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Minimal Morphoelastic Models of Solid Tumour Spheroids: A Tutorial.

Benjamin J Walker1,2, Giulia L Celora3,4, Alain Goriely4

  • 1Department of Mathematical Sciences, University of Bath, Claverton Down, Bath, BA2 7AY, UK. bjw43@bath.ac.uk.

Bulletin of Mathematical Biology
|March 29, 2023
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Summary
This summary is machine-generated.

Mathematical models exploring tumor spheroid growth reveal the significant, yet understudied, role of mechanical forces. This research presents a hierarchy of models, culminating in a minimal, analytically tractable approach that accurately predicts spheroid growth dynamics.

Keywords:
Mathematical modellingMorphoelasticityStress-dependent growthTumour dynamics

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Area of Science:

  • Mathematical Biology
  • Biophysics
  • Computational Biology

Background:

  • Tumor spheroids are crucial in cancer research, with mathematical models extensively used to study their growth.
  • Mechanical effects on spheroid growth are significant but remain less explored theoretically and experimentally.
  • Existing models often exhibit unphysical behaviors or lack analytical tractability.

Purpose of the Study:

  • To formulate a hierarchy of mathematical models to investigate the role of mechanics in spheroid growth.
  • To develop a minimal, analytically tractable model for mechanically regulated spheroid growth.
  • To demonstrate how iterative refinement of simple models can yield reliable emergent behaviors.

Main Methods:

  • Utilizing the theory of morphoelasticity, combining solid mechanics and biological growth.
  • Developing a sequence of mathematical models with increasing complexity.
  • Refining assumptions to create a minimal model free from unphysical behaviors.

Main Results:

  • A hierarchy of models was formulated, exploring mechanically regulated spheroid growth.
  • A minimal model was developed, demonstrating desirable simplicity and analytical tractability.
  • The final model showed favorable agreement with classical experimental results.

Conclusions:

  • Simple mathematical models can provide mechanistic insights into tumor spheroid growth.
  • Iterative model refinement ensures rigorous guarantees of emergent behavior.
  • Mechanics play a critical role in spheroid growth dynamics, and simplified models can effectively capture these effects.