Transient oscillatory force-length behavior of activated airway smooth muscle

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.

Use of human airway smooth muscle in vitro and ex vivo to investigate drugs for the treatment of chronic obstructive respiratory disorders

Isolated airway smooth muscle has been extensively investigated since 1840 to understand the pharmacology of airway diseases. There has often been poor predictability from murine experiments to drugs evaluated in patients with asthma or chronic obstructive pulmonary disease (COPD). However, the use of isolated human airways represents a sensible strategy to optimise the development of innovative molecules for the treatment of respiratory diseases. This review aims to provide updated evidence on the current uses of isolated human airways in validated in vitro methods to investigate drugs in development for the treatment of chronic obstructive respiratory disorders. This review also provides historical notes on the pioneering pharmacological research on isolated human airway tissues, the key differences between human and animal airways, as well as the pivotal differences between human medium bronchi and small airways. Experiments carried out with isolated human bronchial tissues in vitro and ex vivo replicate many of the main anatomical, pathophysiological, mechanical and immunological characteristics of patients with asthma or COPD. In vitro models of asthma and COPD using isolated human airways can provide information that is directly translatable into humans with obstructive lung diseases. Regardless of the technique used to investigate drugs for the treatment of chronic obstructive respiratory disorders (i.e., isolated organ bath systems, videomicroscopy and wire myography), the most limiting factors to produce high-quality and repeatable data remain closely tied to the manual skills of the researcher conducting experiments and the availability of suitable tissue.

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.

Respiratory effects caused by exposure to diesel exhaust particles during moderate exercise: a murine model

Aerobic exercise is an increasing trend worldwide. However, people are increasingly exercising outdoors, alongside roadways where heavy vehicles release diesel exhaust. We analyzed respiratory effects caused by inhaled diesel particulate emitted by vehicles adhering to Brazilian legislation, PROCONVE Phase P7 (equivalent to EURO 5), as well the effects of exposure during moderate-intensity aerobic exercise. Male C57BL/6 mice were divided into four groups for a 4-wk treadmill protocol: CE (n = 8) received intranasal sterile physiological saline and then performed moderate-intensity exercise (control), CS (n = 10) received saline and then remained stationary on the treadmill (control), DS (n = 9) received intranasal diesel exhaust particles and then remained stationary, and DE (n = 10) was exposed to diesel exhaust and then exercised at moderate intensity. Mice were subsequently connected to a mechanical ventilator (SCIREQ flexiVent, Canada) to analyze the following respiratory mechanics parameters: tissue resistance, elastance, inspiratory capacity, static compliance, Newtonian resistance, and pressure-volume loop area. After euthanasia, peripheral pulmonary tissue strips were extracted and subjected to force-length tests to evaluate parenchymal elastic and mechanical properties, using oscillations applied by a computer-controlled force transducer system; parameters obtained were tissue resistance, elastance, and hysteresivity. DS displayed impaired respiratory mechanics for all parameters, in comparison with CS. DE exhibited significantly reduced inspiratory capacity and static compliance, and increased Newtonian resistance when compared with CE. Exposure to diesel exhaust, both during exercise and rest, still exerts harmful pulmonary effects, even at current legislation limits. These results justify further changes in environmental standards, to reduce the health risks caused by traffic-related pollution.NEW & NOTEWORTHY Exercise, while beneficial, is often performed in areas of greater inhaled particulates. Here we show this effect using mice exposed to controlled diesel particle inhalation and moderate aerobic exercise. Diesel particle inhalation, without or with exercise, worsened both respiratory mechanical properties associated with changes in lung tissue mechanics and morphometry.

Flexibility of microstructural adaptations in airway smooth muscle

The airway smooth muscle undergoes an elastic transition during a sustained contraction, characterized by a gradual decrease in hysteresivity caused by a relatively greater rate of increase in elastance than resistance. We recently demonstrated that these mechanical changes are more likely to persist after a large strain when they are acquired in dynamic versus static conditions; as if the microstructural adaptations liable for the elastic transition are more flexible when they evolve in dynamic conditions. The extent of this flexibility is undefined. Herein, contracted ovine tracheal smooth muscle strips were kept in dynamic conditions simulating tidal breathing (sinusoidal length oscillations at 5% amplitude) and then subjected to simulated deep inspirations (DI). Each DI was straining the muscle by either 10%, 20%, or 30% and was imposed at either 2, 5, 10, or 30 min after the preceding DI. The goal was to assess whether and the extent by which the time-dependent decrease in hysteresivity is preserved following the DI. The results show that the time-dependent decrease in hysteresivity seen pre-DI was preserved after a strain of 10%, but not after a strain of 20% or 30%. This suggests that the microstructural adaptations liable for the elastic transition withstood a strain at least twofold greater than the oscillating strain that pertained during their evolution (10% vs. 5%). We propose that a muscle adapting in dynamic conditions forges microstructures exhibiting a substantial degree of flexibility.NEW & NOTEWORTHY This study confirms that airway smooth muscle undergoes an elastic transition during a sustained contraction even when it operates in dynamic conditions simulating breathing at tidal volume. It also demonstrates that the microstructural adaptations liable for this elastic transition withstand a strain that is at least twice as large as the oscillating strain that pertains during their evolution. This degree of flexibility might be an asset with major significant impact for a tissue such as the airway smooth muscle that displays an everchanging shape due to breathing.

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.

Intrapulmonary airway smooth muscle is hyperreactive with a distinct proteome in asthma

Constriction of airways during asthmatic exacerbation is the result of airway smooth muscle (ASM) contraction. Although it is generally accepted that ASM is hypercontractile in asthma, this has not been unambiguously demonstrated. Whether airway hyperresponsiveness (AHR) is the result of increased ASM mass alone or also increased contractile force generation per unit of muscle directly determines the potential avenues for treatment.To assess whether ASM is hypercontractile we performed a series of mechanics measurements on isolated ASM from intrapulmonary airways and trachealis from human lungs. We analysed the ASM and whole airway proteomes to verify if proteomic shifts contribute to changes in ASM properties.We report an increase in isolated ASM contractile stress and stiffness specific to asthmatic human intrapulmonary bronchi, the site of increased airway resistance in asthma. Other contractile parameters were not altered. Principal component analysis (PCA) of unbiased mass spectrometry data showed clear clustering of asthmatic subjects with respect to ASM specific proteins. The whole airway proteome showed upregulation of structural proteins. We did not find any evidence for a difference in the regulation of myosin activity in the asthmatic ASM.In conclusion, we showed that ASM is indeed hyperreactive at the level of intrapulmonary airways in asthma. We identified several proteins that are upregulated in asthma that could contribute to hyperreactivity. Our data also suggest enhanced force transmission associated with enrichment of structural proteins in the whole airway. These findings may lead to novel directions for treatment development in asthma.

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.

Mitigation of airways responsiveness by deep inflation of the lung

Stretching activated strips of airway smooth muscle (ASM) significantly affects both active force and stiffness due to a temporary reduction of the proportion of cycling myosin cross bridges that are bound to their actin binding sites. For the same reason, stretch applied to ASM in situ by a deep inflation (DI) of the lungs is one of the most potent means of reversing bronchoconstriction. When the DI is sufficiently large, however, and is applied while bronchoconstriction is in the process of developing, the subsequent depression in airway resistance is more persistent than can be attributed simply to temporary detachment of ASM cross bridges. In the present study, we use a computational model to demonstrate that this DI-induced ablation of airway responsiveness can be explained by a dose-dependent reduction in the number of cross bridges available to bind to actin when the ASM in the airway wall is stretched above a critical threshold strain and that this disruption of the contractile apparatus recovers over an order of magnitude longer time scale than that of the simple reattachment of unbound cross bridges. NEW & NOTEWORTHY The mechanisms by which deep inflation of the lung reverse bronchoconstriction and affect subsequent airway responsiveness have important potential implications for asthma, yet remain controversial. This study uses computational modeling to posit a mechanism by which sufficiently vigorous inflations applied during active bronchoconstriction not only transiently reverse bronchoconstriction, but also reduce subsequent airways responsiveness for a period of time. Fitting the model to published data in mice supports this notion.

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.

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.

A biomechanical model for fluidization of cells under dynamic strain

Recent experiments have investigated the response of smooth muscle cells to transient stretch-compress (SC) and compress-stretch (CS) maneuvers. The results indicate that the transient SC maneuver causes a sudden fluidization of the cell while the CS maneuver does not. To understand this asymmetric behavior, we have built a biomechanical model to probe the response of stress fibers to the two maneuvers. The model couples the cross-bridge cycle of myosin motors with a viscoelastic Kelvin-Voigt element that represents the stress fiber. Simulation results point to the sensitivity of the myosin detachment rate to tension as the cause for the asymmetric response of the stress fiber to the CS and SC maneuvers. For the SC maneuver, the initial stretch increases the tension in the stress fiber and suppresses myosin detachment. The subsequent compression then causes a large proportion of the myosin population to disengage rapidly from actin filaments. This leads to the disassembly of the stress fibers and the observed fluidization. In contrast, the CS maneuver only produces a mild loss of myosin motors and no fluidization.

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.

Modeling the impairment of airway smooth muscle force by stretch

Imposed length changes of only a small percent produce transient reductions in active force in strips of airway smooth muscle (ASM) due to the temporary detachment of bound cross-bridges caused by the relative motion of the actin and myosin fibers. More dramatic and sustained reductions in active force occur following large changes in length. The Huxley two-state model of skeletal muscle originally proposed in 1957 and later adapted to include a four-state description of cross-bridge kinetics has been widely used to model the former phenomenon, but is unable to account for the latter unless modified to include mechanisms by which the contractile machinery in the ASM cell becomes appropriately rearranged. Even so, the Huxley model itself is based on the assumption that the contractile proteins are all aligned precisely in the direction of bulk force generation, which is not true for ASM. The present study derives a coarse-grained version of the Huxley model that is free of inherent assumptions about cross-bridge orientation. This simplified model recapitulates the key features observed in the force-length behavior of activated strips of ASM and, in addition, provides a mechanistically based way of accounting for the sustained force reductions that occur following large stretch.

MATHEMATICAL MODELING OF VENTILATION DEFECTS IN ASTHMA

Airway narrowing by smooth muscle constriction is a hallmark of asthma attacks that may cause severe difficulties of breathing. However, the causes of asthma and the underlying mechanisms are not fully understood. Bronchoconstriction within a bronchial tree involves complex interactions among the airways that lead to the emergence of regions of poor ventilation (ventilation defects, VDefs) in the lungs. The emphasis of this review is on mathematical modeling of the mechanisms involved in bronchoconstriction and the emergence of the complex airway behavior that leads to VDefs. Additionally, the review discusses characteristic model behaviors and experimental data to demonstrate advances and limitations of different 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.

Modelling airway smooth muscle passive length adaptation via thick filament length distributions

We present a new model of airway smooth muscle (ASM), which surrounds and constricts every airway in the lung and thus plays a central role in the airway constriction associated with asthma. This new model of ASM is based on an extension of sliding filament/crossbridge theory, which explicitly incorporates the length distribution of thick sliding filaments to account for a phenomenon known as dynamic passive length adaptation; the model exhibits good agreement with experimental data for ASM force-length behaviour across multiple scales. Principally these are (nonlinear) force-length loops at short timescales (seconds), parabolic force-length curves at medium timescales (minutes) and length adaptation at longer timescales. This represents a significant improvement on the widely-used crossbridge models which work so well in or near the isometric regime, and may have significant implications for studies which rely on crossbridge or other dynamic airway smooth muscle models, and thus both airway and lung dynamics.

A progressive rupture model of soft tissue stress relaxation

A striking feature of stress relaxation in biological soft tissue is that it frequently follows a power law in time with an exponent that is independent of strain even when the elastic properties of the tissue are highly nonlinear. This kind of behavior is an example of quasi-linear viscoelasticity, and is usually modeled in a purely empirical fashion. The goal of the present study was to account for quasi-linear viscoelasticity in mechanistic terms based on our previously developed hypothesis that it arises as a result of isolated micro-yield events occurring in sequence throughout the tissue, each event passing the stress it was sustaining on to other regions of the tissue until they themselves yield. We modeled stress relaxation computationally in a collection of stress-bearing elements. Each element experiences a stochastic sequence of either increases in elastic equilibrium length or decreases in stiffness according to the stress imposed upon it. This successfully predicts quasi-linear viscoelastic behavior, and in addition predicts power-law stress relaxation that proceeds at the same slow rate as observed in real biological soft tissue.

The importance of synergy between deep inspirations and fluidization in reversing airway closure

Deep inspirations (DIs) and airway smooth muscle fluidization are two widely studied phenomena in asthma research, particularly for their ability (or inability) to counteract severe airway constriction. For example, DIs have been shown effectively to reverse airway constriction in normal subjects, but this is impaired in asthmatics. Fluidization is a connected phenomenon, wherein the ability of airway smooth muscle (ASM, which surrounds and constricts the airways) to exert force is decreased by applied strain. A maneuver which sufficiently strains the ASM, then, such as a DI, is thought to reduce the force generating capacity of the muscle via fluidization and hence reverse or prevent airway constriction. Understanding these two phenomena is considered key to understanding the pathophysiology of asthma and airway hyper-responsiveness, and while both have been extensively studied, the mechanism by which DIs fail in asthmatics remains elusive. Here we show for the first time the synergistic interaction between DIs and fluidization which allows the combination to provide near complete reversal of airway closure where neither is effective alone. This relies not just on the traditional model of airway bistability between open and closed states, but also the critical addition of previously-unknown oscillatory and chaotic dynamics. It also allows us to explore the types of subtle change which can cause this interaction to fail, and thus could provide the missing link to explain DI failure in asthmatics.

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.

A multi-scale approach to airway hyperresponsiveness: from molecule to organ

Airway hyperresponsiveness (AHR), a characteristic of asthma that involves an excessive reduction in airway caliber, is a complex mechanism reflecting multiple processes that manifest over a large range of length and time scales. At one extreme, molecular interactions determine the force generated by airway smooth muscle (ASM). At the other, the spatially distributed constriction of the branching airways leads to breathing difficulties. Similarly, asthma therapies act at the molecular scale while clinical outcomes are determined by lung function. These extremes are linked by events operating over intermediate scales of length and time. Thus, AHR is an emergent phenomenon that limits our understanding of asthma and confounds the interpretation of studies that address physiological mechanisms over a limited range of scales. A solution is a modular computational model that integrates experimental and mathematical data from multiple scales. This includes, at the molecular scale, kinetics, and force production of actin-myosin contractile proteins during cross-bridge and latch-state cycling; at the cellular scale, Ca²⁺ signaling mechanisms that regulate ASM force production; at the tissue scale, forces acting between contracting ASM and opposing viscoelastic tissue that determine airway narrowing; at the organ scale, the topographic distribution of ASM contraction dynamics that determine mechanical impedance of the lung. At each scale, models are constructed with iterations between theory and experimentation to identify the parameters that link adjacent scales. This modular model establishes algorithms for modeling over a wide range of scales and provides a framework for the inclusion of other responses such as inflammation or therapeutic regimes. The goal is to develop this lung model so that it can make predictions about bronchoconstriction and identify the pathophysiologic mechanisms having the greatest impact on AHR and its therapy.

The dynamic face of respiratory research: understanding the effect of airway disease on a lung in constant motion

The lungs are in a constant state of motion. The dynamic nature of tidal breathing, whereby cycles of pressure changes across the lungs cause the chest wall, lung tissue and airways to repeatedly expand and contract, ventilates the lung tissue and allows respiration to occur. However, these regular cycles of tidal inspirations and expirations are punctuated by breaths of differing volumes, most particularly periodic deep inspirations. In normal, healthy subjects, these deep inspirations have a dual effect in reducing airway responsiveness. Firstly, deep inspirations taken under baseline conditions protect the airways against subsequent bronchoconstriction, termed DI bronchoprotection. Secondly, deep inspirations are able to dramatically reverse bronchoconstriction. The ability for deep inspirations to reverse bronchoconstriction appears to be due to both the ability to dilate the airways with a full inspiration to total lung capacity (TLC) and the rate at which the airways re-narrow once tidal breathing is resumed. Deep inspiration reversal is reduced in subjects with asthma and is due both to a reduced ability to dilate the airways as well as an increase in the rate of re-narrowing. On the other hand, DI bronchoprotection is completely absent in asthma. Although the mechanisms behind these abnormalities remain unclear, the inability for deep inspirations to both protect against and fully reverse bronchoconstriction in patients with asthma appears critical in the development of airway hyperresponsiveness. As such, determining the pathophysiology responsible for the malfunction of deep inspirations in asthma remains critical to understanding the disease and is likely to pave the way for novel therapeutic targets.

Multi-scale lung modeling

Multi-scale modeling of biological systems has recently become fashionable due to the growing power of digital computers as well as to the growing realization that integrative systems behavior is as important to life as is the genome. While it is true that the behavior of a living organism must ultimately be traceable to all its components and their myriad interactions, attempting to codify this in its entirety in a model misses the insights gained from understanding how collections of system components at one level of scale conspire to produce qualitatively different behavior at higher levels. The essence of multi-scale modeling thus lies not in the inclusion of every conceivable biological detail, but rather in the judicious selection of emergent phenomena appropriate to the level of scale being modeled. These principles are exemplified in recent computational models of the lung. Airways responsiveness, for example, is an organ-level manifestation of events that begin at the molecular level within airway smooth muscle cells, yet it is not necessary to invoke all these molecular events to accurately describe the contraction dynamics of a cell, nor is it necessary to invoke all phenomena observable at the level of the cell to account for the changes in overall lung function that occur following methacholine challenge. Similarly, the regulation of pulmonary vascular tone has complex origins within the individual smooth muscle cells that line the blood vessels but, again, many of the fine details of cell behavior average out at the level of the organ to produce an effect on pulmonary vascular pressure that can be described in much simpler terms. The art of multi-scale lung modeling thus reduces not to being limitlessly inclusive, but rather to knowing what biological details to leave out.

Could an increase in airway smooth muscle shortening velocity cause airway hyperresponsiveness?

Airway hyperresponsiveness (AHR) is a characteristic feature of asthma. It has been proposed that an increase in the shortening velocity of airway smooth muscle (ASM) could contribute to AHR. To address this possibility, we tested whether an increase in the isotonic shortening velocity of ASM is associated with an increase in the rate and total amount of shortening when ASM is subjected to an oscillating load, as occurs during breathing. Experiments were performed in vitro using 27 rat tracheal ASM strips supramaximally stimulated with methacholine. Isotonic velocity at 20% isometric force (Fiso) was measured, and then the load on the muscle was varied sinusoidally (0.33 ± 0.25 Fiso, 1.2 Hz) for 20 min, while muscle length was measured. A large amplitude oscillation was applied every 4 min to simulate a deep breath. We found that: 1) ASM strips with a higher isotonic velocity shortened more quickly during the force oscillations, both initially (P < 0.001) and after the simulated deep breaths (P = 0.002); 2) ASM strips with a higher isotonic velocity exhibited a greater total shortening during the force oscillation protocol (P < 0.005); and 3) the effect of an increase in isotonic velocity was at least comparable in magnitude to the effect of a proportional increase in ASM force-generating capacity. A cross-bridge model showed that an increase in the total amount of shortening with increased isotonic velocity could be explained by a change in either the cycling rate of phosphorylated cross bridges or the rate of myosin light chain phosphorylation. We conclude that, if asthma involves an increase in ASM velocity, this could be an important factor in the associated AHR.

Remodeling of integrated contractile tissues and its dependence on strain-rate amplitude

Here we investigate the origin of relaxation times governing the mechanical response of an integrated contractile tissue to imposed cyclic changes of length. When strain-rate amplitude is held constant as frequency is varied, fast events are accounted for by actomyosin cross-bridge cycling, but slow events reveal relaxation processes associated with ongoing cytoskeletal length adaptation. Although both relaxation regimes are innately nonlinear, these regimes are unified and their positions along the frequency axis are set by the imposed strain-rate amplitude.

Modeling the dynamics of airway constriction: effects of agonist transport and binding

Recent advances have revealed that during exogenous airway challenge, airway diameters cannot be adequately predicted by their initial diameters. Furthermore, airway diameters can also vary greatly in time on scales shorter than a breath. To better understand these phenomena, we developed a multiscale model that allowed us to simulate aerosol challenge in the airways during ventilation. The model incorporates agonist-receptor binding kinetics to govern the temporal response of airway smooth muscle contraction on individual airway segments, which, together with airway wall mechanics, determines local airway caliber. Global agonist transport and deposition are coupled with pressure-driven flow, linking local airway constrictions with global flow dynamics. During the course of challenge, airway constriction alters the flow pattern, redistributing the agonist to less constricted regions. This results in a negative feedback that may be a protective property of the normal lung. As a consequence, repetitive challenge can cause spatial constriction patterns to evolve in time, resulting in a loss of predictability of airway diameters. Additionally, the model offers new insights into several phenomena including the intra- and interbreath dynamics of airway constriction throughout the tree structure.

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.

History dependence of vital capacity in constricted lungs

Measurements of dynamic force-length behavior of maximally activated strips of smooth muscle during oscillatory length changes show that force decreases well below the isometric force during the shortening phase of the oscillation. The magnitude of the decrease depends on the rate of shortening; for slower shortening, the decrease is smaller and force is larger. Modeling of expiratory flow, based on these data, predicts that vital capacity in constricted lungs depends on the rate of expiration. In maximally constricted lungs, forced vital capacity (FVC) is predicted to be 16% smaller than control, and vital capacity for a very slow expiration (SVC), 31% less than control. These predictions were tested by measuring FVC and SVC in constricted normal subjects. In the first group of 9 subjects, four maneuvers were made following the delivery of two doses of methacholine in the order: SVC, FVC, FVC, SVC. In a second group of 11 subjects, two maneuvers were performed at each dose in the order: FVC, SVC. At the highest dose of methacholine, FVC for both trials in group 1 and for the one trial in group 2 were all approximately 13% less than control, a slightly smaller decrease than predicted. SVC for the 1st trial in group 1 was 27% less than control, also slightly smaller than predicted. The difference between FVC and SVC for this trial, 13%, was close to the predicted difference of 15%. However, SVC for the 2nd trial in group 1 (preceded by 3 vital capacity maneuvers) and for group 2 (preceded by 1) were no different from FVC. We conclude that vital capacity in constricted lungs depends on the dynamic force-length properties of smooth muscle and that the history dependence of the dynamic properties of smooth muscle is more complicated than has been inferred from oscillatory force-length behavior.