Secure storage and sharing of patientsâ\euro™ medical data over the Internet are part of the challenges for emerging healthcare systems. The use of blockchain technology in medical Internet of Things systems can be considered a safe and novel solution to overcome such challenges. Patients with movement disorders require multi-disciplinary management and must continuously receive medical care from a specialist. Due to the increasing costs of face-to-face treatment, especially during the pandemic, patients would highly benefit from remote monitoring and management. The proposed work presents a model for blockchain-based remote management systems for patients with movement disorders, especially those with Parkinsonâ\euro™s disease. The model ensures a high level of integrity and decreases the security risks of medical data sharing.