Abstract: Cancer remains one of the biggest challenges in modern medicine. From the mathematical and computational perspective, there are number of outstanding grand challenges that are impeding our ability to understand, control and cure cancer. Among these, the first and the foremost is our ability to develop a quantitative understanding of tumor formation, tumor growth and tumor metastasis. In particular, the multi-scale processes that regulate events from tumor initiation to tumor metastasis remain elusive. Our ability to combat and cure cancer relies significantly upon determining the key regulators of cancer and identifying the bottlenecks that can be potentially promising targets for intervention. The focus of the proposed research is to develop the multi-scale framework that will allow us to identify such targets.
The proposed work will focus on developing general multi-scale modeling tools that will be able to connect molecular level events with events at the cellular level, multi-cellular and eventually tissue and organ level. In particular, we are interested in capturing changes in adhesion receptor density or structure with cell-matrix and cell-cell adhesion and then connect these effects at the cellular level with continuum models of overall tumor growth rate and morphology with applications in various cancers including ovarian, breast and prostate cancers. These models will be closely connected with experimental studies in our lab that will provide necessary initialization and calibration data.