Detection of Motor-Evoked Potentials Below the Noise Floor: Rethinking the Motor Stimulation Threshold

Abstract

Background:

Motor-evoked potentials (MEP) are one of the most prominent responses to brain stimulation, such as supra-threshold transcranial magnetic stimulation (TMS) and electrical stimulation. Understanding of the neurophysiology and the determination of the lowest stimulation strength that evokes responses requires the detection of even smaller responses, e.g., from single motor units. However, available detection and quantization methods suffer from a large noise floor.

Objective:

This paper develops a detection method that extracts MEPs hidden below the noise floor. With this method, we aim to estimate excitatory activations of the corticospinal pathways well below the conventional detection level.

Methods:

The presented MEP detection method presents a self-learning matched-filter approach for improved robustness against noise. The filter is adaptively generated per subject through iterative learning. For responses that are reliably detected by conventional detection, the new approach is fully compatible with established peak-to-peak readings and provides the same results but extends the dynamic range below the conventional noise floor.

Results:

In contrast to the conventional peak-to-peak measure, the proposed method increases the signal-to-noise ratio by more than a factor of 5. The first detectable responses appear to be substantially lower than the conventional threshold definition of 50 μV median peak-to-peak amplitude.

Conclusion:

The proposed method shows that stimuli well below the conventional 50 μV threshold definition can consistently and repeatably evoke muscular responses and thus activate excitable neuron populations in the brain. As a consequence, the IO curve is extended at the lower end, and the noise cut-off is shifted. Importantly, the IO curve extends so far that the 50 μV point turns out to be closer to the center of the logarithmic sigmoid curve rather than close to the first detectable responses. The underlying method is applicable to a wide range of evoked potentials and other biosignals, such as in electroencephalography.

Introduction

Motor-evoked potentials (MEPs) are an important response phenomenon in brain stimulation, such as transcranial magnetic stimulation (TMS). If motoneurons in the human primary motor cortex are activated directly or indirectly, they respond with action potentials, which are transmitted down the spinal cord to the lower motoneurons [1]. The lower motoneurons route the signals to the muscles, where they can be detected as MEP waves through electromyography (EMG). MEPs provide one of the few directly observable responses of the brain to stimuli. Furthermore, MEPs are a key to understanding the biophysical and neurophysiological mechanisms of brain stimulation, to establishing safety limits, to matching different devices or coils, and to achieving individual dosing [2–5]. The so-called motor threshold is defined based on MEPs as a low stimulation amplitude that generates the first reliably detectable responses and is the key safety as well as dosage reference level [6].

The response amplitudes of several MEPs graphed over the corresponding stimulation strengths forms an s-shaped curve, often named as input–output (IO) or recruitment curve [7–10]. For high stimulation strengths, the responses saturate and form the high-side plateau of the sigmoidal IO curve around several millivolts, dependent on the specific muscle and state of pre-activation [11]. If the stimulation strength is reduced, the response amplitude decreases monotonically until the responses—for resting measurements, i.e., without any pre-activation in the corresponding muscle, as in the focus here—appear to cease entirely and fall below a low-side plateau or noise floor that is formed by endogenous activity, biosignals from unrelated neural and muscular sources, and recording noise [10]. Thus, the dynamic range of MEP amplitudes can exceed a factor of 1000 [12].

Typically, the noise floor forming the low-side plateau for a resting motor system of a conscious subject, e.g., for TMS, can reach above 10 μV peak-to-peak [13]. The resting motor threshold was defined to be slightly above this plateau at 50 μV peak-to-peak median response amplitude as a compromise between detecting subtle responses and sufficient detection robustness [12]. Such threshold definitions assume that they are close to the smallest occurring evoked activity. The noise floor, however, is not a purely technical property of the used amplifier, but—for modern amplifiers—widely depends on externalities, such as the electrode and source impedance, body temperature, and biosignals from unrelated sources [4, 14–16]. Thus, simple technical advances of amplifiers do not solve the problem. According to the established interpretation, smaller responses causally evoked by stimulation of motor efferences might either not exist or could not be detected for physical reasons.

Particularly for neuromodulatory interactions, e.g., repetitive TMS with certain pulse rhythms or patterns, the threshold is physiologically important beyond amplitude individualization and safety [17]. Many protocols, particularly presumably inhibitory 1 Hz as well as patterned protocols such as quadripulse and theta-burst stimulation, use sub-threshold pulses, which are often below 90%, and sometimes below 60% of the resting motor threshold [18–22]. In fact, the pulse amplitude during the modulatory intervention can determine if the intervention is inhibitory, excitatory, or effectless [23–26]. Such definitions may leave the impression that there could be a rather binary threshold, which may have a stochastic nature or blurring due to the high trial-to-trial variability but still demarcate a transition at the threshold or very close to it.

Early research on inhibition also considered that fatigue mechanisms in both the central and the peripheral nervous system as well as in muscles might be involved [27, 28]. Such considerations may encourage rather using subthreshold repetitive protocols and avoiding substantial activation of muscle units. More recent paradigms might want to rule out motor activation and at most aim at some inhibitory interneuron activation. However, do subthreshold stimuli really not activate corticospinal connections and how weak does a stimulus have to be to avoid activation?

So-called active stimulation into a pre-activated motor system is used to find smaller effects of single TMS pulses [29]. However, it is not obviously clear if such active pulses actually immediately depolarize neurons or only modulate endogenous signals, nor the neuron types that are preferably activated. First approaches for looking below the noise floor and finding MEPs averaged the responses to many individual stimuli, as a solution that is also typical for other subtle biosignals, such as in electroencephalography (EEG) [30]. Although these experiments hinted that there is evoked motor activity well below the resting motor threshold, averaging does not solve the problem. Averaging of responses to several different stimulation strengths or even of an entire IO curve would require many trials and lead to unacceptably long session durations. More importantly, however, MEPs are inherently highly variable, which reflects endogenous signaling and modulation of the neuronal target [13, 31]. Averaging extinguishes this variability and the associated information. Furthermore, the variability is not Gaussian but has a highly skewed distribution. Consistent normalization of the intricate heteroscedastic distribution through mathematical transformations is not simple, particularly not for temporal recordings of MEPs [32, 33]. Consequently, averaging does not result in an exemplary representation of the many variable and noisy individual MEPs, but is dominated by outliers [34]. Thus, within a large series of repetitions, very few rare and maybe even spontaneous potentials with the right timing dominate and determine the averaged response.

We propose an adaptive matched-filter method for reliably detecting MEPs also below the noise floor. The method treats each MEP as a composition of multiple motor unit action potentials (MUAPs) that are identical in shape but with different latencies and amplitudes. The latencies and amplitudes of the MUAP components are estimated for each MEP with maximum likelihood, while the MUAP shape itself is learnt from all previous responses of the same subject. With the learnt MUAP shape, the method uses a matched-filter correlation detector to separate a specific MEP response from the noise floor with high sensitivity by reproducing the MEP shape through a weighted sum of multiple MUAPs of the same shape but with different pre-defined time shifts. The MUAP shape is learnt from multiple MEP recordings, each with uncorrelated noise and background activity. Thus, with every additional MEP in a specific session, the common MUAP shape is refined. In contrast to an overall MEP shape in a matched-filter detector as suggested previously, the decomposition into a weighted sum of equally shaped MUAPs most importantly allows simpler detection of the MEP latency on an individual basis [35]. Each of these equally shaped MUAPs receives a different temporal position along an equidistantly spaced grid. The MUAP shape represents the most general pattern that all individual MEPs share and allows recreating them including their potentially different latencies. Thus, it presents many similarities to MEPs and contains just enough features to allow for some shape variability. Thus, if all MEPs have equal latency and little shape variability, the MUAP can converge to the overall averaged MEP shape without performance issues as in previous matched-filter methods. The approach achieves a high signal-to-noise ratio (SNR) through the extraction of the shared MUAP pattern across many responses and therefore shares some characteristics with averaging but translates them to the individual MEPs.

In contrast to simple time-synchronized averaging approaches, the proposed method has several advantages. First, it does not require repetitions at the same stimulation strength but merges information from all applied valid stimuli with a wide range of stimulation strengths. Second, it does not introduce bias due to the non-Gaussian distribution of MEPs and is resilient to infrequent spontaneous potentials in an averaged ensemble [36, 37]. Third, it provides a quantitative response amplitude estimate, such as equivalent peak-to-peak voltage amplitude, for each MEP so that the physiological variability is maintained for subsequent analysis steps and is therefore compatible with all known MEP-based methods such as thresholding or IO curves [32, 38, 39]. Finally, it reveals the distribution of the MUAP population over time per MEP recording, providing detailed latency information that is insensitive to measurement noise.

Conventional MEP detection

Conventionally, the amplitude of MEPs is quantified by their peak-to-peak voltage [40]. While simple, this approach is relatively insensitive to weak MEP waves but highly susceptible to noise. The peak-to-peak measurement is likely to pick outliers of distributions and converts interferences and noises, such as additive Gaussian noise, into highly skewed extreme-value distributions [12, 41]. Strictly, those extreme-value distributions have to be considered for correct statistical analysis, but practically rarely are.

Previous studies suggested using the area under the MEP curve instead of the peak-to-peak reading for greater accuracy and higher tolerance to noises [13, 42, 43]. However, several disadvantages exist: the reading depends on the amplifier filter properties, such as the high-pass filter cutoff; it requires a definition of start and end of an MEP, which varies substantially at weak stimulation strengths; it provides impractical units (volt-seconds) and is incompatible with traditional peak-to-peak quantification as well as established safety rules [44]. Most importantly, the MEP area extraction either needs prior information about beginning, zero-crossing, and end or has to rectify the signal, which introduces bias due to converting Gaussian noise into a one-sided distribution and therefore does not substantially increase the sensitivity. As a consequence, the MEP area is rarely used in practice.

Our earlier work proposed a matched-filter method to extract the EMG amplitude [35]. This method can detect EMG signals that are substantially smaller than the noise floor. However, the method still neglects the variable latency of the response MEP. Fixing the differential latency enabled higher sensitivity with fewer samples by reducing the degrees of freedom. Although variable latency could be accounted for by time-shifting the matched filter, this approach could be inconsistent if the time shift is not inherently estimated and inaccurate for responses with very different latencies.

Material and methods

Assumptions

We assume that each MEP measurement comprises a volley of multiple motor unit (compound) action potentials (MUAPs) that share the same shape but with different latencies and amplitudes. Specifically,

$$s\left(t\right)=\sum _i{x}_i\cdot v\left(t-{\tau }_i\right)+n\left(t\right),x_i\ge 0\text{,}n~N\left(0,{\sigma }^2\right).$$ (1)

where $s\left(t\right)$ is the MEP recording, $v$ denotes the MUAP, $x_i$ are the amplitudes of MUAPs at different time, ${\tau }_i$ refer to the latencies, and $n$ represents the Gaussian noise, while subscript $i$ enumerates the different possible latencies. As specific motor units are not considered to change their polarity once the electrode montage is fixed and to avoid spurious solutions where the optimizer might for example generate negative phases of an MEP with positive MUAP phases through negative weights instead of proper latency detection, we restrict the response to $x_i\ge 0$ for all possible latencies $i$. The concept of the MEP composition is visualized in Fig. 1. Thus, with known MUAP shape, we should ideally extract the population of MUAPs over time $\left(x_i,{\tau }_i\right)$ for each MEP waveform. Per MEP, the MUAP populations reflect the amplitude of the MEP response.

Fig. 1.

An example of MUAP decomposition for a weak MEP response.

Decomposition and evaluation

If the MUAP shape $v$ (represented by a column vector) is known, the weights $x$ can be estimated by a maximum-likelihood approach:

$$\{\begin{array}{l}{x}_{\text{est}}=\text{arg}\underset{x}{\min }{\left|s-T\left(v\right)x\right|}_2^2,\\ T\left(v\right)={\left[\begin{array}{cccc}v& 0& \dots & 0\\ 0& v& \dots & ⋮\\ ⋮& 0& \dots & ⋮\\ ⋮& ⋮& \dots & 0\\ 0& 0& \dots & v\end{array}\right]}_{\left(M+N-1\right)\times N},\\ x={\left[x_1,x_2,\dots ,x_N\right]}^T,\forall x_i\ge 0,\end{array}$$ (2)

In this setup, we enumerate the possible delays of MUAPs by $i$. The actual time resolution is 0.2 ms as determined by the sampling rate of the recording device. The MUAP shape $v$ is a vector of length $M$, and the possible amplitude coefficient vector $x$ is of length $N$. The matrix function $T\left(v\right)$ gathers all time-shifted MUAP templates $v$ and practically defines a basis for the vector subspace of MEPs. Each column of $T\left(v\right)$ matches the time index $i$, and the number of columns (i.e., $N$) reflects the detection time window. In this study, we set the detection window to be $20\mathrm{m}\mathrm{s}\le t\le 44\mathrm{m}\mathrm{s}$, which parsimoniously covers the full dynamics of the MEP of the FDI muscle of all participants in this study while avoiding the TMS artifacts. For other muscles and/or subjects, different or wider windows may be required. Vector $x$ gathers the unknown weights with the dimension matching that of $T\left(v\right)$.

Equation (2) is a typical quadratic programming problem with linear constraints, which can be solved efficiently. In this paper, we use the quadprog solver in MATLAB. Equation (2) resembles matched filter methods in that the best amplitude estimation at the presence of Gaussian noise solves a least-squares problem. The difference is that the proposed method additionally considers unknown latencies and ensures non-negative weights $\left(x_i\right)$. Limiting the amplitudes to non-negative values corresponds to our assumption that each MEP is a sum of actual MUAPs and, henceforth, allows physiological interpretations of the decomposition results.

After the decomposition, the noise-free MEP is estimated by

$$s_{\text{est}}=T\left(v\right)x_{\text{est}}.$$ (3)

Both $s_{\text{est}}$ and $x_{\text{est}}$ can give noise-free quantification of the strength of an MEP response. For example, an element-wise summation of the amplitudes $\Sigma x_{\text{est,}i}$ describes the response strength since it reflects the total recruitment population. Additionally, the individual entries of $x_{\text{est}}$ provide detailed insights of the time delay. Since $s_{\text{est}}$ is practically the MEP without noise, one can of course use $\mathrm{m}\mathrm{a}\mathrm{x}\left(s_{\text{est}}\right)-\mathrm{m}\mathrm{i}\mathrm{n}\left(s_{\text{est}}\right)$ to provide a noise-free estimation of the peak-to-peak voltage Vpp as an MEP reading, which is commonly used by the community.

Recovery of the MUAP shape

If the MUAP weights $x$ are known, the best estimate of the MUAP shape $v$ follows the minimization

$$\{\begin{array}{l}{v}_{\text{est}}=\arg \underset{v}{\min }\sum _k\left({\left|s^{\left(k\right)}-T\left(x^{\left(k\right)}\right)v\right|}_2^2\right),\\ T\left(x\right)={\left[\begin{array}{cccc}x& 0& \dots & 0\\ 0& x& \dots & ⋮\\ ⋮& 0& \dots & ⋮\\ ⋮& ⋮& \dots & 0\\ 0& 0& \dots & x\end{array}\right]}_{\left(M+N-1\right)\times M},\\ x={\left[x_1,x_2,\dots ,x_N\right]}^T,\forall x_i\ge 0,\end{array}$$ (4)

where the matrix function $T\left(x\right)$ organizes the unknown weights $x$ in the same way as $T\left(v\right)$ organizes $v$ in Eq. (2). As such, $T\left(x^{\left(k\right)}\right)v=T\left(v\right)x^{\left(k\right)}$, both attempting to approximate the ground truth $s$. Note that we enumerate the trial by $k$ to differentiate the recordings for the same subject. We combine (2) and (4) to estimate the MUAP shape $v$ and weights $x$ iteratively:

1. Initialize MUAP shape $v$;

2. Feed $v$ to Eq. (2) to update $x$ for each recording;

3. Feed the $x$’s to Eq. (4) to update $v$;

4. Repeat steps 2–3 until $v$ converges.

Thus, we allow the amplitude coefficient (i.e., $x^{\left(k\right)}$) to vary between different recordings, but the MUAP per subject (i.e., $v$) remains identical. In this paper, we initialize the MUAP shape $v$ as the stimulus-synchronized average MEP waveform per subject. In the rare case that all recordings just contain differently sized MEPs but without any larger shape variability and/or latency shifts, that shape will widely prevail. Otherwise, the MUAPs will evolve to shorter shapes, which can also describe more subtle features. Over the iterations, the MUAP shapes deform slightly and stabilize after 4–5 iterations. The MUAP shape develops higher-frequency features and a briefer shape overall after sufficient numbers of iterations (see Fig. 1), which is expected as the MEP is a sum of time-shifted MUAPs and therefore mathematically a low-pass filtered product of the MUAP shape in this formalism. Although the final MUAPs still resemble the MEP waveform (Fig. 2), the approximation error, measured as $\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{n}(|s-T(x)v{{|}_2}^2)$ per subject, is reduced by 40%−50%. We tested the method on a substantial number of actual TMS sessions (see the Supplement). We furthermore observed unexpectedly large robustness of the iterative algorithm since even completely random initialization converged. However, a random seed with its risk of poor convergence, e.g., into spurious solutions, or divergence is not necessary since the average MEP constitutes a good first-order approximation of the individual MEP shape, which the iteration can improve through the additional degrees of freedom of the optimization, and has been demonstrated as potent detector pattern before [35].

Fig. 2.

Learnt MUAP shapes from 21 subjects (one MUAP per subject).

Sensitivity to noise

To benchmark the sensitivity of the proposed method, we generate artificial MEP waveforms using a learnt MUAP shifted by random weights $x$ as ground truth. Gaussian noise is additionally introduced with controlled variance to effect different signal-to-noise-ratios (SNRs). Two detection methods are compared: the proposed method and the conventional peak-to-peak reading. Both methods attempt to evaluate the latency and amplitude of the underlying true MEP.

The evaluation results are shown in Fig. 3 where Row (a) shows an overview of the Vpp estimation error under different SNRs, Rows (b–c) detail the estimation errors of Vpp and latency at selected SNRs, and Row (d) visualizes waveforms for three SNRs. The proposed method has substantial advantages in terms of both Vpp and latency estimation. In particular, the proposed method provides an unbiased estimate of Vpp while the conventional method is susceptible to noise and systematically overestimates the Vpp of weak MEPs.

Fig. 3.

Sensitivity analysis of conventional peak-to-peak (Vpp) detection (“conv.” in the legends) vs. the proposed adaptive learning estimation method (“prop.” in the legends). Both the ground truth MEP and the noise are simulated. Row (a): Vpp estimation error for different signal-to-noise ratios (SNRs). Rows (b–c): Histograms of the Vpp estimation error and the peak time error for SNR = 0.1, 1, and 10. Row (d): Representative waveforms sampled from SNR = 0.1, 1, and 10. Each column of Rows (b–d) has the same SNR. The circles mark the location of the peak values of the conventional (red) and the proposed (blue) method.

Fig. 4 presents a sanity check of false positives, where both detection methods are applied to pure Gaussian noise. The detected MEPs are interpreted as false alarm and should ideally be zero. Again, the proposed method outperforms the conventional one with a large margin.

Fig. 4.

Detection results on Gaussian noise (no MEP contained). An ideal detection method should yield Vpp = 0 due to the absence of MEPs.

When processing real data, we generate the same performance chart as Row (b) of Fig. 3 but refer to the actual standard deviation of the noise, ${\mathrm{\sigma }}_{\text{noise}}$. The performance chart is used to infer a 90^th percentile noise floor (in units of μV) in IO plots.

Sensitivity to the number of MEP recordings

Fig. 5 displays estimated MUAP shapes of 20 subjects. We present four MUAP shapes per subject, each estimated from 5, 20, 50, or 100 randomly sampled recordings (thus random stimulation strength and time) respectively, and colored differently. For many cases, as few as five recordings turn out to already be enough to give a good, stable estimate of the MUAP. Increasing the number of recordings beyond 20 or 50 recordings does not necessarily further evolve the shape, demonstrating the stability of the proposed estimation method. Finally, it is clear that different subjects develop distinct MUAPs regardless of the number of samples, which supports personalized MEP estimation.

Fig. 5.

Estimated MUAP shapes across 20 subjects. Each MUAP shape is zero-mean and normalized.

Fig. 6 shows the estimated IO curves of subject 22 (monophasic pulse) using different template MUAPs. The leftmost panel uses a MUAP from subject 7 based on fie randomly selected MEP recordings, the middle panel one MUAP from subject 22 estimated from only five MEP recordings, and the right panel a MUAP from subject 22 estimated from 100 MEP recordings. For the most part of the IO curves, all three cases are practically identical. Only at weak stimulation amplitudes where the sensitivity plays a larger role, the estimates deviate from each other to a larger degree.

Fig. 6.

Estimated IO curves of subject 22 using MUAPs from different sources.

Results

We evaluated the method experimentally and combined the data acquisition with an earlier study [35]. Twenty-one healthy subjects (aged 18–48, 14 female and 7 male, all right-handed) were recruited from the local community and underwent navigated TMS with concurrent EMG recording. The procedure was approved by the Duke University Institutional Review Board. The subjects received single-pulse TMS with both biphasic and monophasic pulses over the representation of the first dorsal interosseous (FDI) muscle in the left primary motor cortex in the vicinity of the C3 location in the international 10–20 system [45, 46]. A focal figure-of-eight coil (MagVenture B65, Farum, Denmark) was positioned approximately 45° to the interhemispheric fissure to align the induced electric field perpendicularly with the hand-knob gyrus. The coil position with maximum MEP output amplitude in the FDI muscle was identified manually before the procedure. A robotic coil holder maintained the position of the coil throughout the session and compensated subject movements, while subjects were instructed to sit as still as possible [47]. MEPs were recorded and sampled synchronously to the TMS pulse trigger through surface Ag/AgCl electrodes and an MEP amplifier (K800 with SX230FW pre-amplifier, Biometrics Ltd., Gwent, UK) at 5 kHz and 16 bit. The data were low-pass filtered with a fourth-order Butterworth filter with a cut-off frequency of 600 Hz. Recordings with activity of more than 40 μV (peak to peak) within a window of 200 ms before the TMS pulse were marked as facilitated and excluded from the analysis. The individual pulses were at least 8 s apart and inter-pulse timing was uniformly pseudo-randomized to not follow the subject’s expectation or pick up any regular excitability oscillations. We recorded IO curves with likewise pseudo-randomized stimulation amplitudes for each subject.

We performed the above routine for 21 subjects. The learnt MUAP shapes vary by subject but are similar overall (Fig. 2).

IO curves and how weak can stimuli be to still evoke excitatory activations

Fig. 7 displays IO curves extracted from the data with conventional peak-to-peak MEP amplitude measurement and the proposed matched-filter estimator. The 90^th-percentile noise floor overlays in each IO plot mark the background activities. The background activities are gauged from the pre-stimulation MEP recordings, using the corresponding extraction methods as if they are actual post-stimulation recordings. The times of MEP peaks are extracted as follows: for the conventional method, the peak times are obtained by directly finding the peak of the raw recording; for the proposed method, the peak time is obtained from the reconstructed signal $T\left(v\right)x$. More results are shown in the Supplementary Data.

Fig. 7.

IO curves and peak EMG times (black) with moving-window median (red) in three example subjects for three different TMS pulse configurations (monophasic, reverse monophasic, and biphasic). Two types of detection methods are compared. The lower red horizontal line (“90th noise”) refers to the 90^th percentile background activity recorded shortly before the stimulation, using the same extraction method as if they were post-stimulation MEPs. The line above denotes the 50 μV level representing the resting motor threshold level. The current direction is normal unless otherwise denoted in the titles. The x axis denotes the stimulation strength in relative units (machine output); the y axes refer to peak-to-peak MEP amplitudes (Vpp) and time of the first peak after the stimulus. Electrode montages were not moved or reversed in their polarity during a session. The use of polarity-independent metrics and the training to only comparable stimulus–response pairs of one type, session, and subject eliminates the further relevance of the electrode polarity of the bipolar EMG montage.

For weaker stimuli, the conventional method collapses at around the 90^th percentile of background activity and fails to distinguish MEP responses therein. Conventional peak-to-peak measurement after moderate low-pass filtering leads to a lower-side plateau above 5 μV. The proposed estimator, in contrast, is less sensitive to noise as confirmed by the previous section so that responses can be detected and quantified notably below the 5 μV technical noise floor. These weak responses—which were usually considered noise—actually form a noticeable trend that reflects the expected positive stimulation-strength dependency. The trend monotonically decreases until reaching near the 90^th percentile background activity baseline (the “90th noise” marks of Fig. 7). These new baselines are around ¹/₅ (−14 dB) of their conventional counterparts.

As an important observation, the commonly used 50 μV threshold, i.e., the stimulation amplitude that leads to a median response of 50 μV peak-to-peak, no longer marks the onset of first detectable MEPs, but is almost in the center of the sigmoid (see Fig. 7). Thus, it turns out that the point that once was considered a stimulation strength at a level where first detectable responses occur is rather in the middle of the dynamic range of MEPs. The above observations are substantiated by further data shown in Fig. 7. The monotonic trend of weak MEP amplitudes (above the noise floor but below the 50 μV point) is ubiquitous, especially when more measurements are available.

The method allows a visual interpretation. The detection filter as a sum of MUAPs is adaptively and individually trained and practically converges to an equivalent of a band-pass filter to match the MEPs (Fig. 2). The self-learning improves with the number of stimulus–response recordings. It uses similarities in the response data whereas background noise und unrelated biopotentials do not correlate across the recordings so that they can be averaged out. Importantly, the detector is fully linear. Thus, a similar signal-to-noise ratio as demonstrated here is in principle also possible through aggressive low-pass filtering with a similar frequency profile as the MUAPs. Together with baseline and drift removal, it similarly constitutes a band-pass filter. However, the specific frequency characteristics of such a filter are a-priori entirely unclear. Too aggressive filtering would underestimate the MEP size as well as derived metrics such as the motor threshold. Accordingly, aggressive filtering can be safety-critical. Too moderate filtering, on the other hand, lets more than necessary noise and unrelated signals pass. The presented work accordingly generates such information in situ on an individual basis.

Conclusions

We presented a method to detect MEPs in response to TMS. The method is notably more sensitive than conventional peak-to-peak metrics so that responses below the noise floor could be detected. Our analysis indicated that the detection sensitivity could be increased by 14 dB.

In addition to a detection of even smaller MEPs in response to weak stimuli due to the increased sensitivity, the method can also detect the already established dynamic range of the IO curve and provide the same reading in peak-to-peak voltage with lower distortion and higher accuracy. This peak-to-peak voltage of the ideal, noise-free MEP tends to turn out smaller in amplitude, whereas the conventional peak-to-peak detection is highly sensitive to noise, which introduces asymmetric bias and therefore systematically overestimates MEPs.

The formalism is based on matched- or optimum-filter estimation, which is a well-established maximum-likelihood-grade detector in communication systems. Since, in contrast to communication systems, the optimum filter is not known and is individual, the method learns it adaptively on the go. The MEP detection filter or pattern is iteratively improved, and previous measurements can be continuously reappraised with the improved filter.

The method uncovers that stimuli well below the conventional 50 μV threshold definition can consistently and repeatably evoke muscular responses and thus activate excitable neuron populations in the brain. As a consequence, the IO curve is extended at the lower end, and the noise cut-off is shifted. Importantly, the IO curve extends so far that the 50 μV point turns out to be closer to the center of the logarithmic sigmoid rather than close to the first detectable responses.

Finally, the presented method is applicable to other forms of brain or peripheral stimulation as well as potentially to other biosignals representing evoked responses.

Availability

The method used for the analysis and instructions are available at https://github.com/zlduke/MEP-decomposition to the community for free use and further development.