Magnetic Resonance Imaging (MRI) involves very short pulses of very high current. Substantial savings in the high cost of MRI installations may be realised by employing suitable electrical energy storage, for which supercapacitors are strong candidates in view of high specific power and long cycle life. A key question is whether the well-known capacitance degradation with increased frequency is compatible with the complex and highly variable duty cycles of various MRI sequences. Compatibility of the supercapacitor voltage range with the MRI system must also be considered. We present a detailed analysis of power duty profiles in MRI, using actual imaging sequences, that has not been reported previously. We also propose and validate a simplified supercapacitor model that can accurately simulate its performance in the MRI system, involving pulses several orders of magnitude shorter than those considered previously. Results of equivalent experiments involving Lithium-Ion Iron Phosphate (LiFePO4) batteries are also reported. Finally, we present a detailed analysis of the overall energy storage performance in a realistic neurological examination. The study is based on a specific system of our own design and we fully disclose its relevant parameters, so that the results would be of direct practical value to the wider community, including developers of MRI.