A biomechanical model of agonist-initiated contraction in the asthmatic airway

Adipose tissue in the small airways: How much is enough to drive functional changes?

Obesity is a contributing factor to asthma severity; while it has long been understood that obesity is related to greater asthma burden, the mechanisms though which this occurs have not been fully elucidated. One common explanation is that obesity mechanically reduces lung volume through accumulation of adipose tissue external to the thoracic cavity. However, it has been recently demonstrated that there is substantial adipose tissue within the airway wall itself, and that the presence of adipose tissue within the airway wall is related to body mass index. This suggests the possibility of an additional mechanism by which obesity may worsen asthma, namely by altering the behaviour of the airways themselves. To this end, we modify Anafi & Wilson's classic model of the bistable terminal airway to incorporate adipose tissue within the airway wall in order to answer the question of how much adipose tissue would be required in order to drive substantive functional changes. This analysis suggests that adipose tissue within the airway wall on the order of 1%-2% of total airway cross-sectional area could be sufficient to drive meaningful changes, and further that these changes may interact with volume effects to magnify the overall burden.

A dynamical model of TGF-β activation in asthmatic airways

Excessive activation of the regulatory cytokine transforming growth factor $\beta $ (TGF-$\beta $) via contraction of airway smooth muscle (ASM) is associated with the development of asthma. In this study, we develop an ordinary differential equation model that describes the change in density of the key airway wall constituents, ASM and extracellular matrix (ECM), and their interplay with subcellular signalling pathways leading to the activation of TGF-$\beta $. We identify bistable parameter regimes where there are two positive steady states, corresponding to either reduced or elevated TGF-$\beta $ concentration, with the latter leading additionally to increased ASM and ECM density. We associate the former with a healthy homeostatic state and the latter with a diseased (asthmatic) state. We demonstrate that external stimuli, inducing TGF-$\beta $ activation via ASM contraction (mimicking an asthmatic exacerbation), can perturb the system irreversibly from the healthy state to the diseased one. We show that the properties of the stimuli, such as their frequency or strength, and the clearance of surplus active TGF-$\beta $, are important in determining the long-term dynamics and the development of disease. Finally, we demonstrate the utility of this model in investigating temporal responses to bronchial thermoplasty, a therapeutic intervention in which ASM is ablated by applying thermal energy to the airway wall. The model predicts the parameter-dependent threshold damage required to obtain irreversible reduction in ASM content, suggesting that certain asthma phenotypes are more likely to benefit from this intervention.

Soft robotic constrictor for in vitro modeling of dynamic tissue compression

Here we present a microengineered soft-robotic in vitro platform developed by integrating a pneumatically regulated novel elastomeric actuator with primary culture of human cells. This system is capable of generating dynamic bending motion akin to the constriction of tubular organs that can exert controlled compressive forces on cultured living cells. Using this platform, we demonstrate cyclic compression of primary human endothelial cells, fibroblasts, and smooth muscle cells to show physiological changes in their morphology due to applied forces. Moreover, we present mechanically actuatable organotypic models to examine the effects of compressive forces on three-dimensional multicellular constructs designed to emulate complex tissues such as solid tumors and vascular networks. Our work provides a preliminary demonstration of how soft-robotics technology can be leveraged for in vitro modeling of complex physiological tissue microenvironment, and may enable the development of new research tools for mechanobiology and related areas.

Reduced biomechanical models for precision-cut lung-slice stretching experiments

Precision-cut lung-slices (PCLS), in which viable airways embedded within lung parenchyma are stretched or induced to contract, are a widely used ex vivo assay to investigate bronchoconstriction and, more recently, mechanical activation of pro-remodelling cytokines in asthmatic airways. We develop a nonlinear fibre-reinforced biomechanical model accounting for smooth muscle contraction and extracellular matrix strain-stiffening. Through numerical simulation, we describe the stresses and contractile responses of an airway within a PCLS of finite thickness, exposing the importance of smooth muscle contraction on the local stress state within the airway. We then consider two simplifying limits of the model (a membrane representation and an asymptotic reduction in the thin-PCLS-limit), that permit analytical progress. Comparison against numerical solution of the full problem shows that the asymptotic reduction successfully captures the key elements of the full model behaviour. The more tractable reduced model that we develop is suitable to be employed in investigations to elucidate the time-dependent feedback mechanisms linking airway mechanics and cytokine activation in asthma.

An in silico study examining the role of airway smooth muscle dynamics and airway compliance on the rate of airway re-narrowing after deep inspiration

Deep inspirations are a widely studied topic due to their varied effectiveness as a bronchodilator in asthmatic and non-asthmatic patients. Specifically, they are known to be effective at reversing bronchoconstriction in non-asthmatic patients but may fail to prevent bronchoconstriction in asthmatic patients. Inspired by a recent study on the effect of deep inspirations on the rate of re-narrowing of an isolated airway, we investigate whether the latch-bridge dynamics of smooth muscle cross-bridge theory, coupled with non-linear compliance of the airway wall, can account for the reported results: namely that only the rate of renarrowing after DI is sensitive to the interval between deep inspirations, while other measures are unaffected. We develop and present length- and pressure-controlled protocols which mimic both the experiments performed in the study, as well as simulate in vivo conditions respectively. Both protocols are simulated and show qualitative agreement with the results reported by the experiments, suggesting that latch-bridge dynamics coupled with airway wall non-compliance may be sufficient to explain these results. Moreover pressure- and length-controlled protocols show important differences which should be considered when designing in vitro experiments to mimic in vivo conditions.

A review of inflammatory mechanism in airway diseases

BACKGROUND

Inflammation in the lung is the body's natural response to injury. It acts to remove harmful stimuli such as pathogens, irritants, and damaged cells and initiate the healing process. Acute and chronic pulmonary inflammation are seen in different respiratory diseases such as; acute respiratory distress syndrome, chronic obstructive pulmonary disease (COPD), asthma, and cystic fibrosis (CF).

FINDINGS

In this review, we found that inflammatory response in COPD is determined by the activation of epithelial cells and macrophages in the respiratory tract. Epithelial cells and macrophages discharge transforming growth factor-β (TGF-β), which trigger fibroblast proliferation and tissue remodeling. Asthma leads to airway hyper-responsiveness, obstruction, mucus hyper-production, and airway-wall remodeling. Cytokines, allergens, chemokines, and infectious agents are the main stimuli that activate signaling pathways in epithelial cells in asthma. Mutation of the CF transmembrane conductance regulator (CFTR) gene results in CF. Mutations in CFTR influence the lung epithelial innate immune function that leads to exaggerated and ineffective airway inflammation that fails to abolish pulmonary pathogens. We present mechanistic computational models (based on ordinary differential equations, partial differential equations and agent-based models) that have been applied in studying the complex physiological and pathological mechanisms of chronic inflammation in different airway diseases.

CONCLUSION

The scope of the present review is to explore the inflammatory mechanism in airway diseases and highlight the influence of aging on airways' inflammation mechanism. The main goal of this review is to encourage research collaborations between experimentalist and modelers to promote our understanding of the physiological and pathological mechanisms that control inflammation in different airway diseases.

A theoretical model of inflammation- and mechanotransduction-driven asthmatic airway remodelling

Inflammation, airway hyper-responsiveness and airway remodelling are well-established hallmarks of asthma, but their inter-relationships remain elusive. In order to obtain a better understanding of their inter-dependence, we develop a mechanochemical morphoelastic model of the airway wall accounting for local volume changes in airway smooth muscle (ASM) and extracellular matrix in response to transient inflammatory or contractile agonist challenges. We use constrained mixture theory, together with a multiplicative decomposition of growth from the elastic deformation, to model the airway wall as a nonlinear fibre-reinforced elastic cylinder. Local contractile agonist drives ASM cell contraction, generating mechanical stresses in the tissue that drive further release of mitogenic mediators and contractile agonists via underlying mechanotransductive signalling pathways. Our model predictions are consistent with previously described inflammation-induced remodelling within an axisymmetric airway geometry. Additionally, our simulations reveal novel mechanotransductive feedback by which hyper-responsive airways exhibit increased remodelling, for example, via stress-induced release of pro-mitogenic and pro-contractile cytokines. Simulation results also reveal emergence of a persistent contractile tone observed in asthmatics, via either a pathological mechanotransductive feedback loop, a failure to clear agonists from the tissue, or a combination of both. Furthermore, we identify various parameter combinations that may contribute to the existence of different asthma phenotypes, and we illustrate a combination of factors which may predispose severe asthmatics to fatal bronchospasms.

Inter-airway structural heterogeneity interacts with dynamic heterogeneity to determine lung function and flow patterns in both asthmatic and control simulated lungs

Asthma is a disease involving both airway remodelling (e.g. thickening of the airway wall) and acute, reversible airway narrowing driven by airway smooth muscle contraction. Both of these processes are known to be heterogeneous, and in this study we consider a new theoretical model which considers the interactions of both mechanisms: structural heterogeneity (variation in airway remodelling) and dynamic heterogeneity (emergent variation in airway narrowing and flow). By integrating both types of inter-airway heterogeneity in a full human lung geometry, we are able to draw several insights regarding the mechanisms underlying observed ventilation heterogeneity. We show that: (1) bimodal ventilation distributions are driven by paradoxical contraction/dilation patterns for airways of all sizes; (2) structural heterogeneity differences between asthmatic and control subjects significantly influences resulting lung function, and observed ventilation heterogeneity patterns; and (3) individual airway dilation probabilities are uncorrelated with prior airway remodelling of that airway.

Airway Bistability Is Modulated by Smooth Muscle Dynamics and Length-Tension Characteristics

Airway closure has important implications for lung disease, especially asthma; in particular, the prospect of bistability between open and closed (or effectively closed) airway states has been thought to play a prominent role in airway closure associated with the formation of clustered ventilation defects in asthma. However, many existing analyses of closure consider only static airway equilibria; here we construct, to our knowledge, a new model wherein airway narrowing and closure dynamics are modulated by coupling the airway to cross-bridge models of airway smooth muscle dynamics and force generation. Using this model, we show that important qualitative features of airway pressure-radius hysteresis loops are highly dependent on both airway smooth muscle dynamics, and the length-tension relationship. Furthermore, we show that two recent experimental results from intact bronchial segments are both expressions of the same phenomenon: that a monotonically increasing length-tension relationship, with sharply higher tension at longer lengths, is needed to drive the observed changes in low-compliance regions of the baseline pressure-radius curve. We also explore the potential implications of this finding for airway closure in coupled airway models.

Systems Medicine for Lung Diseases: Phenotypes and Precision Medicine in Cancer, Infection, and Allergy

Lung diseases cause an enormous socioeconomic burden. Four of them are among the ten most important causes of deaths worldwide: Pneumonia has the highest death toll of all infectious diseases, lung cancer kills the most people of all malignant proliferative disorders, chronic obstructive pulmonary disease (COPD) ranks third in mortality among the chronic noncommunicable diseases, and tuberculosis is still one of the most important chronic infectious diseases. Despite all efforts, for example, by the World Health Organization and clinical and experimental researchers, these diseases are still highly prevalent and harmful. This is in part due to the specific organization of tissue homeostasis, architecture, and immunity of the lung. Recently, several consortia have formed and aim to bring together clinical and molecular data from big cohorts of patients with lung diseases with novel experimental setups, biostatistics, bioinformatics, and mathematical modeling. This "systems medicine" concept will help to match the different disease modalities with adequate therapeutic and possibly preventive strategies for individual patients in the sense of precision medicine.

Airway and Parenchymal Strains during Bronchoconstriction in the Precision Cut Lung Slice

The precision-cut lung slice (PCLS) is a powerful tool for studying airway reactivity, but biomechanical measurements to date have largely focused on changes in airway caliber. Here we describe an image processing tool that reveals the associated spatio-temporal changes in airway and parenchymal strains. Displacements of sub-regions within the PCLS are tracked in phase-contrast movies acquired after addition of contractile and relaxing drugs. From displacement maps, strains are determined across the entire PCLS or along user-specified directions. In a representative mouse PCLS challenged with 10(-4)M methacholine, as lumen area decreased, compressive circumferential strains were highest in the 50 μm closest to the airway lumen while expansive radial strains were highest in the region 50-100 μm from the lumen. However, at any given distance from the airway the strain distribution varied substantially in the vicinity of neighboring small airways and blood vessels. Upon challenge with the relaxant agonist chloroquine, although most strains disappeared, residual positive strains remained a long time after addition of chloroquine, predominantly in the radial direction. Taken together, these findings establish strain mapping as a new tool to elucidate local dynamic mechanical events within the constricting airway and its supporting parenchyma.

Clustered ventilation defects and bilinear respiratory reactance in asthma

Imaging studies of asthmatics typically reveal clustered ventilation patterns, rather than homogeneous ventilation; furthermore, the variation of these clusters suggests that the causes are at least partially dynamic, rather than structural. Theoretical studies have indicated dynamic mechanisms by which homogeneous ventilation solutions lose stability and clustered solutions emerge. At the same time, it has been demonstrated experimentally that respiratory reactance characteristically has a bilinear relationship with lung volume, and that changes to this relationship are indicative of various aspects of disease progression and control. Moreover, the transition point in the bilinear reactance relationship is thought to relate to reopening/recruitment of airway units, and thus may be connected to the bifurcation via which clustered ventilation solutions emerge. In order to investigate this possibility we develop a new model, including both airway-airway coupling and airway-parenchymal coupling, which exhibits both clustered ventilation defects and also a bilinear reactance relationship. Studying this model reveals that (1) the reactance breakpoint is not coincident with the bifurcation; (2) numerous changes to underlying behaviour can alter the reactance breakpoint in ways which mimic the experimental data; and (3) the location of ventilation defects can be a combination of both structural and dynamic factors.

Systems-level airway models of bronchoconstriction

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 For further resources related to this article, please visit the WIREs website.

Systems physiology of the airways in health and obstructive pulmonary disease

Fresh air entering the mouth and nose is brought to the blood-gas barrier in the lungs by a repetitively branching network of airways. Provided the individual airway branches remain patent, this airway tree achieves an enormous amplification in cross-sectional area from the trachea to the terminal bronchioles. Obstructive lung diseases such as asthma occur when airway patency becomes compromised. Understanding the pathophysiology of these obstructive diseases thus begins with a consideration of the factors that determine the caliber of an individual airway, which include the force balance between the inward elastic recoil of the airway wall, the outward tethering forces of its parenchymal attachments, and any additional forces due to contraction of airway smooth muscle. Other factors may also contribute significantly to airway narrowing, such as thickening of the airway wall and accumulation of secretions in the lumen. Airway obstruction becomes particularly severe when these various factors occur in concert. However, the effect of airway abnormalities on lung function cannot be fully understood only in terms of what happens to a single airway because narrowing throughout the airway tree is invariably heterogeneous and interdependent. Obstructive lung pathologies thus manifest as emergent phenomena arising from the way in which the airway tree behaves a system. These emergent phenomena are studied with clinical measurements of lung function made by spirometry and by mechanical impedance measured with the forced oscillation technique. Anatomically based computational models are linking these measurements to underlying anatomic structure in systems physiology terms. WIREs Syst Biol Med 2016, 8:423-437. doi: 10.1002/wsbm.1347 For further resources related to this article, please visit the WIREs website.

Nonlinear compliance modulates dynamic bronchoconstriction in a multiscale airway model

The role of breathing and deep inspirations (DI) in modulating airway hyperresponsiveness remains poorly understood. In particular, DIs are potent bronchodilators of constricted airways in nonasthmatic subjects but not in asthmatic subjects. Additionally, length fluctuations (mimicking DIs) have been shown to reduce mean contractile force when applied to airway smooth muscle (ASM) cells and tissue strips. However, these observations are not recapitulated on application of transmural pressure (PTM) oscillations (that mimic tidal breathing and DIs) in isolated intact airways. To shed light on this paradox, we have developed a biomechanical model of the intact airway, accounting for strain-stiffening due to collagen recruitment (a large component of the extracellular matrix (ECM)), and dynamic actomyosin-driven force generation by ASM cells. In agreement with intact airway studies, our model shows that PTM fluctuations at particular mean transmural pressures can lead to only limited bronchodilation. However, our model predicts that moving the airway to a more compliant point on the static pressure-radius relationship (which may involve reducing mean PTM), before applying pressure fluctuations, can generate greater bronchodilation. This difference arises from competition between passive strain-stiffening of ECM and force generation by ASM yielding a highly nonlinear relationship between effective airway stiffness and PTM, which is modified by the presence of contractile agonist. Effectively, the airway at its most compliant may allow for greater strain to be transmitted to subcellular contractile machinery. The model predictions lead us to hypothesize that the maximum possible bronchodilation of an airway depends on its static compliance at the PTM about which the fluctuations are applied. We suggest the design of additional experimental protocols to test this hypothesis.

Static and dynamic stress heterogeneity in a multiscale model of the asthmatic airway wall

Airway hyperresponsiveness (AHR) is a key characteristic of asthma that remains poorly understood. Tidal breathing and deep inspiration ordinarily cause rapid relaxation of airway smooth muscle (ASM) (as demonstrated via application of length fluctuations to tissue strips) and are therefore implicated in modulation of AHR, but in some cases (such as application of transmural pressure oscillations to isolated intact airways) this mechanism fails. Here we use a multiscale biomechanical model for intact airways that incorporates strain stiffening due to collagen recruitment and dynamic force generation by ASM cells to show that the geometry of the airway, together with interplay between dynamic active and passive forces, gives rise to large stress and compliance heterogeneities across the airway wall that are absent in tissue strips. We show further that these stress heterogeneities result in auxotonic loading conditions that are currently not replicated in tissue-strip experiments; stresses in the strip are similar to hoop stress only at the outer airway wall and are under- or overestimates of stresses at the lumen. Taken together these results suggest that a previously underappreciated factor, stress heterogeneities within the airway wall and consequent ASM cellular response to this micromechanical environment, could contribute to AHR and should be explored further both theoretically and experimentally.

Airway and Extracellular Matrix Mechanics in COPD

Chronic obstructive pulmonary disease (COPD) is one of the most common lung diseases worldwide, and is characterized by airflow obstruction that is not fully reversible with treatment. Even though airflow obstruction is caused by airway smooth muscle contraction, the extent of airway narrowing depends on a range of other structural and functional determinants that impact on active and passive tissue mechanics. Cells and extracellular matrix in the airway and parenchymal compartments respond both passively and actively to the mechanical stimulation induced by smooth muscle contraction. In this review, we summarize the factors that regulate airway narrowing and provide insight into the relative contributions of different constituents of the extracellular matrix and their biomechanical impact on airway obstruction. We then review the changes in extracellular matrix composition in the airway and parenchymal compartments at different stages of COPD, and finally discuss how these changes impact airway narrowing and the development of airway hyperresponsiveness. Finally, we position these data in the context of therapeutic research focused on defective tissue repair. As a conclusion, we propose that future works should primarily target mild or early COPD, prior to the widespread structural changes in the alveolar compartment that are more characteristic of severe COPD.

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

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

Airway smooth muscle in asthma: linking contraction and mechanotransduction to disease pathogenesis and remodelling

Asthma is an obstructive airway disease, with a heterogeneous and multifactorial pathogenesis. Although generally considered to be a disease principally driven by chronic inflammation, it is becoming increasingly recognised that the immune component of the pathology poorly correlates with the clinical symptoms of asthma, thus highlighting a potentially central role for non-immune cells. In this context airway smooth muscle (ASM) may be a key player, as it comprises a significant proportion of the airway wall and is the ultimate effector of acute airway narrowing. Historically, the contribution of ASM to asthma pathogenesis has been contentious, yet emerging evidence suggests that ASM contractile activation imparts chronic effects that extend well beyond the temporary effects of bronchoconstriction. In this review article we describe the effects that ASM contraction, in combination with cellular mechanotransduction and novel contraction-inflammation synergies, contribute to asthma pathogenesis. Specific emphasis will be placed on the effects that ASM contraction exerts on the mechanical properties of the airway wall, as well as novel mechanisms by which ASM contraction may contribute to more established features of asthma such as airway wall remodelling.

The role of inflammation resolution speed in airway smooth muscle mass accumulation in asthma: insight from a theoretical model

Despite a large amount of in vitro data, the dynamics of airway smooth muscle (ASM) mass increase in the airways of patients with asthma is not well understood. Here, we present a novel mathematical model that describes qualitatively the growth dynamics of ASM cells over short and long terms in the normal and inflammatory environments typically observed in asthma. The degree of ASM accumulation can be explained by an increase in the rate at which ASM cells switch between non-proliferative and proliferative states, driven by episodic inflammatory events. Our model explores the idea that remodelling due to ASM hyperplasia increases with the frequency and magnitude of these inflammatory events, relative to certain sensitivity thresholds. It highlights the importance of inflammation resolution speed by showing that when resolution is slow, even a series of small exacerbation events can result in significant remodelling, which persists after the inflammatory episodes. In addition, we demonstrate how the uncertainty in long-term outcome may be quantified and used to design an optimal low-risk individual anti-proliferative treatment strategy. The model shows that the rate of clearance of ASM proliferation and recruitment factors after an acute inflammatory event is a potentially important, and hitherto unrecognised, target for anti-remodelling therapy in asthma. It also suggests new ways of quantifying inflammation severity that could improve prediction of the extent of ASM accumulation. This ASM growth model should prove useful for designing new experiments or as a building block of more detailed multi-cellular tissue-level models.

Emergence of airway smooth muscle mechanical behavior through dynamic reorganization of contractile units and force transmission pathways

Airway hyperresponsiveness (AHR) in asthma remains poorly understood despite significant research effort to elucidate relevant underlying mechanisms. In particular, a significant body of experimental work has focused on the effect of tidal fluctuations on airway smooth muscle (ASM) cells, tissues, lung slices, and whole airways to understand the bronchodilating effect of tidal breathing and deep inspirations. These studies have motivated conceptual models that involve dynamic reorganization of both cytoskeletal components as well as contractile machinery. In this article, a biophysical model of the whole ASM cell is presented that combines 1) crossbridge cycling between actin and myosin; 2) actin-myosin disconnectivity, under imposed length changes, to allow dynamic reconfiguration of "force transmission pathways"; and 3) dynamic parallel-to-serial transitions of contractile units within these pathways that occur through a length fluctuation. Results of this theoretical model suggest that behavior characteristic of experimentally observed force-length loops of maximally activated ASM strips can be explained by interactions among the three mechanisms. Crucially, both sustained disconnectivity and parallel-to-serial transitions are necessary to explain the nature of hysteresis and strain stiffening observed experimentally. The results provide strong evidence that dynamic rearrangement of contractile machinery is a likely mechanism underlying many of the phenomena observed at timescales associated with tidal breathing. This theoretical cell-level model captures many of the salient features of mechanical behavior observed experimentally and should provide a useful starting block for a bottom-up approach to understanding tissue-level mechanical behavior.

Mechanical interactions between adjacent airways in the lung

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

Multi-scale computational models of the airways to unravel the pathophysiological mechanisms in asthma and chronic obstructive pulmonary disease (AirPROM)

THE RESPIRATORY SYSTEM COMPRISES SEVERAL SCALES OF BIOLOGICAL COMPLEXITY: the genes, cells and tissues that work in concert to generate resultant function. Malfunctions of the structure or function of components at any spatial scale can result in diseases, to the detriment of gas exchange, right heart function and patient quality of life. Vast amounts of data emerge from studies across each of the biological scales; however, the question remains: how can we integrate and interpret these data in a meaningful way? Respiratory disease presents a huge health and economic burden, with the diseases asthma and chronic obstructive pulmonary disease (COPD) affecting over 500 million people worldwide. Current therapies are inadequate owing to our incomplete understanding of the disease pathophysiology and our lack of recognition of the enormous disease heterogeneity: we need to characterize this heterogeneity on a patient-specific basis to advance healthcare. In an effort to achieve this goal, the AirPROM consortium (Airway disease Predicting Outcomes through patient-specific computational Modelling) brings together a multi-disciplinary team and a wealth of clinical data. Together we are developing an integrated multi-scale model of the airways in order to unravel the complex pathophysiological mechanisms occurring in the diseases asthma and COPD.

Activation of store-operated calcium entry in airway smooth muscle cells: insight from a mathematical model

Intracellular dynamics of airway smooth muscle cells (ASMC) mediate ASMC contraction and proliferation, and thus play a key role in airway hyper-responsiveness (AHR) and remodelling in asthma. We evaluate the importance of store-operated entry (SOCE) in these dynamics by constructing a mathematical model of ASMC signaling based on experimental data from lung slices. The model confirms that SOCE is elicited upon sufficient depletion of the sarcoplasmic reticulum (SR), while receptor-operated entry (ROCE) is inhibited in such conditions. It also shows that SOCE can sustain agonist-induced oscillations in the absence of other influx. SOCE up-regulation may thus contribute to AHR by increasing the oscillation frequency that in turn regulates ASMC contraction. The model also provides an explanation for the failure of the SERCA pump blocker CPA to clamp the cytosolic of ASMC in lung slices, by showing that CPA is unable to maintain the SR empty of . This prediction is confirmed by experimental data from mouse lung slices, and strongly suggests that CPA only partially inhibits SERCA in ASMC.

Airway-parenchymal interdependence in the lung slice

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

Continuum vs. spring network models of airway-parenchymal interdependence

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.

Lung damage and airway remodelling in severe asthma

Severe asthma is a heterogeneous disease with substantial unmet clinical need. Airway damage and remodelling is a consequence of complex host-environment interactions and is considered to be the cardinal feature leading onto the development and persistence of airflow obstruction. In this review, we shall bring together recent insights into the causes of airway damage and remodelling that propose key roles for pathogens and mechanical damage in addition to allergens, underlying genetic susceptibility, inflammatory and structural cell interactions, and impaired resolution of damage. We shall consider the consequences of airway remodelling in terms of airway geometry, mechanics and clinical expression of disease. Understanding the causes and consequences of airway damage and remodelling will shed light upon the structure-function relationships required to begin to unravel the complexity of severe asthma and will enable us to target current and novel therapies as we begin to move towards realizing personalized medicine.

Exploring lung physiology in health and disease with lung slices

The development of therapeutic approaches to treat lung disease requires an understanding of both the normal and disease physiology of the lung. Although traditional experimental approaches only address either organ or cellular physiology, the use of lung slice preparations provides a unique approach to investigate integrated physiology that links the cellular and organ responses. Living lung slices are robust and can be prepared from a variety of species, including humans, and they retain many aspects of the cellular and structural organization of the lung. Functional portions of intrapulmonary airways, arterioles and veins are present within the alveoli parenchyma. The dynamics of macroscopic changes of contraction and relaxation associated with the airways and vessels are readily observed with conventional low-magnification microscopy. The microscopic changes associated with cellular events, that determine the macroscopic responses, can be observed with confocal or two-photon microscopy. To investigate disease processes, lung slices can either be prepared from animal models of disease or animals exposed to disease invoking conditions. Alternatively, the lung slices themselves can be experimentally manipulated. Because of the ability to observe changes in cell physiology and how these responses manifest themselves at the level of the organ, lung slices have become a standard tool for the investigation of lung disease.

Possible role of differential growth in airway wall remodeling in asthma

Airway remodeling in patients with chronic asthma is characterized by a thickening of the airway walls. It has been demonstrated in previous theoretical models that this change in thickness can have an important mechanical effect on the properties of the wall, in particular on the phenomenon of mucosal folding induced by smooth muscle contraction. In this paper, we present a model for mucosal folding of the airway in the context of growth. The airway is modeled as a bilayered cylindrical tube, with both geometric and material nonlinearities accounted for via the theory of finite elasticity. Growth is incorporated into the model through the theory of morphoelasticity. We explore a range of growth possibilities, allowing for anisotropic growth as well as different growth rates in each layer. Such nonuniform growth, referred to as differential growth, can change the properties of the material beyond geometrical changes through the generation of residual stresses. We demonstrate that differential growth can have a dramatic impact on mucosal folding, in particular on the critical pressure needed to induce folding, the buckling pattern, as well as airway narrowing. We conclude that growth may be an important component in airway remodeling.

Multiscale mathematical models of airway constriction and disease

Loss of lung function in airway disease frequently involves many complex phenomena and interconnected underlying causes. In many conditions, such as asthmatic airway hyper-responsiveness, hypothesised underlying causes span multiple spatial scales. In cases like this, it is insufficient to take a reductionist approach, wherein each subsystem (at a given spatial scale) is considered in isolation and then the whole is taken to be merely the sum of the parts; this is because there can be significant and important interactions and synergies between spatial scales. Experimentally this can manifest as, for example, significant differences between behaviour in isolated tissue and that seen in vivo, while from a modelling perspective, it necessitates multiscale modelling approaches. Because it is precisely in these complex environs that models have the greatest potential to improve understanding of underlying behaviours, these multiscale models are of particular importance. This paper reviews several examples of multiscale models from the most important models in the literature, with a particular emphasis on those concerned with airway hyper-responsiveness and airway constriction.

The bronchodilator response of in vivo specific airway compliance in adults with asthma

A new technique has been developed to determine in vivo airway compliance in humans that is specific to airway size and transpulmonary pressure, and can be represented as a three-dimensional surface. As yet, the ability of this technique to detect changes in specific airway compliance with disease status has not been demonstrated. The aim of this study was to assess whether this technique could determine changes in airway compliance which are thought to occur with altered smooth muscle tone in adults with asthma. Airway compliance was measured and displayed as a surface in adults with asthma before and after a reduction in smooth muscle tone by bronchodilator administration. Compliance, with respect to airway size, was calculated at three specific lung volumes; functional residual capacity (FRC), total lung capacity (TLC), and midway between FRC and TLC (MID). After bronchodilator, airway compliance increased at FRC and MID in the smaller airways (<3 mm). Furthermore, airway compliance under both conditions was greater in the smaller airways compared to the larger airways. In conclusion, our method may have future utility in assessing changes in airway compliance in respiratory diseases such as asthma.

Influence of airway wall stiffness and parenchymal tethering on the dynamics of bronchoconstriction

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.