Cross-regional theta–beta phase–amplitude coupling between cortex and globus pallidus internus: A computational study

Bei Bai; Xia Shi; Bei Bai; Xia Shi

doi:10.3934/era.2026223

Electronic Research Archive

2026, Volume 34, Issue 7: 5040-5061. doi: 10.3934/era.2026223

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Cross-regional theta–beta phase–amplitude coupling between cortex and globus pallidus internus: A computational study

Bei Bai ¹,
Xia Shi ^{1,2
,
,}

1.
School of Mathematical Sciences, Beijing University of Posts and Telecommunications, Beijing 100876, China
2.
Key Laboratory of Mathematics and Information Networks (Beijing University of Posts and Telecommunications), Ministry of Education, Beijing 100876, China

Received: 30 April 2026 Revised: 25 May 2026 Accepted: 05 June 2026 Published: 10 June 2026

In Parkinson's disease (PD), abnormal oscillations pervade the cortex–basal ganglia–thalamus (CTX-BG-Th) loop. In recent years, more and more evidence has shown the physiological phenomena of exaggerated phase–amplitude coupling (PAC) in PD, suggesting that such coupling contributes to the generation and propagation of pathological oscillations. However, current understanding of how cortical low-frequency rhythms shape downstream pathological activity is still incomplete. In this study, we aim to investigate how the theta-band (3–9 Hz) phase of layer 5 pyramidal tract (E5P) cortical neurons modulates the beta-band (13–30Hz) amplitude of globus pallidus internus (GPi) neurons. The modulation index (MI), time-lag MI analysis, and coherence analysis are introduced to quantify the strength, temporal characteristics, and pathway dependence of PAC. The results indicate that significant cross-regional $ \theta $–$ \beta $ PAC occurs between E5P and GPi in the PD state, and this coupling has time delay characteristics and mainly relies on indirect pathways. In addition, blocking indirect pathways or reducing the $ \theta $ power of E5P will decrease the $ \beta $ oscillation of GPi. These findings elucidate the dynamic mechanism of cortical regulation of GPi related oscillations, providing a theoretical basis for targeted interventions in PD patients through cortical modulation.
- phase–amplitude coupling,
- basal ganglia,
- cortex,
- oscillation,
- Parkinson's disease
Citation: Bei Bai, Xia Shi. Cross-regional theta–beta phase–amplitude coupling between cortex and globus pallidus internus: A computational study[J]. Electronic Research Archive, 2026, 34(7): 5040-5061. doi: 10.3934/era.2026223

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Abstract

In Parkinson's disease (PD), abnormal oscillations pervade the cortex–basal ganglia–thalamus (CTX-BG-Th) loop. In recent years, more and more evidence has shown the physiological phenomena of exaggerated phase–amplitude coupling (PAC) in PD, suggesting that such coupling contributes to the generation and propagation of pathological oscillations. However, current understanding of how cortical low-frequency rhythms shape downstream pathological activity is still incomplete. In this study, we aim to investigate how the theta-band (3–9 Hz) phase of layer 5 pyramidal tract (E5P) cortical neurons modulates the beta-band (13–30Hz) amplitude of globus pallidus internus (GPi) neurons. The modulation index (MI), time-lag MI analysis, and coherence analysis are introduced to quantify the strength, temporal characteristics, and pathway dependence of PAC. The results indicate that significant cross-regional $ \theta $–$ \beta $ PAC occurs between E5P and GPi in the PD state, and this coupling has time delay characteristics and mainly relies on indirect pathways. In addition, blocking indirect pathways or reducing the $ \theta $ power of E5P will decrease the $ \beta $ oscillation of GPi. These findings elucidate the dynamic mechanism of cortical regulation of GPi related oscillations, providing a theoretical basis for targeted interventions in PD patients through cortical modulation.

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