Multimodal bifurcation control of parkinsonian beta oscillations by pedunculopontine nucleus pathways: A unified computational framework revealing dynamic therapeutic targets

Bing Hu; Pinyi Ye; Yuting Zhang; Te Nan; Xiaoye Shi; Bing Hu; Pinyi Ye; Yuting Zhang; Te Nan; Xiaoye Shi

doi:10.3934/era.2026054

Electronic Research Archive

2026, Volume 34, Issue 2: 1173-1194. doi: 10.3934/era.2026054

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Research article

Multimodal bifurcation control of parkinsonian beta oscillations by pedunculopontine nucleus pathways: A unified computational framework revealing dynamic therapeutic targets

1.
Department of Mathematics, School of Mathematical Sciences, Zhejiang University of Technology, Hangzhou 310023, China
2.
College of Information Engineering, Zhejiang University of Technology, Hangzhou 310023, China

Received: 13 November 2025 Revised: 01 January 2026 Accepted: 12 January 2026 Published: 05 February 2026

This study introduces a novel cortico-thalamo-basal ganglia-pedunculopontine nucleus (PPN) (CTBGP) computational framework to investigate how PPN-related pathways control beta oscillations. We observe that PPN-thalamic pathways exert bidirectional Hopf bifurcation control over thalamic beta oscillations, with coupling strength adjustments shifting stable/oscillatory state boundaries; PPN-cortical projection stabilizes cortical beta oscillations through supercritical/subcritical Hopf transitions dependent on coupling strength; PPN-GPi projection modulates cortico-thalamic beta oscillations via interactions with GABAergic GPi-thalamic pathways, enabling coexistence of supercritical/subcritical bifurcations; PPN-STN projection strongly suppress basal ganglia beta oscillations by elevating STN-GPe network activity to saturated states. Notably, three direct PPN inputs (EPN-PPN, STN-PPN, GPi-PPN) collectively regulate beta oscillations through the PPN-STN-GPe axis. This work provides the computational evidence that PPN pathways dynamically control beta oscillations across CTBG subcircuits via bifurcation mechanisms. The identified PPN-STN-GPe axis and thalamic/cortical projections offer novel targets for DBS and pharmacological interventions.
- pedunculopontine nucleus,
- cortical-thalamic-basal ganglia circuit,
- Parkinson's beta oscillation,
- Hopf bifurcation
Citation: Bing Hu, Pinyi Ye, Yuting Zhang, Te Nan, Xiaoye Shi. Multimodal bifurcation control of parkinsonian beta oscillations by pedunculopontine nucleus pathways: A unified computational framework revealing dynamic therapeutic targets[J]. Electronic Research Archive, 2026, 34(2): 1173-1194. doi: 10.3934/era.2026054

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Abstract

This study introduces a novel cortico-thalamo-basal ganglia-pedunculopontine nucleus (PPN) (CTBGP) computational framework to investigate how PPN-related pathways control beta oscillations. We observe that PPN-thalamic pathways exert bidirectional Hopf bifurcation control over thalamic beta oscillations, with coupling strength adjustments shifting stable/oscillatory state boundaries; PPN-cortical projection stabilizes cortical beta oscillations through supercritical/subcritical Hopf transitions dependent on coupling strength; PPN-GPi projection modulates cortico-thalamic beta oscillations via interactions with GABAergic GPi-thalamic pathways, enabling coexistence of supercritical/subcritical bifurcations; PPN-STN projection strongly suppress basal ganglia beta oscillations by elevating STN-GPe network activity to saturated states. Notably, three direct PPN inputs (EPN-PPN, STN-PPN, GPi-PPN) collectively regulate beta oscillations through the PPN-STN-GPe axis. This work provides the computational evidence that PPN pathways dynamically control beta oscillations across CTBG subcircuits via bifurcation mechanisms. The identified PPN-STN-GPe axis and thalamic/cortical projections offer novel targets for DBS and pharmacological interventions.

References

[1]	D. Su, Y. Cui, C.He, P. Yin, R. Bai, J. Zhu, et al., Projections for prevalence of Parkinson's disease and its driving factors in 195 countries and territories to 2050: Modelling study of Global Burden of Disease Study 2021, BMJ, 388 (2025), 080952. http://doi.org/10.1136/bmj-2024-080952 doi: 10.1136/bmj-2024-080952
[2]	M. F. Hnazaee, V. Litvak, Investigating cortico-striatal beta oscillations in Parkinson's disease cognitive decline, Brain, 146 (2023), 3571–3573. https://doi.org/10.1093/brain/awad273 doi: 10.1093/brain/awad273
[3]	S. Little, P. Brown, The functional role of beta oscillations in Parkinson's disease, Parkinsonism Relat. Disord., 20 (2014), 44–48. https://doi.org/10.1016/S1353-8020(13)70013-0 doi: 10.1016/S1353-8020(13)70013-0
[4]	E. Belova, U. Semenova, A. Gamaleya, A. Tomskiy, A. Sedov, Excessive $\alpha$-$\beta$ oscillations mark enlarged motor sign severity and Parkinson's disease duration, Mov. Disord., 38 (2023), 1027–1035. https://doi.org/10.1002/mds.29393 doi: 10.1002/mds.29393
[5]	S. J. van Albada, P. A. Robinson, Mean-field modeling of the basal ganglia-thalamocortical system. Ⅰ: Firing rates in healthy and parkinsonian states, J. Theor. Biol., 257 (2009), 642–663. https://doi.org/10.1016/j.jtbi.2008.12.018 doi: 10.1016/j.jtbi.2008.12.018
[6]	S. J. van Albada, R. T. Gray, P. M. Drysdale, P. A. Robinson, Mean-field modeling of the basal ganglia-thalamocortical system. Ⅱ: dynamics of parkinsonian oscillations, J. Theor. Biol., 257 (2009), 664–688. https://doi.org/10.1016/j.jtbi.2008.12.013 doi: 10.1016/j.jtbi.2008.12.013
[7]	M. Caiola, M. H. Holmes, Model and analysis for the onset of parkinsonian firing patterns in a simplified basal ganglia, Int. J. Neural Syst., 29 (2019), 1850021. https://doi.org/10.1142/S0129065718500211 doi: 10.1142/S0129065718500211
[8]	Z. Wang, B. Hu, L. Zhu, J. Lin, M. Xu, D. Wang, Hopf bifurcation analysis for Parkinson oscillation with heterogeneous delays: A theoretical derivation and simulation analysis, Commun. Nonlinear Sci. Numer. Simul., 114 (2022), 106614. https://doi.org/10.1016/j.cnsns.2022.106614 doi: 10.1016/j.cnsns.2022.106614
[9]	B. Hu, X. Wang, S. Lu, X. Ying, A study of bidirectional control of Parkinson's beta oscillations by basal ganglia, Chaos Solitons Fractals, 195 (2025), 116267. https://doi.org/10.1016/j.chaos.2025.116267 doi: 10.1016/j.chaos.2025.116267
[10]	K. Santhosh, P. P. Dev, B. J. A, Z. Lynton, P. Das, E. Ghaderpour, A modified Gray Wolf Optimization algorithm for early detection of Parkinson's disease, Biomed. Signal Process. Control, 109 (2025), 108061. https://doi.org/10.1016/j.bspc.2025.108061 doi: 10.1016/j.bspc.2025.108061
[11]	G. Marano, S. Rossi, E. M. Marzo, A. Ronsisvalle, L. Artuso, G. Traversi, et al., Writing the future: Artificial intelligence, handwriting, and early biomarkers for Parkinson's disease diagnosis and monitoring, Biomedicines, 13 (2025), 1764. https://doi.org/10.3390/biomedicines13071764 doi: 10.3390/biomedicines13071764
[12]	P. K. Sharma, S. Gentleman, D. T. Dexter, I. S. Pienaar, Stereological analysis of cholinergic neurons within bilateral pedunculopontine nuclei in health and when affected by Parkinson's disease, Brain Pathol., 35 (2025), 70011. https://doi.org/10.1111/bpa.70011 doi: 10.1111/bpa.70011
[13]	N. J. Ray, R. A. Lawson, S. L. Martin, H. P. Sigurdsson, J. Wilson, B. Galna, et al., Free-water imaging of the cholinergic basal forebrain and pedunculopontine nucleus in Parkinson's disease, Brain, 146 (2023), 1053–1064. https://doi.org/10.1093/brain/awac127 doi: 10.1093/brain/awac127
[14]	C. E. Craig, N. J. Jenkinson, J. S. Brittain, M. J. Grothe, L. Rochester, M. Silverdale, et al., Pedunculopontine nucleus microstructure predicts postural and gait symptoms in Parkinson's disease, Mov. Disord., 35 (2020), 1199–1207. https://doi.org/10.1002/mds.28051 doi: 10.1002/mds.28051
[15]	K. Yu, Z. Ren, Y. Hu, S. Guo, X. Ye, J. Li, et al., Efficacy of caudal pedunculopontine nucleus stimulation on postural instability and gait disorders in Parkinson's disease, Acta Neurochir., 164 (2022), 575–585. https://doi.org/10.1007/s00701-022-05117-w doi: 10.1007/s00701-022-05117-w
[16]	A. Davin, S. Chabardès, A. Devergnas, C. Benstaali, C. N. Gutekunst, O. David, et al., Excessive daytime sleepiness in a model of Parkinson's disease improved by low-frequency stimulation of the pedunculopontine nucleus, npj Parkinson's Dis., 9 (2023), 9. https://doi.org/10.1038/s41531-023-00455-7 doi: 10.1038/s41531-023-00455-7
[17]	J. Bourilhon, C. Olivier, H. You, A. Collomb-Clerc, D. Grabli, H. Belaid, et al., Pedunculopontine and cuneiform nuclei deep brain stimulation for severe gait and balance disorders in Parkinson's disease: interim results from a randomized double-blind clinical trial, J. Parkinson's Dis., 12 (2021), 639–653. https://doi.org/10.3233/jpd-212793 doi: 10.3233/jpd-212793
[18]	X. Geng, J. Xie, X. Wang, X. Wang, X. Zhang, Y. Hou, et al., Altered neuronal activity in the pedunculopontine nucleus: An electrophysiological study in a rat model of Parkinson's disease, Behav. Brain Res., 305 (2016), 57–64. https://doi.org/10.1016/j.bbr.2016.02.026 doi: 10.1016/j.bbr.2016.02.026
[19]	I. T. French, K. A. Muthusamy, A review of the pedunculopontine nucleus in Parkinson's disease, Front. Aging Neurosci., 10 (2018), 99. https://doi.org/10.3389/fnagi.2018.00099 doi: 10.3389/fnagi.2018.00099
[20]	E. E. Benarroch, Pedunculopontine nucleus: Functional organization and clinical implications, Neurology, 80 (2013), 1148–1155. https://doi.org/10.1212/WNL.0b013e3182886a76 doi: 10.1212/WNL.0b013e3182886a76
[21]	N. E. Chambers, K. Lanza, C. Bishop, Pedunculopontine nucleus degeneration contributes to both motor and non-motor symptoms of Parkinson's disease, Front. Pharmacol., 10 (2020), 1494. https://doi.org/10.3389/fphar.2019.01494 doi: 10.3389/fphar.2019.01494
[22]	A. Capozzo, T. Florio, R. Cellini, U. Moriconi, E. Scarnati, The pedunculopontine nucleus projection to the parafascicular nucleus of the thalamus: An electrophysiological investigation in the rat, J. Neural Transm., 110 (2003), 733–747. https://doi.org/10.1007/s00702-003-0820-1 doi: 10.1007/s00702-003-0820-1
[23]	N. K. Gut, P. Winn, The pedunculopontine tegmental nucleus-A functional hypothesis from the comparative literature, Mov. Disord., 31 (2016), 615–624. https://doi.org/10.1002/mds.26556 doi: 10.1002/mds.26556
[24]	S. Breit, L. Milosevic, G. Naros, I. Cebi, D. Weiss, A. Gharabaghi, Structural-functional correlates of response to pedunculopontine stimulation in a randomized clinical trial for axial symptoms of Parkinson's disease, J. Parkinson's Dis., 13 (2023), 563–573. https://doi.org/10.3233/JPD-225031 doi: 10.3233/JPD-225031
[25]	P. A. Pahapill, A. M. Lozano, The pedunculopontine nucleus and Parkinson's disease, Brain, 123 (2000), 1767–1783. https://doi.org/10.1093/brain/123.9.1767 doi: 10.1093/brain/123.9.1767
[26]	P. A. Robinson, C. J. Rennie, J. J. Wright, P. D. Bourke, Steady states and global dynamics of electrical activity in the cerebral cortex, Phys. Rev. E, 58 (1998), 3557–3571. https://doi.org/10.1103/PhysRevE.58.3557 doi: 10.1103/PhysRevE.58.3557
[27]	P. A. Robinson, C. J. Rennie, D. L. Rowe, Dynamics of large-scale brain activity in normal arousal states and epileptic seizures, Phys. Rev. E, 65 (2002), 041924. https://doi.org/10.1103/PhysRevE.65.041924 doi: 10.1103/PhysRevE.65.041924
[28]	M. Chen, D. Guo, T. Wang, W. Jing, Y. Xia, P. Xu, et al., Bidirectional control of absence seizures by the basal ganglia: A computational evidence, PLoS Comput. Biol., 10 (2014), 1003495. https://doi.org/10.1371/journal.pcbi.1003495 doi: 10.1371/journal.pcbi.1003495
[29]	M. Chen, D. Guo, M. Li, T. Ma, S. Wu, J. Ma, , et al., Critical roles of the direct GABAergic pallido-cortical pathway in controlling absence seizures, PLoS Comput. Biol., 11 (2015), e1004539. https://doi.org/10.1371/journal.pcbi.1004539 doi: 10.1371/journal.pcbi.1004539
[30]	B. Hu, J. Zhao, Y. Ao, X. Cai, The possible role of electromagnetic induction in the regulation of absence seizures: evidence from a computational model, Nonlinear Dyn., 113 (2025), 2711–2728. https://doi.org/10.1007/s11071-024-10345-z doi: 10.1007/s11071-024-10345-z
[31]	Y. Yu, H. Zhang, L. Zhang, Q. Wang, Dynamical role of pedunculopntine nucleus stimulation on controlling Parkinson's disease, Phys. A: Stat. Mech. Appl., 525 (2019), 834–848. https://doi.org/10.1016/j.physa.2019.04.016 doi: 10.1016/j.physa.2019.04.016
[32]	B. Hu, M. Xu, L. Zhu, J. Lin, Z. Wang, D. Wang, et al., A bidirectional Hopf bifurcation analysis of Parkinson's oscillation in a simplified basal ganglia model, J. Theor. Biol., 536 (2022), 110979. https://doi.org/10.1016/j.jtbi.2021.110979 doi: 10.1016/j.jtbi.2021.110979
[33]	V. Witzig, R. Pjontek, S. K. H. Tan, J. B. Schulz, F. Holtbernd, Modulating the cholinergic system-Novel targets for deep brain stimulation in Parkinson's disease, J. Neurochem., 169 (2025), 16264. https://doi.org/10.1111/jnc.16264 doi: 10.1111/jnc.16264

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