Nonlinear compliance modulates dynamic bronchoconstriction in a multiscale airway model

A Quick Method to Assess Airway Distensibility in Mice

Airway distensibility is defined as the ease whereby airways are dilating in response to inflating lung pressure. If measured swiftly and accurately, airway distensibility would be a useful readout to parse the various elements contributing to airway wall stiffening, such as smooth muscle contraction, surface tension, and airway remodeling. The goal of the present study was to develop a method for measuring airway distensibility in mice. Lungs of BALB/c and C57BL/6 mice from either sex were subjected to stepwise changes in pressure. At each pressure step, an oscillometric perturbation was used to measure the impedance spectrum, on which the constant-phase model was fitted to deduce a surrogate for airway caliber called Newtonian conductance (GN). The change in GN over the change in pressure was subsequently used as an index of airway distensibility. An additional group of mice was infused with methacholine to confirm that smooth muscle contraction changes airway distensibility. GN increased with increasing steps in pressure, suggesting that the extent to which this occurs can be used as an index of airway distensibility. Airway distensibility was greater in BALB/c than C57BL/6 mice, and its variation by sex was mouse strain dependent, being greater in female than male in BALB/c mice with an inverse trend in C57BL/6 mice. Airway distensibility was also decreased by methacholine. This novel method swiftly measures airway distensibility in mice. Airway distensibility was also shown to vary with sex and mouse strain and to be sensitive to the contraction of smooth muscle.

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.

A multiscale sliding filament model of lymphatic muscle pumping

The lymphatics maintain fluid balance by returning interstitial fluid to veins via contraction/compression of vessel segments with check valves. Disruption of lymphatic pumping can result in a condition called lymphedema with interstitial fluid accumulation. Lymphedema treatments are often ineffective, which is partially attributable to insufficient understanding of specialized lymphatic muscle lining the vessels. This muscle exhibits cardiac-like phasic contractions and smooth muscle-like tonic contractions to generate and regulate flow. To understand the relationship between this sub-cellular contractile machinery and organ-level pumping, we have developed a multiscale computational model of phasic and tonic contractions in lymphatic muscle and coupled it to a lymphangion pumping model. Our model uses the sliding filament model (Huxley in Prog Biophys Biophys Chem 7:255-318, 1957) and its adaptation for smooth muscle (Mijailovich in Biophys J 79(5):2667-2681, 2000). Multiple structural arrangements of contractile components and viscoelastic elements were trialed but only one provided physiologic results. We then coupled this model with our previous lumped parameter model of the lymphangion to relate results to experiments. We show that the model produces similar pressure, diameter, and flow tracings to experiments on rat mesenteric lymphatics. This model provides the first estimates of lymphatic muscle contraction energetics and the ability to assess the potential effects of sub-cellular level phenomena such as calcium oscillations on lymphangion outflow. The maximum efficiency value predicted (40%) is at the upper end of estimates for other muscle types. Spontaneous calcium oscillations during diastole were found to increase outflow up to approximately 50% in the range of frequencies and amplitudes tested.

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.

Generalized distribution-moment approximation for kinetic theories of muscular contraction

Crossbridge theory, originally developed by A.F. Huxley more than 60 years ago to explain the behaviour of striated muscle, has since evolved to encompass many different muscle types and behaviours. The governing equations are generally linear hyperbolic partial differential equations, or systems thereof, describing the evolution of probability density functions. Importantly, the macroscopic behaviour is often described not in terms of these distributions themselves, but rather in terms of their first few moments. Motivated by this observation, G.I. Zahalak proposed the distribution-moment approximation to describe the evolution of these moments alone. That work assumed a Gaussian underlying distribution, and was observed to provide reasonable approximation of the moments despite the non-Gaussian character of the underlying distribution. Here we propose two variations on the distribution-moment approximation: (i) a generalized N-moment approximation based on the Gram-Charlier A-series representation, and (ii) perhaps the simplest possible approximation based on a uniform distribution. Study of these variations suggests that Zahalak's original contention may be correct: approximations based on higher order moments may not be worth their complexity. However, the simplified variation shows more promise, with similar accuracy in approximating the moments yet reduced complexity in the derivation of the approximation.

Airway smooth muscle adapting in dynamic conditions is refractory to the bronchodilator effect of a deep inspiration

Airway smooth muscle (ASM) is continuously strained during breathing at tidal volume. Whether this tidal strain influences the magnitude of the bronchodilator response to a deep inspiration (DI) is not clearly defined. The present in vitro study examines the effect of tidal strain on the bronchodilator effect of DIs. ASM strips from sheep tracheas were mounted in organ baths and then subjected to stretches (30% strain), simulating DIs at varying time intervals. In between simulated DIs, the strips were either held at a fixed length (isometric) or oscillated continuously by 6% (length oscillations) to simulate tidal strain. The contractile state of the strips was also controlled by adding either methacholine or isoproterenol to activate or relax ASM, respectively. Although the time-dependent gain in force caused by methacholine was attenuated by length oscillations, part of the acquired force in the oscillating condition was preserved postsimulated DIs, which was not the case in the isometric condition. Consequently, the bronchodilator effect of simulated DIs (i.e., the decline in force postsimulated versus presimulated DIs) was attenuated in oscillating versus isometric conditions. These findings suggest that an ASM operating in a dynamic environment acquired adaptations that make it refractory to the decline in contractility inflicted by a larger strain simulating a DI.

Shortening of airway smooth muscle is modulated by prolonging the time without simulated deep inspirations in ovine tracheal strips

The shortening of airway smooth muscle (ASM) is greatly affected by time. This is because stimuli affecting ASM shortening, such as bronchoactive molecules or the strain inflicted by breathing maneuvers, not only alter quick biochemical processes regulating contraction but also slower processes that allow ASM to adapt to an ever-changing length. Little attention has been given to the effect of time on ASM shortening. The present study investigates the effect of changing the time interval between simulated deep inspirations (DIs) on ASM shortening and its responsiveness to simulated DIs. Excised tracheal strips from sheep were mounted in organ baths and either activated with methacholine or relaxed with isoproterenol. They were then subjected to simulated DIs by imposing swings in distending stress, emulating a transmural pressure from 5 to 30 cmH₂O. The simulated DIs were intercalated by 2, 5, 10, or 30 min. In between simulated DIs, the distending stress was either fixed or oscillating to simulate tidal breathing. The results show that although shortening was increased by prolonging the interval between simulated DIs, the bronchodilator effect of simulated DIs (i.e., the elongation of the strip post- vs. pre-DI) was not affected, and the rate of re-shortening post-simulated DIs was decreased. As the frequency with which DIs are taken increases upon bronchoconstriction, our results may be relevant to typical alterations observed in asthma, such as an increased rate of re-narrowing post-DI.NEW & NOTEWORTHY The frequency with which patients with asthma take deep inspirations (DIs) increases during bronchoconstriction. This in vitro study investigated the effect of changing the time interval between simulated DIs on airway smooth muscle shortening. The results demonstrated that decreasing the interval between simulated DIs not only decreases shortening, which may be protective against excessive airway narrowing, but also increases the rate of re-shortening post-simulated DIs, which may contribute to the increased rate of re-narrowing post-DI observed 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.

Extracellular matrix stiffness regulates human airway smooth muscle contraction by altering the cell-cell coupling

For an airway or a blood vessel to narrow, there must be a connected path that links the smooth muscle (SM) cells with each other, and transmits forces around the organ, causing it to constrict. Currently, we know very little about the mechanisms that regulate force transmission pathways in a multicellular SM ensemble. Here, we used extracellular matrix (ECM) micropatterning to study force transmission in a two-cell ensemble of SM cells. Using the two-SM cell ensemble, we demonstrate (a) that ECM stiffness acts as a switch that regulates whether SM force is transmitted through the ECM or through cell-cell connections. (b) Fluorescent imaging for adherens junctions and focal adhesions show the progressive loss of cell-cell borders and the appearance of focal adhesions with the increase in ECM stiffness (confirming our mechanical measurements). (c) At the same ECM stiffness, we show that the presence of a cell-cell border substantially decreases the overall contractility of the SM cell ensemble. Our results demonstrate that connectivity among SM cells is a critical factor to consider in the development of diseases such as asthma and hypertension.

Effect of Loading History on Airway Smooth Muscle Cell-Matrix Adhesions

Integrin-mediated adhesions between airway smooth muscle (ASM) cells and the extracellular matrix (ECM) regulate how contractile forces generated within the cell are transmitted to its external environment. Environmental cues are known to influence the formation, size, and survival of cell-matrix adhesions, but it is not yet known how they are affected by dynamic fluctuations associated with tidal breathing in the intact airway. Here, we develop two closely related theoretical models to study adhesion dynamics in response to oscillatory loading of the ECM, representing the dynamic environment of ASM cells in vivo. Using a discrete stochastic-elastic model, we simulate individual integrin binding and rupture events and observe two stable regimes in which either bond formation or bond rupture dominate, depending on the amplitude of the oscillatory loading. These regimes have either a high or low fraction of persistent adhesions, which could affect the level of strain transmission between contracted ASM cells and the airway tissue. For intermediate loading, we observe a region of bistability and hysteresis due to shared loading between existing bonds; the level of adhesion depends on the loading history. These findings are replicated in a related continuum model, which we use to investigate the effect of perturbations mimicking deep inspirations (DIs). Because of the bistability, a DI applied to the high adhesion state could either induce a permanent switch to a lower adhesion state or allow a return of the system to the high adhesion state. Transitions between states are further influenced by the frequency of oscillations, cytoskeletal or ECM stiffnesses, and binding affinities, which modify the magnitudes of the stable adhesion states as well as the region of bistability. These findings could explain (in part) the transient bronchodilatory effect of a DI observed in asthmatics compared to a more sustained effect in normal subjects.

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

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

The Strain on Airway Smooth Muscle During a Deep Inspiration to Total Lung Capacity

The deep inspiration (DI) maneuver entices a great deal of interest because of its ability to temporarily ease the flow of air into the lungs. This salutary effect of a DI is proposed to be mediated, at least partially, by momentarily increasing the operating length of airway smooth muscle (ASM). Concerningly, this premise is largely derived from a growing body of in vitro studies investigating the effect of stretching ASM by different magnitudes on its contractility. The relevance of these in vitro findings remains uncertain, as the real range of strains ASM undergoes in vivo during a DI is somewhat elusive. In order to understand the regulation of ASM contractility by a DI and to infer on its putative contribution to the bronchodilator effect of a DI, it is imperative that in vitro studies incorporate levels of strains that are physiologically relevant. This review summarizes the methods that may be used in vivo in humans to estimate the strain experienced by ASM during a DI from functional residual capacity (FRC) to total lung capacity (TLC). The strengths and limitations of each method, as well as the potential confounders, are also discussed. A rough estimated range of ASM strains is provided for the purpose of guiding future in vitro studies that aim at quantifying the regulatory effect of DI on ASM contractility. However, it is emphasized that, owing to the many limitations and confounders, more studies will be needed to reach conclusive statements.

Small airway hyperresponsiveness in COPD: relationship between structure and function in lung slices

The direct relationship between pulmonary structural changes and airway hyperresponsiveness (AHR) in chronic obstructive pulmonary disease (COPD) is unclear. We investigated AHR in relation to airway and parenchymal structural changes in a guinea pig model of COPD and in COPD patients. Precision-cut lung slices (PCLS) were prepared from guinea pigs challenged with lipopolysaccharide or saline two times weekly for 12 wk. Peripheral PCLS were obtained from patients with mild to moderate COPD and non-COPD controls. AHR to methacholine was measured in large and small airways using video-assisted microscopy. Airway smooth muscle mass and alveolar airspace size were determined in the same slices. A mathematical model was used to identify potential changes in biomechanical properties underlying AHR. In guinea pigs, lipopolysaccharide increased the sensitivity of large (>150 μm) airways toward methacholine by 4.4-fold and the maximal constriction of small airways (<150 μm) by 1.5-fold. Similarly increased small airway responsiveness was found in COPD patients. In both lipopolysaccharide-challenged guinea pigs and patients, airway smooth muscle mass was unaltered, whereas increased alveolar airspace correlated with small airway hyperresponsiveness in guinea pigs. Fitting the parameters of the model indicated that COPD weakens matrix mechanical properties and enhances stiffness differences between the airway and the parenchyma, in both species. In conclusion, this study demonstrates small airway hyperresponsiveness in PCLS from COPD patients. These changes may be related to reduced parenchymal retraction forces and biomechanical changes in the airway wall. PCLS from lipopolysaccharide-exposed guinea pigs may be useful to study mechanisms of small airway hyperresponsiveness in COPD.

Interval between simulated deep inspirations on the dynamics of airway smooth muscle contraction in guinea pig bronchi

A certain amount of time is required to achieve a maximal contraction from airway smooth muscle (ASM) and stretches of substantial magnitude, such as the ones imparted by deep inspirations (DIs), interfere with contraction. The duration of ASM contraction without interference may thus affect its shortening, its mechanical response to DIs and the overall toll it exerts on the respiratory system. In this study, the effect of changing the interval between DIs on the dynamics of ASM was examined in vitro. Isolated bronchi derived from guinea pigs were held isotonically and stimulated to both contract and relax, in a randomized order, in response to 10^-5 M of methacholine and 10^-6 M of isoproterenol, respectively. Interference to ASM was inflicted after 2, 5, 10 and 30 min in a randomized order, by imposing a stretch that simulated a DI. The shortening before the stretch, the stiffness before and during the stretch, the post-stretch elongation of ASM and the ensuing re-shortening were measured. These experiments were also performed in the presence of simulated tidal breathing achieved through force fluctuations. The results demonstrate that, with or without force fluctuations, increasing the interval between simulated DIs increased shortening and post-stretch elongation, but not stiffness and re-shortening. These time-dependent effects were not observed when ASM was held in the relaxed state. These findings may help understand to which extent ASM shortening and the regulatory effect of DI are affected by changing the interval between DIs. The potential consequences of these findings on airway narrowing are also discussed.

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.

A Distribution-Moment Approximation for Coupled Dynamics of the Airway Wall and Airway Smooth Muscle

Asthma is fundamentally a disease of airway constriction. Due to a variety of experimental challenges, the dynamics of airways are poorly understood. Of specific interest is the narrowing of the airway due to forces produced by the airway smooth muscle wrapped around each airway. The interaction between the muscle and the airway wall is crucial for the airway constriction that occurs during an asthma attack. Although cross-bridge theory is a well-studied representation of complex smooth muscle dynamics, and these dynamics can be coupled to the airway wall, this comes at significant computational cost-even for isolated airways. Because many phenomena of interest in pulmonary physiology cannot be adequately understood by studying isolated airways, this presents a significant limitation. We present a distribution-moment approximation of this coupled system and study the validity of the approximation throughout the physiological range. We show that the distribution-moment approximation is valid in most conditions, and we explore the region of breakdown. These results show that in many situations, the distribution-moment approximation is a viable option that provides an orders-of-magnitude reduction in computational complexity; not only is this valuable for isolated airway studies, but it moreover offers the prospect that rich ASM dynamics might be incorporated into interacting airway models where previously this was precluded by computational cost.

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.

An in vitro study examining the duration between deep inspirations on the rate of renarrowing

The factors altering the bronchodilatory response to a deep inspiration (DI) in asthma are important to decipher. In this in vitro study, we investigated the effect of changing the duration between DIs on the rate of force recovery post-DI in guinea pig bronchi. The airway smooth muscle (ASM) within the main bronchi were submitted to length oscillation that simulated tidal breathing in different contractile states during 2, 5, 10 or 30min prior to a larger length excursion that simulated a DI. The contractile states of ASM were determined by adding either methacholine or isoproterenol. Irrespective of the contractile state, the duration between DIs neither affected the measured force during length oscillation nor the bronchodilator effect of DI. Contrastingly, the rate of force recovery post-DI in contracted state increased as the duration between DIs decreased. Similar results were obtained with contracted parenchymal strips. These findings suggest that changing the duration between DIs may alter the rate of ASM force recovery post-DI and thereby affect the rate of renarrowing and the duration of the respiratory relief afforded by DI.

Multiscale modeling methods in biomechanics

More and more frequently, computational biomechanics deals with problems where the portion of physical reality to be modeled spans over such a large range of spatial and temporal dimensions, that it is impossible to represent it as a single space-time continuum. We are forced to consider multiple space-time continua, each representing the phenomenon of interest at a characteristic space-time scale. Multiscale models describe a complex process across multiple scales, and account for how quantities transform as we move from one scale to another. This review offers a set of definitions for this emerging field, and provides a brief summary of the most recent developments on multiscale modeling in biomechanics. Of all possible perspectives, we chose that of the modeling intent, which vastly affect the nature and the structure of each research activity. To the purpose we organized all papers reviewed in three categories: 'causal confirmation,' where multiscale models are used as materializations of the causation theories; 'predictive accuracy,' where multiscale modeling is aimed to improve the predictive accuracy; and 'determination of effect,' where multiscale modeling is used to model how a change at one scale manifests in an effect at another radically different space-time scale. Consistent with how the volume of computational biomechanics research is distributed across application targets, we extensively reviewed papers targeting the musculoskeletal and the cardiovascular systems, and covered only a few exemplary papers targeting other organ systems. The review shows a research subdomain still in its infancy, where causal confirmation papers remain the most common. WIREs Syst Biol Med 2017, 9:e1375. doi: 10.1002/wsbm.1375 For further resources related to this article, please visit the WIREs website.

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.

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.

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.

Airway compliance and dynamics explain the apparent discrepancy in length adaptation between intact airways and smooth muscle strips

Length adaptation is a phenomenon observed in airway smooth muscle (ASM) wherein over time there is a shift in the length-tension curve. There is potential for length adaptation to play an important role in airway constriction and airway hyper-responsiveness in asthma. Recent results by Ansell et al., 2015 (JAP 2014 10.1152/japplphysiol.00724.2014) have cast doubt on this role by testing for length adaptation using an intact airway preparation, rather than strips of ASM. Using this technique they found no evidence for length adaptation in intact airways. Here we attempt to resolve this apparent discrepancy by constructing a minimal mathematical model of the intact airway, including ASM which follows the classic length-tension curve and undergoes length adaptation. This allows us to show that (1) no evidence of length adaptation should be expected in large, cartilaginous, intact airways; (2) even in highly compliant peripheral airways, or at more compliant regions of the pressure-volume curve of large airways, the effect of length adaptation would be modest and at best marginally detectable in intact airways; (3) the key parameters which control the appearance of length adaptation in intact airways are airway compliance and the relaxation timescale. The results of this mathematical simulation suggest that length adaptation observed at the level of the isolated ASM may not clearly manifest in the normal intact airway.

Can breathing-like pressure oscillations reverse or prevent narrowing of small intact airways?

Periodic length fluctuations of airway smooth muscle during breathing are thought to modulate airway responsiveness in vivo. Recent animal and human intact airway studies have shown that pressure fluctuations simulating breathing can only marginally reverse airway narrowing and are ineffective at protecting against future narrowing. However, these previous studies were performed on relatively large (>5 mm diameter) airways, which are inherently stiffer than smaller airways for which a preponderance of airway constriction in asthma likely occurs. The goal of this study was to determine the effectiveness of breathing-like transmural pressure oscillations to reverse induced narrowing and/or protect against future narrowing of smaller, more compliant intact airways. We constricted smaller (luminal diameter = 2.92 ± 0.29 mm) intact airway segments twice with ACh (10(-6) M), once while applying tidal-like pressure oscillations (5-15 cmH2O) before, during, and after inducing constriction (Pre + Post) and again while only imposing the tidal-like pressure oscillation after induced constriction (Post Only). Smaller airways were 128% more compliant than previously studied larger airways. This increased compliance translated into 196% more strain and 76% greater recovery (41 vs. 23%) because of tidal-like pressure oscillations. Larger pressure oscillations (5-25 cmH2O) caused more recovery (77.5 ± 16.5%). However, pressure oscillations applied before and during constriction resulted in the same steady-state diameter as when pressure oscillations were only applied after constriction. These data show that reduced straining of the airways before a challenge likely does not contribute to the emergence of airway hyperreactivity observed in asthma but may serve to sustain a given level of constriction.