Dissolution dynamic nuclear polarisation is an emerging clinical technique which enables the metabolism of hyperpolarised 13C-labelled molecules to be dynamically and non- invasively imaged in tissue. The first molecule to gain clinical approval is [1-13C]pyruvate, the conversion of which to [1-13C]lactate has been shown to detect early treatment re- sponse in cancers and correlate with tumour grade. As the technique has recently been translated into humans, accurate and reliable quantitative methods are required in order to detect, analyse and compare regions of altered metabolism in patients. Furthermore, there is a requirement to understand the biological processes which govern lactate pro- duction in tumours in order to draw reliable conclusions from this data. This work begins with a comprehensive analysis of the quantitative methods which have previously been applied to hyperpolarised 13C data and compares these to some novel approaches. The most appropriate kinetic model to apply to hyperpolarised data is determined and some simple, robust quantitative metrics are identified which are suitable for clinical use. A means of automatically segmenting 5D hyperpolarised imaging data using a fuzzy Markov random field approach is presented in order to reliably identify regions of abnormal metabolic activity. The utility of the algorithm is demonstrated on both in silico and animal data. To gain insight into the processes driving lactate metabolism, a mathematical model is developed which is capable of simulating tumour growth and treatment response under a range of metabolic and tissue conditions, focusing on the interaction between tumour and stroma. Finally, hyperpolarised 13C-pyruvate imaging data from the first human subjects to be imaged in Cambridge is analysed. The ability to detect and quantify lactate production in patients is demonstrated through application of the methods derived in earlier chapters. The mathematical approaches presented in this work have the potential to inform both the analysis and interpretation of clinical hyperpolarised 13C imaging data and to aid in the clinical translation of this technique.