Global assessment of myocardial function is widely performed by estimating ejection fraction (EF), but many common cardiac diseases initially affect the myocardium on a regional, rather than global, basis. Computed tomography (CT), most commonly applied to assess the coronary arteries, is a prime candidate for such regional analysis. This doctoral thesis makes steps towards regional CT functional analysis with two clinical and two technical contributions. The first clinical contribution focuses on evaluating the feasibility and utility of functional analysis with currently available CT technology. Our study found that CT strain analysis could identify regional wall motion abnormalities in cardiomyopathy that are not otherwise detected using conventional metrics of myocardial function such as EF. In order for cine CT of the heart to become routine clinical practice, improvements need to be made to the image acquisition protocol. The second clinical contribution focus on making these improvements with results pointing to the possibility of one millisievert range cine CT images with high (>50 milliseconds) temporal resolutions. Moving to technical considerations, a key concern has been how to better characterise the myocardium in CT. To address this, the first technical contribution examines the use of feature-based attribute vectors, which were found to improve image registration towards deriving more reliable motion estimations. The second technical contribution focus on developing a pipeline tailored towards CT strain analysis. Noting that CT naturally provides information in 3D, a 3D hyperelastic biomechanical model fitting method was evaluated. Analysis of an infarction model demonstrated that regional myocardial strain can be estimated in the 3D space and areas of infarction can be detected. By considering both technical and clinical perspectives, these advances will contribute to the the field of regional cardiac functional analysis towards improving patient care.