Chaotic Attractor in Tumor Growth

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

Model equations: , where , , and are functions of time that represent tumor cell density, MDE (mucinous ductal ectasia) concentration, MM (malignant melanoma) concentration and oxygen concentration, respectively. These temporal equations were derived from a reaction-diffusion model from the tumor growth. The model mathematically describes both the processes of carcinogenesis and metastasis, as well as the sensitive dependence of cancer evolution on initial conditions and parameters. On the basis of this chaotic cancer attractor, a generic concept of carcinogenesis and metastasis is formulated.

[more]

Parameters: = tumor cell volume (proliferation/non-proliferation fraction), = glucose level, = number of tumor cells, = diffusion from surface (saturation level), = -decay (MM concentration), = -growth (MDE concentration) and , , are (oxygen concentration) growth and decay parameters.

[less]

Contributed by: Tijana Ivancevic (March 2011)
Open content licensed under CC BY-NC-SA


Snapshots


Details

Reference: T. T. Ivancevic, M. J. Bottema, and L. C. Jain, "A Theoretical Model of Chaotic Attractor in Tumor Growth and Metastasis," arXiv:0807.4272 in Cornell University Library's arXiv.org.



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send