Around the brain in 80 Hz: A Kuramoto model perspective of cortical neuronal activity

Year 2025, Volume: 3 Issue: 2, 111 - 149

Aran Dabbaghchi , Stuart Townley

https://doi.org/10.59292/bulletinbiomath.1664603

Abstract

Understanding the collective behaviour of cortical neurons is a significant subject especially for unravelling brain function and dysfunction, specifically in neural disorders. The Kuramoto model is a mathematical framework that allows us to study synchronization patterns in coupled oscillators and explore the underlying dynamics. In this review, we examine the evolution and application of this model to cortical neural activity, focusing on extensions and variants that capture complex phenomena. We trace the development of the Kuramoto model from Winfree's foundational works to the recent forms including stochastic, second-order, and multi-population variants. Key findings highlight the ability of the model to represent phase transitions from incoherence to synchrony, driven by coupling strength, and its reductions from the high-dimensional form via techniques like the Ott-Antonsen ansatz. Regarding brain disorders, the model shows how excessive synchronization underlies Parkinsonian motor deficits and epileptic seizures, with adaptations such as contrarian nodes and dynamic couplings providing information on desynchronizations. Analytical and numerical results demonstrate critical thresholds and order parameters that determine coherence states aligning with empirical data. Extensions of the model clarify the mechanisms that trigger neural disorders and suggest therapeutic methods such as deep-brain stimulation control and optimizations. Prospective work can refine these models by considering more realistic network topology and adding noise-effect terms, enhancing the predictive and practical power for clinical interventions. This combination highlights the model's capability and relevance in unravelling the brain's oscillatory perspective.

Keywords

Kuramoto Model, Neural Synchronization, Cortical Activity, Brain Neural Disorders

Supporting Institution

Centre for Environmental Mathematics, Environmental and Sustainability Institute, University of Exeter, UK TR10 9FE.

Project Number

1

Thanks

Special thank to Dr. Mehmet Yavuz, the editor-in-chief of the Bulletin of Biomathematics for his great advice.

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