A Three Compartmental Model of the Hemodynamic Response and Oxygen Delivery to Brain

We describe a mathematical model linking changes in cerebral blood flow, blood volume and the blood oxygenation state in response to simulation. The model has three compartments to take into account the fact that the cerebral blood flow and volume ad measured concurrently using laser Doppler flowmetry and optical imaging spectroscopy have contributions from the arterial, capillary as well as the venous compartments of the vasculature. It is an extension to previous one-compartment hemodynamic models which assume that the measured blood volume changes are from the venous compartment only. An important assumption of the model is that the tissue oxygen concentration is a time varying state variable of the the system and is driven by the changes in metabolic demand resulting from changes in neural activity. The model recognises the effects of the pre-capillary arteriolar oxygen perfusion ( that is the situation of the arterial compartment being less than unity). Simulations are used to explore the sensitivity of the model and to optimise the parameters for experimental data. We conclude that the three-compartment model was better than the one-compartment model at capturing the hemodynamics of the response to changes in neural activation following simulation.