Mathematical modeling of brain tumor growth with therapies
Abstract: This talk will discuss how to mathematically model solid brain tumor – glioma – growth under influences of oncolytic viral therapy and radiation, and to identify the function of the immune system in the growth process. Those models are free boundary problems of parabolic partial differential equations which cooperate necessary variables for each biological or medical problem. Particularly, we will present three free boundary problems and their variants. For virotherapy and radiation, our models have four cell populations and virus population with cell convection and virus diffusion, and the free boundary is given by a velocity field. For immune system function, our model describes immune cells follow chemoattractant gradient to the tumor site, and tumor cells convect within the tumor boundary which is moving according to a velocity. Our models have been experimentally verified. I will also describe medical experiments.
