TY - JOUR

T1 - Minimal Morphoelastic Models of Solid Tumour Spheroids: A Tutorial

AU - Walker, Benjamin J

AU - Celora, Giulia

AU - Goriely, Alain

AU - Moulton, Derek

AU - Byrne, Helen

N1 - Funding BJW is supported by the Royal Commission for the Exhibition of 1851. GLC is supported by EPSRC and MRC Centre for Doctoral Training in Systems Approaches to Biomedical Science (grant number EP/L016044/1) and Cancer Research UK. The work of AG was supported by the Engineering and Physical Sciences Research Council grant EP/R020205/1.

PY - 2023/3/3

Y1 - 2023/3/3

N2 - 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 tutorial, we 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, which combines solid mechanics and growth, 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. In doing so, we will see how iterating upon simple models can provide rigorous guarantees of emergent behaviour, which are often precluded by existing, more complex modelling approaches. Perhaps surprisingly, we also demonstrate that the f inal model considered in this tutorial agrees favourably with classical experimental results, highlighting the potential for simple models to provide mechanistic insight whilst also serving as mathematical examples.

AB - 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 tutorial, we 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, which combines solid mechanics and growth, 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. In doing so, we will see how iterating upon simple models can provide rigorous guarantees of emergent behaviour, which are often precluded by existing, more complex modelling approaches. Perhaps surprisingly, we also demonstrate that the f inal model considered in this tutorial agrees favourably with classical experimental results, highlighting the potential for simple models to provide mechanistic insight whilst also serving as mathematical examples.

M3 - Article

JO - Bulletin of Mathematical Biology

JF - Bulletin of Mathematical Biology

SN - 0092-8240

ER -