Multi-scale model of neural entrainment by transcranial alternating current stimulation in realistic cortical anatomy

Transcranial alternating current stimulation (tACS) enables non-invasive modulation of brain activity, holding promise for cognitive research and clinical applications. However, it remains unclear how the spiking activity of cortical neurons is modulated by specific electric field (E-field) distributions. Here, we use a multi-scale computational framework that integrates an anatomically accurate head model with morphologically realistic neuron models to simulate the responses of layer 5 pyramidal cells (L5 PCs) to the E-fields generated by conventional M1-SO tACS. Neural entrainment is quantified by calculating the phase-locking value (PLV) and preferred phase (PPh). We find that the tACS-induced E-field distributions across the L5 surface of interest (SOI) are heterogeneous, resulting in diverse neural entrainment of L5 PCs due to their sensitivities to the direction and intensity of the E-fields. Both PLV and PPh follow a smooth cosine dependency on the E-field polar angle, with minimal sensitivity to the azimuthal angle. PLV exhibits a positive linear dependence on the E-field intensity. However, PPh either increases or decreases logarithmically with E-field intensity that depends on the E-field direction. Correlation analysis reveals that neural entrainment can be largely explained by the normal component of the E-field or by somatic polarization, especially for E-field directed outward relative to the cortical surface. Moreover, cell morphology plays a crucial role in shaping the diverse neural entrainment to tACS. Although the uniform E-field extracted at the soma provides a good approximation for modeling tACS at the cellular level, the non-uniform E-field distribution should be considered for investigating more accurate cellular mechanisms of tACS. These findings highlight the crucial roles of heterogeneous E-field distributions, cell morphology, and E-field non-uniformity in modulating neuronal spiking activity by tACS in realistic neuroanatomy, deepening our understanding of the cellular mechanism underlying tACS. Our work bridges macroscopic brain stimulation with microscopic neural activity, which benefits the development of brain models and derived clinical applications relying on model-driven brain stimulation with tACS-induced weak E-fields.