A poroelastic model of the lung

This work is motivated by the modelling of ventilation and deformation in the lung for understanding the biomechanics of respiratory diseases. The main contribution is the derivation and implementation of a lung model that tightly couples a poroelastic model of lung parenchyma to an airway fluid network. The poroelastic model approximates the porous structure of lung parenchyma using a continuum model that allows us to naturally model changes in physiology by spatially varying material parameters, whilst conserving mass and momentum within the tissue. The proposed model will also take advantage of realistic deformation boundary conditions obtained from image registration, to drive the simulation. A finite element method is presented to discretize the equations in a monolithic way to ensure convergence of the nonlinear problem. To demonstrate the coupling between the poroelastic medium and the network flow model numerical simulations on a realistic lung geometry are presented. These numerical simulations are able to reproduce global physiological realistic measurements. We also investigate the effect of airway constriction and tissue weakening on the ventilation, tissue stress and alveolar pressure distribution and highlight the interdependence of ventilation and deformation.