Motivation. The quantification of fluid flow within complex and patient-specific geometries of the human brain is possible using a computational approach which allows the coupling of fluid stress and structural displacements. Such an analysis is referred to as fluid-structure interaction (FSI). The poroelastic nature of the human brain is used in the computational method, where the displacements of the solid matrix influence the fluid flow, and in turn the fluid stresses create large deformations in the soft tissue of the human brain. We seek to quantify human intracranial dynamics under normal and hydrocephalic conditions with the intent to predict the pathophysiological conditions leading to hydrocephalus and other cerebral disorders.

Methodology. We have developed a process in which MRI images are converted to a discretized mapping of finite elements. The aim is to use the patient-specific brain geometry in conjunction with physical principles of fluid flow and solid mechanics to quantify an individuals' specific intracranial dynamics. The approach proceeds in three stages. In step 1, MRI techniques are used to accurately measure the patients' individual brain geometry and the cerebrospinal fluid (CSF) flow velocities in select regions of interest. In step 2, image reconstruction is used to obtain the dimensions of the CSF pathways and the brain. Grid generation is then used to partition the computational domain into a large number of small finite elements. Step 3 involves the numerical solution of governing equations for fluid motion over the discretized brain geometry.

The brain consists of interstitial fluid, flexible vasculature, blood, cells (neuronal, ependymal, smooth muscle), and CSF. Therefore, patient-specific intracranial dynamics will be assessed in two phases. Initially, the brain will be idealized as a linear elastic solid, and secondly poroelastic properties will be introduced into the mathematical model. This work attempts to thoroughly describe the interaction between the poroelastic structures of the brain, the CSF in which it is submersed and the effect of systolic blood flow on brain and CSF dynamics during the cardiac cycle.

The equations describing fluid-structure interaction are coupled and consist of a nonlinear system of partial differential equations (PDEs). The governing PDEs are discretized using the finite element method. The governing equations for incompressible fluid flow in a poroelastic medium are the continuity, and Darcy's Law (which replaces the momentum equation). The solution for structural displacements is determined via consolidation theory and momentum of the solid matrix. Simultaneous solution approach using inexact Newton method for the non-linear system and a Krylov subspace based method for the linear subsystem (GMRES method) was used instead of fixed-point iteration methods like SIMPLE algorithm [1].

Broader Impact. FSI involving poroelastic materials has important applications in biomedical engineering. One such application is the quantification of the multi-dimensional flow field of cerebrospinal fluid (CSF) in the brain [2]. Another application is the quantification of the deformation of soft tissues and elastic membranes of the human brain under the influence of the pulsatile CSF flow. We expect that our FSI model for the human brain will provide a significant improvement in the understanding of diseases like hydrocephalus for which existing mathematical models are inadequate to describe large tissue displacements.

References

[1] M. Xenos, MB.R. Somayaji and A.A. Linninger, “Soft-tissue fluid-structure interactions in the human brain”, 2nd International Conference “From Scientific Computing to Computational Engineering”, Athens 5-8 July, 2006.

[2] A.A. Linninger, M. Xenos, D. Zhu, MB.R. Somayaji, S. Kondapalli and R. Penn, “Cerebrospinal Fluid Flow in the Normal and Hydrocephalic Human Brain”, IEEE Transactions on Biomedical Engineering, Vol. 54, No. 2, pp. 291-302, 2007.