Intensity- and frequency-specific effects of transcranial alternating current stimulation are explained by network dynamics

Transcranial alternating current stimulation (tACS) can be used to non-invasively entrain neural activity, and thereby cause changes in local neural oscillatory power. Despite an increased use in cognitive and clinical neuroscience, the fundamental mechanisms of tACS are still not fully understood. Here, we develop a computational neuronal network model of two-compartment pyramidal neurons and inhibitory interneurons which mimic the local cortical circuits. We model tACS with electric field strengths that are achievable in human applications. We then simulate intrinsic network activity and measure neural entrainment to investigate how tACS modulates ongoing endogenous oscillations. First, we show that intensity-specific effects of tACS are non-linear. At low intensities (<0.3 mV/mm), tACS desynchronizes neural firing relative to the endogenous oscillations. At higher intensities (>0.3 mV/mm), neurons are entrained to the exogenous electric field. We then further explore the stimulation parameter space and find that entrainment of ongoing cortical oscillations also depends on frequency by following an Arnold tongue. Moreover, neuronal networks can amplify the tACS induced entrainment via excitation-inhibition balance. Our model shows that pyramidal neurons are directly entrained by the exogenous electric field and drive the inhibitory neurons. Our findings can thus provide a mechanistic framework for understanding the intensity- and frequency- specific effects of oscillating electric fields on neuronal networks. This is crucial for rational parameters selection for tACS in cognitive studies and clinical applications.