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Macrophages are innate immune cells that play a key role in conditions as diverse as wound healing, atherosclerosis and cancer. In cancer, macrophages may be characterised as anti-tumour, promoting a wider immune response and phagocytosing tumour cells, or as pro-tumour, suppressing the immune response and promoting blood vessel growth and metastasis. The spatial distribution of macrophages inside a tumour correlates with patient prognosis and treatment response, and is hypothesised to be predictive of macrophage phenotype. In this thesis, we use a combination of mathematical modelling and image analysis to characterise these distribution patterns and understand the mechanisms by which macrophages may infiltrate solid tumours. We have developed an image analysis pipeline for the automated analysis of whole slide histology images, a rich source of spatial data for the investigation of immune cell distributions in vivo. Our pipeline automatically identifies macrophages and other cell types using a combination of superpixellation and Support Vector Machines (SVMs), and we develop summary statistics which characterise distinct macrophage distributions across different tumour indications based on detected cell locations. We validate our pipeline against real data and benchmark it against human pathologists. We then demonstrate its flexibility and robustness in a range of applications across a variety of datasets. We investigate the observed distributions of macrophages further by using the Chaste (Cancer, Heart and Soft Tissue Environment) modelling framework to develop a new agent-based model of macrophage infiltration into solid tumours. We first use our model to simulate in vitro experiments in which inert microbeads infiltrate into multicellular tumour spheroids (MCTSs). This study enables us to investigate the role of passive infiltration caused by spatial variation in cell proliferation and death rates across the MCTS. The interplay between cell proliferation and death drives an advective flow from nutrient-rich, proliferative, regions towards necrotic regions. Our agent-based framework reproduces results from previous continuum models of this process and provides new insight into the observed infiltration patterns that cannot be obtained without resolving the trajectories of individual particles in an agent-based framework. We subsequently extend this model to describe macrophage infiltration into MCTSs via a combination of passive infiltration and chemotaxis in response to colony stimulating factor-1 (CSF-1). This chemoattractant, which is expressed by hypoxic tumour cells, is implicated in metastasis and is a target for immunotherapy treatments currently in Phase I trials at Roche. Finally, we discuss methods of integrating whole slide imaging with our agent-based modelling approaches and compare simulated macrophage distributions with those from in vivo images analysed using our imaging pipeline.

Angiogenesis, the process by which new vessels form from existing ones, is a key event in the development of a large and malignant vascularised tumour. A rapid expansion in in vivo and in vitro angiogenesis research in recent years has led to increased knowledge about the processes underlying angiogenesis and to promising steps forward in the development of anti-angiogenic therapies for the treatment of various cancers. However, substantial gaps in knowledge persist and the development of effective treatments remains a major challenge. In this thesis we study tumour-induced angiogenesis within the context of a highly controllable experimental environment: the cornea micropocket assay. Using a multidisciplinary approach that combines experiments, image processing and analysis, and mathematical and computational modelling, we aim to provide mechanistic insight into the action of two angiogenic factors which are known to play central roles during tumour-induced angiogenesis: vascular endothelial growth factor A (VEGF-A) and basic fibroblast growth factor (bFGF). Image analysis techniques are used to extract quantitative data, which are both spatially and temporally resolved, from experimental images. These data are then used to develop and parametrise mathematical models describing the evolution of the corneal vasculature in response to both VEGF-A and bFGF. The first models developed in this thesis are one-dimensional continuum models of angiogenesis in which VEGF-A and/or bFGF are released from a pellet implanted into a mouse cornea. We also use an object-oriented framework, designed to facilitate the re-use and extensibility of hybrid multiscale models of angiogenesis and vascular tumour growth, to develop a complementary three-dimensional hybrid model of the same system. The hybrid model incorporates a new non-local cell sensing model which facilitates the formation of well-perfused and functional vascular networks in three dimensions. The continuum models are used to assess the utility of the cornea micropocket assay as a quantitative assay for angiogenesis, to characterise proposed synergies between VEGF-A and bFGF, and to generate experimentally testable predictions regarding the effect of anti-VEGF-A therapies on bFGF-induced angiogenesis. Meanwhile, the hybrid model is used to provide context for the comparison that is drawn between the continuum models and the data, to study the relative distributions of perfused and unperfused vessels in the evolving neovasculature, and to investigate the impact of tip cell sensing dysregulation on the angiogenic response in the cornea. We have found that by exploiting a close link with quantitative data we have been able to extend the predictive and hypothesis-testing capabilities of our models. As such, this thesis demonstrates the potential for integrating mathematical modelling with image analysis techniques to increase insight into the mechanisms underlying angiogenesis.