Models for cell migration assays, including PDEs with nonlinear diffusion

Scott McCue (QUT, Brisbane, Australia)

Monday 6th December, 2021 11:00-12:00 ZOOM (ID: 924 6361 4209)


Experimentalists who study cancer invasion and wound repair often employ simple assays such as the in vitro scratch assay to quantify the combined effects of cell proliferation and cell migration on the collective motion of cells in two dimensions.  In turn, these experiments prove to be fruitful for researchers in mathematical biology to test and explore mathematical models for collective cell motion.  I will discuss some of these ideas from the perspective of an applied mathematician, making reference to PDE models such as the Fisher-KPP equation as well as discrete processes based on random walk models.  Then I will spend some time on a hole-closing model for a two-dimensional wound assay that is based on a PDE with nonlinear degenerate diffusion.  The mathematics here is interesting as it involves similarity solutions of the second kind.  Finally, I will touch on slightly more complicated PDE models with nonlinear diffusion that can be used to study problems in similar geometries, such as thin tissue growth in printed bioscaffolds.

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