Cancer is a deadly, complex disease with 14 million new cases diagnosed every year and the endeavour to develop a cure is a global multidisciplinary effort. The complexity of cancer and the resulting vast volume of data derived from its research necessitates a robust and cutting-edge system of mathematical and statistical modelling. This thesis proposes novel mathematical models of quantification and modelling applied to heterogeneous preclinical cancers, focusing on the translation of animal studies into patients with particular emphasis on tumour stroma. The first section of this thesis (quantification) will present different techniques of extracting and quantifying data from bioanalytical assays. The overall aim will be to present and discuss potential methods of obtaining data regarding tumour volume, stromal morphology, stromal heterogeneity, and oxygen distribution. Firstly, a 3D scanning technique will be discusses. This technique aims to assess tumour volume in mice more precisely than the current favoured method (callipers) and record any cutaneous symptoms as well, with the potential to revolutionise tumour growth analysis. Secondly, a series of image processing methods will be presented which, when applied to tumour histopathology, demonstrate that tumour stromal morphology and its microenvironment play a key role in tumour physiology. Lastly, it will be demonstrated through the integration of in-vitro data from various sources that oxygen and nutrient distribution in tumours is very irregular, creating metabolic niches with distinct physiologies within a single tumour. Tumour volume, oxygen, and stroma are the three aspects central to the successful modelling of tumour drug responses over time. The second section of this thesis (modelling) will feature a mathematical oxygen-driven model - utilising 38 cell lines and 5 patient-derived animal models - that aims to demonstrate the relationship between homogeneous oxygen distribution and preclinical tumour growth. Finally, all concepts discussed will be merged into a computational tumour-stroma model. This cellular automaton (stochastic) model will demonstrate that tumour stroma plays a key role in tumour growth and has both positive (at a molecular level) and negative (at both a molecular and tissue level) effects on cancers. This thesis contains a useful set of algorithms to help visualise, quantify, and understand tissue phenomena in cancer physiology, as well as providing a series of platforms to predict tumour outcome in the preclinical setting with clinical relevance.