Modeling tumor growth with peridynamics
- 819 Downloads
Computational models of tumors have the potential to connect observations made on the cellular and the tissue scales. With cellular scale models, each cell can be treated as a discrete entity, while tissue scale models typically represent tumors as a continuum. Though the discrete approach often enables a more mechanistic and biologically driven description of cellular behavior, it is often computationally intractable on the tissue scale. Here, we adapt peridynamics, a theoretical and computational approach designed to unify the mechanics of discrete and continuous media, for the growth of biological materials. The result is a computational model for tumor growth that can represent either individual cells or the tissue as a whole. We take advantage of the flexibility provided by the peridynamic framework to implement a cell division mechanism, motivated by the fact that cell division is the mechanism driving tumor growth. This paper provides a general framework for implementing a new tumor growth modeling technique.
KeywordsPeridynamics Tumor growth Morphogenesis Cell division
Mathematics Subject Classification92C10 74L15
Compliance with ethical standards
This work was supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE-114747.
Conflict of interest
The authors declare that they have no conflict of interest.
- Gatenby R, Gawlinski E (1996) A reaction–diffusion model of cancer invasion. Cancer Res 56(24):5745–5753Google Scholar
- Littlewood D (2015) Roadmap for peridynamic software implementation. SAND Report, Aandia National Laboratories, Albuquerque, NM and Livermore, CAGoogle Scholar
- Mitchell JA (2011) A nonlocal, ordinary, state-based plasticity model for peridynamics. SAND report 3166Google Scholar
- Silling S, Askari E (2005) A meshfree method based on the peridynamic model of solid mechanics. Comput Struct 83(17–18):1526–1535Google Scholar
- Wang Z, Butner J, Kerketta R, Cristini V, Deisboeck TS (2015) Simulating cancer growth with multiscale agent-based modeling. Semin Cancer Biol 30:70–78Google Scholar