Mathematical Examination of Pulmonary Gas Transport

Abstract

A quantitative mathematical examination of contemporary models of pulmonary gas transport and mixing is presented. This examination involved both a reappraisal of the boundary condititons assumed in these models and an exhaustive account of their respective stability and convergence criteria. As a result of this examination a revised single series compartmental mathematical model, derived from physiological data and incorporating revised boundary conditions, is developed to allow for a more faithful simulation of pulmonary gas transport phenomena. The model is used to demonstrate that the expired "phase III slope" or “alveolar plateau slope" of a tracer gas may give an indication of end expiratory stratified concentration differences in the acinus. The model also allows for a comparison between rigid and compliant model predictions at low tidal ventilations...