A model of cerebral blood flow control in hypercapnia

A mathematical model of cerebral blood flow control to increases inP _aCO₂ is developed. The controlled system of the model (the brain) is composed of three well-mixed lumped parameter compartments: blood, cerebral extracellular fluid (ECF), and cerebral intracellular fluid (ICF). The conservation of mass equations are written for three chemical species: molecular carbon dioxide, bicarbonate ion, and hydrogen ion in each compartment, yielding nine first-order nonlinear differential equations. For the controller, cerebral blood flow is assumed a function of the chemical species in the compartments; in particular the hypotheses that blood flow is a function of interstitial fluid pH, or a function of interstitial fluid carbon dioxide tension operating through a proportional controller are investigated in detail. The parameters for these controllers were obtained from data in the physiologic literature as well as experiments performed as part of this study. This model is the first attempt to describe the transient behavior of the cerebral circulatory system to acid base disturbances. When the predictions of the model are compared with experimental data it is found that the model predicts a cerebral blood flow change to hypercapnia consistently slower than that found experimentally. This suggests that the cerebral circulatory response to CO₂ inhalation is not exclusively a function of ECF or CO₂ and that therefore other controls and/or mechanisms play a role as well.