Mathematical model of oxygen transport in the cerebral cortex

Abstract

To estimate the magnitude of hyperemia necessary to support oxidative metabolism in the cerebral cortex during functional activation, a mathematical model of O2 transport from capillary to tissue was developed. Radial and axial gradients of O2 pressure in tissue surrounding a single capillary were calculated at normal and increased cerebral metabolic rates for O2. Cone-shaped tissue geometry and nonlinear oxyhemoglobin dissociation were assumed. Local O2 consumption was assumed to be supported with local tissue pO2 greater than 1 mmHg. The distribution of tissue pO2 was also calculated during moderate hypoxemia (paO2=42 mmHg), using experimental values of red blood cell velocity measured in individual capillaries of the rat cerebral cortex using intravital video-microscopy. The model predicted that moderate increases (≤50%) in cerebral O2 consumption were supported by proportional increases in capillary blood flow. Large increases in O2 consumption (50–110%) were supported by disproportional increases in flow. During moderate hypoxemia, average tissue pO2 decreased but oxygen utilization was sustained when capillary flow was increased to a level measured in experiments. The results suggest a proportional relationship between cerebrocortical blood flow and oxygen consumption in the normal physiological range of functional activation.