Noninvasive Deep Brain Stimulation via Temporally Interfering Electric Fields

Abstract

We report a noninvasive strategy for electrically stimulating neurons at depth. By delivering to the brain multiple electric fields at frequencies too high to recruit neural firing, but which differ by a frequency within the dynamic range of neural firing, we can electrically stimulate neurons throughout a region where interference between the multiple fields results in a prominent electric field envelope modulated at the difference frequency. We validated this temporal interference (TI) concept via modeling and physics experiments, and verified that neurons in the living mouse brain could follow the electric field envelope. We demonstrate the utility of TI stimulation by stimulating neurons in the hippocampus of living mice without recruiting neurons of the overlying cortex. Finally, we show that by altering the currents delivered to a set of immobile electrodes, we can steerably evoke different motor patterns in living mice.

Keywords: brain; cortex; deep brain stimulation; electromagnetic; hippocampus; neuromodulation; noninvasive; optogenetics; transcranial direct current stimulation; transcranial magnetic stimulation.

Graphical abstract

Figure 1

Concept of TI Stimulation and Validation of Neural Activation in Intact Mouse Brain (A–C) TI concept. (A) Electric field vectors ${\overline{E}}_1\left(x,y\right)$ and ${\overline{E}}_2\left(x,y\right)$ (gray and blue arrows respectively) resulting from alternating currents $I_1$ and $I_2$ simultaneously applied to the scalp of a simplified head model (simulated as a cylinder filled with saline). $I_1$ and $I_2$ are applied at kHz frequencies $f_1$ (1 mA at 1 kHz in this example, applied across the gray electrodes) and $f_2$ (1 mA at 1.04 kHz, across the blue electrodes) that are higher than the range of frequencies of normal neural operation, so that neurons are driven only at the difference frequency. Field amplitudes were normalized to maximum. The field vectors are taken at a time point in which the two currents were applied in-phase from top to bottom electrodes. (B) Magnified views of the electric field vectors ${\overline{E}}_1$ and ${\overline{E}}_2$ (again normalized to maximum) in the regions indicated by boxes in A and indicated by Roman numerals (left), with plots (right) of time-domain sinusoidal waveforms of the electric field amplitudes $E_{1\hat{y}}\left(t\right)$ (gray) and $E_{2\hat{y}}\left(t\right)$ (blue) along the $\hat{y}$ direction, as well as the envelope resulting from the superposition of the two fields, i.e., $E_{1\hat{y}}\left(t\right)+E_{2\hat{y}}\left(t\right)$ (red). $E_{AM\hat{y}}\left(t\right)$ is the envelope modulation waveform along the $\hat{y}$ direction (black dashed line). (C) Color map (normalized to maximum) of the spatial distribution of the envelope modulation amplitude along the $\hat{y}$ direction (as plotted for two points in B), for the modeled configuration shown in A. (D–J) TI effects on neural activity, assessed with in vivo whole cell patch clamp in anesthetized mouse. (D–F) Representative neural responses from a single patched neuron in the somatosensory cortex undergoing TI stimulation (D) (gray waveform, stimulation at 2.01 kHz, 100 μA amplitude, 0.25 s ramp-up, 1.75 s duration, 0.25 s delay; blue waveform, 2 kHz, 100 μA amplitude, 0.25 s ramp up, 2 s duration, no delay), 10 Hz stimulation (E) (blue waveform, 10 Hz, 200 μA amplitude, 0.25 s ramp-up period, 2 s duration) and high-frequency stimulation (F) (blue waveform, 2 kHz, 200 μA amplitude, 0.25 s ramp-up, 2 s duration). Showing (i) spike raster plots, (ii) traces of current-clamp recording and (iii) magnified views of the trace regions indicated by boxes in (ii). Traces were filtered using a fifth-order Butterworth band-stop filter with cutoff frequencies of 1 kHz and 15 kHz and with a third order Butterworth high-pass filter with a cutoff frequency of 100 Hz to remove 10 Hz and 2 kHz stimulation artifacts; see Figures S1A–S1I for non-filtered traces. (G and H) Representative neural responses from a single patched neuron in hippocampus undergoing TI stimulation (G); gray waveform, stimulation at 2.01 kHz, 400 μA amplitude, 0.5 s ramp-up, 2 s duration, 0.5 s ramp-down; blue waveform, 2 kHz, 400 μA amplitude, 0.5 s ramp up, 2 s duration, 0.5 s ramp-down; shown are (i) traces of current-clamp recording and (ii) magnified views of the trace regions indicated by boxes in (i) and high-frequency stimulation (H); gray waveform, 2 kHz, 400 μA amplitude, 0.5 s ramp-up, 2 s duration, 0.5 s ramp-down; blue waveform, 2 kHz, 400 μA amplitude, 0.5 s ramp-up, 2 s duration, 0.5 s ramp-down). Traces were filtered using a fifth order Butterworth band-stop filter with cutoff frequencies of 1 kHz and 15 kHz to remove 2 kHz stimulation artifacts. (I) Spike frequency in neurons undergoing stimulation, as assessed by whole patch clamp in anesthetized mice (plotted are mean ± SD). (i) Neurons in somatosensory cortex, from left to right: 10 Hz stimulation (200 μA, n = 7 cells from 4 mice), TI stimulation with 1 kHz + 1.01 kHz (current sum 200 μA, n = 6 cells from 2 mice), TI stimulation with 2 kHz + 2.01 kHz (current sum 200 μA, n = 7 cells from 3 mice), 1 kHz stimulation (200 μA, n = 5 cells from 2 mice), 2 kHz stimulation (200 μA, n = 6 cells from 3 mice). (ii) Neurons in hippocampus, from left to right: stimulation with two sinusoids at 10 Hz (current sum 714 ± 367 μA mean ± SD, n = 6 cells from 3 mice), TI stimulation with 2 kHz + 2.01 kHz (current sum 733 ± 100 μA, n = 8 cells from 4 mice), stimulation with two sinusoids at 2 kHz (current sum 880 ± 178 μA, n = 5 cells from 3 mice). Dashed lines, mean spontaneous firing rate; stimulation duration, ∼2 s; $\ast \ast \ast$ indicates p < 1.0E-20 for comparison of mean firing rate of a condition versus mean spontaneous firing rate, and n.s. indicates no significant difference between indicated conditions, for post hoc tests following one-way ANOVA with factor of stimulation condition; see Table S1 for full statistics from cortical and hippocampal recordings. See Figures S1J and S1K for traces at different currents for the conditions corresponding to (G)–(H). (J) Fraction of cells that transiently spiked during the high-frequency stimulation ramp-ups (pooled together are 1 kHz with no TI and 2 kHz with no TI); ‘0.25 s, Crtx’, ramp-up period 0.25 s, neurons in cortex, n = 6 cells from 2 mice; ‘0.5 s, Crtx’, ramp-up period 0.5 s, neurons in cortex, n = 6 cells from 3 mice; ‘0.5 s, Hipp’, ramp-up period 0.5 s, neurons in hippocampus, n = 5 cells from 3 mice.

Figure S1

Patch-Clamp Recordings from Cells Undergoing TI Stimulation, Related to Figure 1 (A) to (I) Removal of artifacts from current-clamp recordings as in Figure 1. (i) Trace of current-clamp recording, with (ii–iv) magnified views of the regions indicated by boxes in (i); α, artifact caused by connecting stimulation and recording grounds ($I_1=I_2=0$ at this point); β, artifact caused by disconnecting stimulation and recording grounds ($I_1$ and $I_2$ are forced to zero at this point). (A) to (C) TI stimulations as in Figure 1D ($I_1$, 2.01 kHz, 100 μA amplitude, 0.25 s ramp-up, 1.75 s duration, 0.25 s delay relative to $I_2$; $I_2$, 2 kHz, 100 μA amplitude, 0.25 s ramp up, 2 s duration). (A) Raw recording trace. (B) Trace of (A), filtered using a fifth order Butterworth band-stop filter with cutoff frequencies of 1 kHz and 15 kHz. (C) Trace of (B), further filtered using a third order Butterworth high-pass filter with a cutoff frequency of 100 Hz; this is the trace shown in Figure 1D. (D–F) Are as in (A)–(C) but for the case of Figure 1F ($I_1$, 2 kHz, 200 μA amplitude, 0.25 s ramp-up, 2 s duration). (G–I) Are as in (A)–(C) but for the case of Figure 1E ($I_1$, 10 Hz, 200 μA amplitude, 0.25 s ramp-up period, 2 s duration); ringing in (Iii) is filtering distortion due to the Gibbs phenomenon. (J and K) Representative neural responses from a single patched neuron in the hippocampus, the neuron of Figures 1G and 1H, undergoing TI stimulation (J); gray waveform, stimulation at 2.01 kHz; blue waveform, 2 kHz) or high-frequency stimulation (K); gray waveform, 2 kHz; blue waveform, 2 kHz) with current amplitude of (i) 400 μA; (ii) 300 μA; (iii) 200 μA. The stimulation order was (iii), (ii), (i) with 2 s intervals between consecutive stimulations. Trace regions containing artifacts caused by connecting stimulation and recording devices (i.e., before current amplitudes are ramped up) are indicated by boxes, with magnified views shown above the boxes. (L–N) Representative neural responses from a single patched neuron in the anesthetized mouse somatosensory cortex undergoing repeated TI stimulation (gray waveform, stimulation at 2.01 kHz, 100 μA amplitude, 0.25 s ramp-up, 1.75 s duration, 0.25 s delay relative to blue waveform; blue waveform, 2 kHz, 100 μA amplitude, 0.25 s ramp up, 2 s duration, no delay) with 2 s intervals between repetitions. (i) Neural response trace, (ii) magnified view of region indicated by a box in (i). (L) Representative trace from the first stimulation period. (M) Representative trace from the 10th stimulation period. (N) Representative trace from the 20th stimulation period. To remove stimulation artifacts, all traces in the figure were filtered using a fifth order Butterworth band-stop filter with cutoff frequencies of 1 kHz and 15 kHz.

Figure S2

Simulation of TI Fields in a Phantom, Related to Figure 2 An alternating current $I_1$ was applied to a phantom via one pair of surface electrodes (gray) at a ∼kHz frequency, $f_1$. A second alternating current $I_2$ was simultaneously applied to the phantom via a second pair of surface electrodes (black) at a ∼kHz frequency $f_2=f_1+\Delta f$ where $\Delta f\ll f_1$. The electrodes were electrically isolated. The spatial distributions of the electric fields ${\overline{E}}_1$ and ${\overline{E}}_2$, from currents $I_1$ and $I_2$ respectively, were simulated independently using a finite element method. The spatial distribution of the envelope modulation amplitude from the superposition of ${\overline{E}}_1$ and ${\overline{E}}_2$ was computed for a projection direction radial to the surface of the phantom, i.e., $\left|E_{AM\hat{r}}\left(x,y\right)\right|$, and for a projection direction tangential to the surface of the phantom, i.e., $\left|E_{AM\hat{t}}\left(x,y\right)\right|$, using $\left|{\overrightarrow{E}}_{AM}\left(\overrightarrow{n,}x,y\right)\right|=\left|\left|\left({\overrightarrow{E}}_1\left(x,y\right)+{\overrightarrow{E}}_2\left(x,y\right)\right)\cdot \overrightarrow{n}\right|-\left|\left({\overrightarrow{E}}_1\left(x,y\right)-{\overrightarrow{E}}_2\left(x,y\right)\right)\cdot \overrightarrow{n}\right|\right|$, where $\overrightarrow{n}$ is a unit vector in radial or tangential direction. The maximal envelope amplitude $\left|E_{AM}^{max}\left(x,y\right)\right|$ that was generated by the vector fields ${\overrightarrow{E}}_1$ and ${\overrightarrow{E}}_2$ at locations $\left(x,y\right)$ across all directions was computed in post-processing as described in the STAR Methods. (A–F) Cylindrical phantom model. The phantom model was a cylinder with a 50 mm diameter and 10 mm height that was filled with a saline solution (conductivity $0.333S/m$). Figure panels show (i) envelope modulation amplitude $\left|E_{AM\hat{r}}\left(x,y\right)\right|$, (ii) envelope modulation amplitude $\left|E_{AM\hat{t}}\left(x,y\right)\right|$ and (iii) maximal envelope modulation amplitude along any direction $\left|E_{AM}^{max}\left(x,y\right)\right|$. Color-maps are in units of V/m. Distances were normalized to the phantom’s radius. (A–C) The volume targeted for large envelope modulation amplitude is largely independent of electrode size. (A) Envelope modulation amplitude maps. 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 = 0.39 and a normalized large base size of b = 1.96 (geometry as in Figure 2A). The amplitudes of currents $I_1$ and $I_2$ were 1 mA. (B) As (A) but with approximately 8× larger electrodes (normalized electrode size of 1.3) at the vertices of the lower base while holding the space between the edges of these two electrodes fixed. (C) Contours of $1/e$ of the peak value of the envelope modulation amplitude. Electrodes at the small trapezoid base had a normalized size of 0.16 (black; corresponding to envelope modulation maps in (A)), 0.5 (blue), and 1.3 (green; corresponding to envelope modulation maps in (B)). (D–F) Steering of the large envelope modulation volume between two pairs of fixed electrodes. (D) Envelope modulation amplitude maps. The two pairs of electrodes (gray and black) were placed at a rectangular geometry with a normalized length of 1.96 (geometry as in Figure 2C). The amplitudes of currents $I_1$ and $I_2$ were 1 mA as in (A). (E) As (D) but current $I_1$ between the gray electrode pair was increased by $\Delta I=0.6mA$ and current $I_2$ between the black electrode pair was decreased by the equal $\Delta I$ (i.e., total current $I_1+I_2$ was not changed), so that the current ratio $I_1\text{:}{I}_2$ was $4:1$. (F) Contours of $1/e$ of the peak value of the envelope modulation amplitude. Current ratio $I_1:I_2$ was 1:1 (black; corresponding to envelope modulation maps in (D)), 2.5:1 (blue), and 4:1 (green; corresponding to envelope modulation maps in (E). (G) to (L) Spherical phantom model. The phantom model was a conductive sphere with a 50 mm diameter. The electrodes were arranged in a rectangular geometry with a normalized length of 1.96 (geometry as in Figure 2C). Panels (H) to (K) show envelope modulation amplitude distributions in (i) the electrode plane and (ii) a plane perpendicular to the plane of the electrodes as schematized in (G) (N and S indicate the north and south poles of the sphere, respectively). Color-maps are in units of V/m. Distances were normalized to phantom radius. (G) Schematic illustration of the phantom model showing (i) in-plane and (ii) a perpendicular plane with respect to the plane of the electrodes. (H and I) Sphere with homogeneous conductivity of $0.333S/m$. (H) Envelope modulation amplitude maps of $\left|E_{AM\hat{r}}\left(x,y\right)\right|$. (I) Envelope modulation amplitude maps of $\left|E_{AM}^{max}\left(x,y\right)\right|$. (J and K) Sphere with inhomogeneous conductivity consisting of 4 layers: scalp ($d=0.05$, $\sigma =0.333S/m$), skull ($d=0.085$, $\sigma =0.0083S/m$), cerebrospinal fluid ($d=0.023$, $\sigma =1.79S/m$) and brain ($d=0.83$, $\sigma =0.333S/m$), where $d$ is the normalized layer thickness. (J) Envelope modulation amplitude maps of $\left|E_{AM\hat{r}}\left(x,y\right)\right|$. (K) Envelope modulation amplitude maps of $\left|E_{AM}^{max}\left(x,y\right)\right|$. (L) Comparison of normalized full width at half maxima (FWHM) of envelope modulation amplitude maps (i) $\left|E_{AM\hat{r}}\left(x,y\right)\right|$ and (ii) $\left|E_{AM}^{max}\left(x,y\right)\right|$ in the plane of the electrodes when the phantom was: a homogeneous cylindrical plate (‘cylinder’; panels (A) to (F)), homogeneous sphere (‘sphere’; panels (H) and (I)) and inhomogeneous 4-layer sphere (‘sphere 4-layer’; panels (J) and (K)) of equal diameter (50 mm). $FWH{M}_{\hat{x}}$ and $FWH{M}_{\hat{y}}$ are FWHM along $\hat{x}$ and $\hat{y}$ directions, respectively. (M and N) Cylindrical phantom model with different number of fields. $n$ alternating currents $\left\{I_1,I_2,\dots ,I_n\right\}$ at different kHz frequencies $\left\{f_1,f_2,\dots ,f_n\right\}$ were applied simultaneously to a phantom (as in Figure 2) via $n$ pairs of surface electrodes. Electrode pairs were placed at the circumference with equal spacing and applied currents of 1 mA. Shown is (i) a time-domain plot of sinusoidal waveforms of the electric field amplitudes $\left\{E_{1\hat{y}}\left(t\right),E_{2\hat{y}}\left(t\right),\dots ,E_{n\hat{y}}\left(t\right)\right\}$ along the $\hat{y}$ direction, as well as the waveform resulting from the superposition of the fields, i.e., $\sum E_{1\hat{y}}\left(t\right),E_{2\hat{y}}\left(t\right),\dots ,E_{n\hat{y}}\left(t\right)$ (red). $E_{AM\hat{y}}\left(t\right)$ is the envelope of the superposition waveform along the $\hat{y}$ direction (black dashed line). Shown in (ii) is the maximal envelope amplitude across all directions $\left|E_{AM}^{max}\left(x,y\right)\right|$; color-maps are values normalized to the maximum value. (M) TI fields with $n=2$ alternating currents $\left\{I_1,I_2\right\}$ applied via electrode pairs {gray, black} at frequencies $\left\{f_1=1kHz,f_2=1.04kHz\right\}$. Panel (i) is as in Figure 1Bi and panel (ii) is as in Diii, replotted here for comparison with TI fields with $n=4$. Half width half maximum (HWHM) of the main peak normalized to the phantom radius is 0.49, computed along the white dashed line. (N) TI fields with $n=4$ alternating currents $\left\{I_1,I_2,I_3,I_4\right\}$ applied via electrode pairs {blue, black, green, gray} at frequencies {f₁ = 1.04 kHz, f₂ = 9 kHz, f₃ = 90 kHz, f₄ = 100 kHz}. The maximal envelope amplitude $\left|E_{AM}^{max}\left(x,y\right)\right|$ that was generated by $n>2$ vector fields was approximated using $2\cdot min\left\{{\overrightarrow{E}}_1\left(\overrightarrow{r}\right),{\overrightarrow{E}}_2\left(\overrightarrow{r}\right),\dots ,{\overrightarrow{E}}_n\left(\overrightarrow{r}\right)\right\}$. HWHM of the main peak normalized to the phantom radius is 0.23, computed along the white dashed line. (iii) Magnified view of the boxed region in (i), plotted without the superposition waveform.

Figure S3

Design, Implementation, and Characterization of TI Stimulator, Related to Figure 2, Figure 3, Figure 4, Figure 5 and STAR Methods 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 $\left(C{H}_1\right)$, 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 $\left(C{H}_2\right)$, 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 $I_1\left(A\right)=\left(V_1\left(V\right)/500\right)$ and the amplitude of current $I_2$ of CH2 between nodes 2A and 2B was calibrated such that $I_2\left(A\right)=\left(V_2\left(V\right)/500\right)$. 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 $1kHz$ 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 $I_{measured}$ 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 $I_{measured\left(RMS\right)}$ in μA against the RMS amplitude of the current that was programmed in the device $I_{programmed\left(RMS\right)}$ in μA, where $I_{programmed\left(RMS\right)}=\left(I_1/\sqrt{2}\right)=\left(V_1\left(V\right)/\sqrt{2}\cdot 500\right)$, 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). (E and F) Effect of channel isolation on distribution of envelope amplitude. An alternating current $I_1$ 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 $\hat{x}$ and $\hat{y}$ directions 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 $\left|E_{AM\hat{x}}\left(x,y\right)\right|$ along $\hat{x}$ direction; (ii) envelope modulation amplitude map $\left|E_{AM\hat{y}}\left(x,y\right)\right|$ (projection along $\hat{y}$ direction). Dashed lines cross at the peak of the envelope modulation amplitude distribution, i.e., ${\left|E_{AM\hat{x}}\right|}_{max}$ and ${\left|E_{AM\hat{y}}\right|}_{max}$. 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 $\left|E_{AM\hat{x}}\right|$ around its peak has a normalized half width at half maximum along the $\hat{x}$ direction $HWH{M}_{\hat{x}}=0.46$ and a normalized half width at half maximum along the $\hat{y}$ direction $HWH{M}_{\hat{y}}=0.46$. The spread of $\left|E_{AM\hat{y}}\right|$ around its peak is $HWH{M}_{\hat{x}}=0.51$ and $HWH{M}_{\hat{y}}=0.95$. (F) Same as (E) but when currents were applied without electrical isolation between the current sources. The peak of the envelope modulation amplitude was located along the midline of the trapezoid at its small base as in (E) however the distribution of the envelope modulation amplitude was significantly more dispersed. The amplitude of $\left|E_{AM\hat{x}}\right|$ at the end of the $\hat{x}$ direction dashed line (normalized distance of 0.51 from center) was 0.76 of its maximal value. The spread of $\left|E_{AM\hat{x}}\right|$ around its maximal value had a normalized $HWH{M}_{\hat{x}}=0.95$. The amplitude of $\left|E_{AM\hat{y}}\right|$ at the end of the $\hat{y}$ direction dashed line was 0.91 of its maximal value. The spread of $\left|E_{AM\hat{y}}\right|$ around its maximal value had a normalized $HWH{M}_{\hat{y}}=0.83$.

Figure 2

Steerability of TI, Probed via Both Computational Modeling and a Tissue Phantom For each condition (A)–(E), we simulated the interferential electric field envelope modulation (projected along: i, x-direction, ii, y-direction) that would result from electrodes at the locations indicated by the rectangles (the gray electrodes forming a pair, with an alternating current $I_1$ applied at 1 kHz, and the black electrodes forming a second pair, with an alternating current $I_2$ applied at 1.02 kHz), passing the currents described below in the individual panel caption sections. For exact coordinates of electrodes and numerical values of the peak envelope modulation amplitude, location, and width, see Table 1. We also experimentally measured in a tissue phantom (a non-conductive cylinder of 50 mm diameter and 10 mm height that was filled with a saline solution, with 1 mm diameter silver wire electrodes at various points around the perimeter of the phantom) these two amplitudes (iii, x-direction, iv, y-direction); channels were isolated as described in Figure S3. Finally, we plotted, along line cuts through the simulated (lines) and experimental (dots) datasets, the interferential electric field envelope amplitudes for the x-direction (v) and the y-direction (vi). Simulated and experimental values along the vertical line cut were plotted in gray, and along the horizontal line cut, in black; values were normalized to the peak. Color-maps in i-iv are in V/m. Envelope modulation amplitude maps in iii and iv are a linear interpolation of the measured values. Distances in v and vi were normalized to the phantom’s radius and shown relative to the center of the phantom. Circles in line plots v and vi are measured envelope modulation amplitudes without interpolation. (A) Electrodes were placed in a trapezoidal geometry with a narrow base, and amplitudes of currents $I_1$ and $I_2$ were set to 1 mA. (B) Electrodes were placed in a trapezoidal geometry with a wider base, with currents as in (A). (C) Electrodes were placed in a rectangle, with currents as in (A). (D) Electrodes as in (C), but now with currents in the ratio $I_1:I_2=1:2.5$ (holding the sum at 2 mA). (E) Electrodes as in (C), but now with currents in the ratio $I_1:I_2=1:4$ (holding the sum at 2 mA).

Figure S4

Application of TI to Stimulation of Mouse Hippocampus, Related to Figure 3 (A) Quasi-electrostatic finite element method (FEM) mouse model simulation of 10 Hz and 2 kHz stimulations, corresponding to Figures 3A–3C and Figures 3D–3F, respectively. Showing (i) field amplitude map $\left|E_{\hat{r}}\left(x,y\right)\right|$ of simulated fields along the direction $\hat{r}$ orthogonal to the brain surface, and (ii) plot of field amplitude $\left|E_{\hat{r}}\left(r\right)\right|$ along dashed line in (i) that is perpendicular to the brain surface. In this case, two alternating currents at a frequency of 10 Hz and amplitude of 125 μA were simulated at electrode sites with a 1.5 mm gap. (B) As in (A) but for TI stimulation, corresponding to Figures 3G–3I, showing the envelope modulation amplitude $\left|E_{AM\hat{r}}\left(x,y\right)\right|$. (C) As in (B) but for TI stimulation with a larger inter-electrode spacing, corresponding to (D-F). Scale-bars for (A), (B), (C) 1 mm. Distances are measured from the surface of the brain. Color-maps are values in V/m. Mouse anatomical model (x, y, z) resolution was (42 μm, 42 μm, 700 μm) respectively. (D–F) Experimental probing of hippocampal activation with TI stimulation but with a large inter-electrode distance. TI stimulation with anesthetized mice as in Figures 3G–3I but electrodes were placed at a larger distance from each other on the skull (relative to bregma: at anteroposterior (AP) −2 mm, mediolateral (ML) −0.25 mm, and AP −2 mm, ML 4.25 mm). Currents were applied in a 10 s-on, 10 s-off pattern for 20 min. Shown is a representative image montage of a slice of stimulated brain showing c-fos expression (stained with anti-c-fos, shown in green). Grey rectangles illustrate electrode lateral positions. Boxed regions are highlighted in (E). (E) C-fos (green) overlaid with 4′,6-diamidino-2-phenylindole (DAPI) (blue) staining to highlight individual cell nuclei, from boxed regions i to iv in (D). (F) Percentage of c-fos–positive cells within a DAPI-labeled cortical area (500 μm x 500 μm) underneath the electrode $\left(Crt{x}_{UE}^{+}\right)$, a contralateral cortex area ($Crt{x}_{UE}^{-}$; 500 μm x 500 μm), a cortex area (1500 μm x 500 μm) between the stimulating electrodes $\left(Crt{x}_{BE}^{+}\right)$, an area in the contralateral cortex area ($Crt{x}_{BE}^{-}$; 1500 μm x 500 μm), a dentate gyrus area (500 μm x 500 μm) in the hippocampus of the stimulated hemisphere $\left(Hip{p}^{+}\right)$, and a dentate gyrus area of the hippocampus in the contralateral (non-stimulated) hemisphere ($Hip{p}^{-};$ 500 μm x 500 μm). Bars show mean values ± SD, n = 4 mice. Significance was analyzed by one-way ANOVA with Bonferroni post hoc test; for full statistics see Table S2. Scale bar for (D) 0.5 mm; scale bars for (E) 25 μm.

Figure 3

Application of TI to Stimulation of Mouse Hippocampus without Recruitment of Overlying Cortex (A) 10 Hz stimulation with anesthetized mice bearing two electrodes made of saline-filled tubes (1.5 mm outer diameter) placed on the skull surface (relative to bregma: at anteroposterior (AP) −2 mm, mediolateral (ML) −0.25 mm, and AP −2 mm, ML 2.75 mm). Currents (125 μA per electrode pair) were applied in a 10 s-on, 10 s-off pattern for 20 min. Shown is a representative image montage of a slice of stimulated brain showing c-fos expression (stained with anti-c-fos, green). Grey rectangles illustrate electrode mediolateral positions. Boxed regions are highlighted in (B). (B) c-fos (green) overlaid with 4′,6-diamidino-2-phenylindole (DAPI, blue) staining to highlight individual cell nuclei, from boxed regions i to iv from (A). (C) Percentage of c-fos–positive cells within a DAPI-labeled cortical area (500 μm x 500 μm) underneath the electrode $\left(Crt{x}_{UE}^{+}\right)$, a contralateral cortex area $(Crt{x}_{UE}^{-}$; 500 μm x 500 μm), a dentate gyrus area (500 μm x 500 μm) in the hippocampus of the stimulated hemisphere $\left(Hip{p}^{+}\right)$ and a dentate gyrus area of the hippocampus in the contralateral (non-stimulated) hemisphere ($Hip{p}^{-};$ 500 μm x 500 μm). Bars show mean values ± SD; n = 3 mice. (D–F) As in (A)–(C), but for the case where the currents are delivered at 2 kHz frequency; n = 4 mice in (F). (G–I) As in A-C, but for the case of TI stimulation with the lateral electrodes driven at 2 kHz and the medial electrodes driven at 2.01 kHz. The two pairs of electrodes were electrically isolated (see Figure S3 for description of isolation). In (I), c-fos–positive neurons were analyzed in the locations analyzed in (C) and (F), but also in a cortex area (1000 μm x 500 μm) between the stimulating electrodes $\left(Crt{x}_{BE}^{+}\right)$ and in the contralateral cortex area ($Crt{x}_{BE}^{-}$; 1000 μm x 500 μm); n = 4 mice. Significance in (C), (F), and (I) was analyzed by one-way ANOVA with Bonferroni post hoc test, ^∗p < 0.05, ^∗∗∗p < 0.00001; for full statistics for Figure 3, see Table S2; scale bars for (A), (D), and (G) represent 0.5 mm; scale bars for (B), (E), and (H) represent 25 μm.

Figure 4

Safety Assessments for TI Stimulation (A–H) Immunohistochemical characterization of cellular and synaptic markers after TI stimulation of awake mice. Stimulating currents ($I_1$, 2.01 kHz, 125 μA; $I_2$, 2 kHz, 125 μA) were applied in a 10 s-on, 10 s-off pattern for 20 min with 0.5 s ramp-up and ramp-down periods, via two electrodes placed on the skull surface (relative to bregma: at anteroposterior (AP) −2 mm, mediolateral (ML) −0.25 mm, and AP −2 mm, ML 2.75 mm), as in Figure 3G–3I. For each panel, subpanels show (i) representative immunohistochemically stained slices and (ii and iii) mean ± SEM of immunohistochemical values as described below for individual panel caption sections. Stim⁺, brain regions from stimulated hemisphere; Stim⁻, brain regions from the contralateral, unstimulated hemisphere; Sham, brain regions from mice that underwent the same procedure but with $I_1$ and $I_2$ set to 0 μA. Significance was characterized using one-way ANOVA; n = 2 sections from 5 mice each. Scale bars for (i) are 50 μm. (A) NeuN staining and cleaved caspase-3 staining, from a cortical region underneath the lateral electrode (Ctx_ULE). (ii) NeuN intensity. (iii) Cleaved caspase-3 intensity. (B) As in (A) but for the dentate gyrus of the hippocampus (DG), with additionally (iv) number of cleaved caspase-3 positive cells. (C) γH2AX staining from Ctx_ULE to assess DNA damage. (ii) γH2AX intensity. (D) As in (C) but from the DG. (E) Iba1 staining from Ctx_ULE. (ii) Iba1 intensity. (iii) Number of Iba1-positive cells. (F) As in (E) but from the DG. (G) Synaptophysin (Syp) staining from Ctx_ULE. (ii) Syp intensity. (H) As in (G) but from the DG. See Figures S5A–S5I for immunohistochemical assessment of cortex regions underneath the electrode that was located centrally, as well as between the electrodes; see Figures S5J–S5O for immunohistochemical assessment of CA1 region of the hippocampus. See Table S3 for full statistics of cortical and hippocampal regions. (I) Measurement of tissue temperature. High-frequency stimulating currents ($I_1$, 2 kHz, 500 μA; $I_2$, 2 kHz, 500 μA) were simultaneously applied with 0.5 ramp-up and ramp-down periods via two electrodes placed on the skull surface as in (A)–(H). The temperature of the brain tissue underneath the lateral electrodes was measured using an invasive thermocouple probe during 60 s of stimulation (‘Stim’ period) as well as 30 s before (‘Pre’ period) and 30 s after (‘Post’ period) stimulation. Plotted is (i) instantaneous change in brain temperature from baseline as a function of time; black bar indicates period of stimulation. (ii) Maximal increase in brain temperature from the baseline (i.e., pre-stimulation) mean temperature. Shown are mean ± SD; significance calculated via one-way ANOVA; p = 0.8091; n = 6 mice; see Table S3 for full statistics.

Figure S5

Safety Assessment of Temporal Interference Stimulation, Related to Figure 4 Immunohistochemical measurement of cellular and synaptic markers after TI stimulation (as in Figure 4) of awake mice showing (i) representative immunohistochemically stained slices and (ii-iii) mean ± s.e.m of immunohistochemical values as described below in the individual panel caption sections; Stim⁺, brain regions from stimulated hemisphere; Stim⁻, brain regions from the contralateral hemisphere that was not stimulated; Sham, brain regions from mice that underwent the same procedure but with current amplitudes of currents $I_1$ and $I_2$ set to 0 μA. Significance was characterized using one way ANOVA; n = 5 mice, 2 sections from each mouse; scale bars for (i) 50 μm. (A–I) Cortex. (A) NeuN staining and cleaved caspase-3 staining for a cortical region underneath the midline (central) electrode (Ctx_UCE). (ii) NeuN intensity. (iii) Cleaved caspase-3 intensity. (B) As in (A) but for a cortical region between the electrodes (Ctx_BtwE). (C) γH2AX staining for Ctx_UCE. (ii) γH2AX intensity. (D) As in (C) but for Ctx_BtwE. (E) Synaptophysin (Syp) staining for Ctx_UCE. (ii) Syp intensity. (F) As in (E) but for Ctx_BtwE. (G) Iba1 staining for Ctx_UCE. (ii) Iba1 intensity. (iii) Number of Iba1 positive cells. (H) As in (G) but for Ctx_BtwE. (I) γH2AX staining for cortical regions of CK-p25 mouse, an established mouse model of neurodegeneration, with neuronal atrophy, reduced synaptic density and pronounced DNA damage (Cruz et al., 2003, Dobbin et al., 2013, Kim et al., 2008), plotted here as a positive staining control for the utilized antibodies. (J–P) Hippocampus. (J) NeuN and cleaved caspase-3 staining for CA1 region of the hippocampus (CA1). (ii) NeuN intensity. (iii) Cleaved caspase-3 intensity. (iv) Number of cleaved caspase-3 cells. (K) γH2AX staining for CA1. (ii) γH2AX intensity. (L) Synaptophysin (Syp) staining for CA1. (ii) Syp intensity. (M) Iba1 staining for CA1. (ii) Iba1 intensity. (iii) Number of Iba1 positive cells. (N) GFAP staining for dentate gyrus of the hippocampus (DG). (ii) GFAP intensity. (iii) Number of GFAP-positive cells. (O) As in (N) but for CA1. (P) Staining for DG and CA1 regions of CK-p25 mouse, an established mouse model of neurodegeneration, with neuronal atrophy, reduced synaptic density and pronounced DNA damage (Cruz et al., 2003, Dobbin et al., 2013, Kim et al., 2008), plotted here as a positive staining control for the utilized antibodies. (i) NeuN and cleaved caspase-3 staining. (ii) γH2AX staining. See Table S3 for full statistics for this figure.

Figure 5

Application of TI to Steerable Probing of Mouse Motor Cortex Functionality (A) Currents $I_1$ and $I_2$ were applied simultaneously (0.5 s ramp-up, 6 s stimulation, 0.5 s ramp-down) to anesthetized head-fixed mice and motor activity was video-recorded (including 1.5 s pre-stimulation and post-stimulation periods). Current $I_1$ was applied via a 1 mm diameter skull electrode (white circle; relative to bregma, AP −1.5 mm, ML +2 mm, n = 5 mice; or AP −1.5 mm, ML −2 mm, n = 4 mice) paired with a 5-8 mm diameter electrode (white ellipse). Current $I_2$ was applied via a similarly sized skull electrode (black circle; relative to bregma, AP −1.5 mm, ML −0.5 mm, n = 5 mice; or AP −1.5 mm, ML +0.5 mm, n = 4 mice) paired with a 5-8 mm diameter electrode (black ellipse). (B and C) Characterization of motor threshold. Current ratio $I_1\text{:}{I}_2$ was fixed at 1:4. Shown is mean motor threshold ± SD (n = 6 mice). Significance calculated using one-way ANOVA followed by post-hoc test with Bonferroni correction for multiple comparisons. (B) Comparison of motor thresholds with TI stimulation at different difference frequencies and a fixed 2 kHz carrier frequency; p = 0.88; see Table S4 for full statistics for (B). (C) Comparison of motor thresholds with TI stimulation at different carrier frequencies and fixed 10 Hz difference frequency; ^∗p < 0.05, ^∗∗p < 0.0005; see Table S4 for full statistics for (C). (D–F) Steerable motor cortex activation. Current $I_1$ at a frequency of 1 kHz and current $I_2$ at a frequency of 1.01 kHz were applied at different amplitude ratios $I_1:I_2$ but with a fixed current sum $I_1+I_2$ (776 μA ± 167 μA; mean ± SD; n = 9 mice). (D) Evoked movements of the forepaws. (E) Evoked movements of the whiskers. (F) Evoked movements of the ears. (i) Number of animals, out of a total of 9 animals, in which the TI stimulation with $I_1:I_2$ current ratios of 1:2, 1:4 or 1:8 (‘$I_1<I_2$’), and with $I_1\text{:}{I}_2$ current ratios of 2:1, 4:1 or 8:1 (‘$I_1>I_2$’) evoked a movement ipsilateral to $I_1$ electrode (white) or contralateral to $I_1$ electrode (gray). Significance of number of responders was characterized using Fisher’s exact test; ^∗p < 0.05, ^∗∗p < 0.005, ^∗∗∗p < 0.00001. See Table S4 for full statistics. (ii) Evoked movements ipsilateral to $I_1$ electrode (white) and contralateral to $I_1$ electrode (gray) at different current ratios $I_1:I_2$. Shown values are mean ± SEM; n = 9 mice. Ear movements were visually scored on the following scale: 0, no movement; 1, weak movement; 2, strong movement; 3, very strong movement. Significance of evoked movement for each current ratio was characterized using an unpaired t test versus null hypothesis of no movement, thresholding at p < 0.0025, Bonferroni corrected for multiple comparisons; ^∗p < 0.0025, ^∗∗p < 0.00001; significance between current ratios was calculated using one-way ANOVA followed by post hoc test with Bonferroni correction for multiple comparisons; ^∗p < 0.05. See Table S4 for full statistics.