Advancements in Mathematical Approaches for Deciphering Deep Brain Stimulation: A Systematic Review

Abstract

Deep brain stimulation (DBS) is a prominent therapy for neurodegenerative disorders, particularly advanced Parkinson’s disease (PD), offering relief from motor 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 abnormal oscillations 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 delve into DBS effectiveness in countering synchrony within neuronal ensembles. Although the traditional closed-loop control policies perform well in DBS technique research, computational and energy challenges in controlling large amounts of neurons prompt investigation into event-triggered strategies, subsequently machine learning emerges for 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 disease and proposing potential applications in the interdisciplinary field of clinical treatment, control, and artificial intelligence.

Keywords

Deep brain stimulation / neuronal network / dimension reduction / control theory / machine learning

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