Numerical simulation using the generalized immersed finite element method: An application to hydrocephalus
Open Access
- Author:
- Roy, Saswati
- Graduate Program:
- Engineering Science and Mechanics
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- November 05, 2012
- Committee Members:
- Corina Stefania Drapaca, Dissertation Advisor/Co-Advisor
Francesco Costanzo, Committee Chair/Co-Chair
Sulin Zhang, Committee Member
Panagiotis Michaleris, Committee Member
Luca Heltai, Special Member
Jonathan S Pitt, Special Member
Francesco Costanzo, Dissertation Advisor/Co-Advisor - Keywords:
- fluid-structure interaction
immersed finite element method
hydrocephalus
computational biomechanics - Abstract:
- % Place abstract below. The immersed finite element method (IFEM), belonging to the class of so-called immersed methods, is an emerging computational method for analyzing fluid-structure interaction (FSI) problems. Immersed methods have been gaining wide use in the analysis of biomechanical systems. In this dissertation, we are interested in analyzing a pathological state of the cerebral system known as hydrocephalus using an immersed method. During hydrocephalus, there is an abnormal accumulation of the cerebrospinal fluid (CSF) in the lateral ventricles of the brain. As a result, the ventricles distend and compress the brain tissue and disrupt the the normal functioning of the brain. The current therapies for hydrocephalus are surgical in nature, like shunt implants and endoscopic third ventriculostomy (ETV), and aim to divert the excess CSF from the ventricles into appropriate resorption sites. However, patients generally suffer from many post-surgical complications and hence there is an overriding need to gain a deeper understanding of the biomechanics of hydrocephalus in order to improve the treatment protocols. An effort in this direction is to develop computational models of hydrocephalic brains that will not only foster a better understanding of the biomechanical aspects of the disease among the clinicians but also enable them to use these models for prognosis. The biomechanical models of hydrocephalus that have been proposed so far have focused either only on the CSF dynamics or the deformation of the brain parenchyma described using different material models. However, modeling hydrocephalus as an FSI problem is relatively new. In this dissertation, we study the mechanics of hydrocephalus as an FSI problem by modeling the brain parenchyma as a deformable, incompressible Neo-Hookean solid that is submerged in CSF which is modeled as a Newtonian fluid. For analyzing this FSI problem, we use the fully variational formulation of the IFEM developed by Heltai and Costanzo (2012). In this method, like in other immersed methods, the discretization of the solid and the fluid domains are independent of each other and the fluid is treated in an Eulerian framework and the deformation of the solid is analyzed in a Lagrangian framework. In the fully variational setting the exchange of information between the fluid and solid domains (i.e. the interpolation of the velocity of the solid from the background fluid field and the spreading of the forces, arising due to the elasticity of the solid, in the fluid domain) is achieved using the standard infrastructure of the finite element method. This method is capable of handling of FSI involving both incompressible and compressible solids and the density and the viscosity of the solid need not be the same as those of the fluid. Moreover, the method has the potential to be easily extended for a poroelastic solid. We have developed a custom C++ based numerical code to implement the generalized IFEM. We present the numerical experiments that we have performed to the establish the correctness of our numerical implementation. We show that we obtain convergence rates that are in accordance with those found in the literature. We show that our numerical simulations give physically relevant results for viscometry tests. We also present some new tests for both incompressible and compressible solids that can be used for gauging the accuracy of the numerical implementation. We finally present some simple two-dimensional simulations that we have performed to model the deformation of the brain parenchyma when the CSF viscosity is varied. We see that higher viscosity of the CSF has an impact on the recovery time of a pre-deformed brain parenchyma. Such a numerical study has not been hitherto undertaken and may provide a better insight into outcome of ETV.