A mathematical model of the relationship between cerebral blood volume and intracranial pressure changes: the generation of plateau waves

Abstract

The relationship between intracranial pressure (ICP), cerebral blood volume (CBV), cerebrospinal fluid dynamics, and the action of cerebral blood-flow (CBF) regulatory mechanisms is examined in this work with the help of an original mathematical model. In building the model, particular emphasis is placed on reproducing the mechanical properties of proximal cerebral arteries and small pial arterioles, and their active regulatory response to perfusion pressure and cerebral blood flow changes. The model allows experimental results on cerebral vessel dilatation and cerebral blood-flow regulation, following cerebral perfusion pressure decrease, to be satisfactorily reproduced. Moreover, the effect of cerebral blood volume changes--induced by autoregulatory adjustments--on the intracranial pressure time pattern can be examined at different levels of arterial hypotension. The results obtained with normal parameter values demonstrate that, at the lower limits of autoregulation, when dilatation of small arterioles becomes maximal, the increase in cerebral blood volume can cause a significant, transient increase in intracranial pressure. This antagonism between intracranial pressure and autoregulatory adjustments can lead to instability of the intracranial system in pathological conditions. In particular, analysis of the linearized system "in the small" demonstrates that an impairment in cerebrospinal fluid (CSF) reabsorption, a decrease in intracranial compliance and a high-regulatory capacity of the cerebrovascular bed are all conditions which can lead the system equilibrium to become unstable (i.e., the real part of at least one eigenvalue to turn out positive). Accordingly, mathematical simulation "in the large," in the above-mentioned conditions, exhibits intracranial pressure periodic fluctuations which closely resemble, in amplitude, duration, frequency and shape, the well-known Lundberg A-waves (or plateau waves).