Relation between the electric field and activation of cortical neurons in transcranial electrical stimulation

To address the brain areas and circuits affected by transcranial electrical stimulation (tES), which had been used widely to treat psychiatric and neurological diseases, the stimulus-induced electric field in the cortex was calculated using a head model that reflects anatomical information. To obtain detailed information at the macroscopic and microscopic levels, multi-scale modeling was proposed that integrates the head model with multi-compartmental models of cortical neurons. Our goal was to use multi-scale modeling to describe the relation between the stimulus-induced electric field and neuronal responses during tES. We simulated sub- and supra-threshold neuronal responses to stimulus-induced uniform and realistic electric fields. For the realistic electric field, multi-scale models that combined the head model derived from structural MRIs and multi-compartmental models of neurons were constructed. Then, we simulated the steady-state membrane polarization for sub-threshold stimulation and the excitation threshold for supra-threshold stimulation by varying the tES montages. The electric field calculated was decomposed into two orthogonal components, the radial and tangential fields, which were compared to the neuronal responses. The stimulus-induced electric field depended strongly on stimulus parameters, and neuronal excitability showed a higher correlation with the radial field. We demonstrated that neurons exhibited linear polarization during sub-threshold stimulation depending on the local radial field intensity that resulted in a significant relation regardless of the tES montage. Supra-threshold stimulation showed a stronger relation with the radial field, but rather complex patterns of excitation thresholds depending on neurons’ morphological features. Our results indicated that cortical neurons are affected greatly by the relative direction of the stimulus-induced electric field, which may be a necessary step toward a detailed understanding of tES’ potential mechanisms. •We proposed the multi-scale models that combine the head model and neuronal models.•We analyzed the relation between electric field and neuronal excitability.•Neuronal excitability showed a strong correlation with the radial field for sub/supra-threshold stimulations.•Supra-threshold stimulation yielded complex patterns of excitation thresholds.•The multi-scale models may improve understanding at macroscopic and microscopic levels.