| Abstract: |
| Recognising that the complexity of Glioblastoma (GBM) progression requires ever more sophisticated cross-scale interlinked processes to be considered in our modelling approaches, in this work we propose three novel advancements of the multiscale moving boundary framework introduced and established in Trucu et al. 2013 (https://doi.org/10.1137/110839011) and further developed in Robyn and Trucu 2019 (https://doi.org/10.1007/s11538-019-00598-w) and Szabolcs Suveges et al. 2021 (https://doi.org/10.3390/math9182214) by which the presence of the extracellular matrix fibres present at the interface is accounted for alongside with the availability of nutrients within sensing regions of the GBM cells. These will not only enable us to determine more realistic laws for the tumour boundary movement, but also to explore non-local go-or-grow collective cell motility behaviours arising within the bulk of the tumour, as well as to formulate mathematical the emergence of isotropic-to-anisotropic transition within the GBM cell population transport during the invasion of the surrounding brain tissue. These framework developments allow us to explore the emergence of cellular stress caused by both hypoxic behaviour and GBM treatment that lead to acquiring resistance and result in GBM relapse. This further addressed by considering the impact that key metabolic components have over the GBM progression and relapse in the presence treatment. |
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