Predicting the phase distribution during multi-channel transcranial alternating current stimulation in silico and in vivo

Abstract

Background: Transcranial alternating current stimulation (tACS) is a widely used noninvasive brain stimulation (NIBS) technique to affect neural activity. TACS experiments have been coupled with computational simulations to predict the electromagnetic fields within the brain. However, existing simulations are focused on the magnitude of the field. As the possibility of inducing the phase gradient in the brain using multiple tACS electrodes arises, a simulation framework is necessary to investigate and predict the phase gradient of electric fields during multi-channel tACS.

Objective: Here, we develop such a framework for phasor simulation using phasor algebra and evaluate its accuracy using in vivo recordings in monkeys.

Methods: We extract the phase and amplitude of electric fields from intracranial recordings in two monkeys during multi-channel tACS and compare them to those calculated by phasor analysis using finite element models.

Results: Our findings demonstrate that simulated phases correspond well to measured phases (r = 0.9). Further, we systematically evaluated the impact of accurate electrode placement on modeling and data agreement. Finally, our framework can predict the amplitude distribution in measurements given calibrated tissues' conductivity.

Conclusions: Our validated general framework for simulating multi-phase, multi-electrode tACS provides a streamlined tool for principled planning of multi-channel tACS experiments.

Keywords: Finite element method; Nonhuman primate experiment; Phasor analysis; Transcranial alternating current stimulation.

Figure. 1.

A) Illustration of the location of sEEG electrodes and tACS electrodes. Three and two sEEG electrodes were used for further data analysis for monkey 1 and monkey 2, respectively. The sEEG electrodes were located along the anterior-posterior direction with the frontal cortex (A1 and B1), the medial prefrontal cortex (A2), and the anterior hippocampus (A3 and B2) as the endpoints, respectively. B) Illustration of volumetric head models, including the scalp, skull, CSF, GM, WM, and eyes. C) Location of tACS electrodes in head models. The red and blue represent the active electrodes (anterior and posterior electrodes, respectively), and the black represents the return electrode. The alternating current with a consistent phase of 0° was applied through the anterior electrode (red), while the alternating current with a phase varying from 0° to 360° was applied through the posterior electrode (blue). The amplitude of the current was fixed to 0.1 mA. D) The pipeline for the phasor simulation.

Figure. 2.

Comparison between simulations and in vivo measurements for four representative stimulation conditions (45°, 135°, 225°, and 315°). A) The phase distribution at all sEEG electrodes in monkey 1. B) The polar graph with the phase and the normalized amplitude at all contacts of sEEG electrode A2 in monkey 1. Colored circles represent individual contacts in the sEEG electrode, with a gradual color gradient along the anterior-posterior direction. The outermost circular line in the polar graph represents the normalized amplitude of 1, with an interval of 0.2 between circular lines.

Figure. 3.

Comparison between simulations and in vivo measurements for the phase. A, B) Illustration of the phase distribution at all sEEG electrodes during 45° stimulation condition for both monkeys. C, D) The example correlation between simulated and measured phases for 45° stimulation condition (left panel). The polar graph depicts the correlation values between measurements and simulations for each stimulation condition for both monkeys (right panel). The red line in the polar graph denotes the significance level of $p=0.05$, while the outermost circular line in the polar graph represents a correlation value of 1, with an interval of 0.2 between circular lines.

Figure. 4.

Comparison between simulations and in vivo measurements for the amplitude. A, B) Illustration of the amplitude distribution at all sEEG electrodes during the 45° stimulation condition for both monkeys. C, D) The example correlation between simulated and measured amplitudes for 45° stimulation condition (left panel). The polar graph depicts the correlation values for each stimulation condition for both monkeys (right panel). The red line in the polar graph denotes the significance level of $p=0.05$, while the outermost circular line in the polar graph represents a correlation value of 1, with an interval of 0.2 between circular lines.

Figure. 5.

Effects of a small displacement of the return electrode. The mean correlation values between simulated and measured results (phase and amplitude) for all stimulation conditions as the return electrode was moved in steps of 5 mm for A) monkey 1 and C) monkey 2. The black circle indicates the center of the displacement (the original position of the return electrode), while the dots in head models represent the return electrode locations. B, D) Mean correlation values for the phase and amplitude with a distance from the center along the inferior-superior (left panel) and anterior-posterior directions (right panel).

Figure. 6.

Effects of employing the optimal conductivity in the computational simulations for monkey 1 (left column) and monkey 2 (right column). A) Comparison of the correlation of the amplitude with that obtained by applying the optimal conductivity. The cross symbols with the solid line are associated with the simulated amplitude obtained by applying the initial conductivity, and the circle symbols with the dotted line are associated with the simulated amplitude when applying the optimal conductivity. B) Correlation values for all 22 stimulation conditions when either applying initial or optimal conductivities. The red line represents the significance level of $p=0.05$. C) The absolute amplitude error for all stimulation conditions ($n=22$) between measured and simulated amplitudes obtained by either applying the initial or optimal conductivities (*$p<0.05$). The ‘Initial’ represents the error between the measured amplitude and simulated amplitude when applying the initial conductivity, while the ‘Optimal’ represents the error between the measure amplitude and simulated amplitude when applying the optimal conductivity.