Reproducible magnetophosphene thresholds induced by transcranial alternating magnetic stimulation in humans: a replication study

Abstract

Magnetophosphenes, flickering visual percepts induced by extremely low-frequency magnetic fields (ELF-MF), represent the most sensitive and reproducible human response to induced electric fields and form a cornerstone of international exposure guidelines. Transcranial Alternating Magnetic Stimulation (tAMS), a recent non-invasive stimulation method, can elicit magnetophosphenes without scalp sensations, but its reliability and underlying mechanisms require replication for further validation. This replication study quantified magnetophosphene perception thresholds in 62 healthy participants exposed to sinusoidal magnetic fields (0–50 mT) at 20, 50, and 60 Hz. Three stimulation configurations were tested: retinal (RET), global head (GLO), and occipital (OCC). Perception probability was modeled using mixed-effects logistic regressions based on rate of change of magnetic flux density over time (dB/dt) as the primary metric. tAMS robustly induced magnetophosphenes, reproducing the threshold patterns reported by Legros et al. (2024). RET and GLO exposures produced steep dose-response curves and low thresholds, whereas OCC stimulation yielded minimal effects. Thresholds were strongly frequency-dependent, with highest sensitivity at 20 Hz. Regression slopes from the original and replication datasets showed high concordance (r = 0.965), confirming reproducibility. The spatial and frequency profiles consistently support a retinal, rod-mediated origin of magnetophosphenes. This replication study validates tAMS as a reliable method for eliciting magnetophosphenes and confirms their retinal origin across exposure conditions. These results strengthen the use of magnetophosphene thresholds as a benchmark for ELF-MF safety standards and underscore the potential of tAMS as a precise, comfortable, and confound-free neuromodulation tool for future diagnostic and therapeutic applications.

Introduction

Magnetophosphenes, achromatic flickering visual perception occurring without light stimuli, have long been recognized as a reproducible reliable biomarker of the central nervous system’s (CNS) response to extremely low-frequency (ELF) magnetic fields (MF) (< 300 Hz) of sufficient strength. First observed in the late 19th century by d’Arsonval¹, magnetophosphenes have since become essential in studies on human sensitivity to ELF-MF exposures. Indeed, they not only provide a non-invasive way to assess the effects of these fields on the human CNS, but their strong connection with ELF-MF exposure has established them as a conservative benchmark² for setting international safety limits for both public and occupational exposure.

Indeed, international standards and guidelines from organizations such as the International Commission on Non-Ionizing Radiation Protection (ICNIRP) and the Institute of Electrical and Electronics Engineers’ International Committee on Electromagnetic Safety (IEEE-ICES) aim to prevent adverse effects and mitigate potential health risks by keeping ELF-MF exposure well below levels known to induce phosphenes, which could signal nervous system modulation as consequences of electrostimulation^3,4.

Recently, the study of magnetophosphenes has expanded beyond safety applications to include explorations of novel brain stimulation technologies, notably transcranial Alternating Magnetic Stimulation (tAMS)⁵. tAMS builds upon the physical principles of conventional transcranial magnetic stimulation (TMS), in which time-varying magnetic fields induce electric currents in neural tissue via electromagnetic induction. However, whereas standard TMS delivers brief, high-intensity magnetic pulses designed to elicit action potentials in cortical neurons^6,7, tAMS employs continuous sinusoidal waveforms at lower intensities. Rather than triggering direct neuronal firing, this approach is designed to generate subthreshold oscillatory electric fields⁵.

Unlike traditional non-invasive electric brain stimulation methods that require direct contact with the scalp using electrodes, tAMS uses sinusoidal MF to induce low-intensity electric fields (EF) directly in the brain non-invasively. This new approach generates EF values similar to those produced by transcranial Alternating Current Stimulation (tACS)⁵ which, interestingly, also induces phosphenes, known, in this case, as “electrophosphenes”^8–20. Note that frequency classification differs across disciplines. The ELF range in the bioelectromagnetic context goes up to 300 Hz, whereas in non-invasive brain stimulation (NIBS) research, rhythmic stimulation typically spans 1 to 100hz, corresponding to the endogenous neural oscillatory bands. As such, ELF range herein overlaps frequencies commonly targeted in NIBS.

tACS delivers low-amplitude sinusoidal currents to modulate brain activity²¹. Yet the EF distribution is significantly influenced by the anatomical properties of the head, which act as conductive or resistive pathways¹¹. The high resistance of the scalp and skull impedes current penetration, with the skull serving as a major barrier due to its low conductivity and variable thickness. Conversely, the highly conductive cerebrospinal fluid (CSF) redistributes currents across the brain’s surface, often reducing the depth of EF penetration¹¹. Within the brain, the differential conductivities of gray and white matter, alongside the orientation of neural structures, further shape the field distribution and its physiological effects. Blood vessels, due to the high conductivity of blood, introduce additional pathways for current redistribution^22,23. These anatomical factors lead to significant variability in EF distribution and stimulation efficacy across individuals¹¹.

Legros et al⁵. demonstrated that tAMS can effectively induce magnetophosphenes under controlled conditions. This finding suggests that tAMS could contribute to brain stimulation research. Unlike tACS, the tAMS’ELF-MF penetrate anatomical structures without being hindered, bypassing the resistive and conductive barriers imposed by the scalp, skull, and fluids^5,24–28. This property enables tAMS to generate deeper EF with greater strength, enhanced spatial focus, and orientation independence, providing potentially a precise and effective means of neural modulation. Additionally, by leveraging ELF-MF, tAMS overcomes key limitations of tACS, including skin discomfort and sensory cues at the scalp^22,29–32 By eliminating these confounds, tAMS improves participant comfort and could ensure more reliable interpretation of stimulation-induced neural effects, presenting a promising alternative for both experimental and therapeutic applications. Nonetheless, both tACS and tAMS techniques highlight phosphenes as a recognized intrinsic side-effect of non-invasive time-varying brain stimulations.

The precise anatomical origins of phosphene induction remain a topic of ongoing debate. With tACS, researchers have proposed three potential mechanisms: (1) phosphenes may originate in the cerebral cortex^15–18, (2) they may arise from retinal-level processes^{8,10,13,19,20}, or (3) both the retina and cortical regions may contribute, given their interconnected roles in visual perception¹⁵. Yet, by leveraging precise field orientation at specific anatomical targets and dosimetry models, Legros et al., using tAMS, have provided evidence that phosphenes are prone to being generated at the retinal level, most likely at the rod level⁵.

Although magnetophosphenes are promising for both basic neuroscience and regulatory purposes, the reliability of their induction using tAMS, especially across varying experimental conditions, requires thorough validation. While tAMS has shown potential, establishing its reliability in consistently evoking magnetophosphenes is crucial for ensuring it can be used reliably in research and potential future clinical contexts.

To address this, the present study aims to replicate and evaluate the reliability of tAMS in consistently inducing magnetophosphenes under precise experimental conditions. Specifically, we aim to (1) Assess the reproducibility of magnetophosphene thresholds by replicating experimental conditions and evaluating induction consistency across MF intensities (0–50 mT) and frequencies (20, 50, 60 Hz); (2) further provide evidence to clarify whether phosphenes originate from cortical or retinal modulation, or both; and (3) explore the translational relevance of magnetophosphene induction for the development of tAMS as a potential non-invasive brain stimulation tool.

By confirming the reproducibility of these findings, this study aims to further support the methodological relevance of tAMS for potential neuromodulation research and potential clinical applications, including diagnostic and therapeutic interventions. Furthermore, the results have significant implications for international safety standards, offering critical data that could shape guidelines and reaffirm magnetophosphenes as a robust indicator of safe ELF-MF exposure.

Materials and methods

This study followed a methodological framework similar to that described by Legros et al. (2024)⁵. All participants provided written informed consent prior to participation. The study protocol was reviewed and approved by the Institutional Review Board of the EuroMov Digital Health in Motion (DHM) Center (IRB-EM, notice no. 2111B) and complied with the ethical principles outlined in the Declaration of Helsinki for research involving human participants.

Participants

Sixty-five healthy volunteers participated in the study conducted at the EuroMov DHM Laboratory in Montpellier, France. Three of them were excluded due to recording data issue or non-respect of instructions. Individuals were excluded if they self-reported any history of the following: eye or retinal issues, claustrophobia, head injuries, neurological or cardiovascular diseases, chronic illnesses, a predisposition to seizures, permanent metal devices above the neck, or recreational drug use. Additionally, individuals with stimulators such as cardiac pacemakers, neural stimulators, auto-defibrillator, cochlear implants or insulin pump were ineligible. To minimize potential biases related to EF generation, participants were instructed to avoid exercise, alcohol, caffeine, and nicotine for 24 h before testing³⁰.

Experimental devices

This study replicated the methodological framework described in Legros et al⁵., whose exposure systems, coil geometries, dosimetric properties, and safety architecture were reproduced exactly for the present work. All MF generation systems, including coil construction, amplifier characteristics, winding configurations, and cooling mechanisms, were built according to the specifications reported in the original publication. As such, the technical description of the stimulation apparatus, field uniformity, dosimetry, and operational safety is provided in detail in Legros et al.⁵ and is not repeated here. Anatomically realistic modeling of induced current densities in retinal (see Fig. 2 in⁵) and in situ electric field in intracranial tissues (see Fig. 3 in⁵) has previously been performed for the same stimulation configurations.

Fig. 2.

Logistic regression models of magnetophosphene perception probability as a function of dB/dt (T/s) for each frequency-location combination. The rows correspond to frequency conditions (20 Hz, 50hz, 60 Hz), and columns to location conditions (OCC, RET, GLO). Points represent observed perception rates; solid lines show model predictions with 95% confidence intervals (shaded areas). Vertical dashed lines indicate perception thresholds (50% probability). Top axis shows the corresponding magnetic flux density (B, mT_RMS).

Fig. 3.

Comparison of Odds Ratios Between the Original Study and the Replication Across Frequencies and Stimulation Exposition. Original effects were plotted as black diamonds with 95% CI bars, while replication effects were plotted as colored (green = replicated; red = not replicated). The dashed vertical reference line at OR = 1 was added to indicate the null effect.

Experimental procedure

Phosphenes familiarization

Given the subjective and unfamiliar nature of phosphene perception, it was essential to ensure that participants understood what was expected and could reliably report their perceptions. To achieve this, a preliminary session was conducted before the experimental phase to familiarize participants with the visual characteristics of magnetophosphenes. This session took place under controlled conditions in total darkness, with participants keeping their eyes closed throughout and no prior visual dark adaptation was permitted. The familiarization process utilized the global exposure system and consisted of five stimulations, each lasting five seconds.

During this session, participants experienced three stimulations at a magnetic flux density of 25 mT with frequencies of 20 Hz, 50 Hz, and 60 Hz. Additionally, two stimulations were performed at 50 mT with frequencies of 20 Hz and 50 Hz. These higher flux densities were included because of their demonstrated efficacy in eliciting magnetophosphene perception³³. To provide adequate time for perceptual feedback and prevent carry-over effects, a 30-second interval was maintained between each stimulation.

Following each stimulation, participants engaged in a brief discussion to confirm whether they had perceived phosphenes and to describe their experiences. This iterative process allowed participants to develop a clear understanding of magnetophosphene characteristics and ensured reliable reporting. Once participants demonstrated sufficient familiarity with the phenomenon, the main experimental phase began.

Experimental phase

The volunteers were randomly assigned to three experimental groups corresponding to the 20 Hz, 50 Hz, and 60 Hz conditions, with group sizes of 20, 22, and 20 participants respectively (Table 1). In opposition to Legros et al⁵., the 100 Hz condition was not reconducted in this study. The rationale for this decision was taken given that no clear phosphene threshold has been established at this frequency in previous studies^5,34.

Table 1.

Participant demographics and group characteristics for the 20 Hz, 50 Hz, and 60 Hz experimental conditions.

Frequency	Age (years)	N	Sex (F/M)
20 Hz	22.6±2.9	20	5/15
50 Hz	24.0±4.0	22	10/12
60 Hz	26.2±8.8	20	15/5
Total	24.3±5.9	62	30/32

To further assess intra-study reliability and replicability, five different experimenters were involved in the data collection. They were randomly assigned to participants across sessions to minimize experimenter-specific effects and to evaluate the consistency of the observed effects independently of the experimenter.

During the experimental phase, participants were exposed to 11 MF levels, ranging from 0 to 50 mT in 5 mT increments, for each of the coil location modality: RET, OCC, GLO (Fig. 1). Participants were blinded to stimulation frequency and intensity. The experimenter was aware of the assigned frequency group, and blind to the intensity. The order of MF levels was randomized using a LabVIEW program. Therefore, the study employed a single-blinded protocol.

Fig. 1.

Schematic representation of the experimental protocol. Participants underwent three exposure conditions (Retina, Occipital, and Global) in a randomized order at a single stimulation frequency. Each block included a 5-minute dark adaptation followed by 11 intensities applied five times each, totaling 55 stimulations per condition.

Participants were seated comfortably in an armchair and given a 5-minute dark adaptation period in complete obscurity before the exposure session commenced. This darkness was maintained throughout the session to ensure consistent experimental conditions. Each MF level was presented in five trials per participant, with each trial consisting of a 5-second MF exposure followed by a 5-second rest period. To avoid any auditory cues, participants wore earplugs throughout the session.

During each trial, participants had the opportunity to indicate whether they perceived the stimulations by pressing a button. Responses were recorded as binary outcomes: a button press (“1”) indicated perception (“yes”), while no press (“0”) indicated no perception (“no”). Participants were instructed to report phosphenes only when reasonably confident that a visual percept was present.

Statistical analysis

The magnetic field can be expressed as Eq. (1):

1

where is the field amplitude (in mT) and is the frequency (in Hz). The convention in this paper is to express the root mean square (RMS) quantities, as exposure guidelines and standards typically express exposure and dose limits in these terms. The key dosimetric parameters are the current density (J in A/m²) and the EF (V/m) induced in brain or retina. The EF is directly proportional to dB/dt, such that Eq. (2):

2

Logistic regressions

The use of dB/dt as a metric has several key advantages. First, since the induced EF (per Maxwell-Faraday’s law) is proportional to dB/dt, this provides us with a metric that takes frequency into account (since the derivative of a sine is a cosine with frequency as a multiplicative factor). Second, this facilitates comparisons with previous literature, where dB/dt has been widely used as a metric. For each frequency, the 1/0 binary responses were entered into a mixed logistic regression model with predictor (or independent) variables (1) the dB/dt and (2) the coil position (RET, OCC or GLO), and a random intercept for each participant. With the press (1 or 0) as dependent variables, the model was formulated as (3):

3

The coefficients, b permits an estimate of the response odds ratio per increment of dB/dt. Mixed logistic regression modelling was performed using R (v.2025.09.1), implemented with the lme4 package^35,36. The glmer function of the lme4 package was used for the model and each coil position was used as the reference condition to calculate the estimates using the following formula (as in Legros et al.⁵):

Model = glmer(Press ~ Coil position + dB/dt + (1|Subject), family = binomial, data = data, glmer Control (optimizer = “bobyqa”)).

To differentiate the effect of dB/dt between the different coil positions, a similar model was fitted separately for each coil position, with the 1/0 binary response as a dependent variable, and dB/dt as a fixed effect, and a random intercept for each participant. Before fitting these coil-specific models, we verified for each frequency-specific full model (containing both coil position and dB/dt as fixed effects) that a coil position x dB/dt interaction was significantly present, which was the case for all frequencies (all interaction p-values < 0.01). The glmer function calculates significance of the estimates was calculated by asymptotic Wald tests.

Finally, a Bonferroni correction was applied, resulting in a threshold for significance of 0.05/9 (9 being the number of models fitted), i.e. a threshold of p = 0.05/9 = 0.0055.

Moreover, experimenter identity was added as a fixed effect to evaluate whether it influenced the outcomes. This factor showed no significant effects and did not improve model fit, as indicated by higher Akaike and Bayesian Information Criterion (AIC and BIC) values compared with the reduced model. Because it provided no explanatory value, experimenter identity was removed from the final inferential models.

Comparison between original and replication results

To evaluate the consistency between the original study and the present replication, two complementary analyses were conducted: (i) a comparison of odds ratios (ORs) across studies, and (ii) a correlation analysis of regression coefficients.

For each frequency and exposure condition, we extracted the OR and their 95% CIs from both the original publication and the replication dataset. We then constructed a forest plot to visually compare the magnitude and precision of ORs across the two studies.

To quantify the overall concordance between studies, we computed the correlation between the original regression coefficients () and the replication coefficients (). Each data point in the correlation analysis corresponded to one frequency-exposure pair (n = 9).

Pearson’s correlation coefficient (r) was used due to the continuous, linear nature of the coefficients.

Together, the forest plot of ORs and the coefficient correlation analysis provide both effect-size and model-slope comparisons, allowing a comprehensive evaluation of reproducibility across studies.

Results

Perception threshold

Figure 2 shows the logistic regression curves for each frequency and exposure site. For these same combinations, Table 2 reports the estimated regression coefficients, their associated p-values, the ORs per one-unit increase in dB/dt with corresponding 95% CIs, as well as the conditional R² indicating the proportion of variance explained by the model.

Table 2.

Logistic regression results for each frequency and exposure site.

Frequency	Exposure	β (SE)	z-value	p-value	OR	95% CI	R2c
20 Hz	OCC	0.18 (0.08)	2.12	0.034	1.19	[1.01–1.41]	0.008
	RET	1.33 (0.10)	12.92	< 0.0001	3.77	[3.08–4.61]	0.40
	GLO	1.50 (0.09)	15.87	< 0.0001	4.50	[3.73–5.41]	0.57
50 Hz	OCC	0.18 (0.04)	4.25	< 0.0001	1.20	[1.10–1.31]	0.05
	RET	0.81 (0.05)	15.12	< 0.0001	2.24	[2.02–2.49]	0.57
	GLO	0.78 (0.05)	15.52	< 0.0001	2.18	[1.98–2.41]	0.58
60 Hz	OCC	0.20 (0.05)	4.02	< 0.0001	1.22	[1.11–1.34]	0.1
	RET	0.70 (0.05)	14.12	< 0.0001	2.01	[1.82–2.21]	0.62
	GLO	0.68 (0.05)	14.92	< 0.0001	1.97	[1.80–2.16]	0.65

β = coefficient for dB/dt; OR = odds ratio per 1-unit increase in dB/dt. Bold p-values indicate Bonferroni-significant effects; R²c = Conditional r-square.

Across all conditions, OCC stimulation displayed shallow slopes with small regression coefficients at all frequencies (β ≈ 0.18–0.20), and Bonferroni-corrected significance only at 50 Hz and 60 Hz. In contrast, RET and GLO stimulation produced much steeper dose-response functions and markedly lower dB/dt thresholds.

RET showed the strongest frequency effect, with the largest slope at 20 Hz (β = 1.33, p < 0.001) and high odds ratios (OR = 3.77 at 20 Hz; OR = 2.0–2.2 at 50–60 Hz). GLO displayed a similar pattern, with the highest OR at 20 Hz (OR = 4.50; 95% CI [3.73–5.41]) and progressively smaller effects at higher frequencies.

Across modalities, a clear frequency-dose pattern emerged: 20 Hz consistently produced the lowest perceptual thresholds and the steepest psychometric functions, especially in RET and GLO conditions.

A small number of participants (n = 6) spontaneously described transient colored phosphene percepts (e.g., blue, purple, green or yellow), in addition to the more commonly reported achromatic flickering sensations.

Experimenter replicability

Including experimenter identity as a fixed effect did not enhance model fit relative to the model without this factor (likelihood ratio test: χ²(4) = 4.95, p = 0.29). Consistently, both AIC and BIC values were higher for the model that included experimenter identity (AIC = 5621.6, BIC = 5686.7) compared to the reduced model (AIC = 5618.5, BIC = 5654.7). In addition, none of the experimenter-specific coefficients reached statistical significance (all p > 0.23). Collectively, these findings indicate that perceptual outcomes were not systematically affected by the experimenter, supporting strong intra-study replicability.

Comparison with the original study

Across all stimulation frequencies and exposition conditions, replication models yielded ORs broadly consistent in magnitude with those reported in the original study. As illustrated in Fig. 3, most replication confidence intervals overlapped with the original ORs, indicating successful replication for the majority of conditions (i.e., 95% ICs overlapped and same direction). The only exception was the 50 Hz RET condition, where the replication OR was higher and its 95% CI did not overlap with the original estimate. Overall, the replication confirmed the primary observation that perception probability increases monotonically with dB/dt across all frequencies, with strong alignment with the original effect sizes for 8 out of 9 comparisons.

A strong linear association was observed between the original study’s coefficients and those obtained in the present replication (Fig. 4). The correlation was r = 0.965 (r² = 93%), indicating an excellent concordance across the nine frequency–exposure combinations. Data points are consistently aligned close to the fitted regression line, with confidence bands capturing all observations. The dashed diagonal line (perfect 1:1 concordance) shows that most coefficients were slightly higher in the replication than in the original dataset, but the deviations were small and systematic across modalities. Together, these analyses indicate a high reproducibility of dose–response slopes across frequencies and exposure sites.

Fig. 4.

Correlation of logistic regression estimates between original and replication studies. (Dashed Line = 1:1 Agreement, Black Line = Linear Fit, Shaded Area = 95% CI).

Table 3 presents the 50% perception thresholds obtained in the replication study for each frequency-exposure condition, in terms of magnetic flux density (B in mT_RMS) and dB/dt (T/s _RMS), along with their 95% CIs, and the corresponding values ​​reported in the original study where available. The thresholds observed in the replication are generally lower than those of the original study for the retinal and global conditions.

Table 3.

Threshold 50% comparison original vs. replication.

Frequency	Exposure	B50% [95% CI] (mTRMS) Replic	B50% (mTRMS) Original	dB/dt50% [95% CI] Replic	dB/dt50% Original
20	OCC	304.8 [4.9–604.6]	NA	38.3 [0.6–76.0]	NA
	RET	45.6 [38.7–52.5]	62.03	5.7 [4.9–6.6]	7.79
	GLO	31.5 [27.5–35.6]	37.49	4.0 [3.5–4.5]	4.71
50	OCC	148.3 [64.0–232.6]	NA	46.6 [20.1–73.1]	NA
	RET	31.2 [26.4–36.0]	45.99	9.8 [8.3–11.3]	14.45
	GLO	22.1 [17.5–26.6]	28.12	6.9 [5.5–8.4]	8.83
60	OCC	123.8 [66.7 −180.8]	79.47	46.7 [25.1–68.2]	29.96
	RET	32.1 [27.7–36.5]	43.23	12.1 [10.4–13.7]	16.3
	GLO	23.8 [19.9–27.8]	27.94	9.0 [7.5–10.5]	10.53

Discussion

This study replicated the main findings of Legros et al. (2024)⁵ regarding magnetophosphene induction by ELF-MF delivered through tAMS. Across three frequencies (20, 50, and 60 Hz) and three exposure configurations (retinal, global, and occipital), we reproduced the characteristic dose–response pattern demonstrating that magnetophosphenes are robustly induced during retinal and global exposures, but minimally during occipital stimulation⁵. Logistic regression slopes, perceptual thresholds, and effect sizes closely matched those reported in the original study, with strong linear correspondence across exposure–frequency combinations. This confirms that magnetophosphene induction via tAMS is a reliable and reproducible physiological phenomenon.

The replication also confirmed two core mechanistic signatures: (1) a clear frequency dependence, with the lowest thresholds and steepest psychometric curves at 20 Hz^{5,19,32,33,37}; and (2) markedly greater sensitivity to retinal and global stimulation compared with occipital stimulation⁵. Together, these outcomes reinforce the interpretation that magnetophosphenes originate predominantly from retinal activation, likely involving rod photoreceptors whose temporal response properties align with the observed frequency effects³⁸. Occipital stimulation again failed to produce strong or consistent perceptual responses (Fig. 2) despite generating higher cortical electric fields in prior dosimetry models⁵, supporting the conclusion that cortex-level activation is insufficient to induce phosphenes in this frequency range²⁰.

A single divergence emerged at 50 Hz during retinal stimulation (Fig. 3), where the replication produced a steeper slope (Fig. 2) and higher odds ratio compared with the original estimate. However, the direction and qualitative pattern of the effect remained unchanged, and confidence intervals across the other conditions exhibited strong overlap (Fig. 3). This localized divergence may reflect subtle differences in coil placement (i.e., orientation and distance from the eye), but does not alter the broader mechanistic interpretation.

Beyond the regression slopes, the 50% perceptual thresholds reported in Table 3 further reinforce the reproducibility of the tAMS-induced magnetophosphene response. Across frequencies, RET and GLO conditions consistently yielded lower thresholds than OCC stimulation, replicating the spatial selectivity observed in the original study. Notably, the replication produced systematically lower thresholds for RET and GLO compared with Legros et al.⁵. For example, at 20 Hz, retinal thresholds decreased from 62.0 mT_RMS to 45.6 mT_RMS, and global thresholds from 37.5 mT_RMS to 31.5 mT_RMS. These shifts, though modest, are mechanistically consistent with the higher logistic slopes observed in the present data and likely reflect slight coil positioning differences. Importantly, the relative pattern of thresholds across exposure conditions remained unchanged, with GLO < RET ≪ OCC for all tested frequencies. This highly conserved ordering provides convergent evidence for a retinal origin of magnetophosphene induction and underscores the robustness of threshold-based metrics across laboratories, and it is consistent with prior dosimetric and psychophysical investigations⁵. At the same time, it is important to note that the retina is anatomically and functionally part of the CNS. The retina is a laminated neural structure derived from the embryonic neural tube and shares canonical neuronal, synaptic, and circuit-level properties with other CNS tissues^39,40. Owing to its accessibility and well-characterized organization, it provides a uniquely tractable in vivo model for investigating the sensitivity of neural tissue to weak oscillatory electric fields. Accordingly, magnetophosphene perception reflects a genuine neurophysiological interaction with CNS structures. As such, tAMS-induced magnetophosphenes constitute a reproducible physiological marker of neural responsiveness to alternating magnetic fields, even if they do not, on their own, demonstrate full cortical neuromodulation.

These findings matter for two reasons. First, they provide crucial evidence for the reproducibility of magnetophosphene thresholds, strengthening the validity of these thresholds as a physiological benchmark in exposure safety science^3,4. Robust replication across laboratories is essential because magnetophosphenes anchor international ELF-MF exposure limits and represent one of the earliest detectable human responses to induced electric fields^2,3,41–43. Second, the work establishes tAMS as a stable and operator-independent method for delivering controlled ELF-MF stimulation^5,27,33. Indeed, beyond replicating the main effects reported by Legros et al.⁵, our protocol explicitly accounted for experimenter-related variability as a potential source of noise or bias. Data were collected by five different experimenters, yet statistical analyses showed that none significantly influenced perceptual responses or model fit. This inter-experimenter stability suggests that the magnetophosphene thresholds observed here reflect robust physiological properties of the visual system rather than operator-dependent effects.

Unlike tACS, which is confounded by electrode montage and scalp sensations^32,44–46, tAMS offers a more uniform and perceptually neutral approach for probing retinal neurophysiology and weak-field neuronal sensitivity. This enhances its potential as a future methodological tool in neuromodulation and diagnostic research.

This study advances the field by providing one of the first high-powered, replications of tAMS-induced magnetophosphenes, confirming that their magnitude, frequency dependence, and spatial specificity are not laboratory or operator-dependent. By demonstrating strong congruence with the original observations, the results reinforce the retinal origin hypothesis and provide a robust empirical foundation for future work investigating both the biophysics of weak electric fields and the development of tAMS-based neuromodulation strategies. While the present findings demonstrate a robust neurophysiological interaction with tAMS, they should not be interpreted as direct evidence of cortical neuromodulation or brain stimulation efficacy. In particular, studies combining tAMS with TMS-evoked potentials, or behavioral paradigms will be critical to establish its efficacy as a neuromodulation tool.

Several limitations warrant consideration. Only three frequencies were tested, precluding full characterization of the higher-frequency range examined previously; perception was assessed using binary responses, which capture detection but not perceptual quality or intensity; and although coil placement followed strict procedures, small variations may influence local retinal field strengths. Finally, measurements were conducted exclusively in dark-adapted conditions, limiting generalizability to naturalistic environments.

Looking forward, several avenues merit exploration. Because only three frequencies were tested, future studies should extend the stimulation range to better map the full ELF domain where thresholds remain poorly defined. Beyond binary detection, collecting perceptual quality ratings or continuous intensity measures could refine psychometric modeling. Importantly, phosphene reports are inherently subjective; developing objective physiological markers of magnetophosphene induction would substantially strengthen the field. Approaches such as electroencephalography (EEG) or functional Near-Infrared Spectroscopy (fNIRS) may help identify cortical correlates associated with retinal activation, offering a pathway toward reliable biomarkers that complement subjective perception and improve mechanistic understanding.

Overall, the replication provides strong evidence that tAMS reliably evokes magnetophosphenes through retinal mechanisms, confirms the robustness of threshold patterns across frequencies and exposure sites, and further supports the use of tAMS as a reproducible tool for studying human sensitivity to ELF-MF.

Author contributions

EF : Writing – Ethics approval, Visualization, Performed the experiments & Data Acquisition, Validation, Formal analysis, Writing - Methods & Results, Writing – review & editing. MP : Performed the experiment, Data Acquisition. MM : Data Acquisition, Writing – review & editing. JB : Performed the experiments & Data Acquisition. AC : Writing – Ethics approval, Methodology, Performed the experiments & Data Acquisition. NB : Performed the experiments & Data Acquisition, Writing – review & editing, Writing – original draft, Visualization, Validation, Methodology, Investigation, Conceptualization, Supervison.

Funding

This project was sponsored by: Hydro-Québec (Canada) (http://www.hydroquebec.com/en/); EDF-RTE (France) (http://www.edf.com/the-edf-group-42667.html) (http://www.rte-france.com/fr/).

The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Data availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author on request, to any qualified researcher.

Declarations

Competing interests

The authors declare no competing interests.

Ethics declarations

This study was approved by the Institutional Review Board of the EuroMov Digital Health in Motion (DHM) Center (IRB-EM, notice no. 2111B) and complied with the ethical principles outlined in the Declaration of Helsinki for research involving human participants. All participants gave their informed consent.