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Multiscale models for tumor cell migration: deterministic and stochastic approaches
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Tumor cell invasion is an essential step in the metastatic cascade. 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 diffusion, 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 effects of subcellular events on the behavior of an entire cell population. We present two model classes: one is concerned with acid-mediated cancer invasion and involves random effects on the subcellular level, the latter being combined with the macroscale of the tumor and tissue. The other model class is in a pure deterministic setting and uses kinetic transport equations (mesoscale) and ODEs (microscale) to assess the macroscopic behavior of glioma cells in brain, based on DTI data.