant We =0.14 and changed the Womersley paramter from α = 8.5 to α = 17. Note that, in order to keep the Weber number constant, the oscillatory amplitude s had to be reduced at higher Womersley numbers. In general, unbounded oscillatory pipe flows show a decrease of the stokes layer thickness with increasing frequency. We therefore would expect also a decrease of the structures. The streaming patterns are presented in Fig. 5. It can be seen that the penetration depth of the inner vortex-like streaming pattern decreases with increasing Womersley numbers. Additionally the streaming pattern has changed its shape. For lower Womersley numbers the streaming path-lines have an elliptic shape. As α increases the outer vortex-like structure increases in size and deforms the path-lines in the inner vortex-like streaming region into the shape of a triangle. From this observation we conclude that the size of the inner and outer vortex-like streaming motion is not necessary correlated to the stokes layer thickness in the tube. The velocity profiles at the position of the maximum streaming velocity are presented in Fig. 6. It can be seen that the maximum streaming velocities are constant for all Womersley numbers. Consequently, in order to keep the maximum streaming velocity constant one may increase the oscillation amplitude to compensate for lower frequencies at constant Weber number or vice versa. However, if the goal is to achieve a maximum penetration depth into the liquid collumn, it is necessary to increase the amplitude since the penetration depth of the streaming pattern correlates directly with the oscillation amplitude.

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Fig. 5 Superposed particle images for 35 subsequent periods at We = 0.14, a) α = 8.5, b) α = 10.5, c) α = 12.1, d) α = 13.5

Transferred to the application in lung flow, i.e. the tidal volume, rather than the ventilation frequency for effective exchange of mass via liquid bridges. As already stated by Fang et al. [22] steady streaming effects are more enhanced by increasing tidal volume. The influence of frequency is only marginal.

3.2 Instability at the Interface In this section the conditions for capillary instabilities at the air-liquid interface are discussed in relation to possible break-up of the liquid bridges into smaller droplets within the lung. The stability of the interface is influenced by pressure perturbations due to time-dependent fluid acceleration and capillary forces due to fluid-wall relative motion [16]. Under HFV such conditions are forced onto the liquid brigdes either by oscillatory pressure or wall motion. The resulting inferface oscillations can be described by the Mathieu equation [16], [17]. At excitation frequencies close to the natural frequency of the free

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r/R

Fig. 6 Axial velocity profiles at the location of the maximum streaming velocity at W e = 0.14 for different Womersley numbers.

surface wave the surface becomes unstable and breaks up forming smaller droplets. The natural frequency can be calculated according to [23]   k2 σ 2 ωmn = gkmn 1 + mn tanh(kmn h). (1) gρ Here, g denotes the gravity, h is the liquid depth and kmn the n-th eigenvalue of the equation dJm (kmn r )|r=R = 0. (2) dr Jm (kmn r) is a Bessel function. The eigenvalues of equation 2 give the axisymmetric and asymetric modes, respectively. The values calculated by equation 1 are valid only for the inviscid case. In reality, the influence of viscosity shifts the natural frequencies to lower values. Damping by viscosity is incoporated in the equations by the parameter δ according to [18] which denotes the ratio of actual to critical damping and then the viscous-shifted frequency ω ˆ mn reads ω ˆ mn = ωmn (1 − δ). (3) The forcing amplitude A0 at which instability occurs is −1

A0 = [k1 tanh(k1 h)]



(ω 2 − ω ˆ 12 )2 δ + (2ω 2 )2 2

 12 .

(4)

In equation 4, ω is the excitation angular frequency, k1 and ω ˆ 1 are the wavenumber and viscous natural frequency of the n = 1 mode, respectively.

176

K. Bauer, H. Chaves, and C. Br¨ ucker

1 −6

k01, ν = 31 ⋅ 10

2

m /s, R = 6mm

k01, ν = 31 ⋅ 10−6 m2/s, R = 1mm k01, ν = 0

0.9

excitation amplitude [mm]

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0

5

10

15

20

25

30

35

40

−1

excitation frequency ω/2π [s ]

Fig. 7 instability chart, analytical results for experimental conditions

Fig. 7 shows exemplaryly the stability chart for the harmonic mode k01 with and without damping, i.e. for the invsicid case and the viscosity of the liquid used during our experiments. Furthermore, a stability curve for a cylinder of smaller radius (R = 1mm) is added. As can be seen in Fig. 7, as damping, i.e. viscosity is reduced to zero, the natural frequency is slightly shifted to higher values. However, the threshold amplitude to induce instability decreases to zero. Hence, in general the lower the viscosity the smaller the amplitudes are to successfully excite instabilities.

1 k01, ν = 31 ⋅ 10−6 m2/s k02, ν = 31 ⋅ 10−6 m2/s

0.9

k11, ν = 31 ⋅ 10−6 m2/s

excitation amplitude [mm]

−6

m /s

−6

m /s

−6

m /s

−6

2

k12, ν = 31 ⋅ 10

0.8

k21, ν = 31 ⋅ 10 k31, ν = 31 ⋅ 10

0.7

exp, ν = 31 ⋅ 10

2 2 2

m /s

0.6 0.5 0.4 0.3 0.2 0.1 0 0

5

10

15

20

25

30

35

40

excitation frequency ω/2π [s−1]

Fig. 8 instability chart, analytical results for experimental conditions

Transport at Air-Liquid Bridges under High-Frequency Ventilation

177

Reducing the tube diameter in turn leads to the need of higher amplitudes to reach instability. In Fig. 8 the analytical results for several modes are presented. For frequencies below 10Hz, instability occurs only at very high amplitudes. As the frequency increases a minimum amplitude of about 0.2mmm at 30Hz is necessary to induce a harmonic instability. As the amplitudes further increase single modes can not be separated anymore. Rather a superposition of harmonic and subharmonic oscillations will occur. The conditions at which instability of the free surface could be observed experimentally were included for frequencies from 20Hz to 40Hz at distinct measurement points in Fig. 8. The corresponding experimental images of the free surface shape are shown in Fig. 9. For the lower frequencies of 20Hz and 25Hz (Fig. 9 a) and b) strong asymmtric surface contours can be seen. These shapes oscillate with half of the excitation frequency which clearly indicates their subharmonic character. Furthermore, as can seen by the stability chart in Fig. 8, several harmonic and subharmonic modes are superposed, whereas the subharmonics dominate. At 35 and 40Hz (Fig. 9 d) and e) ) the amplitudes to induce instability have strongly decreased and obviously the second harmonic mode (compare Fig. 8) is dominating the surface motion.

Fig. 9 Visualization of the free surface contour for varying frequencies at which harmonic and subharmonic instabilities occur, a) 20Hz, b) 25Hz, c) 30Hz, d) 35Hz, e) 40Hz

178

K. Bauer, H. Chaves, and C. Br¨ ucker

2

1.5

axial velocity [mm/s]

1

0.5

0

−0.5

−1 α=10.5 α=10.5, wall α=15.0 α=14.8 α=14.8, wall

−1.5

−2 −1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

r/R

Fig. 10 Axial streaming velocity for varying boundary conditions

3.3 Coupling of Both Effects Under HFOV conditions with ventilation frequencies usually higher than 15Hz, it is reasonable that the streaming motion near air-liquid bridges is influenced also by the instability of the surface. Therefore, we repeated our experiments with the same setup but varying boundary conditions at the top of the fluid collumn (free air-liquid interface or membrane at the top). As Fig. 11 a) and d) shows, the free surface influence was supressed by adding a floating membrane which prevented free surface oscillations. For the cases presented here, the amplitude was kept constant and the frequency increased from 15Hz to 30Hz. For both cases of Fig. 11 a) and d) the streaming patterns are approximately equal. In contrast, for a free surface we can see in Fig. 11 b) and e) the streaming patterns have strongly changed when changing the frequency. Therefore, the different modes of instabilities therefore lead to varying streaming patterns.

4 Discussion In this paper we have analyzed the streaming flow and stability of oscillatory pipe flow with a free surface. The experimental model used here could be compared to a liquid-bridge type occlusion in the human airways according to the order of magnitude of the characteristic flow numbers. The consequence of the presence of the interface and its motion induces a net streaming motion in the liquid near to the interface. The results clearly reveal the increase of size and velocity of the streaming motion in the liquid collumn for increasing Weber-number. The case of lower viscosity leads to lower damping of instabilities as described above and therefore obviously to higher streaming

Transport at Air-Liquid Bridges under High-Frequency Ventilation

179

Fig. 11 Visualization of steady streaming patterns a constant excitation amplitude of 0.5mm, a) liquid-wall interface, α = 10.5 (f = 15Hz), We = 0.041, b) free surface, α = 10.5 (f = 15Hz), We = 0.041, c) free surface, α = 15.0 (f = 15Hz), We = 0.041, d) liquid-wall interface, α = 14.8 (f = 30Hz), We = 0.162, e) free surface, α = 14.8 (f = 15Hz), We = 0.162

velocities. Without the influence of the free surface but a floating membrane interface the streaming velocity is reduced about 50% of the cases with free surface and otherwise identical flow parameters. This suggests an amplification of steady streaming due to free surface instabilities which increases as liquid viscosity is decreased. Therefore, the results have demonstrated that there exists a strong coupling between the steady streaming conditions and the non-linear instability behavior of the liquid-gas interface. These steady streaming effects could be used to enhance mass exchange through the liquid bridges. For break up of the bridges a certain oscillatory ampitude has to exceeded which depends on the non-linear free surface oscillations.

Acknowledgments The authors gratefully acknowledge the support of this project by the Deutsche Forschungsgemeinschaft, grant # BR 1494/7-2.

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References 1. Haselton, F.R., Scherer, P.W.: Flow visualization of steady streaming in oscillatory flow through a bifurcating tube. J. Fluid Mech. 123, 315 (1982) 2. Lighthill, J.: Acoustic streaming. J. Sound Vib. 61, 391 (1978) 3. Womersley, J.R.: Method for the calculation of velocity, rate flow, and viscous drag in arteries when the pressure gradient is known. J. Physiol. 127, 553 (1955) 4. Gaver, D.P., Grotberg, J.B.: An experimental investigation of oscillating flow in a tapered channel. J. Fluid Mech. 172, 47 (1986) 5. Gaver III, D.P., Jensen, O.E., Halpern, D.: Surfactant and Airway Liquid Flowa. Lung Surfactant Function and Disorder 201, 191–227 (2005) 6. Eckmann, D.M., Grotberg, J.B.: Oscillatory flow and mass transport in a curved tube. J. Fluid Mech. 188, 509 (1988) 7. Wang, D.M., Tarbell, J.M.: Nonlinear analysis of flow in an elastic tube (artery): steady streaming effect. J. Fluid Mech. 239, 341 (1992) 8. Dragon, C.A., Grotberg, J.B.: Oscillatory flow and mass transport in a flexible tube. J. Fluid Mech. 231, 135 (1991) 9. Goldberg, I.S., Zhang, Z., Tran, M.: Steady streaming of fluid in the entrance region of a tube during oscillatory flow. Phys. Fluids 11(10), 2957–2962 (1999) 10. Wei, H., Fujioka, H., Hirschl, R.B., Grotberg, J.B.: A model of flow and surfactant transport in an oscillatory alveolus partially filled with liquid. Phys. Fluids. 17, 31510 (2005) 11. Halpern, D., Grotberg, J.B.: Surfactant effects on fluid-elastic instabilities of liquid lined flexible tubes - a model of airway closure. J. Biomech. Eng.-Trans. ASME 115, 271 (1993) 12. Nicolas, J.A., Rivas, D., Vega, J.M.: On the steady streaming flow due to highfrequency vibration in nearly inviscid liquid bridges. J. Fluid Mech. 354, 147 (1998) 13. Lee, C.P., Anilkumar, A.V., Wang, T.G.: Streaming generated in a liquid bridge due to nonlinear oscillations driven by the vibration of an endwall. Phys. Fluids 8(12), 3234 (1996) 14. Cheng, G., Ueda, T., Sugiyama, K., Toda, M., Fukada, T.: Compositional and functional changes of pulmonary surfactant in a guinea-pig model of chronic asthma. Respir. Med. 95(3), 180–186 (2001) 15. Muscedere, J.G., Mullen, J.B.M., Gan, K., Slutsky, A.S.: Tidal ventilation at low airway pressures can augment lung injury. Am. J. Respir. Care Med. 149, 1327–1334 (1994) 16. Ito, T., Tsuji, Y., Kukita, Y.: Interface waves excited by vertical vibration of stratified fluids in a circular cylinder. J. Nucl. Sci. Technol. 36(6), 508–521 (1999) 17. Tipton, C.R., Mullin, T.: An experimental study of Faraday waves formed on the interface between two immiscible liquids. Phys. Fluids 16(7), 2336–2341 (2004) 18. Henderson, D.M., Miles, J.W.: Single-mode faraday waves in small cylinders. J. Fluid Mech. 213, 95–109 (1990)

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19. Dreyfuss, D., Saumon, G.: Role of tidal volume, FRC and end-inspiratory volume in the developement of pulmonary edema following mechanical ventilation. Am. Rev.Respir. Dis. 148, 1194–1203 (1993) 20. Fuhrman, T.M.: Pulmonary barotrauma in mechanical ventilation. Chest 104(3), 987 (1993) 21. Krishnan, J.A., Brower, R.G.: High-Frequency Ventilation for Acute Lung Injury and ARDS. Chest 118, 795–807 (2000) 22. Fang, C.P., Cohen, B.S., Lipmann, M.: Aerosol tracer study of gas convectivetransport to 0.1 cm airways by high-frequency ventilation in a human lung airway cast. Exp. Lung Research 18, 615–632 (1992) 23. Royon-Lebeaud, A., Hopfinger, E.J., Cartellier, A.: Liquid sloshing and wave breaking in circular and square-base cylindrical containers. J. Fluid Mech. 577, 467–494 (2007)

Author Index

Adami, S. 67 Adams, N.A. 67 Affeld, Klaus 49 Armbruster, Caroline

Krenkel, Lars 107 Kuebler, Wolfgang M. 129

Bauer, Katrin 167 Bickenbach, Johannes 97 Boenke, D. 81 Br¨ ucker, Christoph 167

Puderbach, M.

Frederich, O. 33 Friedrich, Janet 107

81 67 33

Kalthoff, Daniel 107 Kauczor, H.-U. 33 Kertzscher, Ulrich 49 Klaas, M. 81 Knels, L. 67 K¨ obrich, Rainer 107 Koch, E. 67 Koch, T. 67

33

Rausch, Sophie 1 Rivoire, Julien 107 Rossaint, Rolf 97

Dassow, Constanze 129 David, Matthias 107

Henze, A. Hu, X.Y. Hylla, E.

33

Meinzer, H.-P. 33 Meissner, S. 67 Mertens, Michael 49

Chaves, Humberto 167 Comerford, Andrew 1 Czaplik, Michael 97

Gamerdinger, Katharina Guttmann, Josef 129

Ley-Zaporozhan, J. Liu, Yang 155 Liu, YuXuan 155 Luo, HaiYan 155

49

129

Schirrmann, Kerstin 49 Scholz, Alexander-Wigbert K. Schreiber, Laura Maria 107 Schr¨ oder, W. 81 Schumann, Stefan 129 Schwenninger, David 129 Soodt, T. 81 Terekhov, Maxim Thiele, F. 33

107

Wagner, Claus 107 Wall, Wolfgang A. 1 Wang, X. 33 Wegner, I. 33 Wiechert, Lena 1 Wolf, Ursula 107 Wong, Martin CM 155

107

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