Stimulating currents were generated using a custom device consisting of two electrically isolated current sources. To isolate the channels, each waveform was supplied via a balanced pair of current sources that were driven in precisely opposite phase, a technique that we call anti-phasic current drive.

(A) Schematics of the electronic circuitry of the stimulator. (i) Dual channel stimulation with anti-phasic current drive isolation. In channel 1 ( C H 1 ) , a voltage waveform V 1 at a frequency f 1 was applied to the positive (+) input of a voltage-controlled current source (J1) that had its negative (−) input grounded, resulting in a current waveform I 1 at node 1A that was in-phase with waveform V 1 . An equal voltage waveform V 1 at a frequency f 1 was applied to the negative (−) input of a second voltage-controlled current source (J2) that had its positive (+) input grounded, resulting in a current waveform − I 1 at node 1B that is anti-phase with waveform V 1 . In channel 2 ( C H 2 ) , a second voltage waveform V 2 at a frequency f 2 was converted in an equivalent way to an in-phase current waveform I 2 at node 2A by a voltage-controlled current source (J3) and to an anti-phase current waveform − I 2 at node 2B by a voltage-controlled current source (J4). The amplitude of current I 1 of C H 1 between nodes 1A and 1B was calibrated such that I 1 ( A ) = ( V 1 ( V ) / 500 ) and the amplitude of current I 2 of CH2 between nodes 2A and 2B was calibrated such that I 2 ( A ) = ( V 2 ( V ) / 500 ) . A ground or reference electrode (Ref) was provided to carry any imbalance currents from the paired current sources and to prevent charging of the body relative to earth ground. (ii) Dual channel stimulation without isolation. As in (i), but nodes 1B and 2B were connected to the GND of the device.

(B) Characterization of channel isolation. (i) Schematic of the experiment setup. Voltage waveform V 1 of C H 1 was set to 1 kHz and 0.5 V resulting in a current I 1 between nodes 1A and 1B at the same frequency and an amplitude of 1 mA. The output nodes 1A and 1B were connected to a load made of a bridge of 6 resistors with 1 kΩ resistance each. Voltage waveform V 2 of C H 2 was set to 1.1 kHz and 0.5 V resulting in a current I 2 between nodes 2A and 2B at the same frequency and an amplitude of 1 mA. The output nodes 2A and 2B were connected to the same resistor bridge load as shown in the schematics. The frequency spectrum of the currents was measured using a FFT spectrum analyzer (SR770, Stanford Research) at the output of C H 1 between nodes 1A and 1B, the output of C H 2 between nodes 2A and 2B, and across the resistor bridge between nodes 1A and 2B. (ii) Ratio of the FFT amplitude at the cross-talk frequency (i.e., f 2 at the output nodes 1A and 1B of C H 1 and f 1 at the output nodes 2A and 2B of C H 2 ) and the FFT amplitude at the channel’s set frequency (i.e., f 1 at the output nodes 1A and 1B of C H 1 and f 2 at the output nodes 2A and 2B of C H 2 ). FFT ratio across C H 1 − C H 2 between the output node 1A of C H 1 and the output node 2B of C H 2 is the ratio of the FFT amplitude of f 1 and the FFT amplitude of f 2 . (The total harmonic distortion of the current source was < 0.08% at 100 Hz and < 0.4% at 10 kHz, measured with 9 harmonics on 1 kΩ load resistor.)

(C) Characterization of output current for different load resistances. Voltage waveform V 1 of C H 1 was set to 1 k H z and 0.5 V resulting in a current I 1 between nodes 1A and 1B of the same frequency and an amplitude of 1 mA. The output nodes 1A and 1B were connected to loads with resistances between 100 Ω and 100 kΩ. The output nodes 2A and 2B of C H 2 were grounded. The current flowing between nodes 1A and 1B was measured using a digital ammeter. The panel shows the amplitude of the measured currents I m e a s u r e d in mA against the load resistance in Ω.

(D) Characterization of output current for different set frequencies. Voltage waveform V 1 of C H 1 was set to a range of frequencies between 0.1 Hz and 50 kHz with a range of amplitudes between 0.5 mV and 0.5 V, resulting in a current I 1 between 1A and 1B nodes of the same frequencies and with amplitudes that ranged between 1 μA and 1 mA. The output nodes 1A and 1B were connected to a load with a resistance of 10 kΩ. The output nodes 2A and 2B of C H 2 were grounded. The current flowing between nodes 1A and 1B was measured using a digital ammeter. The panel shows 7 line plots of the RMS amplitude of the measured currents I m e a s u r e d ( R M S ) in μA against the RMS amplitude of the current that was programmed in the device I p r o g r a m m e d ( R M S ) in μA, where I p r o g r a m m e d ( R M S ) = ( I 1 / 2 ) = ( V 1 ( V ) / 2 ⋅ 500 ) , for frequencies 0.1 Hz, 1 Hz, 10 Hz, 100 Hz, 1kHz, 10 kHz and 50 kHz. (Note that the line plots of frequencies between 0.1 Hz and 10 kHz are overlapping).

I 1 was applied to a phantom at a frequency of 1 kHz via one pair of electrodes (gray). A second alternating current I 2 was applied to the phantom at a frequency of 1.02 kHz via a second pair of electrodes (black). The phantom was a non-conductive cylinder of 50 mm diameter and 10 mm height that was filled with a saline solution. The two pairs of electrodes (gray and black) were placed in an isosceles trapezoid geometry such that each electrode pair was located at the vertices of one lateral side. The trapezoid had a normalized small base size of a = 1.39 and a normalized large base size of b = 1.96. The amplitudes of currents I 1 and I 2 were 1 mA. The envelope modulation amplitude from temporal interference of two electric fields projected along the x ˆ and y ˆ directions was measured using a lock-in amplifier as in (E and F) Effect of channel isolation on distribution of envelope amplitude. An alternating currentwas applied to a phantom at a frequency of 1 kHz via one pair of electrodes (gray). A second alternating currentwas applied to the phantom at a frequency of 1.02 kHz via a second pair of electrodes (black). The phantom was a non-conductive cylinder of 50 mm diameter and 10 mm height that was filled with a saline solution. The two pairs of electrodes (gray and black) were placed in an isosceles trapezoid geometry such that each electrode pair was located at the vertices of one lateral side. The trapezoid had a normalized small base size of a = 1.39 and a normalized large base size of b = 1.96. The amplitudes of currentsandwere 1 mA. The envelope modulation amplitude from temporal interference of two electric fields projected along theanddirections was measured using a lock-in amplifier as in Figure 2 (see also STAR Methods for a detailed description of the phantom measurement). Envelope modulation amplitude maps are a linear interpolation (interpolation factor 2) between the measured values. Color-maps show values normalized to maximal envelope modulation amplitude. Distances were normalized to the phantom’s radius and are shown relative to the center of the phantom. High isolation is required between the two current sources in order to focus the region with large envelope modulation amplitude deep into the phantom.

(E) Envelope modulation amplitude maps when currents were applied with a high level of electrical isolation between the current sources. (i) Envelope modulation amplitude map | E A M x ˆ ( x , y ) | along x ˆ direction; (ii) envelope modulation amplitude map | E A M y ˆ ( x , y ) | (projection along y ˆ direction). Dashed lines cross at the peak of the envelope modulation amplitude distribution, i.e., | E A M x ˆ | m a x and | E A M y ˆ | m a x . The volume of large envelope modulation amplitude was located along the midline of trapezoid at its small base with a peak at x = 0 and y = 0.49. The spread of | E A M x ˆ | around its peak has a normalized half width at half maximum along the x ˆ direction H W H M x ˆ = 0.46 and a normalized half width at half maximum along the y ˆ direction H W H M y ˆ = 0.46 . The spread of | E A M y ˆ | around its peak is H W H M x ˆ = 0.51 and H W H M y ˆ = 0.95 .