Dynamics of prostate cancer stem cells with diffusion and organism response.
We develop a systems based model for prostate cancer, as a sub-system of the organism. We accomplish this in two stages. We first start with a general ODE that includes organism response terms. Then, to account for normally observed spatial diffusion of cell populations, the ODE is extended to a PDE that includes spatial terms. Numerical solutions of the full PDE are provided, and are indicative of traveling wave fronts. This motivates the use of a well known transformation to derive a canonically related (non-linear) system of ODEs for traveling wave solutions. For biological feasibility, we show that the non-negative cone for the traveling wave system is time invariant. We also prove that the traveling waves have a unique global attractor. Biologically, the global attractor would be the limit for the avascular tumor growth. We conclude with comments on clinical implications of the model.
Quinn
Terrance
T
Department of Mathematical Sciences, Middle Tennessee State University, Murfreesboro, 37132, USA. tquinn@mtsu.edu
Sinkala
Zachariah
Z
D002471:Cell Transformation, Neoplastic / Q000473:pathology*; D003198:Computer Simulation; D006801:Humans; D008297:Male; D008954:Models, Biological; D011230:Precancerous Conditions / Q000473:pathology* / Q000503:physiopathology*; D011471:Prostatic Neoplasms / Q000473:pathology* / Q000503:physiopathology*; D013234:Stem Cells / Q000473:pathology* / Q000502:physiology*