Integrative Mathematical Models of Intracranial Pressure Dynamics

Open Access
Author:
Evans, Davis James
Area of Honors:
Engineering Science
Degree:
Bachelor of Science
Document Type:
Thesis
Thesis Supervisors:
  • Corina Stefania Drapaca, Thesis Supervisor
  • Joseph Paul Cusumano, Thesis Supervisor
  • Osama O Awadelkarim, Honors Advisor
Keywords:
  • Mathematical Model
  • Brain
  • Intracranial Pressure
  • Dynamics
Abstract:
Intracranial Pressure (ICP) monitoring has been shown to provide valuable physiological information for patients suffering from brain disorders such as hydrocephalus and traumatic brain injury. Currently, all reliable methods for measuring ICP involve drilling through the skull to place a pressure probe inside the brain. As a result, intracranial pressure is only measured in the most critical cases. Mathematical models that relate ICP to other noninvasive measurements could contribute to better diagnostic and treatment protocols. For instance, such mathematical models could have the capability to predict ICP in real time without the need for invasive direct measurements. In this thesis, we examine in detail the dynamics and stability of the Ursino model that predicts ICP from measurements of arterial blood pressure. We study how the equilibria vary with the model parameters and, aided by numerical simulations, we obtain bifurcation diagrams for the system. Expanding upon the work of Ursino et al., we show that the model exhibits both forward and reverse Hopf bifurcations in certain parameter regimes. We also present global phase portraits of the system in interesting parameter configurations. Whereas the problem of ICP dynamics is fundamentally (though not entirely) mechanical in nature, the Ursino model was derived using an electrical circuit analogy. Thus, following the work of Marmarou et al., we propose a new low-dimensional mechano-hydraulic model of ICP dynamics that couples the hydraulics of the ventricular cerebrospinal fluid (CSF) system with the brain tissue mechanics. We investigate the dynamics of the new model, and discuss how the model can be expanded to include the cerebral vasculature, as well.