Multiscale Modeling of the Mammalian Respiratory System

Abstract

Lower spatial-dimension models of lung physiology are helpful for understanding important phenomena, including gas-exchange, metabolism, and especially lumped tissue mechanics. However, they lack the spatial character that is fundamental in understanding diseases such as emphysema. Three-dimensional (3D) computational fluid dynamics (CFD) models can account for the spatial variation of flow and deposition in the lung, but they lack the physiological sophistication of lower-dimensional models and cannot accommodate distal lung compliance. In this study, I developed and validated a multiscale computational framework for efficiently combining 3D CFD models of mammalian respiration with the lower-dimensional models of lung physiology. In particular, I demonstrate the efficient linkage of multiple sets of ODE's describing the distal lung mechanics to imaging-based 3D CFD model of the pulmonary airway to incorporate physiologically appropriate outlet boundary conditions' for airflow simulations. Specifically, I extended a nonlinear Krylov accelerator for accelerating Newton iterations and further reduced cost by eliminating explicit evaluation of the Jacobian matrix. In contrast to monolithic schemes, which are efficient but require consistent discretization, the scheme may be used to link ODE's and PDE's to any finite element or finite volume solver, including commercial solvers, wherein the user has access to outer iterations. To validate the method, I coupled imaging-based rodent pulmonary geometry with measured lobar compliance from live anesthetized rats, subjected to ³He MRI. I then compared predicted lobar flows with experimentally measured lobar flows. I found that the addition of the coupled equations dramatically improved the accuracy of the airflow predictions. The performance of the method was comparable to monolithic schemes, in most cases requiring a single CFD evaluation per time step. Though in this thesis, the mechanics of distal airways and the parenchyma are represented by multiple sets of RLC circuits, the framework is designed to accommodate lower-dimensional models of lung mechanics and lung function of arbitrary complexity. This new accelerator allows us to begin combining CFD pulmonary models with lower-dimensional pulmonary models with little overhead and great flexibility.