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.

The role of contractile unit reorganization in force generation in airway smooth muscle

Airway smooth muscle (ASM) cells undergo remodelling and reside in a tissue structure that is subject to heterogenous stress distributions that change dynamically during the breathing cycle. In this paper, we develop a structural model of an ASM cell that consists of contractile units (actin and myosin filaments) in series and parallel, anchored to a nonlinearly elastic cytoskeleton. We mimic a typical experimental protocol that involves isometric force generation through triggering of the contractile machinery, followed by oscillatory length fluctuation of the cell. We use the model to predict the effect of a single instance of rearrangement of the contractile machinery, combined with strain-stiffening of the cytoskeleton, on the force generated by the sarcomeres, and the total force generated by the cell. By linking intra-cellular events to whole-cell behaviour, the model reveals mechanistic relationships between structural properties and cell-level force–length loops. We show how contractile force, shortening velocity and sarcomere operating lengths vary as the internal cell architecture is altered. Additionally, we show how interactions between the internal contractile machinery and cytoskeletal structure play a role in the regulation of force generation and hysteresis of the cell.

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

This paper presents a modelling framework in which the local stress environment of airway smooth muscle (ASM) cells may be predicted and cellular responses to local stress may be investigated. We consider an elastic axisymmetric model of a layer of connective tissue and circumferential ASM fibres embedded in parenchymal tissue and model the active contractile force generated by ASM via a stress acting along the fibres. A constitutive law is proposed that accounts for active and passive material properties as well as the proportion of muscle to connective tissue. The model predicts significantly different contractile responses depending on the proportion of muscle to connective tissue in the remodelled airway. We find that radial and hoop-stress distributions in remodelled muscle layers are highly heterogenous with distinct regions of compression and tension. Such patterns of stress are likely to have important implications, from a mechano-transduction perspective, on contractility, short-term cytoskeletal adaptation and long-term airway remodelling in asthma.

Theoretical Models for the Quantification of Lung Injury Using Ventilation and Perfusion Distributions

This paper describes two approaches to modelling lung disease: one based on a multi-compartment statistical model with a log normal distribution of ventilation perfusion ratio (V˙/Q˙) values; and the other on a bifurcating tree which emulates the anatomical structure of the lung. In the statistical model, the distribution becomes bimodal, when theV˙/Q˙values of a randomly selected number of compartments are reduced by 85% to simulate lung disease. For the bifurcating tree model a difference in flow to the left and right branches coupled with a small random variation in flow ratio between generations results in a log normal distribution of flows in the terminal branches. Restricting flow through branches within the tree to simulate lung disease transforms this log normal distribution to a bi-modal one. These results are compatible with those obtained from experiments using the multiple inert gas elimination technique, where log normal distributions ofV˙/Q˙ratio become bimodal in the presence of lung disease.

Quantification of lung injury using ventilation and perfusion distributions obtained from gamma scintigraphy

This paper explores the potential of isotope V/Q lung scans to quantify lung disease. Areas of restricted perfusion in subjects with a pulmonary embolus (PE) were identified in 3D reconstructions of V/Q images achieved using anatomical data from the Visible Human Project. From these, the extent of lung damage was quantified. Significant differences in the values of both LogSD V and LogSD Q (p > 0.05) obtained from plots of V and Q against Log(V/Q) were found between normal subjects and subjects with a PE, but no correlation was found between either of these parameters and the degree of lung damage in subjects with a PE (p > 0.05). Whilst V/Q values were log normally distributed, the V/Q distributions from the subjects with a PE failed to show the bimodal distribution predicted from theoretical considerations and MIGET measurements previously reported. There was a statistically significant difference in the mean and standard deviation values of the V/Q distributions between normal subject and subjects with a PE (p < 0.05) but not in the median values (p > 0.05). There was no correlation between the mean, median and standard deviation of the distributions from the subjects with a PE and the percentage of damage present (p > 0.05).

Radiological imaging as the basis for a simulation software of ventilation in the tracheo-bronchial tree

The inhaled route is a promising new way for administering drugs to the human body. Flow and particle deposition in the human respiratory tract depends on the individual's anatomy as well as on the drug composition. A European Framework V Program supported project is currently developing a simulation tool for assessment of drug distribution and deposition. This tool relies heavily on the input of radiological data sets, which are obtained in humans. Both high temporal and spatial resolutions are required, and CT and MRI (including hyperpolarized helium-3 MRI) are applied. The radiological data are integrated into computation fluid dynamics software, which is capable of assessing air-flow profiles and compartmental behaviours. This is complemented by pharmacokinetic models, which should result in a simulation tool that will be of use for the theoretical design of new inhaled therapies. This article describes the special imaging requirements of each region of the respiratory tract and the feasibility of these sophisticated radiological techniques with a view of using these data in a simulation model of the lung.

A model for time-dependent flow in (giraffe jugular) veins: uniform tube properties

Computations are reported for a one-dimensional model of time-dependent flow in collapsible tubes representing long mammalian veins. The tubes are taken to have uniform intrinsic properties and we concentrate on the effect of longitudinal gravity. The main application is to the jugular vein of the upright giraffe, with given inflow rate from the head, a given pressure, slightly above the external, atmospheric pressure, at the downstream (vena caval) end, and a variety of initial conditions. We show that: (i) previously calculated steady flows are the long time limits of unsteady computations, although only after a considerable time in which slowly-decaying waves and elastic jumps propagate up and down, (ii) steady flows are indeed not found when the steady-flow analysis shown them not to exist, although the consequent unsteadiness is of such small amplitude as to be practically unimportant, (iii) the time taken for the flow to become steady when the neck is raised from the horizontal or the head-down position can be several seconds longer than the neck-raising time itself (3-7s). We also find that roll-waves do not develop despite having been previously predicted for long collapsible tubes. Further application is made to the effect of postural changes on human neck and leg veins.

Blood pressure and flow rate in the giraffe jugular vein

Experimental measurements in the jugular veins of upright giraffes have shown that the internal pressure is somewhat above atmospheric and increases with height above the heart. A simple model of steady viscous flow in an inverted U-tube shows that these observations are inconsistent with a model in which the blood vessels in the head and neck are effectively rigid and the system resembles a siphon. Instead, the observations indicate that the veins are collapsed and have a high resistance to flow. However, laboratory experiments with collapsible drain tubing in place of the down arm of the U-tube show internal pressure to be exactly atmospheric and uniform with height. A model of viscous flow in a collapsible tube with non-uniform properties is used to suggest that the observed pressure distribution may be a consequence of the intrinsic cross-sectional area and/or compliance of the veins increasing with distance towards the heart, or the external, tissue pressure falling. Finally, the effect of fluid inertia on steady flow in vertical collapsible tubes with uniform intrinsic properties is analysed, and it is shown that a phenomenon of flow limitation is theoretically possible, in which the supercritical flow in the collapsed vein cannot return to the presumably subcritical flow in the open vena cava, even with the help of an 'elastic jump', if the flow rate is too large. The computed critical flow-rate, of about 80 ml s-1, is about twice the flow-rate estimated to be present in the normal giraffe jugular vein. If there were circumstances in which flow limitation occurred in the jugular veins, it would mean that the cerebral blood flow would be limited by downstream conditions, not directly by local requirements.