Advancements in Mathematical Approaches for Deciphering Deep Brain Stimulation: A Systematic Review (CSIAM Transactions on Life Sciences, 2025)
Deep brain stimulation (DBS) is a prominent therapy for neurodegenerative disorders, particularly advanced Parkinson’s disease (PD), offering relief frommotor symptoms and lessening dependence on dopaminergic drugs. Yet, theoretically comprehending either DBS mechanisms or PD neurophysiology remains elusive,highlighting the importance of neuron modeling and control theory. Neurological disorders ensues from abnormal synchrony in neural activity, as evidenced by abnormaloscillations in the local field potential (LFP). Complex systems are typically characterized as high-dimensional, necessitating the application of dimensional reduction techniques pinpoint pivotal network tipping points, allowing mathematical models delveinto DBS effectiveness in countering synchrony within neuronal ensembles. Althoughthe traditional closed-loop control policies perform well in DBS technique research,computational and energy challenges in controlling large amounts of neurons promptinvestigation into event-triggered strategies, subsequently machine learning emergesfor navigating intricate neuronal dynamics. We comprehensively review mathematical foundations, dimension reduction approaches, control theory and machine learning methods in DBS, for thoroughly understanding the mechanisms of brain diseaseand proposing potential applications in the interdisciplinary field of clinical treatment,control, and artificial intelligence.