Biomedical Engineering Reference
In-Depth Information
Chapter 19
Constitutive and Computational Aspects
in Tumor Therapies of Multiphasic Brain Tissue
Wolfgang Ehlers and Arndt Wagner
Abstract
The present contribution concerns the constitutive modeling and the nu-
merical simulation of brain tissue with a specific focus on tumor therapies carried
out by so-called convection-enhanced delivery processes (CED). The multiphasic
modeling approach is based on the Theory of Porous Media (TPM) and proceeds
from a volumetric homogenization of the underlying micro-structure. The brain tis-
sue model exhibits an elastic solid skeleton (cells and vascular walls), which is per-
fused by two liquids, the blood and the interstitial fluid. The latter is treated as
a mixture of two components, namely, a liquid solvent and a dissolved therapeu-
tic solute. The inhomogeneous and anisotropic nature of the white-matter tracts is
considered by a spatial diversification of the permeability tensors, obtained from
Diffusion Tensor Imaging (DTI). Numerically, the strongly coupled solid-liquid-
transport problem is simultaneously approximated in all primary unknowns (uppc-
formulation) using mixed finite elements and solved in a monolithic manner with an
implicit time-integration scheme. Within this procedure, numerical examples of the
CED under two- and three-dimensional conditions are discussed.
19.1 Introduction and Treatment Options for Brain Tumors
After a medical detection of a brain tumor, the conventional treatment proceeds
from a highly invasive removal of the tumor in combination with radiotherapy or
chemotherapy. However, the healing success is still low, because malignant tumors
are strongly resistant and regrow frequently. Therefore, the development of alterna-
tive and effective treatments is subject of current research.
Any suitable therapeutic agent reaching the malignant brain tumor can have the
desired therapeutic outcome. Basically, there are several methods for the application
ยท
W. E h l e r s (
A. Wagner
Institute of Applied Mechanics (CE), University of Stuttgart, Pfaffenwaldring 7, 70569 Stuttgart,
Germany
A. Wagner
)
