Viscoelastic behavior of a lung alveolar duct model

Relaxation and creep response of the alveolar lung to diagnosis and treatments for respiratory and lung disorders

BACKGROUND

The lung Extracellular Matrix (ECM) contains a considerable part of the parenchymal cells. It contains three essential components: elastin and collagen within a proteoglycan (PG) viscoelastic network. Elastin provides the lung's elasticity property, a necessity for normal breathing, while collagen prepares structural support and strength, and PGs give stability and cushioning within tissue loading. Bacterial and viral respiratory diseases are dependent on changes in the ECM ingredients, which result in an alteration of the lung tissue strength.

PURPOSE

In the present study, this variation was investigated by changing the volume ratio of the ECM ingredients in the viscoelastic model.

RESULTS

As a result, the relaxation curves continuously declined by reducing the volume ratios of elastin, collagen, and PGs; subsequently, the lung stiffness decreased. Also, the Standard Linear Solid (SLS) model-based results demonstrated excellent accordance with empirical data with only minor deviations. The resting relaxation modulus and the creep modulus for the ECM tissue were 51 kPa and approximately 0.02 kPa, respectively, and the maximum total modulus of elasticity reached 121 kPa.

CONCLUSIONS

Moreover, this model demonstrates individual alveolar mechanical behaviours and adds another pathway to the generalized Kelvin-Voigt and Maxwell models in predicting the progress of lung diseases.

Quasi-dynamic breathing model of the lung incorporating viscoelasticity of the lung tissue

We advanced a novel model to calculate viscoelastic lung compliance and airflow resistance in presence of mucus, accounting for the quasi-linear viscoelastic stress-strain response of the parenchyma (alveoli) tissue. We adapted a continuum-based numerical modeling approach for the lung, integrating the fluid mechanics of the airflow within individual generations of the bronchi and alveoli. The model accounts for elasticity of the deformable bronchioles, resistance to airflow due to the presence of mucus within the bronchioles, and subsequent mucus flow. Simulated quasi-dynamic inhalation and expiration cycles were used to characterize the net compliance and resistance of the lung, considering the rheology of the mucus and viscoelastic properties of the parenchyma tissue. The structure and material properties of the lung were identified to have an important contribution to the lung compliance and airflow resistance. The secondary objective of this work was to assess whether a higher frequency and smaller volume of harmonic air flow rate compared to a normal ventilator breathing cycle enhanced mucus outflow. Results predict, lower mucus viscosity and higher excitation frequency of breathing are favorable for the flow of mucus up the bronchi tree, towards the trachea.

Whole-lung finite-element models for mechanical ventilation and respiratory research applications

Mechanical ventilation has been a vital treatment for Covid-19 patients with respiratory failure. Lungs assisted with mechanical ventilators present a wide variability in their response that strongly depends on air-tissue interactions, which motivates the creation of simulation tools to enhance the design of ventilatory protocols. In this work, we aim to create anatomical computational models of the lungs that predict clinically-relevant respiratory variables. To this end, we formulate a continuum poromechanical framework that seamlessly accounts for the air-tissue interaction in the lung parenchyma. Based on this formulation, we construct anatomical finite-element models of the human lungs from computed-tomography images. We simulate the 3D response of lungs connected to mechanical ventilation, from which we recover physiological parameters of high clinical relevance. In particular, we provide a framework to estimate respiratory-system compliance and resistance from continuum lung dynamic simulations. We further study our computational framework in the simulation of the supersyringe method to construct pressure-volume curves. In addition, we run these simulations using several state-of-the-art lung tissue models to understand how the choice of constitutive models impacts the whole-organ mechanical response. We show that the proposed lung model predicts physiological variables, such as airway pressure, flow and volume, that capture many distinctive features observed in mechanical ventilation and the supersyringe method. We further conclude that some constitutive lung tissue models may not adequately capture the physiological behavior of lungs, as measured in terms of lung respiratory-system compliance. Our findings constitute a proof of concept that finite-element poromechanical models of the lungs can be predictive of clinically-relevant variables in respiratory medicine.

Inflation instability in the lung: an analytical model of a thick-walled alveolus with wavy fibres under large deformations

Inflation of hollow elastic structures can become unstable and exhibit a runaway phenomenon if the tension in their walls does not rise rapidly enough with increasing volume. Biological systems avoid such inflation instability for reasons that remain poorly understood. This is best exemplified by the lung, which inflates over its functional volume range without instability. The goal of this study was to determine how the constituents of lung parenchyma determine tissue stresses that protect alveoli from instability-related overdistension during inflation. We present an analytical model of a thick-walled alveolus composed of wavy elastic fibres, and investigate its pressure-volume behaviour under large deformations. Using second-harmonic generation imaging, we found that collagen waviness follows a beta distribution. Using this distribution to fit human pressure-volume curves, we estimated collagen and elastin effective stiffnesses to be 1247 kPa and 18.3 kPa, respectively. Furthermore, we demonstrate that linearly elastic but wavy collagen fibres are sufficient to achieve inflation stability within the physiological pressure range if the alveolar thickness-to-radius ratio is greater than 0.05. Our model thus identifies the constraints on alveolar geometry and collagen waviness required for inflation stability and provides a multiscale link between alveolar pressure and stresses on fibres in healthy and diseased lungs.

Percolation of collagen stress in a random network model of the alveolar wall

Fibrotic diseases are characterized by progressive and often irreversible scarring of connective tissue in various organs, leading to substantial changes in tissue mechanics largely as a result of alterations in collagen structure. This is particularly important in the lung because its bulk modulus is so critical to the volume changes that take place during breathing. Nevertheless, it remains unclear how fibrotic abnormalities in the mechanical properties of pulmonary connective tissue can be linked to the stiffening of its individual collagen fibers. To address this question, we developed a network model of randomly oriented collagen and elastin fibers to represent pulmonary alveolar wall tissue. We show that the stress–strain behavior of this model arises via the interactions of collagen and elastin fiber networks and is critically dependent on the relative fiber stiffnesses of the individual collagen and elastin fibers themselves. We also show that the progression from linear to nonlinear stress–strain behavior of the model is associated with the percolation of stress across the collagen fiber network, but that the location of the percolation threshold is influenced by the waviness of collagen fibers.

Correlating Local Volumetric Tissue Strains with Global Lung Mechanics Measurements

The mechanics of breathing is a fascinating and vital process. The lung has complexities and subtle heterogeneities in structure across length scales that influence mechanics and function. This study establishes an experimental pipeline for capturing alveolar deformations during a respiratory cycle using synchrotron radiation micro-computed tomography (SR-micro-CT). Rodent lungs were mechanically ventilated and imaged at various time points during the respiratory cycle. Pressure-Volume (P-V) characteristics were recorded to capture any changes in overall lung mechanical behaviour during the experiment. A sequence of tomograms was collected from the lungs within the intact thoracic cavity. Digital volume correlation (DVC) was used to compute the three-dimensional strain field at the alveolar level from the time sequence of reconstructed tomograms. Regional differences in ventilation were highlighted during the respiratory cycle, relating the local strains within the lung tissue to the global ventilation measurements. Strains locally reached approximately 150% compared to the averaged regional deformations of approximately 80-100%. Redistribution of air within the lungs was observed during cycling. Regions which were relatively poorly ventilated (low deformations compared to its neighbouring region) were deforming more uniformly at later stages of the experiment (consistent with its neighbouring region). Such heterogenous phenomena are common in everyday breathing. In pathological lungs, some of these non-uniformities in deformation behaviour can become exaggerated, leading to poor function or further damage. The technique presented can help characterize the multiscale biomechanical nature of a given pathology to improve patient management strategies, considering both the local and global lung mechanics.

Alveolar Tissue Fiber and Surfactant Effects on Lung Mechanics—Model Development and Validation on ARDS and IPF Patients

Goal: Alveolar compliance is a main determinant of lung airflow. The compliance of the alveoli is a function of their tissue fiber elasticity, fiber volume, and surface tension. The compliance varies during respiration because of the nonlinear nature of fiber elasticity and the time-varying surface tension coating the alveoli. Respiratory conditions, like acute respiratory distress syndrome (ARDS) and idiopathic pulmonary fibrosis (IPF) affect fiber elasticity, fiber volume and surface tension. In this paper, we study the alveolar tissue fibers and surface tension effects on lung mechanics. Methods: To better understand the lungs, we developed a physiology-based mathematical model to 1) describe the effect of tissue fiber elasticity, fiber volume and surface tension on alveolar compliance, and 2) the effect of time-varying alveolar compliance on lung mechanics for healthy, ARDS and IPF conditions. Results: We first present the model sensitivity analysis to show the effects of model parameters on the lung mechanics variables. Then, we perform model simulation and validate on healthy non-ventilated subjects and ventilated ARDS or IPF patients. Finally, we assess the robustness and stability of this dynamic system. Conclusions: We developed a mathematical model of the lung mechanics comprising alveolar tissue and surfactant properties that generates reasonable lung pressures and volumes compared to healthy, ARDS, and IPF patient data.

A viscoelastic two-dimensional network model of the lung extracellular matrix

The extracellular matrix (ECM) comprises a large proportion of the lung parenchymal tissue and is an important contributor to the mechanical properties of the lung. The lung tissue is a biologically active scaffold with a complex ECM matrix structure and composition that provides physical support to the surrounding cells. Nearly all respiratory pathologies result in changes in the structure and composition of the ECM; however, the impact of these alterations on the mechanical properties of the tissue is not well understood. In this study, a novel network model was developed to incorporate the combinatorial effect of lung tissue ECM constituents such as collagen, elastin and proteoglycans (PGs) and used to mimic the experimentally derived length-tension response of the tissue to uniaxial loading. By modelling the effect of collagen elasticity as an exponential function with strain, and in concert with the linear elastic response of elastin, the network model's mechanical response matched experimental stress-strain curves from the literature. In addition, by incorporating spring-dashpot viscoelastic elements, to represent the PGs, the hysteresis response was also simulated. Finally, by selectively reducing volume fractions of the different ECM constituents, we were able to gain insight into their relative mechanical contribution to the larger scale tissue mechanical response.

A Physiologically Informed Strategy to Effectively Open, Stabilize, and Protect the Acutely Injured Lung

Acute respiratory distress syndrome (ARDS) causes a heterogeneous lung injury and remains a serious medical problem, with one of the only treatments being supportive care in the form of mechanical ventilation. It is very difficult, however, to mechanically ventilate the heterogeneously damaged lung without causing secondary ventilator-induced lung injury (VILI). The acutely injured lung becomes time and pressure dependent, meaning that it takes more time and pressure to open the lung, and it recollapses more quickly and at higher pressure. Current protective ventilation strategies, ARDSnet low tidal volume (LVt) and the open lung approach (OLA), have been unsuccessful at further reducing ARDS mortality. We postulate that this is because the LVt strategy is constrained to ventilating a lung with a heterogeneous mix of normal and focalized injured tissue, and the OLA, although designed to fully open and stabilize the lung, is often unsuccessful at doing so. In this review we analyzed the pathophysiology of ARDS that renders the lung susceptible to VILI. We also analyzed the alterations in alveolar and alveolar duct mechanics that occur in the acutely injured lung and discussed how these alterations are a key mechanism driving VILI. Our analysis suggests that the time component of each mechanical breath, at both inspiration and expiration, is critical to normalize alveolar mechanics and protect the lung from VILI. Animal studies and a meta-analysis have suggested that the time-controlled adaptive ventilation (TCAV) method, using the airway pressure release ventilation mode, eliminates the constraints of ventilating a lung with heterogeneous injury, since it is highly effective at opening and stabilizing the time- and pressure-dependent lung. In animal studies it has been shown that by “casting open” the acutely injured lung with TCAV we can (1) reestablish normal expiratory lung volume as assessed by direct observation of subpleural alveoli; (2) return normal parenchymal microanatomical structural support, known as alveolar interdependence and parenchymal tethering, as assessed by morphometric analysis of lung histology; (3) facilitate regeneration of normal surfactant function measured as increases in surfactant proteins A and B; and (4) significantly increase lung compliance, which reduces the pathologic impact of driving pressure and mechanical power at any given tidal volume.

Heterogeneous structure and surface tension effects on mechanical response in pulmonary acinus: A finite element analysis

BACKGROUND

The pulmonary acinus is a dead-end microstructure that consists of ducts and alveoli. High-resolution micro-CT imaging has recently provided detailed anatomical information of a complete in vivo acinus, but relating its mechanical response with its detailed acinar structure remains challenging. This study aimed to investigate the mechanical response of acinar tissue in a whole acinus for static inflation using computational approaches.

METHODS

We performed finite element analysis of a whole acinus for static inflation. The acinar structure model was generated based on micro-CT images of an intact acinus. A continuum mechanics model of the lung parenchyma was used for acinar tissue material model, and surface tension effects were explicitly included. An anisotropic mechanical field analysis based on a stretch tensor was combined with a curvature-based local structure analysis.

FINDINGS

The airspace of the acinus exhibited nonspherical deformation as a result of the anisotropic deformation of acinar tissue. A strain hotspot occurred at the ridge-shaped region caused by a rod-like deformation of acinar tissue on the ridge. The local structure becomes bowl-shaped for inflation and, without surface tension effects, the surface of the bowl-shaped region primarily experiences isotropic deformation. Surface tension effects suppressed the increase in airspace volume and inner surface area, while facilitating anisotropic deformation on the alveolar surface.

INTERPRETATION

In the lungs, the heterogeneous acinar structure and surface tension induce anisotropic deformation at the acinar and alveolar scales. Further research is needed on structural variation of acini, inter-acini connectivity, or dynamic behavior to understand multiscale lung mechanics.

Coupling of EIT with computational lung modeling for predicting patient-specific ventilatory responses

Providing optimal personalized mechanical ventilation for patients with acute or chronic respiratory failure is still a challenge within a clinical setting for each case anew. In this article, we integrate electrical impedance tomography (EIT) monitoring into a powerful patient-specific computational lung model to create an approach for personalizing protective ventilatory treatment. The underlying computational lung model is based on a single computed tomography scan and able to predict global airflow quantities, as well as local tissue aeration and strains for any ventilation maneuver. For validation, a novel “virtual EIT” module is added to our computational lung model, allowing to simulate EIT images based on the patient's thorax geometry and the results of our numerically predicted tissue aeration. Clinically measured EIT images are not used to calibrate the computational model. Thus they provide an independent method to validate the computational predictions at high temporal resolution. The performance of this coupling approach has been tested in an example patient with acute respiratory distress syndrome. The method shows good agreement between computationally predicted and clinically measured airflow data and EIT images. These results imply that the proposed framework can be used for numerical prediction of patient-specific responses to certain therapeutic measures before applying them to an actual patient. In the long run, definition of patient-specific optimal ventilation protocols might be assisted by computational modeling.

NEW & NOTEWORTHY In this work, we present a patient-specific computational lung model that is able to predict global and local ventilatory quantities for a given patient and any selected ventilation protocol. For the first time, such a predictive lung model is equipped with a virtual electrical impedance tomography module allowing real-time validation of the computed results with the patient measurements. First promising results obtained in an acute respiratory distress syndrome patient show the potential of this approach for personalized computationally guided optimization of mechanical ventilation in future.

A comprehensive computational human lung model incorporating inter-acinar dependencies: Application to spontaneous breathing and mechanical ventilation

In this article, we propose a comprehensive computational model of the entire respiratory system, which allows simulating patient-specific lungs under different ventilation scenarios and provides a deeper insight into local straining and stressing of pulmonary acini. We include novel 0D inter-acinar linker elements to respect the interplay between neighboring alveoli, an essential feature especially in heterogeneously distended lungs. The model is applicable to healthy and diseased patient-specific lung geometries. Presented computations in this work are based on a patient-specific lung geometry obtained from computed tomography data and composed of 60,143 conducting airways, 30,072 acini, and 140,135 inter-acinar linkers. The conducting airways start at the trachea and end before the respiratory bronchioles. The acini are connected to the conducting airways via terminal airways and to each other via inter-acinar linkers forming a fully coupled anatomically based respiratory model. Presented numerical examples include simulation of breathing during a spirometry-like test, measurement of a quasi-static pressure-volume curve using a supersyringe maneuver, and volume-controlled mechanical ventilation. The simulations show that our model incorporating inter-acinar dependencies successfully reproduces physiological results in healthy and diseased states. Moreover, within these scenarios, a deeper insight into local pressure, volume, and flow rate distribution in the human lung is investigated and discussed. Copyright © 2016 John Wiley & Sons, Ltd.

Breakdown of lung framework and an increase in pores of Kohn as initial events of emphysema and a cause of reduction in diffusing capacity

Purpose

Pulmonary emphysema is the pathological prototype of chronic obstructive pulmonary disease and is also associated with other lung diseases. We considered that observation with different approaches may provide new insights for the pathogenesis of emphysema.

Patients and methods

We reviewed tissue blocks of the lungs of 25 cases with/without emphysema and applied a three-dimensional observation method to the blocks. Based on the three-dimensional characteristics of the alveolar structure, we considered one face of the alveolar polyhedron as a structural unit of alveoli and called it a framework unit (FU). We categorized FUs based on their morphological characteristics and counted their number to evaluate the destructive changes in alveoli. We also evaluated the number and the area of pores of Kohn in FUs. We performed linear regression analysis to estimate the effect of these data on pulmonary function tests.

Results

In multivariable regression analysis, a decrease in the number of FUs without an alveolar wall led to a significant decrease in the diffusing capacity of the lung for carbon monoxide (DLCO) and DLCO per unit alveolar volume, and an increase in the area of pores of Kohn had a significant effect on an increase in residual capacity.

Conclusion

A breakdown in the lung framework and an increase in pores of Kohn are associated with a decrease in DLCO and DLCO per unit alveolar volume with/without emphysema.

Stress concentration around an atelectatic region: a finite element model

Lung parenchyma surrounding an atelectatic region is thought to be subjected to increased stress compared with the rest of the lung. Using 37 hexagonal cells made of linear springs, Mead et al. (1970) measured a stress concentration greater than 30% in the springs surrounding a stiffer central cell. We re-examine the problem using a 2D finite element model of 500 cells made of thin filaments with a non-linear stress-strain relationship. We study the consequences of increasing the central stiff region from one to nine contiguous cells in regular hexagonal honeycombs and random Voronoi honeycombs. The honeycomb structures were uniformly expanded with strains of 15%, 30%, 45% and 55% above their resting, non-deformed geometry. The curve of biaxial stress vs. fractional area change has a similar shape to that of the pressure-volume curve of the lung, showing an initial regime with relatively flat slope and a final regime with decreasing slope, tending toward an asymptote. Regular honeycombs had little variability in the maximum stress in radially oriented filaments adjacent to the central stiff region. In contrast, some filaments in random Voronoi honeycombs were subjected to stress concentration approximately 16 times the average stress concentration in the radially oriented filaments adjacent to the stiff region. These results may have implications in selecting the appropriate strategy for mechanical ventilation in ARDS and defining a "safe" level of alveolar pressure for ventilating atelectatic lungs.

Lung parenchymal mechanics

The lung parenchyma comprises a large number of thin-walled alveoli, forming an enormous surface area, which serves to maintain proper gas exchange. The alveoli are held open by the transpulmonary pressure, or prestress, which is balanced by tissues forces and alveolar surface film forces. Gas exchange efficiency is thus inextricably linked to three fundamental features of the lung: parenchymal architecture, prestress, and the mechanical properties of the parenchyma. The prestress is a key determinant of lung deformability that influences many phenomena including local ventilation, regional blood flow, tissue stiffness, smooth muscle contractility, and alveolar stability. The main pathway for stress transmission is through the extracellular matrix. Thus, the mechanical properties of the matrix play a key role both in lung function and biology. These mechanical properties in turn are determined by the constituents of the tissue, including elastin, collagen, and proteoglycans. In addition, the macroscopic mechanical properties are also influenced by the surface tension and, to some extent, the contractile state of the adherent cells. This chapter focuses on the biomechanical properties of the main constituents of the parenchyma in the presence of prestress and how these properties define normal function or change in disease. An integrated view of lung mechanics is presented and the utility of parenchymal mechanics at the bedside as well as its possible future role in lung physiology and medicine are discussed.

Coupled and reduced dimensional modeling of respiratory mechanics during spontaneous breathing

In this paper, we develop a total lung model based on a tree of 0D airway and acinar models for studying respiratory mechanics during spontaneous breathing. This model utilizes both computer tomography-based geometries and artificially generated lobe-filling airway trees to model the entire conducting region of the lung. Beyond the conducting airways, we develop an acinar model, which takes into account the alveolar tissue resistance, compliance, and the intrapleural pressure. With this methodology, we compare four different 0D models of airway mechanics and determine the best model based on a comparison with a 3D-0D coupled model of the conducting airways; this methodology is possible because the majority of airway resistance is confined to the lower generations, that is, the trachea and the first few bronchial generations. As an example application of the model, we simulate the flow and pressure dynamics under spontaneous breathing conditions, that is, at flow conditions driven purely by pleural space pressure. The results show good agreement, both qualitatively and quantitatively, with reported physiological values. One of the key advantages of this model is the ability to provide insight into lung ventilation in the peripheral regions. This is often crucial because this is where information, specifically for studying diseases and gas exchange, is needed. Thus, the model can be used as a tool for better understanding local peripheral lung mechanics without excluding the upper portions of the lung. This tool will be also useful for in vitro investigations of lung mechanics in both health and disease.

Particle transport and deposition: basic physics of particle kinetics

The human body interacts with the environment in many different ways. The lungs interact with the external environment through breathing. The enormously large surface area of the lung with its extremely thin air-blood barrier is exposed to particles suspended in the inhaled air. The particle-lung interaction may cause deleterious effects on health if the inhaled pollutant aerosols are toxic. Conversely, this interaction can be beneficial for disease treatment if the inhaled particles are therapeutic aerosolized drugs. In either case, an accurate estimation of dose and sites of deposition in the respiratory tract is fundamental to understanding subsequent biological response, and the basic physics of particle motion and engineering knowledge needed to understand these subjects is the topic of this article. A large portion of this article deals with three fundamental areas necessary to the understanding of particle transport and deposition in the respiratory tract. These are: (i) the physical characteristics of particles, (ii) particle behavior in gas flow, and (iii) gas-flow patterns in the respiratory tract. Other areas, such as particle transport in the developing lung and in the diseased lung are also considered. The article concludes with a summary and a brief discussion of areas of future research.

On the Stability of Lung Parenchymal Lesions with Applications to Early Pneumothorax Diagnosis

Spontaneous pneumothorax, a prevalent medical challenge in most trauma cases, is a form of sudden lung collapse closely associated with risk factors such as lung cancer and emphysema. Our work seeks to explore and quantify the currently unknown pathological factors underlying lesion rupture in pneumothorax through biomechanical modeling. We hypothesized that lesion instability is closely associated with elastodynamic strain of the pleural membrane from pulsatile air flow and collagen-elastin dynamics. Based on the principles of continuum mechanics and fluid-structure interaction, our proposed model coupled isotropic tissue deformation with pressure from pulsatile air motion and the pleural fluid. Next, we derived mathematical instability criteria for our ordinary differential equation system and then translated these mathematical instabilities to physically relevant structural instabilities via the incorporation of a finite energy limiter. The introduction of novel biomechanical descriptions for collagen-elastin dynamics allowed us to demonstrate that changes in the protein structure can lead to a transition from stable to unstable domains in the material parameter space for a general lesion. This result allowed us to create a novel streamlined algorithm for detecting material instabilities in transient lung CT scan data via analyzing deformations in a local tissue boundary.

A model of surfactant-induced surface tension effects on the parenchymal tethering of pulmonary airways

We developed a computational model of lung parenchyma, which is comprised of individual alveolar chamber models. Each alveolus is modeled by a truncated octahedron. Considering the force balance between the elastin and collagen fibers laying on the alveolar membrane and the pressures acting on the membrane, we computed the deformations of the parenchyma with a finite element method. We focused on the effect of surfactant on the force of parenchymal tethering an airway. As the lung inflates, the parenchyma becomes stiffer and the tethering force becomes stronger. As the alveolar surfactant concentration is reduced, the lung volume at a fixed alveolar pressure decreases, and thus, the tethering force becomes weaker. The distortion of parenchyma caused by the deformation of an airway extends widely around the airway. The displacement of parenchyma decays with distance from the airway wall, but deviates from the prediction based on a theory for a continuum material. Using results obtained from the present lung parenchyma model, we also developed a simple 1-dimensional model for parenchyma tethering force on an airway, which could be utilized for the analysis of liquid/gas transports in an axis-symmetric elastic airway. The effective shear modulus was calculated from the pressure-volume relation of parenchyma. By manipulating the pressure-volume curve, this simple model may be used to predict the parenchyma tethering force in diseased lungs.

Geometric hysteresis of alveolated ductal architecture

Low Reynolds number airflow in the pulmonary acinus and aerosol particle kinetics therein are significantly conditioned by the nature of the tidal motion of alveolar duct geometry. At least two components of the ductal structure are known to exhibit stress-strain hysteresis: smooth muscle within the alveolar entrance rings, and surfactant at the air-tissue interface. We hypothesize that the geometric hysteresis of the alveolar duct is largely determined by the interaction of the amount of smooth muscle and connective tissue in ductal rings, septal tissue properties, and surface tension-surface area characteristics of surfactant. To test this hypothesis, we have extended the well-known structural model of the alveolar duct by Wilson and Bachofen (1982, "A Model for Mechanical Structure of the Alveolar Duct," J. Appl. Physiol. 52(4), pp. 1064-1070) by adding realistic elastic and hysteretic properties of (1) the alveolar entrance ring, (2) septal tissue, and (3) surfactant. With realistic values for tissue and surface properties, we conclude that: (1) there is a significant, and underappreciated, amount of geometric hysteresis in alveolar ductal architecture; and (2) the contribution of smooth muscle and surfactant to geometric hysteresis are of opposite senses, tending toward cancellation. Quantitatively, the geometric hysteresis found experimentally by Miki et al. (1993, "Geometric Hysteresis in Pulmonary Surface-to-Volume Ratio during Tidal Breathing," J. Appl. Physiol. 75(4), pp. 1630-1636) is consistent with little or no smooth muscle tone in anesthetized rabbits in control conditions, and with substantial smooth muscle activation following methacholine challenge. The observed local hysteretic boundary motion of the acinar duct would result in irreversible acinar flow fields, which might be important mechanistic contributors to aerosol mixing and deposition deep in the lung.

Linking microscopic spatial patterns of tissue destruction in emphysema to macroscopic decline in stiffness using a 3D computational model

Pulmonary emphysema is a connective tissue disease characterized by the progressive destruction of alveolar walls leading to airspace enlargement and decreased elastic recoil of the lung. However, the relationship between microscopic tissue structure and decline in stiffness of the lung is not well understood. In this study, we developed a 3D computational model of lung tissue in which a pre-strained cuboidal block of tissue was represented by a tessellation of space filling polyhedra, with each polyhedral unit-cell representing an alveolus. Destruction of alveolar walls was mimicked by eliminating faces that separate two polyhedral either randomly or in a spatially correlated manner, in which the highest force bearing walls were removed at each step. Simulations were carried out to establish a link between the geometries that emerged and the rate of decline in bulk modulus of the tissue block. The spatially correlated process set up by the force-based destruction lead to a significantly faster rate of decline in bulk modulus accompanied by highly heterogeneous structures than the random destruction pattern. Using the Karhunen-Loève transformation, an estimator of the change in bulk modulus from the first four moments of airspace cell volumes was setup. Simulations were then obtained for tissue destruction with different idealized alveolar geometry, levels of pre-strain, linear and nonlinear elasticity assumptions for alveolar walls and also mixed destruction patterns where both random and force-based destruction occurs simultaneously. In all these cases, the change in bulk modulus from cell volumes was accurately estimated. We conclude that microscopic structural changes in emphysema and the associated decline in tissue stiffness are linked by the spatial pattern of the destruction process.

Current standards for characterizing microscopic structural changes in emphysema are based on estimating the amount of tissue loss using stereological techniques. However, several previous studies reported that, in emphysema, there is a lack of correlation between stereological indices of tissue structure and increases in lung compliance, which is the inverse of tissue stiffness. In this study, we developed a novel three-dimensional computational model to show that the amount of tissue loss is not the sole determinant of increased lung compliance in emphysema. A key component that needs to be considered is the pattern of tissue destruction, which we demonstrate has a significant effect on the rate of decline in stiffness. Our findings also indicate that the heterogeneity observed at the microscopic scale in emphysema is a signature of the spatial history of the destruction process. These results highlight the importance of characterizing the heterogeneity of lung tissue structure in order to be able to relate microscopic structural changes to macroscopic functional measures such as lung compliance.

Image-based modeling of lung structure and function

The current state-of-the-art in image-based modeling allows derivation of patient-specific models of the lung, lobes, airways, and pulmonary vascular trees. The application of traditional engineering analyses of fluid and structural mechanics to image-based subject-specific models has the potential to provide new insight into structure-function relationships in the individual via functional interpretation that complements imaging and experimental studies. Three major issues that are encountered in studies of airflow through the bronchial airways are the representation of airway geometry, the imposition of physiological boundary conditions, and the treatment of turbulence. Here we review some efforts to resolve each of these issues, with particular focus on image-based models that have been developed to simulate airflow from the mouth to the terminal bronchiole, and subjected to physiologically meaningful boundary conditions via image registration and soft-tissue mechanics models.

Theoretical modeling of the interaction between alveoli during inflation and deflation in normal and diseased lungs

Alveolar recruitment is a central strategy in the ventilation of patients with acute lung injury and other lung diseases associated with alveolar collapse and atelectasis. However, biomechanical insights into the opening and collapse of individual alveoli are still limited. A better understanding of alveolar recruitment and the interaction between alveoli in intact and injured lungs is of crucial relevance for the evaluation of the potential efficacy of ventilation strategies. We simulated human alveolar biomechanics in normal and injured lungs. We used a basic simulation model for the biomechanical behavior of virtual single alveoli to compute parameterized pressure-volume curves. Based on these curves, we analyzed the interaction and stability in a system composed of two alveoli. We introduced different values for surface tension and tissue properties to simulate different forms of lung injury. The data obtained predict that alveoli with identical properties can coexist with both different volumes and with equal volumes depending on the pressure. Alveoli in injured lungs with increased surface tension will collapse at normal breathing pressures. However, recruitment maneuvers and positive endexpiratory pressure can stabilize those alveoli, but coexisting unaffected alveoli might be overdistended. In injured alveoli with reduced compliance collapse is less likely, alveoli are expected to remain open, but with a smaller volume. Expanding them to normal size would overdistend coexisting unaffected alveoli. The present simulation model yields novel insights into the interaction between alveoli and may thus increase our understanding of the prospects of recruitment maneuvers in different forms of lung injury.

Respiratory flow phenomena and gravitational deposition in a three-dimensional space-filling model of the pulmonary acinar tree

The inhalation of micron-sized aerosols into the lung's acinar region may be recognized as a possible health risk or a therapeutic tool. In an effort to develop a deeper understanding of the mechanisms responsible for acinar deposition, we have numerically simulated the transport of nondiffusing fine inhaled particles (1 mum and 3 microm in diameter) in two acinar models of varying complexity: (i) a simple alveolated duct and (ii) a space-filling asymmetrical acinar branching tree following the description of lung structure by Fung (1988, "A Model of the Lung Structure and Its Validation," J. Appl. Physiol., 64, pp. 2132-2141). Detailed particle trajectories and deposition efficiencies, as well as acinar flow structures, were investigated under different orientations of gravity, for tidal breathing motion in an average human adult. Trajectories and deposition efficiencies inside the alveolated duct are strongly related to gravity orientation. While the motion of larger particles (3 microm) is relatively insensitive to convective flows compared with the role of gravitational sedimentation, finer 1 microm aerosols may exhibit, in contrast, complex kinematics influenced by the coupling between (i) flow reversal due to oscillatory breathing, (ii) local alveolar flow structure, and (iii) streamline crossing due to gravity. These combined mechanisms may lead to twisting and undulating trajectories in the alveolus over multiple breathing cycles. The extension of our study to a space-filling acinar tree was well suited to investigate the influence of bulk kinematic interaction on aerosol transport between ductal and alveolar flows. We found the existence of intricate trajectories of fine 1 microm aerosols spanning over the entire acinar airway network, which cannot be captured by simple alveolar models. In contrast, heavier 3 microm aerosols yield trajectories characteristic of gravitational sedimentation, analogous to those observed in the simple alveolated duct. For both particle sizes, however, particle inhalation yields highly nonuniform deposition. While larger particles deposit within a single inhalation phase, finer 1 microm particles exhibit much longer residence times spanning multiple breathing cycles. With the ongoing development of more realistic models of the pulmonary acinus, we aim to capture some of the complex mechanisms leading to deposition of inhaled aerosols. Such models may lead to a better understanding toward the optimization of pulmonary drug delivery to target specific regions of the lung.

Stress distribution in a three dimensional, geometric alveolar sac under normal and emphysematous conditions

Pulmonary emphysema is usually the result of chronic exposure to cigarette smoke in at risk individuals. To investigate the hypothesis that lung damage in emphysema results from coincident weakening in the structural properties of the tissue and increased mechanical forces—as one explanation of the continued development of pulmonary emphysema after smoking cessation—we developed a three dimensional, geometric dodecahedron-based acinar model. Using the model numerical analysis of the stress distribution in normal conditions could be compared with those resulting in emphysematous conditions. Finite element analysis was used to evaluate the model at a number of lung inflation levels, using quasi-static loading of the alveolar pressure. When internal alveolar pressure was increased along with the adjustment of the material properties to represent a weakening of one wall in the acinus, increased stress resulted at the perimeters of the weakened area. In particular this increased stress was localized at the junction points of the internal alveolar septa. It was also found that under the proposed simulated emphysematous conditions, a significant disruption in the stress distribution within the acinus model occurred at low, rather than high, lung volumes. This is supportive of the physiological observation that destruction of the diseased tissue can occur under less stress than those existing in the normal state.

A model morphology of the pulmonary acinus

A variation of a mathematical model of the structure of a pulmonary ventilatory unit is used to generate its internal ductal tree and associated alveolar architecture. The model unit comprises a space-filling block of regular polyhedra; ducts and alveoli were formed by opening specific common faces between polyhedra. The model employs a physically reasonable optimization strategy of maximizing gas exchange while minimizing the mean transit time to ventilate the ventilatory unit (assumed to be proportional to the mean path length) in order to create the ductal tree. The sensitivity of the global architecture to the competitive optimization parameters used and the tree structure are compared with independently published measurements. The study concludes that it is possible to model the detailed architecture of a unit using a simple space-invariant uniform modular structure for both alveoli and ductal parts. The close similarity between model and experimental measurement strongly suggests that the optimization used to create the unit is a likely one from a functional biological standpoint. The insensitivity of the architecture to the competition between the optimization parameters supports the belief that it is not important to consider the detailed measured size distribution of alveoli when considering how the large structure of the ventilatory unit is built up.

A 4-Dimensional Model of the Alveolar Structure

The alveolar structure, a space-filling branching duct system with alveolar openings, is one of the most complicated structures in the living body. Although its deformation during ventilation is the basic knowledge for lung physiology, there has been no consensus on it because of technical difficulties of dynamic 3-dimensional observation in vivo. It is known that the alveolar duct wall (primary septa) in the fetal lung is deformed so as to obtain the largest inner space and the widest surface area, and that the secondary septa grow just before birth and their free ridges form the alveolar entrance rings (mouths) containing abundant elastin fibers. We have constructed a 4-dimensional alveolar model according to this morphogenetic process, where the alveolar deformation is modeled by a combination of springs and hinges, corresponding to elastin fibers at alveolar mouths and junctions of alveolar septa, respectively. The model includes a hypothesis that alveolar mouths are closed at minimum volume and that closed alveoli are stabilized by the alveolar lining liquid film containing a surfactant. Morphometric characteristics of the model were consistent with previous reports. Furthermore, the model explained how the alveolar number and size could change during ventilation. Using in vivo microscopy, we validated our model by an analysis of the dynamic inflation and deflation of subpleural alveoli. Our model, including the alveolar mouth-closure hypothesis, can explain the origin of phase IV in a single breath nitrogen washout curve (closing volume) and mechanism of alveolar recruitment/derecruitment.

A model of non-uniform lung parenchyma distortion

A finite element model of mammalian lung parenchyma is used to study the effect of large non-uniform distortions on lung elastic behaviour. The non-uniform distortion is a uni-axial stretch from an initial state of uniform pressure expansion. For small distortions, the parenchymal properties are linearly isotropic and described by two elastic moduli. However, for large distortions, the parenchyma has anisotropic non-linear elastic properties described by five independent elastic moduli dependent on the degree of distortion; they are computed for a range of distortions and initial pressures. Ez, the Young's modulus in the direction of stretch, increases significantly with distortion (epsilon(z)) while Ex, the Young's modulus in the plane perpendicular to the stretch, is approximately constant. The greater the initial pressure, the bigger the difference between the two moduli at larger distortion strains. The shear modulus G(xz) is approximately independent of degree of distortion except at the highest initial pressure. The Poisson's ratio, nu(xz) is approximately constant with distortion strain for lower initial pressures, but increases significantly with epsilon(z) at higher pressures. Model predictions of the relation between G(xz) and initial uniform inflation pressure show a good correlation with reported experimental data for small distortion strains in a range of species. The model also exhibits similar behaviour to the experimentally measured uni-axial large deformations of a tri-axially pre-loaded block of parenchyma (Hoppin et al., 1975, Journal of Applied Physiology 39, 742-751).

Effect of small flow reversals on aerosol mixing in the alveolar region of the human lung

It has been suggested that irreversibility of alveolar flow combined with a stretched and folded pattern of streamlines can lead to a sudden increase in mixing in the lung. To determine whether this phenomenon is operative in the human lung in vivo, we performed a series of bolus studies with a protocol designed to induce complex folding patterns. Boli of 0.5- and 1-microm-diameter particles were inhaled at penetration volumes (V(p)) of 300 and 1,200 ml in eight subjects during short periods of microgravity aboard the National Aeronautics and Space Administration Microgravity Research Aircraft. Inspiration was from residual volume to 1 liter above 1 G functional residual capacity. This was followed by a 10-s breathhold, during which up to seven 100-ml flow reversals (FR) were imposed at V(p) = 300 ml and up to four 500-ml FR at V(p) = 1,200 ml, and by an expiration to residual volume. Bolus dispersion and deposition were calculated from aerosol concentration and flow rate continuously monitored at the mouth. There was no significant increase in dispersion and deposition with increasing FR except for dispersion between 0 and 7 FR at V(p) = 300 ml with 0.5-microm-diameter particles, and this increase was small. This suggested that either the phenomenon of stretch and fold did not occur within the number of FR we performed or that it had already occurred during the one breathing cycle included in the basic maneuver. We speculate that the phenomenon occurred during the basic maneuver, which is consistent with the high degree of dispersion and deposition observed previously in microgravity.