Mathematical and computational modeling approaches have been applied to every aspect of tumor growth from mutation acquisition and tumorigenesis to metastasis and treatment response. My research focuses on developing mathematical approaches that are able to address critical questions associated with vascular tumor progression and targeted therapeutics. In order to improve therapeutic outcomes for cancers, a substantial amount of research is now focusing on the molecular biology of the tumors in an attempt to selectively target pathways involved in tumor progression. Increased understanding of molecular mechanisms and basic pathways in the pathogenesis of cancers is leading to the targeted manipulation of these pathways, and new cell-specific approaches to cancer therapy that operate at the molecular level are now being developed. Some of the new approaches aim specifically to inhibit tumor growth and spread by targeting the tumor microenvironment, while others focus on specific protein or signal transduction pathways associated with tumor cell and/or blood vessel proliferation and survival. With an eye toward addressing critical challenges associated with targeted molecular therapeutics, my collaborators and I have developed a suite of mathematical models that are designed to optimize the use of targeted drug treatment strategies. These mathematical models connect the molecular events associated with cancer stem cell-driven tumor growth and/or tumor-induced blood vessel formation with the temporal changes in tumor cell and/or endothelial cell proliferation, migration and survival, and link these dynamics to tumor growth, vascular composition, and therapeutic outcome. We use these models to investigate the integrated effects of various molecular players on the bidirectional communication (i.e. crosstalk) between endothelial cells and tumor cells that contribute to and enhances key aspects of tumorigenesis and can lead to evasive therapeutic resistance.