Mathematical modeling and computational studies for proliferation kinetics of tumor growth with spatial-temporal dynamics

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Solid tumors are heterogeneous in composition. Cancer stem cells (CSCs) are a highly tumorigenic cell type found in developmentally diverse tumors that are believed to be resistant to standard chemotherapeutic drugs and responsible for tumor recurrence. Thus understanding the tumor growth kinetics and spatial composition 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. With a close integration with designed experiments, the main aims of this project are (1) to further develop and evaluate mathematical models to explore underlying mechanisms and biological factors to control the balance of tumor growth; (2) to develop both stochastic and continuous mathematical models to better understand the spatial structures of CSC populations during tumor growth; (3) to design fast and efficient numerical methods to solve the proposed mathematical models with moving and complex domains.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. Therefore, principles and techniques from multi-scale, stochastic and continuous models incorporated with new computational algorithms will be employed to achieve the study goals. By integrating complex regulatory networks and spatial distributions of nutrients during tumor growth to control proliferation, differentiation and cell layers of CSCs, the transformative studies and novel methodologies in this project will help revealing the underlying mechanisms to regulate the dynamics and spatial distributions of CSC derived cell lineages. 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. This project will mentor students through multidisciplinary training to advance their own scientific knowledge as well as contribute to the wider scientific body. The mathematical and computational toolbox to be developed in this work will also help to initiate a new project oriented course on computational biology for better training of both graduate and undergraduate students.