A Piecewise-Linear Model of Intracranial Pressure Dynamics

Abstract

Elevated intracranial pressure (ICP) is an extremely dangerous condition for patients suffering from traumatic brain injury, hydrocephalus, or related neurological disorders. To make informed decisions when treating such patients, clinicians must understand how the body controls ICP by regulating the rates at which cerebrospinal fluid (CSF) is formed and reabsorbed. Mathematical models can aid in this task. Of particular interest are models that can help us understand the transition between the stable, approximately constant values of ICP found in healthy individuals, and pathological oscillatory behaviors such as those observed with plateau waves, in which ICP exhibits steady oscillations between high and low pressures. In this paper, we develop a mathematical model of ICP dynamics with the goal of illustrating how the transition to oscillatory ICP dynamics can arise from processes that regulate CSF formation. A simple low-dimensional model is built that couples brain tissue mechanics and CSF hydraulics. Balance of mass and linear momentum result in a damped linear oscillator in terms of a single configuration variable representing deformation of brain tissue caused by changes in ICP. We focus on the case where the CSF supply rate is regulated by a piecewise mechanism based on the total volume of CSF. We show that the resulting piecewise-linear dynamical system can exhibit limit cycles in a manner consistent with plateau waves. We conclude by physically interpreting our results and discussing their potential clinical implications.