A mathematical model of intracranial pressure dynamics for brain hypothermia treatment

Abstract

Brain hypothermia treatment is used as a neuroprotectant to decompress the elevated intracranial pressure (ICP) in acute neuropatients. However, a quantitative relationship between decompression and brain hypothermia is still unclear, this makes medical treatment difficult and ineffective. The objective of this paper is to develop a general mathematical model integrating hemodynamics and biothermal dynamics to enable a quantitative prediction of transient responses of elevated ICP to ambient cooling temperature. The model consists of a lumped-parameter compartmental representation of the body, and is based on two mechanisms of temperature dependence encountered in hypothermia, i.e. the van’t Hoff's effect of metabolism and the Arrhenius’ effect of capillary filtration. Model parameters are taken from the literature. The model is verified by comparing the simulation results to population-averaged data and clinical evidence of brain hypothermia treatment. It is possible to assign special model inputs to mimic clinical maneuvers, and to adjust model parameters to simulate pathophysiological states of intracranial hypertension. Characteristics of elevated ICP are quantitatively estimated by using linear approximation of step response with respect to ambient cooling temperature. Gain of about 4.9 mmHg °C −1, dead time of about 1.0 h and a time constant of about 9.8 h are estimated for the hypothermic decompression. Based on the estimated characteristics, a feedback control of elevated ICP is introduced in a simulated intracranial hypertension of vasogenic brain edema. Simulation results suggest the possibility of an automatic control of the elevated ICP in brain hypothermia treatment.