Health and medical data frequently contain sensitive patient information that must be protected. Existing visual security schemes for medical images exhibit limitations in the imperceptibility of cipher images and the performance of image reconstruction. This paper introduces and evaluates a novel approach called Visual Meaningful Image Encryption (VMIE) for securing medical images. The proposed VMIE scheme employs a chaotic system based on the Duffing equation for initial encryption. Medical images are processed and encrypted in a sparse domain. A Bidirectional Chaotic Magic Transformation (BCMT) algorithm is then applied to scramble the sparse medical images. The scrambled data undergoes compression and diffusion. An adaptive embedding strategy employing the Discrete Cosine Stockwell Transform (DCST) integrates confidential data into the host image. The performance of the proposed chaotic system is validated through theoretical analysis and numerical simulation. Simulation results, along with comparisons to existing schemes, demonstrate the efficacy of the VMIE method in enhancing visual security and its suitability for natural images. The VMIE approach presented in this paper offers a promising solution for securing medical images, effectively addressing the limitations of current visual security schemes.