A compartmental brain model for chemical transport and CO2 controlled blood flow

A compartmental transport model is developed, capable of predicting the evolution of CO2, HCO-3 and H+ in the cerebrovascular system. In the model, the transport of these components is simulated at a subset of three compartments: cerebrospinal fluid (CSF), capillary-choroid plexus and brain tissue, belonging to a seven compartmental assembly representing the entire brain. The remaining ones are; artery, vein, venous sinus and jugular bulb. The model accounts for advection associated with non-steady perfusion fluxes across semi-previous boundaries. Pressures, associated with perfusion, are solved in the seven-compartment model. The three-compartment transport model also takes into account changes in compartmental volume due to displacement of its boundaries, diffusion through boundaries and rate of generation of substances by chemical reactions. A first-order reaction rate is assumed in the CSF compartment. A parameter estimation method is then developed to assess boundary diffusivities from time-averaged observed values of perfusion pressure, tension of carbon dioxide, pH values, and concentration of free hydrogen and bicarbonate ions. An equation of state describing the regulation of flow from arteries to capillaries, as a function of CO2 tension in the CSF, is then suggested. Upon solving all coupled mass balance equations, and for a pre-evaluated perfusion pressure in the artery and capillary compartments, one can estimate the change in arteries to capillaries conductance at every time step. Boundary diffusivities between the capillary, cerebrospinal fluid and brain tissue compartments, were estimated. A sensitivity analysis proves the consistency between model predictions and available clinical observations, this, in terms of the influence of the parameter associated with CO2 metabolic rate on CO2 tension. It was shown that decrease of this tension caused an abrupt pressure fall at the first instant which later increased to an asymptotic value. This, however, was not evident in the capillaries at which pressure slightly falls and then remains constant.