University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
My research interests lie in the field of Mathematical Oncology; specifically, I study multiscale approaches to modeling and simulating the process of angiogenesis, which is the process by which new blood vessels are created from existing vasculature. My current work focuses on investigating the relationship betweeen stochastic, discrete models of angiogenesis that are formulated at the cellular level to continuous approaches that focus on larger-scale (e.g., tissue-level) behavior.
I work in the Wolfson Centre for Mathematical Biology on the modeling of tumor-induced angiogenesis, which is the process by which blood vessels grow and develop from existing vasculature. Typically tumors initially grow in an environment in which diffusion is the main means of nutrient transport, however after a certain period of time the tumor becomes too large for diffusion to carry these substances to every cell. This causes some tumor cells to become hypoxic, and in response they release tumor angiogenic factors (TAFs) that can initiate angiogenesis, re-establish nutrient delivery for the tumor, and provide the tumor with a route for metastasis. I specifically study multiscale approaches to angiogenesis modeling, from continuum models on the macroscopic scale to stochastic, discrete agent-based models (ABMs) on the microscale. My long-term goal is to improve current angiogenesis models and enhance their predictive power, thereby assisting biologists, clinicians, and pharmacists at developing optimal anti-angiogenic treatments for specific individuals.
- Graduate Teaching Assistant - Mathematical Institute, Oxford
- Academic Year 2018-2019 - Further Mathematical Biology (B5.5)
- Academic Year 2018-2019 - Numerical Solutions to Differential Equations I (B6.1)
- Academic Year 2019-2020 - Further Mathematical Biology (B5.5)
- Academic Year 2019-2020 - Nonlinear Systems (MMSC, B5.6)
- Graduate Teaching Assitant - Balliol College, Oxford
- Academic Year 2020-2021 - Probability (M3)
- Academic Year 2020-2021 - Introductory Calculus (M3)
Last Updated October 2020
Prizes, awards, and scholarships:
Keasbey Memorial Foundation Graduate Scholarship - Awarded December 2017
Major / recent publications:
Multiscale modeling and simulation of traveling waves in biology: A review.
Martinson, W; Byrne, H; Maini, P
Rendiconti di Matematica (accepted for publication 13/07/2019)