Mathematical modeling tools and software for BME applications

Fred J. Vermolen, Amit Gefen

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


We consider a sequence of applications of hybrid cell-based finite-element models. These models are based on treating cells as individual particles, like in particle models. The behavior of the cells (regarding division, mutation, differentiation, death, migration, mechanical-chemical activity) depends on the environment they are in. The cells themselves influence their environment as well. Parameters like chemical concentrations and mechanical strains are modeled by the finite-element method. The applications involve cancer, wound healing, wound contracture, and the regeneration of a vascular network from preexisting blood vessels (angiogenesis). The current article is merely descriptive and does not highlight the mathematical details, such as the exact description of partial and stochastic differential equations involved in the studies.

Original languageEnglish
Title of host publicationEncyclopedia of Biomedical Engineering
Number of pages8
ISBN (Electronic)9780128051443
ISBN (Print)9780128048290
StatePublished - 1 Jan 2019


  • Cell death
  • Cell division
  • Cell migration
  • Chemotaxis
  • Durotaxis
  • Finite-element method
  • Particle method
  • Random walk
  • Stochastic model


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