A mathematical model of cerebral blood flow control in anaemia and hypoxia

Key points The control of cerebral blood flow in hypoxia, anaemia and hypocapnia is reviewed with an emphasis on the links between cerebral blood flow and possible stimuli. A mathematical model is developed to examine the changes in the partial pressure of oxygen in brain tissue associated with changes in cerebral blood flow regulation produced by carbon dioxide, anaemia and hypoxia. The model demonstrates that hypoxia, anaemia and hypocapnia, alone or in combination, produce varying degrees of cerebral hypoxia, an effect exacerbated when blood flow regulation is impaired. The suitability of brain hypoxia as a common regulator of cerebral blood flow in hypoxia and anaemia was explored, although we failed to find support for this hypothesis. Rather, cerebral blood flow appears to be related to arterial oxygen concentration in both anaemia and hypoxia. A mathematical model is developed to examine the changes in the partial pressure of oxygen in brain tissue associated with changes in cerebral blood flow regulation produced by carbon dioxide, anaemia and hypoxia. The model simulation assesses the physiological plausibility of some currently hypothesized cerebral blood flow control mechanisms in hypoxia and anaemia, and also examines the impact of anaemia and hypoxia on brain hypoxia. In addition, carbon dioxide is examined for its impact on brain hypoxia in the context of concomitant changes associated with anaemia and hypoxia. The model calculations are based on a single compartment of brain tissue with constant metabolism and perfusion pressure, as well as previously developed equations describing oxygen and carbon dioxide carriage in blood. Experimental data are used to develop the control equations for cerebral blood flow regulation. The interactive model illustrates that there are clear interactions of anaemia, hypoxia and carbon dioxide in the determination of cerebral blood flow and brain tissue oxygen tension. In both anaemia and hypoxia, cerebral blood flow increases to maintain oxygen delivery, with brain hypoxia increasing when cerebral blood flow control mechanisms are impaired. Hypocapnia superimposes its effects, increasing brain hypoxia. Hypoxia, anaemia and hypocapnia, alone or in combination, produce varying degrees of cerebral hypoxia, and this effect is exacerbated when blood flow regulation is degraded by conditions that negatively impact cerebrovascular control. Differences in brain hypoxia in anaemia and hypoxia suggest that brain oxygen tension is not a plausible sensor for cerebral blood flow control.