Analysis and validation of a mathematical model for intracranial pressure dynamics

Lumped parameter, compartmental models provide a promising method for mathe matically studying the dynamics of human intracranial pressure. In this mod eling approach, a system of fully time-dependent differential equations for interacting compartmental pressures is obtained by considering the intracr anial system to be confined within the almost-rigid skull and developing co ntinuity equations associated with conservation of mass. Intracranial volum es and flows are related to compartmental pressure differences through comp liance and resistance parameters. In the nonlinear case where compliances a re not constant, there is a lack of physical information about these parame ters. Consequently, it is vital that any mathematical model with an assumed pressure-dependent compliance be validated through comparison with experim ental data. The present work develops a logistic representation for the com pliance between the cerebrospinal fluid and brain matter compartments. The nonlinear mathematical model involving this logistic compliance is validate d here by comparing its predicted response for bolus injections of cerebros pinal fluid to laboratory data generated in an animal model. Comparison wit h the animal studies fully supports the validity of the mathematical model with the logistic compliance.