A simple mathematical model of the interaction between intracranial pressure and cerebral hemodynamics

Abstract

A simple mathematical model of intracranial pressure (ICP) dynamics oriented to clinical practice is presented. It includes the hemodynamics of the arterial-arteriolar cerebrovascular bed, cerebrospinal fluid (CSF) production and reabsorption processes, the nonlinear pressure-volume relationship of the craniospinal compartment, and a Starling resistor mechanism for the cerebral veins. Moreover, arterioles are controlled by cerebral autoregulation mechanisms, which are simulated by means of a time constant and a sigmoidal static characteristic. The model is used to simulate interactions between ICP, cerebral blood volume, and autoregulation. Three different related phenomena are analyzed: the generation of plateau waves, the effect of acute arterial hypotension on ICP, and the role of cerebral hemodynamics during pressure-volume index (PVI) tests. Simulation results suggest the following: 1) ICP dynamics may become unstable in patients with elevated CSF outflow resistance and decreased intracranial compliance, provided cerebral autoregulation is efficient. Instability manifests itself with the occurrence of self-sustained plateau waves. 2) Moderate acute arterial hypotension may have completely different effects on ICP, depending on the value of model parameters. If physiological compensatory mechanisms (CSF circulation and intracranial storage capacity) are efficient, acute hypotension has only negligible effects on ICP and cerebral blood flow (CBF). If these compensatory mechanisms are poor, even modest hypotension may induce a large transient increase in ICP and a significant transient reduction in CBF, with risks of secondary brain damage. 3) The ICP response to a bolus injection (PVI test) is sharply affected, via cerebral blood volume changes, by cerebral hemodynamics and autoregulation. We suggest that PVI tests may be used to extract information not only on intracranial compliance and CSF circulation, but also on the status of mechanisms controlling CBF.

Numerical Modeling of the Intracranial Pressure using Windkessel Models

“…Others studies using electrical modeling have been carried out, as the study proposed by Ursino et al [25], where a global representation of the cerebrospinal system including the surrounding arterial and venous network was developed, to understand the auto-regulation of the intracranial pressure. Inter alia, simulation of injection test were made for different parameters, in order to validate the model and study ICP response.…”

Anomalous Venous Blood Flow and Iron Deposition in Multiple Sclerosis

“…The blood leaves the brain by using the back propulsion of the residual arterial pressure (vis a tergo), complemented by antegrade postural and respiratory mechanisms (vis a fronte) as shown in Figure 3 (Ursino and Lodi, 1997;Schaller, 2004;Menegatti and Zamboni, 2008).…”

Post-craniectomy Intracranial Pressure Dynamics:A Novel Compartmental Model of Generalized Monro-Kellie Principle

“…Ursino [5] developed a novel mathematical model, which describes the quantitative interactions of different intracranial compartments. Without reducing the simulation effectiveness, Ursino and Lodi [6] offered a simplified simulation model for more practical uses. On specific areas researchers have developedbinsights on different biological parts including human intracranial biomechanical parameters, cerebrovascular autoregulation mechanism, pressure volume index [7][8][9][10][11][12][13][14] etc.…”