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Mathematical Model for an Idealized Cerebral Aneurysm

Research Area: Volume 1 Issue 2, August - 2013 Year: 2013
Type of Publication: Article Keywords: Biological model, Mathematical Model and Nonlinear
Authors:
  • Keerty Shrivastava
  • Rajesh Shrivastava
  • Ramakant Bhardwaj
Journal: IJNIST Volume: 1
Number: 2(6) Pages: 94-104
Month: August
ISSN: 2321-0468
Abstract:
This REU research project presents mathematical modeling of the fluid structure interaction between the arterial wall, the blood within, and the cerebrospinal fluid surrounding an idealized cerebral aneurysm. A Voigt damped mass-spring model for the biological tissue is utilized. The pulsatile blood flow is modeled by a sinusoidal function and the cerebrospinal fluid flow is modeled by a simplified Navier-Stokes Equation. Our objective was to study the behavior of the exterior wall of the aneurysm as we vary the amount of damping in the viscoelastic tissue and as we vary the periodic blood force. An exact solution is presented in which partial differential equation are used to solve the coupled system of partial differential equations with boundary conditions. An approximation of the boundary condition at the aneurysm wall is also presented in which the pressure from the cerebrospinal fluid is assumed to vary linearly over space. The mathematical modeling and solving processes are examined from the perspective of a high school mathematics teacher for the purpose of incorporating into the classroom.
Full text: IJNIST6.pdf

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