Multiphasic modelling of human brain tissue for intracranial drug-infusion studies

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Abstract

A direct intracranial infusion of a therapeutic solution into the extra-vascular space of human brain tissue is a promising medical application for the effective treatment of malignant brain tumours [1]. The advantage of this method, compared to an intra-vascular medication, is the targeted delivery with the circumvention of the blood-brain barrier (BBB), which prohibits the passing of therapeutic macro-molecules across the vascular walls into the brain parenchyma.

The prediction of the resulting therapeutical distribution by a numerical simulation is challenging, since the spreading is affected by the complex nature of living brain tissue. For this purpose, a macroscopic continuum-mechanical model is established within the Theory of Porous Media (TPM), proceeding from a homogenisation of the underlying micro-structure [5]. The ternary four-component model consists of an elastically deformable solid skeleton (composed of tissue cells and vascular walls), which is perfused by two mobile but separated liquid phases, the blood and the overall interstitial fluid (treated as a real two-component mixture of the liquid solvent and the dissolved therapeutic solute). The strongly coupled solid-liquid-transport problem is simultaneously approximated in all primary unknowns using mixed finite elements (uppc-formulation) and consequently solved in a monolithic manner with an implicit time-integration scheme.

This numerical investigation allows the computational study of several circumstances influencing the irregular distribution of infused drugs, as observed in clinical studies. Therefore, the microstructural perfusion characteristics in the extra-cellular space of the white-matter tracts are considered by a spatial diversification of the anisotropic permeability tensors, provided by Diffusion Tensor Imaging (DTI). Furthermore, Magnetic Resonance Angiography (MRA) enables the in vivo location of blood vessels within the brain tissue. Finally, the selection of appropriate material parameters has a crucial influence on the drug distribution profile and further occurring effects beyond. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

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