Dynamics of prostate cancer stem cells with diffusion and organism response |
| |
Authors: | Terrance Quinn Zachariah Sinkala |
| |
Institution: | Department of Mathematical Sciences Box 34, Middle Tennessee State University, Murfreesboro, TN 37132, USA |
| |
Abstract: | 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. |
| |
Keywords: | Cancer stem cells Avascular tumor Solid tumor Global attractor Traveling wave Diffusion Ordinary and partial differential equations Prostate |
本文献已被 ScienceDirect 等数据库收录! |
|