Skip to main content
SpringerLink
Log in

The beta oscillation conditions in a simplified basal ganglia network

  • Research Article
  • Published:
Cognitive Neurodynamics Aims and scope Submit manuscript

Abstract

Parkinson’s disease is a type of motor dysfunction disease that is induced mainly by abnormal interactions between the subthalamic nucleus (STN) and globus pallidus (GP) neurons. Periodic oscillatory activities with frequencies of 13–30 Hz are the main physiological characteristics of Parkinson’s disease. In this paper, we built a class of STN–GP networks to explore beta oscillation conditions. A theoretical formula was obtained for generating oscillations without internal GP connections. Based on this formula, we studied the effects of cortex inputs, striatum inputs, coupling weights and delays on oscillation conditions, and the theoretical results are in good agreement with the numerical results. The onset mechanism can be explained by the model, and the internal GP connection has little effect on oscillations. Finally, we compared oscillation conditions with those in previous studies and found that the delays and coupling weights required for generating oscillations may decrease as the number of nuclei increases. We hope that the results obtained will inspire future theoretical and experimental studies.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

  • Ahn S, Zauber SE, Worth RM, Witt T, Rubchinsky LL (2015) Interaction of synchronized dynamics in cortex and basal ganglia in Parkinson’s disease. Eur J Neurosci 42(5):2164–2171

    Article  Google Scholar 

  • Ahn S, Zauber SE, Worth RM, Rubchinsky LL (2016) Synchronized beta-band oscillations in a model of the globus pallidus-subthalamic nucleus network under external input. Front Comput Neurosci 10:134

    Article  Google Scholar 

  • Alcacer C, Andreoli L, Sebastianutto I, Jakobsson J, Fieblinger T, Cenci MA (2017) Chemogenetic stimulation of striatal projection neurons modulates responses to Parkinson’s disease therapy. J Clin Investig 127(2):720–734

    Article  Google Scholar 

  • Belluscio MA, Escande MV, Keifman E, Riquelme LA, Murer MG, Zold CL (2014) Oscillations in the basal ganglia in Parkinson’s disease: role of the striatum. Basal Ganglia 3(4):203–212

    Article  Google Scholar 

  • Bergman H, Wichmann T, Karmon B, Delong MR (1994) The primate subthalamic nucleus. II. Neuronal activity in the MPTP model of parkinsonism. J Neurophysiol 72(2):507

    Article  CAS  Google Scholar 

  • Brown P, Oliviero A, Mazzone P, Insola A, Tonali P, Di Lazzaro V (2001) Dopamine dependency of oscillations between subthalamic nucleus and pallidum in Parkinson’s disease. J Neurosci 21:1033–1038

    Article  CAS  Google Scholar 

  • Camara C, Isasi P, Warwick K, Ruiz V, Aziz T, Stein J, Bakštein E (2015) Resting tremor classification and detection in Parkinson’s disease patients. Biomed Signal Proces 16:88–97

    Article  Google Scholar 

  • Cole SR, van der Meij R, Peterson EJ, De Hemptinne C, Starr PA, Voytek B (2017) Nonsinusoidal beta oscillations reflect cortical pathophysiology in Parkinson’s disease. J Neurosci 2017:2208–16

    Google Scholar 

  • Dasdemir Y, Yildirim E, Yildirim S (2017) Analysis of functional brain connections for positive-negative emotions using phase locking value. Cogn Neurodyn 11(6):487–500

    Article  Google Scholar 

  • Dayan P, Abbott LF (2001) Theoretical neuroscience. MIT Press, Cambridge

    Google Scholar 

  • Dovzhenok A, Rubchinsky LL (2012) On the Origin of Tremor in Parkinson’s Disease. PLoS ONE 7(7):e41598

    Article  CAS  Google Scholar 

  • Fujimoto K, Kita H (1993) Response characteristics of subthalamic neurons to the stimulation of the sensorimotor cortex in the rat. Brain Res 609(1–2):185

    Article  CAS  Google Scholar 

  • Gillies A, Willshaw D, Li Z (2002) Subthalamic-pallidal interactions are critical in determining normal and abnormal functioning of the basal ganglia. Proc R Soc B Biol Sci 269(1491):545

    Article  Google Scholar 

  • Hallworth NE, Wilson CJ, Bevan MD (2003) Apamin-sensitive small conductance calcium-activated potassium channels, through their selective coupling to voltage-gated calcium channels, are critical determinants of the precision, pace, and pattern of action potential generation in rat subthalamic nucleus neurons in vitro. J Neurosci 23(20):7525–7542

    Article  CAS  Google Scholar 

  • Holgado AJ, Terry JR, Bogacz R (2010) Conditions for the generation of beta oscillations in the subthalamic nucleus-globus pallidus network. J Neurosci 30(37):12340

    Article  CAS  Google Scholar 

  • Holt AB, Netoff TI (2014) Origins and suppression of oscillations in a computational model of Parkinson’s disease. J Comput Neurosci 37(3):505–521

    Article  Google Scholar 

  • Hu B, Guo Y, Zou X et al (2018) Controlling mechanism of absence seizures by deep brain stimulus applied on subthalamic nucleus. Cogn Neurodyn 12(1):103–119

    Article  Google Scholar 

  • Humphries MD, Stewart RD, Gurney KN (2006) A physiologically plausible model of action selection and oscillatory activity in the basal ganglia. J Neurosci 26(50):12921

    Article  CAS  Google Scholar 

  • Jankovic J (2008) Parkinson's disease: clinical features and diagnosis. J Neurol Neurosurg Psychiatry 79:368–376

    Article  CAS  Google Scholar 

  • Jiancheng S, Min L, Chusheng H (2017) Cooperative effect of random and time-periodic coupling strength on synchronization transitions in one-way coupled neural system: mean field approach. Cogn Neurodyn 11(4):1–8

    Article  Google Scholar 

  • Kim SY, Lim W (2016) Dynamical responses to external stimuli for both cases of excitatory and inhibitory synchronization in a complex neuronal network. Cogn Neurodyn 11(5):1–19

    Google Scholar 

  • Kim SY, Lim W (2018) Burst synchronization in a scale-free neuronal network with inhibitory spike-timing-dependent plasticity. arXiv:1803.07256

  • Kita H (2007) Globus pallidus external segment. Prog Brain Res 160(1):111

    Article  CAS  Google Scholar 

  • Kita H, Kitai ST (1991) Intracellular study of rat globus pallidus neurons: membrane properties and responses to neostriatal, subthalamic and nigral stimulation. Brain Res 564(2):296–305

    Article  CAS  Google Scholar 

  • Kita H, Nambu A, Kaneda K, Tachibana Y, Takada M (2004) Role of ionotropic glutamatergic and GABAergic inputs on the firing activity of neurons in the external pallidum in awake monkeys. J Neurophysiol 92(5):3069–84

    Article  CAS  Google Scholar 

  • Kita H, Tachibana Y, Nambu A, Chiken S (2005) Balance of monosynaptic excitatory and disynaptic inhibitory responses of the globus pallidus induced after stimulation of the subthalamic nucleus in the monkey. J Neurosci 25(38):8611

    Article  CAS  Google Scholar 

  • Kumar A, Cardanobile S, Rotter S, Aertsen A (2011) The role of inhibition in generating and controlling Parkinson’s disease oscillations in the basal ganglia. Front Syst Neurosci 5:86

    Article  Google Scholar 

  • Lebedev MA, Wise SP (2000) Oscillations in the premotor cortex: single-unit activity from awake, behaving monkeys. Exp Brain Res 130(2):195

    Article  CAS  Google Scholar 

  • Leblois A, Boraud T, Meissner W, Bergman H, Hansel D (2006) Competition between feedback loops underlies normal and pathological dynamics in the basal ganglia. J Neurosci 26:3567–3583

    Article  CAS  Google Scholar 

  • Levy R, Hutchison WD, Lozano AM, Dostrovsky JO (2000) High-frequency synchronization of neuronal activity in the subthalamic nucleus of parkinsonian patients with limb tremor. J Neurosci 20(20):7766–7775

    Article  CAS  Google Scholar 

  • Little S, Brown P (2014) The functional role of beta oscillations in Parkinson’s disease. Parkinsonism Relat Disord 20:S44–S48

    Article  Google Scholar 

  • Malekmohammadi M, Herron J, Velisar A, Blumenfeld Z, Trager MH, Chizeck HJ, Brontë-Stewart H (2016) Kinematic adaptive deep brain stimulation for resting tremor in Parkinson’s disease. Mov Disord 31(3):426–428

    Article  Google Scholar 

  • Marsden JE, McCracken M (2012) The Hopf bifurcation and its applications. Springer, Berlin

    Google Scholar 

  • Moustafa AA, Chakravarthy S, Phillips JR, Gupta A, Keri S, Polner B, Frank MJ, Jahanshahi M (2016) Motor symptoms in Parkinson’s disease: a unified framework. Neurosci Biobehav Rev 68:727–740

    Article  Google Scholar 

  • Muralidharan V, Balasubramani PP, Chakravarthy VS, Lewis SJG, Moustafa AA (2013) A computational model of altered gait patterns in parkinson’s disease patients negotiating narrow doorways. Front Comput Neurosci 7(7):190

    Google Scholar 

  • Nakanishi H, Kita H, Kitai ST (1987) Intracellular study of rat substantia nigra pars reticulata neurons in an in vitro slice preparation: electrical membrane properties and response characteristics to subthalamic stimulation. Brain Res 437(1):45–55

    Article  CAS  Google Scholar 

  • Park C, Worth RM, Rubchinsky LL (2011) Neural dynamics in parkinsonian brain: the boundary between synchronized and nonsynchronized dynamics. Phys Rev E 83(4):042901

    Article  Google Scholar 

  • Pavlides A, Hogan SJ, Bogacz R (2012) Improved conditions for the generation of beta oscillations in the subthalamic nucleus-globus pallidus network. BMC Neurosci 36(2):2229–2239

    Google Scholar 

  • Pavlides A, Hogan SJ, Bogacz R (2015) Computational models describing possible mechanisms for generation of excessive beta oscillations in Parkinson’s disease. PLoS Comput Biol 11(12):e1004609

    Article  Google Scholar 

  • Paz JT, Deniau JM, Charpier S (2005) Rhythmic bursting in the cortico-subthalamo-pallidal network during spontaneous genetically determined spike and wave discharges. J Neurosci 25(8):2092

    Article  CAS  Google Scholar 

  • Rubin JE, Terman D (2004) High frequency stimulation of the subthalamic nucleus eliminates pathological thalamic rhythmicity in a computational model. J Comput Neurosci 16(3):211

    Article  Google Scholar 

  • Schiff JL (2013) The Laplace transform: theory and applications. Springer, Berlin

    Google Scholar 

  • Schultz W, Romo R (1988) Neuronal activity in the monkey striatum during the initiation of movements. Exp Brain Res 71(2):431–6

    Article  CAS  Google Scholar 

  • Shouno O, Tachibana Y, Nambu A, Doya K (2017) Computational model of recurrent subthalamo-pallidal circuit for generation of parkinsonian oscillations. Front Neuroanat 11:21

    Article  Google Scholar 

  • Surmeier DJ, Graves SM, Shen W (2014) Dopaminergic modulation of striatal networks in health and Parkinson’s disease. Curr Opin Neurobiol 29:109–117

    Article  CAS  Google Scholar 

  • Terman D, Rubin JE, Yew AC, Wilson CJ (2002) Activity patterns in a model for the subthalamopallidal network of the basal ganglia. J Neurosci 22:2963–2976

    Article  CAS  Google Scholar 

  • van Albada SJ, Robinson PA (2009) Mean-field modeling of the basal ganglia thalamocortical system. I: firing rates in healthy and parkinsonian states. J Theor Biol 257(4):642–663

    Article  Google Scholar 

  • van Albada SJ, Gray RT, Drysdale PM, Robinson PA (2009) Meanfield modeling of the basal ganglia-thalamocortical system. II: dynamics of parkinsonian oscillations. J Theor Biol 257(4):664–688

    Article  Google Scholar 

  • Vogels T, Rajan K, Abbott L (2005) Neural network dynamics. Annu Rev Neurosci 28:357–376

    Article  CAS  Google Scholar 

  • Wang JY, Yang XL, Sun ZK (2018) Suppressing bursting synchronization in a modular neuronal network with synaptic plasticity. Cogn Neurodyn 12(6):625–636

    Article  Google Scholar 

  • Yi GS, Wang J, Deng B, Wei XL (2017) Complexity of resting-state EEG activity in the patients with early-stage Parkinson’s disease. Cogn Neurodyn 11(2):147–160

    Article  Google Scholar 

Download references

Acknowledgements

This research was supported by the National Science Foundation of China (Grant Nos. 11602092); the Natural Science Foundation of Hubei Province (Grant No. 2018CFB628); the China Postdoctoral Science Foundation (Grant No. 2018M632184); the National Undergraduate Training Program for Innovation and Entrepreneurship of Huazhong Agricultural University (Grant Nos. 201710504092, 201810504104) and the Scientific and technological innovation fund for college students (SRF) of Huazhong Agricultural University (Grant No. 2018323).

Author information

Authors and Affiliations

  1. Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou, 310023, China

    Bing Hu

  2. Key Laboratory of Systems Biology, Innovation Center for Cell Signaling Network, Institute of Biochemistry and Cell Biology, Shanghai Institute of Biological Sciences, Chinese Academy of Sciences, Shanghai, 200031, China

    Bing Hu

  3. Department of Mathematics and Statistics, College of Science, Huazhong Agricultural University, Wuhan, 430070, China

    Xiyezi Diao, Heng Guo, Shasha Deng, Yu Shi, Yuqi Deng & Liqing Zong

Authors
  1. Bing Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xiyezi Diao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Heng Guo
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Shasha Deng
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Yu Shi
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Yuqi Deng
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Liqing Zong
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Bing Hu.

Appendix

Appendix

See Table 1.

Table 1 The detailed sources of the parameters employed in the simulations
Full size table

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hu, B., Diao, X., Guo, H. et al. The beta oscillation conditions in a simplified basal ganglia network. Cogn Neurodyn 13, 201–217 (2019). https://doi.org/10.1007/s11571-018-9514-0

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11571-018-9514-0

Keywords

Search

Navigation