New Mathematical Models for Optimal Anti-Cancer Therapy

The objective of this award at the Interface of the Biological, Mathematical and Physical Sciences, and Engineering (BIOMAPS) is the development and optimization of new mathematical models for cancer treatment. In particular, the first part of the project involves developing mathematical models of intra-tumor heterogeneity and radiation induced cellular plasticity. The work will develop optimized radiation delivery schedules that incorporate therapy induced plasticity as well as normal tissue toxicity constraints and maintain clinical feasibility. This will be done using both non-linear programming techniques and heuristic methods such as simulated annealing. The PI will collaborate with a radiation biologist to further calibrate and validate mathematical models with mouse experiments. The second part of the project deals with modeling the impact of spatial tissue structure on cancer initiation and progression. Using tools from the field of interacting particle systems (such as duality and refined results about random walks) simplified models will be developed that allow for field cancerization to be studied.

If successful, the results of this research will lead to improvements in radiation therapy delivery schedules, and improvements in treatment and surveillance of epithelial cancers. The primary goal of this work is to develop new mathematical models for the evolution of cancer, and then to furthermore apply optimization techniques to these models to learn improved methods of treating the disease. In particular, radiation fractionation schedules will be developed that are predicted to improve patient survival, and further surveillance recommendations will be developed for the treatment of epithelial cancer. These results will have the potential to improve patient survival and quality of life. This work will also contribute to the solution of nonlinear optimization problems and the study of spatial stochastic processes.