|Time:||Feb. 3, 2016, 3:30pm-4:30pm.|
|Place:||106 McAllister Building.|
|Speaker:||Urszula Ledzewicz Southern Illinois University Edwardsville|
|Title:||Optimal Control for Multi-Targeted Cancer Therapies: Results and Open Problems|
Modern cancer treatment protocols are multi-targeted and take into account highly diverse subpopulations of cancerous cells with widely varying therapeutic sensitivities all embedded into the tumor microenvironment. This includes the vasculature as well as the elements of the immune system. Because of this complexity, dosage, frequency and sequencing of therapeutic agents may have a major effect on the outcome of treatment.
There is mounting medical evidence that "more is not necessarily better" and a properly calibrated dose which takes into account this complexity can lead to a better outcome. This has generated a search for what is called the biologically optimal dose (BOD) in the medical literature.
Formulating mathematical models with an objective that reflects the overall goal of the therapy, like minimizing the tumor size and side effects, maximizing immune system etc., leads to optimal control problems where mathematical analysis can answer some of these questions in a theoretical framework. In this talk, we present some of these problems starting with a model for heterogeneous tumor populations under chemotherapy and consider models for monotherapy of the anti-angiogenic inhibitors alone and combined with chemo and radiotherapy. Tumor-immune interactions under treatment will also be addressed leading to a single-input multi-target model for metronomic chemotherapy which is a new treatment protocols currently widely discussed in the medical literature. The resulting optimal control problems will be analyzed with the tools of geometric optimal control giving raise to challenging aspects related to singular controls, chattering controls and an overall synthesis of solutions. Some results and open questions coming from this analysis will be presented which are relevant and interesting both from the mathematical point of view and biomedical perspective.