DNA-based data storage is a new technology in computational and synthetic biology, that offers a solution for long-term, high-density data archiving. Given the critical importance of medical data in advancing human health, there is a growing interest in developing an effective medical data storage system based on DNA. Data integrity, accuracy, reliability, and efficient retrieval are all significant concerns. Therefore, this study proposes an Effective DNA Storage (EDS) approach for archiving medical MRI data. The EDS approach incorporates three key components (i) a novel fraction strategy to address the critical issue of rotating encoding, which often leads to data loss due to single base error propagation; (ii) a novel rule-based quaternary transcoding method that satisfies bio-constraints and ensure reliable mapping; and (iii) an indexing technique designed to simplify random search and access. The effectiveness of this approach is validated through computer simulations and biological experiments, confirming its practicality. The EDS approach outperforms existing methods, providing superior control over bio-constraints and reducing computational time. The results and code provided in this study open new avenues for practical DNA storage of medical MRI data, offering promising prospects for the future of medical data archiving and retrieval.