Continuum vs. spring network models of airway-parenchymal interdependence

Modeling Ventilator-Induced Lung Injury and Neutrophil Infiltration to Infer Injury Interdependence

Acute respiratory distress syndrome (ARDS) and ventilator-induced lung injury (VILI) are heterogeneous conditions. The spatiotemporal evolution of these heterogeneities is complex, and it is difficult to elucidate the mechanisms driving its progression. Through previous quantitative analyses, we explored the distributions of cellular injury and neutrophil infiltration in experimental VILI and discovered that VILI progression is characterized by both the formation of new injury in quasi-random locations and the expansion of existing injury clusters. Distributions of neutrophil infiltration do not correlate with cell injury progression and suggest a systemic response. To further examine the dynamics of VILI, we have developed a novel computational model that simulates damage (cellular injury progression and neutrophil infiltration) using a stochastic approach. Optimization of the model parameters to fit experimental data reveals that the range and strength of interdependence between existing and new damaged regions both increase as mechanical ventilation patterns become more injurious. The interdependence of cellular injury can be attributed to mechanical tethering forces, while the interdependence of neutrophils is likely due to longer-range cell signaling pathways.

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.

Spatiotemporal distribution of cellular injury and leukocytes during the progression of ventilator-induced lung injury

Supportive mechanical ventilation is a necessary lifesaving treatment for acute respiratory distress syndrome (ARDS). This intervention often leads to injury exacerbation by ventilator-induced lung injury (VILI). Patterns of injury in ARDS and VILI are recognized to be heterogeneous; however, quantification of these injury distributions remains incomplete. Developing a more detailed understanding of injury heterogeneity, particularly how it varies in space and time, can help elucidate the mechanisms of VILI pathogenesis. Ultimately, this knowledge can be used to develop protective ventilation strategies that slow disease progression. To expand existing knowledge of VILI heterogeneity, we document the spatial evolution of cellular injury distribution and leukocyte infiltration, on the micro- and macroscales, during protective and injurious mechanical ventilation. We ventilated naïve mice using either high inspiratory pressure and zero positive end-expiratory pressure ventilation or low tidal volume with positive end-expiratory pressure. Distributions of cellular injury, identified with propidium iodide staining, were microscopically analyzed at three levels of injury severity. Cellular injury initiated in diffuse, quasi-random patterns, and progressed through expansion of high-density regions of injured cells termed "injury clusters." The density profile of the expanding injury regions suggests that stress shielding occurs, protecting the already injured regions from further damage. Spatial distribution of leukocytes did not correlate with that of cellular injury or ventilation-induced changes in lung function. These results suggest that protective ventilation protocols should protect the interface between healthy and injured regions to stymie injury propagation.

A Personalized Spring Network Representation of Emphysematous Lungs From CT Images

Emphysema is a progressive disease characterized by irreversible tissue destruction and airspace enlargement, which manifest as low attenuation area (LAA) on CT images. Previous studies have shown that inflammation, protease imbalance, extracellular matrix remodeling and mechanical forces collectively influence the progression of emphysema. Elastic spring network models incorporating force-based mechanical failure have been applied to investigate the pathogenesis and progression of emphysema. However, these models were general without considering the patient-specific information on lung structure available in CT images. The aim of this work was to develop a novel approach that provides an optimal spring network representation of emphysematous lungs based on the apparent density in CT images, allowing the construction of personalized networks. The proposed method takes into account the size and curvature of LAA clusters on the CT images that correspond to a pre-stressed condition of the lung as opposed to a naïve method that excludes the effects of pre-stress. The main findings of this study are that networks constructed by the new method 1) better preserve LAA cluster sizes and their distribution than the naïve method; and 2) predict different course of emphysema progression compared to the naïve method. We conclude that our new method has the potential to predict patient-specific emphysema progression which needs verification using clinical data.

Integrative Computational Models of Lung Structure-Function Interactions

Anatomically based integrative models of the lung and their interaction with other key components of the respiratory system provide unique capabilities for investigating both normal and abnormal lung function. There is substantial regional variability in both structure and function within the normal lung, yet it remains capable of relatively efficient gas exchange by providing close matching of air delivery (ventilation) and blood delivery (perfusion) to regions of gas exchange tissue from the scale of the whole organ to the smallest continuous gas exchange units. This is despite remarkably different mechanisms of air and blood delivery, different fluid properties, and unique scale-dependent anatomical structures through which the blood and air are transported. This inherent heterogeneity can be exacerbated in the presence of disease or when the body is under stress. Current computational power and data availability allow for the construction of sophisticated data-driven integrative models that can mimic respiratory system structure, function, and response to intervention. Computational models do not have the same technical and ethical issues that can limit experimental studies and biomedical imaging, and if they are solidly grounded in physiology and physics they facilitate investigation of the underlying interaction between mechanisms that determine respiratory function and dysfunction, and to estimate otherwise difficult-to-access measures. © 2021 American Physiological Society. Compr Physiol 11:1501-1530, 2021.

Virtual patients for mechanical ventilation in the intensive care unit

BACKGROUND

Mechanical ventilation (MV) is a core intensive care unit (ICU) therapy. Significant inter- and intra- patient variability in lung mechanics and condition makes managing MV difficult. Accurate prediction of patient-specific response to changes in MV settings would enable optimised, personalised, and more productive care, improving outcomes and reducing cost. This study develops a generalised digital clone model, or in-silico virtual patient, to accurately predict lung mechanics in response to changes in MV.

METHODS

An identifiable, nonlinear hysteresis loop model (HLM) captures patient-specific lung dynamics identified from measured ventilator data. Identification and creation of the virtual patient model is fully automated using the hysteresis loop analysis (HLA) method to identify lung elastances from clinical data. Performance is evaluated using clinical data from 18 volume-control (VC) and 14 pressure-control (PC) ventilated patients who underwent step-wise recruitment maneuvers.

RESULTS

Patient-specific virtual patient models accurately predict lung response for changes in PEEP up to 12 cmH₂O for both volume and pressure control cohorts. R² values for predicting peak inspiration pressure (PIP) and additional retained lung volume, V_frc in VC, are R²=0.86 and R²=0.90 for 106 predictions over 18 patients. For 14 PC patients and 84 predictions, predicting peak inspiratory volume (PIV) and V_frc yield R²=0.86 and R²=0.83. Absolute PIP, PIV and V_frc errors are relatively small.

CONCLUSIONS

Overall results validate the accuracy and versatility of the virtual patient model for capturing and predicting nonlinear changes in patient-specific lung mechanics. Accurate response prediction enables mechanically and physiologically relevant virtual patients to guide personalised and optimised MV therapy.

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.

Integrated lung tissue mechanics one piece at a time: Computational modeling across the scales of biology

The lung is a delicately balanced and highly integrated mechanical system. Lung tissue is continuously exposed to the environment via the air we breathe, making it susceptible to damage. As a consequence, respiratory diseases present a huge burden on society and their prevalence continues to rise. Emergent function is produced not only by the sum of the function of its individual components but also by the complex feedback and interactions occurring across the biological scales - from genes to proteins, cells, tissue and whole organ - and back again. Computational modeling provides the necessary framework for pulling apart and putting back together the pieces of the body and organ systems so that we can fully understand how they function in both health and disease. In this review, we discuss models of lung tissue mechanics spanning from the protein level (the extracellular matrix) through to the level of cells, tissue and whole organ, many of which have been developed in isolation. This is a vital step in the process but to understand the emergent behavior of the lung, we must work towards integrating these component parts and accounting for feedback across the scales, such as mechanotransduction. These interactions will be key to unlocking the mechanisms occurring in disease and in seeking new pharmacological targets and improving personalized healthcare.

The micromechanics of lung alveoli: structure and function of surfactant and tissue components

The mammalian lung´s structural design is optimized to serve its main function: gas exchange. It takes place in the alveolar region (parenchyma) where air and blood are brought in close proximity over a large surface. Air reaches the alveolar lumen via a conducting airway tree. Blood flows in a capillary network embedded in inter-alveolar septa. The barrier between air and blood consists of a continuous alveolar epithelium (a mosaic of type I and type II alveolar epithelial cells), a continuous capillary endothelium and the connective tissue layer in-between. By virtue of its respiratory movements, the lung has to withstand mechanical challenges throughout life. Alveoli must be protected from over-distension as well as from collapse by inherent stabilizing factors. The mechanical stability of the parenchyma is ensured by two components: a connective tissue fiber network and the surfactant system. The connective tissue fibers form a continuous tensegrity (tension + integrity) backbone consisting of axial, peripheral and septal fibers. Surfactant (surface active agent) is the secretory product of type II alveolar epithelial cells and covers the alveolar epithelium as a biophysically active thin and continuous film. Here, we briefly review the structural components relevant for gas exchange. Then we describe our current understanding of how these components function under normal conditions and how lung injury results in dysfunction of alveolar micromechanics finally leading to lung fibrosis.

Modeling the Progression of Epithelial Leak Caused by Overdistension

Mechanical ventilation is necessary for treatment of the acute respiratory distress syndrome but leads to overdistension of the open regions of the lung and produces further damage. Although we know that the excessive stresses and strains disrupt the alveolar epithelium, we know little about the relationship between epithelial strain and epithelial leak. We have developed a computational model of an epithelial monolayer to simulate leak progression due to overdistension and to explain previous experimental findings in mice with ventilator-induced lung injury. We found a nonlinear threshold-type relationship between leak area and increasing stretch force. After the force required to initiate the leak was reached, the leak area increased at a constant rate with further increases in force. Furthermore, this rate was slower than the rate of increase in force, especially at end-expiration. Parameter manipulation changed only the leak-initiating force; leak area growth followed the same trend once this force was surpassed. These results suggest that there is a particular force (analogous to ventilation tidal volume) that must not be exceeded to avoid damage and that changing cell physical properties adjusts this threshold. This is relevant for the development of new ventilator strategies that avoid inducing further injury to the lung.

Resistance to alveolar shape change limits range of force propagation in lung parenchyma

We have recently shown that if the lung parenchyma is modeled in 2 dimensions as a network of springs arranged in a pattern of repeating hexagonal cells, the distortional forces around a contracting airway propagate much further from the airway wall than classic continuum theory predicts. In the present study we tested the hypothesis that this occurs because of the negligible shear modulus of a hexagonal spring network. We simulated the narrowing of an airway embedded in a hexagonal network of elastic alveolar walls when the hexagonal cells of the network offered some resistance to a change in shape. We found that as the forces resisting shape change approach about 10% of the forces resisting length change of an individual spring the range of distortional force propagation in the spring network fell of rapidly as in an elastic continuum. We repeated these investigations in a 3-dimensional spring network composed of space-filling polyhedral cells and found similar results. This suggests that force propagation away from a point of local parenchymal distortion also falls off rapidly in real lung tissue.

Theoretical calculation of bending stiffness of alveolar wall

The bending stiffness of the alveolar wall is theoretically analyzed in this study through analytical modeling. First, the alveolar wall facet and its characteristics were geometrically simplified and then modeled using known physical laws. Bending stiffness is shown to be dependent on alveolar wall thickness, density, Poisson's ratio and speed of the longitudinal wave. The normal bending stiffness of the alveolar wall was further determined. For the adult human, the normal bending stiffness is calculated to be 71.0-414.7 nNm, while for the adult mouse it is 1.9-30.0 nNm. The results of this study can be used as a reference for future pulmonary emphysema and fibrosis studies, as the bending stiffness of alveolar wall will be lower and higher, respectively; than the theoretically determined normal values.

Mechanical interactions between adjacent airways in the lung

The forces of mechanical interdependence between the airways and the parenchyma in the lung are powerful modulators of airways responsiveness. Little is known, however, about the extent to which adjacent airways affect each other's ability to narrow due to distortional forces generated within the intervening parenchyma. We developed a two-dimensional computational model of two airways embedded in parenchyma. The parenchyma itself was modeled in three ways: 1) as a network of hexagonally arranged springs, 2) as a network of triangularly arranged springs, and 3) as an elastic continuum. In all cases, we determined how the narrowing of one airway was affected when the other airway was relaxed vs. when it narrowed to the same extent as the first airway. For the continuum and triangular network models, interactions between airways were negligible unless the airways lay within about two relaxed diameters of each other, but even at this distance the interactions were small. By contrast, the hexagonal spring network model predicted that airway-airway interactions mediated by the parenchyma can be substantial for any degree of airway separation at intermediate values of airway contraction forces. Evidence to date suggests that the parenchyma may be better represented by the continuum model, which suggests that the parenchyma does not mediate significant interactions between narrowing airways.

Influence of parenchymal heterogeneity on airway-parenchymal interdependence

To estimate the influence of parenchymal heterogeneities on airway-parenchymal interdependence, we considered a circular airway embedded within elastic parenchyma modeled as (1) a hexagonal spring network, (2) a triangular spring network, or (3) a continuum. The deformation in the parenchyma due to active airway contraction was simulated using the finite element method. Random perturbations of elastic moduli in the parenchyma did not significantly affect the overall pattern of force transmission. By contrast, when elastic moduli were increased along a path projecting radially outward from the airway, the hexagonal spring network model predicted significantly increased force along this line as the airway contracted, but this was not observed in other two models. These results indicate that tissue heterogeneities generally have minimal effect on the global nature of airway-parenchymal interdependence. However, in the exceptional circumstance of scar tissue aligned radially from the airway wall, parenchymal distortion forces may propagate much farther from the airway wall than was previously thought.

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.

Airway-parenchymal interdependence in the lung slice

The explanted lung slice has become a popular in vitro system for studying how airways contract. Because the forces of airway-parenchymal interdependence are such important modulators of airway narrowing, it is of significant interest to understand how the parenchyma around a constricting airway in a lung slice behaves. We have previously shown that the predictions of the 2-dimensional distortion field around a constricting airway are substantially different depending on whether the parenchyma is modeled as an elastic continuum versus a network of hexagonally arranged springs, which raises the question as to which model best explains the lung slice. We treated lung slices with methacholine and then followed the movement of a set of parenchymal landmarks around the airway as it narrowed. The resulting parenchymal displacement field was compared to the displacement fields predicted by the continuum and hexagonal spring network models. The predictions of the continuum model were much closer to the measured data than were those of the hexagonal spring network model, suggesting that the parenchyma in the lung slice behaves like an elastic continuum rather than a network of discrete springs. This may be because the alveoli of the lung slice are filled with agarose in order to provide structural stability, causing the parenchyma in the slice to act like a true mechanical continuum. How the air-filled parenchyma in the intact lung behave in vivo remains an open question.