Stability analysis and neural control of subcortical oscillations in Parkinson's excitatory-inhibitory network

Freezing of gait (FoG) is a common and disabling symptom of Parkinson's disease (PD), characterized by impaired motor control due to altered oscillatory activity and disrupted synchronization within the cortico-subcortical basal ganglia-thalamus network. Current therapeutic strategies, including deep brain stimulation, often fail to fully alleviate FoG, highlighting the need for innovative approaches to better understand and manage this complex symptom. This study investigates the steady-state dynamics underlying FoG by employing equilibrium point analysis of the physiologically connected network in both healthy and PD configurations. An artificial neural network (ANN) controller, adapted from existing designs with modifications, is used to restore stability in the PD network dynamics. Using a Kuramoto model, we examined the synchronization behaviour of interconnected nuclei constrained by excitation-inhibition communication, focussing on phase balance dynamics through stability analysis of equilibrium points. The simulations indicate that the adaptive ANN controller can modulate these phase dynamics by targeting either the subthalamic nucleus (STN) and substantia nigra pars reticulata (SNr) or the STN and globus pallidus pars interna (GPi), leading to improved control of substantia nigra pars compacta (SNc) synchronization within the network. This research enhances the theoretical understanding of the mechanisms underlying the functional architecture, specifically the excitatory-inhibitory network involved in FoG. It also demonstrates that a modified neural control approach, which targets the minimal number of nuclei and adapts internally without reliance on external sensory feedback, indicates the potential to modulate network dynamics in a theoretical setting.