Recommendations for the Safe Application of Temporal Interference Stimulation in the Human Brain Part II: Biophysics, Dosimetry, and Safety Recommendations

ABSTRACT

Temporal interference stimulation (TIS) is a new form of transcranial electrical stimulation (tES) that has been proposed as a method for targeted, noninvasive stimulation of deep brain structures. While TIS holds promise for a variety of clinical and nonclinical applications, little data is yet available regarding its effects in humans and its mechanisms of action. To inform the design and safe conduct of experiments involving TIS, researchers require quantitative guidance regarding safe exposure limits and other safety considerations. To this end, we undertook a two‐part effort to determine frequency‐dependent thresholds for applied currents below which TIS is unlikely to pose risk to humans in terms of heating or unwanted stimulation. In Part II of this effort, described here, we draw on a previously compiled list (see Part I) of adverse effects (AEs) reported for transcranial direct/alternating current stimulation (tDCS/ACS), deep brain stimulation (DBS), and TIS to determine biophysics‐informed exposure metrics for assessing safety. Using an in silico approach, we conduct multiphysics simulations of various tACS, DBS, and TIS exposure scenarios in an anatomically detailed head and brain model. By matching the stimulation in terms of the identified exposure metrics, we infer frequency‐dependent TIS parameters that produce exposure conditions equivalent to those known to be safe for tACS and DBS. Based on the results of our simulations and existing knowledge regarding tES and DBS safety, we propose frequency‐dependent thresholds below which TIS voltages and currents are unlikely to pose a risk to humans. Safety‐related data from ongoing and future human studies are required to verify and refine the thresholds proposed here.

Summary

• In Part II of this two‐part effort, we conduct numerical simulations to compute biophysics‐informed exposure metrics and establish frequency‐dependent current thresholds for the safe application of temporal interference stimulation (TIS) in humans.

• Our simulations reveal that TIS can safely apply higher currents than conventional transcranial electrical stimulation (tES) methods. Furthermore, we offer guidance on practical aspects of safe stimulation, such as electrode size and placement, and electrode–scalp contact.

• The proposed safety guidelines for TIS are based on comprehensive modeling of electric fields, current densities, charge injection, neural activation predictors, and induced heating, ensuring that the exposures are consistent with current best practices for tES.

1. Introduction

Temporal interference stimulation (TIS), an emerging variant of transcranial electrical stimulation (tES), has been suggested as a technique for noninvasively targeting deep brain structures (Grossman et al. 2017). This method employs two or more periodically varying electric (E‐)fields, delivered through scalp electrodes at slightly different frequencies in the kHz range. Although these individual frequencies are too high to elicit neural spiking directly, the difference between these frequencies modulates the field “envelope” at a frequency that falls within the normal range of the brain's electrical activity (1–100 Hz), and can influence neural activity. This enables the electrical modulation of specific brain regions or networks at desired locations, with reduced impact on adjacent or superficial areas. Additionally, adjusting the intensities of the currents to each electrode pair enables a degree of control over the stimulation focus without relocating the electrodes. However, high‐precision targeting remains an area of active research, and some uncertainty regarding the direct effects of high‐frequency carriers persists.

TIS is considered promising for various clinical and nonclinical uses (Grossman, Okun, and Boyden 2018; Lee et al. 2020; Rampersad et al. 2019), yet, the body of knowledge of TIS' impacts in humans, both adverse and beneficial, remains limited. It is crucial to investigate the potential risks TIS may pose to human subjects, especially in comparison to more established tES methods like transcranial alternating current stimulation (tACS) and transcranial direct current stimulation (tDCS).

In Part I of this two‐part study, we reviewed the basic principles of tDCS, tACS, deep brain stimulation (DBS), and TIS, and surveyed associated adverse effects (AEs) from scientific literature and regulatory and clinical databases. Here (Part II), we use simulations to integrate existing empirical knowledge regarding tES safety with (bio‐)physical principles and establish boundaries for the safe use of TIS in research and clinical settings. The design and analysis of these simulations are informed by the current‐limiting AEs identified in Part I, which, in turn, help to suggest safety‐relevant field exposure quantities. Using a detailed model of the head and brain, we conduct simulations of conventional tES, DBS, and TIS, and calculate the resulting field exposure metrics (peak field strengths, current densities, charge accumulation, and heating) under normal (safe) operating conditions for tES and DBS. From this data, we derive frequency‐dependent current thresholds for TIS that produce equivalent (or smaller) field exposures in the head/brain. Consideration is paid to the (bio‐)physical principles thought to underlie TIS' effects in the brain, as well as the modality of current delivery, and spatial specificity of neuromodulation. This work is a first step toward delineating the parameter space of safe and effective TIS in humans, with an eye toward future trials and experiments that will help close existing gaps in the literature.

2. (Bio‐)Physics of Electrical Stimulation

We begin by reviewing how E‐fields interact physically with neurons and highlight relevant exposure metrics to enable comparisons across electrical stimulation regimes. In addition to the mechanisms of electrical neurostimulation, several other safety‐relevant aspects, including device‐tissue interface reactions, thermal effects, and charge injection, are also discussed in view of potential AEs. Finally, a list of hypothesized TIS mechanisms of action is enumerated.

2.1. Biophysical Fundamentals of EM‐Neuron Interactions

Low‐frequency E‐fields (up to ~150 Hz), typical of neurostimulation applications, interact with neurons via several distinct mechanisms (Miranda et al. 2007). In general, these mechanisms hinge on the de‐/hyperpolarization of neural membranes in the presence of electromagnetic (EM) fields (see Figure 1). At dendritic and axonal terminals, membrane polarization can be initiated by the tangential E‐field component, $E_{\tan }$, which drives axial currents, resulting in a build‐up of charge. Alternatively, in nonterminal compartments, transmembrane charge may accumulate as a consequence of heterogeneous $E_{\tan }$, causing an imbalance between incoming and outgoing axial currents. For long membrane tracts in the resting state, the rate of change of the membrane potential in response to an applied field is given by $-{\lambda }^2\frac{\delta E_{\tan }}{\delta l}$ where $\lambda$ is the membrane space constant. This term is referred to as the activating function (AF)¹⁶⁸ and is used to predict the location(s) at which stimulation is likely to occur, as well as the stimulation threshold. A large AF can result from a spatially heterogeneous field or from a rapid change in fiber orientation. A special case of field heterogeneity occurs when fibers cross an interface with dielectric contrast such as at the boundary between tissues with differing electrical conductivities. The amplitude of these local E‐field discontinuities across the interface is given by $\Delta E_n=2\left(\frac{{\sigma }_1-{\sigma }_2}{{\sigma }_1+{\sigma }_2}\right)\underset{¯}{E}\cdot \underset{¯}{n}$, where $\underset{¯}{E}$ is the applied field, ${\sigma }_1$ and ${\sigma }_2$ are the conductivities of the two tissues, and $\underset{¯}{n}$ is the normal vector at the interface (Miranda et al. 2007). Tissue heterogeneity‐induced gradients most strongly affect axons perpendicular to the interface, inducing a membrane depolarization of $\lambda \Delta E_n/2$. When the depolarization at a neurite terminal is sufficient to initiate an action potential (AP), this is referred to as “end‐node stimulation.” In contrast, stimulation induced along a fiber tract by any means (tissue heterogeneity or large E‐field gradients) is referred to as “central‐node stimulation.”

Figure 1.

Illustration of different conditions for electric stimulation. (i) Large E‐field intensities along the fiber and in proximity to axon terminals (end‐node stimulation). (ii) Axonal curvature within a homogeneous field, inducing a large E‐field gradient along the trajectory. (iii) Large E‐field gradients along the axon (central‐node stimulation). (iv) Local E‐field gradients induced at interfaces between tissues with different electrical conductivities.

The relative contributions of these two membrane polarization mechanisms (tangential fields at endings and spatially heterogeneous tangential fields along fibers) are dependent on the modality of brain stimulation. In typical tES setups, where large electrodes (≥ 5 cm²) are used, the E‐field directly below the electrode is relatively homogeneous, and any field heterogeneity is primarily a consequence of cortical gyrification. Therefore, while sub‐millimeter neural somas are exposed to relatively small E‐field gradients, neurite termination may cause significant membrane depolarization in dendrites (and through the dendritic arbor, soma polarization). Tissue heterogeneity‐related contributions may be relevant for axons with high curvature, for those passing near to CSF, and for those crossing between brain regions with dielectric contrast (e.g., gray to white matter). The situation is reversed when considering DBS, where the stimulation is applied by millimeter‐sized electrodes in direct contact with tissue. In this case, axons and somata are exposed to large, local E‐field gradients within relatively homogeneous regions of tissues (see also Section 3).

It is important to note that the degree of exposure‐induced membrane depolarization and associated stimulation thresholds are frequency‐dependent. Thus, low‐frequency tACS and high‐frequency TIS carrier signals have different stimulation thresholds, even when exposure strengths are matched. For alternating current (AC) exposure at frequencies with periods that are short or comparable with respect to membrane time constants (on the order of 3 ms for unmyelinated C‐fibers and 0.3 ms for myelinated fibers), the membrane capacitance results in low‐pass filtering, such that polarizability is inversely proportional to frequency. This is reflected in the linearly frequency‐dependent exposure thresholds in exposure safety guidelines (International Commission on Non‐Ionizing Radiation Protection 2020). At sufficiently high frequencies (order of 100 kHz), the frequency dependence of dielectric properties must also be considered when determining in vivo exposure conditions.

2.2. Device–Tissue Interactions

Here, we summarize the principal physical mechanisms of (adverse) interactions between delivered currents and tissues at the frequencies relevant for brain stimulation. These include phenomena at the electrode–electrolyte interface, electrolyte–tissue interface, and within the tissue, including various electrochemical processes, frequency‐dependent current penetration, and thermal effects. Quantities relevant to safety such as the amount of injected charge and the charge density are discussed.

2.2.1. Reactions at the Interface

Important electrochemical reactions and biological processes occur at the interface between the electrode and the tissue/electrolyte with which it is in contact. In DBS, a metal electrode directly contacts brain tissue (electrode–tissue interface), while in tES, a conductive gel forms a buffer layer between the electrode and the scalp, giving rise to two boundaries (electrode–electrolyte and electrolyte–tissue). At an electrode–electrolyte interface, charge transfer is mediated by non‐Faradaic reactions (no electron transfer across the interface) and Faradaic reactions (electrons move between electrode and electrolyte) (Merrill, Bikson, and Jefferys 2005). Safe stimulation parameters should be identified to avoid the onset of irreversible reactions resulting in damage to the electrode, or the generation of toxic reaction products at the electrode–gel–skin interfaces.

The presence of reversible (e.g., charging and discharging of neural membranes) and irreversible processes at the electrode/electrolyte‐tissue interface causes the impedance across the boundary to exhibit strong frequency dependence in response to electrical stimulation, which modifies the effective waveform that reaches the target. One effect commonly observed during long‐duration/continuous stimulation is charge accumulation and concomitant electrode polarization due to weak DC leakage currents present in current sources for pulsed or alternating electrical stimulation (Ghazavi and Cogan 2018).

In humans, applied currents evoke a variety of biophysical and physiological changes including alterations in skin conductance, increased blood flow, and sweating, all of which depend on the intensity, frequency, and duration of the current (Yang et al. 2017). Changes in skin impedance below tES electrodes are typically measurable within seconds following the delivery of currents (Prausnitz 1996). Nonohmic behavior initiates at relatively small applied DC voltages (> 1 V), and skin conductance can fluctuate during stimulation by an order of magnitude or more. Additionally, skin‐electrode contact impedance decreases monotonically between 0 and 100 kHz, with the precise relationship depending on the properties of the materials involved. Typically, the quality of the electrode‐skin contact is monitored during tES experiments by measuring the contact impedance before and during the application of currents. Changes in the electrode–skin contact (e.g., due to dehydration of the conducting sponges or solidification of the conductive paste) may affect the safe delivery of currents.

2.2.2. Thermal Effects

Thermal effects at the frequencies of interest for NIBS and TIS (kHz range) are mainly due to Joule (resistive) heating that results from the motion of ions within the tissues due to voltage differences between the electrodes. Local temperature increases as a result of EM absorption that do not exceed 1°C are generally considered to be safe (International Commission on Non‐Ionizing Radiation Protection 2010; IEEE 2020). For medical applications, a 2°C increase is considered safe by the FDA (ISO 2017) and various international standards, though in special cases (e.g., magnetic resonance imaging [MRI]) this limit may be exceeded, particularly, under “controlled conditions.” The risk of thermal damage is commonly assessed using standardized exposure metrics, such as the volume‐averaged SAR, defined as:

$$\langle \mathrm{SAR}\rangle =\frac{1}{V}∰\frac{\sigma \left(\vec{r}\right){\left|\vec{E}\right|}^2}{\rho \left(\vec{r}\right)}d\vec{r},$$ (1)

where $\rho \left(\vec{r}\right)$ is the mass density. SAR expresses the rate per unit mass at which energy is absorbed by a tissue. However, the exposure‐induced heating depends on tissue properties (e.g., perfusion, heat capacity) and the power distribution (which impacts thermal diffusion). Furthermore, thermal sensitivity and the resulting damage depend on many factors, including tissue‐specific thermotolerance (i.e., resistance to thermal cytotoxicity), rate of heating (Dewhirst et al. 2003), local temperature, and duration of exposure. To estimate the degree of tissue‐specific thermal damage, various thermal dose models have been proposed (Yung et al. 2010). These include the cumulative equivalent minutes at 43°C dose (CEM43), which converts a transient temperature exposure to an equivalent number of minutes of heat exposure at 43°C in terms of tissue damage. The conversion for periods of near‐constant temperature is calculated as

$${\mathrm{CEM}}_{43}=\Delta t{R}^{(43-T)},$$ (2)

where R is a constant equal to 0.25 for T < 43°C and 0.5 for T > 43°C (n.b. some references assume $R=0$ below 39°C). CEM43 safety and/or efficacy thresholds have been proposed for various tissues and applications (e.g., MRI radiofrequency [RF] safety [van Rhoon et al. 2013] and thermal medicine). The lowest thermal dose damage thresholds have been associated with brain tissue heating and blood–brain barrier disruption (2 min, while the threshold for skin is 21 min according to ISO 14708‐2:2019) (ISO 2019). CEM43 originates from the Arrhenius tissue damage model, $\Omega \left(t\right)=A{\int }_0^t{e}^{-\frac{E_a}{\mathit{RT}}}d\tau$, where$e^{-\mathrm{\Omega }}$ represents the surviving cell fraction (or other damage measures), and A and $E_a$ are tissue‐specific constants. Unlike the Arrhenius model, the CEM43 model shifts the tissue specificity into the damage thresholds, avoiding the use of poorly characterized A and $E_a$ parameters. It also accounts for a known transition in temperature dependence of the damage rate occurring at 42.5°C–43°C (reflected in the change of the value of R).

It has been argued that temperature increases in the brain > 1°C can have long‐term effects on brain tissue (LaManna et al. 1989). While temperature increases in the range of 1°C have been found below tDCS electrodes for 2 mA of current applied for 20 min, the majority of this heating is attributable to the insulating properties of skin, and to changes in blood perfusion as a result of vasodilation (i.e., the “flare effect”) (Khadka et al. 2018). Current‐related heating, in contrast, is known to be orders of magnitude lower. Furthermore, power deposition in brain tissue is considerably lower, and perfusion cooling much more effective, due to extensive vascularization. Antal et al. estimate that power deposition in the brain resulting from 1 mA of applied current is on the order of 0.1 mW/kg, which is about five orders of magnitude less than endogenous metabolic heat production (~11 W/kg) (Antal et al. 2017). In general, the FDA accepts temperature increases of up to 2°C in most tissues (in accordance with some CEM43 definitions that also assume zero contribution to the thermal dose from temperatures below 39°C) and up to 0.1°C in the brain (van Rhoon et al. 2013; International Electrotechnical Commission 2010).

2.2.3. Charge Injection

Damage to tissues associated with the delivery of currents is also dependent on the amount of charge injected within each phase of the stimulation cycle. The charge density is typically compared against the “Shannon limit” (Shannon 1992), provided by the formula $\log \left(D\right)=k-\log \left(Q\right)$, where $D$ is the charge density (in µC/cm [Grossman, Okun, and Boyden 2018]), $k$ is an adjustable parameter (typically between 1.5 and 2), and $Q$ is the charge per phase (in µC per phase). This quantity defines the charge threshold at which damage occurs. However, the Shannon limit is chiefly used in the context of bioelectronic medicine where microelectrodes (diameter < 300 µm) are common (Cogan et al. 2016), and is not appropriate for other stimulation scenarios involving large electrode diameters, or for predicting damage far from the electrode. For DBS electrodes, alternative limits for $D$ and $Q$ were proposed based on tissue damage studies (Wei and Grill 2009; Kuncel and Grill 2004).

As an electrode's charge injection capacity is inversely proportional to its area, the larger scalp electrodes typical of tES produce charge densities well below those encountered in invasive applications such as DBS and implant‐mediated nerve stimulation. Furthermore, the pulse shape of most electrical stimulation applications is designed to be charge balanced (e.g., biphasic symmetric or asymmetric) to avoid the buildup of charge within the tissue. Thus, the low current densities and charge‐balanced pulse waveforms typical of tES applications (including TIS) mean that tissue damage directly associated with charge injection is highly unlikely.

2.3. List of Mechanistic TIS Hypotheses

• In a recent in vitro study of carbachol‐induced gamma oscillations in rodent hippocampal slices supported by computational network modeling, Esmaeilpour et al. explored the mechanisms underlying the response of deep brain regions to TIS (Esmaeilpour et al. 2021). They propose that sensitivity to TIS is determined by the neural membrane time constant, which, for axonal compartments, in particular, approaches the kHz carrier frequency (time constant approx. 1–10 ms). On the other hand, their simulations suggest that selectivity is primarily governed by network adaptation mechanisms with response times shorter than the beat frequency, namely, gamma‐aminobutyric acid (GABAB) receptor dynamics, and possibly short‐term facilitation and depression, and spike‐frequency adaptation via ionic current modulation. Future studies that clarify the role of axonal membranes and network adaptation mechanisms in the response of deep brain tissue to TIS are needed.

• Alternatively, in a simulation study of multi‐compartment Hodgkin–Huxley (HH) axons, Mirzakhalili et al. argue that neural demodulation of the amplitude‐modulated stimulus depends on the capacity of cell membranes to perform signal rectification (Mirzakhalili et al. 2020). They observe that rectification before low‐pass filtering is a method for demodulating multiplied and convolved signals (Oppenheim, Schafer, and Stockham 1968), and could be achieved in practice through nonlinearities in axonal ion channel dynamics. In particular, simulations revealed that rectification occurred due to differences in the conductance values between sodium and potassium channels, and differences in the speed of activation versus inactivation in sodium channels (Mirzakhalili et al. 2020). These properties were tied to the resonance frequency of the axon and predicted the optimum beat frequency for TIS.

• Similarly, Cao et al. advance the argument that both FitzHugh–Nagumo and HH neuron models demodulate amplitude‐modulated signals through transient charge imbalances (Cao et al. 2020). As above, fast, depolarizing sodium currents activate with increases in the envelope. Hyperpolarizing potassium channels respond more slowly, leading to transient charge accumulation inside the cell, briefly depolarizing the membrane. Here, the key quantities responsible for sensitivity to TIS are ion channel time constants, in contrast to Mirzakhalili et al. who emphasize the intrinsic membrane time constant of axonal fibers (Mirzakhalili et al. 2020).

• In the same vein, Plovie et al. simulated various single‐compartment neuron models (HH, Frankenhaeuser–Huxley [FH], leaky integrate‐and‐fire [LIF], exponential integrate‐and‐fire [EIF], and adaptive and exponential integrate‐and‐fire [AdEx]) to explore TI mechanisms (Plovie et al. 2022). To this end, they define a “TI zone” as the range of input currents over which an amplitude‐modulated TI signal induces firing at the difference frequency while an unmodulated carrier at the same frequency does not. Furthermore, they investigate whether nonlinearities in the Goldman–Hodgkin–Katz (GHK) flux equation could be responsible for the neural response to TIS by comparing versions of the FH and HH models in which this term has been linearized (or not) using a first‐order Taylor expansion. They find that LIF models (and variants) cannot reproduce experimentally known responses to TIS, while the FH and HH models (and linearized variants) can. Thus, they conclude that GHK nonlinearity is not a necessary driver of the neural response to TIS. Furthermore, by varying the time constants and steady‐state values of the FH and HH ion channels, they demonstrate that the response to TIS exposure depends sensitively on nonlinearities in voltage‐dependent ion channel gating dynamics (Plovie et al. 2022).

3. Computational Characterization and Comparison of Electric Brain Stimulation Modalities

The mechanisms of electrical stimulation as well as potential associated health risks depend both on the stimulation settings (EM exposure, pulse shape, stimulation intensity) and on the electrophysiological, thermal, and electrochemical sensitivity/stimulability of the exposed brain tissues. Exposure distributions can vary considerably across stimulation modalities and electrode configurations. To help clarify this variation and facilitate an appraisal of TIS safety, we conducted a comparative analysis of exposure metrics for tACS, tDCS, DBS, and TIS based on computational modeling in an anatomically detailed human head model (see Section 5.7). To this end, generic but representative setups for each modality were modeled numerically using EM and thermal simulations with realistic current strengths. On this basis, we inferred which of the application‐specific safety concerns likely apply to TIS. Our investigation explored the effects of frequency and electrode shape and placement on heating and current density in brain and skin tissues.

All simulations were performed using the Sim4Life (ZMT Zurich MedTech AG, Switzerland) platform for computational life science, in conjunction with the MIDA (Iacono et al. 2015) reference anatomical human head model, developed by the IT'IS Foundation in collaboration with the FDA for computational investigations (Center for Devices and Radiological Health 2019). The MIDA model, generated from multimodal image data, includes dura and skull layers, and various stimulation targets. EM simulations were conducted using Sim4Life's low‐frequency electro‐quasistatic and ohmic current‐dominated solvers (structured finite element method) with Dirichlet voltage boundary conditions at the active electrodes, and current normalization. Isotropic conductivity was assumed for all tissues. Conductivity magnitudes for each tissue were assigned using the IT'IS low‐frequency database (Hasgall 2018). The computational domain (electrodes and head) was discretized using a rectilinear grid with an isotropic resolution of 0.5 mm in the brain and the tES electrodes, and 0.2 mm for the DBS electrode. E‐fields were normalized to a 1 mA input current (per channel, in the case of TIS) to ensure meaningful field comparisons. Worst‐case cathodic AF distributions were estimated using the largest absolute magnitude eigenvalue of the Hessian matrix of the electric potential (Duffley et al. 2019).

The following exposure setup conditions were selected for simulation:

• tES (tACS, tDCS, and TIS require equivalent electro‐quasistatic simulations): A typical setup comprising two circular electrodes, each with a surface area of 1.5, 3, 25, or 50 cm², and an input current of 1 mA, was simulated as described above. E‐field, current density, and AF all scale linearly with the total current, while power deposition and temperature scale quadratically. For sinusoidal currents, root mean square (RMS) peak E‐field and current density differ by a factor of $\sqrt{2}$ (RMS and peak quantities for non‐sinusoidal exposures differ by other amounts). Here, we report peak values, reflecting typical clinical practice (however, note that reporting across the literature is not consistent). Thus, the deposited power and concomitant temperature increase for tACS is half that of tDCS.

• DBS: The E‐field exposure in conventional DBS was calculated in the MIDA head model using a simplified model of the Medtronic 3389 DBS lead oriented along a realistic implantation trajectory with the two inner electrodes centered in the globus pallidus (GP). Stimulation was achieved using a bipolar electric current applied between the two inner electrodes. Active electrode surfaces were assigned Dirichlet boundary conditions, with voltages calibrated to result in 1 mA of input current (passive electrodes were modeled as perfect conductors). Dielectric tissue properties were identical to those used in tES and TIS simulations.

3.1. Peak E‐ and J‐Field Strengths

Figure 2 depicts the E‐field distributions produced by (top, panel (i)) a four‐contact, bipolar DBS electrode (modeled after Medtronic's 3389 neurostimulator), and (bottom, panel (ii)) a tES setup for three different diameters of circular electrode (fields normalized to 1 mA peak input current).

Figure 2.

DBS‐ and tES‐induced E‐field distributions. (i) Induced E‐field distributions for a DBS electrode in bipolar configuration at 1 mA of input current (cf. Medtronic 3389 neurostimulator). (ii) tES field distributions for electrode placements identical to Pair 1 in Figure 3, computed for circular electrodes with surface areas of 3, 25, and 50 cm² and a 1 mA input current. Scale: 0 to −150 dB (reference: max value in DBS simulation; 10 dB per color step—one order of magnitude in field strengths for two steps) was chosen, demonstrating relatively minor brain exposure differences between different patch size when compared to DBS).

Figure 3.

Comparing TIS and tES. Comparison between conventional single pair tES (left) and total TIS high‐frequency E‐field exposure (middle), as well as the corresponding low‐frequency TIS modulation magnitude distribution (right). The total TIS carrier frequency E‐field map (middle) shows the maximal high‐frequency field magnitude achieved for in‐phase, constructive interference.

Spatial field peaks are reported separately for skin (in view of skin sensations) and brain (stimulation safety and efficacy). We applied 2 mm averaging to field values (E‐field and current density [J‐field]), as proposed by the ICNIRP 2010 guidelines, to obtain macroscopically relevant quantities and avoid numerical artifacts caused by the volume discretization or by segmentation‐related sharp dielectric contrasts (International Commission on Non‐Ionizing Radiation Protection 2010). 2 mm averaging is suitable for external current sources, but poorly captures the much stronger field gradients near small, implanted electrodes. For point‐like sources (1/r ² distance dependence), averaging has an impact below 20% at r > 8 mm, while this occurs for r > 4 mm for line‐like sources (1/r distance dependence), for example, near sharp electrode edges. Note that for a DBS lead, the separation r does not necessarily represent the distance to the lead center line, but can be the distance to a sharp electrode feature, such that the field divergence is in immediate proximity to the tissue. At a distance of 2 mm (0.8 mm for line‐like sources), 2 mm averaging can produce two‐fold differences over baseline; in our simulations, the unaveraged peak values at the DBS electrode are as high as 1110 V/m/mA due to strong field gradients, while unaveraged peak tES exposure is 2.3 and 80 V/m/mA in the brain and skin, respectively. Hence, relying on averaged quantities near the electrode can be misleading.

For this analysis, we define the region of “activated” brain tissue to be the volume in which the 2 mm averaged E‐field is > 90% of its peak value. This operational threshold highlights the region exposed to the highest electric field intensities—those most likely to be physiologically relevant. We selected 90% empirically as a reasonable demarcation of near‐peak field magnitudes to facilitate comparisons between stimulation modalities. The activated brain volume was 1.4 mm³ for tES (3 cm² electrode size; peak: 1.6 V/m), and 7 mm³ for DBS (peak: 145 V/m). Thus, peak intracranial E‐fields induced by DBS were about two orders of magnitude greater than those produced by tES, as were the field gradients, with a factor of 40 difference in focality. Regarding current density, for DBS we found a 2 mm line averaged J‐field peak of 35 A/m² localized in the GP near the electrodes. For tES exposure, we found a 2 mm line‐averaged J‐field peak of 0.4 A/m² in the brain. In the skin, the corresponding quantities for DBS and tES were 0.002 and 5.1 A/m², respectively.

3.2. TIS

The location and magnitude of the maximum E‐field amplitude modulation provide information about the likelihood of TIS neuromodulation, while the combined E‐field strength governs safety‐relevant physical interactions with the tissues (e.g., thermal heating). To ensure safe and effective TIS, the spatial distribution of both the TI amplitude modulation and the total E‐field strength must be estimated to minimize off‐target stimulation and AEs. Figure 4 compares the distributions of total and directional maximum amplitude modulation (amplitude modulation of the projection along the local principal fiber orientation obtained from DTI data), as well as the total and directional combined high‐frequency E‐fields for a generic TIS setup. Note that the TIS electrode montage and steering parameters were not optimized for a specific target, and that no effort was made to avoid hotspots. The current ratio was fixed at 1:3 (blue electrode pair: 0.5 mA; red electrode pair: 1.5 mA).

Figure 4.

TI amplitude modulation magnitude and combined high‐frequency E‐field distributions. Note that the electrode montage and steering parameters have not been optimized for a specific target and that no effort has been made to reduce exposure hot spots elsewhere. Blue electrodes, 0.5 mA; red electrodes, 1.5 mA (current ratio of 1:3). (i) Maximum TI amplitude modulation magnitude (along any orientation). (ii) Directional TI amplitude modulation magnitude projected along the DTI‐derived principal local fiber orientation. (iii) Combined high‐frequency E‐field (i.e., total field magnitude for in‐phase channel contributions). (iv) Directional projection of the combined high‐frequency E‐field (i.e., high‐frequency field component projected along the principle orientation of local neural tracts).

As the low‐frequency modulation amplitude is dominated by the weaker field (see Part I, Section 5.1), it is maximal in regions where the two channels' exposures are both high and of similar magnitude, permitting deeper and more localized targeting. However, TI remains subject to physical constraints—that is, TI exposure peaks (foci) are typically subsets of the high‐frequency peaks and it can be difficult to avoid their occurrence at locations with dielectric features (such as nearby CSF—ventricles, sulci) that bundle and guide current flow, conductive implants, or conductivity heterogeneity (e.g., dielectric contrast) and anisotropy. Tissue structure (e.g., strongly preferential fiber/neuron orientations) may further increase TI exposure localization, which can help or hinder in targeting the desired structure. To avoid TIS of overlying structures, either the electrodes must be sufficiently separated, or E‐fields in the off‐target structures must be nearly perpendicular. See Figure 4 for a depiction of the shift in TI modulation amplitude toward the electrode pair with the weaker current (blue pair).

3.3. Thermal Increase

Thermal simulations were conducted in the MIDA head model based on the Pennes Bioheat Equation (PBE) (Pennes 1948):

$$\rho c\partial T/\partial t=\nabla ·(k\nabla T)+\rho Q+\rho S-{\rho }_b{\rho }_b\rho \omega (T-T_b),$$ (3)

where ρ and c are the density and the specific heat capacity distributions, k is the thermal conductivity, Q the specific metabolic heat generation rate, S the SAR (obtained from coupled EM simulations), ω the perfusion rate, and ρ _b , c_b , and T _b are the density, specific heat capacity, and temperature of the arterial blood. Instead of solving for the absolute tissue temperature, we used the PBE to calculate the temperature increase $\Delta \mathit{T}$ with respect to the steady‐state temperature distribution. This is possible so long as the temperature dependence of perfusion can be ignored. In addition to improving numerical accuracy, this approach avoids the need to consider metabolic heat generation, external temperature, and arterial blood temperature. Simulations were performed with Sim4Life's stationary PBE solver using the time‐averaged power density as a heat source (DBS pulsation is much faster than the thermal time‐constant). Tissue thermal properties were assigned from the IT'IS database of thermal and dielectric tissue properties (Hasgall 2018). Convective boundary conditions were applied at the interface with the external air and internal airways (convection coefficient h = 30 W/m²/K internally, h = 6 W/m²/K on the external surface) to account for active convection. In the presence of multiple currents (e.g., TIS channels), coherent field superposition was used for identical frequencies, and incoherent superposition (i.e., SAR addition) was used when the frequencies differed.

Figure 5 illustrates the steady‐state temperature increase $\Delta T$ distribution for 1 mA of input current. A peak temperature increase of $\Delta T/I^2$ = 0.026°C/(mA)² was found for the DBS implant, while an increase of 0.002°C/(mA)² was found for the tDCS setup using the smallest electrode size (3 cm²). For larger electrodes, the temperature increase was smaller than 0.001°C/(mA)² or smaller than 0.1°C for 10 mA. The temperature increased roughly in inverse proportion to the electrode area. In both cases, heating was confined to an area near the electrodes, and was well below the threshold for direct tissue damage.

Figure 5.

Simulated steady‐state temperature increase distributions for DBS and tES. Input current of 1 mA, bipolar electrode configuration (top‐left), various electrode sizes. Heating is principally localized near the electrodes, such that brain heating is minimal for tES. In all cases, heating is well below thresholds for direct tissue damage.

3.4. AF and Volume of Tissue Activated

While the AF is most frequently utilized in mechanistic investigations of neurostimulation, it also provides an efficient means of estimating the volume of tissue activated in applications such as DBS device design (Butson and McIntyre 2006). However, AF peak magnitude data must be interpreted with care, since: (i) the AF distribution can show divergent behavior near sharp electrode features, which also results in strong dependence on the discretization resolution and shape of the electrode, (ii) the AF is not well defined at dielectric interfaces (such as the gray matter/white matter interface, a highly relevant interaction site), and (iii) even within a single tissue such as white matter, heterogeneity, and anisotropy may affect the AF in ways that are difficult to capture in computational models. With these limitations in mind, Figure 6 shows qualitative AF distributions in the brain for DBS and tACS, obtained by spectral decomposition of the Hessian matrix of the electric potential, from which we extracted and plotted the maximal absolute eigenvalues. The maximal absolute eigenvalue of the Hessian matrix is proportional to the AF of a fiber oriented along the direction of the corresponding eigenvector, which is the most stimulable orientation. Also, contributions to the AF due to dielectric contrast at the interfaces between tissues were omitted in this calculation, as was the influence of brain tissue heterogeneity, meaning that these data provide only a qualitative picture of stimulation likelihood. The actual AF threshold for neurostimulation depends on fiber type and pulse shape. As the figure illustrates, AF‐related neurostimulation effects are significantly stronger for DBS than for tES. Since the peak AF is sensitive to dielectric heterogeneity and to numerical errors related to discretization, we also report the 99.9th isopercentile for the brain and for the skin, that is, the AF level exceeded in the top 0.1% of the combined brain tissues (1.2 mL) and of the skin (0.25 mL).

Figure 6.

Volume of tissue activated (DBS). Cross‐section images of the maximal Hessian eigenvalue distributions for the electric potential, a measure of the maximal normalized AF of arbitrarily oriented straight fibers (left: bipolar DBS; right: tES; current magnitude: 1 mA; electrode size: 3 cm²).

3.5. Comparison of Exposure Metrics

The results of the biophysical exposure simulations are summarized in Table 1, which constitutes the basis for comparing TIS with established neurostimulation modalities to propose safety thresholds:

Table 1.

Dosimetric and thermal exposure quantities for typical tDCS, tACS, DBS, and TIS configurations. All exposures assume an input current of 1 mA. For tACS and DBS, the charge is calculated per phase (e.g., half‐period for sinusoidal currents).

Modality	Contact surface (cm2)	2 mm Averaged E‐field (V/m)		2 mm Averaged J‐field (A/m2)		Input current (mA)	Duration (s)	Charge (C)	Charge/phase (C)	Delta T c (mK)		AF peak/99.9% (V/m2)c
		Brain	Skin	Brain	Skin					Peak	GM	Skin	Brain
tDCS	0.5	1.7	87	0.4	15	1	1800	1.8	1.8	18	1.1	4.8 M/15 k	5.1 k/420
	1.5	2.0	50	0.5	8.6	1	1800	1.8	1.8	4.4	0.5	370 k/1.3 k	2.1 k/280
	3	1.6	30	0.4	5.1	1	1800	1.8	1.8	2.5	0.6	280 k/1.4 k	2 k/270
	25	0.8	7.9	0.2	1.4	1	1800	1.8	1.8	0.2	0.04	71 k/1.2 k	1.5 k/240
	50	0.3	5.9	0.1	1.0	1	1800	1.8	1.8	0.1	0.0	58 k/990	880/130
tACS	0.5	1.7	87	0.4	15	1	n/a	n/a	3.2e−5	18	1.1	4.8 M/15 k	5.1 k/420
	1.5	2.0	50	0.5	8.6	1	n/a	n/a	3.2e−5	4.4	0.5	370 k/1.3 k	2.1 k/280
	3	1.6	30	0.4	5.1	1	n/a	n/a	3.2e−5	2.5	0.6	280 k/1.4 k	2 k/270
	25	0.8	7.9	0.2	1.4	1	n/a	n/a	3.2e−5	0.2	0.04	71 k/1.2 k	1.5 k/240
	50	0.3	5.9	0.1	1.0	1	n/a	n/a	3.2e−5	0.1	0.0	58 k/990	880/130
DBSa	0.06	145	0.0	35	2e−3	1	n/a	n/a	5e−7	26	26	0 k/	13 M/250
TISb 1:1	3	0.3	0.2	0.07	0.04	1 + 1	n/a	n/a	n/a	n/a	n/a	—	—
HF 1:1	3	1.7	31	0.4	5.3	1 + 1	n/a	n/a	3.2e−7	2.5	0.6	300 k	13 M/250

Abbreviations: GM, gray matter; HF, high frequency.

^a Simulation data refer to a DBS frequency of 130 Hz.

^b TIS values refer to the envelope modulation magnitude.

^c 99.9th isopercentile of the AF in skin and combined brain tissues.

For the same electrode montage and total current, the combined field exposure magnitude (carrier) for TIS is less than or equal to that of tACS, with more spatial dispersion, as a consequence of being distributed across a greater number of electrodes. However, TIS carrier frequencies are one to two orders of magnitude higher, making it far less likely to result in direct neuromodulation. Both tACS and TIS (at least when using only two high‐frequency carriers) have diminished peak field strengths and reduced focality in the brain in comparison to DBS. The low‐frequency modulation envelope magnitude distribution of TIS is more localized than that of tACS, but as it is dominated by the weaker field, it is never larger than the tACS field, and its local maxima/foci are typically a subset of those generated by tACS. We also note that the stimulation efficacy of the TI modulation magnitude should not be compared directly to tACS field strengths at the same frequency, since TIS requires an additional demodulation step and the mechanisms of action are different. All modalities investigated resulted in minimal heating that would not be expected to cause direct thermal tissue damage. With respect to heating, charge, current, and interface effects, TIS is comparable to tACS.

In summary, the procedural aspects of TIS and tACS are largely overlapping, despite certain differences; TIS is more focal, uses high‐frequency carriers that are less likely to elicit direct neurostimulation near the electrodes at similar current magnitudes (especially with multi‐kHz carriers and in accordance with observations from TIS experiments), and is capable of modulating deeper brain structures. Compared to DBS, which also targets deep brain regions with enhanced focality, TIS is nearer to tACS in terms of the magnitude and size of local maxima. Thus, safety considerations for tACS also broadly apply to TIS, with two additional TIS‐specific concerns: (i) in TIS, the higher frequencies of applied currents increase the magnitude threshold required to evoke skin sensations, which would otherwise serve as cautionary signals and (ii) TIS may entail the use of electrode montages that would normally be avoided owing to the possibility of activating nearby cortical or cerebellar structures. Furthermore, the biophysical mechanisms of TIS are still poorly understood, warranting a degree of general caution.

3.6. Multichannel TIS

In standard practice, TIS is achieved via interfering fields across two channels (i.e., two electrode pairs). However, increasing the number of channels can improve stimulation focality, especially when the additional channels utilize separate carrier frequencies. In general, each channel pair (and associated carrier frequency) will produce a unique spatial pattern of unwanted exposure, but an overlapping distribution of desired exposure at the target. Thus, multichannel, multi‐carrier frequency TIS can enhance the contrast between exposures in target and off‐target regions to improve focality. Furthermore, so long as the modulation ratio at the target remains constant, the total current is conserved as the number of channel pairs increases, thereby reducing the current delivered over each individual channel. Accordingly, the same safety thresholds proposed for two‐channel TIS also apply to the multichannel case, provided that the electrodes are sufficiently well separated. With due care, it may even be possible to increase the total current used with multichannel TIS following a thorough, setup‐specific safety assessment.

3.7. Additional Considerations for Frequencies > 10 kHz

The possibility of using frequency carriers on the order of 10–100 kHz for TIS merits discussion, though the capacity of neurons to demodulate such fields is as of yet unknown. In this frequency range, direct effects resulting from exposure to high‐frequency fields are expected to be further diminished relative to lower frequencies, as safety guidelines specify current thresholds proportional to frequency (International Commission on Non‐Ionizing Radiation Protection 2010; IEEE 2020). Recent research has demonstrated the safety and efficacy of TIS using a 20 kHz base frequency, offering preliminary evidence for the neuromodulatory potential of very high frequency carriers (Wang et al. 2024). However, at such high frequencies, the relative importance of capacitive currents (compared to ohmic currents) may no longer be negligible, and additional simulations accounting for the frequency dependence of dielectric materials would be needed to quantify whether and how the exposure quantities summarized in Table 1 are affected.

3.8. Electrode Size and Placement

To investigate the impact of electrode size and separation distance on tissue exposure under highly controlled conditions, we developed a simplified, cylindrical head model (see Figure 7) comprising the following tissues: skin, SAT, galea, skull (three layers: cortical inner and outer table with cancellous diploe in between), dura, CSF, gray and white matter. Table 2 summarizes the tissue dielectric and geometric properties. Circular electrodes with varying surface areas (1.5, 3, and 25 cm²) were placed on the head model as shown in Figures 7 and 8. This arrangement was discretized using a homogeneous rectilinear grid with 0.2 mm resolution. Field distributions were calculated for varying interelectrode separations, employing Sim4Life's ohmic current‐dominated low‐frequency EM solver with Dirichlet voltage boundary conditions at the active electrodes (inactive electrodes were excluded from the simulations), and with total current normalized to 1 mA. Peak values for current density and E‐field magnitude were reported for each simulation condition over the set of all combinations of electrode sizes and separations.

Figure 7.

Simplified head model geometry. (i) Geometry of the simplified, cylindrical head model, with detail of the tissue layers: epidermis, dermis, SAT, galea, three skull layers (cortical inner and outer table, cancellous bone), dura, CSF, gray, and white matter. The external diameter of the head model is 18.6 cm and the external diameter of the white matter is 15.4 cm. The height of the cylinder is 12 cm. Electrodes for every condition were placed as illustrated in (i). (ii) Detail of the head model, along with the rectilinear grid used for discretization.

Table 2.

Head model parameters: thicknesses and electric conductivities (Hasgall 2018).

Tissue name	Thickness (mm)	Conductivity (S/m)
Skin (epidermis and dermis)	(0.07 + 1.8)	0.17
SAT	3	0.057
Galea	0.8	0.368
Cortical bone (outer)	2.6	0.0035
Cancellous bone	2.0	0.082
Cortical bone (inner)	2.6	0.0035
Dura	0.6	0.461
CSF	1	1.71
Gray matter	2.5	0.24
White matter	15.4	0.265

Figure 8.

2 mm averaged current density. Values for (i) skin and (ii) brain (gray matter) of the simplified head model for three different electrode sizes (1.5, 3, and 25 cm²) as a function of the interelectrode separation (length of the shortest geodesic path on the skin surface). Small blue squares: 2 mm averaged peak current density for simulations with a floating electrode that does not contribute current (shown in (iii)). (iii) Current density distribution for 3 cm² electrodes in the absence (left) and presence (right) of an additional electrode that does not provide current but may enhance the field as a result of edge effects.

E‐field enhancement is apparent at the electrode border, which is a result of the sharp conductor edge and strong local curvature of field lines. The effect is most pronounced for electrodes in close proximity, as the edge effects of the two electrodes begin to merge, pushing local skin exposures higher, and as the conductance of the scalp current pathway increases relative to the transcranial pathway. Such scalp shunting effects dominate for brain exposure, which in consequence leads to a net reduction of brain current density with increasing separation (see Figure 8; scalp currents fall from 70% at 4 mm separation to 5% at 200 mm for the simplified model, in agreement with findings from the detailed head model). The influence of electrode separation on peak E‐field and current density falls below 20% at a distance of approximately 50 mm. At these distances, scalp currents are below 30%. Electrode size is an important determinant of skin exposure since: (i) current density below the electrode is inversely proportional to the electrode area (by definition), (ii) edge effects, which are safety and sensation limiting in the skin, are directly related to electrode edge length. Specifically, edge field strength and current density are inversely proportional to edge length; a log‐log linear regression of the data in Figure 8 reveals a diameter dependence exponent of 0.94 with R ² = 99%, and (iii) power deposition and heating, which are dominated by edge effects, scale with the square of field magnitude, and, therefore, in roughly inverse proportion to electrode area. The impact of electrode size on brain exposure, however, does not show a systematic dependence (exponent: 0.17, R ² = 90%). Instead, it is expected that aspects such as skull thickness (electrode location‐ and subject‐dependent), CSF coverage, scalp shunting, and local cortical folding, dominate the amount of current reaching the brain.

Figure 9 shows the distributions and peak values of current density and E‐field in the skin and brain for a fixed input current of 1 mA as a function of electrode separation (3 cm² electrode area). The presence of passive electrodes, or electrodes operated at different frequencies (as required for TIS), can lead to important edge effects due to field concentration at sharp conductor features. Figure 8 illustrates this principle; E‐field and current density in the scalp are markedly increased in close proximity to the electrodes in the presence of an additional electrode that does not provide current. In TIS, which requires the use of multiple electrodes operating at different frequencies, such effects may have safety implications, or cause skin sensations that affect blinding or trigger functional and/or behavioral responses. Local field enhancement and concentration is also an issue near invasively placed electrodes (either sensing or stimulating) and can affect targeting or cause unwanted stimulation (see Section 5.9).

Figure 9.

Current density distributions for increasing electrode separations. Simulations were conducted using a simplified head model, 3 cm² electrodes, and 1 mA of input current.

4. Current Threshold Proposal

Based on the analysis of the computed exposure metrics and interaction physics for conventional tES and DBS, we propose safety thresholds for TIS designed to prevent thermal damage and direct stimulation. To this end, we scaled the normalized (1 mA input current) field distributions for tACS, tDCS, and DBS to reflect typical operating conditions (falling within established safety standards for each modality). After extracting the previously described safety‐relevant exposure metrics for the scaled field distributions, we computed frequency‐dependent current thresholds that result in equivalent TIS‐induced exposure magnitudes. Considering all safety‐relevant effects in each frequency band, the proposed thresholds represent the largest current magnitudes that meet all safety criteria. It must be noted, however, that the thresholds may not guarantee sensation‐free stimulation, which can disrupt study blinding but do not affect health.

Modern tES stimulation protocols regularly utilize total currents on the order of 2 mA (see Supporting Information S1: Table A.2 in Part I; average current amplitude: 1.7 mA; range: 0.75–2 mA), and early work with TIS in human subjects has applied up to 4 mA of total current (up to 3 mA in a single channel), in the 2–8 kHz range without eliciting AEs (personal correspondence with collaborators). Assuming an electrode size of 1.5 cm², this translates to peak 2 mm averaged E‐field values in the brain of approximately 8 V/m in the low‐frequency range, and 5 V/m for kHz exposures. In the skin, the corresponding values are 80–200 V/m in the low‐frequency range and up to 90 V/m for kHz exposures. To better understand the effects of localized DBS, we turn our attention to DBS. DBS targets (GP and the subthalamic nucleus [STN]) are well contained within a sphere of radius 15 mm (based on Medtronic 3389 DBS neurostimulator placed in the GP; sphere centered on the geometrical center of the four contacts), outside of which it may be assumed that DBS exposure does not directly affect brain activity. Typically, DBS employs voltages in the range of 5–14 V (see Part I, Supporting Information S1: Table A.2; average voltage: 6.6 V), which produce currents of up to 20 mA [clinically reported impedances are in the 0.5–1.5 kΩ range (Wei and Grill 2009), while simulations typically report 0.6–1.2 kΩ (Satzer et al. 2014)]. The associated peak‐averaged E‐fields in the brain outside the sphere are roughly 7 V/m but can reach 30 V/m.

Current thresholds for TIS were derived by comparing TI‐induced brain E‐field magnitudes, the difference frequency modulation amplitude, and the total current per channel with standard exposure conditions for tES, and with peak off‐target field magnitudes for DBS. This approach suggests that TIS exposures are likely safe for currents in the range of 3–5 mA at typical tES frequencies and for currents spanning 15–30 mA for typical DBS frequencies of up to 200 Hz. Our analysis is limited by the sparse availability of data for kHz tES, and the consequent lack of safe use history at higher exposure levels. ICNIRP guidelines specify that independent of contact area, currents of ≤ 1 mA for f ≤ 2.5 kHz and ≤ 0.4 f mA (f in kHz) for f > 2.5 and ≤ 100 kHz are safe for occupational exposure (International Commission on Non‐Ionizing Radiation Protection 2010). The ICNIRP threshold currents are based on data from WHO guidelines (World Health Organization, United Nations Environment Programme, and International Radiation Protection Association 1993), which draws upon the work of Chatterjee, Wu, and Gandhi (1986) on threshold currents for perception and let‐go, and Bernhardt (Bernhardt 1985, 1986) for effects on excitable cells. Further support from experimental perception and muscle tetanus data and theoretical modeling can be found in Figure 8 of Reilly (Reilly 1989), which also shows a strong frequency‐dependent threshold increase starting below 1 kHz and exceeding the maximal sub‐kHz threshold above 2.5 kHz. Thus, extrapolated to a neurostimulation context, field exposures and stimulation currents with applied frequencies above 2.5 kHz would be safer than those of the same amplitude at lower frequencies. Note: occupational safety guidelines are of limited applicability to electrical neuromodulation, where stimulation is applied intentionally under controlled conditions. By contrast, safety guidelines provide limits for unintended contact currents and accept nonhazardous sensations as benign side‐effects (International Commission on Non‐Ionizing Radiation Protection 2010). Given the tradeoff between the strength and duration of threshold stimulation (Reilly and Diamant 2011), and in accordance with INCIRP guidelines (International Commission on Non‐Ionizing Radiation Protection 2010), we propose the following structure for safe exposure limits: constant stimulation thresholds up to a chosen frequency (ICNIRP guidelines suggest 2.5 kHz; simulations of myelinated and unmyelinated A‐ and C‐fibers suggest < 1 kHz), beyond which thresholds increase linearly with frequency. On this basis, TI currents up to 16 mA below 2.5 kHz, 30 mA at 4 kHz, and > 500 mA at 100 kHz are theoretically acceptable. However, since tissue heating is proportional to the square of current, thermal safety considerations become relevant for the increased current thresholds allowed at high frequencies (around 5 kHz). For typical tES and DBS current magnitudes (and accounting for DBS interpulse intervals), skin and brain temperature increases remain in the mK range. Even the highest clinical DBS magnitudes only increase temperature nearby the implant by tenths of a Kelvin (Elwassif et al. 2006). Our simulations show that current magnitudes below 15 mA result in peak temperature increases in the brain of no more than 0.2 K, which is considered safe. At these current strengths, skin heating is well below the 2 K threshold accepted by the FDA for medical applications. Even for the comparatively conservative ICNIRP (International Commission on Non‐Ionizing Radiation Protection 2010) and IEEE (IEEE 2020) safety guidelines, currents on the order of 100 mA would be required to exceed the 1 K limit. Charge injection is not a limiting factor for TIS since the charge injected per phase is proportionally reduced with increasing frequency.

The safety thresholds described above are summarized in Table 3. These thresholds were established to promote safety, but do not ensure stimulation devoid of sensation. While such sensory perception might compromise study blinding, it does not constitute a health risk. All quantities were computed for 3 cm² TIS electrodes, reflecting common practice. Larger electrode areas would tend to increase current thresholds, while poor electrical contact (resulting in reduced contact area) or closely neighboring electrodes would reduce the thresholds for safe current exposure. Smaller electrodes may be used provided that the maximum current is reduced in proportion to the electrode contact area.

Table 3.

Proposed safety thresholds for TIS by exposure metric (3 cm² electrodes). Selection of exposure mechanisms was motivated by reported AEs. Thresholds are based on mechanistic considerations, dosimetric simulations of tDCS, tACS, DBS, and TIS, and the literature‐informed history of safely applied conventional electrical stimulation. Thresholds are formulated in terms of measurable TIS application parameters (applied currents and voltages).

Metric	Relevance	< 2.5 kHz	2.5–100 kHz
E‐field brain (peak)	Brain stimulation	16 mA (30 V/m, DBS outside stimulation zone)	16 mA × f/2.5 kHz (30 V/m × f/2.5 kHz, DBS outside stimulation zone)
E‐field skin (peak)	Skin stimulation	7 mA (200 V/m, tACS)	7 mA × f/2.5 kHz (200 V/'m × f/2.5 kHz, tACS)
Total current (peak)	Electrode–tissue interface effects	18 mA (DBS)	18 mA × f/2.5 kHz (DBS with frequency scaling)
Charge/phase (peak)	Electrochemistry	400 mA × f/1 kHz (1.3 mC, tACS)	400 mA × f/1 kHz (1.3 mC, tACS)
Brain temperature increase (peak)	Brain heating	14 mA (0.1°C, FDA)	14 mA (0.1°C, FDA)
Skin temperature increase (peak)	Skin heating	100 mA (2°C, FDA)	100 mA (2°C, FDA)
Applied voltage (peak‐to‐peak)	Leakage current	60 V (IEC/ISO 60601‐1)	60 V (IEC/ISO 60601‐1)

Note: Exposure quantities are shown in parentheses together with the reference application/standard used to define the threshold. All quantities are expressed as peak values (not RMS) except for applied voltage, which is formulated as peak‐to‐peak to ensure consistency with leakage current. Values in bold highlight the lowest effect thresholds and the metrics that may limit TIS exposure. All quantities were computed based solely on the direct effects of applied currents and voltages. IEC/ISO: joint technical committee of the International Organization for Standardization and the International Electrotechnical Commission. Stimulation zone: A sphere of radius 15 mm, centered on the DBS contacts (based on Medtronic 3389 neurostimulator) and encompassing the GP and the STN, beyond which stimulation effects are considered undesirable.

These limits do not consider E‐field‐induced sensations in the skin, since they manifest well before safety becomes relevant. Drawing on available data, TIS currents of at least 7 mA can be applied without exceeding skin field exposures commonplace in tES. Assuming that thresholds scale linearly with frequency above 2.5 kHz, this implies an acceptable current level of > 10 mA at 4 kHz and > 200 mA at 100 kHz. Basic simulations of 1 μm C‐fiber stimulation (relevant for sympathetic neural activation; A‐ and B‐fibers in the skin affect sensation and are not safety relevant) suggest that activation occurs at approximately 1.6, 6, 160, and 1000 mA, for 1, 2.5, 4, and 100 kHz, respectively. Sensations have been reported during stimulation in the 1–4 kHz frequency range for currents > 2–4 mA (Hsu, Farahani, and Parra 2021). Average current density (ICNIRP 2010 averaging protocol [International Commission on Non‐Ionizing Radiation Protection 2010]) in the skin beneath the electrode was on the order of 0.1–1.5 mA/cm² per mA of electrode current (dependent on electrode size), and 0.008–0.05 mA/cm² per mA of applied current in brain tissue below the electrode. In rodents, unaveraged current densities of up to 32 mA/cm² (500 µA over a 1.6 mm² electrode) at 1 kHz, applied repeatedly in 6 s intervals, have been reportedly used without inducing behavioral AEs (Grossman et al. 2017).

5. Discussion

Considering the sparsity of empirical studies that employ TIS as a neuromodulatory strategy, we endeavored here to synthesize existing data regarding the safety of tACS, tDCS, and DBS with respect to thermal effects and unwanted stimulation to identify safe operating conditions for TIS in terms of frequency‐dependent current intensities, considering electrode shape and placement. TIS and tACS are readily comparable, owing to the close correspondence of the transcranial current delivery, exposure conditions, current intensities, and (bio‐)physical principles at play. Extrapolation of safety aspects from tACS to TIS is possible with due consideration to differences in operating frequency (within a few tens of Hz for tACS, a few kHz for TIS) and the interferential nature of TIS. On the other hand, DBS, like TIS, aims at selectively activating deep brain structures, providing a qualified reference point for the expected biophysical response to optimally focused TIS. While a complete characterization of TIS safety in humans awaits additional investigation, we can draw upon available research and clinical experience with related technologies to help define the relevant endpoints for monitoring, as regards both safety and effectiveness.

5.1. Physical and Chemical Effects

To date, there have few reports of TIS‐associated AEs, all mild to moderate, and with no significant differences between sham and active conditions (Grossman et al. 2017; Esmaeilpour et al. 2021; Piao et al. 2022). For carrier frequencies < 2 kHz and current amplitudes < 2 mA, TIS is comparable to tACS in terms of the magnitude and extent of fields and currents, and no physical or chemical damage has been observed for either technique. Safety guidelines suggest that safety thresholds for applied current are proportional to frequency above 2.5 kHz. However, empirical data for TIS are lacking, and such extrapolation should be supported by basic safety experiments. Using detailed simulations in a human head model with an input current of 1 mA and an electrode area of 3 cm², we found that skin heating is on the order of a few milliCelsius, while spatial peak current density and field strengths are on the order of 5 A/m² and 30 V/m, respectively. According to the Shannon model for charge‐induced tissue damage, this yields comparable exposure values to those of local stimulation methods such as DBS. Electrode materials and conductive gel should be chosen to minimize irritation to the skin (see Section 2.2.1).

5.2. Skin Sensations, Phosphenes, and Ramping

The use of multi‐kHz frequencies in TIS considerably increases direct stimulation thresholds in the scalp, where little constructive interference is present, as compared to the lower frequencies characteristic of tACS. Thus, tingling sensations, phosphenes, and unwanted stimulation of facial nerves are improbable for currents ≤ 2 mA and are unlikely to confound blinding procedures. Existing skin exposure guidelines and the established history of safe use for tES further ensure safety with regard to unwanted facial nerve stimulation, especially when frequency‐dependent response attenuation is accounted for. Nevertheless, such sensations must be carefully monitored and human subjects/patients should be questioned regarding their occurrence. It has been observed for TIS, in particular, that ramping up the current strength rapidly causes transient neural activity (Grossman et al. 2017), which may cross the threshold for perception. Therefore, care must be taken to increase currents sufficiently slowly; ramping times of a few seconds appear sufficient to avoid such stimulation artifacts (personal correspondence with collaborators). These observations are consistent with the biophysical principles outlined in Sections 2.1 and 3.

5.3. Electrode Size and Placement

The choice of electrode size and placement is driven both by the stimulation target and by safety concerns. In general, power deposition and exposure‐induced heating are minor, and limited by skin sensations. Nevertheless, practitioners may seek to minimize these quantities by selecting larger electrodes (edge effects are inversely proportional to the diameter), ensuring high‐quality electrical contacts (lower and more even current density), and by avoiding sharp edges (field concentration). Employing larger surfaces is practical for remote return electrodes, but may compromise treatment efficacy when applied to electrodes near the target region due to focality degradation (more current overlap in overlying structures), necessitating an analysis of the risk‐reward tradeoff when selecting electrode shape and placement. Particular caution is advised when multiple electrodes are placed in close proximity (< 3 cm) due to the superposition of edge effects. Our analysis of edge and proximity effects also applies in the case of passive electrodes (electrodes that do not provide current) and electrodes operated at different frequencies (as required for TIS), which tend to concentrate the local field. Furthermore, the spatial extent of the conductive contact gel must also be considered; seemingly well‐separated electrodes may effectively behave as though they were in close proximity if the gel extends sufficiently, while large electrode areas can still result in small contact areas for poor gel coverage. Proper skin and electrode preparation is necessary to mitigate the risk of persistent skin lesions and subjects should be encouraged to report any discomfort to prevent skin irritation (Antal et al. 2017). Finally, in cases where a single electrode is used as the common return electrode for multiple TIS current channels, it is important to consider that the total power deposition—and similarly the total temperature increase—is equal to the summed combination from all channels (incoherent field superposition).

5.4. Short‐ and Long‐Term Neuromodulatory Effects

At a standard tES current amplitude of approximately 1 mA per channel, direct suprathreshold TIS is not expected from either the high‐frequency carrier or the low‐frequency modulation. Instead, neuromodulation occurs in the subthreshold regime via membrane polarization and synchronization of network activity. Conservatively, AEs associated with tACS (see Part I, Section 3.4) should be monitored when applying TIS. However, as multi‐kHz frequencies are unlikely to evoke stimulation, and since the low‐frequency modulation must first undergo a rectification and/or mixing process, the actual stimulation efficacy of TIS is likely lower than that of tACS for the same exposure magnitude. Furthermore, as TIS aims to produce localized stimulation in deep brain structures, DBS‐like AEs are also possible (see Part I, Supporting Information S1: Table A.3). Yet, because local DBS brain exposure strengths are generally two orders of magnitude higher than those of TIS, and since, unlike TIS, DBS is applied chronically for months or years, DBS‐associated AEs are presumably less likely for TIS.

The analogy between TIS and tACS/DBS has several limitations. In particular, direct comparisons between the E‐field magnitude of low‐frequency stimulation and the TIS modulation magnitude are precluded by the unknown efficacy of signal rectification and/or nonlinear frequency mixing by neurons. Comparing high‐frequency field exposure strengths in TIS to the field strengths in tACS/DBS is also not appropriate given the discrepancy in frequencies and attendant differences in the neural response.

Little is known about the long‐term effects of TIS. Particularly, for modulation frequencies in the alpha to theta band, attention must be paid to the possibility of alterations in various cognitive functions. Following the logic of Klink et al. (2020), if cognitive enhancements are possible with tACS, then AEs in the domain of cognition should also be possible. Furthermore, as long‐term TIS applied in regular sessions over a period of weeks or months may lead to plasticity‐dependent changes, treatment cessation could result in withdrawal symptoms, the occurrence of which should be monitored.

5.5. Planning, Monitoring, Training, and Reporting

In TIS, the added complexity of selectively targeting deep structures using multiple, interacting currents/fields requires proper treatment planning and optimization, which is generally undertaken using computational modeling. Simulations are strongly recommended, both as a means of improving focality, and as a source of exposure information to guide safety assessments. It remains to be seen whether and how individualization of treatment parameters to accommodate inter‐subject anatomical variations affect treatment outcomes. Should such differences prove significant, subject‐specific treatment planning will be required for the design of optimal stimulation configurations. Due to the novelty of TIS and the importance of adhering to safety protocols, the planning and delivery of TIS should be executed by trained personnel. We refer the reader to a recent review paper by the International Federation of Clinical Neurophysiology (IFCN) summarizing the requirements for training (Fried et al. 2021), which might need to be adapted specifically when training staff for TIS administration. In addition, it will be important to systematically assess the uncertainty associated with modeling predictions, to determine the reliability of performance and safety predictions, and the required safety margins.

5.6. Risk–Benefit Analysis

Similar to other brain stimulation approaches, a thorough risk–benefit analysis must undergird both clinical and research applications. For example, DBS is usually applied in refractory diseases where the considerable risks of surgery are worth the anticipated benefits. In the case of TIS, the risk–benefit balance of TIS is currently unknown, as no therapeutic application of TIS has yet been yet demonstrated. However, with minimal risk of AEs and appreciable potential therapeutic benefits, the clinical use TIS is likely justified in most cases. Particular caution must be exercised when targeting deep brain structures in view of their central role in regulating core physiological functions (e.g., heartbeat, breathing, thermoregulation), and the potential to trigger anxiety or other severe responses. In particular, structures such as the amygdala (emotion/fear processing) or regions in the brain stem should be avoided. Indications regarding critical brain structures might be derived from observed AEs related to DBS (Part I, Supporting Information S1: Table A.3). As with tES, care is required in identifying patient populations with heightened susceptibility to certain AEs (e.g., predisposition to manic episodes, prior history/family history of neurologic/psychiatric disorders or seizures). Despite one report of seizure, many thousands of sessions of tES have been performed without incident. Thus, accurate patient history and seizure propensity should be taken into account before tES treatments, but do not necessarily preclude subjects from tES treatment. Particular caution must also be exercised when exposing populations such as infants, children, and/or adolescents, whose brains are still developing.

5.7. Mechanistic Pathways and TI Planning Optimization Metrics

The current lack of a clear mechanism(s) of action for TIS complicates safety assessments and treatment optimization, in part by frustrating efforts to establish a suitable exposure metric that relates to stimulation efficacy and selectivity. For example, the observed shift of the TIS focus toward the weaker current source (Grossman et al. 2017) agrees with predictions based on the modulation envelope magnitude distribution. In contrast, a stimulation mechanism based on second‐order frequency mixing would predict an effect size that scales with the product of the local exposure magnitudes of the two sources and, therefore, despite support from electrophysiological data, cannot explain steering. Furthermore, in highly structured tissues (e.g., layer five cortical pyramidal cells, hippocampal complexes, collinear axonal projections), the preferred field orientation of a neural population likely requires the consideration of projected field quantities, rather than the full field magnitude. AF concepts, as suggested by Mirzakhalili et al. also imply that field heterogeneity, rather than field magnitude alone, must be considered (Mirzakhalili et al. 2020). Other important factors include the influence of ongoing neural activity, and differences between brain regions in terms of susceptibility to stimulation. Therefore, dedicated experiments designed to explore the mechanisms of action of TIS are needed.

As a corollary to the above discussion, the modeling work presented here is limited by the assumption of the homogeneity of brain tissue biophysical properties. Thus, cell type‐specific properties including membrane polarizability and threshold potential are not considered in the predicted response to applied E‐fields or TI amplitude modulation. These difficulties are further compounded in the absence of knowledge concerning TIS mechanisms, which may exert differential effects depending on ongoing neural dynamics or subpopulation characteristics. The availability of such information is limited, though attempts have been made to aggregate knowledge of the neural properties of certain populations (e.g., in the hippocampus) (Wheeler et al. 2015).

5.8. Physical Limits on Targeting

An intriguing benefit of TIS is the potential for noninvasive steering of the focus (Grossman et al. 2017). However, the physics of EM fields, in particular, the impedances of different pathways to current flow, introduces complexities that may either inhibit or facilitate targeting. For example, longer paths along highly conductive media (e.g., CSF) may have less overall impedance than shorter paths through highly resistive media (e.g., cortical bone). Thus, geometric length is not identical to effective electrical length. Current may flow through the scalp to locations where the skull offers less resistance or may preferentially follow paths that maximize flow through highly conductive CSF, while reducing the length of passage through brain tissue (“current shunting”). Similarly, brain tissue, especially white matter, is anisotropic, and conductivity along fiber orientations can be up to an order of magnitude higher than in the transverse direction. Computational modeling enables all these factors to be considered during optimization and treatment planning.

5.9. Implants

Local field enhancement and concentration is a concern not only for external electrodes (see Section 3.8), but also conductive implants (e.g., invasive stimulation and/or recording electrodes) as their presence can result in unwanted stimulation or affect targeting. For a systematic investigation of tES implant safety, with particular considerations for TIS, see Karimi et al. (2024). No transcranial stimulation should be performed in individuals with highly conductive brain implants in direct proximity to neural tissue without an extensive and careful risk assessment.

5.10. Conservativeness and Safety Margins

The exposure limits derived in this study are not expected to require large additional safety margins, since (i) most evaluations are relative to classic tES, such that uncertainties compensate. For example, a tissue property change that increases tES fields will increase the TIS modulation amplitude by a similar amount, since TIS is primarily driven by the weaker of its two (tES‐like) channels, (ii) large safety margins are already built into absolute dosimetric limits (e.g., the FDA limit on temperature increase of 0.1 K), and (iii) skin sensations limit scalp exposure as these occur before important (safety‐relevant) AEs. Nevertheless, systematic confidence interval quantification is an important next step (see Section 5.12).

5.11. Limitations

In general, it should be noted that we cannot rule out bias in the selection of the tACS, tDCS, and DBS literature considered here, as our search focused on recent reviews. In addition, literature reporting negative results was generally not included (and is less likely to have been published). We also note the following limitations affecting our analysis of the simulation data reported in the preceding sections:

• Since the exact mechanisms of TI exposure‐related neuromodulation have not been clarified, there remains a possibility that exposure metrics other than those described here are relevant to safety.

• The stimulation configurations used in tACS, tDCS, TIS, and DBS were not comprehensively explored and inter‐subject subject variability was not considered.

• Little experimental data exists for brain stimulation at high frequency, necessitating physics‐based extrapolations from stimulation at other frequencies.

• Proposed limits for exposure‐related quantities apply to adult heads and should not be used in investigations that include pediatric subjects, or subjects with anatomical anomalies (e.g., skull fractures, brain lesions, implanted electrodes).

5.12. Research Needs

In view of the above limitations, we suggest the following as priorities for future research:

• A systematic experimental assessment of single neuron and neural network responses to varying TIS exposure conditions (carrier and modulation frequency, modulation depth, relative orientation of fields from different channels) to confirm that the relevant exposure quantities have been accounted for in the proposed safety thresholds. This may also require a consideration of pulse shapes and stimulation schemes with more than two channels.

• An assessment of uncertainty to ascertain the confidence intervals associated with model‐based predictions. Aspects such as the variability of inter‐subject anatomy and tissue properties, tissue heterogeneity and anisotropy, segmentation accuracy, and numerical convergence must also be considered. Corresponding work is underway; see Cassarà et al. (2023) for a report of preliminary results.

6. Conclusion

TIS promises to unlock new opportunities for noninvasive, targeted, DBS. However, as an emerging technique, considerable effort is still needed to establish a foundation of knowledge to support future developments. In particular, guidance regarding exposure limits and other safety concerns, necessary for obtaining regulatory approvals and conducting research, is lacking. To this end, we drew upon available data and expertise in electrical neuromodulation to inform a preliminary analysis of TIS exposure safety. To compensate for gaps in the TIS literature, biophysical arguments were used to translate knowledge from common tES and DBS modalities to TIS, considering a wide range of safety‐relevant interactions. This work was a two‐part effort; Part I comprises a review and summary of the biophysical mechanisms, potential safety concerns, and reported AEs of tES and DBS. In Part II, described here, we employed dosimetric and biophysical modeling to support comparisons across different electrical neurostimulation modalities and derive a preliminary proposal for frequency‐dependent safety thresholds for TIS currents. As the understanding of TIS' safe operating conditions are continually refined, this technique's unique combination of non‐invasiveness and focality at depth promises to unlock a wide array of new possibilities in both clinical and research settings.

Conflicts of Interest

Esra Neufeld and Alvaro Pascual‐Leone are minority shareholders and board members of TI Solutions AG. Niels Kuster is a shareholder of NF Technology Holdings AG, which is a minority shareholder of TI Solutions AG. He is also a board member of TI Solutions AG. Sabine J. Regel is the CEO of TI Solutions AG. The other authors declare no conflicts of interest.

Supporting information

Supporting information.

Data Availability Statement

All data will be made available upon reasonable request to the corresponding author.