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 O(2) and CO(2)) 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 O(2) and CO(2) 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 O(2) and CO(2) tensions in arterial blood, and in muscle venous and mixed venous blood when ventilation was abruptly changed.

Is a Raised Bicarbonate, Without Hypercapnia, Part of the Physiologic Spectrum of Obesity-Related Hypoventilation?

“…Th is is physiologically plausible, as brief transient periods of hypoventilation, seen in upper airways obstruction, only leads to a rise in CO 2 to mixed venous levels, with the rise thereaft er very much slower. 15,16 More prolonged hypoventilation, with attendant rises in the partial pressure of arterial CO 2 , are required to promote bicarbonate generation and renal reabsorption of bicarbonate.…”

Importance of metabolism variations in a model of extracorporeal carbon dioxide removal

“…To take this into account in our approach, the relation between the O 2 concentration and the O 2 partial pressure is based on the work of Grodins et al [14]. The relations between CO 2 concentration, pH in plasma and CO 2 partial pressure are based on the work of Trueb et al [15].…”

Towards a virtual lung: multi-scale, multi-physics modelling of the pulmonary system

“…Although their assumptions are simplistic, such models have proved to be useful in understanding mechanisms of pulmonary control. For example, Trueb et al (1971) predicted changes in arterial PO 2 and PCO 2 in response to changes in ventilation using a simple lumped gas exchange model. Simple descriptions of gas exchange are also necessary for coupling with more complex models that describe the interaction of the cardiovascular and respiratory systems, and that incorporate airway mechanics, gas exchange and blood flow (Liu et al 1998).…”