Minimal Morphoelastic Models of Solid Tumour Spheroids #

Benjamin Walker, Giulia L Celora, Alain Goriely, Derek E Moulton, Helen M Byrne

11:10 Tuesday in 4Q56.

Part of the Chemo-mechanical couplings in growing tissues session.

Abstract #

Tumour spheroids have been the focus of a variety of mathematical models, ranging from Greenspan’s classical study of the 1970s through to contemporary agent-based models. Of the many factors that regulate spheroid growth, mechanical effects are perhaps some of the least studied, both theoretically and experimentally, though experimental enquiry has established their significance to tumour growth dynamics. In this talk, we will formulate a hierarchy of mathematical models of increasing complexity to explore the role of mechanics in spheroid growth, all the while seeking to retain desirable simplicity and analytical tractability. Beginning with the theory of morphoelasticity, we successively refine our assumptions to develop a somewhat minimal model of mechanically regulated spheroid growth that is free from many unphysical and undesirable behaviours, and also agrees favourably with classical experimental results.