Biophysical Journal 11: 810-834 (1971)
© 1971 the Biophysical Society

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A Mathematical Model of the Controlled Plant of the Réspiratory System

ABSTRACT

Ability to predict the dynamic response of oxygen, carbon dioxide tensions, and pH in blood and tissues to abrupt changes in ventilation is important in the mathematical modeling of the respiratory system. In this study, the controlled plant (the amount and distribution of O₂ and CO₂) of the respiratory system is modeled. Although the body tissues are divided into a finite number of "compartments" (three tissue groups), in contrast to earlier models, the blood and tissue gas tensions within each compartment are considered to be continuously distributed in time and in one spatial coordinate. The mass conservation equations for oxygen and carbon dioxide involved in the blood-tissue gas exchange are described by a set of partial differential equations which take into account convection of O₂ and CO₂ caused by the flow of blood as well as diffusion due to local tension gradients. Nonlinear algebraic equations for the dissociation curves, which take into account the Haldane and Bohr effects in blood, are used to obtain the relationships between concentrations and partial pressures. Time-variable delays caused by the arterial and venous transport of the respiratory gases are also included. The model so constructed successfully reproduced actual O₂ and CO₂ tensions in arterial blood, and in muscle venous and mixed venous blood when ventilation was abruptly changed.