Hi, I'm Chloé from Paris, currently reading for a DPhil in Mathematical Biology in Oxford.
I'm a 4th year doctoral student at the Wolfson Centre for Mathematical Biology, which is part of the Department of Mathematics at the University of Oxford, and I am supervised by Prof Helen Byrne and Prof Philip Maini.
My research interests lie in the development and analysis of mechanistic mathematical models that describe biological systems, with a particular focus on medical applications. More precisely, I am interested in studying the mechanisms underpinning solid tumour growth, invasion and response to treatment.
As part of my DPhil, I have been working on two main projects. In the first project, I aim to investigate how different mechanisms for growth control influence tumour responses to radiotherapy (RT) and hyperthermia (HT), applied alone and in combination, as evidence suggests HT is a promising candidate for enhancing the efficacy of RT. In the second project, I aim to study tumour cell invasion into healthy tissue using continuum and discrete approaches.
Investigating the influence of growth arrest mechanisms on tumour responses to radiotherapy (joint with Philip K. Maini and Helen M. Byrne)
Cancer is a heterogeneous disease and tumours of the same type can differ greatly at the genetic and phenotypic levels. Understanding how these differences impact sensitivity to treatment is an essential step towards patient-specific treatment design. In this paper, we investigate how two different mechanisms for growth control may affect tumour cell responses to fractionated radiotherapy (RT) by extending an existing ordinary differential equation model of tumour growth. In the absence of treatment, this model distinguishes between growth arrest due to nutrient insufficiency and competition for space and exhibits three growth regimes: nutrient-limited (NL), space limited (SL) and bistable (BS), where both mechanisms for growth arrest coexist. We study the effect of RT for tumours in each regime, finding that tumours in the SL regime typically respond best to RT, while tumours in the BS regime typically respond worst to RT. For tumours in each regime, we also identify the biological processes that may explain positive and negative treatment outcomes and the dosing regimen which maximises the reduction in tumour burden.
Combining Mechanisms of Growth Arrest in Solid Tumours: A Mathematical Investigation (joint with Helen M. Byrne and Philip K. Maini)
The processes underpinning solid tumour growth involve the interactions between various healthy and tumour tissue components and the vasculature, and can be affected in different ways by cancer treatment. In particular, the growth-limiting mechanisms at play may influence tumour responses to treatment. In this paper, we propose a simple ordinary differential equation model of solid tumour growth to investigate how tumour-specific mechanisms of growth arrest may affect tumour response to different combination cancer therapies. We consider the interactions of tumour cells with the physical space in which they proliferate and a nutrient supplied by the tumour vasculature, with the aim of representing two distinct growth arrest mechanisms. More specifically, we wish to consider growth arrest due to (1) nutrient deficiency, which corresponds to balancing cell proliferation and death rates, and (2) competition for space, which corresponds to cessation of proliferation without cell death. We perform numerical simulations of the model and a steady-state analysis to determine the possible tumour growth scenarios described by the model. We find that there are three distinct growth regimes: the nutrient- and spatially limited regimes and a bi-stable regime, in which both growth arrest mechanisms are simultaneously active. Thus, the proposed model has the features required to investigate and distinguish tumour responses to different cancer treatments.
Travelling-wave analysis of a model of tumour invasion with degenerate, cross-dependent diffusion (joint with Faustino Sánchez-Garduño, Helen M. Byrne, Philip K. Maini, Tommaso Lorenzi)
In this paper, we carry out a travelling-wave analysis of a model of tumour invasion with degenerate, cross-dependent diffusion. We consider two types of invasive fronts of tumour tissue into extracellular matrix (ECM), which represents healthy tissue. These types differ according to whether the density of ECM far ahead of the wave front is maximal or not. In the former case, we use a shooting argument to prove that there exists a unique travelling wave solution for any positive propagation speed. In the latter case, we further develop this argument to prove that there exists a unique travelling wave solution for any propagation speed greater than or equal to a strictly positive minimal wave speed. Using a combination of analytical and numerical results, we conjecture that the minimal wave speed depends monotonically on the degradation rate of ECM by tumour cells and the ECM density far ahead of the front.
Master's Dissertation: Mathematical modelling of tumour growth
The increasing cancer burden on society has motivated the development of new therapies to complement existing ones. Hyperthermia has garnered significant interest, showing noteworthy potential to act synergistically with radiotherapy. In this paper, we extend a spatially-resolved mathematical model for tumour growth proposed by Greenspan (Stud. Appl. Math., 1972), first incorporating treatments of hyperthermia alone and then combined with radiation. We use this first model to compare the Jung (Jung, Radiat. Res., 1986) and AlphaR (Brüningk et al. Int. J. Hyperth., 2018) survival functions, which we use to represent hyperthermia treatment effects. We also compare this model’s predictions to experimental data and data generated by a cellular automaton model developed by Brüningk et al. (J. Royal Soc. Interface, 2018). Model simulations do not align with the data, underlining modifications required to enhance the accuracy of our model’s predictions. We lastly investigate the benefits of a combination therapy, specifically showing that treatment efficacy differences between a uni-modal and a multi-modal therapy increase with tumour hypoxia. Even though our model requires improvements, our work suggests that tumour composition may be important for clinical applications in terms of predicting tumour response to combined hyperthermia and radiotherapy.
Mathematical modelling of tumour responses to combined treatments of hyperthermia and radiotherapy (Oct 2021). ISMCO 2021
Phenotypic coexistence as a facilitator of tumour invasion (May 2021). Academix 2021: Intercollegiate Conference, University of Oxford, UK
Modelling the response of solid tumours to hyperthermia (Jan 2021). Wolfson Centre for Mathematical Biology Group Meeting, University of Oxford, UK
Phenotypic switching and coexistence as a hallmark of successful cancer invasion (May 2020). Mathematical Oncology Group, University of Oxford, UK
(website is work in progress!)
contact me at chloe [dot] colson [at] my institution