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Title: An interacting particle approach to problems in cancer : osteocyte network formation and histology analysis
Author: Taylor-King, Jake Patrick
ISNI:       0000 0004 6498 0968
Awarding Body: University of Oxford
Current Institution: University of Oxford
Date of Award: 2017
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Two important factors in cancer progression are: metastatic ability, cancer spreading and disrupting healthy function of bodily processes; and heterogeneity, the variation in different cancers caused by genetics, the microenvironment, and stochasticity. In this thesis, we investigate two scenarios of interest using models and techniques inspired by interacting particle systems. First, we model osteocyte network formation. Within bone, dendritic osteocytes form a spatial network allowing communication between osteocytes and osteoblasts located on the bone surface. This communication network facilitates coordinated bone formation. In the presence of a cancer, osteocytes manifest with either over- or under-developed phenotypes. Preliminary studies measuring the number of osteocytes per unit area show that the number density of osteocytes changes between healthy and pathological bone. We develop a mathematical framework to describe spatial networks, and present a stochastic agent-based model for bone formation. Our approach allows us to probe both network structure and number density of osteocytes in bone. Analysis of our model is possible via mean-field equations. We consider variations of our model to predict how changing measurable biological parameters relating to osteoblast differentiation can allow for different morphologies. We use our model to hypothesise reasons for the limited efficacy of zoledronate therapy on metastatic breast cancer. Second, we model the diffusive microenvironment between cells to aid with pathology slide analysis. Intra-tumor phenotypic heterogeneity limits accuracy of clinical diagnostics and hampers the efficiency of anti-cancer therapies. Dealing with this cellular heterogeneity requires adequate understanding of its sources; phenotypes of tumour cells integrate hardwired (epi-)mutational differences with responses to microenvironmental cues. The latter come in the form of both direct physical interactions, and gradients of secreted signalling molecules. Here, we develop a partial differential equation based model that allows the separation of phenotypic responses to signalling gradients within tumour microenvironments from the combined influence of responses mediated by direct physical contact and hardwired (epi-)genetic differences. We apply our model for the analyses of breast cancer histological specimens. Our approach allows partial deconvolution of the complex inputs that shape phenotypic heterogeneity of tumour cells, and identifies cells that significantly impact gradients of signalling molecules.
Supervisor: Chapman, Jon ; Basanta, David Sponsor: Engineering and Physical Sciences Research Council
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Mathematical modelling ; Applied mathematics ; Histology analysis