arrow
Volume 11, Issue 1
A Bistable Field Model of Cancer Dynamics

C. Cherubini, A. Gizzi, M. Bertolaso, V. Tambone & S. Filippi

Commun. Comput. Phys., 11 (2012), pp. 1-18.

Published online: 2012-11

Export citation
  • Abstract

Cancer spread is a dynamical process occurring not only in time but also in space which, for solid tumors at least, can be modeled quantitatively by reaction and diffusion equations with a bistable behavior: tumor cell colonization happens in a portion of tissue and propagates, but in some cases the process is stopped. Such a cancer proliferation/extinction dynamics is obtained in many mathematical models as a limit of complicated interacting biological fields. In this article we present a very basic model of cancer proliferation adopting the bistable equation for a single tumor cell dynamics. The reaction-diffusion theory is numerically and analytically studied and then extended in order to take into account dispersal effects in cancer progression in analogy with ecological models based on the porous medium equation. Possible implications of this approach for explanation and prediction of tumor development on the lines of existing studies on brain cancer progression are discussed. The potential role of continuum models in connecting the two predominant interpretative theories about cancer, once formalized in appropriate mathematical terms, is discussed.


  • Keywords

  • AMS Subject Headings

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{CiCP-11-1, author = {}, title = {A Bistable Field Model of Cancer Dynamics}, journal = {Communications in Computational Physics}, year = {2012}, volume = {11}, number = {1}, pages = {1--18}, abstract = {

Cancer spread is a dynamical process occurring not only in time but also in space which, for solid tumors at least, can be modeled quantitatively by reaction and diffusion equations with a bistable behavior: tumor cell colonization happens in a portion of tissue and propagates, but in some cases the process is stopped. Such a cancer proliferation/extinction dynamics is obtained in many mathematical models as a limit of complicated interacting biological fields. In this article we present a very basic model of cancer proliferation adopting the bistable equation for a single tumor cell dynamics. The reaction-diffusion theory is numerically and analytically studied and then extended in order to take into account dispersal effects in cancer progression in analogy with ecological models based on the porous medium equation. Possible implications of this approach for explanation and prediction of tumor development on the lines of existing studies on brain cancer progression are discussed. The potential role of continuum models in connecting the two predominant interpretative theories about cancer, once formalized in appropriate mathematical terms, is discussed.


}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.270710.220211a}, url = {http://global-sci.org/intro/article_detail/cicp/7351.html} }
TY - JOUR T1 - A Bistable Field Model of Cancer Dynamics JO - Communications in Computational Physics VL - 1 SP - 1 EP - 18 PY - 2012 DA - 2012/11 SN - 11 DO - http://doi.org/10.4208/cicp.270710.220211a UR - https://global-sci.org/intro/article_detail/cicp/7351.html KW - AB -

Cancer spread is a dynamical process occurring not only in time but also in space which, for solid tumors at least, can be modeled quantitatively by reaction and diffusion equations with a bistable behavior: tumor cell colonization happens in a portion of tissue and propagates, but in some cases the process is stopped. Such a cancer proliferation/extinction dynamics is obtained in many mathematical models as a limit of complicated interacting biological fields. In this article we present a very basic model of cancer proliferation adopting the bistable equation for a single tumor cell dynamics. The reaction-diffusion theory is numerically and analytically studied and then extended in order to take into account dispersal effects in cancer progression in analogy with ecological models based on the porous medium equation. Possible implications of this approach for explanation and prediction of tumor development on the lines of existing studies on brain cancer progression are discussed. The potential role of continuum models in connecting the two predominant interpretative theories about cancer, once formalized in appropriate mathematical terms, is discussed.


C. Cherubini, A. Gizzi, M. Bertolaso, V. Tambone & S. Filippi. (2020). A Bistable Field Model of Cancer Dynamics. Communications in Computational Physics. 11 (1). 1-18. doi:10.4208/cicp.270710.220211a
Copy to clipboard
The citation has been copied to your clipboard