## 1 Introduction  
In the era of digital healthcare transformation, the Internet of Medical Things (IoMT) has emerged as a form of critical infrastructure, enabling healthcare providers to collect, analyze, and utilize vast amounts of patient data efficiently [1]. The proliferation of IoMT devices has facilitated unprecedented levels of patient monitoring and care, enabling rapid innovations in personalized medicine and remote healthcare delivery [2]. The goal of collaborative healthcare management in geographically distributed IoMT networks is to efficiently allocate and manage resources across various edge devices to meet healthcare demands effectively. However, as IoMT adoption grows, so do the challenges associated with ensuring security, privacy, and compliance, particularly in distributed healthcareenvironments [3]. A recent survey highlights the landscape of IoMT adoption, revealing that wearable devices are the leading IoMT category, utilized by 69.6% of surveyed healthcare organizations [2]. Remote patient monitoring systems follow with a 62.3% adoption rate, and smart medical equipment is used by 60.2% of organizations. This diverse usage emphasizes the necessity for robust strategies to manage multi-device IoMT environments effectively [4; 5]. The geographically distributed IoMT networks, where medical devices and edge computing resources are deployed across multiple locations, offer key advantages such as reduced latency in critical care scenarios, improved resilience, and enhanced compliance with regional health data regulations. These architectures are vital for meeting the demands of global healthcare delivery and ensuring uninterrupted service during localized disruptions or emergencies [6]. However, they offer significant safety concerns. The need to protect sensitive health information across a variety of locations, defend against a broader spectrum of online cyber threats, and ensure compliance under distinct healthcare regulatory standards increases layers of complexities as cited in [7]. Although several advanced security measures have been designed for IoMT, significant barriers still remain in meeting the security requirements of geographically dispersed healthcare networks. These problems include critical communication overhead that causes latency in time-sensitive medical applications, challenges with data integrity across various medical devices, and scalability issues arising from the incapacity of current security mechanisms to manage increasing amounts of health data [8]. Additionally, it is common for medical device combinations to be non-standardized, which leads to hazards and discrepancies. Inadequate visibility in auditing and monitoring further contributes to the inability to identify and address medical security issues in healthcare settings [9]. Furthermore, providing comprehensive security will require a lot of processing and storage power for a medical device with limited resources, which will affect its overall effectiveness and cost. Due to these difficulties, an effective solution for IoMT contexts is urgently needed. The suggested architecture, EdgeGuard, combines federated learning's privacy with blockchain's decentralized security [9; 10]. It is specifically designed for the IOMT. This is the whole framework that, on the one hand, enhances health data security and optimizes resource management in collaborative healthcare environments and, on the other, permits safe and effective cooperation between dispersed medical devices and edge nodes. EdgeGuard is an innovative framework that seeks to redefine the contours of secure and efficient data management in IoMT networks. It leverages blockchain technology, adaptive federated learning, and edge computing capabilities to address significant limitations of current approaches in healthcare data security and privacy [3; 11]. EdgeGuard implements a novel decentralized architecture that optimizes resource utilization across diverse IoMT devices while ensuring robust data privacy and integrity [12].