The purpose of my PhD is to use statistical techniques to answer questions regarding cell spreading. Understanding how cells migrate, proliferate and aggregate tells us how wounds begin to heal, how cancers invade new tissues and how defects can occur in developing embryos. My main research focus is bridging the gap between experiments and established mathematical models of cell spreading through analysis and parameter inference using Approximate Bayesian Computation. My supervisors are Ruth Baker and Mat Simpson.
In the summers of 2011 and 2013 I completed summer projects based in Oxford, and these are outlined below:
I completed a 6 week summer placement at Oxford Partial Differential Equations group on the topic of “broadband invisibility”, with the aim of finding sharp bounds for solutions to the 3D Helmholtz equation. (2011) On the scattered field generated by a ball inhomogeneity of constant index in dimension three - Yves Capdeboscq, George Leadbetter and Andrew Parker: http://www.ams.org/books/conm/577/
Statistical Inference using CUDA
I completed a 10 week summer placement at Oxford e-Research Centre in collaboration with Diamond Light Source Ltd and sponsored by Nvidia. The aim of the project was to speed up an existing program used for protein crystallography, by implementing the CUDA parallel processing language. (2013) CUDA optimised statistical inference techniques - Jackknife and Blocked Bootstrap: https://github.com/andrew-parker/COSIT
As part of the doctoral training centre programme, each student spends the latter end of their first year undergoing two short projects in two different current research groups, before deciding what research to continue with in their PhD. The titles and abstracts for my projects are as follows:
Cell Pushing in Exclusion Processes
Cell migration and proliferation are integral to the proper functioning of many biological processes. Techniques have been developed to investigate these processes in a quantified way, through both individual-based models and population-level models. We seek to compare these two scales by deriving partial differential equations from the decision rules for a single cell in the individual-based model, extended into the new context of cell pushing interactions. Intrinsic to many of these individual-based models is the requirement of an underlying lattice on which cells reside and are constricted to move. We extend current exclusion processes which are lattice-based to incorporate a probability of cell-cell pushing, which has been observed experimentally, and consider how this model changes when put into a lattice-free context. We show that the averaged behaviour of individual-based models can be replicated well by solving the corresponding PDE for different possible pushing mechanisms, and that pushing in the off-lattice case provides a strikingly different result to the on-lattice case.
Model Choice for Heart Models
There are many established mathematical models of cardiac cells which are used in order to gain further understanding into the heart. These models are typically of the form of ODE models, which are motivated using a combination of the physics behind electrical conductance and experimental observations. Unfortunately, there is difficulty in choosing what model is best suited to specific individual cases, due to the intrinsic variability between subjects. We elucidate this difficulty by inferring the best model and parameter choice on experimental data, using approximate Bayesian computation. This approach has been used previously in evolutionary biology, amongst other disciplines, but has not yet been applied in the context of heart models. We will also determine whether the same heart model can capture the effects of going from healthy cells to diseased cells by altering the parameters of the model, or whether a completely new model is needed to capture the effects of this change.
I completed my undergraduate Masters degree in Mathematics (MMath) with a First from Mansfield College, University of Oxford in 2013. Presently, I am a second year DPhil student at the Systems Biology Doctoral Training Centre, based in the Mathematical Institute. Outside of my research I have several hobbies, ranging from juggling and archery to baking and board games! I am also engaged to my fiancée Sarah Medley, and we are planning to wed in 2016!
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