Abstract
The present contribution concerns the constitutive modeling and the numerical 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 tissue model exhibits an elastic solid skeleton (cells and vascular walls), which is perfused 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 therapeutic 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.
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Notes
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Porous media Adaptive Nonlinear finite element solver based on Differential Algebraic Systems (http://www.get-pandas.com).
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Acknowledgements
The diffusion tensor MRI brain dataset was obtained by courtesy of G. Kindlmann (Scientific Computing and Imaging Institute, University of Utah) and A. Alexander (W.M. Keck Laboratory for Functional Brain Imaging and Behavior, University of Wisconsin-Madison). Furthermore, proofreading by Dr. Nils Karajan is gratefully acknowledged.
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Ehlers, W., Wagner, A. (2013). Constitutive and Computational Aspects in Tumor Therapies of Multiphasic Brain Tissue. In: Holzapfel, G., Kuhl, E. (eds) Computer Models in Biomechanics. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-5464-5_19
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