Title: Mathematical Analysis of a Clonal Evolution Model of Tumor Cell Proliferation
Speaker: Glenn Webb (Vanderbilt University)
Abstract: An analysis is given for a partial differential equation model of a cancer cell population. The model structures the population with respect to cell age and cell telomere length. A continuous telomere length structure is assumed, which corresponds to the clonal model of tumor cell growth. This assumption leads to a model with a non-standard non-local boundary condition. The global existence and qualitative behavior of solutions are investigated. An analysis is made of the effect of telomere restoration on cancer cell dynamics. The results indicate that without telomere restoration, the cell population typically extinguishes. With telomere restoration, exponential growth is observed in the linear model. The effect of crowding induced mortality on the qualitative behavior of solutions is investigated in a nonlinear version of the model. Numerical simulations are given for various examples of the models.
