A mathematical model for lung gas exchange: Quantitative determination of pulmonary dysfunction.

Abstract

In an effort to quantitate pulmonary dysfunction in patients with respiratory failure, a mathematical model which describes the exchange of oxygen and carbon dioxide in the lung has been developed. The whole lung is modelled as a set of separate gas exchange units in parallel in which the conditions known to cause hypoxemia may be represented. These conditions include ventilation-perfusion mismatch, venous blood shunt, large ventilatory dead space, and diffusion impairment. The model parameters which describe these conditions in each gas exchange unit are: the fraction of total cardiac output perfusing the unit, the ventilation-perfusion ratio, and the oxygen diffusion-perfusion ratio. Also, a lung blood shunt and ventilatory dead space are modeled. The model parameters are determined by measuring a series of cardiac outputs and steady state mixed venous and arterial blood gases (O$\sb2$ and CO$\sb2$), at different levels of inspired oxygen concentration (FIO$\sb2$). The changes in FIO$\sb2$ are kept small in order to minimize any potential lung reaction to changes in oxygen concentration. The number of measurements at different levels of FIO$\sb2$ depends on the number of gas exchange units used to model the entire lung. The inputs to the model are the mixed venous blood gases, cardiac output, ventilatory conditions, and blood properties. The output is the total gas exchange. The model parameters are fitted numerically to the measured data by minimizing the chi-square statistic between the measured and modelled total gas exchange at the various levels of FIO$\sb2$. The lung model simulation and parameter estimation are performed with a computer program written in FORTRAN. The estimated parameters obtained from two experiments with dogs, in which large shunts were induced from selectively ventilating a single lung, and from patients with ARDS requiring mechanical ventilation correlated to the anticipated degree shunting and dead space ventilation. The model may be used to predict lung gas exchange performance under a variety of input conditions, such as different levels of inspired oxygen concentrations, minute ventilation, or pulmonary blood flows during extracorporeal oxygenation. It may also be used as a research or diagnostic tool for the characterization of pulmonary function.