Table of Contents
Journal of Nonlinear Dynamics
Volume 2016, Article ID 2869083, 12 pages
http://dx.doi.org/10.1155/2016/2869083
Research Article

Nonlinear Dynamics and Analysis of Intracranial Saccular Aneurysms with Growth and Remodeling

Department of Mathematical Sciences, George Mason University, Fairfax, VA 22030, USA

Received 30 March 2016; Accepted 5 May 2016

Academic Editor: Giovanni P. Galdi

Copyright © 2016 Manal Badgaish et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A new mathematical model for the interaction of blood flow with the arterial wall surrounded by cerebral spinal fluid is developed with applications to intracranial saccular aneurysms. The blood pressure acting on the inner arterial wall is modeled via a Fourier series, the arterial wall is modeled as a spring-mass system incorporating growth and remodeling, and the surrounding cerebral spinal fluid is modeled via a simplified one-dimensional compressible Euler equation with inviscid flow and negligible nonlinear effects. The resulting nonlinear coupled fluid-structure interaction problem is analyzed and a perturbation technique is employed to derive the first-order approximation solution to the system. An analytical solution is also derived for the linearized version of the problem using Laplace transforms. The solutions are validated against related work from the literature and the results suggest the biological significance of the inclusion of the growth and remodeling effects on the rupture of intracranial aneurysms.