A Novel Multi-Scale Engineering Framework for Personalized Neuromodulation in Parkinson's Disease: Integrating Control Theory, Bayesian Inference, and Neural Dynamics

This conceptual paper introduces a groundbreaking framework, termed Multi-Scale Adaptive Neuromodulation Engineering (MANE), at the intersection of biomechanical engineering, control theory, and clinical neuroscience. MANE aims to revolutionize personalized neuromodulation therapies for Parkinson's disease (PD) by integrating multi-scale neural modeling—from cellular ion channels to network dynamics—with adaptive control systems and time-varying Bayesian inference for real-time parameter optimization amid disease progression and biological rhythms. We derive detailed mathematical formulations, including stochastic extensions of the FitzHugh-Nagumo (FHN) equations for neural excitability, engineering control laws with stability proofs, and spatio-temporal kernels for Bayesian optimization. Supported by reproducible Python simulations using parameter ranges derived from public datasets such as the REMAP multimodal dataset, Parkinson's Progression Markers Initiative (PPMI), Neural Activity Dataset for Parkinson's Disease on Kaggle, and OpenNeuro repositories, the framework incorporates advanced sensitivity analysis (Sobol methods), quantitative statistics, Bayesian updating for uncertainty quantification, and falsifiability assessments. Applications to closed-loop deep brain stimulation (DBS) are emphasized, with strategies for programming adaptive DBS to track beta power fluctuations. The framework is linked to credible real-world data from sources like the REMAP dataset and mPower study, fostering unprecedented creativity in guiding therapeutic interventions, enhancing understanding of PD pathophysiology, and providing actionable insights for clinical translation and scientific advancement.