Mathematical models of oxygen and carbon dioxide storage and transport: interstitial fluid and tissue stores and whole-body transport.

This article describes a mathematical model of whole-body O2 and CO2 transport. The model includes representation of the acid-base chemistry of the blood, interstitial fluid, and tissues, plus transport of O2 and CO2 between compartments representing tissues, interstitial fluid, arterial and venous blood, and lungs. The model includes equations for calculation of all concentrations in the compartments, including equations describing the physicochemical properties and reaction equations of interstitial fluid and tissues. In addition, the model includes equations that describe the flow of substrate between the compartments and differential equations allowing calculation of the changes in state variables caused by the flow of substrates between the compartments. This model is designed to calculate the effects of metabolic and respiratory perturbations, such as variation in breathing pattern or production of strong acid at the tissues. The model reproduces the results of published experiments when used to simulate (1) normal conditions in the lungs, arterial and venous blood, interstitial fluid, and tissues during normal ventilation; (2) the characteristic two-exponential response to changes in minute ventilation; and (3) the relationship between arterial blood values of PCO2 and HCO3,p during inspiration of different fractions of CO2.