Mathematical modelling and imaging of asthmatic airways - Hiorns, Jonathan E. (2014)
The hyper-responsiveness of airway smooth muscle to certain external stimuli, and the associated remodelling of the airway wall, is central to the development of asthma, making it of widespread clinical significance. In this thesis, mathematical models for the asthmatic airway embedded in parenchymal tissue are presented. The stiffening due to recruitment of collagen fibres and force generation by smooth muscle is taken into account, to develop a nonlinear elastic model for the airway wall. The contractile force of the muscle is governed by the dynamically changing subcellular crossbridge populations. A nonlinear elastic and, to take into account the viscoelasticity of the lung, a linear viscoelastic model for the parenchyma are developed. Consistent with experimental findings, deforming the airway passively, the model predicts strain-stiffening on inflation and deflation. The displacements predicted within the parenchyma are much smaller when the airway is inflated internally than externally, due to the airway wall shielding the parenchyma. Stress heterogeneities are predicted within the thickened airway wall when active contractile forcing is applied, which may contribute to further remodelling of the wall. If tidal stretching is applied to a contracted airway, the model predicts that the contractile force reduces, resulting in a reversal of bronchoconstriction. This is more exaggerated when the parenchyma is viscoelastic. Image analysis techniques are also developed to investigate data from lung-slice experiments, whereby pharmacological stimuli can be added to segments of lung tissue to stimulate smooth muscle contraction. By tracking the lumen area and fitting to exponential functions, two timescales of contraction are found to exist, consistent with the mathematical model predictions, and that the ratio of the timescales is robust. Methods are also developed and tested to find the displacement field of the tissue surrounding the airway lumen and it is shown that there are important heterogeneities within the tissue.