Computational Cell-Based Modeling and Visualization of Cancer Development and Progression

Jiao Chen*, Daphne Weihs, Fred J. Vermolen

*Corresponding author for this work

Research output: Chapter in Book/Conference proceedings/Edited volumeChapterScientific


This paper presents a review of the role of mathematical modeling in investigating cancer progression, focusing on five models developed in our group. A brief overview of computational modeling progress is presented, followed by introduction of several mathematical formalisms (e.g., stochastic differential equations), numerical methods (e.g., finite element method, Green's functions, and combinations of time integration), and Monte Carlo simulations, which are currently used to quantify the underlying biomedical mechanisms, to approximate the results and to evaluate the impact of the input variables. Next, we provide specific examples of the computational models that we developed aimed at predicting the dynamics of the initiation and progression of cancer. Our simulation results show qualitative consistency with references and/or available experimental observations. Finally, perspectives are drawn on the possibilities of mathematical modeling for the prospects of cancer understanding and treatment therapies.

Original languageEnglish
Title of host publicationNew Developments on Computational Methods and Imaging in Biomechanics and Biomedical Engineering
EditorsJoão Manuel R. S. Tavares, Paulo Rui Fernandes
Place of PublicationCham
Number of pages27
ISBN (Electronic)978-3-030-23073-9
ISBN (Print)978-3-030-23072-2
Publication statusPublished - 2019

Publication series

NameLecture Notes in Computational Vision and Biomechanics
ISSN (Print)2212-9391
ISSN (Electronic)2212-9413


  • Angiogenesis
  • Cancer progression
  • Cell deformation
  • Cell migration
  • Immune responses
  • Mathematical modeling
  • Metastasis
  • Numerical method


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