Investigating the impact of growth arrest mechanisms on tumour growth and responses to radiotherapy and hyperthermia

Thesis

Developing targeted and effective treatment strategies for patients is at the forefront of cancer research today. Combination therapies that exploit different ways to treat cancer cells, while minimising adverse side-effects, have gained increased traction in recent years. In particular, hyperthermia (HT) has emerged as a promising candidate for enhancing tumour responses to radiotherapy (RT), a well-established cancer treatment used to treat more than 50% of cancer patients. However, an incomplete understanding of the interactions between RT and HT is hindering their combined use in the clinic. Inter- and intra-tumoural heterogeneity also impacts cancer progression and sensitivity to treatment. In this thesis, we develop a mathematical framework to characterise how two different mechanisms of growth control, namely growth arrest due to nutrient insufficiency and due to competition for space, may influence tumour dynamics during disease progression and under HT and/or RT.

We first develop a simple ordinary differential equation model of tumour growth which distinguishes between nutrient and space limited growth control. We find that there are three distinct growth regimes: nutrient limited, space limited and bistable, where both mechanisms of growth arrest coexist. We then extend our model to study the responses of tumours in each regime to RT and HT individually and in combination. In each regime, we determine the biological processes that may underpin positive and negative treatment outcomes and assess which treatment (RT, HT or RT + HT) and dosing regimen maximise the reduction in tumour burden. This work enables us to generate a set of hypotheses that may explain some of the widely varying tumour behaviours observed experimentally and clinically.

With a view to extending the preceding work to investigate how nutrient and space limited mechanisms of growth arrest influence tumour invasion, we study a simple model of tumour cell invasion into healthy tissue. This process has frequently been modelled by systems of coupled partial differential equations involving degenerate, cross-dependent diffusion. We propose a minimal model that captures these features, while remaining an- alytically tractable. We carry out a travelling wave analysis and prove the existence and uniqueness of two types of invasive fronts of tumour cells into the extracellular matrix (ECM), which differ according to whether the density of the ECM ahead of the wave front is at carrying capacity or not. We also establish relationships between the speed of invasion and key model parameters.

Authors: Colson, C

• DOI: 10.5287/ora-9ee4oxk5v
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: cancer; partial differential equations; mathematical modelling; ordinary differential equations
• Subjects: Biological systems--Mathematical models; Mathematical analysis; Applied mathematics; Lungs--Cancer--Epidemiology--Mathematical models