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Computational modelling of drug infusion into the anisotropic white‐matter tracts of the human brain
Author(s) -
Wagner Arndt,
Ehlers Wolfgang
Publication year - 2011
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201110058
Subject(s) - white matter , interstitial fluid , interstitial space , porous medium , brain tissue , permeability (electromagnetism) , diffusion , soft matter , anisotropy , drug delivery , materials science , diffusion mri , distribution (mathematics) , biomedical engineering , mechanics , magnetic resonance imaging , chemistry , porosity , physics , pathology , thermodynamics , nanotechnology , medicine , mathematics , radiology , mathematical analysis , optics , membrane , composite material , biochemistry , colloid
Unfortunately, the human brain is compromised by an amount of brain diseases, such as strokes or cerebral tumours. In this contribution, special attention is paid to the constitutive modelling procedure and the numerical simulation of the so‐called convection‐enhanced delivery process, where an effective treatment of malignant brain tumours is achieved by bypassing the blood‐brain barrier via a direct infusion of therapeutic agents into the extra‐vascular space of the brain tissue using implanted catheters. The modelling approach of the complex brain‐tissue aggregate proceeds from the Theory of Porous Media including an elastically deformable solid skeleton, provided by the tissue cells and the vascular walls. The tissue is permeated by two liquid phases, the blood and the interstitial fluid. In order to describe a distribution process of the inserted drugs, the interstitial fluid phase is treated as a chemical solution of two components, the liquid solvent and the dissolved therapeutic solute. The inhomogeneous anisotropic nature of the white‐matter tracts is considered by spatially varying permeability tensors, obtained by diffusion‐weighted magnetic resonance imaging. The strongly coupled solid‐liquid transport problem is simultaneously approximated in all primary unknowns using mixed finite elements and solved in a monolithic manner with an implicit time‐integration scheme. The numerical investigation is applied to un‐bloody numerical studies. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)