Mathematical Modeling, Computational and Experimental Investigation of the Dynamics of Heterogeneity in Breast Cancer

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Despite aggressive clinical treatment including surgical resection, radiation, and chemotherapy, tumor recurrence is essentially universal. Therapeutic failure is due, in part, to tumor cell heterogeneity, derived from both genetic and non-genetic sources, which contributes to therapeutic resistance and tumor progression. Understanding this heterogeneity is the key for the development of targeted cancer-preventative and -therapeutic interventions. One of the currently prevailing models explaining intratumoral heterogeneity is the cancer stem cell (CSC) hypothesis. Oncogene HER2 is a well-studied oncogene known for its role in promoting cancer cell survival and proliferation, and recently implicated in generation and maintenance of CSCs. Thus understanding the HER2 signaling is critical for development of novel strategies for cancer treatment, while tumor growth is a very complicated phenomenon involving many inter-related processes across a wide range of spatial and temporal scales, which makes the mathematical modeling and computation very challenging. This research seeks to employ modeling techniques and computational studies to address complex issues arising from tumor growth at the interface of mathematics, chemical engineering and biology. Successful completion of this project will also have a significant impact on public health, as the research findings can be used to develop diagnostics, prognostics, and therapeutics to more specifically target cancer stem cells. The proposed research of mathematical modeling and experimental studies for cancer cells creates a unique multidisciplinary research environment that attracts both undergraduate and graduate students (especially women and minority students) from all disciplines to join our research team.With a close integration with experiments, the PI will perform multi-scale modeling and computational investigation of HER2 signaling in modulating CSC population in cancer tumor growth with spatial-temporal dynamics. To better explore HER2 signaling for better understanding the heterogeneity in breast cancer, PI shall develop a multi-scale model coupled cell signaling with cell population to study the dynamics control of CSCs. This control mechanism capitalizes on emerging evidences in literature, and correlates with recent findings from new observed experimental data. It is widely believed that a key mechanism for proper maintenance of a cell lineage to occur is the formation and substance of the stem cell niche, a microenvironment where stem cells reside in a tissue. To explore the CSCs' spatial patterns for tumor growth, PI will also develop a continuum PDE model coupled HER2 signaling with multistage cell lineage models and spatial effects of nutrients. Specific tasks are: (1) to investigate the roles of HER2 signaling in controlling and maintenance of CSCs, and develop and evaluate multi-scale models to explore underlying mechanisms and biological factors to control the balance of tumor growth; (2) to further develop continuous mathematical models to better understand the spatial structures of CSC populations during tumor growth with different effects of various biological factors; (3) to design fast and efficient numerical methods for solving the mathematical models with moving and complex domains.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.