System identification of Local Field Potentials under Deep Brain Stimulation in a healthy primate

Abstract

High frequency (HF) Deep Brain Stimulation (DBS) in the Sub-Thalamic Nucleus (STN) is a clinically recognized therapy for the treatment of motor disorders in Parkinson Disease (PD). The underlying mechanisms of DBS and how it impacts neighboring nuclei, however, are not yet completely understood. Electrophysiological data has been collected in PD patients and primates to better understand the impact of DBS on STN and the entire Basal Ganglia (BG) motor circuit. We use single unit recordings from Globus Pallidus, both pars interna and externa segments (GPi and GPe) in the BG, in a normal primate before and after DBS to reconstruct Local Field Potentials (LFPs) in the region. We then use system identification techniques to understand how GPe LFP activity and the DBS signal applied to STN influence GPi LFP activity. Our models suggest that when no stimulation is applied, the GPe LFPs have an inhibitory effect on GPi LFPs with a 2-3 ms delay, as is the case for single unit neuronal activity. On the other hand, when DBS is ON the models suggest that stimulation has a dominant effect on GPi LFPs which mask the inhibitory effects of GPe.

Brain modeling for control: A review

“…Network control models of this form have been used extensively, particularly over the past decade, to study various aspects of brain function and dynamics (see, e.g. (Chen and Sarma, 2017;Gu et al, 2015;Kenett et al, 2018;Schiff, 2011;Becker et al, 2018;Yang et al, 2021;Singh et al, 2020;Pedoto et al, 2010;Nozari and Cortés, 2020)). Arguably, the most distinctive feature of these models compared to the classical dynamical systems models of the brain is the presence of the control input u(t).…”

“…Even though both works train their ARX models on simulated rather than experimental data, their pragmatic and data-driven methodology can be valuable in mitigating the complexity of the DBS mechanism. The latter is in turn achieved by focusing only on the end-to-end, input-output mapping from tunable stimulation parameters to neural biomarkers of interest in any disorders, or even behavioral measurements similar to those studied in (Medvedev et al, 2019).As far as learning parametric input-output models from real-world data is concerned, most of the existing DBS literature focuses on non-human subjects, including rodents (Behrend et al, 2009;Wang et al, 2017), rhesus macaques (Pedoto et al, 2010), or swines (Trevathan et al, 2017). In (Pedoto et al, 2010), the authors extend the work in (Santaniello et al, 2010) to data collected from non-human primates (NHPs) via an experimental design that involved varying the stimulation frequency randomly while keeping the amplitude fixed.…”

“…The latter is in turn achieved by focusing only on the end-to-end, input-output mapping from tunable stimulation parameters to neural biomarkers of interest in any disorders, or even behavioral measurements similar to those studied in (Medvedev et al, 2019).As far as learning parametric input-output models from real-world data is concerned, most of the existing DBS literature focuses on non-human subjects, including rodents (Behrend et al, 2009;Wang et al, 2017), rhesus macaques (Pedoto et al, 2010), or swines (Trevathan et al, 2017). In (Pedoto et al, 2010), the authors extend the work in (Santaniello et al, 2010) to data collected from non-human primates (NHPs) via an experimental design that involved varying the stimulation frequency randomly while keeping the amplitude fixed. Although the model learned from this design could not generalize as well as the one in (Santaniello et al, 2010), it is interesting to note that a relatively low-order scalar model was able to explain a large portion of the variance seen in the real data.…”

Predictive Modeling of Evoked Intracranial EEG Response to Medial Temporal Lobe Stimulation in Patients with Epilepsy

“…Finally, a third body of work has specifically pursued data-driven predictive modeling of the brain's response to neurostimulation. Multiple studies have used linear autoregressive models to fit the neural activity triggered by neurostimulation [28][29][30][31] while others have opted for nonlinear kernel-based autoregressive modeling [32,33]. However, these works have mainly focused on univariate modeling (i.e., modeling the neurostimulation-evoked response at a single measurement source), while modeling the evoked network response has remained more challenging [34][35][36].…”

“…30 in that same channel, the past M samples U M (t) 31 of stimulation input, the past P samples Y P i (t) of 32 iEEG in other channels, and the bilinear interactions 33 U(t)Y L k (t) between the stimulation input and iEEG 34 output (cf. Methods for details).…”