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    Karolak, Aleksandra Markov, Dmitry A. McCawley, Lisa J. and Rejniak, Katarzyna A. 2018. Towards personalized computational oncology: from spatial models of tumour spheroids, to organoids, to tissues. Journal of The Royal Society Interface, Vol. 15, Issue. 138, p. 20170703.

    Rocha, H. L. Almeida, R. C. Lima, E. A. B. F. Resende, A. C. M. Oden, J. T. and Yankeelov, T. E. 2018. A hybrid three-scale model of tumor growth. Mathematical Models and Methods in Applied Sciences, Vol. 28, Issue. 01, p. 61.

    Inokawa, Hiroshi Katayama, Norihiro and Nakao, Mitsuyuki 2016. Evaluation of multidrug cancer chronotherapy based on cell cycle model under influences of circadian clock. p. 1439.

    Wang, Zhihui Butner, Joseph D. Cristini, Vittorio and Deisboeck, Thomas S. 2015. Integrated PK-PD and agent-based modeling in oncology. Journal of Pharmacokinetics and Pharmacodynamics, Vol. 42, Issue. 2, p. 179.

    Taffetani, Matteo de Falco, Carlo Penta, Raimondo Ambrosi, Davide and Ciarletta, Pasquale 2014. Biomechanical modelling in nanomedicine: multiscale approaches and future challenges. Archive of Applied Mechanics, Vol. 84, Issue. 9-11, p. 1627.

    Milde, Florian Tauriello, Gerardo Haberkern, Hannah and Koumoutsakos, Petros 2014. SEM++: A particle model of cellular growth, signaling and migration. Computational Particle Mechanics, Vol. 1, Issue. 2, p. 211.

    Hatzikirou, Haralampos Chauviere, Arnaud Bauer, Amy L. Leier, André Lewis, Michael T. Macklin, Paul Marquez-Lago, Tatiana T. Bearer, Elaine L. and Cristini, Vittorio 2012. Integrative physical oncology. Wiley Interdisciplinary Reviews: Systems Biology and Medicine, Vol. 4, Issue. 1, p. 1.

    D'Antonio, Gianluca Macklin, Paul and Preziosi, Luigi 2012. An agent-based model for elasto-plastic mechanical interactions between cells, basement membrane and extracellular matrix. Mathematical Biosciences and Engineering, Vol. 10, Issue. 1, p. 75.

    Deisboeck, Thomas S. Wang, Zhihui Macklin, Paul and Cristini, Vittorio 2011. Multiscale Cancer Modeling. Annual Review of Biomedical Engineering, Vol. 13, Issue. 1, p. 127.

  • Print publication year: 2010
  • Online publication date: October 2010

6 - Discrete cell modeling

from Part I - Theory

In this chapter, we introduce discrete cancer-cell modeling, assess the strengths and weaknesses of the available discrete cell modeling approaches, sample the major discrete cell modeling approaches employed in current computational cancer modeling, and introduce a discrete agent-based cell modeling framework. This framework currently being developed by the present authors and collaborators will be used to implement the next-generation multiscale cancer-modeling framework detailed in Chapter 7.

A brief review of discrete modeling in cancer biology

Thus far we have discussed continuum modeling, in which cancer is modeled at the tissue scale and the effects of individual cells are averaged out. We now turn our attention to discrete models, in which the behavior of one or more individual cells as they interact with one another and the microenvironment is addressed.

Discrete modeling has enjoyed a long history in applied mathematics and biology, dating as far back as the 1940s when John von Neumann applied lattice crystal models to study the necessary rule sets for self-replicating robots. Perhaps the most famous early example of discrete biological modeling is John Conway's 1970 “game of life,” a two-dimensional rectangular lattice of “cells” that changed color according to rules based upon the colors of the neighboring cells. Even simple rules can lead to complex emergent behavior, and Conway's model was later shown to be Turing complete. Today, discrete cell modeling has advanced to study a broad swath of cancer biology, spanning carcinogenesis, tumor growth, invasion, and angiogenesis.

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Multiscale Modeling of Cancer
  • Online ISBN: 9780511781452
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