Understanding lung tissue mechanics in terms of mathematical models

The mechanical properties of lung tissue are important determinants of the overall mechanical behaviour of the lung itself. Our understanding of lung tissue mechanics is embodied in various mathematical models, that relate measurements of transpulmonary pressure to lung volume and flow. The purpose of this paper is to review the most basic and important of these models. Firstly, the single-compartment linear model of lung tissue is invoked to explain measurements of transpulmonary pressure and volume under quasi-static conditions, when volume excursions are modest. The exponential nonlinear extension of this model may be used to account for measurements made when volume approaches total lung capacity. Secondly, the Kelvin body as a model of the viscoelastic properties of lung tissue is considered, as a means for accounting for tissue stress adaptation and the frequency dependencies of tissue resistance and elastance. The Prandtl body is also invoked to explain tissue plastoelasticity, manifest in quasi-static hysteresis between transpulmonary pressure and volume. Finally, some more complicated and intricate extensions of these models are considered.