  Among the major factors controlling the cerebral blood flow (CBF) - cerebral
perfusion pressure, arterial partial pressure of oxygen (PaO2), cerebral
metabolism, arterial partial pressure of carbon dioxide (PaCO2), and cardiac
output, the effect of PaCO2 is peculiar in being independent of autoregulatory
CBF mechanisms and it allows to explore the full range of the CBF. We have
developed a simple physical model, and have derived a simple four parameter
formula, relating the CBF to PaCO2. The parameters can be extracted in an easy
way, directly from the experimental data. With this model five experimental
data sets of human, rats, baboons and dogs were well fitted. The same type of
parametrization was also used successfully for fitting experimental data of
PaO2 of dogs. We have also looked on the dependence of the parameters on other
factors and were able to evaluate their dependence on the mean arterial blood
pressure.
