Synchronization and resilience in the Kuramoto white matter network model with adaptive state-dependent delays

The Journal of Mathematical Neuroscience

Seong Hyun Park¹  Jérémie Lefebvre² 

[1] University of Toronto, St. George, 40 St. George St., M5S 2E4, Toronto, Canada;Krembil Research Institute, University Health Network, 60 Leonard Avenue, M5T 2S8, Toronto, Canada;University of Toronto, St. George, 40 St. George St., M5S 2E4, Toronto, Canada;Krembil Research Institute, University Health Network, 60 Leonard Avenue, M5T 2S8, Toronto, Canada;University of Ottawa, Gendron Hall, 30 Marie Curie, K1N 6N5, Ottawa, Canada;

关键词: White matter plasticity;    Kuramoto model;    Synchronization;    Delay differential equations;   

DOI  :  10.1186/s13408-020-00091-y

来源: Springer

【 摘 要 】

White matter pathways form a complex network of myelinated axons that regulate signal transmission in the nervous system and play a key role in behaviour and cognition. Recent evidence reveals that white matter networks are adaptive and that myelin remodels itself in an activity-dependent way, during both developmental stages and later on through behaviour and learning. As a result, axonal conduction delays continuously adjust in order to regulate the timing of neural signals propagating between different brain areas. This delay plasticity mechanism has yet to be integrated in computational neural models, where conduction delays are oftentimes constant or simply ignored. As a first approach to adaptive white matter remodeling, we modified the canonical Kuramoto model by enabling all connections with adaptive, phase-dependent delays. We analyzed the equilibria and stability of this system, and applied our results to two-oscillator and large-dimensional networks. Our joint mathematical and numerical analysis demonstrates that plastic delays act as a stabilizing mechanism promoting the network’s ability to maintain synchronous activity. Our work also shows that global synchronization is more resilient to perturbations and injury towards network architecture. Our results provide key insights about the analysis and potential significance of activity-dependent myelination in large-scale brain synchrony.

【 授权许可】

CC BY