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| Tumor cell invasion is an essential stage in the development of cancer. Tumor cells migrate through the surrounding tissue (normal cells, extracellular matrix, interstitial fluid) towards blood or lymph vessels which they penetrate and thus access the blood flow. They are carried by blood circulation to distant locations where they extravasate and develop new tumours, a phenomenon known as metastasis. The invasive spread of cancer cells is highly complex, as it is influenced by various dynamics ranging from the subcellular level (microscale) through the mesoscopic level of individual cells and up to the macroscale of a cell population, the latter involving processes like diff usion, chemotaxis or haptotaxis, separately or in a conjugate way.
The mathematical modeling of these features leads to multiscale settings interconnecting two or all three of these scales and allowing to assess the e ffects of subcellular events on the behavior of an entire cell population. We present a class of multiscale models characterizing glioma invasion in white brain matter. Gliomas are rarely curable brain tumors arising from abnormal glial cells in the brain. In particular, the most agressive type, glioblastoma multiforme, has a poor prognosis with a median survival rate less than one year. Complex therapy approaches including surgical resection of neoplastic tissue, radio- and chemotherapy can still not ensure a complete healing of the patient and are part of ongoing research. Currently, Diffusion Tensor Imaging (DTI) is the preferred radiological method in glioma prognosis, which also allows to infer the white matter fibre structure of the brain in a noninvasive way. Kinetic transport equations provide an appropriate framework to include such patient specific DTI data into a micro-meso model for glioma growth. |
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