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
References:
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M. Stephanie et al., Clinical subtypes of Parkinson's disease, Movement Disorders, 26 (2011), 51-58. doi: 10.1002/mds.23346.  Google Scholar

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A. ZaidelD. ArkadirZ. Israel and H. Bergman, Akineto-rigid vs. tremor syndromes in Parkinsonism, Current Opinion in Neurology, 22 (2009), 387-393.  doi: 10.1097/WCO.0b013e32832d9d67.  Google Scholar

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P. Choongseok, R. M. Worth and L. L. Rubchinsky, Neural dynamics in Parkinsonian brain: The boundary between synchronized and nonsynchronized dynamics, Physical Review E, 83 (2011), 042901. doi: 10.1103/PhysRevE.83.042901.  Google Scholar

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V. S. ChakravarthyD. Joseph and R. S. Bapi, What do the basal ganglia do? A modeling perspective, Biol. Cybernet., 103 (2010), 237-253.  doi: 10.1007/s00422-010-0401-y.  Google Scholar

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H. Marwan, My 25 stimulating years with DBS in Parkinson's disease, Journal of Parkinson's Disease, 7 (2017), S33–S41. doi: 10.3233/JPD-179007.  Google Scholar

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L. Hofmann et al., Modified pulse shapes for effective neural stimulation, Front Neuroeng, 4 (2011), 1. doi: 10.3389/fneng.2011.00009.  Google Scholar

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Y. Guo and J. E. Rubin, Multi-site stimulation of subthalamic nucleus diminishes thalamocortical relay errors in a biophysical network model, Neural Netw., 24 (2011), 602-616.  doi: 10.1016/j.neunet.2011.03.010.  Google Scholar

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R. Q. SoA. R. Kent and W. M. Grill, Relative contributions of local cell and passing fiber activation and silencing to changes in thalamic fidelity during deep brain stimulation and lesioning: a computational modeling study, Journal of Computational Neuroscience, 32 (2012), 499-519.  doi: 10.1007/s10827-011-0366-4.  Google Scholar

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Y. Smith et al., Microcircuitry of the direct and indirect pathways of the basal ganglia, Neuroscience, 86 (1998), 353-387. doi: 10.1016/s0306-4522(98)00004-9.  Google Scholar

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D. Terman et al., Activity patterns in a model for the subthalamopallidal network of the basal ganglia, The Journal of Neuroence, 22 (2002), 2963-2976. doi: 10.1523/jneurosci.22-07-02963.2002.  Google Scholar

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J. E. Rubin and D. Terman, High frequency stimulation of the subthalamic nucleus eliminates pathological thalamic rhythmicity in a computational model, Journal of Computational Neuroscience, 16 (2004), 211-235.  doi: 10.1023/B:JCNS.0000025686.47117.67.  Google Scholar

[21]

H. Daniel et al., The effects of electrode material, charge density and stimulation duration on the safety of high-frequency stimulation of the subthalamic nucleus in rats, Journal of Neuroscience Methods, 138 (2004), 207-216. doi: 10.1016/j.jneumeth.2004.04.019.  Google Scholar

[22]

M. C. Rodriguez-Oroz et al., Bilateral deep brain stimulation in Parkinson's disease: A multicentre study with 4 years follow-up, Brain, 128 (2005), 2240-2249. doi: 10.1093/brain/awh571.  Google Scholar

[23]

A. A. Kuhn et al., High-frequency stimulation of the subthalamic nucleus suppresses oscillatory activity in patients with Parkinson's disease in parallel with improvement in motor performance, Journal of Neuroscience, 28 (2008), 6165-6173. doi: 10.1523/JNEUROSCI.0282-08.2008.  Google Scholar

[24]

S. Fei et al., Model-based evaluation of closed-loop deep brain stimulation controller to adapt to dynamic changes in reference signal, Frontiers in Neuroscience, 13 (2019), 956. doi: 10.3389/fnins.2019.00956.  Google Scholar

[25]

K. KumaraveluD. T. Brocker and W. M. Grill, A biophysical model of the cortex-basal ganglia-thalamus network in the 6-OHDA lesioned rat model of Parkinson's disease, Journal of Computational Neuroscience, 40 (2016), 207-229.  doi: 10.1007/s10827-016-0593-9.  Google Scholar

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F. Steigerwald et al., Neuronal activity of the human subthalamic nucleus in the parkinsonian and nonparkinsonian state, Journal of Neurophysiology, 100 (2008), 2515-2524. doi: 10.1152/jn.90574.2008.  Google Scholar

show all references

References:
[1]

M. Stephanie et al., Clinical subtypes of Parkinson's disease, Movement Disorders, 26 (2011), 51-58. doi: 10.1002/mds.23346.  Google Scholar

[2]

A. ZaidelD. ArkadirZ. Israel and H. Bergman, Akineto-rigid vs. tremor syndromes in Parkinsonism, Current Opinion in Neurology, 22 (2009), 387-393.  doi: 10.1097/WCO.0b013e32832d9d67.  Google Scholar

[3]

C. HammondH. Bergman and P. Brown, Pathological synchronization in Parkinson's disease: Networks, models and treatments, Trends in Neurosciences, 30 (2007), 357-364.  doi: 10.1016/j.tins.2007.05.004.  Google Scholar

[4]

P. Choongseok, R. M. Worth and L. L. Rubchinsky, Neural dynamics in Parkinsonian brain: The boundary between synchronized and nonsynchronized dynamics, Physical Review E, 83 (2011), 042901. doi: 10.1103/PhysRevE.83.042901.  Google Scholar

[5]

V. S. ChakravarthyD. Joseph and R. S. Bapi, What do the basal ganglia do? A modeling perspective, Biol. Cybernet., 103 (2010), 237-253.  doi: 10.1007/s00422-010-0401-y.  Google Scholar

[6]

J. E. Rubin, Computational models of basal ganglia dysfunction: The dynamics is in the details, Current Opinion in Neurobiology, 46 (2017), 127-135.  doi: 10.1016/j.conb.2017.08.011.  Google Scholar

[7]

A. L. Benabid et al., Functional neurosurgery for movement disorders: A historical perspective, Progress in Brain Research, 175 (2009), 379-391. doi: 10.1016/S0079-6123(09)17525-8.  Google Scholar

[8]

M. Astrom, Modelling, simulation, and visualization of deep Brain stimulation, [Ph.D. thesis], Linkoping University, Linkoping, Sweden, (2011). Google Scholar

[9]

H. Marwan, My 25 stimulating years with DBS in Parkinson's disease, Journal of Parkinson's Disease, 7 (2017), S33–S41. doi: 10.3233/JPD-179007.  Google Scholar

[10]

X. L. ChenY. Y. XiongG. L. Xu and X. F. Liu, Deep Brain Stimulation, Intervent Neurol, 1 (2012), 200-212.  doi: 10.1159/000353121.  Google Scholar

[11]

J. C. Lilly et al., Brief, Noninjurious Electric Waveform for Stimulation of the Brain, Science, 121 (1955), 468-469. doi: 10.2307/1681665.  Google Scholar

[12]

X. F. Wei and W. M. Grill, Impedance characteristics of deep brain stimulation electrodes in vitro and in vivo, Journal of Neural Engineering, 6 (2009), 046008. doi: 10.1088/1741-2560/6/4/046008.  Google Scholar

[13]

L. Hofmann et al., Modified pulse shapes for effective neural stimulation, Front Neuroeng, 4 (2011), 1. doi: 10.3389/fneng.2011.00009.  Google Scholar

[14]

Y. Guo and J. E. Rubin, Multi-site stimulation of subthalamic nucleus diminishes thalamocortical relay errors in a biophysical network model, Neural Netw., 24 (2011), 602-616.  doi: 10.1016/j.neunet.2011.03.010.  Google Scholar

[15]

O. V. Popovych et al., Pulsatile desynchronizing delayed feedback for closed-loop deep brain stimulation, PLoS ONE, 3 (2017), e0173363. doi: 10.1371/journal.pone.0173363.  Google Scholar

[16]

O. V. Popovych and P. A. Tass, Adaptive delivery of continuous and delayed feedback deep brain stimulation - a computational study, Scientific Reports, 9 (2019), 10585. doi: 10.1038/s41598-019-47036-4.  Google Scholar

[17]

R. Q. SoA. R. Kent and W. M. Grill, Relative contributions of local cell and passing fiber activation and silencing to changes in thalamic fidelity during deep brain stimulation and lesioning: a computational modeling study, Journal of Computational Neuroscience, 32 (2012), 499-519.  doi: 10.1007/s10827-011-0366-4.  Google Scholar

[18]

Y. Smith et al., Microcircuitry of the direct and indirect pathways of the basal ganglia, Neuroscience, 86 (1998), 353-387. doi: 10.1016/s0306-4522(98)00004-9.  Google Scholar

[19]

D. Terman et al., Activity patterns in a model for the subthalamopallidal network of the basal ganglia, The Journal of Neuroence, 22 (2002), 2963-2976. doi: 10.1523/jneurosci.22-07-02963.2002.  Google Scholar

[20]

J. E. Rubin and D. Terman, High frequency stimulation of the subthalamic nucleus eliminates pathological thalamic rhythmicity in a computational model, Journal of Computational Neuroscience, 16 (2004), 211-235.  doi: 10.1023/B:JCNS.0000025686.47117.67.  Google Scholar

[21]

H. Daniel et al., The effects of electrode material, charge density and stimulation duration on the safety of high-frequency stimulation of the subthalamic nucleus in rats, Journal of Neuroscience Methods, 138 (2004), 207-216. doi: 10.1016/j.jneumeth.2004.04.019.  Google Scholar

[22]

M. C. Rodriguez-Oroz et al., Bilateral deep brain stimulation in Parkinson's disease: A multicentre study with 4 years follow-up, Brain, 128 (2005), 2240-2249. doi: 10.1093/brain/awh571.  Google Scholar

[23]

A. A. Kuhn et al., High-frequency stimulation of the subthalamic nucleus suppresses oscillatory activity in patients with Parkinson's disease in parallel with improvement in motor performance, Journal of Neuroscience, 28 (2008), 6165-6173. doi: 10.1523/JNEUROSCI.0282-08.2008.  Google Scholar

[24]

S. Fei et al., Model-based evaluation of closed-loop deep brain stimulation controller to adapt to dynamic changes in reference signal, Frontiers in Neuroscience, 13 (2019), 956. doi: 10.3389/fnins.2019.00956.  Google Scholar

[25]

K. KumaraveluD. T. Brocker and W. M. Grill, A biophysical model of the cortex-basal ganglia-thalamus network in the 6-OHDA lesioned rat model of Parkinson's disease, Journal of Computational Neuroscience, 40 (2016), 207-229.  doi: 10.1007/s10827-016-0593-9.  Google Scholar

[26]

F. Steigerwald et al., Neuronal activity of the human subthalamic nucleus in the parkinsonian and nonparkinsonian state, Journal of Neurophysiology, 100 (2008), 2515-2524. doi: 10.1152/jn.90574.2008.  Google Scholar

Figure 1.  The pulsatile stimulation pattern of the high-frequency charge-balanced square pulse waveform of the DBS
Figure 2.  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
Figure 3.  The sketch of the pulse-delay-pulse (PDP) waveform of the DBS
Figure 4.  The effect of the stimulation frequency on EI with PDP-type DBS on STN-GPe site
Figure 5.  The effect of the stimulation frequency on EI with PDP-type DBS on STN-GPi site
Figure 6.  The effect of the stimulation frequency on EI with PDP-type DBS on GPi-GPe site
Figure 7.  The influence of the stimulation frequency on $ \beta $ power of GPi with the PDP-type DBS on STN-GPe site
Figure 8.  The influence of the stimulation frequency on $ \beta $ power of GPi with the PDP-type DBS on STN-GPi site
Figure 9.  The influence of the stimulation frequency on $ \beta $ power of GPi with the PDP-type DBS on GPi-GPe site
Figure 10.  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
Figure 11.  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
Figure 12.  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
Figure 13.  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
Table 1.  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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