Traveling wave speed and profile of a “go or grow” glioblastoma multiforme model
Tursynkozha A. Kashkynbayev A. Shupeyeva B. Rutter E.M. Kuang Y.
April 2023Elsevier B.V.
Communications in Nonlinear Science and Numerical Simulation
2023#118
Glioblastoma multiforme (GBM) is a fast-growing and deadly brain tumor due to its ability to aggressively invade the nearby brain tissue. A host of mathematical models in the form of reaction–diffusion equations have been formulated and studied in order to assist clinical assessment of GBM growth and its treatment prediction. To better understand the speed of GBM growth and form, we propose a two population reaction–diffusion GBM model based on the ‘go or grow’ hypothesis. Our model is validated by in vitro data and assumes that tumor cells are more likely to leave and search for better locations when resources are more limited at their current positions. Our findings indicate that the tumor progresses slower than the simpler Fisher model, which is known to overestimate GBM progression. Moreover, we obtain accurate estimations of the traveling wave solution profiles under several plausible GBM cell switching scenarios by applying the approximation method introduced by Canosa.
Glioblastoma , Go or grow , Partial differential equations , Traveling wave
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Department of Mathematics, Nazarbayev University, Astana, 010000, Kazakhstan
Department of Applied Mathematics, University of California, Merced, 5200 North Lake Rd., Merced, 95343, CA, United States
School of Mathematical and Statistical Sciences, Arizona State University, Tempe, 85287, AZ, United States
Department of Mathematics
Department of Applied Mathematics
School of Mathematical and Statistical Sciences
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