Mathematical Oncology: Models, analysis,simulation and applications
This project aims to undertake mathematical research with a strong multidisciplinary and translational component by studying several real problems arising in oncology. The main goal is to explore the viability of mathematical models as real ancillary tools in the understanding of the complexity of some primary brain tumors (gliomas) and other related malignant neoplasms. We plan to study those models and use them to devise optimum strategies combining standard radiotherapy, chemotherapy and antiangiogenic therapy with novel therapies such as those targeting the metabolism and thromboembolism in gliomas and other tumor types. Specifically, we will develop and study theoretically and numerically a set of mathematical models at the microscopic and macroscopic levels dealing with low and high grade gliomas: from diffuse astrocytoma to anaplastic astrocytoma and glioblastoma. Our models, based on ordinary and partial differential equations will incorporate the dynamics of the various cell phenotypes, oxygen conditions and metabolites encountered in the tumor environment together with the remodelling of the tumor vasculature. In close collaboration with oncologists, these models will be tested to assess their validity in obtaining new prognostic metrics of individual patients with gliomas and to monitor and optimize the response to different therapy modalities by setting appropriate mathematical optimization problems. We also plan to extend the modelling techniques and results to other types of cancer and to describe well-known clinical observations regarding the surgical resection of primary tumors and the subsequent explosion of distant tumor metastases.
Ministerio de Economía y Competitividad (2013-2015)
Universidad de Castilla-La Mancha