General Information

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Project Description

Tumor growth can be modeled as a Galton-Watson process, a branching stochastic process in which cells divide normally, acquire mutations, or die at discrete time steps. Many studies have modeled cancer growth using Galton-Watson processes without consideration of spatial constraints. However, when a cancer cell divides, daughter cells may inhabit different regions than its parent cell; consequently, one would expect that significant cell diffusion occurs during neoplastic growth. Incorporating such spatial dynamics in mathematical models may lead to new insights about the evolution of tumors. Our goal is to develop a mathematical framework for understanding spatiotemporal cancer dynamics.

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Weekly Log

Week 1:

After meeting the other participants and being welcomed into the program, I met with my mentor, Subho, to discuss the research I will be doing for the next eight weeks. He described some of the basic mechanisms of neoplastic growth and how stochastic branching process models are used to describe tumor evolution. Then, he stated the question of interest: What mathematical insights can be obtained from stochastic models of cancer which incorporate spatial details? Under his suggestion, I reviewed literature to search for previous analysis of analogous birth-death processes in fields outside of oncology as a starting point. Luckily, I found a paper which used the theory of birth-death processes to model chemical reactions, and explicated how to completely determine the equations which govern the simple birth-death process. Finally, I finished writing up my introductory presentation Saturday morning.

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Presentations

• First Presentation

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Additional Information

• My Mentor: Dr. Subhajyoti De
• My Lab: SjD Laboratory