Applied Mathematics and Mechanics >
Transcranial electrical stimulation enhancing brain network integration: a dynamic modeling study
Received date: 2025-12-12
Revised date: 2026-02-05
Online published: 2026-03-31
Supported by
Project supported by the National Natural Science Foundation of China (Nos. 12472053 and 12332004), Beijing Natural Science Foundation (No. 1242008), and Young Elite Scientists Sponsorship Program by CAST (No. 2024-2026QNRC001)
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The transcranial electrical stimulation (tES) has the potential to modulate the brain cognitive function. However, the dynamic mechanisms underlying this modulation remain incompletely understood. Based on a whole-brain network dynamic model, this study investigates the regulatory mechanisms of tES on brain integration levels and its restorative effects under conditions of structural lesion. The results demonstrate that in normal networks, both the integration level and synchronization level exhibit an inverted U-shaped relationship with the global coupling strength γ, peaking in the central region of the parameter space. Under unilateral or bilateral tES, the integration level shows a bidirectional regulatory effect related to the stimulation intensity. The moderate stimulation enhances the integration peak while maintaining the inverted U-shaped curve, whereas excessive stimulation leads to a decline in integration. In structural lesion models, both focal node lesions and diffuse connection losses lead to a reduction in the integration level, with more severe connection losses resulting in more significant decline in integration. Further research reveals that the impact of node lesions on integration is modulated by the inhibitory gain β, and the appropriate adjustment to β can mitigate the functional decline caused by lesions. At specific stimulation intensities, tES can partially restore the integration capacity of the lesion network. However, the restorative effect is simultaneously dependent on both β and γ. This study suggests that tES may influence multi-scale information integration by modulating nodal excitability and network dynamic stability. The relevant findings provide a theoretical basis for parameter optimization and target selection in individualized neuromodulation strategies for diseases such as stroke and traumatic brain injury.
Haodong WANG , Ying YU , Qingyun WANG . Transcranial electrical stimulation enhancing brain network integration: a dynamic modeling study[J]. Applied Mathematics and Mechanics, 2026 , 47(4) : 719 -740 . DOI: 10.1007/s10483-026-3371-9
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