A Mathematical Model of Human Respiration at Altitude

Abstract

We developed a mathematical model of human respiration in the awake state that can be used to predict changes in ventilation, blood gases, and other critical variables during conditions of hypocapnia, hypercapnia and these conditions combined with hypoxia. Hence, the model is capable of describing ventilation changes due to the hypocapnic-hypoxia of high altitude. The basic model is that of Grodins et al. [Grodins, F. S., J. Buell, and A. J. Bart. J. Appl. Physiol. 22:260-276, 1967]. We updated the descriptions of (1) the effects of blood gases on cardiac output and cerebral blood flow, (2) acid-base balance in blood and tissues, (3) O2 and CO2 binding to hemoglobin and most importantly, (4) the respiratory-chemostat controller. The controller consists of central and peripheral sections. The central chemoceptor-induced ventilation response is simply a linear function of brain P(CO2) above a threshold value. The peripheral response has both a linear term similar to that for the central chemoceptors, but dependent upon carotid body P(CO2) and with a different threshold and a complex, nonlinear term that includes multiplication of separate terms involving carotid body P(O2) and P(CO2). Together, these terms produce 'dogleg'-shaped curves of ventilation plotted against P(CO2) which form a fan-like family for different values of P(CO2). With this chemical controller, our model closely describes a wide range of experimental data under conditions of solely changes in P(CO2) and for short-term hypoxia coupled with P(CO2) changes. This model can be used to accurately describe changes in ventilation and respiratory gases during ascent and during short-term residence at altitude. Hence, it has great applicability to studying O2-delivery systems in aircraft.