Patient-specific computer models of the human atria have the potential to aid clinical intervention in the treatment of cardiac arrhythmias if suitably validated. An anatomically accurate, patient-specific map of the electrical conductivity of the left atrial tissue is obtained using data from delayed-enhancement magnetic resonance imaging (MRI), and validated against clinical electroanatomic mapping measurements. The patient-specific intensity maps from two accepted image segmentation and registration techniques are evaluated and compared, and the approach is shown to be highly sensitive to the technique used. The segmentation technique and direction of the maximum intensity projection are both critical in interpreting regions of fibrosis from the patient specific intensity maps. The clinical data suggests a linear relationship between the intensity and the local conduction velocity, which is incorporated into the atrial model through calibration of the conductivity tensor. Simulations of the resulting atrial models produce activation patterns that strongly correlate with clinical recordings. A novel semi-automated algorithm is used for landmark selection for image registration for spatially comparing the electroanatomical and MRI based images. The thesis concludes with a discussion of using the resulting computational model to interrogate the underlying structural and functional substrates of patients with atrial fibrillation.