New Mathematical Models for Optimal Anti-Cancer Therapy

生物、数学和物理科学与工程（BIOMAPS）交叉奖的目标是开发和优化用于癌症治疗的新数学模型。特别是，该项目的第一部分涉及到发展肿瘤内异质性和辐射诱导的细胞可塑性的数学模型。这项工作将制定优化的放射递送时间表，结合治疗诱导的可塑性以及正常组织毒性限制，并保持临床可行性。这将使用非线性规划技术和启发式方法（如模拟退火）来完成。PI将与一名辐射生物学家合作，通过小鼠实验进一步校准和验证数学模型。该项目的第二部分涉及空间组织结构对癌症发生和发展的影响建模。使用来自相互作用粒子系统领域的工具（例如关于随机游走的对偶性和精炼结果），将开发简化模型，允许研究场癌变。如果成功，这项研究的结果将导致放射治疗递送时间表的改进，以及上皮性癌症的治疗和监测的改进。这项工作的主要目标是为癌症的进化建立新的数学模型，然后进一步将优化技术应用于这些模型，以学习治疗疾病的改进方法。特别是，将制定预计可提高患者生存率的放射分治计划，并将制定用于上皮性癌症治疗的进一步监测建议。这些结果将有可能改善患者的生存和生活质量。这项工作也将有助于解决非线性优化问题和空间随机过程的研究。

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.