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Analysis and Validation of a Mathematical Model for Intracranial Pressure Dynamics

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  • W.D. Lakin
  • J. Yu
  • P.L. Penar

Abstract

Lumped parameter, compartmental models provide a promising Method for mathematically studying the dynamics of human intracranial pressure. In this modeling approach, a system of fully time-dependent differential equations for interacting compartmental pressures is obtained by considering the intracranial system to be confined within the almost-rigid skull and developing continuity equations associated with conservation of mass. Intracranial volumes and flows are related to compartmental pressure differences through compliance and resistance parameters. In the nonlinear case where compliances are not constant, there is a lack of physical information about these parameters. Consequently, it is vital that any mathematical model with an assumed pressure-dependent compliance be validated through comparison with experimental data. The present work develops a logistic representation for the compliance between the cerebrospinal fluid and brain matter compartments. The nonlinear mathematical model involving this logistic compliance is validated here by comparing its predicted response for bolus injections of cerebrospinal fluid to laboratory data generated in an animal model. Comparison with the animal studies fully supports the validity of the mathematical model with the logistic compliance.

Suggested Citation

  • W.D. Lakin & J. Yu & P.L. Penar, 1999. "Analysis and Validation of a Mathematical Model for Intracranial Pressure Dynamics," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 5(1), pages 55-73, March.
    • Handle: RePEc:taf:nmcmxx:v:5:y:1999:i:1:p:55-73
    DOI: 10.1076/mcmd.5.1.55.3623
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