A multiscale model for glioma spread including cell-tissue interactions and proliferation

Abstract

Glioma is a broad class of brain and spinal cord tumors arising from glia cells, which are the main brain cells that can develop into neoplasms. They are highly invasive and lead to irregular tumor margins which are not precisely identifiable by medical imaging, thus rendering a precise enough resection very difficult. The understanding of glioma spread patterns is hence essential for both radiological therapy as well as surgical treatment. In this paper we propose a multiscale model for glioma growth including interactions of the cells with the underlying tissue network, along with proliferative effects. Our current accounting for two subpopulations of cells to accomodate proliferation according to the go-or-grow dichtomoty is an extension of the setting in [16]. As in that paper, we assume that cancer cells use neuronal fiber tracts as invasive pathways. Hence, the individual structure of brain tissue seems to be decisive for the tumor spread. Diffusion tensor imaging (DTI) is able to provide such information, thus opening the way for patient specific modeling of glioma invasion. Starting from a multiscale model involving subcellular (microscopic) and individual (mesoscale) cell dynamics, we perform a parabolic scaling to obtain an approximating reaction-diffusion-transport equation on the macroscale of the tumor cell population. Numerical simulations based on DTI data are carried out in order to assess the performance of our modeling approach.

A Multiscale Modeling Approach to Glioma Invasion with Therapy

“…In the following we will use the syntagma 'cell surface receptors' for all kinds of receptors involved in cell-tissue adhesion and will concentrate on integrins when referring to chemotherapeutical agents which aim at inhibiting migration and proliferation. For further discussions on the issue of glioma-tissue adhesion we refer to [17,19]. The two cancer cell densities of interest satisfy on the mesoscale the system of partial integrodifferential equations…”

“…The function λ(y) denotes as in [17,19,18] the turning rate of the cells. Motivated by existing experimental evidence (see e.g., [46]) that integrins expressed by resting cells cannot in general bind their ligands, we assume this also for our model, as we did in [19].…”

“…In [19] we considered a model for glioma invasion relying on the go-or-grow hypothesis. In this work we extend that setting in order to account for therapy.…”

“…Mathematical models for the therapy of glioma have also been considered in [2,51,52], however in a much simplified monoscale case not able to account for the highly infiltrative behavior of this type of cancer. Here we start from the multiscale setting introduced in [19] to describe the evolution of a heterogeneous tumor consisting of migrating and proliferating glioma cells moving along white matter tracts of white matter. The anisotropic structure of the brain is assessed from diffusion tensor imaging (DTI) data and the model involves on the microscopic, subcellular scale the receptor binding dynamics to the tissue fibers, while the individual cell dynamics are modeled on the mesoscale via kinetic transport equations.…”

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AbstractWe consider the multiscale model for glioma growth introduced in [19] and extend it to account for therapy effects. Thereby, three treatment strategies involving surgical resection, radio-, and chemotherapy are compared for their efficiency.

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