Mathematical model of oxygen transport in the cerebral cortex

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 (