Network state transitions under deep brain stimulation: A Wilson-Cowan model of Parkinson's Disease

Parkinson's disease is characterized by pathological beta-band oscillations ([Formula: see text]) arising from dopamine-depletion-induced instability in the basal ganglia-thalamocortical network. Although deep brain stimulation of the subthalamic nucleus is the most effective therapy for advanced Parkinson's disease, the mechanistic relationship between stimulation amplitude and network-state transitions remains poorly delineated, limiting the rational design of adaptive closed-loop protocols. We addressed this gap using a seven-population Wilson-Cowan mean-field model in which the Parkinsonian state was induced by reducing the STN→ GPe coupling weight from 19 to 5 and the DCN→ Th(Vim) cerebellar drive from 25 to 20. Six complementary analyses were applied across a continuous deep brain stimulation amplitude sweep of [Formula: see text]-15 a.u.: time-domain dynamics, Welch power spectral density, steady-state population profiling, Dose-response characterization using three validated metrics, phase-portrait geometry and bifurcation analysis. Three novel Dose-response metrics were introduced and supports: beta-band power suppression [Formula: see text], thalamic relay preservation and STN oscillation amplitude reduction. The Parkinson's disease network produced sustained [Formula: see text] beta oscillations, a multi-harmonic spectral profile and a large-amplitude STN→ GPe limit cycle. Sub-therapeutic stimulation ([Formula: see text]) left pathological dynamics unchanged; intermediate stimulation ([Formula: see text]) partially disrupted the oscillatory cycle; and high-amplitude stimulation ([Formula: see text]) abolished both beta oscillations and thalamic relay function via the GPi inhibitory cascade, constituting a model of functional thalamotomy. A transitional therapeutic window [Formula: see text] was identified in which beta suppression and thalamic preservation coexist, corroborated across all six analytical perspectives. Bifurcation analysis confirmed that reduced STN→ GPe gain is the primary instability mechanism, with cerebellar drive as a modulatory parameter. These findings provide mechanistically rigorous explanations of amplitude-dependent network state changes and offer a quantitative framework for adaptive closed-loop deep brain stimulation design.