Abstract—Cancer stem cells (CSCs) are cancer cells that exhibit stem cell-like properties. They are immune to standard chemotherapy and are often implicated for relapse and metastasis. Modeling of CSC-caused relapse is difficult as organisms tend to die before the relapse can be studied, and thus in silico models are ideal but are in development. Two kinds of CSC-induced tumor growth were modeled mathematically and visually using the mass-action and spatial models. Mathematical models of population growth and a better understanding of cancer stem cell population dynamics and neural networks can be achieved by applying discrete stochastic models, automata theory, and cellular automaton. Due to its wide range of possibilities, cellular automata theory opens up new field of mathematical applications in cancer modeling and providing a bridge between bioinformatics and individualized cancer modeling.

Index Terms—Cancer stem cell, cellular automata, tumorigenesis, stochastic, gompertzian growth.

A. Q. Ninh is with the California State University, Fullerton, CA, 92708 USA (e-mail: andrewninh@ieee.org).

 

Cite:Andrew Q. Ninh, "Two Discrete Stochastic Cellular Automata Models of Cancer Stem Cell Proliferation," International Journal of Bioscience, Biochemistry and Bioinformatics vol. 3, no. 5, pp. 479-482, 2013.