## 3 Problem Formulation  
### System Model  
More than a thousand devices form a vast network of IoMT healthcare data resources. The adaptive federated learning model, with its dynamic aggregation, is recognized as a well-known system in the field of IoMT. This novel idea has changed the concept and analysis of medical data. It ensures privacy and security in these increasingly developing digital health systems. Edge devices, local datasets, central servers, edge servers, local and global models, adaptive aggregation functions, blockchain security layers, and more, are the main components used in this proposed model. The following are the main parts of our system:  
1. **Edge devices** (\(\mathcal{ED}=\{ed_{1},ed_{2},\ldots,ed_{N}\}\)): The different numbers of IOMT \(N\) edge devices range in terms of their computing and sensing capabilities. These edge devices are important components of our distributed learning setup from simple fitness trackers to cutting-edge medical equipment. 2. **Local datasets** (\(\mathcal{DS}=\{DS_{1},DS_{2},\ldots,DS_{N}\}\)): Every edge device \(ed_{i}\) tracks a local dataset, thus reflecting a different portion of global health data. These datasets are characterized by their size \(|DS_{i}|\) and a quality metric \(q_{i}\in[0,1]\). 3. **Edge servers** (\(\mathcal{ES}=\{es_{1},es_{2},\ldots,es_{M}\}\)): A collection of \(M\) edge servers arranged specifically to enable intermediate aggregation and computational offloading. These servers improve system scalability and responsiveness by acting as a link between the central server and resource-limited peripheral devices. This makes our whole system work better and faster, especially when dealing with lots of devices that might not be very powerful on their own. 4. **Central server** (\(\mathcal{CS}\)): A high-performance central server that orchestrates the federated learning process, aggregates model updates, and maintains the global model. It is responsible for initiating learning rounds and disseminating the updated global model to edge devices. 5. **Global and local models** (\(w_{g},w_{l}\)): A shared neural network with \(d\) parameters; the global model \(w_{g}\in\mathbb{R}^{d}\) represents the collective knowledge extracted from various medical data sources across the network. Collection \(\mathcal{W}\) consists of local model instances, where the model parameters trained on the local dataset \(DS_{i}\) of edge device \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Work**} & **Privacy** & **Security** & **Resource** & **Data Quality** & **Device** & **Healthcare** \\  & **Preservation** & **Mechanism** & **Optimization** & **Assessment** & **Reliability** & **Specific** \\ \hline
[8] Pattern Recognition & DP & Encryption & No & No & No & Yes \\ \hline
[15] Privacy-preserving FL & DP + MPC & No & No & No & Yes \\ \hline
[16] WBAN-based FL & DP + HE & Blockchain & Energy-aware & No & No & Yes \\ \hline
[17] I-UDEC Framework & FL & Blockchain & 2 Ts-DRL & No & No & No \\ \hline
[18] DFT-based FL & DP + DFT & No & Communication & No & No & Yes \\ \hline EdgeGuard (Ours) & DP + MPC & Lightweight Blockchain & Resource-aware & Yes & Yes & Yes \\ \hline \hline \end{tabular} DP: differential privacy, MPC: multi-party computation, HE: homomorphic encryption, DFT: discrete Fourier transform, 2 Ts-DRL: two-timescale deep reinforcement learning, FL: Federated Learning.  
\end{table} 
Table 1: Comparison of related works in blockchain-secured federated learning for healthcare. \(ed_{i}\) are represented by each \(w_{l}\in\mathbb{R}^{d}\). These local models feed into the global model and are updated regularly, enabling a distributed learning process that protects data privacy and makes use of the IoMT network's collective insights. 6. **Communication links** (\(\mathcal{L}=\{l_{ij}\}\)): The group of communication lines that link the central server, edge servers, and edge devices. The bandwidth \(b_{ij}\) and latency \(\lambda_{ij}\) of each connection \(l_{ij}\) are its key characteristics. 7.