Abstract
Glioblastoma (GBM) is the most aggressive primary brain tumor with a short median survival. Tumor recurrence is a clinical expectation of this disease and usually occurs along the resection cavity wall. However, previous clinical observations have suggested that in cases of ischemia following surgery, tumors are more likely to recur distally. Through the use of a previously established mechanistic model of GBM, the Proliferation Invasion Hypoxia Necrosis Angiogenesis (PIHNA) model, we explore the phenotypic drivers of this observed behavior. We have extended the PIHNA model to include a new nutrient-based vascular efficiency term that encodes the ability of local vasculature to provide nutrients to the simulated tumor. The extended model suggests sensitivity to a hypoxic microenvironment and the inherent migration and proliferation rates of the tumor cells are key factors that drive distal recurrence.
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Notes
We denote this as f to represent fuel for the cells, to avoid reusing n which is already assigned to necrotic cells.
It is well known that nutrient concentrations in blood (such as glucose concentration) fluctuate throughout a single day; however, we are interested in modeling tumor growth over many days and months, so only consider the average nutrient concentration across these daily fluctuations.
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Acknowledgements
The authors gratefully acknowledge funding from the National Cancer Institute (R01CA164371, U54CA193489) and the School of Mathematical Sciences at the University of Nottingham.
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Recurrence Results of Other PIHNA Simulations
Recurrence Results of Other PIHNA Simulations
We present the results of PIHNA simulations that were not shown in the main text. The trends in distant recurrence patterns that we observe in the main text all hold in these simulations, supporting our observations regarding \(D_h/D_c\), \(\beta \), \(\gamma \), \(D_c\) and \(\rho \) (Figs. 9, 10, 11, 12, 13, 14).
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Curtin, L., Hawkins-Daarud, A., Porter, A.B. et al. A Mechanistic Investigation into Ischemia-Driven Distal Recurrence of Glioblastoma. Bull Math Biol 82, 143 (2020). https://doi.org/10.1007/s11538-020-00814-y
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DOI: https://doi.org/10.1007/s11538-020-00814-y