# American Institute of Mathematical Sciences

doi: 10.3934/era.2021048
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## Multiple-site deep brain stimulation with delayed rectangular waveforms for Parkinson's disease

 School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China

* Corresponding author: shixiabupt@163.com

Received  December 2020 Revised  May 2021 Early access July 2021

Fund Project: This work is supported by the National Natural Science Foundation of China (Grant no. 11772069)

Deep brain stimulation (DBS) alleviates the symptoms of tremor, rigidity, and akinesia of the Parkinson's disease (PD). Over decades of the clinical experience, subthalamic nucleus (STN), globus pallidus externa (GPe) and globus pallidus internal (GPi) have been chosen as the common DBS target sites. However, how to design the DBS waveform is still a challenging problem. There is evidence that chronic high-frequency stimulation may cause long-term tissue damage and other side effects. In this paper, we apply a form of DBS with delayed rectangular waveform, denoted as pulse-delay-pulse (PDP) type DBS, on multiple-site based on a computational model of the basal ganglia-thalamus (BG-TH) network. We mainly investigate the effects of the stimulation frequency on relay reliability of the thalamus neurons, beta band oscillation of GPi nucleus and firing rate of the BG network. The results show that the PDP-type DBS at STN-GPe site results in better performance at lower frequencies, while the DBS at GPi-GPe site causes the number of spikes of STN to decline and deviate from the healthy status. Fairly good therapeutic effects can be achieved by PDP-type DBS at STN-GPi site only at higher frequencies. Thus, it is concluded that the application of multiple-site stimulation with PDP-type DBS at STN-GPe is of great significance in treating symptoms of neurological disorders in PD.

Citation: Xia Shi, Ziheng Zhang. Multiple-site deep brain stimulation with delayed rectangular waveforms for Parkinson's disease. Electronic Research Archive, doi: 10.3934/era.2021048
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##### References:
The pulsatile stimulation pattern of the high-frequency charge-balanced square pulse waveform of the DBS
The structure of the sparse connectivity within the basal ganglia-thalamus (BG-TH) network. Excitatory connections and inputs are represented with triangle, while inhibitory connections and inputs are represented with circle
The sketch of the pulse-delay-pulse (PDP) waveform of the DBS
The effect of the stimulation frequency on EI with PDP-type DBS on STN-GPe site
The effect of the stimulation frequency on EI with PDP-type DBS on STN-GPi site
The effect of the stimulation frequency on EI with PDP-type DBS on GPi-GPe site
The influence of the stimulation frequency on $\beta$ power of GPi with the PDP-type DBS on STN-GPe site
The influence of the stimulation frequency on $\beta$ power of GPi with the PDP-type DBS on STN-GPi site
The influence of the stimulation frequency on $\beta$ power of GPi with the PDP-type DBS on GPi-GPe site
The effects of the stimulation frequency on the average firing rate of STN, GPe, and GPi neurons with PDP-type DBS on STN-GPe site
Spike rasters of the BG network. Spike rasters of each nucleus within the BG neural network model are plotted under the (a) health state, (b) Parkinsonian state, (c) traditional 130Hz STN-DBS, (d) 40 Hz PDP-type DBS on STN-GPe and (e) 100 Hz PDP-type DBS on STN-GPe
The effects of the stimulation frequency on the average firing rate of STN, GPe, and GPi neurons with PDP-type DBS on GPi-GPe site
Spike rasters of the BG network. Spike rasters of each nucleus within the BG neural network model are plotted under the (a) health state, (b) Parkinsonian state, (c) traditional 130 Hz STN-DBS, (d) 40 Hz PDP-type DBS on GPi-GPe and (e) 100 Hz PDP-type DBS on GPi-GPe
Model parameters under healthy and Parkinsonian conditions
 Parameter Healthy condition Parkinsonian condition $I_{a p p_{-} STN}$ $33 \mu\mathrm{A} / \mathrm{cm}^{2}$ $23 \mu\mathrm{A} / \mathrm{cm}^{2}$ $I_{a p p_{-} GPe}$ $20 \mu\mathrm{A} / \mathrm{cm}^{2}$ $7 \mu\mathrm{A} / \mathrm{cm}^{2}$ $I_{a p p_{-} GPi}$ $23 \mu\mathrm{A} / \mathrm{cm}^{2}$ $17 \mu\mathrm{A} / \mathrm{cm}^{2}$
 Parameter Healthy condition Parkinsonian condition $I_{a p p_{-} STN}$ $33 \mu\mathrm{A} / \mathrm{cm}^{2}$ $23 \mu\mathrm{A} / \mathrm{cm}^{2}$ $I_{a p p_{-} GPe}$ $20 \mu\mathrm{A} / \mathrm{cm}^{2}$ $7 \mu\mathrm{A} / \mathrm{cm}^{2}$ $I_{a p p_{-} GPi}$ $23 \mu\mathrm{A} / \mathrm{cm}^{2}$ $17 \mu\mathrm{A} / \mathrm{cm}^{2}$
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