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A Mathematical Model of Tissue–Blood Carbon Dioxide Exchange during Hypoxia

Pulmonary and Critical Care Medicine Division, George Washington University, Washington, DC

Correspondence and requests for reprints should be addressed to Guillermo Gutierrez, M.D., Ph.D., Director, Pulmonary and Critical Care Medicine Division, George Washington University, 2150 Pennsylvania Avenue, N.W., Suite 5-404, Washington, DC 20037. E-mail: ggutierrez{at}mfa.gwu.edu

A two-compartment mass transport model of tissue CO₂ exchange is developed to examine the relative contributions of blood flow and cellular hypoxia (dysoxia) to increases in tissue and venous blood CO₂ concentration. The model assumes perfectly mixed homogeneous conditions, steady-state equilibrium, and CO₂ production occurring exclusively at the tissues. The behavior of the model is compared with published data derived from an isolated dog hindlimb preparation subjected to either reductions in blood flow (ischemic hypoxia) or decreases in arterial PO₂ (hypoxic hypoxia). The results of the model corroborate the experimental finding of greater venous and tissue CO₂ concentrations with ischemic hypoxia than with hypoxic hypoxia. The model also predicts increases in tissue CO₂ concentration under conditions of adequate O₂ supply if CO₂ transfer from tissue to blood becomes impaired. Consequently, from a theoretical perspective, it appears that increases in the tissue or venous blood CO₂ concentration are neither sensitive nor specific markers of tissue dysoxia. The results of the model support the notion that changes in tissue and venous blood CO₂ concentration during dysoxia reflect primarily alterations in vascular perfusion and not scarcity in cellular energy supply.

Key Words: CO₂ production • oxygen delivery • oxygen consumption • tissue oxygenation • venous PCO₂

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