Standardizing TMS Intensity Across Different Coils Using Individualized Electric Field Modeling

ABSTRACT

Quantitative measures for Transcranial Magnetic Stimulation (TMS) intensity are needed to ensure safe and consistent application in therapeutic and research settings. However, resting motor thresholds (rMTs), commonly used to determine stimulation intensity, depend on the coil used. Unless motor mapping and treatment coils are identical, re‐thresholding is necessary, increasing patient discomfort and potentially introducing variability across studies. These considerations raise an unresolved fundamental question: does individual rMT reflect a consistent cortical electric field (E‐field) magnitude independent of coil geometry? We tested the hypothesis that rMT corresponds to a coil‐invariant cortical E‐field magnitude and evaluated a computational method for predicting stimulator output across different coils using a reference rMT. Thirteen healthy, right‐handed participants were recruited; ten were included in the primary analysis. Participants underwent TMS with two figure‐of‐eight coils of different sizes. E‐field distributions were simulated using a fast multipole boundary element method, in free space and within personalized MRI‐based head models. rMT prediction accuracy was compared between a detailed five‐layer and a simplified three‐layer head model, and both were evaluated against direct rMT scaling using the reference coil. The personalized E‐field‐based approach significantly improved rMT prediction accuracy over direct scaling (p < 0.001). The root‐mean‐square error (RMSE) was 1.26% and 1.32% of maximum stimulator output (MSO) for detailed and simplified models, versus 6.1% MSO for direct scaling. Individual rMT corresponds to a constant cortical E‐field magnitude ratio across coil types. E‐field‐based prediction offers a more accurate, coil‐independent method for standardizing TMS intensity, reducing the need for repeated thresholding.

Summary

• rMT corresponds to an approximately unity cortical E‐field magnitude ratio across coil types under matched conditions

• E‐field‐based prediction yields rMT with ~1.3% MSO RMSE versus direct scaling ~6.1%

• The simplified and realistic head models result in similar E‐field ratios for the fixed coil orientation, whereas the cortical E‐fields differ when evaluated in free space (i.e., without a head model)

Using individualized electric‐field (E‐field) simulations, we show that cortical E‐field values required for neuronal activation remain consistent across coil types. This allows stimulation intensity to be predicted from a single motor‐threshold measurement, providing a physiologically meaningful, device‐independent TMS dosing metric that reduces patient burden and improves reproducibility.

1. Introduction

Transcranial magnetic stimulation (TMS) is a non‐invasive technique that uses time‐varying magnetic fields to induce electric fields (E‐fields) in targeted brain regions, enabling neuronal activation (Terao and Ugawa 2002). Due to its capability to induce strong suprathreshold E‐fields in the intracranial space safely and painlessly, TMS has gained wide application in both research (Oliveri et al. 2000) and clinical settings (Rossini and Rossi 2007). Some TMS protocols and devices are FDA‐approved for treating various neurological and psychiatric disorders, such as treatment‐resistant depression (TRD) (Connolly et al. 2012), obsessive‐compulsive disorder (OCD) (Cohen et al. 2021), migraine (Irwin et al. 2018) as well as for aiding in smoking cessation (Young et al. 2021). TMS has also received FDA approval for presurgical functional mapping of motor and language areas (Tarapore et al. 2016). As the application domain of TMS continues to grow, coil designs are increasingly tailored to specific needs, which is not only essential for optimizing outcomes but may also introduce large variability in stimulation parameters across clinical and research settings (Talebinejad and Musallam 2010; Epstein 2008).

In clinical applications, different coils are utilized for specific purposes, such as motor threshold (rMT) assessments and therapeutic repetitive TMS (rTMS) interventions. Coils for motor assessments are generally light in weight, designed for enhanced maneuverability and precision in targeting, while those designed for therapeutic applications are heavier and prioritize effective cooling during prolonged use. Prior research indicates that rMT in units of stimulator output can differ significantly between coil types (Wang et al. 2023). This is expected, as extensive computational and empirical comparisons have demonstrated that differences in coil wire winding geometries fundamentally alter the focality, depth of penetration, and overall distribution of the induced E‐field (Deng et al. 2013; Drakaki et al. 2022; Thielscher and Kammer 2004). Consequently, if different coil models are used for rMT assessment and treatment for patients undergoing TMS therapy, it may be necessary to perform re‐thresholding when the coil is changed. This additional step potentially complicates clinical workflows and introduces variability in treatment administration.

While certain coil pairs, like the MagVenture C‐B60 and Cool‐B65 (MagVenture, Farum, Denmark), are designed with near‐identical coil geometries for interchangeability within specific applications (e.g., mapping/assessment vs. therapy), broader standardization across coils remains a significant challenge. Differences in coil winding geometry, construction materials, and coil‐stimulator interfaces across manufacturers result in large variability in the induced E‐fields (Drakaki et al. 2022; Lu and Ueno 2017) that is considered the primary physical quantity determining TMS‐induced neuronal activation (Siebner et al. 2022). Although advances in computational modeling have enabled subject‐specific estimation of E‐fields within anatomically realistic head models (Stenroos and Koponen 2019; Dannhauer et al. 2024), and prior work has explored links between calculated E‐fields and physiological outcomes (Laakso et al. 2018; Opitz et al. 2013), a fundamental question remains open: is the cortical E‐field magnitude required to reach a specific neural activation threshold (e.g., rMT) constant irrespective of the coil design when factors like coil position, orientation, pulse waveform, subject state and anatomy are fixed? Confirming different aspects of the E‐field invariance would support its use as a physiologically valid and coil‐independent metric for TMS intensity, offering an alternative to conventionally reported device‐specific output settings.

Here, we propose and validate a method that uses computational E‐field modeling to predict the necessary stimulator output across different coils based on a single rMT measurement. We employed a recently developed approach based on the boundary element method (BEM) with a direct E‐field solver leveraging fast multipole method (FMM) for lower‐upper (LU) decomposition of the system matrix to ensure high computational accuracy and speed (Makaroff, Qi, et al. 2023). Since the E‐field simulation is significantly influenced by the tissue compartments included in the head model (Antonakakis et al. 2019; Nummenmaa et al. 2013), we conducted simulations using two subject‐specific head models of different complexity to assess the sensitivity of the predictions to such modeling assumptions. The first model is a detailed five‐layer representation that includes the scalp, skull, cerebrospinal fluid (CSF), grey matter, and white matter, comprehensively depicting a realistic head conductivity profile. The second model is a simplified three‐layer representation consisting of the scalp, skull, and intracranial space, which offers an alternative solution suitable for a wide range of clinical settings (Ponasso et al. 2024) where magnetic resonance imaging (MRI) quality may pose a challenge for highly accurate segmentation and meshing of the boundaries of cortical grey matter that may be only a few millimeters thick (Gopinath et al. 2024).

Through computational and experimental validation, we demonstrate that adjusting stimulator settings based on consistent E‐field values enables uniform stimulation across different coil types. This approach has the potential to better standardize stimulation intensity, enhancing cross‐study comparability and improving clinical outcomes by reducing variability in TMS dosing.

2. Methods

Thirteen healthy, right‐handed participants (6 males, 7 females; mean age ± SD: 33 ± 14 years) with no history of neurological or psychiatric disorders were recruited for this study. Ten participants were included in the primary analysis, while a subset of three participants underwent an additional three‐coil comparison (reported in the Supporting Information). Exclusion criteria included contraindications for MRI or TMS, such as metallic implants, electronic devices, pregnancy, or a history of epilepsy. All participants provided written informed consent prior to participation. The study protocol was approved by the institutional review board (IRB) at Massachusetts General Hospital and followed the guidelines of the Declaration of Helsinki.

2.1. MRI Acquisition

Participants attended two experimental sessions scheduled on separate days (Figure 1). Structural MRI scans were acquired using a 3 T Siemens Skyra scanner (Siemens Healthcare, Erlangen, Germany) during the first session. T1‐weighted scans were acquired using a MEMPRAGE sequence with the following parameters: TR = 2530 ms, TE = 1.76 ms, flip angle = 7°, FOV = 256 × 256 mm², and voxel size = 1 × 1 × 1 mm³. T2‐weighted images from T2‐SPACE sequence maintained consistent readout bandwidth, FOV, and voxel dimensions with the T1‐weighted scans, while utilizing a TR = 3200 ms, TE = 566 ms, and flip angle = 120°. The MRI scans were used to ensure precise coil placement over the motor cortex using neuronavigation (Localite GmbH, Bonn, Germany) and enabled offline subject‐specific modeling of the E‐field induced during stimulation.

FIGURE 1.

Schematic diagram of the experimental procedure. (A) Structural MRI was performed during the first visit to obtain personalized T1‐ and T2‐weighted images. (B) Resting motor threshold (rMT) measurements were conducted during a separate visit. The motor hotspot was first identified using the Cool‐B35 coil, followed by rMT measurement. Subsequently, rMT for the C‐B60 coil was measured at the same location. Coil positioning was monitored and verified using a neuronavigation system.

2.2. TMS Procedure

On the second visit, participants underwent rMT measurements with two TMS coil types: Cool‐B35 and C‐B60 (with coil winding outer diameters of 2 × 46 mm and 2 × 75 mm, respectively). TMS was delivered to the left primary motor cortex (M1) using a TMS stimulator (MagPro X100, MagVenture), with coil positioning guided by the neuronavigation system. The smaller Cool‐B35 coil was first used to identify the motor hotspot, defined as the scalp location where stimulation consistently elicited the largest motor‐evoked potentials (MEPs) from the first dorsal interosseous (FDI) muscle (Kleim et al. 2007). The motor hotspot search was performed manually by an experienced TMS operator using neuronavigation guidance. The search was initiated over the hand area of the left primary motor cortex (“inverted Ω”) and the coil was moved iteratively across nearby scalp positions to identify the location that produced the largest and most consistent MEPs in the FDI muscle. At each position, several pulses were delivered before moving to the next location, and the coil orientation was maintained at approximately 45° to the midline. The smaller coil was used first because its higher focality allowed more precise hotspot localization; if the larger, less focal coil had been used first, the identified hotspot might not have corresponded optimally to that of the smaller coil, reducing spatial consistency in the coil comparison. Once the hotspot was located, rMT was measured with the Cool‐B35 coil. The same location and orientation were then used to remeasure the rMT with the larger C‐B60 coil, enabling a direct within‐subject comparison between the two coil types. The orientation for both coils was about 45° to the anterior–posterior axis. The rMT was defined as the lowest stimulation intensity that produced MEPs ≥ 50 μV peak‐to‐peak in at least 5 out of 10 consecutive trials (Rothwell et al. 1999).

2.3. EMG Measurement

Surface electromyography (EMG) recordings were obtained from the FDI muscle of the dominant hand using TMS‐compatible Ag/AgCl C‐shaped electrodes (Easycap GmbH, Wörthsee, Germany) in a bipolar belly‐tendon configuration. The ground electrode was positioned over the ulnar styloid process. Before electrode placement, the skin was prepared with abrasive gel to reduce impedance to below 10 kΩ. EMG signals were recorded at a sampling rate of 20 kHz (Bittium NeurOne, Oulu, Finland) and were subsequently band‐pass filtered between 20 and 1000 Hz. Participants were instructed to remain fully relaxed throughout the procedure, and pre‐stimulus EMG activity was visually inspected online to exclude trials with muscle pre‐activation or excessive artifact. MEP amplitudes were defined as the peak‐to‐peak amplitude of EMG responses occurring within a 20–50 ms window following TMS pulses (Schoisswohl et al. 2024). The measurements were performed in an electromagnetically shielded room to minimize electromagnetic noise in the EMG recordings.

2.4. E‐Field Simulation and rMT Prediction

E‐field simulations at the mid‐grey layer (i.e., middle space between the boundaries of grey and white matters) were conducted offline at the exported coil positions from the neuronavigation system for each TMS session. These simulations were performed using the BEM‐FMM‐LU method for both coils (Makaroff, Qi, et al. 2023). E‐field simulations were based on detailed coil models that incorporated the full coil geometry, including the winding layout and outer housing. The TMS models were based on previous work (Makaroff, Nguyen, et al. 2023; Tang et al. 2025). To validate the simulated coil models, the magnetic field distributions were measured using a commercially available probe MagProbe 3D (MagVenture), mounted on a custom‐built computer numerical control positioning system. The probe was used to scan peak dB/dt values in the measurement plane, enabling comparison between measured and simulated coil field distributions, maintaining an error within ±5% of the probe's accuracy.

Two head models were generated from MRI data using the SimNIBS software with the headreco pipeline (Saturnino et al. 2019): (1) a detailed five‐layer model consisting of the scalp, skull, cerebrospinal fluid (CSF), grey matter, and white matter; and (2) a simplified three‐layer model comprising the scalp, skull, and intracranial space. Tissue conductivities were assigned as follows: scalp (0.465 S/m), skull (0.01 S/m), CSF (1.654 S/m), grey matter (0.275 S/m), white matter (0.126 S/m), and intracranial space (0.685 S/m, as an average value across CSF, grey, and white matters) (Wagner et al. 2004). In addition to subject‐specific simulations, E‐field computations in free space were performed to directly compare the intrinsic field profiles of the two coils without tissue conductivity boundaries, with sampling over the same mid‐grey‐layer surface used in the head‐model analysis.

The E‐fields were simulated for both coils at their respective rMT values. Additionally, E‐fields were calculated for the C‐B60 coil at 100% maximum stimulator output (MSO). Then predicted rMTs for the C‐B60 coil were derived using a ratio of E‐field values (Equation 1). The mean E‐field values in the 80%–100% maximum range were used in all analyses.

$$E_{\mathrm{th}}=-\frac{d{I}_{\mathrm{B}35}}{\mathit{dt}}\times L_{\mathrm{B}35}\left(r\right)=-\frac{d{I}_{\mathrm{B}60}}{\mathit{dt}}\times L_{\mathrm{B}60}\left(r\right),\frac{\mathit{dI}}{\mathit{dt}}\propto \%\mathrm{MSO}$$ (1)

where $E_{\mathrm{th}}$ is the E‐field threshold required to elicit neuronal stimulation. The terms $\frac{d{I}_{\mathrm{B}35}}{\mathit{dt}}$ and $\frac{d{I}_{\mathrm{B}60}}{\mathit{dt}}$ represent the rate of current change for the Cool‐B35 and C‐B60 coils, respectively. $L_{\mathrm{B}35}\left(r\right)$ and $L_{\mathrm{B}60}\left(r\right)$ denote the spatially dependent coil sensitivity profiles computed separately for each coil using the BEM‐FMM‐LU simulations, which are influenced by factors such as coil geometry, wire winding, head anatomy, and tissue conductivity.

In detail, let ${\mathcal{E}}_{\mathrm{B}35}$ denote the full set of E‐field magnitudes sampled across the cortical surface when stimulating with the Cool‐B35 coil at the subject's measured rMT intensity, and ${\mathcal{E}}_{\mathrm{B}60}$ be the full set of E‐field values for the C‐B60 coil at 100% MSO. Then, $\max \left({\mathcal{E}}_{\mathrm{B}35}\right)$ and $\max \left({\mathcal{E}}_{\mathrm{B}60}\right)$ are the respective maximum E‐field values in those sets.

Define the E‐field subsets in the 80%–100% maximum range as follows:

$$E_{\mathrm{B}35}\subseteq {\mathcal{E}}_{\mathrm{B}35}\mathit{\text{where}}{E}_{\mathrm{B}35}=\left\{{\epsilon }_i\in {\mathcal{E}}_{\mathrm{B}35}|0.8\max \left({\mathcal{E}}_{\mathrm{B}35}\right)\le {\epsilon }_i\le \max \left({\mathcal{E}}_{\mathrm{B}35}\right)\right\}$$

$$E_{\mathrm{B}60}\subseteq {\mathcal{E}}_{\mathrm{B}60}\mathit{\text{where}}{E}_{\mathrm{B}60}=\left\{{\epsilon }_j\in {\mathcal{E}}_{\mathrm{B}60}|0.8\max \left({\mathcal{E}}_{\mathrm{B}60}\right)\le {\epsilon }_j\le \max \left({\mathcal{E}}_{\mathrm{B}60}\right)\right\}$$

Then, the predicted rMT for the C‐B60 coil is computed as:

$$\mathrm{rM}{\mathrm{T}}_{\mathrm{B}60\_\text{predicted}}=\left(\frac{\frac{1}{\left|E_{\mathrm{B}35}\right|}{\sum }_{{\epsilon }_i\in E_{\mathrm{B}35}}{\epsilon }_i}{\frac{1}{\left|E_{\mathrm{B}60}\right|}{\sum }_{{\epsilon }_j\in E_{\mathrm{B}60}}{\epsilon }_j}\right)\times 100$$ (2)

where: $\left|E_{\mathrm{B}35}\right|$ and $\left|E_{\mathrm{B}60}\right|$ denote the number of E‐field samples in the delineated sets for Cool‐B35 and C‐B60, respectively; ${\epsilon }_i$ and ${\epsilon }_j$ are the individual E‐field values within the 80%–100% maximum range.

The quantitative analysis involved two separate comparisons. First, we compared the measured C‐B60 rMT with the Cool‐B35 rMT using a linear regression model of y = b × x. Second, we assessed the correlation between the predicted and measured rMT values for the C‐B60 coil, assuming an ideal one‐to‐one correspondence (y = b × x, with b ≡ 1) for the E‐field‐based approach. The quality of both models was assessed through R² values and residual analysis. Paired t‐tests were used to compare matched measurements between two conditions. For comparisons involving three groups, one‐way analysis of variance (ANOVA) was performed, followed by Fisher's protected least significant difference (LSD) post hoc tests when the omnibus ANOVA was significant. Given the limited number of group comparisons, this method was selected to balance statistical sensitivity and control of Type I error.

3. Results

As expected, based on the different wire winding geometries, the measured rMT values showed a significant difference between the two coils (paired t‐test, p < 0.05), with 62% ± 14% MSO (83 ± 20 A/μs) for the Cool‐B35 and 42% ± 6% MSO (63 ± 9 A/μs) for the C‐B60 (Figure 2A). On average, the rMT for C‐B60 was 1.48 ± 0.15 times lower than that of Cool‐B35. In free space, the E‐field at rMT was significantly higher for C‐B60 (paired t‐test, p < 0.01), by a factor of 1.08 ± 0.03. However, when computed using personalized either simplified or detailed head models, the E‐field values at rMT did not differ between the two coils (Figure 2B). Figure 3 shows an example of computationally estimated cortical E‐field distribution for both Cool‐B35 and C‐B60 coils using the two different head models.

FIGURE 2.

Within‐subject comparison of TMS intensity and corresponding E‐field values at rMT for different coil types. (A) TMS intensity at rMT is shown in both % maximum stimulator output (%MSO) and the rate of current change (dI/dt). (B) Corresponding E‐field values were estimated in free space or using simplified and detailed head models. In each boxplot, the central line represents the median, the box edges indicate the 25th and 75th percentiles (interquartile range, IQR), and the whiskers extend to the most extreme data points within 1.5 times the IQR. The colored dotted lines connect the paired measured values for each participant. An asterisk (*) indicates a statistically significant difference between coil types (p < 0.05, paired t‐test).

FIGURE 3.

Representative E‐field distributions at the respective rMT intensities for the Cool‐B35 and C‐B60 coils. The simulation was performed using (A) a detailed and (B) a simplified head model. The dashed regions highlight the 80%–100% maximum E‐field range. Note both models show a similar intensity range between the two coils.

To investigate the accuracy of different “coil‐to‐coil” rMT prediction methods, we compared the rMT values measured with C‐B60 values with those derived from three approaches: (1) a direct scaling from Cool‐B35 with b = 0.66 (found with the least squares method), (2) a simplified E‐field model, and (3) a detailed E‐field model. Direct scaling exhibited the largest deviation from measured rMT (RMSE = 6.1%, R² = 0.49; Figure 4A), while E‐field models showed higher accuracy (simplified: RMSE = 1.32%, R² = 0.95; detailed: RMSE = 1.26%; R² = 0.96; Figure 4B,C). The residual analysis further confirmed these trends (Figure 4D), with direct scaling showing a mean residual of 3.2 ± 2.4 compared to 1 ± 0.8 (simplified) and 0.8 ± 1.0 (detailed). A repeated‐measures ANOVA (F(2,18) = 6.00, p = 0.01) and post hoc least significant difference tests revealed that direct scaling differed significantly from both E‐field methods (p = 0.04 vs. simplified; p = 0.01 vs. detailed), while no significant difference was detected between the two E‐field approaches. Maximum deviations from measured rMT were 7% MSO (direct scaling), 2% MSO (simplified), and 3% MSO (detailed).

FIGURE 4.

Comparative analysis of C‐B60 coil rMT prediction methodologies based on Cool‐B35 data as input. (A) Linear regression showing direct scaling from Cool‐B35 to C‐B60 rMT values. (B) Simplified E‐field model predictions versus measured C‐B60 rMT values. (C) Detailed E‐field model predictions versus measured C‐B60 rMT values. Shaded regions in panels (A), (B), and (C) represent the estimated standard error in the regression fit. (D) Residual error analysis across all methods. Asterisks (*) indicate statistically significant differences (p < 0.05, ANOVA with LSD post hoc analysis). Compared to direct scaling, both E‐field–based methods yielded significantly lower prediction errors, with the detailed model achieving the highest accuracy.

4. Discussion

This study introduces an E‐field‐based method to standardize TMS stimulator output across different coil designs. Traditionally, TMS intensity is adjusted relative to the rMT, but studies have pointed out that rMT varies significantly across commonly used coil types, indicating that this must be considered in the experimental design (Wang et al. 2023). Unless equivalent by design, separate rMT measurements are needed for each coil, which increases experiment duration, participant discomfort, and accumulation of experimental error. By providing a consistent metric for stimulation intensity, our approach directly addresses these challenges, making it possible to better standardize stimulation intensity across different coils for each individual person. This method may enhance reproducibility in both research and clinical applications.

Our findings demonstrate that directly scaling rMT across coil types introduces substantial error, while the E‐field–based approach obtained from personalized head models provides significantly more accurate estimations. The most precise predictions were achieved using a detailed five‐layer head model, with only slightly reduced accuracy when using a simplified three‐layer model. Although the five‐layer model offers higher accuracy, its application may be limited by the spatial resolution of the MRI acquisition. Even a standard clinical MRI scan, though not optimized for tissue segmentation, can reasonably delineate and localize grey and white matter layers. However, its resolution may still be insufficient to generate a mesh of these layers with the precision (Gopinath et al. 2024) needed for reliable E‐field simulations (Gomez et al. 2020). The simplified, three‐layer model may be a practical alternative for such cases. In this work, to directly compare detailed and simplified head models for E‐field‐based rMT prediction, the E‐field values were projected onto the mid‐grey matter layer of a detailed head model. To further assess the clinical feasibility of this E‐field‐based approach, rMT was also estimated using E‐field values from a curvilinear surface within the intracortical space, located 5 mm below the CSF boundary. The low mean absolute error of 1.5% MSO between measured and these rMT estimates supports the robustness of the three‐layer model for clinical applications (Table S1). As expected, there are some systematic differences in the absolute amplitudes of the E‐fields between simplified and realistic models, due to the conductivity profiles being different. Since the prediction model is based on the E‐field ratio between the coils, the absolute amplitudes do not have an influence on the accuracy. However, from the standardization viewpoint, it would be useful to determine the best “effective” conductivity for the simplified model to give the best amplitude match between the two. Indeed, this has been proposed for electromagnetic brain mapping (Stenroos and Nummenmaa 2016) that could be readily extended to brain stimulation.

While direct scaling between coils would be an attractive and simple approach in clinical settings, our results indicate that it is substantially less accurate than subject‐specific E‐field modeling. This suggests that precise coil‐to‐coil correspondence cannot be reliably estimated without accounting for individual anatomy. However, in scenarios where subject‐specific E‐field simulations are not clinically feasible, an intermediate alternative is to utilize the coil's primary E‐field in free space with coil‐to‐cortex distance correction. As our data show, utilizing free‐space E‐field parameters still yields a better correspondence between coils than relying solely on stimulator output metrics without any spatial E‐field information (Figure 2B).

Under matched coil position, orientation, and head‐modeling conditions, our findings suggest that rMT corresponds to a relatively stable cortical E‐field magnitude within a given individual across different coil types. In many participants, the estimated E‐field values within the sampled high‐field cortical region clustered around approximately 100–120 V/m, supporting the view that cortical E‐field strength may serve as a more physiologically relevant reference for TMS dosing than device‐specific stimulator output alone. Importantly, this observation should not be interpreted as defining a universal absolute threshold in V/m across individuals, nor as identifying the exact local field at the true neural activation site. Rather, it indicates that, within the empirically defined cortical region used in the present analysis, this range may provide a useful initial estimate of stimulation threshold under controlled conditions.

Because the exact functional hotspot and underlying neural activation locus were not directly known, we approximated the relevant cortical target using the region spanning 80%–100% of the maximum E‐field. This provided a practical macroscopic criterion for coil‐to‐coil comparison, intended to capture the high‐field cortical region most likely to overlap the relevant motor target. Although this choice remains empirical, additional sensitivity analyses showed that prediction accuracy changed only modestly when the E‐field threshold range was varied across a broad interval (50%–100%, in 5% increments; Table S2), indicating that the method is relatively robust to the precise percentile cutoff used to define the sampled region. The present model also operates at the anatomical and electromagnetic macroscopic scale and does not incorporate microscopic determinants of activation, such as local neuronal morphology, cytoarchitecture, or white matter fiber orientation, which should be considered in future work.

Beyond electromagnetic factors, rMT is influenced by physiological variables not explicitly captured by the present E‐field model, including fluctuations in cortical excitability, attention, arousal, and pharmacological modulation. In addition, the ratio‐based formulation assumes that coil‐to‐coil differences in motor threshold can be approximated from relative cortical E‐field magnitudes under matched stimulation conditions. Although this approximation reduces sensitivity to absolute modeling errors and performs well in the present data, it may not fully capture the nonlinear and state‐dependent dynamics of neuronal recruitment near threshold. Accordingly, our framework addresses the biophysical standardization of stimulation intensity across coils but does not fully account for inter‐individual or intra‐individual variability arising from these non‐electromagnetic and nonlinear factors. Nevertheless, when TMS procedures are carefully standardized, rMT has been shown to exhibit good within‐subject test–retest reliability (Schambra et al. 2015), supporting its use as a reasonably stable reference measure for individualized dosing.

It is important to note that in this study, coil‐to‐coil rMT prediction models were evaluated using a fixed coil orientation. Previous studies have demonstrated that coil orientation significantly affects rMT values (Richter et al. 2013; Balslev et al. 2007). Since the intracranial space is modeled as homogeneous in the simplified model, it exhibits reduced E‐field variation with respect to orientation changes, which may lead to greater discrepancies in rMT prediction accuracy when coil orientation varies (Bungert et al. 2017). In addition, part of the directional specificity is also likely to be of neuronal origin (Seo et al. 2017; Radman et al. 2009), as different neuronal populations are maximally sensitive to different E‐field orientations. However, from the practical viewpoint of predicting the rMT between two coils, our data show that for the commonly used orientation (~45° to the anterior–posterior axis), the accuracy is quite remarkable (RMSE ~1% MSO). Future studies will include an assessment of coil‐to‐coil predictions across multiple orientations to comprehensively validate the approach.

It is worth mentioning that the accuracy of our rMT estimations depends on precise optical coil localization to the cortical hotspot. Additional rMT measurements on a single subject revealed that when the coils were positioned at the optimal location (determined by the lowest rMT), the discrepancy between predicted and measured rMT was 1% MSO (51% vs. 52% MSO, respectively). However, when the coil was placed about 10 mm apart from the optimal location, the prediction error increased to 8% MSO (48% vs. 56% MSO). This discrepancy can be explained by the underlying assumption of our approach: the E‐field threshold required to elicit a motor response (E_th) within the functional motor region is invariant across coil geometries. However, the exact cortical activation region is unknown in this study; therefore we approximate E_th using the average E‐field magnitude within the top 80%–100% of the maximum field, assuming that this high‐intensity region overlaps the motor hotspot when the coil is optimally placed. However, if the coil is misaligned, the 80%–100% E‐field regions for the two coils may fall outside the true motor area due to non‐linear differences in their E‐field distribution. As a result, even if the E_th values are similar, the high‐intensity E‐field value may not reflect the activation threshold of the motor region, leading to larger prediction errors (for illustration of these effects, see Figure S1).

Several methods have been proposed for mapping cortical regions associated with motor function, which could aid in more precise coil placement (Weise et al. 2023; Gomez et al. 2021). Future research will focus on integrating real‐time E‐field monitoring into individualized brain models to enhance the capability of finding the true scalp “hot spot” (Daneshzand et al. 2021), thereby increasing the precision of the rMT. This localization challenge also applies to re‐thresholding procedures that do not employ modeling: inaccurate identification of the scalp hot spot during mapping will correspondingly compromise rMT estimates for the treatment coil.

In a subset of participants (n = 3), the detailed head model exhibited a marginally higher prediction error than the simplified model. This discrepancy may be driven by nonlinear differences in the spatial distribution and decay of the E‐fields between the two coils. Specifically, if the maximum E‐field is not perfectly aligned with the true functional hotspot, these differences in spatial spread can alter how effectively each coil stimulates the relevant motor target. These observations emphasize that precise scalp coil positioning is a critical determinant of prediction accuracy. It is also noteworthy that cortical mapping in our procedure was performed using the Cool‐B35 coil, which provides more focal stimulation and may therefore have facilitated accurate hotspot localization. Overall, the results indicate that the approach is reasonably robust, provided that coil placement is closely matched to the functional target.

Comparisons of E‐field profiles between different coil designs played critical role in early studies that established fundamental principles of TMS‐induced activation, particularly to localize the cortical sites responsible for motor responses. These investigations demonstrated that motor thresholds for hand movements are primarily associated with superficial cortical regions, with effective stimulation localized to the gyrus lip or sulcal wall rather than deeper white matter structures (Epstein et al. 1990; Rudiak and Marg 1994). A central assumption underlying these early studies was that the E‐field magnitude at the stimulation site remains consistent across coil types. Here, we provide the first experimental evidence validating this assumption under matched coil orientation, position, and head‐modeling conditions. Importantly, we show that achieving consistency in E‐field values requires subject‐specific head models, as estimates based on free‐space conditions can result in substantial discrepancies.

The present study does not address the question of determining the absolute stimulation depth or locus. Rather, our aim was to test whether the peak cortical E‐field amplitude predicts the rMT for a given individual subject irrespective of the coil used. Because our findings demonstrate a very high matching accuracy between the E‐fields, the top of the gyrus appears to be a plausible candidate for the stimulation locus close to the threshold. While the discontinuity of the normal component of the E‐field at the grey‐white interface has been proposed as a mechanism for TMS activation, modeling studies indicate that at low intensities near rMT, the lowest threshold activations predominantly occur within the grey matter (Aberra et al. 2020; Salvador et al. 2011). Taken together, these physiological considerations support sampling within the grey matter rather than exactly at the tissue boundary. We therefore used the mid‐grey layer as a practical sampling surface, as evaluating the E‐field directly at tissue boundaries is complicated in BEM‐based framework by the discontinuity of the normal E‐field component at the interface. Consequently, the mid‐grey layer provides both a physiologically relevant site and a robust, reproducible approximation for comparing rMT predictions across conditions. Future studies combining individualized head modeling with neuronal activation models may help refine this interpretation.

Despite the highly accurate rMT prediction results, several limitations should be considered. First, the relatively small sample size may limit the generalizability of the findings. In addition, because the study included only healthy participants, the applicability of the results to clinical populations remains uncertain. Nevertheless, the findings were consistent across participants and showed good reproducibility, supporting the robustness of the main observation within this cohort. Second, validation was performed using only two figure‐of‐eight coils, and therefore the generalizability of the method to other coil geometries remains to be established. Nonetheless, the two tested coils differed substantially in size, providing an initial proof‐of‐principle across distinct focality profiles. Additional measurements in three subjects using a third figure‐of‐eight coil (MRI‐B91, MagVenture; outer diameter: 2 × 2 layers × 79/92 mm) yielded a similarly matched cortical E‐field magnitude at rMT across all three coils (Table S3), further supporting the underlying hypothesis.

Moreover, our approach was performed with a fixed current direction and magnetic pulse waveform, and its performance under varying stimulation conditions remains to be evaluated. Incorporating models such as the strength–duration curve (Peterchev et al. 2011), which accounts for the relationship between pulse duration and neural excitability thresholds, could extend our pipeline to predict the rMT across different TMS pulse durations. Furthermore, by combining this model with empirical fitting techniques, it may be possible to develop a unified framework capable of estimating rMT for different TMS waveforms, including monophasic, biphasic, and polyphasic pulses (Casula et al. 2018; Goetz and Deng 2017). We also note that %MSO is only an indirect device‐specific measure of output, and its relationship to the rate of change of coil current (dI/dt) may deviate from linearity across the full stimulation range, particularly at higher outputs, depending on stimulator electronics and pulse‐shaping characteristics. Since the induced E‐field is more directly proportional to dI/dt, direct dI/dt readouts from the stimulator, when available, may provide a more robust basis for E‐field‐based standardization. In addition, future implementations could incorporate adaptive threshold‐hunting methods such as PEST to reduce the number of stimuli required for rMT determination and improve procedural efficiency while maintaining comparable threshold estimates (Borckardt et al. 2006).

Our findings align with prior research highlighting E‐field magnitude as a reliable determinant of neural activation (Numssen et al. 2024). By shifting towards E‐field–based standardization of activation thresholds, the proposed approach minimizes the variability inherent in MSO‐based methods, improving the comparability of TMS protocols across studies. This standardization is particularly valuable in multi‐site studies and meta‐analyses, where coil‐related differences can otherwise confound outcomes. In clinical practice, tailoring TMS parameters based on individualized E‐field modeling, rather than relying on a one‐size‐fits‐all rMT, may lead to more precise and consistent therapeutic interventions for neurological and psychiatric disorders.

5. Conclusion

In summary, this study demonstrates that E‐field–based standardization offers a precise and reliable method for determining TMS stimulator output across different coil types. By addressing the limitations of conventional dosing strategies, this approach can potentially enhance reproducibility, comparability, and therapeutic efficacy in both research and clinical settings. Future research initiatives should focus on refining real‐time E‐field estimation techniques and incorporating these methods into routine TMS protocols to maximize their clinical utility.

Author Contributions

Evgenii Kim: writing – review and editing, writing – original draft, visualization, software, investigation, formal analysis, data curation, methodology, validation. Mohammad Daneshzand: writing – review and editing, software, investigation, data curation, validation. Keren Zhu: writing – review and editing, software. Danyal Fareed Bhutto: writing – review and editing, software, data curation. Teresa Jacobson Kimberley: writing – review and editing, investigation. Dylan Edwards: writing – review and editing, investigation. Netri Pajankar: writing – review and editing, project administration, data curation. Parker Kotlarz: writing – review and editing, project administration. Tommi Raij: writing – review and editing, investigation. Sergey N. Makaroff: writing – review and editing, software, investigation. Aapo Nummenmaa: supervision, resources, methodology, investigation, funding acquisition, conceptualization, writing – review and editing, validation.

Funding

This work was supported by NIH R01MH128421, R01DC020891, P41EB030006, S10OD028668, K01MH138823, R01MH130490, R01EB035484, K24DC018603, R01NS126337, and the Chernowitz Medical Research Foundation.

Conflicts of Interest

Aapo Nummenmaa is named inventor in patents and patent applications related to TMS. Tommi Raij and Mohammad Daneshzand are named inventors in patent applications related to TMS.

Supporting information

Table S1: Resting motor thresholds (rMT) measured with the C‐B60 coil for each individual and corresponding rMT values predicted using a simplified three‐layer head model. Predictions were based on electric field (E‐field) estimates sampled at two locations: the mid‐grey matter surface and a curvilinear surface 5 mm beneath the cerebrospinal fluid (CSF) boundary. The mean absolute error (MAE) reflects the average absolute difference between measured and predicted rMT values. All values are reported as a percentage of the maximum stimulator output (% MSO).

Table S2: Sensitivity analysis of prediction accuracy across different E‐field threshold ranges used to define the sampled region. RMSE values changed only modestly as the threshold range was varied from 50%–100% to 95%–100% in 5% increments, indicating that model performance was relatively robust to the precise percentile cutoff used.

Table S3: Comparison of simulated E‐field magnitudes at resting motor threshold across three TMS coils (Cool‐B35, C‐B60, MRI‐B91) for individual participants.

Figure S1: Impact of coil positioning on electric field (E‐field)‐based resting motor threshold (rMT) prediction accuracy. The left column shows two coils (Cool‐B35 and C‐B60) positioned relative to the cortex under optimal (top) and non‐optimal (bottom) conditions. The right column displays corresponding simplified 1D E‐field distributions along a representative cortical axis (blue: Cool‐B35; orange: C‐B60), with matched E‐field within functional motor locus (E_th). Under optimal positioning, both coils generate overlapping regions of 80%–100% maximum E‐field intensity, enabling accurate rMT predictions. In contrast, when both coils are displaced from the cortical hotspot, differences in field focality and spatial decay lead to non‐overlapping 80%–100% E‐field regions, resulting in increased rMT prediction errors.

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.