Variability of pulse width in transcranial magnetic stimulation

Objective. There is a high variability in the physiological effects of transcranial magnetic brain stimulation, resulting in limited generalizability of measurements. The cause of the variability is assumed to be primarily based on differences in brain function and structure of the stimulated individuals, while the variability of the physical properties of the magnetic stimulus has so far been largely neglected. Thus, this study is dedicated to the systematic investigation of variability in the pulse width of different TMS pulse sources at different stimulation intensities. Approach. The pulse widths of seven MagVenture® pulse sources were measured at the output of 10%–100% stimulation intensity in 10% increments via Near Field Probe and oscilloscope. The same C-B60 coil was used to deliver biphasic pulses. Pulse widths were compared between pulse sources and stimulation intensities. Main results. The mean sample pulse width was 288.11 ± 0.37 µs, which deviates from the value of 280 µs specified by the manufacturer. The pulse sources and stimulation intensities differ in their average pulse width (p’s < .001). However, the coefficient of variation within the groups (pulse source; stimulation intensity) were moderately low (CV = 0.13%–0.67%). Significance. The technical parameter of pulse width shows deviations from the proposed manufacturer value. According to our data, within a pulse source of the same manufacturer, the pulse width variability is minimal, but varies between pulse sources of the same and other pulse source models. Whether the observed variability in pulse width has potential physiological relevance was tested in a pilot experiment on a single healthy subject, showing no significant difference in motor evoked potential amplitude and significant difference in latencies. Future research should systematically investigate the physiological effects of different pulse lengths. Furthermore, potential hardware ageing effects and pulse amplitude should be investigated.


Introduction
Transcranial magnetic stimulation (TMS) is a non-invasive brain stimulation technique used for research, diagnostic and treatment purposes worldwide.Stimulation of the human cortex is achieved by an induced electrical current, due to the rapidly changing magnetic field, which passes through the skull and depolarizes the superficial neurons perpendicular to the current [1].This technique is applied in dedicated laboratories and clinics on a daily basis, but the physiological effect and output parameters such as motor evoked potentials (MEPs) or transcranial evoked potentials (TEPs) are prone to high variability [2][3][4][5][6].Factors contributing to the variability in the resulting output parameters of TMS are not only due to individual subject factors like different anatomical structures [7] or the intrinsic state of the brain prior to stimulation [8] but could also be the result of different technical, TMS-related factors, e.g.use of different pulse sources, coils, waveforms, stimulation intensity or data pre-processing approaches [5,[9][10][11].Additionally, the variety of setups between different TMS studies potentially influences results and hampers comparability across studies [12].This could be further complicated by variations of the output within a single TMS pulse source, i.e. within one TMS machine.The term stimulator refers to the combination of coil and pulse source.In this article, however, the variability of the pulse source from one manufacturer connected to the same coil is examined.
In 2015, van Doren et al conducted an experiment in which they compared pulse sources from different manufacturers regarding their generation of magnetic fields, artefacts and output parameters (MEPs, TEPs).As expected, they found a linear increase of the field strength accompanied with a linear increase of the pulse source output for each TMS system.Technical parameters e.g.magnetic field strength, magnetic flux duration and artefact trajectory differed between the examined manufacturers (MagStim®, Deymed®, MagVenture®).The analysis of physiological outcome parameters also showed differences between the manufacturers in resting motor threshold and MEP latency [13].In detail, the testing of the MagVenture® device resulted in higher magnetic field strength, shorter duration of the magnetic field, reversed current direction by default, as well as lower resting motor threshold, shorter recovery time from the TMS-induced artefact and shorter latency of the MEPs in contrast to the MagStim® and the Deymed® systems.Concurrently the baseline activity was noisier with the MagVenture® system as compared to the other systems.There were no differences with respect to validity of the MEPs (number of valid, in analysis included MEPs), MEP amplitudes (mean x, coefficient of variation CV), latency or amplitude of the second part segment of the TMS artefact occurring 5-8 ms after stimulation, or latency or amplitude of the TEPs.Although the reported differences [13] refer to inter-pulse source comparisons, variations in hardware parameters such as manufacturing tolerances as well as usage phenomena could lead to output changes within the same pulse source models of one manufacturer.
As to our knowledge, no systematic analysis of stimulus variability within and between same model pulse sources is available.With the present experiment we aim to investigate the pulse width of 7 pulse sources of the same manufacturer (MagVenture®) connected to the same coil at varying stimulation intensities.In addition, the potential physiological effects of pulse width will be investigated via MEP peak-to-peak amplitude and latency in a healthy person.
Based on the physical aging and manufacturing changes of the electronic hardware, significant changes in pulse width are expected to occur between different TMS devices of the same model and manufacturer.This could potentially affect measured output variables of cortico-spinal excitability [14] and hamper the comparability, interpretability and generalizability of non-invasive brain stimulation studies using TMS, as the device statuses vary between clinical or research laboratories.

Methods
The pulse width (in µs) of a total of n = 7 pulse sources (2 MagPro R30 and 5 MagPro X100) from the same manufacturer MagVenture® were measured.The pulse width was calculated based on the derivation of the signal and the time difference between the maxima and minima of the derivation.All pulses were given with the same figure-of-8 (Fo8) coil (C-B60, MagVenture®, Farum, Denmark).Every procedure consisted of one pulse per intensity (10%-100% Maximum Stimulator Output [MSO] in 10% increments), with a minimum interval of 5 s between pulses to account for the recharge delay of the device and operator time.Since it can be assumed that the electronic system is constant within an operating point or intensity, one pulse per intensity is sufficient for pulse width determination.For all pulse sources, the same setup with a biphasic pulse shape, default current direction (posterior-anterior anterior-posterior [PA-AP] current direction in the coil) and 1000 ms recharge delay was applied.The pulse width was acquired with an Analog Discovery 2 oscilloscope plus the Discovery BNC-adapter, the WaveForms Software (Version 3.1.1.34,all Digilent, USA) and the Near Field Probe with 50 Ω impedance.To ensure a constant placement of the Near Field Probe, it was fixed in the middle of the coil, perpendicular to the handle.The setup was kept constant for all measurements.
In the second experiment the pulse source with the shortest and the longest pulse width (Experiment 1) were used to generate contralateral MEPs with 120% resting motor threshold (RMT) stimulation intensity in one healthy, right-handed participant.The same Fo8 coil utilized for the pulse width determination was used for stimulation.The pulse width during stimulation and the time between the pulse output and the trigger output were recorded for each pulse source.A detailed description of the measurement procedure and methods can be found in the supplementary material.

Statistical analysis
The statistical analyses were carried out with SPSS (V29.0.1.0,IBM, New York, USA).Mean (x) and standard deviation (SD) of the dependent variable pulse width (µs) were calculated per pulse source over all intensities and per intensity level over all pulse sources (10%-100% MSO in 10% steps).Due to the small sample size, non-parametric tests were calculated to determine differences in central tendencies with the Friedman-test.In case of significant differences, post-hoc comparisons were calculated via Dunn-Bonferroni-tests.Due to multiple testing corrections, the corrected p-values were interpreted in case of post-hoc comparisons.To determine variability, the coefficient of variation was calculated using the following formula: CV = ((SD ÷ x) × 100) pulse source-and intensity-wise.The significance level was set at 5% for all analyses.

Results
Due to deviations in conventional pulse amplitude and width despite grounding, which suggest a technical malfunction, one pulse source of the type X100 was excluded from the analyses.Pulse source characteristics, mean pulse widths and CV are depicted pulse source-wise (table 1) and for the different intensity levels (table 2).The mean pulse width of all pulse sources was 288.11 ± 0.37 µs.On average, the pulse width within a pulse source varies 0.13% ± 0.03% and within a stimulation intensity 0.67% ± 0.01%.In the sequential step it was also examined by Friedman-test whether the CV-values differ significantly between the pulse sources as well as between the intensities, which is not the case (p = .416and p = .437).A Friedman-test showed significant differences between the pulse widths of the six pulse sources (χ 2 (5) = 49.77,p < .001,n = 10 intensities) and between the pulse widths at varying stimulation intensities (χ 2 (9) = 51.30,p < .001,n = 6 pulse sources).Following significant post-hoc tests (Dunn-Bonferroni-tests) comparisons are depicted in table 3, showing significant differences of pulse width between individual pulse sources and low and high intensities.In figure 1, the pulse width of the individual pulse sources is depicted as a function of intensity, including the deviating pulse source 7.
Figure 2 shows the pulse width as a function of stimulation intensity of all pulse sources.Detailed results of the electrophysiological measurement from Experiment 2 can be found in the supplementary material.In sum, there was no significant difference between the central tendencies of the peak-to-peak MEP amplitudes elicited via biphasic PA-AP current direction with pulse source S3 and S4 (z = −0.149,p = .898)and a significant difference between the latencies (z = −2.423,p = .014).On average, the time delay between the pulse output and the trigger output was 5.106 ± 0.059 µs for S3 and 4.984 ± 0.008 µs for S4.The mean pulse width during electrophysiological stimulation was 290.56 ± 0.03 µs for S3 and 285.29 ± 0.07 µs for S4.
The graph shows the derivation of the recorded signal, respectively the pulse width of all recorded pulse sources at 50 %MSO.Pulse source 7 which was excluded from analysis shows derivations in amplitude and width.

Discussion
To the best of our knowledge, this is the first study investigating the pulse widths of different TMS pulse source models using the same coil type from the same manufacturer.Single pulses were delivered from 10 %MSO in steps of 10 up to 100 %.The pulse width was recorded for each step for each pulse source.Six pulse sources of the manufacturer MagVenture® were analysed, two MagPro R30 and four MagPro X100.The same Fo8 coil was used for all measurements.Recharge delay and the default biphasic current direction were kept constant for every pulse and pulse source.The statistical analyses demonstrate significant differences in pulse width between individual pulse sources and between different stimulation intensities.The CV shows only slight variability within a pulse source (0.13% ± 0.03%) and within a stimulation intensity (0.67% ± 0.01%), which indicates the comparability of research results with the same technical pulse source within and between laboratories.Nevertheless, it is necessary to prove this low variability also on the whole stimulator level.
The mean pulse width of all pulse sources was 288.11 ± 0.37 µs, which is surprisingly higher than the proposed 280 µs in the manufacturer manual.As depicted in figure 2, not one measured value reached the expected 280 µs.If this deviation of approximately 8 µs has a physiological effect is to debate.First experiments using monophasic pulses showed that an increased pulse width leads to a lower motor threshold [14,15].However, these results refer to monophasic pulses, which differ in their physiological effects from biphasic ones [16].In addition, the compared pulse widths in the experiments [14,15] were 30, 60 and 120 respectively 30 and 80 µs.
Using biphasic pulses, significantly shorter latencies of MEPs with a MagVenture® system with 320 µs pulse width in comparison to a Deymed® and MagStim® system with 380 µs pulse width each were measured [13].Even though the stimulation effect of TMS depends on the pulse width [14], based on the current literature we could not assume that an 8 µs deviation from the expected 280 µs probably does evoke significant physiological differences.Investigation of the possible effects of different pulse widths was tested in a first approach in the second experiment.
The differences in pulse width occurred between high and low %MSO, with broader pulses at low intensities.The intermediate intensities of 40, 50 and 60 %MSO were not affected.The pulse width was determined by the derivation of the signal and the time difference between the maxima and the minima of this derivation.These differences between high and low intensities could primarily be due to a combination of a true difference and analytical systematic measurement error.It probably results from the fact that the point at which the start or end of the pulse is determined depends on the pulse amplitude.Therefore, when the amplitude changes, the point of maximum or minimum slope will shift.Likely, it does not describe solely an actual pulse width change, but also a systematic error caused by the measurement procedure.In addition, the voltage-dependent parts of the pulse source play a role, as they may change characteristics.This would explain why the pulse width decreases at higher voltage.However, this is manufacturer-specific and cannot be considered in more detail.But this also does not explain the deviations of the excluded pulse source in figure 1, which persisted despite grounding.A technical defect could be assumed here, which only became apparent during the measurement.
To investigate the potential physiological effects of different pulse widths of TMS, we additionally measured one participant via electromyography.MEPs were recorded in a healthy person using the pulse sources with the longest and shortest pulse width.The amplitudes of this pilot measurement did not differ significantly depending on the pulse source.However, the MEP latency was significantly higher when elicited with longer pulse width.These results are consistent with the results of van Doren and colleagues, who also found a shorter MEP latency with a shorter pulse width and no differences in MEP amplitude.The reported differences in latency occurred at a pulse width difference of 60 µs between stimulators from different manufacturers [13], but are observable in the present study in one person at approximately 5 µs pulse width difference within two pulse sources from one manufacturer.However, these results and comparability should be interpreted with caution, as they relate to the measurement of only one subject and do not consider a variety of technical and physiological parameters.In order to draw clear conclusions about the physiological relevance of pulse width, more systematic studies including more pulse sources and participants should be conducted in the future.
Due to the significant differences in pulse widths both within and between pulse sources, performing a pulse width measurement parallel to common stimulation paradigms can be useful for any research or clinical laboratory.In addition to the Near Field Probe, an oscilloscope and recording and evaluation software are required to carry out these measurements.The Near Field E-Probe must be fixed to the coil and connected to the oscilloscope using a BNC cable.When a pulse is triggered, the pulse length must then be measured in the recording software and can be exported for analysis.For a detailed description of the measurement settings the reader is referred to the supplementary material.As these devices are not part of standard clinical equipment and would have to be purchased separately, manufacturers could integrate an automatic measurement of the pulse width and amplitude output into the pulse source in the future to make it universally accessible.

Conclusion
The measured pulse width differs from the proposed manufacturer value.According to our evidence, the pulse width variability within a pulse source of the same manufacturer is minimal.However, the pulse width varies between pulse sources of the same and other models.Differences in pulse width between high-and low intensities are probably the result of systematic analytical measurement error and actual value changes.The potential physiological effects of pulse width variability should be the subject of further systematic research.Furthermore, potential hardware ageing effects and variations of pulse amplitude should be investigated.In sum, there is only minimal inter-and intra-pulse source variability in the pulse width of biphasic pulses across pulse sources of two different models and intensities from one manufacturer.

Figure 1 .
Figure 1.The graph shows the derivation of the recorded signal, respectively the pulse width of all recorded pulse sources at 50% MSO.Pulse source 7 which was excluded from analysis shows derivations in amplitude and width.

Figure 2 .
Figure 2. Pulse width (µs) and stimulation intensity (%MSO).The graph shows the pulse width as a function of the stimulation intensity.Each dashed line represents one pulse source, the mean of all sources is depicted as a solid line.

Table 1 .
Pulse source characteristics and pulse width.

Table 2 .
Pulse source characteristics and pulse width.
CV = coefficient of variation; MSO = maximum pulse source output; SD = standard deviation; x = mean.