Electric field envelope focality in superficial brain areas with linear alignment montage in temporal interference stimulation

Temporal interference stimulation (TIS) uses two pairs of conventional transcranial alternating current stimulation (tACS) electrodes, each with a different frequency, to generate a time-varying electric field (EF) envelope (EFE). The EFE focality in primary somatosensory and motor cortex areas of a standard human brain was computed using newly defined linear alignment montages. Sixty head volume conductor models constructed from magnetic resonance images were considered to evaluate interindividual variability. Six TIS and two tACS electrode montages were considered, including linear and rectangular alignments. EFEs were computed using the scalar-potential finite-difference method. The computed EFE was projected onto the standard brain space for each montage. Computational results showed that TIS and tACS generated different EFE and EF distributions in postcentral and precentral gyri regions. For TIS, the EFE amplitude in the target areas had lower variability than the EF strength of tACS. However, bipolar tACS montages showed higher focality in the superficial postcentral and precentral gyri regions than in TIS. TIS generated greater EFE penetration than bipolar tACS at depths < 5 – 10 mm below the brain surface. From group-level analysis, tACS with a bipolar montage was preferred for targets < 5 – 10 mm in depth (gyral crowns) and TIS for deeper targets. TIS with a linear alignment montage could be an effective method for deep structures and sulcal walls. These findings provide valuable insights into the choice of TIS and tACS for stimulating specific brain regions.


Introduction
Transcranial electric stimulation (tES) [1] and transcranial magnetic stimulation [2] are noninvasive methods for brain tissue neuromodulation.They are often used to treat neurological and psychiatric disorders [3] and for neuroscience research, such as cognition [4] and pain perception [5].
Well-known methods in tES are transcranial direct current stimulation (tDCS) and transcranial alternating current stimulation (tACS).In tES, a current is injected into the head via a set of electrodes, inducing an electric field (EF) in the targeted cortical area of the brain.The locations of electrodes (called montage) differ depending on the target region.The EF induced in the brain acts as a physical agent in these stimulation methods.Unlike invasive (direct) stimulation, EF in the brain's cortical area induced in tES is distorted by the shape and anatomy of the head.
Computational physical simulation is a powerful tool for medical applications, especially for the brain with a complex structure (e.g.Refs.[6,7]).In the last two decades, computational studies for tES have been extensively reported by separate groups [8][9][10][11][12].One main feature is that cerebrospinal fluid (CSF) has higher conductivity than brain tissues, resulting in nonuniform and widespread EF distribution [13,14].The EF in different head models is variable (hereafter defined as intersubject variability), and the EF strength in nontarget regions is comparable to or higher than that in the target area [15].Therefore, substantial efforts have been made to target specific brain areas [9,[14][15][16][17].In addition, a limitation of tES methods is that the target areas are typically limited to the brain's cortical region, whereas a few studies have evaluated its performance in deep regions [18].Therefore, the EF focality, which is relative to the EF strength in the target area compared to that in the remaining regions, and the EF strength are weak when deeper brain regions are targeted.Several studies have proposed using the temporal interference stimulation (TIS) method for the noninvasive neuromodulation of the brain because it might stimulate deep brain regions without activating the superficial parts.It has been used to stimulate peripheral nerves in deep body regions (e.g., sacral nerve stimulation) [19,20].This method applied two currents at a few kilohertz up to 10 kHz to generate a beat wave with a frequency difference of 10-40 Hz using two sets of conventional tACS electrode montages.TIS exploits the low-pass filtering effect of the passive cell membrane that may be accompanied by rectification of the ionic part [21][22][23].Typically, the envelope amplitude for the induced EF might be relatively small in nontarget regions.
Several studies have computed the induced EF envelope (EFE) magnitude in specific brain regions with TIS.In Ref. [24], there were similarities between TIS and tACS for computed field strengths in deep brain regions (hippocampus and pallidum) of a single anatomically realistic head model, considering different montages and current ratios.TIS stimulated smaller areas outside the target regions compared to tACS.In Ref. [25], three head models were considered to evaluate individual differences of EFEs in the hippocampus with optimized stimulation parameters.In Ref. [26], 25 head models were considered to evaluate EFE variability in the primary motor cortex, hippocampus, and thalamus for different montages.EFE focality in deep brain regions was discussed with other stimulation methods for a single-head model in Ref. [27] and for multiple electrode pairs in three head models in Ref. [28].Thus, a limited number of head models were used in previous TIS modeling studies, except for [26].In addition, studies on TIS have mostly focused on stimulating deep brain regions [24,25,27], whereas tES for a somewhat deeper cortical region is also of interest (lower limb) [29,30].However, whether the cortical region can be stimulated focally with TIS has not been explored (i.e., at which depth TIS becomes more effective than conventional tES).
Another important issue is focal stimulation.In conventional tES, focal stimulation, even in the cortex region, is not straightforward.In Ref. [31], the focality of conventional tES was extensively discussed, particularly in the primary motor cortex.It mainly showed that EF focality in conventional tES was achieved at the cost of increased interindividual variability.Although EFE in the cortical region has been computed (e.g.Ref. [26]), its focality compared to conventional tACS has been insufficiently discussed.The focality and interindividual consistency of conventional tES can be improved using a pair of small electrodes in a bipolar montage [31,32], hereinafter termed the "bipolar high-definition (HD) montage," which could compare favorably to TIS for superficial stimulation.In conventional tES modeling, 13 subjects were required to estimate the standard deviation (SD) of the EF for high reproducibility (correlation of 0.9) [33].However, the number of subjects required for EFE reproducibility for TIS remains undiscussed, preventing the discussion of focal stimulation at the group-level.In addition, electrode montages for TIS are designed to target deep brain regions rather than cortical regions.Thus, additional consideration is needed for TIS electrode montage for cortical stimulation.
In this study, EFE focality in primary somatosensory and motor areas (i.e., the brain's cortical regions) was evaluated using TIS with newly defined linear montages compared to tACS with a bipolar HD montage.Supposing that TIS is effective, especially for deeper cortical regions, this study also investigated which depth is a criterion for switching from tACS to TIS.Thirty head models and their mirrored models, corresponding to 60 cases, were used to evaluate interindividual variability.Two pairs of tACS electrodes based on the 10-10 system were used.Furthermore, the number of head models required for generalizable group-level analysis of TIS was studied.

Head models
T1-and T2-weighted structural magnetic resonance imaging (MRI) scans of 22 male participants (ages 21-55 years) were obtained from a repository (NAMIC: Brain Multimodality, 3.0 T MRI scanner, 1 mm voxel size, available online at http://hdl.handle.net/1926/1687).Images from two subjects were excluded because of poor image quality near the eyes, skull/imaging artifacts near the cerebellum, and poor skull-CSF contrast.Additional T1-and T2-weighted structural MRI scans (Verio; Siemens, Ltd., Erlangen, Germany) were acquired from 10 males (aged 21-24 years) using a 3.0 T MRI scanner at the National Institute for Physiological Science, Japan.Sixty models (i.e., 30 male subjects ages 31.38 ± 12.18 years and their mirrored models) were used.
For these MRI scans, voxel anatomical human head models (at a resolution of 0.5 mm) were reconstructed in the computational domain.These models were segmented into 16 tissues.The human head was modeled as a "volume conductor" without considering the microscopic nature of biological tissues [34].The corresponding electrical conductivity values [35] were assigned to each tissue.Tissue conductivity was assumed to be linear and anisotropic.The detailed electrical conductivity values for the tissues were obtained from Ref. [33] (e.g., gray matter 0.2 S/m, white matter 0.14 S/m, and scalp 0.1 S/m).Fig. 1 (a) shows a schematic of the human head model.

Electrode modeling
The electrode is composed of a rubber sheet.Typically, the electrode is soaked in a normal saline solution to maintain the continuity of electrical conductivity between the skin and the electrode.In this study, a 1-mm-thick rubber sheet (12 × 12 mm, conductivity of 30 S/m) [33,36,37] within a rectangular sponge (20 × 20 mm) soaked in normal saline solution (1.6 S/m) [36,38] was modeled.The current was injected into the rubber (Fig. 1(b)).The total injection current was normalized to 2 mA for tACS and TIS, which were within the range of the current amplitude in tACS experiments [39].

Scalar-Potential Finite-Difference (SPFD) method and TIS modeling
The head models comprised voxels, each assigned an electrical conductivity value.EF was calculated using the SPFD method [40] in the frequency domain.SPFD equations were based on Stevenson's method [41], which was applicable to the solution of low-frequency induction problems.The following equation was solved: where σ and φ denote the tissue conductivity and scalar potential, respectively.The scalar potential was defined as an unknown at each voxel node.The conductance was assigned to the edges with tissue conductivity, and the average value was used for adjacent voxels.Using simultaneous equations for current based on Kirchhoff's current law at all nodes, the scalar potential was evaluated using the multigrid method [42] as a preprocessor with successive overrelaxation [43].Six multigrid levels were used, and the calculation was continued until the relative residual was <10 − 6 [4].Multigrid methods were characterized by the simultaneous use of additional auxiliary grids corresponding to coarser step widths, reducing the computational costs.EF was calculated by dividing the scalar potential difference between adjacent voxels by the node distance.Fig. 1 (c) shows a schematic explanation and definition of typical envelope-modulated waveforms.It indicates the maximum, minimum, and depth of the envelope, which were used to quantify neural activation.In TIS modeling, two EF distributions (E 1 and E 2 ) for each tACS electrode pair were superposed, and the EFE amplitude was computed using the following formula: This formula determines the maximum EFE amplitude over all possible directions (the envelope amplitude is direction-dependent).For tACS modeling, the EFE amplitude was the same as the EF strength.In a previous study [44], a multiscale simulation demonstrated that activation changes based on the envelope depth.Because this computational result explained the experimental results in rats [22], this metric was used in this study.

Electrode montages
In Fig. 2, two tACS circuits were attached to the scalp to model TIS.Based on previous studies [31], two bipolar HD tACS montages and six TIS montages were chosen to target postcentral and precentral gyri regions where S1 and M1 were located, respectively.The electrode positions were restricted to those defined in the 10-10 system [45], as shown in Fig. 2. For tACS, either C3 or CP3 was used as the reference for S1 and M1 stimulation, respectively.In this montage, two electrodes were positioned 5.1 ± 0.4 cm apart at a 45 • angle in the anterior-posterior direction, placing the target below their center (Fig. 2 (a) and (e)).A similar bipolar HD montage was confirmed to generate a high focal cortical EF in tDCS [31].In TIS, five linear and one rectangular montages were defined regarding the electrode positions in tACS.TIS montages in which the inner electrodes matched the tACS conditions were considered (see Fig. 2 (b) and (f)).In addition, montages in which the center of each electrode pair aligned with either C3 or CP3 were considered.Two directions of electrode pairs (at every 45 • ) for targeting the postcentral gyrus were considered (see Fig. 2 (c) and (d)).One direction, aligned to the height direction, was excluded because one of the electrode locations overlapped with the pinna's position.When targeting the precentral gyrus, two montages shown in Fig. 2 (f) and (g), similar to Fig. 2 (b) and (c), were considered in addition to a rectangular montage (Fig. 2 (h)) [46,47].
The ratio of the current amplitude in the TIS was adjusted to maximize the EFE amplitude.The current ratio was 4:6 or 5:5 after this group-level adjustment (effective digit = 1).In Table 1, eight montages

Table 1
Definition of eight montages for targeting the postcentral gyrus (I-IV) and precentral gyrus regions (V-VIII).Montages I and V were from tACS, and the remaining were from TIS.

Montages
First pair Second pair Current ratio were defined, in which I-IV and V-VIII targeted the postcentral and precentral gyri regions, respectively.Earlier studies have discussed the shift of the stimulation area for different current amplitudes with TIS [22,44,48].

EF and EFE amplitude analysis at the group level
EF and EFE amplitudes calculated in an individual brain surface were mapped on the Montreal Neurological Institute (MNI) template brain surface using the intersubject registration method [49].The resultant EF dataset comprised EF values at 247,395 vertices on the cortical surface of the MNI template brain for 60 subjects.The group-level (mean) distributions of EF and EFE amplitudes for tACS and TIS in postcentral and precentral gyri, where S1 and M1 were located, respectively, were calculated.To evaluate focality, the hand regions of S1 and M1 were specified in terms of the MNI coordinates [50,51].EF and EFE amplitudes within the coordinate volumes of (− 38 ± 10, − 24 ± 10, and 58 ± 10) and (− 36 ± 10, − 24 ± 10, and 58 ± 10) were calculated for the hand regions of S1 and M1, respectively.
The relative SD (RSD) was used to measure EFE variability relative to the mean.RSD is a measure that evaluates the intersubject variability at each location in the brain.The RSD was calculated by dividing the SD of the EFE amplitude at each vertex by the mean using the following equation: x where x i is the computed EFE amplitude in each subject and x is the mean of all subjects.To assess the generalizability of the findings, the effect of group size on the group-level (i.e., mean or SD) EFE amplitude was evaluated using Monte Carlo simulations [33].Similar to a previous study, two nonintersecting groups of equal size were randomly selected from the 60 participants.Using the computed EFE amplitude in each participant, Pearson correlations in the group-level EFE data were computed in the precentral gyrus [33].The process was repeated 500 times for each group size, and the sample mean ± SD of the correlation were computed.A large correlation coefficient indicates that the sample size is sufficient to remove the effect of intersubject variability on group-level EFE amplitude data.

EFE amplitude in the region of interest
Fig. 3 shows the distribution of the EFE amplitude in the postcentral gyrus, where S1 was located at the group-level.For proper evaluation, EFE distribution was normalized by its maximum value in target postcentral and precentral gyri areas.For montages II and III, the maximum EFE amplitude was observed in the postcentral gyrus rather than the precentral gyrus.In the postcentral gyrus, specifically on the wall of the central sulcus where S1 was located, the normalized EFE amplitude was higher for TIS than for tACS.In all montages of TIS, normalized EFE amplitudes of ≥0.4 were observed at the wall of the postcentral gyrus, which was higher than that of the tACS montage.The EFE RSD was small in the places where the envelope amplitude was generally high.However, high RSD was observed around the S1 hand area, where the sulcal shape was complex.A similar trend was observed for the M1 area (Fig. 4), where the maximum EFE amplitude was observed for montages VI and VII.Comparing the linear (VII) and rectangular (VIII) montages, deeper penetration and larger variability were observed in the rectangular montage (VIII) than in the line (VII) montage.
Table 2 (a) lists the ratio of the maximum EFE amplitude in nontarget areas to that in the S1 hand area.The ratio for neighboring areas in montage II was <1, suggesting that the stimulation was focused on the target area.Similarly, this tendency was observed even for the M1 hand area, as shown in Table 2 (b).Excluding montages VI and VII, the relative EF in the target hand area was close to 1.0.Fig. 5 shows a comparison of EFs at different depths.The EF was normalized to a depth of 0-5 mm for each montage.In Fig. 5, TIS is more efficient in producing EF at 10 mm or deeper than tACS for different TIS montages.

Effect of group size
Fig. 6 shows the correlations in the group-level mean ± SD of the EFE amplitude calculated in the entire precentral gyrus and over the M1 hand region for tACS and TIS.The correlations between the mean ± SD for M1 regions were slightly higher for tACS than for TIS.The number of subjects required to obtain a correlation of 0.95 for the mean in the precentral gyrus was n = 12 and 18 for TIS and tACS, respectively.The correlation for the mean over the hand M1 region reached r = 0.9 for a group size of n = 10 and 13 for tACS and TIS, respectively.The SD correlation of the EFE amplitude for the precentral gyrus was 0.7 for n = 20 and 0.79 for n = 30 for TIS and 0.8 and 0.84, respectively, for tACS, suggesting that more subjects are required for SD estimation in TIS.

Discussion and summary
The induced EFE amplitude was computed using newly defined

Table 2
Maximum EFE amplitude when targeting the (a) S1 and (b) M1 hand areas and their neighboring areas.Relative EFE amplitude in the corresponding region normalized by the maximum value in (a) S1 and (b) M1 hand areas for the montages defined in Table 1 electrode montages (i.e., line alignment for TIS), along with their variability, in superficial brain regions.The computed EFE was compared to bipolar HD montages of tACS.Group-level analysis was used to evaluate the EF and EFE amplitudes in two target cortical areas (S1 in the postcentral gyrus and M1 in the precentral gyrus) to clarify the differences between the applicable regimes of TIS and tACS.
From the group-level distribution, TIS and tACS showed high EF and EFE amplitudes near the target area.In TIS, higher EFE was observed in a deeper part of the target area (cerebral sulcus) compared to tACS (Figs. 3 and 4).For S1 and M1 hand knob targets, the SD of the EFE amplitude was low in the places where the EFE was high (Figs. 3 and 4).
Unlike a rectangular montage for TIS, a line alignment provided a more focal EFE amplitude in the target area.Compared to montages VI and VII, the RSD was high for montage VIII.The line alignment montage may provide an option for targeting relatively shallower regions with TIS.
In Table 2, TIS focality was slightly smaller than that of tACS in terms of the maximum EFE amplitude in the target areas.The current strength was adjusted as an effective digit of 1 % or 10 %; thus, the difference may be insignificant.In Table 2, the EFE in the precentral gyrus of montage VII was >1.2, suggesting less focality in M1 hand regions.This could not be resolved even if the current ratio was changed.However, when the inner electrode of the two electrode pairs was moved by 10 mm, this issue was improved (the ratio was <1.1).This result suggested that the EFE is focal just around the center of the electrodes in the line montage, unlike the rectangular montage.This was similar to the tradeoff relationship observed in tACS [31].
For regions at depths <5-10 mm, tACS (in the PA montage) provides superior focality (Figs. 3 and 4).At a depth of >10 mm, the mean normalized EFE amplitude was larger for TIS than for tACS (Fig. 5).This might be a criterion for stimulation where the target area is slightly deeper than the superficial region.Thus, the stimulation of deep and superficial brain regions located slightly deeper than the hand knob, such as the motor area of the leg, would be a potential application of TIS.
From the group-level analysis of EF and EFE amplitude (Fig. 6), the number of subjects required for tACS and TIS was comparable to the hemispheric average.However, the number of subjects required to target the precentral gyrus and analyze SD was higher.Although this discussion focused on the EFE amplitude in the precentral gyrus, a similar trend was observed in the postcentral gyrus.For the group-level analysis in relatively shallower regions, the number of subjects required for a low SD (0.8) was 20, suggesting that the conclusions derived from studies using a lesser number of subjects might differ at the group-level [24,25,27], although these studies discussed deep brain regions.Instead, this study supported the protocol in Ref. [26], in which 20 head models were considered.
Direct experimental validation of the computational approach in TIS is still challenging as it is not straightforward to measure the EF in an intact body.Instead, this approach has been validated for source localization of brain activity in electroencephalography [52], confirming better performance than the conventional approach.The source localization and brain stimulation are reciprocal.The computational code has also been verified by intercomparison of induced EF calculations of external electric or magnetic field exposure for human protection [53,54].
One limitation of this study is based on EF or EFE distributions, which are surrogates of neural activation but do not necessarily correspond to the neural response [55].Another limitation of this approach is that uncertainty sources exist in the EF computation.For example, MR data were taken from two repositories; thus, its quality might have influenced the computational results.The uncertainty of the segmentation or generating voxel model would be <10 % [56].The assignment of electrical conductivity is another factor to consider [57], especially at the frequency band for tACS.These uncertainty sources may affect the EFE amplitude, although it may marginally influence the number of participants needed for robustness (Fig. 6).
In summary, TIS with a linear alignment montage is a promising tool for the focal stimulation of relatively shallow regions (>5-10 mm from the brain surface).The hot spot of the EFE with this montage was formed around the center of montages with a higher focality than that of the rectangular montage.For the group-level analysis, ~20 head models are required, which is larger than the tACS.Future research includes the validation of group-level EFE in superficial brain regions by comparison to experimental results stimulation outcomes and testing new targets located between cortical and deep brain regions.

Declaration of competing interest
The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Akimasa Hirata reports financial support was provided by Japan Society for the Promotion of Science.If there are other authors, they declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Fig. 1 .
Fig. 1.(a) Visualization of a representative anatomical human head model, (b) cross-sectional view of the electrodes, and (c) schematic explanation of the waveform in an interference stimulation for two waves at 1 mV/m.

Fig. 3 .
Fig. 3. Mean ± SD of the EFE amplitude at the group-level in the entire brain [upper row (white line outlining the postcentral gyrus)] and gyral wall of the postcentral gyrus where S1 was located (lower row) for different montages: (a) I (tACS) and TIS for montages (b) II, (c) III, (d) IV, (e) VI, (f) VII, and (g) VIII.EF or EFE amplitudes were normalized by the maximum value in the postcentral gyrus.

Fig. 4 .
Fig. 4. Mean ± SD of the EFE amplitude at the group-level in the entire brain [upper row (white line outlining the precentral gyrus)] and gyral wall of the precentral gyrus where M1 was located (lower row) for different montages: (a) V (tACS) and TIS for montages (b) II, (c) III, (d) IV, (e) VI, (f) VII, and (g) VIII.EF or EFE amplitudes were normalized by the maximum value in the precentral gyrus.

Fig. 5 .
Fig. 5. Normalized EF or EFE amplitude in the volume of (a) postcentral and (b) precentral gyri averaged over 60 participants.The amplitude was normalized to a depth of 0-5 mm for each montage.Error bars indicate the mean ± SD.

Fig. 6 .
Fig.6.Effect of group size on the group-level EFE measured (mean ± SD) on the surface of the precentral gyrus and hand M1 regions for the following montages: (a) tACS (V) and (b) TIS (VI).The mean ± SD of group-level EFE were calculated for two groups of equal size in the precentral gyrus and hand M1 region.Correlations in vertex-wise data were calculated among 500 randomly selected pairs for each group size (mean ± SD).