HD-BrainWatch: A Multimodal Sensor-Fusion and Privacy-Preserving Federated-Learning Framework for Cognitive Risk Inference under Hypertension–Diabetes Comorbidity

摘要

We present HD-BrainWatch, a theoretical methodological framework for multimodal cognitive risk inference under federated, privacy-preserving training in the hypertension–diabetes (HD) comorbidity population. HD comorbidity carries an odds ratio of 1.53 for dementia relative to either condition alone, yet no existing HD management platform produces a cognitive output signal. We formalize four contributions. (i) A multimodal sensor input space X_t = {x_HR, x_BP, x_CGM, x_HRV, x_act, x_sleep} and an HD cognitive risk inference problem as a federated optimization task with explicit (ε, δ)-differential privacy constraints. (ii) The gut-brain perturbation index (GBPI), a novel CGM-derived composite biomarker mechanistically grounded in the glycaemia–gut–brain causal pathway, whose theoretical properties — monotonicity, bounded range, sensitivity coefficients, and statistical efficiency over HbA1c — are derived. (iii) A formal privacy-utility analysis under Rényi DP composition, yielding theoretical upper bounds on utility degradation as a function of privacy budget ε, federated rounds T, and dataset size, without simulation. (iv) A comparative architectural analysis demonstrating theoretical advantages of cross-attention transformers and FedProx over single-modality, late-fusion, and FedAvg alternatives, grounded in published convergence theorems and information-theoretic arguments. The framework is specified in sufficient mathematical detail to enable independent implementation; pre-specified evaluation methodology, governance architecture, and limitations are provided.