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Influence Of Parenchymal Heterogeneity On Airway-Parenchymal Interdependence
Abstract
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.
... Mead and colleagues (153) calculated that a fully collapsed alveolus could increase distending pressure in adjacent patent alveoli fivefold. This phenomenon is well documented at the alveolar/septal scale in isolated lungs in response to alveolar flooding (154), at greater scale in fixed tissue as described above, and in the increased VA and VA variability measured in animal models of pulmonary fibrosis (10,(155)(156)(157). ...
... Finite element simulations employing an idealized network of alveoli (155) show that the stiffening of a single central alveolus, or a cluster of alveoli, without reducing VA intensifies septal wall strain in the remaining patent alveoli. Because the morphology of pulmonary fibrosis is characterized by alveolar collapse, where VA approaches zero, we have included finite element simulations of an idealized alveolar network that is based on a previously published model (157) and described in the online supplement ( Figure E2). The model shows that a single collapsed and stiffened alveolus, representing an atelectatic alveolus, raises the maximum septal strain (e max ) at FRC to nearly equal the septal strain predicted at TLC in the open portions of the normal lung. ...
... In simulated networks in which a contiguous pathway of strained septa is present, force transmission can occur over longer distances (157), which is an important consideration because the fibroblast foci seen in pulmonary fibrosis may form an interconnected network (162) that may facilitate long-range force coupling. Although there are conflicting data on this point (163), if the fibroblastic foci do not form an interconnected network, then transmission of force through the stiffened foci will still extend through large regions of the parenchyma. ...
... We represented the alveolar walls in the parenchyma as pin-joined springs arranged in a repeating hexagonal pattern, as this represents the conventional idealization of the appearance of a thin slice of lung tissue (Mead et al., 1970;Wilson, 1972). We found, somewhat unexpectedly, that such a network produces long-range transmission of forces in response to the distortion produced by the narrowing of the embedded airway (Ma and Bates, 2012;Ma et al., 2013a). By contrast, when the springs are arranged in a repeating triangular pattern, or the parenchyma is represented as an elastic continuum, the elastic forces fall off rapidly with distance from the airway wall (Ma and Bates, 2012), in apparent accord with existing theory about airway-parenchymal interdependence (Lai-Fook, 1979;Wilson, 1972). ...
... As in our previous studies Bates, 2012, 2014;Ma et al., 2013a;Ma et al., 2013b), the middle section of the network was removed to represent the airway lumen. The springs around the perimeter of the resulting hole represent the airway wall, and each has a stiffness that is ten times that of each of the springs in the parenchymal network, which themselves were assigned a stiffness of unity. ...
... The procedure we used for simulating airway contraction in both the 2D and 3D models was similar to that used in our previous studies Bates, 2012, 2014;Ma et al., 2013a;Ma et al., 2013b). The nodes around the outer boundary of the network were fixed in place such that the length of each spring in the network was 11% above its zero-load length, so the network began in a pre-stressed state. ...
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.
Copyright © 2015. Published by Elsevier B.V.
... The elastic elements were connected via frictionless pin joints. This representation has a long history of use as a model of mechanical interdependence and parenchymal stability (25,28), and we have used it recently in detailed investigations of airway-parenchymal interdependence (21)(22)(23). ...
... When the airways were relatively far apart their degrees of airway narrowing did not change with separation distance. This is because of the stable plateau in parenchymal distortion force that arises further than about three airway diameters when an airway contracts within a hexagonal spring network, as we have shown in previous publications (21)(22)(23). We refer to this region as the far field. ...
... We also made other simplifying assumptions that could have affected our results. For example, we assumed the parenchyma to be homogeneous and isotropic, although we have recently demonstrated that parenchymal heterogeneities are unlikely to have a major effect except in rather special cases (22). Similarly, we assumed regional ventilation throughout the lung to be homogeneous, whereas in reality it can be quite variable resulting in different degrees of small airway inflation, so our results pertain only to an average airway. ...
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 2-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 versus 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 2 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.
... Predictive mechanical simulations of whole organs necessitate accurate constitutive models of the underlying tissue. The non-linear mechanical response of the lung parenchyma has been described using several phenomenological hyperelastic constitutive laws, which include exponential strain energy densities (Fung, 1974;Tawhai et al., 2009;Ma et al., 2013), polynomials models (Berger et al., 2016;Yoshihara et al., 2017), and linear combinations of the former (Rausch et al., 2011;Birzle et al., 2018;Birzle et al., 2019). These phenomenological approximations require the determination of material constants for experimental data, which has been approached from uniaxial tensile experiments (Rausch et al., 2011;Bel-Brunon et al., 2014), biaxial stretching (Gao et al., 2006) and volumetric expansion tests (Birzle et al., 2018;Birzle et al., 2019). ...
... In this study, we consider five constitutive models specifically developed for describing the parenchyma mechanical response of human lungs (Ma et al., 2013;Berger et al., 2016;Yoshihara et al., 2017) and Wistar rats (Rausch et al., 2011;Birzle et al., 2019). These tissue models were chosen because they represent the state of the art in lung tissue modeling. ...
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.
... From analyses performed by Ryans et al. (2019), we assume the equilibrium hole radius is proportional to the cubic root of the weighted average of acinus volume within a distance of 5R AW,0 from the airway axis, where R AW,0 is R AW at zero transmural pressure. This behavior is consistent with the finite-element model by Ma et al. (2013). We also assumed the equilibrium hole radius R H,FRC is equal to R AW,FRC when the surrounding acinus volume is at the Functional Residual Capacity, V FRC . ...
... This model includes the airflow between airways and acini, surfactant transport in the liquid lining, and parenchymal tethering between the acini that surrounds airways. As shown above, these simulations demonstrate physiologically realistic macroscale PV relationships and predict microscale strain distributions that deviate from the uniform strain state (Ma et al., 2013). This deviation occurs due to ventilationinduced airflow pressures and non-equilibrium Laplace pressures resulting from surfactant physicochemical interactions (West, 1977(West, , 2012Krueger and Gaver, 2000;Notter, 2000). ...
We present a computational multi-scale model of an adult human lung that combines dynamic surfactant physicochemical interactions and parenchymal tethering between ~16 generations of airways and subtended acini. This model simulates the healthy lung by modeling nonlinear stress distributions from airway/alveolar interdependency. In concert with multi-component surfactant transport processes, this serves to stabilize highly compliant interacting structures. This computational model, with ~10 k degrees of freedom, demonstrates physiological processes in the normal lung such as multi-layer surfactant transport and pressure–volume hysteresis behavior. Furthermore, this model predicts non-equilibrium stress distributions due to compliance mismatches between airway and alveolar structures. This computational model provides a baseline for the exploration of multi-scale interactions of pathological conditions that can further our understanding of disease processes and guide the development of protective ventilation strategies for the treatment of acute respiratory distress syndrome (ARDS).
... The respective strain energy functions and material parameters are summarized in Table 5. The material model of Gao et al. (2005) was not included since it behaves similar to the material model of Ma et al. (2013). In the following, two different deformation states are used for the comparison, namely large volumetric deformations and volume-preserving uniaxial tension. ...
... Some material models proposed in the literature and compared here are surprisingly not stress-free in the reference configuration. In detail, Ma et al. (2013) and Tawhai et al. (2009) (2017) was not fitted to experimental data. Bel-Brunon et al. (2014) and Rausch et al. (2011) utilized agarose for the preparation of their tissue samples. ...
In this paper, a coupled inverse analysis is proposed to identify nonlinear compressible hyperelastic material models described by two sets of experiments. While the overall approach is applicable for different materials, here it will be presented for viable lung parenchyma. Characterizing the material properties of lung parenchyma is essential to describe and predict the mechanical behavior of the respiratory system in health and disease. During breathing and mechanical ventilation, lung parenchyma is mainly subjected to volumetric deformations along with isochoric and asymmetric deformations that occur especially in diseased heterogeneous lungs. Notwithstanding, most studies examine lung tissue in predominantly isochoric tension tests. In this paper, we investigate the volumetric material behavior as well as the isochoric deformations in two sets of experiments: namely, volume–pressure-change experiments (performed with 287 samples of 26 rats) and uniaxial tension tests (performed with 30 samples of 5 rats). Based on these sets of experiments, we propose a coupled inverse analysis, which simultaneously incorporates both measurement sets to optimize the material parameters. Accordingly, we determine a suitable material model using the experimental results of both sets of experiments in one coupled identification process. The identified strain energy function with the corresponding material parameters [Formula presented] is validated to model both sets of experiments precisely. Hence, this constitutive model describes the complex volumetric and isochoric nonlinear material behavior of lung parenchyma. This derived material model can be used for nonlinear finite element simulations of lung parenchyma and will help to quantify the stresses and strains of lung tissue during spontaneous and artificial breathing; thus, allowing new insights into lung function and biology.
... The respective strain energy functions and material parameters are summarized in Table 5. The material model of Gao et al. (2005) was not included since it behaves similar to the material model of Ma et al. (2013). In the following, two different deformation states are used for the comparison, namely large volumetric deformations and volumepreserving uniaxial tension. ...
... Some material models proposed in the literature and compared here are surprisingly not stress-free in the reference configuration. In detail, Ma et al. (2013) and Tawhai et al. (2009) utilize a prestress in their simulations. This might be the reason why the use of such a strain energy function did not work at all. ...
In this paper, a coupled inverse analysis is proposed to identify nonlinear compressible hyperelastic material models described by two sets of experiments. While the overall approach is applicable for different materials, here it will be presented for viable lung parenchyma. Characterizing the material properties of lung parenchyma is essential to describe and predict the mechanical behavior of the respiratory system in health and disease. During breathing and mechanical ventilation, lung parenchyma is mainly subjected to volumetric deformations along with isochoric and asymmetrical deformations that occur especially in diseased heterogeneous lungs. Notwithstanding, most studies examine lung tissue in predominantly isochoric tension tests. In this paper, we investigate the volumetric material behavior as well as the isochoric deformations in two sets of experiments: namely, volume-pressure-change experiments (performed with 287 samples of 26 rats) and uniaxial tension tests (performed with 30 samples of 5 rats). Based on these sets of experiments, we propose a coupled inverse analysis, which simultaneously incorporates both measurement sets to optimize the material parameters. Accordingly, we determine a suitable material model using the experimental results of both sets of experiments in one coupled identification process. The identified strain energy function with the corresponding material parameters Ψ = 356.7 Pa (I_1 − 3) + 331.7 Pa (I_3^{−1.075} − 1) + 278.2 Pa (I_3^{-1/3} I_1 - 3)^3 + 5.766 Pa (I_3^{1/3} − 1)^6 is validated to model both sets of experiments precisely. Hence, this constitutive model describes the complex volumetric and isochoric nonlinear material behavior of lung parenchyma. This derived material model can be used for nonlinear finite element simulations of lung parenchyma and will help to quantify the stresses and strains of lung tissue during spontaneous and artificial breathing; thus, allowing new insights into lung function and biology.
... Random Voronoi cellular structures are typically used to model materials made of heterogeneously shaped cells. Although 2D models do not give identical results as 3D models Ma, Breen and Bates (Ma et al., 2013) utilized 2D non-linear springs to provide insights about network behavior a hexagonal-like array of the lung parenchyma, Ito et al. (2006) used a similar 2D network of hexagonal arrays and analyzed how the distribution of forces changes and the maximum force increases by adding non-linearity. Suki and Bates (2008) used a 2D Voronoi-like array of non-linear springs to model the lung parenchyma. ...
... For the mechanical behavior of the lung tissue they considered a stress-strain curve with exponential stiffening. Here, we model two-dimensional cellular structures made of hexagonal and Voronoi cells, using an approach similar to Ma et al. (2013), Ito et al. (2006) and Suki and Bates (2008) respectively, where the filaments also represent the stress bearing elements in the parenchyma. ...
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. (J Appl Physiol 28: 596-608, 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 towards 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.
... To close our formulation, specific constitutive models for tissue and surfactant are needed. In the case of pulmonary tissue, for simplicity, we adopt an exponential-like material model with an energy density function that reads [21,45,74] Ψ hyp = c exp aJ 2 ...
Surface tension arising in the air-liquid interface of alveolar tissue is a fundamental mechanism in lung physiology that explains lung recoil and hysteresis during breathing. Despite its importance, surface tension dynamics are poorly addressed in computational models of the lungs, due to its complex multiscale physicochemical nature. In this study, we formulate a poromechanical framework that seamlessly incorporates the effect of surfactant-dependent surface tension in porous media for the prediction of lung hysteretic response. Using an internal variable formalism, we apply the Coleman-Noll procedure to establish an expression for the stress tensor that includes surface tension akin to the Young-Laplace law. Based on this formulation, we construct non-linear finite-element models of human lungs to simulate pressure-volume curves and lung response during mechanical ventilation. Our results show that surfactant-dependent surface tension notably modulates pressure-volume curves and lung mechanics. In particular, our model captures the influence of surfactant dynamics on lung hysteresis and compliance, predicting the transition from an insoluble reversible regime to a dissipative one governed by Langmuir kinetics. We envision that our continuum framework will enable lung simulations where surfactant-related phenomena are directly considered in predictions, with important applications to modeling respiratory disease and lung response to mechanical ventilation.
... This theory has been bolstered in subsequent computational analyses employing, e.g., finite element spring networks (Wilson and Bachofen, 1982;Makiyama et al., 2014;Albert et al., 2019) or systems of differential equations (Ma et al., 2023) to show that stress accumulates heterogeneously in the lung parenchyma, with the largest stresses found near areas with greater extents of injury. Other spring network simulations have shown that tethering (or stiffening) has both localized and longer lengthscale effects on the distribution of lung stress and strain (Ma et al., 2013;Ma et al., 2015;Hall et al., 2023). Probabilistic methods, based on experimental data, have also been employed to understand the forces contributing to injury propagation, the mechanisms of injury heterogeneity, and the rich-get-richer mechanisms of VILI pathogenesis and offer a complementary perspective to deterministic mechanical models (Mattson et al., 2022;Mattson and Smith, 2023). ...
Introduction
Acute respiratory distress syndrome (ARDS) presents a significant clinical challenge, with ventilator-induced lung injury (VILI) being a critical complication arising from life-saving mechanical ventilation. Understanding the spatial and temporal dynamics of VILI can inform therapeutic strategies to mitigate lung damage and improve outcomes.
Methods
Histological sections from initially healthy mice and pulmonary lavage-injured mice subjected to a second hit of VILI were segmented with Ilastik to define regions of lung injury. A scale-free network approach was applied to assess the correlation between injury regions, with regions of injury represented as ‘nodes’ in the network and ‘edges’ quantifying the degree of correlation between nodes. A simulated time series analysis was conducted to emulate the temporal sequence of injury events.
Results
Automated segmentation identified different lung regions in good agreement with manual scoring, achieving a sensitivity of 78% and a specificity of 85% across ‘injury’ pixels. Overall accuracy across ‘injury’, ‘air’, and ‘other’ pixels was 81%. The size of injured regions followed a power-law distribution, suggesting a ‘rich-get-richer’ phenomenon in the distribution of lung injury. Network analysis revealed a scale-free distribution of injury correlations, highlighting hubs of injury that could serve as focal points for therapeutic intervention. Simulated time series analysis further supported the concept of secondary injury events following an initial insult, with patterns resembling those observed in seismological studies of aftershocks.
Conclusion
The size distribution of injured regions underscores the spatially heterogeneous nature of acute and ventilator-induced lung injury. The application of network theory demonstrates the emergence of injury ‘hubs’ that are consistent with a ‘rich-get-richer’ dynamic. Simulated time series analysis demonstrates that the progression of injury events in the lung could follow spatiotemporal patterns similar to the progression of aftershocks in seismology, providing new insights into the mechanisms of injury distribution and propagation. Both phenomena suggest a potential for interventions targeting these injury ‘hubs’ to reduce the impact of VILI in ARDS management.
... However, the dynamic changes in heterogeneities during injury progression are complex, and the underlying mechanisms driving the progression are difficult to elucidate. One approach to understanding the causes and effects of spatial heterogeneity is through computational approaches such as the finite element method (FEM) that allow analysis of the microscale pattern of stress and strain propagation based on parenchymal tethering forces [27][28][29][30]. However, validation and verification of these predictions through experiments remains an elusive goal. ...
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.
... These arrays have inherent anisotropy due to the limited rotational symmetries of their alveolar units, whereas actual lung tissue is essentially isotropic even in the normal lung (Weed et al., 2015). The mechanical consequences of such anisotropies have been studied (Ma et al., 2013) but are still not fully understood. Furthermore, models based on regular repeating unit structures cannot account for the natural variability in alveolar size that the lung displays (Parameswaran et al., 2009). ...
Pulmonary Fibrosis (PF) is a deadly disease that has limited treatment options and is caused by excessive deposition and cross-linking of collagen leading to stiffening of the lung parenchyma. The link between lung structure and function in PF remains poorly understood, although its spatially heterogeneous nature has important implications for alveolar ventilation. Computational models of lung parenchyma utilize uniform arrays of space-filling shapes to represent individual alveoli, but have inherent anisotropy, whereas actual lung tissue is isotropic on average. We developed a novel Voronoi-based 3D spring network model of the lung parenchyma, the Amorphous Network, that exhibits more 2D and 3D similarity to lung geometry than regular polyhedral networks. In contrast to regular networks that show anisotropic force transmission, the structural randomness in the Amorphous Network dissipates this anisotropy with important implications for mechanotransduction. We then added agents to the network that were allowed to carry out a random walk to mimic the migratory behavior of fibroblasts. To model progressive fibrosis, agents were moved around the network and increased the stiffness of springs along their path. Agents migrated at various path lengths until a certain percentage of the network was stiffened. Alveolar ventilation heterogeneity increased with both percent of the network stiffened, and walk length of the agents, until the percolation threshold was reached. The bulk modulus of the network also increased with both percent of network stiffened and path length. This model thus represents a step forward in the creation of physiologically accurate computational models of lung tissue disease.
... At larger length scales, organ-scale imaging techniques such as positron emission tomography (24,25) and computed tomography (26,27) can be used to observe regional distributions of injury and inflammation. However, organ-scale imaging techniques do not have the necessary resolution to observe the microscale pattern of injury propagation where parenchymal tethering forces operate (28)(29)(30)(31). ...
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 macro- scales, 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 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 in order to stymie injury propagation.
... This model was further developed and applied to simulate the time course and lung mechanical impairment of pulmonary fibrosis as well as pulmonary emphysema including response to lung volume reduction surgery (Bates et al. 2007;Mishima et al. 1999;Mondoñedo and Suki 2017). In addition, spring models were used to understand aspects of alveolar and alveolarairway interdependence Bates 2012, 2014;Ma et al. 2013aMa et al. , b, 2015Mead et al. 1970;Makiyama et al. 2014;Bates et al. 2007). It has long been understood that alveolar interdependence plays an important role in the determining strain at the level of individual septa (Mead et al. 1970;Perlman et al. 2011). ...
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.
... There is evidence to suggest that this may be the case. For example, although qualitative quasi-linear viscoelastic behavior and PL stress relaxation arise naturally in models of lung tissue exhibiting sequentiality [16] , the predicted exponent in the PL relationship is much too large unless this mechanism is embedded in a multi-scale structure [16,153,154] . The same kind of behavior has been shown to occur in models comprised of fractal-like ladder networks of mechanical elements [103,104] . ...
This review provides the latest developments and trends in the application of fractional calculus (FC) in biomedicine and biology. Nature has often showed to follow rather simple rules that lead to the emergence of with complex phenomena as a result. Of these, the paper addresses the properties in respiratory lung tissue, whose natural solutions arise from the midst of FC in the form of non-integer differ-integral solutions and non-integer parametric models. Diffusion of substances in human body, e.g. drug diffusion, is also a phenomena well known to be captured with such mathematical models. FC has been employed in neuroscience to characterize the generation of action potentials ans spiking patters but also in charaterizing bio-systems (e.g. vegetable tissues). Despite the natural complexity, biological systems belong as well to this class of systems, where FC has offered parsimonious yet accurate models. This review paper is a collection of results and literature reports who are essential to any versed engineer with multidisciplinary applications and bio-medical in particular.
... Changes in static lung volumes during PR may be explained by breathing exercise training, inhalatory pharmacological optimization and use of supplemental oxygen when necessary [37,41] . Those modifications can be responsible for an improvement in pulmonary parenchymal interdependence [42,43] and, as previously pointed out by Weibel's studies on lung morphometry, a regional reduction in air trapping may have a role in the optimization of capillary circulation, allowing the so-called 'angle vessels' to return to a more physiological status, thus increasing the regional gas to blood ratio [44,45] , and therefore explaining the increase in KCO, paralleled by an improvement in gas exchange. A reduction in static hyperinflation can be also responsible for an improvement in the lung regional hypoxemic vasoconstriction observed in patients with COPD [41] . ...
Background:
Lung diffusing capacity (DLCO) and lung volume distribution predict exercise performance and are altered in COPD patients. If pulmonary rehabilitation (PR) can modify DLCO parameters is unknown.
Objectives:
To investigate changes in DLCO and ventilation inhomogeneity following a PR program and their relation with functional outcomes in patients with COPD.
Methods:
This was a prospective, observational, multicentric study. Patients were evaluated before and after a standardized 3-week PR program. Functional assessment included body plethysmography, DLCO, transfer factor (KCO) and alveolar volume (VA), gas exchange, the 6-min walking test (6MWT) and exercise-related dyspnea. Patients were categorized according to the severity of airflow limitation and presence of ventilation inhomogeneity, identified by a VA/TLC <0.8.
Results:
Two hundred and fifty patients completed the study. Baseline forced expiratory volume in 1 s (FEV1) % predicted (mean ± SD) was 50.5 ± 20.1 (76% males); 137 patients had a severe disease. General study population showed improvements in 6MWT (38 ± 55 m; p < 0.01), DLCO (0.12 ± 0.63 mmol × min-1 kPa-1; p < 0.01), lung function and dyspnea. Comparable improvements in DLCO were observed regardless of the severity of disease and the presence of ventilation inhomogeneity. While patients with VA/TLC <0.8 improved the DLCO increasing their VA (177 ± 69 ml; p < 0.01), patients with VA/TLC >0.8 improved their KCO (8.1 ± 2.8%; p = 0.019). The latter had also better baseline lung function and higher improvements in 6MWT (14.6 ± 6.7 vs. 9.0 ± 1.8%; p = 0.015). Lower DLCO at baseline was associated with lower improvements in 6MWT, the greatest difference being between subjects with very severe and mild DLCO impairment (2.7 ± 7.4 vs. 14 ± 2%; p = 0.049).
Conclusions:
In COPD patients undergoing a PR program, different pathophysiological mechanisms may drive improvements in DLCO, while ventilation inhomogeneity may limit improvements in exercise tolerance.
Rationale:
Lung injury results in intra-tidal alveolar recruitment and derecruitment (R/D) and alveolar collapse, creating stress concentrators that increase strain and aggravate injury.
Objective:
To describe alveolar micromechanics during mechanical ventilation in bleomycin-induced lung injury and surfactant replacement therapy.
Methods:
Structure and function were assessed in rats one (D1) and three (D3) days after intratracheal bleomycin instillation and subsequent to surfactant replacement therapy (SRT). Pulmonary system mechanics were measured during ventilation with positive end-expiratory pressures (PEEP) between 1 and 10 cmH2O followed by perfusion fixation at end-expiratory airway opening pressures (Pao) of 1, 5, 10, and 20cmH2O for quantitative analyses of lung structure. Lung structure and function were used to parameterize a physiologically-based multi-compartment computational model of alveolar micromechanics.
Measurements and main results:
In healthy controls, numbers of open alveoli remained stable in a range of Pao=1-20cmH2O while bleomycin-challenged lungs demonstrated progressive alveolar derecruitment with Pao<10cmH2O. At D3, approximately 40% of alveoli remained closed at high Pao while alveolar size heterogeneity increased. Simulations of injured lungs predicted that alveolar recruitment pressures were much greater than the derecruitment pressures so that minimal intra-tidal R/D occurred during mechanical ventilation with a tidal volume of 10ml/kg bodyweight over a range of PEEP. However, the simulations also predicted a dramatic increase in alveolar strain with injury that we attribute to alveolar interdependence.
Conclusion:
In progressive lung injury, alveolar collapse with increased distension of patent (open) alveoli dominates alveolar micromechanics. PEEP and surfactant substitution reduce alveolar collapse and dynamic strain but increase static strain.
Understanding lung and airway behavior presents a number of challenges, both experimental and theoretical, but the potential rewards are great in terms of both potential treatments for disease and interesting biophysical phenomena. This presents an opportunity for modeling to contribute to greater understanding, and here, we focus on modeling efforts that work toward understanding the behavior of airways in vivo, with an emphasis on asthma. We look particularly at those models that address not just isolated airways but many of the important ways in which airways are coupled both with each other and with other structures. This includes both interesting phenomena involving the airways and the layer of airway smooth muscle that surrounds them, and also the emergence of spatial ventilation patterns via dynamic airway interaction. WIREs Syst Biol Med 2016, 8:459–467. doi: 10.1002/wsbm.1349
This article is categorized under:
• Analytical and Computational Methods > Dynamical Methods
• Models of Systems Properties and Processes > Mechanistic Models
• Models of Systems Properties and Processes > Organ, Tissue, and Physiological Models
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.
Clustered ventilation defects are a hallmark of asthma, typically seen via imaging studies during asthma attacks. The mechanisms underlying the formation of these clusters is of great interest in understanding asthma. Because the clusters vary from event to event, many researchers believe they occur due to dynamic, rather than structural, causes. To study the formation of these clusters, we formulate and analyze a lattice-based model of the lung, considering both the role of airway bistability and a mechanism for organizing the spatial structure. Within this model we show how and why the homogeneous ventilation solution becomes unstable, and under what circumstances the resulting heterogeneous solution is a clustered solution. The size of the resulting clusters is shown to arise from structure of the eigenvalues and eigenvectors of the system, admitting not only clustered solutions but also (aphysical) checkerboard solutions. We also consider the breathing efficiency of clustered solutions in severely constricted lungs, showing that stabilizing the homogeneous solution may be advantageous in some circumstances. Extensions to hexagonal and cubic lattices are also studied.
Based on the structural characteristics of the gear drive pin, the use of Pro/E software parametric feature modeling capabilities to complete the three-dimensional shape of the gear, the gear and then use MECHANICA module to complete the creation of the finite element model, and finally using ANSYS finite element model of computing gear solving and simulation, thus completing the gear of virtual design. The design, high efficiency, easy operation, easy to modify the designer; it is in the engineering field has a certain reference.
Baseline ventilation heterogeneity is associated with airway hyperresponsiveness (AHR) in asthma; however, it is unknown whether increased baseline ventilation heterogeneity leads to AHR or both are independent effects of similar disease pathophysiology. Reducing functional residual capacity (FRC) in healthy subjects increases baseline ventilation heterogeneity and airway responsiveness, but the relationship between the two is unclear. The aim was to determine whether an increase in baseline ventilation heterogeneity due to a reduction in FRC correlated with the increase in response to methacholine. In 13 healthy male subjects, ventilation heterogeneity was measured by multiple-breath N(2) washout before a cumulative high-dose (0.79-200 μmol) methacholine challenge. On a separate day, the protocol was performed with chest wall strapping (CWS) to reduce FRC. Indexes of ventilation heterogeneity in the convection-dependent (Scond) and diffusion-convection-dependent (Sacin) airways were calculated from the multiple-breath N(2) washout. CWS decreased FRC by 15.6 ± 2.7% (P < 0.0001). CWS increased the percent fall in forced expiratory volume in 1 s during bronchial challenge (P = 0.006), and the magnitude of this effect was independently determined by the effect of CWS on Sacin and FRC (r(adj)(2) = 0.55, P = 0.02). This suggests that changes in baseline ventilation heterogeneity in healthy subjects are sufficient to increase airway responsiveness, independent of the presence of disease pathology.
Acute lung injury is characterized by heterogeneity of regional mechanical properties, which is thought to be correlated with disease severity. The feasibility of using respiratory input impedance (Z
rs) and computed tomographic (CT) image registration for assessing parenchymal mechanical heterogeneity was evaluated. In six dogs, measurements of Z
rs before and after oleic acid injury at various distending pressures were obtained, followed by whole lung CT scans. Each Z
rs spectrum was fit with a model incorporating variable distributions of regional compliances. CT image pairs at different inflation pressures were matched using an image registration algorithm, from which distributions of regional compliances from the resulting anatomic deformation fields were computed. Under baseline conditions, average model compliance decreased with increasing inflation pressure, reflecting parenchymal stiffening. After lung injury, these average compliances decreased at each pressure, indicating derecruitment, alveolar flooding, or alterations in intrinsic tissue elastance. However, average compliance did not change as inflation pressure increased, consistent with simultaneous recruitment and strain stiffening. Image registration revealed peaked distributions of regional compliances, and that small portions of the lung might undergo relative compression during inflation. The authors conclude that assessments of lung function using Z
rs combined with the structural alterations inferred from image registration provide unique but complementary information on the mechanical derangements associated with lung injury.
The explanation for prone and supine differences in tissue density and pleural pressure gradients in the healthy lung has been inferred from several studies as compression of dependent tissue by the heart in the supine posture; however, this hypothesis has not been directly confirmed. Differences could also arise from change in shape of the chest wall and diaphragm, and because of shape with respect to gravity. The contribution of this third mechanism is explored here. Tissue density and static elastic recoil were estimated in the supine and prone left human lung at functional residual capacity using a finite-element analysis. Supine model geometries were derived from multidetector row computed tomography imaging of two subjects: one normal (subject 1), and one with small airway disease (subject 2). For each subject, the prone model was the supine lung shape with gravity reversed; therefore, the prone model was isolated from the influence of displacement of the diaphragm, chest wall, or heart. Model estimates were validated against multidetector row computed tomography measurement of regional density for each subject supine and an independent study of the prone and supine lung. The magnitude of the gradient in density supine (-4.33%/cm for subject 1, and -4.96%/cm for subject 2) was nearly twice as large as for the prone lung (-2.72%/cm for subject 1, and -2.51%/cm for subject 2), consistent with measurements in dogs. The corresponding pleural pressure gradients were 0.54 cmH(2)O/cm (subject 1) and 0.56 cmH(2)O/cm (subject 2) for supine, and 0.29 cmH(2)O/cm (subject 1) and 0.27 cmH(2)O/cm (subject 2) for prone. A smaller prone gradient was predicted without shape change of the "container" or support of the heart by the lung. The influence of the heart was to constrain the shape in which the lung deformed.
Both continuum and micromechanical models have been used to describe the mechanics of lung parenchyma. Different authors, using different models, have come to different conclusions about parenchymal stability. We show that the continuum model, augmented by bounds on the elastic moduli obtained from recent micromechanical modeling, yields the same conclusions about stability that have been obtained from purely micromechanical modeling: if the lung were homogeneous, it would be stable; local atelectasis would not occur at positive transpulmonary pressure. However, the same analysis yields the prediction that if the surface-to-volume ratio is not uniform throughout the lung, regions of higher surface density collapse if surface tension is large and insensitive to surface area. A micromechanical model that illustrates regional collapse is described.
To investigate if airway-parenchymal interdependence may account for differing bronchial responsiveness between inbred rat strains, Fisher and Lewis 12-wk-old male rats were anesthetized, tracheostomized, and placed in a pressure plethysmograph. Functional residual capacity, total lung capacity [lung volume at transpulmonary pressure (PL) of 30 cmH2O], and specific compliance were determined and were found to be similar. Rats were paralyzed and mechanically ventilated. Concentration-response curves were constructed by calculating lung resistance (RL) and lung elastance (EL) after nebulization of saline and then doubling doses of methacholine (0.0625-512 mg/ml). In Fisher (n = 8) and Lewis (n = 7) rats RL and EL were again determined at a lung volume corresponding to 2 cmH2O PL above FRC. The doubling, maximal, and half-maximal effective concentrations were determined for RL and EL. The doubling of effective concentrations of RL and EL were significantly less for Fisher rats. Other groups of Fisher (n = 5) and Lewis (n = 5) rats were similarly exposed to three concentrations of methacholine (64, 128, and 256 mg/ml), and determinations of RL and EL were made at lung volume corresponding to PL of 0, 2, 4, and 8 cmH2O. In both groups, Lewis rats exhibited a significant effect of volume on maximal RL and EL, whereas Fisher rats did not. The absence of volume effect on bronchoconstriction in the hyperresponsive Fisher strain is consistent with the hypothesis that altered airway-parenchymal interdependence contributes to bronchial hyperresponsiveness.
We discuss the advantages and problems associated with fitting geometric data of the human torso obtained from magnetic resonance imaging, with high-order (bicubic Hermite) surface elements. These elements preserve derivative (C
1) continuity across element boundaries and permit smooth anatomically accurate surfaces to be obtained with relatively few elements. These elements are fitted to the data with a new nonlinear fitting procedure that minimizes the error in the fit while maintainingC
1 continuity with nonlinear constraints. Nonlinear Sobelov smoothing is also incorporated into this fitting scheme. The structures fitted along with their corresponding root meansquared error, number of elements used, and number of degrees of freedom (df) per variable are: epicardium (0.91 mm, 40 elements, 142 df), left lung (1.66 mm, 80 elements, 309 df), right lung (1.69 mm, 80 elements, 309 df), skeletal muscle surface (1.67 mm, 264 elements, 1,010 df), fat layer (1.79 mm, 264 elements, 1,010 df), and the skin layer (1.43 mm, 264 elements, 1,010 df). The fitted surfaces are assembled into a combined finite element/boundary element model of the torso in which the exterior surfaces of the heart and lungs are modeled with two-dimensional boundary elements and the layers of the skeletal muscle, fat, and skin are modeled with finite elements. The skeletal muscle and fat layers are modeled with bicubic Hermite linear elements and are obtained by joining the adjacent surface elements for each layer. Applications for the torso model include the forward and inverse problems of electrocardiography, defibrillation studies, radiation dosage studies, and heat transfer studies.
Airway smooth muscle contraction is the central event in acute airway narrowing in asthma. Most studies of isolated muscle have focused on statically equilibrated contractile states that arise from isometric or isotonic contractions. It has recently been established, however, that muscle length is determined by a dynamically equilibrated state of the muscle in which small tidal stretches associated with the ongoing action of breathing act to perturb the binding of myosin to actin. To further investigate this phenomenon, we describe in this report an experimental method for subjecting isolated muscle to a dynamic microenvironment designed to closely approximate that experienced in vivo. Unlike previous methods that used either time-varying length control, force control, or time-invariant auxotonic loads, this method uses transpulmonary pressure as the controlled variable, with both muscle force and muscle length free to adjust as they would in vivo. The method was implemented by using a servo-controlled lever arm to load activated airway smooth muscle strips with transpulmonary pressure fluctuations of increasing amplitude, simulating the action of breathing. The results are not consistent with classical ideas of airway narrowing, which rest on the assumption of a statically equilibrated contractile state; they are consistent, however, with the theory of perturbed equilibria of myosin binding. This experimental method will allow for quantitative experimental evaluation of factors that were previously outside of experimental control, including sensitivity of muscle length to changes of tidal volume, changes of lung volume, shape of the load characteristic, loss of parenchymal support and inflammatory thickening of airway wall compartments.
During bronchoconstriction elastic after-loads arise due to distortion of lung parenchyma by the narrowing airway. In the present study, the functional effect of parenchymal elastic after-load on airway narrowing was determined.
Airway narrowing was measured in vivo over a range of transpulmonary pressures and compared with in vitro narrowing measured at corresponding transmural pressures. Bronchi were generation 10 with internal diameters of ∼4 mm. In vivo luminal narrowing was measured by videobronchoscopy in anaesthetised and ventilated pigs. In vitro luminal narrowing was measured by videoendoscopy in isolated bronchial segments. Airways were activated by maximum vagal nerve stimulation and maximum electrical field stimulation in vivo and in vitro , respectively.
At 5 cmH 2 O, stimulation produced a 35.9±3.2% (n = 6) and a 36.5±2.4% (n = 11) decrease in lumen diameter in vivo and in vitro , respectively. At 30 cmH 2 O, luminal narrowing fell to 23.7±2.0% in vivo and 23.4±2.5% in vitro . There was no difference between luminal narrowing in vivo and in vitro at any pressure.
In conclusion, these findings suggest that in mid-sized, cartilaginous bronchi, parenchymal elastic after-loads do not restrict airway narrowing.
We developed a network model in an attempt to characterize heterogeneity of tissue elasticity of the lung. The model includes a parallel set of pathways, each consisting of an airway resistance, an airway inertance, and a tissue element connected in series. The airway resistance, airway inertance, and the hysteresivity of the tissue elements were the same in each pathway, whereas the tissue elastance (H) followed a hyperbolic distribution between a minimum and maximum. To test the model, we measured the input impedance of the respiratory system of ventilated normal and emphysematous C57BL/6 mice in closed chest condition at four levels of positive end-expiratory pressures. Mild emphysema was developed by nebulized porcine pancreatic elastase (PPE) (30 IU/day x 6 days). Respiratory mechanics were studied 3 wk following the initial treatment. The model significantly improved the fitting error compared with a single-compartment model. The PPE treatment was associated with an increase in mean alveolar diameter and a decrease in minimum, maximum, and mean H. The coefficient of variation of H was significantly larger in emphysema (40%) than that in control (32%). These results indicate that PPE treatment resulted in increased time-constant inequalities associated with a wider distribution of H. The heterogeneity of alveolar size (diameters and area) was also larger in emphysema, suggesting that the model-based tissue elastance heterogeneity may reflect the underlying heterogeneity of the alveolar structure.
We discuss the advantages and problems associated with fitting geometric data of the human torso obtained from magnetic resonance imaging, with high order (bicubic Hermite) surface elements. These elements preserve derivative (C 1 ) continuity across element boundaries and permit smooth anatomically accurate surfaces to be obtained with relatively few elements. These elements are fitted to the data with a new non-linear fitting procedure that minimises the error in the fit whilst maintaining C 1 continuity with non-linear constraints. Non-linear Sobelov smoothing is also incorporated into this fitting scheme. The structures fitted along with their corresponding Root Mean Squared (RMS) error, number of elements used and number of degrees-of-freedom (dof) per variable are: epicardium (0.91 mm, 40 elements, 142 dof), left lung (1.66 mm, 80 elements, 309 dof), right lung (1.69 mm, 80 elements, 309 dof), skeletal muscle surface (1.67 mm, 264 elements, 1010 dof), fat layer (1.79 mm, 264 e...
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.
Dynamic changes in lung volume during breathing and alteration of posture are both known to influence the distribution of perfusion within the lung. Here we couple computational models of pulmonary blood flow and parenchymal tissue mechanics to produce a novel flow model that predicts tissue deformation simultaneously with flow distributions at different lung volumes and postures. The model is used to study the effect of lung volume on flow distribution as a result of normal variation in axial and radial tethering forces. Finite deformation elasticity is used to predict volume changes of the lung tissue and resultant tethering pressures within the tissue. A finite element model of the pulmonary arterial network is embedded within the lung volume and deforms with the tissue. The spatial distribution of steady-state blood flow is predicted using the Poiseuille resistance (including gravity), conservation of mass, and a vascular pressure–radius relationship. Blood flow gradients with respect to gravitationally dependent height are calculated. Gradients are predicted to be consistently steeper in the supine (compared with prone) model due to increased tissue deformation. Decreased lung volume resulted in increased gravitationally dependent flow gradients, predominantly due to the effect of axial vessel stretch on the length and the radius of the arterial vessels. Copyright © 2010 John Wiley & Sons, Ltd.
Airway hyper-responsiveness (AHR), a hallmark of asthma, is a highly complex phenomenon characterised by multiple processes manifesting over a large range of length and time scales. Multiscale computational models have been derived to embody the experimental understanding of AHR. While current models differ in their derivation, a common assumption is that the increase in parenchymal tethering pressure P(teth) during airway constriction can be described using the model proposed by Lai-Fook (1979), which is based on intact lung experimental data for elastic moduli over a range of inflation pressures. Here we reexamine this relationship for consistency with a nonlinear elastic material law that has been parameterised to the pressure-volume behaviour of the intact lung. We show that the nonlinear law and Lai-Fook's relationship are consistent for small constrictions, but diverge when the constriction becomes large.
The outward tethering forces exerted by the lung parenchyma on the airways embedded within it are potent modulators of the ability of the airway smooth muscle to shorten. Much of our understanding of these tethering forces is based on treating the parenchyma as an elastic continuum; yet, on a small enough scale, the lung parenchyma in two dimensions would seem to be more appropriately described as a discrete spring network. We therefore compared how the forces and displacements in the parenchyma surrounding a contracting airway are predicted to differ depending on whether the parenchyma is modeled as an elastic continuum or as a spring network. When the springs were arranged hexagonally to represent alveolar walls, the predicted parenchymal stresses and displacements propagated substantially farther away from the airway than when the springs were arranged in a triangular pattern or when the parenchyma was modeled as a continuum. Thus, to the extent that the parenchyma in vivo behaves as a hexagonal spring network, our results suggest that the range of interdependence forces due to airway contraction may have a greater influence than was previously thought.
Understanding how tissue remodeling affects airway responsiveness is of key importance, but experimental data bearing on this issue remain scant. We used lung explants to investigate the effects of enzymatic digestion on the rate and magnitude of airway narrowing induced by acetylcholine. To link the observed changes in narrowing dynamics to the degree of alteration in tissue mechanics, we compared our experimental results with predictions made by a computational model of a dynamically contracting elastic airway embedded in elastic parenchyma. We found that treatment of explanted airways with two different proteases (elastase and collagenase) resulted in differential effects on the dynamics of airway narrowing following application of ACh. Histological corroboration of these different effects is manifest in different patterns of elimination of collagen and elastin from within the airway wall and the surrounding parenchyma. Simulations with a computational model of a dynamically contracting airway embedded in elastic parenchyma suggest that elastase exerts its functional effects predominately through a reduction in parenchymal tethering, while the effects of collagenase are more related to a reduction in airway wall stiffness. We conclude that airway and parenchymal remodeling as a result of protease activity can have varied effects on the loads opposing ASM shortening, with corresponding consequences for airway responsiveness.
The pressure-diameter (PD) behavior of intact pulmonary vessels was measured roentgenographically at several fixed deflation transpulmonary pressures (Ptp). At any constant vascular pressure (Pv), the intact-vessel diameter was larger for higher Ptp. The behavior of the parenchyma was described by a nonlinear analysis. An excised-vessel PD behavior was computed which was consistent with both nonlinear parenchymal behavior and measured intact-vessel PD behavior. Estimates of Px', the difference between the perivascular pressure and the pleural pressure, as a function of Ptp and Pv were obtained. For physiological values of Pv, mean values of Px' for arteries were -1 cmH2O at Ptp of 4 cmH20 and decreased almost linearly to -15 cmH20 at Ptp of 25 cmH2O. Veins showed a similar behavior, but Px' was more positive. Increasing Pv raised Px' and decreasing Pv lowered Px' at all values of Ptp. These results indicate that the interdependence effect is small at functional residual capacity, increases with lung inflation, and is greater for arteries than veins.
At several transpulmonary pressures (Ptp), the pressure-diameter (PD) behavior of the largest intraparenchymal arterial segment in the isolated pig lung was compared with the behavior of the segment after its excision from the parenchyma and its extension to lengths equivalent to those in the intact state. For physiological changes in length, as may occur with lung inflation during Ptp changes from 4 to 25 cmH2O, excised-vessel diameters did not change significantly at a constant transmural pressure. The excised-vessel PD behavior was not significantly different from the intact-vessel PD behavior at a Ptp of 4 cmH2O. At any constant arterial pressure, intact-vessel diameters became larger as Ptp increased. Estimates of the perivascular pressure (Px) obtained by directly comparing intact-vessel and excised-vessel PD curves were as follows: 1) Px was equal to pleural pressure at a Ptp approximating the functional residual capacity; 2) Px decreased almost linearly as Ptp increased; and 3) Px decreased with a fall in arterial pressure. These results are consistent with direct measurements of the perivascular interstitial fluid pressure.
A method that interrelates lung pressure-volume behavior, bronchial pressure-diameter behavior, and parenchymal shear modulus is presented. The method was used to predict changes in intraparenchymal bronchial diameter that occurred when lobe pressure-volume behavior and parenchymal shear modulus were markedly changed by inducing air trapping in isolated dog lobes. Predictions agreed with measurements, thereby supporting the general method. Measured values for the shear modulus were approximately 0.7 times the transpulmonary pressure for the control state. Estimated values for the peribronchial pressure difference from pleural pressure during a deflation pressure-volume maneuver for transpulmonary pressures below 12 cmH2O were small, approximately +/- 1 cmH2O, its sign being positive or negative, depending on whether the bronchus was dilated or contricted.
Spherical and cylindrical holes were cut in the parenchyma of isolated dog lung lobes. The holes were insufflated with tantalum dust and the hole diameters were measured along the deflation limb of the lobe pressure-volume curve from transpulmonary pressures of 20 to 0 cmH2O. Hole volume as a fraction of lobe volume was found to be independent of transpulmonary pressure. The hole volume relative to the amount of tissue removed was used to determine the displacement at the hole boundary. A comparison of this displacement with the displacement predicted by a continuum mechanics analysis provides evidence for the applicability of the methods of continuum mechanics and further evidence that the shear modulus of the parenchyma is relatively small.
We studied the dynamics of respiratory mechanical parameters in anesthetized tracheostomized paralyzed dogs challenged with a bolus of histamine injected either venously (venous group) or arterially (arterial group). The venous group was further divided into two groups: the first was bilaterally vagotomized and received hexamethonium bromide (denervated group), and the second also received atropine sulfate (atropine group). In the venous group, tissue resistance (Rti) and tissue elastance (Eti) increased biphasically, whereas airway resistance was monophasic and synchronized with the second rise of the tissue parameters. In the arterial group, Rti, Eti, and airway resistance increased synchronously. The denervated and atropine groups showed dynamics similar to those of the venous group. We postulate that the first phase observed in Rti and Eti in the venous group is due to constriction of the smooth muscles of the peripheral airways and blood vessels distorting the parenchyma. The second and larger phase is then due to histamine reaching the bronchial circulation and constricting the central airways, again distorting the parenchyma. The results from the arterial group support this hypothesis, whereas those from the denervated group ascertain that none of the phases observed in the venous group was due to nervous reflexes.
Lung compliance is generally considered to represent a blend of surface and tissue forces, and changes in compliance in vivo are commonly used to indicate changes in surface forces. There are, however, theoretical arguments that would allow contraction of airway smooth muscle to affect substantially the elasticity of the lung. In the present study we evaluated the role of conducting airway contraction on lung compliance in vivo by infusing methacholine (MCh) at a constant rate into the bronchial circulation. With a steady-state MCh infusion of 2.4 micrograms/min into the bronchial perfusate (perfusate concentration = 0.7 microM), there was an approximate doubling of lung resistance and a 50% fall in dynamic compliance. There were also significant decreases in chord compliance measured from the quasi-static pressure-volume curves and in total lung capacity and residual volume. When the same infusion rate was administered into the pulmonary artery, no changes in lung mechanics were observed. These results indicate that the conducting airways may have a major role in regulating lung elasticity. This linkage between airway contraction and lung compliance may account for the common observation that pharmacological challenges given to the lung usually result in similar changes in lung compliance and airway conductance. Our results also suggest the possibility that the lung tissue resistance, which dominates the measurement of lung resistance in many species, might in fact reflect the physical properties of conducting airways.
The objective of this investigation was to determine the minimum transpulmonary pressure (PL) at which the forces of interdependence between the airways and the lung parenchyma can prevent airway closure in response to maximal stimulation of the airways in excised canine lobes. We first present an analysis of the relationship between PL and the transmural pressure (Ptm) that airway smooth muscle must generate to close the airways. This analysis predicts that airway closure can occur at PL less than or equal to 10 cmH2O with maximal airway stimulation. We tested this prediction in eight excised canine lobes by nebulizing 50% methacholine into the airways while the lobe was held at constant PL values ranging from 25 to 5 cmH2O. Airway closure was assessed by comparing changes in alveolar pressure (measured by an alveolar capsule technique) and pressure at the airway opening during low-amplitude oscillations in lobar volume. Airway closure occurred in two of the eight lobes at PL = 10 cmH2O; in an additional five it occurred at PL = 7.5 cmH2O. We conclude that the forces of parenchymal interdependence per se are not sufficient to prevent airway closure at PL less than or equal to 7.5 cmH2O in excised canine lobes.
Tantalum powder was insufflated into pulmonary lobar blood vessels to measure X ray changes in vascular diameter as transpulmonary pressure (Ptp) and vascular pressure (P) were changed. When both Ptp and P were raised, the vessel was consistently larger than when P was raised alone. The amount of effective outward pressure exerted on a vessel by the surrounding lung as it expanded from a low Ptp to be 1-2 cmH 2O/cmH 2O increase in Ptp was estimated. This effect of interdependence was much less at high Ptp. Similar changes were found in both small (2 mm) and larger (5 mm) blood vessels.
The direct contribution of forces in tree structures in the lung to lung recoil pressure and changes in recoil pressure induced by alterations of the forces are analyzed. The analysis distinguishes the contributions of axial and circumferential tensions in the trees and indicates that only axial tensions directly contribute to static recoil. This contribution is derived from analysis of the axial forces transmitted across a random plane transecting the lung. The change in recoil pressure induced by changes in axial tension is similarly derived. Alterations of circumferential tensions in the trees indirectly change recoil by causing nonuniform deformations of the surrounding lung parenchyma, and a continuum elasticity solution for the stress induced by the deformations is derived. Sample calculations are presented for the airway tree based on available data on airway morphometric and mechanical properties. The increase in recoil pressure accompanying increases in axial and circumferential tensions with contraction of airway smooth muscle is also analyzed. The calculations indicate that axial stresses in the airway tree out to bronchioles directly contribute only a small fraction of the static recoil pressure. However, it is found that contraction of smooth muscle in these airways can increase recoil pressure appreciably (10-20%), mainly by the deformation of the parenchyma with increases in circumferential tension in smaller airways. The results indicate that the geometric and mechanical properties of the airway tree are such that only peripheral elements of the tree can substantially affect the elastic properties of the lung. The possible contributions of vascular trees for which data on mechanical and morphometric properties are more limited are also discussed.
The bronchus and artery, embedded in the lung parenchyma, were modeled as adjoining cylindrical tubes in an elastic continuum. Solutions using finite-element analysis of nonuniform stress and strain occurring from an initial uniform state were computed for a reduction in arterial pressure. Maximal nonuniform principal and shear stresses in the parenchyma, equal to 2.5 times the mean periarterial stresses, occurred in the region adjacent to the bronchial-arterial joint. Bronchial cross section became oval and elongated along the line passing through the centers of the tubes, whereas arterial cross section elongated at right angles to this line. These predicted changes in shape of bronchus and artery were verified by radiographic measurements in isolated lobes, held at constant transpulmonary pressures of 4 and 25 cmH2O while arterial pressure was varied. Results suggest that peribronchovascular interstitial fluid pressure may be nonuniform and that the bronchial-arterial joint may be the preferential site for emphysematous perivascular lesions, which may occur on lung hyperinflation.
The constriction of pulmonary airways is limited by the tethering effect exerted by parenchymal attachments. To characterize this tethering effect at the scale of intraparenchymal airways, we studied the pattern of parenchymal distortion due to bronchoconstriction in a rat lung explant system. First, we measured the elastic modulus under tension for 2% (wt/vol) agarose alone (37.6 +/- 1.5 kPa) and for agarose-filled lung (5.7 +/- 1.3 kPa). The latter is similar to the elastic modulus of air-filled lung at total lung capacity (4.5-6 kPa) (S. J. Lai-Fook, T. A. Wilson, R. E. Hyatt, and J. R. Rodarte. J. Appl. Physiol. 40: 508-513, 1976), suggesting that explants can be used as a model of lung tissue distortion. Subsequently, confocal microscopic images of fluorescently labeled 0.5-mm-thick explants prepared from agarose-filled rat lungs inflated to total lung capacity (48 ml/kg) were acquired. Images were taken before and after airway constriction was induced by direct application of 10 mM methacholine, and the pattern of parenchymal distortion was measured from the displacement of tissue landmarks identified in each image for 14 explants. The magnitude of the radial component of tissue displacement was calculated as a function of distance from the airway wall and characterized by a parameter, b, describing the rate at which tissue movement decreased with radial distance. The parameter b was 0.994 +/- 0.19 (SE), which is close to the prediction of b = 1 of micromechanical modeling (T. A. Wilson. J. Appl. Physiol. 33: 472-478, 1972). There was significant variability in b, however, which was correlated with the fractional reduction in airway diameter (r = 0.496). Additionally, parenchymal distortion showed significant torsion with respect to the radial direction. This torsion was similar in concentric zones around the airway, suggesting that it originates from inhomogeneity in the parenchyma rather than inhomogeneous airway constriction. Our results demonstrate the significance of the nonlinear mechanical properties of alveolar walls and the anisotropy of the parenchyma in determining the nature of airway-parenchymal interdependence.
The forces of parenchymal interdependence in the lung are potent inhibitors of airway smooth muscle shortening, as evidenced by the marked dependence of bronchial responsiveness on lung volume. In this study we developed a mathematical-computer model of the effects of parenchymal interdependence on airway smooth muscle shortening. A three-dimensional network of cuboidal alveolar walls was tethered at its boundaries and surrounded a single airway with mechanical properties identical to the alveolar parenchyma. The walls were assigned highly nonlinear properties so that the pressure-volume behavior of the model matched that measured in dogs. Constriction of the airway was achieved by increasing the circumferential tension in the airway wall, and then solving the force-balance equations of the model to calculate the equilibrium configurations of the airway wall and all the interconnecting alveolar walls. The changes in airway resistance predicted by the model at various transpulmonary pressures (P
tp were compared to those obtained by the alveolar capsule oscillator technique in dogs during induced bronchoconstriction at various P
tp (Balassy et al., J. Appl. Physiol. 78:875–880, 1995). The model matched the data reasonably well at P
tp values above about 0.5 kPa, but was too responsive at lower P
tp We were able to make the model match the data at all P
tpby including an additional stiffness term, such as might conceivably arise from the airway wall itself.
Collagen and elastin are thought to dominate the elasticity of the connective tissue including lung parenchyma. The glycosaminoglycans on the proteoglycans may also play a role because osmolarity of interstitial fluid can alter the repulsive forces on the negatively charged glycosaminoglycans, allowing them to collapse or inflate, which can affect the stretching and folding pattern of the fibers. Hence, we hypothesized that the elasticity of lung tissue arises primarily from 1) the topology of the collagen-elastin network and 2) the mechanical interaction between proteoglycans and fibers. We measured the quasi-static, uniaxial stress-strain curves of lung tissue sheets in hypotonic, normal, and hypertonic solutions. We found that the stress-strain curve was sensitive to osmolarity, but this sensitivity decreased after proteoglycan digestion. Images of immunofluorescently labeled collagen networks showed that the fibers follow the alveolar walls that form a hexagonal-like structure. Despite the large heterogeneity, the aspect ratio of the hexagons at 30% uniaxial strain increased linearly with osmolarity. We developed a two-dimensional hexagonal network model of the alveolar structure incorporating the mechanical properties of the collagen-elastin fibers and their interaction with proteoglycans. The model accounted for the stress-strain curves observed under all experimental conditions. The model also predicted how aspect ratio changed with osmolarity and strain, which allowed us to estimate the Young's modulus of a single alveolar wall and a collagen fiber. We therefore identify a novel and important role for the proteoglycans: they stabilize the collagen-elastin network of connective tissues and contribute to lung elasticity and alveolar stability at low to medium lung volumes.
A fundamental question in the field of mechanotransduction is how forces propagate inside a cell. Recent experiments have shown that a force of a physiological magnitude, applied via a focal adhesion, can propagate a long distance into the cell. This observation disagrees with existing models that regard the cell as a homogeneous body. We show that this "action at a distance" results from the inhomogeneity in the cell: a prestressed and stiff actin bundle guides the propagation of forces over long distances. Our models highlight the enormous ratios of the prestress and the modulus of the actin bundle to the modulus of the cytoskeleton network. For a normal cell, the models predict that forces propagate over characteristic lengths comparable to the size of the cell. The characteristic lengths can be altered, however, by treatments of the cell. We provide experimental evidence and discuss biological implications.
Several reports show that the nucleus is 10 times stiffer than the cytoplasm. Hence, it is not clear if intra-nuclear structures can be directly deformed by a load of physiologic magnitudes. If a physiologic load could not directly deform intra-nuclear structures, then signaling inside the nucleus would occur only via the mechanisms of diffusion or translocation. Using a synchronous detection approach, we quantified displacements of nucleolar structures in cultured airway smooth muscle cells in response to a localized physiologic load ( approximately 0.4 microm surface deformation) via integrin receptors. The nucleolus exhibited significant displacements. Nucleolar structures also exhibited significant deformation, with the dominant strain being the bulk strain. Increasing the pre-existing tensile stress (prestress) in the cytoskeleton significantly increased the stress propagation efficiency to the nucleolus (defined as nucleolus displacement per surface deformation) whereas decreasing the prestress significantly lowered the stress propagation efficiency to the nucleolus. Abolishing the stress fibers/actin bundles by plating the cells on poly-L-lysine-coated dishes dramatically inhibited stress propagation to the nucleolus. These results demonstrate that the prestress in the cytoskeleton is crucial in mediating stress propagation to the nucleolus, with implications for direct mechanical regulation of nuclear activities and functions.
A new model is proposed for force transmission through the cytoskeleton (CSK). A general discussion is first presented on the physical principles that underlie the modeling of this phenomenon. Some fundamental problems of conventional models--continuous and discrete--are examined. It is argued that mediation of focused forces is essential for good control over intracellular mechanical signals. The difficulties of conventional continuous models in describing such mediation are traced to a fundamental assumption rather than to their being continuous. Relevant advantages and disadvantages of continuous and discrete modeling are discussed. It is concluded that favoring discrete models is based on two misconceptions, which are clarified. The model proposed here is based on the idea that focused propagation of mechanical stimuli in frameworks over large distances (compared to the mesh size) can only occur when considerable regions of the CSK are isostatic. The concept of isostaticity is explained and a recently developed continuous isostaticity theory is briefly reviewed. The model enjoys several advantages: it leads to good control over force mediation; it explains nonuniform stresses and action at a distance; it is continuous, making it possible to model force propagation over long distances; and it enables prediction of individual force paths. To be isostatic, or nearly so, CSK networks must possess specific structural characteristics, and these are quantified. Finally, several experimental observations are interpreted using the new model and implications are discussed. It is also suggested that this approach may give insight into the dynamics of reorganization of the CSK. Many of the results are amenable to experimental measurements, providing a testing ground for the proposed picture, and generic experiments are suggested.
We measured the mechanical properties of the respiratory system of C57BL/6 mice using the optimal ventilation waveform method in closed- and open-chest conditions at different positive end-expiratory pressures. The tissue damping (G), tissue elastance (H), airway resistance (Raw), and hysteresivity were obtained by fitting the impedance data to three different models: a constant-phase model by Hantos et al. (Hantos Z, Daroczy B, Suki B, Nagy S, Fredberg JJ. J Appl Physiol 72: 168-178, 1992), a heterogeneous Raw model by Suki et al. (Suki B, Yuan H, Zhang Q, Lutchen KR. J Appl Physiol 82: 1349-1359, 1997), and a heterogeneous H model by Ito et al. (Ito S, Ingenito EP, Arold SP, Parameswaran H, Tgavalekos NT, Lutchen KR, Suki B. J Appl Physiol 97: 204-212, 2004). Both in the closed- and open-chest conditions, G and hysteresivity were the lowest and Raw the highest in the heterogeneous Raw model, and G and H were the largest in the heterogeneous H model. Values of G, Raw, and hysteresivity were significantly higher in the closed-chest than in the open-chest condition. However, H was not affected by the conditions. When the tidal volume of the optimal ventilation waveform was decreased from 8 to 4 ml/kg in the closed-chest condition, G and hysteresivity significantly increased, but there were smaller changes in H or Raw. In summary, values of the obtained mechanical properties varied among these models, primarily due to heterogeneity. Moreover, the mechanical parameters were significantly affected by the chest wall and tidal volume in mice. Contribution of the chest wall and heterogeneity to the mechanical properties should be carefully considered in physiological studies in which partitioning of airway and tissue properties are attempted.
We do not yet have a good quantitative understanding of how the force-velocity properties of airway smooth muscle interact with the opposing loads of parenchymal tethering and airway wall stiffness to produce the dynamics of bronchoconstriction. We therefore developed a two-dimensional computational model of a dynamically narrowing airway embedded in uniformly elastic lung parenchyma and compared the predictions of the model to published measurements of airway resistance made in rats and rabbits during the development of bronchoconstriction following a bolus injection of methacholine. The model accurately reproduced the experimental time-courses of airway resistance as a function of both lung inflation pressure and tidal volume. The model also showed that the stiffness of the airway wall is similar in rats and rabbits, and significantly greater than that of the lung parenchyma. Our results indicate that the main features of the dynamical nature of bronchoconstriction in vivo can be understood in terms of the classic Hill force-velocity relationship operating against elastic loads provided by the surrounding lung parenchyma and an airway wall that is stiffer than the parenchyma.
Excessive airway obstruction is the cause of symptoms and abnormal lung function in asthma.
As airway smooth muscle (ASM) is the effecter controlling airway calibre, it is suspected that dysfunction of ASM contributes to the pathophysiology of asthma. However, the precise role of ASM in the series of events leading to asthmatic symptoms is not clear. It is not certain whether, in asthma, there is a change in the intrinsic properties of ASM, a change in the structure and mechanical properties of the noncontractile components of the airway wall, or a change in the interdependence of the airway wall with the surrounding lung parenchyma. All these potential changes could result from acute or chronic airway inflammation and associated tissue repair and remodelling.
Anti-inflammatory therapy, however, does not “cure” asthma, and airway hyperresponsiveness can persist in asthmatics, even in the absence of airway inflammation. This is perhaps because the therapy does not directly address a fundamental abnormality of asthma, that of exaggerated airway narrowing due to excessive shortening of ASM.
In the present study, a central role for airway smooth muscle in the pathogenesis of airway hyperresponsiveness in asthma is explored.
Structure–function correlations in pulmonary fibrosis Physiologic basis of respira-tory disease
- A Gonzalez
- M S Ludwig
Gonzalez, A., Ludwig, M.S., 2005. Structure–function correlations in pulmonary fibrosis. In: Hamid, Q., Shannon, J., Martin, J. (Eds.), Physiologic basis of respira-tory disease. BC Decker, Inc., Hamilton, pp. 77–84.
Structure-function correlations in asthma
- M S Ludwig
- Q Hamid
- J Shannon
- J Martin
Ludwig, MS. Structure-function correlations in asthma. In: Hamid, Q.; Shannon, J.; Martin, J., editors.
Physiologic basis of respiratory disease. Hamilton: BC Decker, Inc.; 2005. p. 105-113.
Structure-function correlations in pulmonary fibrosis
- A Gonzalez
- M S Ludwig
- Q Hamid
- J Shannon
- J Martin
Gonzalez, A.; Ludwig, MS. Structure-function correlations in pulmonary fibrosis. In: Hamid, Q.;
Shannon, J.; Martin, J., editors. Physiologic basis of respiratory disease. Hamilton: BC Decker,
Inc.; 2005. p. 77-84.
Finite element structural analysis
- T Y Yang
Yang, TY. Finite element structural analysis. Englewood Cliffs, NJ: Prentice-Hall; 1986.
Structure–function correlations in pulmonary fibrosis
- Gonzalez
Structure–function correlations in asthma
- Ludwig