The role of fractional diffusion in the growth of a tumour

Ariel Ramìrez Torres (University of Glasgow)

Thursday 28th January 14:00-15:00 ZOOM (ID: 986 3052 9663)

Abstract

Topic: Applied Mathematics Seminar-Atherton
Start Time : Feb 4, 2021 01:50 PM

Meeting Recording:
https://uofglasgow.zoom.us/rec/share/2LM6xKk_yy-OdbfN6ZayhRz0G2BeiXrt0BvSZCy9ttbZMKGEFzgz3Y1PvTmmElKL.JhZK1-rPLgjKUIe5

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The diffusion of chemical species in a tumour plays a key role in its growth. In general, Fick’s law of diffusion is assumed for describing their evolution, but recent experimental studies indicate some inconsistencies. Based on these indications, we aim to highlight and study the influence of a non-Fickean type of diffusion processes that could be acting in an avascular tumour. In particular, we consider a diffusion equation for the evolution of the chemical species (in fact, nutrients) that accounts for spatial non-local interactions and that involves notions from Fractional Calculus. We describe the growth of the tumour in terms of mass transfer among its constituents and the structural changes occurring in its interior in response to growth. We perform numerical simulations for a benchmark problem, and the results reveal the relevance of embracing a non-local framework.

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