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This proceedings volume brings together the invited papers from the Respiratory Biomechanics Symposium of the First World Congress of Biomechanics held in La Jolla, California from August 3D-September 4, 1990. The respiratory system offers many opportunities to apply the different branches of traditional mechanics. Tissue defonnations and stresses during lung expansion can be analyzed using the principles of solid mechanics. Fluid mechanical problems in the lung are unique. There is the matched distribution of two fluids, gas and blood, in two beautifully intertwined, branched conduit systems. The reversing flow of the gas phase presents different problems than the pulsatile flow of the non-Newtonian fluid that is the blood. On the smaller scale, there is the flux of fluids and solutes across the capillary membrane. Finally, there is the problem of coupling fluid and solid mechanics to understand the overall behavior of the respiratory system. In this symposium, we have chosen to address the basic processes that contribute to the gas and fluid exchange functions of the lung. Section 1, Lung Tissue Mechanics, provides an historical background and, then, presents more recent work on the structure of the lung parenchyma, the mechanics of the tissue, and the effects of the bounding membrane, the visceral pleura.

Inhaltsverzeichnis

Frontmatter

Lung Tissue Mechanics

Frontmatter

Lung Tissue Mechanics: Historical Overview

Abstract
In this brief an article it is impossible to critically review the many papers on the solid mechanics of the lung parenchyma. I shall therefore present a framework into which investigations may be placed and provide a somewhat restricted bibliography.
James R. Ligas

Architecture of Lung Parenchyma

Abstract
Two essential tasks of the mammalian lung are to provide a large gas-exchanging surface and to promote both the supply of oxygen-rich air to this surface and the removal of waste gasses from it. The mammalian lung solves the problem of providing ample surface by being, in large part, an open-celled foam, and it accomplishes the supply and removal of gasses by passively changing its volume while under varying tension. Neither solution is the only one available to an organism; the exchanging surfaces of avian lungs are more similar to bundled tubes, and air is propelled through this constant-volume array by the action of peripheral sacs.
E. H. Oldmixon

Volume-Pressure Hysteresis of the Lungs

Abstract
Recoil due to tissue elastic forces and surface tension are the principal mechanisms which counter balance the inflating transpulmonary pressure of the lungs. The stress-strain properties of the elastic elements and surface tension-area relationships of surfactant are not sufficient to describe the mechanical behavior of the lungs because of the complex arrangement of the alveoli and alveolar ducts (Figure 1.).
Robert R. Mercer

Lung Tissue Mechanics

Abstract
Lung parenchyma consists of millions of interconnecting cellular units, called alveoli, that are homogeneously distributed between two parallel repeatedly branching networks, the pulmonary airways and vasculature. On the alveolar scale (100 μm) the forces in the tissue membranes are heterogeneously oriented. However on a scale that encompasses several alveoli, the macroscopic properties of lung parenchyma can be defined in terms of average stesses and average strains. On this scale the lung parenchyma is fairly homogeneous and isotropic (1). For small quasistatic deformations, the lung parenchyma is assumed to behave elastically. However, the lung is known to exhibit both viscous and plastic properties. The lung also undergoes changes in volume that are outside the range of linear elasticity. For large changes in volume, the inelastic behavior of the lung is accentuated. Thus, the concept of elasticity as applied to the lung is restricted to small changes in distortion.
Stephen J. Lai-Fook

Pleural Mechanics

Abstract
The visceral pleura is a thin membrane which completely surrounds the lung and is tightly adherent to the parenchymal tissue. It contains elastic fibers which form an irregular network with no preferential orientation [1]. Although many physiologic roles have been proposed for this membrane, we limit our focus to the effects of the pleura on lung mechanics. Specifically, what is the relationship between stress and strain for the pleural membrane? And what implication does this relationship have for the overall mechanical function of the lung?
James R. Ligas

Respiratory Fluid Mechanics and Transport

Frontmatter

Respiratory Fluid Mechanics and Transport

Abstract
The last decade was a period of significant progress in our understanding of gas phase fluid mechanics and species or mass transport in the airways. Several factors contributed to this advance. Detailed measurements of airway geometry from the nasal passages to the alveolar level, made possible by advances in computer-based imaging and microscopy systems, revealed the complex geometry in which gas flow and mass transport take place, even in normal lungs. Introduction of high-frequency ventilation (HFV) techniques with frequencies of 20 or more times resting breathing rates underscored the sensitivity of pressure gradients and velocity distributions to subtle changes in airway geometry and mechanical properties, and focused attention on mechanisms for mass transport under these conditions. The need to understand factors affecting gas exchange at elevated frequencies reopened questions of the interaction of respiratory mechanics with gas exchange. A third factor was the ready availability of computational resources through introduction of the microcomputer, and the continued enhancement of execution speed, memory and storage in medium and large-scale computer systems. These permitted extensive investigation of nonlinear parameter estimation techniques and complex computer simulations as innovative approaches for data analysis.
Mary A. Farrell Epstein

Impedance of Laminar Oscillatory Flow Superimposed on a Continuous Turbulent Flow: Application to Respiratory Impedance Measurement

Abstract
Measurement of respiratory impedance by Forced Oscillations is an efficient method for characterizing the mechanical behavior of the respiratory system [11, 12]. Recently, this method has been shown to enable early detection of airway abnormalities in subjects exposed to respiratory irritants [2]. The advantage of this non-invasive method is that it does not require cooperation from the patient, allowing him to breathe spontaneously through a connecting tube, usually flushed by a constant bias flow [2,11,15]. This is possible because the oscillating system is opened to the atmosphere by means of a hole or a side tube intended to be a low pass filter for the oscillations [12]. Surprisingly, the interaction between the quasi-steady component (spontaneous breathing and/or bias flow) and the oscillatory component of flow has rarely been considered from a fundamental point of view, except for two recent studies in laminar flow conditions [5,7]. However, a crucial problem remains for the case when the continuous component of flow becomes turbulent: then a linear phenomenon, i.e., the oscillatory flow component [12], is superimposed on a typically non-linear phenomenon, i.e., the turbulent component.
B. Louis, D. Isabey

Current Issues in Understanding Acoustic Impedance of the Respiratory System

Abstract
Most commonly used pulmonary function tests require patients to perform some sort of gymnastic respiratory maneuver such as a forced expiration. These tests are therefore restricted to conscious, cooperative adult humans. Measurements of mechanical, or input acoustic impedance of the respiratory system (Zin) can be made in animals, non-cooperative adults and children, and infants. The first measurements of Zin, made in normal human subjects were reported by Dubois et al. in 1956 [3]. There were certain characteristics of Zin that suggested that the normal respiratory system behaved as though all of the alveoli could be lumped into a single compartment. The single compartment model that they proposed consisted of 6-elements and is illustrated in Fig. 1. If this were the appropriate model and if we could make Zin measurements over the appropriate frequency range, there is the potential of estimates of at least two parameters that are of clinical importance, airway resistance (Raw) and thoracic gas volume which is directly related to alveolar gas compression compliance (Cg). At about the same time that DuBois’ work was published, Otis et al. [18] reported that Zin in patients with diseases of the lung did not behave like a single compartment system. Specifically, they found that the effective compliance of the system was frequency dependent. This implies that there would also be a frequency dependent drop in the real part of Zin (Re) for low frequencies; a characteristic not found in normals and one that is not consistent with the 6-element model. Otis et al. suggested that these phenomena were due to inhomogeneities in the parallel airway/tissue pathways.
Andrew C. Jackson

Effects of Curvature, Taper and Flexibility on Dispersion in Oscillatory Pipe Flow

Abstract
The primary function of the lung is the exchange of oxygen and carbon dioxide. Other substances, such as anesthetics, aerosols, and toxins, are delivered and removed from the lungs by a similar process. Mass transport in the lung depends on convection, diffusion, and their interaction during oscillatory flow. High frequency ventilation (HFV) is an alternative type of ventilation under investigation (Bohn et al. 1980). In HFV, relatively small tidal volumes of air (35–150 ml) are delivered at high frequencies (5–30 Hz), so that pulmonary barotrauma and cardiac impairment are avoided.
James B. Grotberg

Interactions Between Lung Mechanics And Gas Transport

Abstract
Lung mechanics, in the broadest sense, encompasses both the behavior of solid tissue and the dynamics of gas and liquid flow within the tissue. Gas transport, which refers to the simultaneous bulk flow and diffusion of gases between the airway opening and the alveolar membranes, interacts with lung mechanics in two ways: the movement of gas molecules within each airway branch and airspace is affected by local velocity fields; and the blending of molecules at airway branch points depends on the distribution of flow imposed by the tidal deformation of elastic tissue. Nearly 100 years ago, in a classic paper that set the stage for comtemporary studies of these processes, Bohr (1) postulated that transport of respiratory gases could be modeled in a lung consisting of a proximal dead space compartment terminating in a blind-ended alveolar compartment. Gas was assumed to translate through the rigid dead space by bulk flow in the absence of gas mixing, while gas in the distensible alveolar compartment was perfectly mixed. This simple two-compartment model has become an incredibly important tool in the conceptualization of lung function, and is the underlying basis of routine clinical tests such as the single-breath nitrogen washout and the carbon monoxide diffusing capacity tests.
James S. Ultman

Nonclassical Features of Gas Transport and Exchange at the Alveolar Level

Abstract
The transport and exchange of oxygen in the lung can be viewed conceptually as serial processes. Accordingly, the conductance for the combined transport and exchange process, G c , represents the reciprocal sum of separate conductances for intrapulmonary mixing, G mix , and for alveolar capillary exchange, D L [9]. Although G mix and D L are lumped-parameter macroscale conductances, they must account implicitly for transport and exchange complexities at the microscale (i.e. alveolar duct and alveolar capillary) level.
William J. Federspiel

Flow Dynamics of the Nasal Passage

Abstract
The nasal passage is the natural conduit for directing air into the lungs during breathing at rest and is largely responsible for filtering, warming and humidifying the inspired air. Filtration is achieved primarily by the inertial impaction of airborne particles within the external nose and nasal cavities where the inspired air enters at high velocity and is diverted by abrupt changes in airway direction and geometry [1]. Warming and humidification are accomplished largely by convection, conduction and mass transport within channels formed by the turbinates of the nasal cavities (Figure 1). The large wall surface area and narrow width of these channels increase the transport efficiency [2].
Kevin J. Sullivan, H. K. Chang

Pulmonary Circulation

Frontmatter

Elasticity of Pulmonary Blood Vessels in Human Lungs

Abstract
The mechanical properties of pulmonary blood vessels are essential factors influencing the distribution of pulmonary blood flow, regional volume distribution of blood and pulse wave propagation throughout the lung. These properties affect the pressure-flow relationship, and the change in total blood volume in response to an alteration in blood pressure. In order to formulate such problems, mechanical property data for blood vessels of all generations of the human lung are needed and are gathered in our laboratory. In particular, vessel diameter as a function of transmural pressure are measured for each vessel generation.
R. T. Yen, D. Tai, Z. Rong, B. Zhang

Distensibility of the Pulmonary Capillaries

Abstract
A sheet flow has been employed as a morphometric idealization of the vascular space of the pulmonary capillaries (Sobin and Fung, 1972 and Fung, 1980). In this model, blood flows in between two membranes and around the posts holding the membranes apart at a sheet thickness h. Because of the distensibility of the pulmonary capillaries, the thickness increases when the transmural pressure (Ptm), the capillary blood pressure minus the alveolar gas pressure, is increased. As one increases the transpulmonary pressure (Ptp), the alveolar gas pressure minus the pleural pressure, to inflate the lung to a larger volume, the surface area of all alveolar sheets becomes larger. Since the blood volume of the pulmonary capillaries is related to the product of the sheet thickness and the surface area in the sheet flow model, we have the following incremental relation to describe the distensibility of the pulmonary capillaries
$$ \Delta V_c /V_c = \Delta P_{tp} /E_1 + \Delta P_{tm} /E_2 $$
(1)
where E1 and E2 are elastic moduli and Δ represents the increment of the quantity that follows.
J. S. Lee, L. P. Lee

Recruitment of Pulmonary Capillaries

Abstract
Recruitment of pulmonary capillaries is an important component of gas exchange reserve that is utilized during exercise to meet the demand for increased oxygen uptake. However, important gaps exist in our understanding of the way in which alterations of pulmonary hemodynamics, with the attendant redistribution of pulmonary blood flow, affect capillary recruitment. The major reason that many aspects of pulmonary microcirculatory function are poorly understood is the considerable technical difficulty in studying pulmonary micro-vessels directly. The classical direct approach of in vivo microscopy is plagued by problems with tissue movement during the cardiorespiratory cycles. Nevertheless, important information has come historically from in vivo microscopy of the lung. The directness of this approach continues to make the technique attractive today.
Wiltz W. Wagner

Pulsatile pulmonary capillary pressure measured with the arterial occlusion technique

Abstract
Pulsatile flow waves have been known to exist in the pulmonary capillary bed since the introduction of the N2O bolus technique [5, 10]. Although direct measurement of pressure pulsatility in the lung microvessels has yet to be performed, indirect methods have been used to assess the cyclic variations of the pulmonary capillary pressure during pulsatile perfusion [9, 7]. Recently, it has been suggested [3, 13, 6] that these periodic oscillations could be traced by measuring the vascular occlusion pressures [4, 2, 11, 1] repeatedly during the pulsatile pressure cycle. We describe an application of this technique in isolated left lower lobes (LLL) of canine lungs perfused by means of a pulsatile blood pump.
Jean-Michel Maarek, H. K. Chang

Sites of Pulmonary Vasoconstriction: Indirect and Direct Measurements

Abstract
Because pulmonary capillary pressure is an important factor in the fluid balance of the lungs, there has been considerable interest in methods for determining it and the arteriovenous sites of pulmonary vasoconstriction. Since pulmonary arterial and venous pressures but not capillary pressure can be measured directly, the methods have, in general, been indirect (Dawson, 1984; Dawson et al., 1989). In our laboratory, we have used two complementary indirect methods; the vascular occlusion method (Linehan et al., 1982) and the low viscosity bolus method (Dawson et al., 1988).
John H. Linehan, Christopher A. Dawson

The Use of Mathematics and Advanced Technology to Measure and Evaluate Lung Fluid Exchange and Solute Balance

Frontmatter

An Error Analysis of Pulmonary Vascular Permeability Measurements Made with Positron Emission Tomography

Abstract
Positron emission tomography (PET) is a powerful, quantitative, nuclear medicine imaging technique, useful for studying many problems in lung physiology and biochemistry (1). With PET, compounds are labeled with positron-emitting isotopes. After being administered either. intravascularly or inhalationally, the tissue activity concentration of the isotope is determined with an imaging device similar in appearance to an X-ray computed tomography scanner. Multiple two-dimensional images are then reconstructed from the activity data and interpreted to represent a physiologic process of interest. PET derives its power from several factors: (1) the labeled compounds are themselves biologically important; (2) the isotope half-life is often sufficiently short that studies may be repeated if desirable; (3) the isotope tissue concentration can be determined quantitatively, accurately, and in many instances, noninvasively; and (4) the activity distribution can be located with great accuracy. Because of this latter feature in particular, the activity data can be presented regionally, in an image format, so that measurements may be correlated with other regionally specific measurements over time.
D. P. Schuster, J. Markham, J. Kaplan, T. Warfel, M. Mintun

Evaluation of Lung Vascular Permeability by External Scanning of Gamma Emitter Activity

Abstract
A minimally invasive method for measuring and analyzing lung transvascular protein flux would be useful for diagnosing and monitoring patients with lung injury. We have developed a method which detects movement of radiolabeled albumin from plasma to lung interstitium using sodium iodide detectors that are located outside the body, and positioned over the lung. The technique is similar to methods reported by Gorin (1,2), Prichard and Lee (3,4), and Dauber et al. (5).
Robert J. Roselli, Valerie J. Abernathy, William R. Riddle, Richard E. Parker, N. Adriene Pou

Use of Mathematics in Assessing Solute Exchange Across the Lung Epithelium

Abstract
Our early attempts to understand the role of the lung epithelium in the pathophysiology of lung edema and alveolar flooding were hampered by a lack of techniques for specifically assessing changes in lung epithelial permeability to proteins. Consequently, we have developed two methods for assessing solute exchange across the lung epithelium: 1) the use of nuclear imaging techniques to measure the rate of clearance of aerosolized 99mTc-labeled tracers from the air spaces of the lungs, and 2) the analysis of the clearance of these tracers via the lung lymphatics. Both of these methods employ mathematical modeling techniques to obtain the maximum amount of information from the data.
B. T. Peterson, M. L. Collins, J. C. Connelly, J. W. McLarty, D. Holiday, L. D. Gray

On Line Colorimetric Determinations of Transvascular Fluid and Protein Transport in Isolated Lobes

Abstract
A commonly used method to estimate transvascular fluid exchange in organs is based on measurements of weight changes with time. Following changes in pulmonary capillary hydrostatic pressure (Pc), weight changes in characteristic fashion. A fast change in weight, assumed to represent vascular volume adaptations, is followed by slow exponential changes, which are thought to represent transvascular fluid exchange associated with the change in Pc. The analysis of the slow exponential weight change constitutes one of the most common approaches to determinations of vascular membrane and transvascular force readjustment in isolated lung preparations such as that depicted in Figure 1.
L. Oppenheimer, E. Furuya, K. P. Landolfo, D. Huebert

Fractal analysis of lung fluid flow

Abstract
The human lung brings a continuous flow of blood into close proximity with a cyclic flow of air so that respiratory gases can readily diffuse between these two fluids. Nature has created an intricate arrangement of spaces to accomplish this task. A 3-dimensional cylinder of venous blood leaving the right ventricle is transformed into a nearly 2-dimensional film of blood by the time it arrives at the alveolus. At the same time, a bolus of inhaled air is divided into smaller streams and pockets until its surface area approaches 100 m2. Both processes distribute a fluid through a repeatedly bifurcating network. The configuration of these networks as well as their relative sizes have been difficult to summarize using the conventional language of Euclidean geometry [7].
James E. McNamee

The Roles of Small Molecules as Probes of Endothelial Barrier Function in the Lung: Novel Measurement Methods and Molecular Probes

Abstract
Dysfunction of the barrier properties of endothelial cells is implicated in a number of vascular diseases. One of the more prominent problems is the edema of the lungs seen with Adult Respiratory Distress Syndrome (1,2). Fluid accumulates in the lungs of such patients even though pulmonary pressures are relatively normal. Experimental and patient studies suggest that the primary defect is an increased permeability of the lung vascular capillaries to fluid and macromolecules (3,4,5,6). A variety of methods have been used to assess such malfunctions in experimental animal models of ARDS and in patients. These range from straightforward measurements of lung water by post mortem desiccation and weighing to experimental measurement of lung lymph flow and analysis of protein content as compared to plasma protein concentration.
Thomas R. Harris

Integrating Mechanics and Transport in Assessing Respiratory Function

Frontmatter

Integrating Mechanics and Transport in Assessing Respiratory Function

Abstract
The lungs serve a primary function of exchanging gases between the body and the outside environment. Efficiency of this exchange process is strongly affected by the relative matching of ventilation and perfusion, a relationship which the body goes to great lengths to preserve. However, the efficiency of the lung deteriorates in the presence of lung disease and under conditions of environmental stress. The response of this gas exchange process to stress is largely dependent on the degree of heterogeneity in the lung and the perturbations caused by the pathological or environmental stress.
Michael P. Hlastala

Airway Heat and Water Exchange

Abstract
Hyperventilation of dry or cool air causes respiratory heat and water loss, and elicits airflow obstruction in patients with exercise-induced asthma. Though the mechanism by which heat and/or water fluxes are transduced to local airway narrowing remains uncertain, considerable insight has been gained. Theoretical and experimental analyses of intra-airway heat and water transfers have demonstrated that: (1) increasing minute ventilation (MV) promotes further penetration of cool, dry, inspired gas into the lung before it has been fully warmed and humidified to alveolar gas conditions; (2) lowering inspired gas temperature or humidity at fixed MV increases local heat/water losses, but the axial distribution of those losses remains largely unchanged; (3) the net change in airway wall temperature or hydration depends importantly upon the effectiveness of local heat and water replenishing sources that resist the airway cooling and dessication promoted by local heat/water losses. Experimentally documented sequelae of dry gas hyperpnea include broncho-constriction (found in the central airways of guinea pigs and of human asthmatic subjects, and in the dog lung periphery), broncho-vascular arterial dilatation (confirmed in dogs and sheep, and possibly in normal humans), and broncho-vascular hyperpermeability (demonstrated in guinea pigs and ferrets). One or several facets of the physical events that accompany dry gas hyperpnea lead to the release of bronchoactive and vasoactive mediators (including eicosanoids and tachykinins, from animal studies) that could conceivably provoke airflow obstruction by direct stimulation of airway smooth muscle, or by promoting broncho-vascular engorgement and/or hyperpermeability, with consequent edema formation.
Julian Solway

Quantitation of the Regional Distribution of Pulmonary Blood Flow by Fractal Analysis

Abstract
The structure of the pulmonary vascular tree following its initial segmental divisions can be described by a regular recursive algorithm. This vascular structure has fractal properties in that each successive branching is similar to its parent branch over many orders of scale. While the anatomic structure has fractal properties, it remained to be demonstrated that the actual flow distribution of blood within the lung could also be described by a fractal model. We have developed a means of obtaining very high resolution blood flow images of dog lungs, and have demonstrated a previously unsuspected degree of flow heterogeneity. We sought to determine whether the measured heterogeneity of flow (in contrast to the anatomical structure of the pulmonary arteries) could also be described by a fractal model. The method we utilized to demonstrate fractal flow distributions was that developed by Bassingthwaighte and colleagues (1) to describe the heterogeneity of cardiac blood flow.
H. Thomas Robertson, Robb W. Glenny

Elucidation of Principles of Gas Exchange by Means of Soluble Tracer Species

Abstract
Because the lung is inaccessible to direct evaluation of events on a fine regional basis in-vivo, its properties are usually inferred from global gas exchange data taken from arterial blood and expired gas. This presentation briefly reviews the many uses of tracer gases of varying physicochemical properties in estimating both global and distributed physiological parameters. In each, the necessary mathematical and physiological underpinnings will be discussed, as will the information content and associated limitations. Approaches to be covered include: (1) Using gases of different molecular weight to infer the importance of rates of diffusion in gas exchange processes that involve both diffusive and convective movement; (2) Using gases of different blood: gas partition coefficients to infer the importance of the convective processes involved in gas exchange, and ventilation/perfusion mismatching, in particular; (3) Using carefully selected gases and procedures to measure variables related to global function (eg, pulmonary blood flow, lung tissue volume, lung gas volume, and lung closing volume); and (4) Using gases with unique chemical properties to determine the importance of chemical rates of reaction between hemoglobin and the gaseous ligands O2, CO2, and CO. While all of these techniques have well-known limitations, they have at the same time greatly increased our understanding of how the lung works. When used within the constraints imposed by those limits, they continue to form a group of very useful investigative tools that continue to increase our insights into both normal and abnormal gas exchange processes.
Peter D. Wagner
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