<?xml version="1.0" encoding="UTF-8"?> <article key="pdf/512" mdate="2010-05-27 00:00:00"> <author>Zachariah Sinkala</author> <title>Evolutionary of Prostate Cancer Stem Cells in Prostate Duct</title> <pages>597 - 607</pages> <year>2010</year> <volume>4</volume> <number>5</number> <journal>International Journal of Mathematical and Computational Sciences</journal> <ee>https://publications.waset.org/pdf/512</ee> <url>https://publications.waset.org/vol/41</url> <publisher>World Academy of Science, Engineering and Technology</publisher> <abstract>A systems approach model for prostate cancer in prostate duct, as a subsystem of the organism is developed. It is accomplished in two steps. First this research work starts with a nonlinear system of coupled FokkerPlank equations which models continuous process of the system like motion of cells. Then extended to PDEs that include discontinuous processes like cell mutations, proliferation and deaths. The discontinuous processes is modeled by using intensity poisson processes. The model incorporates the features of the prostate duct. The system of PDEs spatial coordinate is along the proximal distal axis. Its parameters depend on features of the prostate duct. The movement of cells is biased towards distal region and mutations of prostate cancer cells is localized in the proximal region. Numerical solutions of the full system of equations are provided, and are exhibit traveling wave fronts phenomena. This motivates the use of the standard transformation to derive a canonically related system of ODEs for traveling wave solutions. The results obtained show persistence of prostate cancer by showing that the nonnegative cone for the traveling wave system is time invariant. The traveling waves have a unique global attractor is proved also. Biologically, the global attractor verifies that evolution of prostate cancer stem cells exhibit the avascular tumor growth. These numerical solutions show that altering prostate stem cell movement or mutation of prostate cancer cells lead to avascular tumor. Conclusion with comments on clinical implications of the model is discussed. </abstract> <index>Open Science Index 41, 2010</index> </article>