Multiscale mathematical models of airway constriction and disease.

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