Optimal control of directional deep brain stimulation in the parkinsonian neuronal network

The effect of conventional deep brain stimulation (DBS) on debilitating symptoms of Parkinson's disease can be limited because it can only yield the spherical field. And, some side effects are clearly induced with influencing their adjacent ganglia. Recent experimental evidence for patients with Parkinson's disease has shown that a novel DBS electrode with 32 independent stimulation source contacts can effectively optimize the clinical therapy by enlarging the therapeutic windows, when it is applied on the subthalamic nucleus (STN). This is due to the selective activation in clusters of various stimulation contacts which can be steered directionally and accurately on the targeted regions of interest. In addition, because of the serious damage to the neural tissues, the charge-unbalanced stimulation is not typically indicated and the real DBS utilizes charge-balanced bi-phasic (CBBP) pulses. Inspired by this, we computationally investigate the optimal control of directional CBBP-DBS from the proposed parkinsonian neuronal network of basal ganglia-thalamocortical circuit. By appropriately tuning stimulation for different neuronal populations, it can be found that directional steering CBBP-DBS paradigms are superior to the spherical case in improving parkinsonian dynamical properties including the synchronization of neuronal populations and the reliability of thalamus relaying the information from cortex, which is in a good agreement with the physiological experiments. Furthermore, it can be found that directional steering stimulations can increase the optimal stimulation intensity of desynchronization by more than 1 mA compared to the spherical case. This is consistent with the experimental result with showing that there exists at least one steering direction that can allow increasing the threshold of side effects by 1 mA. In addition, we also simulate the local field potential (LFP) and dominant frequency (DF) of the STN neuronal population induced by the activation of 32 different contacts with optimal stimulation intensity and immediately after the stimulation, respectively. These can reveal regional differences in pathological activity within STN nucleus. It is shown that in line with the experimental results directional steering stimulation can induce the low-amplitude LFP which implies the occurrence of desynchronizing regime, as well as the distribution of DF can locate at the 13-40 Hz of beta frequency range. Hopefully, the obtained results can provide theoretical evidences in exploring pathophysiologic activity of brain.