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

  • Jiao ChenEmail author
  • Daphne Weihs
  • Fred J. Vermolen
Chapter
Part of the Lecture Notes in Computational Vision and Biomechanics book series (LNCVB, volume 33)

Abstract

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.

Keywords

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

Notes

Acknowledgements

This study is financially supported by the China Scholarship Council and the authors are very grateful for this funding. The authors declare that they do not have any conflicts of interest.

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Authors and Affiliations

  1. 1.Delft Institute of Applied MathematicsDelft University of TechnologyDelftThe Netherlands
  2. 2.Faculty of Biomedical EngineeringTechnion-Israel Institute of TechnologyHaifaIsrael

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