Automatic jitter measurement in needle-detected motor unit potential trains

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Computers in Biology and Medicine 149 (2022) 105973

Available online 18 August 2022

Automatic jitter measurement in needle-detected motor unit potential trains

^☆

Armando Malanda

^a^,^*

, Daniel W. Stashuk

^b

, Javier Navallas

^a

, Javier Rodríguez-Falces

^a

, Ignacio Rodríguez-Carre˜no

^c

, C´esar Valle

^a

, Oscar Garn´es-Camarena

^d

aDepartment of Electrical, Electronics and Communication Engineering, Public University of Navarra, Campus de Arrosadía, 31006, Navarra, Spain

bSystem Design Engineering Department, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada

cBusiness Department, Faculty of Economics and Business, University of Navarra, Edificio Amigos, Campus Universitario, 31009, Pamplona, Navarra, Spain

dClinical Neurophysiology Service of the Fundaci´on Jim´enez Díaz University Hospital, Madrid, Spain

A R T I C L E I N F O Keywords:

Concentric needle electrode Jitter estimation Motor unit potential Neuromuscular disorders

Neuromuscular transmission instability Single fiber potential

A B S T R A C T

In an active motor unit (MU), the time intervals between the firings of its muscle fibers vary across successive MU activations. This variability is called jitter and is increased in pathological processes that affect the neuromuscular junctions or terminal axonal segments of MUs. Traditionally, jitter has been measured using single fiber electrodes (SFEs) and a difficult and subjective manual technique. SFEs are expensive and reused, implying a potential risk of patient infection; so, they are being gradually substituted by safer, disposable, concentric needle electrodes (CNEs). As CNEs are larger, voltage contributions from individual fibers of a MU are more difficult to detect, making jitter measurement more difficult. This paper presents an automatic method to estimate jitter from trains of motor unit potentials (MUPs), for both SFE and CNE records. For a MUP train, segments of MUPs generated by single muscle fibers (SF MUP segments) are found and jitter is measured between pairs of these segments. Segments whose estimated jitter values are not reliable, according to several SF MUP segment characteristics, are excluded. The method has been tested in several simulation studies that use mathematical models of muscle fiber potentials. The results are very satisfactory in terms of jitter estimation error (less than 10% in most of the cases studied) and mean number of valid jitter estimates obtained per simulated train (greater than 1.0 in many of the cases and less than 0.5 only in the most complicated). A preliminary study with real signals was also performed, using 19 MUP trains from 3 neuropathic patients. Jitter measurements obtained by the automatic method were compared with those extracted from a commercial system (Keypoint) and the edition and supervision of an expert electromyographer. From these measurements 63% were taken from equivalent interval pair sites within the time span of the MUP trains and, as such, were considered as compatible measurements.

Differences in jitter of these compatible measurements were very low (mean value of 1.3 μs, mean of absolute differences of 2.97 μs, 25% and 75% percentile intervals of − 0.85 and 3.82 μs, respectively). Although new tests with larger number of real recordings are still required, the method seems promising for clinical practice.

Abbreviations: SFE, Single fiber electrode; CNE, Concentric needle electrode; MU, Motor unit; AAP, Axonal action potential; NMJ, Neuromuscular junction; MFAP, Muscle fiber action potential; MFP, Muscle fiber potential; MUP, Motor unit potential; MUPT, Motor unit potential train; IPI, Inter potential interval; EMG, Elec- tromyography; SFP, Single fiber potential; MCD, Mean consecutive differences; SD, Standard deviation; SF, Single fiber; DTW, Dynamic time warping; SVM, Support vector machine; SF-MUP, Single fiber motor unit potential; ALJ, Average local jitter; RI, Reliability indicator; Dur, Duration; SPJV, Segment pair jitter variability;

SPMTI, Segment pair mean time interval.

☆This work has been supported by the Spanish Ministry of Science, Education, and Universities, under the “Salvador de Madariaga” 2018 Program and by the Spanish Ministry of Education and Research, under the PID2019-109062RB-I00 project. Open Access funding provided by the Public University of Navarra.

* Corresponding author.

E-mail addresses: [email protected] (A. Malanda), [email protected] (D.W. Stashuk), [email protected] (J. Navallas), javier.rodriguez@

unavarra.es (J. Rodríguez-Falces), [email protected] (I. Rodríguez-Carre˜no), [email protected] (C. Valle), [email protected] (O. Garn´es- Camarena).

Contents lists available at ScienceDirect

Computers in Biology and Medicine

journal homepage: www.elsevier.com/locate/compbiomed

https://doi.org/10.1016/j.compbiomed.2022.105973

Received 12 March 2022; Received in revised form 28 July 2022; Accepted 13 August 2022

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1. Introduction

A motor unit (MU) consists of a motor neuron, located in the anterior horn of the spinal cord, its axon and all of the skeletal muscle fibers connected to the axon. The activation of a motor neuron generates a propagating trans-axolemma axonal action potential (AAP), which travels along its axon and axonal branches to their respective neuromuscular junction (NMJ). Following the processes of NMJ transmission, a pair of propagating trans-sarcolemma muscle fiber action potentials (MFAPs) are generated along its connected muscle fiber. The MFAPs propagate in opposite directions away from the NMJ towards each respective muscle tendon. An MFAP will generate a muscle fibre potential (MFP) over the surface of an extracellular electrode. Usually, only MFAPs propagating towards an extracellular electrode generate mean- ingful MFPs. The sum of the MFPs generated by the fibers of a MU is called a motor unit potential (MUP). During muscle contraction, MUs are repeatedly activated and thus a set of consecutive MUPs, or a MUP train (MUPT), is detected.

Because of the common motor neuron origin, the MFPs of the different fibers of a MU are generated more or less synchronously, except for small temporal shifts due to different AAP conduction times to each respective NMJ and different NMJ transmission times. Each axonal branch and NMJ will have an expected conduction time and transmission time. Therefore, there will be some expected inter potential interval (IPI) between each pair of MFPs contributing to a MUP. In addition, the AAP conduction and NMJ transmission times have associated variances. The variance of the AAP conduction times is expected to be much less than that of the NMJ transmission times. As such, the measurement of the variance of IPIs between pairs of selected MFPs -technically referred as jitter- [1] represents for the most part the variance of NMJ transmission times. Different pathophysiological conditions can cause increased jitter. Diseases of the neuromuscular junction, such as, myasthenia gravis [2–5], congenital myasthenic syndrome [6]

and the Lambert-Eaton myasthenic syndrome [7] alter and sometimes block the transmission of impulses to muscle fibers, consistently increasing the level of jitter [8]. Besides, botulinum neurotoxin in- jections seem to increase neurophysiological jitter [9,10]. In neuropa- thies, during the initial stages of reinnervation that follows muscle fiber

denervation, new neuromuscular junctions are immature and produce MFPs with relatively high levels of jitter, as observed in amyotrophic lateral sclerosis [11,12], multifocal motor neuropathy [13], diabetic neuropathy [14], chronic radiculopathy [15], or Guillain-Barr´e syndrome [16]. Finally, muscle reinnervation is also present in age-related sarcopenia, and high jitter values can be observed in the muscles of elderly people [17].

Traditionally, jitter has been measured during electromyographic (EMG) examinations using single fiber (SF) electrodes [2,5,6,8,9,14,18].

The detection area of these electrodes has very small surface (approx.

0.005 mm²) [19,20]. The technique consists of capturing MUPTs with MUPs comprised of at least two sufficiently large and sufficiently temporally separated potentials. These potentials, detected using SF electrodes, are thus referred as single fiber potentials (SFPs) (Fig. 1). The assumption is that an SFP is an MFP and thus represents the activity of a single muscle fiber. In successive MUPs across the MUPT, the IPI between SFP pairs is measured, and the jitter is calculated as the mean of the absolute differences of consecutive IPI measurements (“mean consecutive differences” or MCD) [1,20,21], which is a measurement similar to the standard deviation (SD) of the measured IPIs [22]. Several conditions have been put forward for considering two SFPs as MFPs, and hence valid for jitter assessment. Ekstedt qualitatively formulated the need of clean and smooth biphasic spikes with identical shapes across the potentials of the train [23]. Stålberg and Sanders established quantitative conditions for these potentials (amplitude between 200 μV and 20 mV, rise time less than 300 μs, and no extra phases or turns [24, 25]. Rodriguez et al. extended these studies, showing the need to further limit the amplitude and rise time ranges and incorporating the rise time variability (RTV) as a new parameter to assess the validity of jitter measurements (trains with an RTV higher than 20 μs should be excluded) [26]. Likewise, Zalewska et al. established elaborate criteria to validate jitter values, based on an estimation of fiber diameter extracted from the MUP shape [27].

In addition to these reliability problems, arising from the problem of selecting which SFPs are actually MFPs, the actual clinical procedure for jitter estimation is time consuming and technically difficult, and the electrodes are expensive and, reusable, presenting a potential risk of infection.

Fig. 1. Recording (A) and IPI variability (B) of a MUP composed of two MFPs.

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Because they are easy to use, cheap and disposable, concentric needle electrodes are currently the type of electrode most often used for clinical examinations. Therefore, there is an increasingly widespread trend in clinical practice for using concentric needle electrodes to perform jitter measurements [3,4,10,12,15,17,19–21,39]. However, because conventional and facial concentric needle electrodes have larger detection surfaces (approx. 0.070 mm²and 0.019 mm², respectively) [28] than SF needle electrodes, contributions of several MFPs may be present in the MUPs, making the estimation of jitter even more difficult [28] and requiring a very careful interpretation of the results [29]. The recorded potentials are filtered with high pass filters with cutoff frequencies (1000 Hz) higher than those used with SF electrodes (500 Hz) [28,30] or acceleration filters [31]. These filters attenuate low frequency signal contributions, which mainly come from fibers distant from the electrode, and they narrow MUP peaks, allowing better separation of different MUP components.

In any case, the task of estimating jitter is complicated and requires a considerable amount of time and skill to obtain signals with at least two clearly recognizable and dispersed SFPs and several well-behavior characteristics: one positive and one negative peak, constant-shape ris- ing face, no shoulders or notches and no gross amplitude variation [20, 21].

Abdelmaseeh et al. published an automatic method for the determination of jitter from concentric needle records [32]. This method used the technique called “Dynamic time warping” (DTW) for locally align the potentials of the MUP trains in a non-liner fashion. Then a machine learning technique, “Support vector machine” (SVM), was used for characterizing consecutive constant-length overlapping signal segments of the MUP trains as being well-behaved or badly behaved for jitter estimation, as they attained little or large jitter error in the training stage of the algorithm using simulated EMG signals. In the operating stage, MUP trains were aligned and segments characterized and determined by the SVM as valid or non-valid for jitter assessment. Finally jitter measurement was obtained from pairs of valid segments estimating a feature related to the standard deviation of their time differences. This method is computationally complex and includes a classifier trained using examples extracted from simulated signals; to date, as far as we know, it has not been used to process real signals from normal or pathological muscles.

More recently, a new technique called “near fiber segment jitter”, was proposed to evaluate MU instability of the near fibers significantly contributing to the analyzed MUP [33]. Near fiber MUPs were obtained with the use of a low-pass-double-differentiation filter and a template was selected among the MUPs of the MUP train and segmented into non-constant length non-overlapping segments; MUPs of the MUP train were then aligned to the near fiber template in a segment-to-segment basis. MUPs contaminated with contributions of other MUs, with regard to average mean amplitude consecutive differences across aligned segments in the MUP train, were excluded from the MUP train. Finally, an average measure of the jitter associated with the near fibers was obtained by a weighted average of the shape similarities of the involved MUP segments. This technique was tested with simulated data and also from EMG data from three subjects (control, neurogenic and myopathic), obtaining consistent correlation between jitter measurements and the physiological changes included in the simulation or presumably existing in the subjects’ muscles. However, no direct evaluation of the precision of these measurements was indicated.

The work presented here describes a new automatic algorithm grounded on the properties of the signals comprising a MUPT in the presence of jitter. This algorithm has been tested using a set of synthetic signals generated with a MUP simulator based on MFP generation models [34], as well as a bank of MUPTs extracted from muscles of three subjects within routine clinical EMG studies.

2. Materials and methods 2.1. Automatic measurement of jitter

1) MUP Alignment and Local Jitter Measurement

Fig. 2 shows several potentials from a MUPT superimposed, where each MUP is composed of two MFPs. In Fig. 2A, to calculate jitter, all potentials are initially aligned using the first positive peak and then the SD of the time intervals to the second positive peak are measured. (The MCD could be used alternatively for the jitter measurement, but the explanation is clearer for the SD). However, in general, the alignment and analysis points (as long as they have a sufficient expected time interval between them), can be selected to be any pair of time samples in the MUP, even if they do not correspond to peaks (Fig. 2B).

Let us explain alignment and jitter measurement in more detail.

These procedures are tightly related, as the MUPs within a train need first to be aligned at an alignment point (Fig. 3A), previous to the measurement of the time dispersion of these MUPs at an analysis point (Fig. 3B).

MUP Alignment: Let {xi(t)} be the set of N MUPs comprising a MUPT and let t0 be the selected alignment point. The MUP centroid, ̂x(t), is defined as the L-width segment of the element of {xi(t)} that is closest to the ensemble- averaged MUP template of the train within the L width alignment region, centered at t0. The centroid segment ̂x(t) serves as a reference to align the MUPs of {xi(t)} around t0.

̂x(t) = centroid{xi(t)}, t0− L − 1

2 <t < t0+L − 1 2 ,

i = 1, .., N (1)

(To attain symmetry, L should be an odd number).

To align each MUP of {xi(t)} to the centroid segment ̂x(t) a matching segment of xi(t), ˘xi(t), of width M, also centered at t0, is used.

˘xi(t) =

⎧⎨

⎩

xi(t) if t0− M − 1

2 <t < t0+M − 1 2 0, otherwise

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where M < L and M is also odd.

Matching segment ˘xi(t) is shifted a number of samples Δ and its shape similarity (match) with centroid segment ̂x(t) is measured (φ_i(Δ)).

φ_i(Δ) = Match(˘xi(t − Δ), ̂x(t)) (3)

This is repeated for all possible shifts across the alignment search interval given by

− L + M

2 <Δ <L − M

2 (4)

Therefore, shifting of the matching segment ˘xi(t) does not exceed the limits of the interval defining the centroid segment ̂x(t). The maximum shape match value across the alignment search interval yields the number of samples (Δmatch,i) that MUP xi(t) is to be shifted for optimal alignment:

φ_i( Δmatch,i

)= Max⏟⏞⏞⏟

(−L+M)/2< Δ < (L− M)/2

{φ_i(Δ)} (5)

yi(t) = xi

(t − Δmatch, i

) (6)

This process is repeated for each xi(t) and {yi(t)}, the set of N shifted MUPs, constitutes the aligned MUPT. Minimum Euclidean distance, maximum cross-correlation or other similar distance measurements can be used for selecting the centroid MUP segment in (1) and for the matching procedure in (3). In this work, the Euclidean distance was used for both of these tasks.

Local Jitter Measurement: Given a set yi(t) of N MUPs of a MUPT

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aligned with time point t0, jitter at time point t1 relative to t0 will be referred as J(t0,t1). To measure J(t0,t1), basically the same procedure as for time alignment is followed, except that at the end of the procedure the potentials of the MUPT are not shifted. Instead, the SD of the optimal offsets between potentials of the set y_i(t) and a reference potential segment (i.e. a new MUP centroid of this set) is computed. Formally, expressions (1) to (5) are valid, with the mere change of xi by yi and t0 by

t1. The procedure is as follows.

A new centroid MUP segment, ̂y(t), centered at t1 is defined:

̂y(t) = centroid{yi(t)}, t1− L − 1

2 <t < t1+L − 1

2 ,i = 1, .., N (7) For each aligned potential in {yi(t)}, a matching segment, ˘y_i(t), of width M, also centered at t1, is used.

Fig. 2. Jitter measurement (alignment and analysis points marked by vertical bars).

Fig. 3. MUPT before alignment (A) and after alignment (B). Alignment and analysis time points are marked with vertical bars. The L-wide window delimiting the centroid segments (large cages) and the M-wide window delimiting the matching segments (small cages) are shown around the alignment point (A) and analysis point (B), respectively.

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˘y_i(t) =

⎧⎨

⎩

yi(t) if t1− M − 1

2 <t < t1+M − 1 2 0, otherwise

(8) Matching segment ˘y_i(t) is shifted a number of samples Δ and its shape similarity (match) with the centroid segment ̂y(t) is measured (φi(Δ)).

φ_i(Δ) = Match(˘y_i(t − Δ), ̂y(t)) (9)

This is repeated for all possible shifts across the alignment search interval given by

− L + M

2 <Δ <L − M

2 (10)

The maximum shape match value across the alignment search in- terval yields the number of samples (Δmatch,i) that MUP y_i(t) should be shifted for optimal alignment:

φ_i( Δmatch,i

)= ⏟̅⏞⏞̅⏟Max

(−L+M)/2<Δ<(L− M)/2

{φ_i(Δ)} (11)

Therefore, Δmatch,i is considered the actual delay between the matching segment ˘y_i(t) and the reference centroid ̂y(t). Finally, the local jitter around time t1 is given by the SD of the optimal offsets (Δmatch,i) across the N MUPs of the MUPT:

J(t0,t1) = ⏟⏞⏞⏟SD

i=1, ..,N

{Δmatch,i

} (12)

2) Single Fiber MUP Segments

Studies with simulated MUP trains show that, depending on the time interval between two MFPs, the measured jitter may differ significantly from the actual variation in NMJ transmission associated with the two source fibers (i.e. the true jitter). As an example, Fig. 4 shows a simulated MUP train composed of two MFP trains. Taken them separately, each MUP train has a particular and independent time dispersion, characterized by its jitter measurement (σ₁ and σ₂, respectively) (Fig. 4A). When the potentials of these trains are summed to form the MUP train (Fig. 4B), the first and second positive peaks can be associated

with the first and second MFP trains. The dispersion measured in these peaks (σ^′₁and σ^′₂, respectively) are no longer the same as that of the isolated MFP trains.

This can be due to the superposition of MFPs of the activated MU.

Only when two MFPs are temporally separated by at least 0.5 ms, can the measured jitter be consistently expected to closely approximate the true jitter [22]. When the time separation is less, there can be significant overlap between the MFPs and the measured jitter will not be reliable.

Therefore, it is necessary to find segments of a MUP, generated mainly by a single MFP, i.e. single-fiber MUP (SF-MUP) segments, temporally separated by at least 0.5 ms. The variation in the time intervals between a pair of suitably temporally separated SF-MUP segments across the MUPs of a MUPT will then be able to accurately represent the variation in NMJ transmission times associated with the source fibers.

Fig. 5A shows three simulated MFPs which are ensemble-added to create the MUP shown in Fig. 5B. The SF-MUP segments of this MUP are marked in Fig. 5C. In this example, the different MFPs that make up the MUP are known, so it is easy to find the SF-MUP segments. However, in real cases, MUP composition is not known and the problem of finding SF- MUP segments is complex.

The following example reveals the key to detecting SF-MUP segments. In Fig. 6, a MUPT is formed from two MFPs which overlap significantly only between 4.0 and 4.5 ms (Fig. 6A). The resulting (reference) MUP is shown in Fig. 6B. To build the MUPT, the two MFPs are time shifted by a random amount and summed together. This operation is repeated until the whole train is obtained (Fig. 6C). The time shifts are such that the overall jitter value between the two MFPs is 50 μs (reference jitter value). In Fig. 6D the train has been aligned using the first negative peak. In the first part of the MUP, corresponding to the first MFP, there is no noticeable shape variability. In contrast, the part of the MUP relative to the second MFP does have jitter, as is the case in Fig. 2A. Local jitter values can be examined across all of the temporal instants of the MUP duration, with respect to a given alignment point (local jitter scan). Fig. 6G shows the local jitter scan of the MUPs of the example, using the first negative peak as the alignment point. This jitter scan has values of zero within the interval around the first negative peak (i.e. between 2.5 and 3.5 ms) and around the second peak (i.e. between

Fig. 4. Two MFP trains and the jitter in the timing of the positive peaks (A). MUPT composed of the same two MFP trains and the jitter that measures the variability in the time intervals between the two positive peaks (B). The estimates of jitter in A and B differ.

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Fig. 5. Three MFPs (A) comprising a MUP (B). SF-MUP segments of the MUP (C).

Fig. 6. An example of a MUP (B) composed of two MFPs (A). A MUPT train is formed by including independent jitter to each MUFPs (C). MUPT aligned at at different points (circles) (D–F). Jitter scans (G–I).

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4.5 and 5.5 ms) has values close to that of the simulated jitter (50 μs).

Fig. 6F and Fig. 6I are similar and somewhat symmetrical with respect to Fig. 6D and Fig. 6G. Here the local jitter scan shown in Fig. 6I is with respect to using the second positive peak as the alignment point, around which (i.e. between 4.5 and 5.5 ms) there is no noticeable shape variability and local jitter values of zero. In contrast, the local jitter values around the first peak (i.e. between 2.5 and 3.5 ms) are close to the simulated jitter. In Fig. 6E, the train was aligned using the point at 4.1 ms, in the region of overlap between the two MFPs. Neither at the alignment point, nor before nor after, do MUP potentials overlap in a single line (i.e. they do have some shape variability at these points). In addition, the values of local jitter with respect to using the point at 4.1 ms for alignment do not drop to zero around the alignment point (Fig. 6H).

The reason for the non-zero jitter scan values is that around the alignment point near 4.1 ms there is some MUP variability, due to the variable summation of the two contributing MFPs, whose occurrence time variations cannot be simultaneously eliminated by aligning the MUPs at this point. The MUP segments between 2.5 and 3.5 ms and between 4.5 and 5.5 ms are SF-MUP segments, while the MUP segment around 4.1 ms is not a SF-MUP segment.

This analysis shows that jitter can be measured using two SF- MUP segments, one serving as an alignment point and the other as an analysis point. However, when the measurement is made between two MUP segments, of which none or only one of them is a SF-MUP segment, jitter cannot be estimated reliably (Fig. 6E). In addition, this analysis shows that an alignment point will only be useful for measuring jitter if its associated local jitter scan has some values equal to or close to zero (Fig. 6D, G, F, I).

3) Neighborhood Jitter

In general, given an alignment point within a SF-MUP segment, the resulting local jitter scan will have values of zero or close to zero in the region around the alignment point. As such, the concept of neighborhood jitter may be helpful.

Neighborhood Jitter: Let {xi(t)} be the set of N MUPs comprising a

MUPT and let t0 be the selected alignment point. The neighborhood jitter value at t0, NJ(t0)is defined as the square root of the sum of squares of the local jitter values at time points t − δ and t + δ , taking t0 as the alignment point:

NJ(t0) =

̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅

(J(t0,t0− δ))²+ (J(t0,t0+δ))²

√

(13) where δ is a small/local time shift.

If the neighborhood jitter value at a particular point in time is small enough, that point will be considered to belong to a SF-MUP segment and valid for measuring jitter. It is necessary to detect pairs of SF-MUP segment points between which jitter can be measured.

Based on this, neighborhood jitter values can be examined along the entire duration of a MUP (neighborhood jitter scan). Fig. 7 shows the neighborhood jitter scan calculated for a MUPT comprised of MUPs formed by five MFPs, in which the simulated jitter for each fiber was 50 μs. Four SF-MUP segments, where the neighborhood jitter scan has values below a selected threshold (10 μs in this case), are marked. Points in these segments are potentially valid for calculating jitter.

4) Estimation of jitter between SF-MUP segments

For each pair of SF-MUP segments, the first segment can be used to choose alignment points and the second segment to choose analysis points. A different value of jitter will be extracted from each pair of alignment and analysis points. If the first SF-MUP segment (Segi) con- tains Ni time samples and the.

second segment (Segj) contains Nj time samples, there will be a total of Ni⋅Nj jitter measurements for this segment pair. A global value is estimated by calculating a weighted average among these measurements such that samples with local jitter values close to zero will have greater weights in the estimation of the jitter than samples with larger local jitter values. More precisely, the segment jitter estimate associated with the segment pair (Segi,Segj) is

Fig. 7. MUPT (A) and its neighborhood jitter scan (B). The same four SF-MUP segments are shown in each figure.

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SJ( Segi,Segj

)= 1 KU

∑^Nⁱ

m=1

∑^N^j

n=1

[J( τim,τjn

)⋅(U − NJ(τim))⋅( U − NJ(

τjn

))]

(14) where J(τα,τβ) is the jitter estimate between the time samples τα

(alignment point) and τβ (analysis point); NJ(τ)is the neighborhood jitter estimated at sample time τ; τim and τjn are time samples corre- sponding to the segments Segi and Segj, respectively, U is the threshold for defining the SF-MUP segments from the local jitter scan; and KU is a normalization factor given by

KU=∑^Nⁱ

m=1

∑^N^j

n=1

[(U − NJ(τim))⋅( U − NJ(

τjn

))] (15)

It may happen that two of the SF-MUP segments selected from the local jitter scan correspond to the same MFP. See as an example the interval around 3.8 ms and the interval around 4 ms of the MUP of Fig. 5B. They are both marked as SF-MUP segments in Fig. 5C, and the two correspond to the second MFP comprising the MUP, as plotted in Fig. 5A. In this case, the jitter estimated for this segment pair will have a very small value, since the jitter between these segments will be measured with reference to the same MFP. In other words, the measurement will be the time difference variations between one MFP and itself. This pair of segments will not be valid for jitter estimation. But it is not enough to remove it from the set of valid segment pairs, the segments and segment pairs must be rebuilt completely.

In the example of Fig. 7, suppose that the segments Seg2 and Seg3

correspond to the same MFP, then the segment pairs [Seg1, Seg2] and [Seg1, Seg3] will correspond to a jitter estimation for the same MFP pair, so the jitter values obtained for them should not be given as separate and independent results, but should be aggregated to give a single result. The same would happen with the pairs of segments [Seg2, Seg4] and [Seg3, Seg4]. That is why when this situation occurs the SF-MUP segments must be recomposed, joining the time samples of those that correspond to the same MFP (Seg2 and Seg3 in this case) and re-estimating the jitter between the new pairs of SF-MUPs.

5) Reliability of Jitter Measurements

At this point, it may be useful to characterize the segments by means of two parameters: duration (number of time samples) and average local jitter value (ALJ) within the segment. These parameters are related to the reliability of the jitter estimate in the sense that long and small ALJ segments lead to highly reliable jitter estimates. So, intervals whose duration is below a given duration threshold or whose ALJ is above a given jitter threshold are discarded. The jitter between every pair of valid segments can then be estimated.

An overall indicator of reliability (RI) for each segment pair and for its corresponding jitter estimate, aggregating the duration (Dur) and the ALJ of the two intervals of the pair, can be defined as:

RI(i, j) =Dur(i) ALJ(i)+Dur(j)

ALJ(j) (16)

Some features applicable to the pairs of segments can also be related to the reliability of the jitter estimate. One of these is called the “segment pair jitter variability” (SPJV), i.e., the mean variability of the jitter values obtained as the alignment point is kept fixed and the analysis point varies along the analysis segment, and that obtained as the analysis point is kept fixed and the alignment point varies along the alignment segment. Thus, for each segment pair, two SPJV figures can be computed as:

SPJV⁽¹⁾(i, j) =1 Ni

∑^Nⁱ

m=1

{ SD{

J( τim,τjn

)}

n=1, Nj

} (17)

SPJV⁽²⁾(i, j) =1 Nj

∑^N^j

n=1

{ SD{

J( τim,τjn

)}

m=1,Ni

} (18)

It is considered that high SPJV values indicate that there is some factor disturbing the jitter measurement, rendering it unreliable.

Another such factor is the mean time interval between the two segments of the pair (SPMTI), as close intervals are more likely to correspond to the same MFP, for which the jitter measurement would be senseless. So, any segment pairs whose SPJV are above a given variability threshold or whose SPMTI is below a given time threshold are discarded.

Finally, if there are N SF-MUP segments, there will be (N

2 )

=^{N⋅(N− 1)}₂ different segment pairs, but only N-1 of them are, in fact, independent.

Going back to the example of Fig. 7, we may have independent jitter estimates between the pair [Seg1, Seg2] , and between [Seg2, Seg3] , but then the estimate between [Seg1, Seg3] will not be independent of the previous two. So, from all the possible pairs and discounting those already discarded for having high SPJV or low SPMTI, the N-1 inde- pendent couples that have the highest average reliability as given by (16) are chosen.

6) The Jitter Algorithm

Initially, the MUPs in the train are filtered using a low-pass- acceleration filter [17,31,33]. This filter narrows MUPs and sharpens their peaks. As the peaks narrow, the overlap between neighboring peaks is reduced, which may increase the number and size of the SF-MUP segments discovered and, therefore, the possibility of finding additional valid segment pairs.

The jitter estimation algorithm proposed in this work takes a MUPT and obtains a set of valid SF-MUP segments, each with an independent estimate of jitter. Below is a summary of the main steps in pseudocode:

1. Acceleration filtering (Sect. 2.A.6)

2. Calculation of a local jitter scan (Sect. 2.A.1, 2.A.3) 3. Extraction of SF-MUP segments (Sect. 2.A.2-2.A.3)

4. Estimation of the jitter between pairs of SF-MUP segments (Sect.

2.A.4)

5. Detection of pairs of segments corresponding to the same fiber (Sect. 2.A.4)

6. Recomposition of independent SF-MUP segments (Sect. 2.A.3, 2.

A.4)

7. Characterization of SF-MUP segments (duration and ALJ) (Sect.

2.A.5)

8. Exclusion of non-reliable segments (Sect. 2.A.5)

9. Estimation of the jitter between new pairs of SF-MUP segments (Sect. 2.A.4)

10. Characterization of pairs of SF-MUP segments (SPJV and SPMTI) (Sect. 2.A.5)

11. Exclusion of non-reliable SF-MUP segment pairs (Sect. 2.A.5) 12. Selection of the most reliable SF-MUP segment pairs, each asso-

ciated to a jitter estimate (Sect. 2.A.5).

2.2. Simulation tests

A set of simulation studies were conducted to study the performance of the method, using a MUP simulator based on Dimitrov’s convolu- tional MFP model [34]. A concentric needle electrode was considered. It was placed perpendicular to MU fibers, with the center of the elliptical active tip in the coordinate origin (Fig. 8). The long axis of the ellipse was coincident with the Z axis of the 3-dimensional space representing the system, whereas the short ellipse axis coincided with the X (axial) axis (Fig. 8B). Y axis indicated the orthogonal distance of a point to the plane holding the active tip surface (i.e., the XZ plane) (Fig. 8A). For each fiber, the axial distance (i.e., the neuromuscular

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junction-to-electrode distance in the X dimension) was established as a random variable between 10 and 25 mm (mean, SD and maximum MFP temporal separation of 1.875, 1.082 and 3.75 ms, respectively). Its radial distance was established by its Y and Z coordinates, that were taken as two independent random variables uniformly distributed within the intervals [0.1, 0.5] and [− 0.3 0.3] mm, respectively.

The following parameter values were also established by default:

length of muscle fibers: 63 mm; conduction velocity: 4 m/s; 50 potentials per MUPT; 3 MFPs per MUP; jitter level: 50 μs; segments of 15 ms containing the MUPs; sampling frequency: 200 kHz; concentric electrode with an active tip area of 0.070 mm2 (axis of 580 and 50 μm).

Random Gaussian noise was added to the signal trains; the SD of its amplitude was set to 10 μV.

Apart from these, various thresholds and window widths used in the algorithm are: centroid width (L): 1.25 ms; matching segment width (M): 0.25 ms; jitter threshold for obtaining SF-MUP segments from neighborhood jitter scan: 10 μs; jitter threshold for considering a pair of SF-MUP segments valid for jitter estimation: 12.5 μs; Minimum temporal separation for considering a pair of SF-MUP segments valid for jitter estimation: 0.5 ms; maximum acceptable SPJV: 0.005; minimum acceptable SF-MUP segment duration (Dur): 0.08 ms; Maximum neighborhood jitter average acceptable for a SF-MUP segment: 7 μs.

The following studies were carried out in which one of these parameters was subject to variation, keeping the rest at their reference values:

- Study 1: variation of the simulated jitter value for all the MFPs in the MUPTs (from 25 to 125 μs in steps of 25 μs);

- Study 2: variation of the number of MFPs that form the MUPs (from 2 to 5);

- Study 3: variation of the number of MUPs per MUPT (5 and from 10 to 100 in steps of 10);

- Study 4: only two MFPs composing the MUP; the interval limiting the position of the first fiber in the Y coordinate was [0.1, 0.2] mm; the interval limiting the position of the second fiber in the Y coordinate varied in the study as follows: [0.1, 0.2], [0.2, 0.3], [0.3, 0.4], [0.4, 0.5] and [0.5, 0.6] mm;

- Study 5: only two MFPs composing the MUP; the interval limiting the position of the first fiber in the X coordinate (neuromuscular junction-to-electrode distance) was [10, 12.5] mm; the interval limiting the position of the second fiber in the X coordinate varied in the study as follows: [10, 12.5], [12.5, 15], [15, 17.5], [17.5, 20], [20, 22.5] and [22.5, 25] mm. These intervals correspond to [minimum, maximum] MFP temporal separation of [0, 0.625], [0, 1.25],

[0.625, 1.875], [1.25, 2.50], [1.875, 3.125], [2.50, 3.75] ms, respectively);

- Study 6: variation of the noise level in the MUP signals (SD values:

2.5, 5, 10, 20, 40, 80 μV).

In each study and for each value of the specific parameter under analysis, 100 MUPTs were simulated. Each of the 50 potentials composing each MUPT was shifted a Gaussian random amount according to the specified jitter level. Then the real jitter associated to a MUPT was calculated as the SD of the random shifts. Using the new algorithm, several jitter estimates, corresponding to the pairs of detected and valid SF-MUP segments, were obtained for each train and corresponding estimation errors were calculated as the differences between the jitter estimates and the real jitter values. Relative errors were then extracted by dividing by the real jitter values. Statistical analysis of these errors was summarized in “boxplot” figures and curves for the median and several percentiles. For the 100 simulated trains, the number of valid MUPTs (i.e., in which jitter was estimated reliably at least once) and the number of pairs of SF-MUP segments (i.e., the number of final jitter estimation values) were also assessed.

2.3. Tests with real signals

To further evaluate the described algorithms 14 real EMG signals were processed. These were 20 sec-long signals recorded from muscles of three neuropathic patients during routine clinical examination at the Clinical Neurophysiology Department of the Jim´enez Díaz Foundation University Hospital, Madrid, Spain, using a Keypoint system (v.3.22), 0.5–10 kHz or 1–10 kHz bandpass filtering and facial concentric needle electrodes (uptake area of 0.019 mm²). The study presented here was carried out in accordance with the Declaration of Helsinki for experi- ments involving humans and was approved by the Ethical Committee of the aforementioned Hospital. Clinical information about the three subjects and the specific filter used for the recording are given in Table 1.

From each EMG signal one MUP train was extracted using a trigger threshold. For each MUPT, the Keypoint marked a number of peaks. The highest negative peak was used as the reference peak (alignment site).

The time lag between the reference peak and each one of the other peaks was computed and for each the mean of absolute consecutive differences (MCD) across the MUPs of the train was calculated, following the standard procedure in jitter studies [1,20,21]. Manual editing was performed by an expert electromyographer (OGC) and consisted of excluding train potentials that strayed from the general trend and dis- carding peaks that were not reliable for alignment or jitter measurement Fig. 8. Schematic cross section (A) and axial view (B) of a motor unit comprised of three muscle fibers and a recording concentric needle electrode.

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(i.e. those that were too aberrant in shape or too noisy). A set of 19 MUP trains were extracted and used for this analysis. While, the raw EMG signals were digitally recorded by the Keypoint system, the specific extracted MUPs could not be digitally exported. Therefore, for each raw EMG signal, a screenshot of the Keypoint extracted MUPs was captured (Fig. 9A) and the corresponding EMG signal was decomposed using DQEMG [40]. For each EMG signal DQEMG extracted several MUP trains (Fig. 9B-D). From these MUP trains, the one which most closely matched the Keypoint extracted MUP train, as assessed by visual comparison with the corresponding screenshot (in this case, MUP 1 shown in Fig. 9B), was selected for automatic jitter analysis (Fig. 9E). Internal parameters of the automatic technique were set to the same values as for the simulation tests.

Table 1

Clinical information about the three subjects, the specific filter used in the study and the EMG signal duration.

Subject Muscle Symptoms EMG Diagnosis Filter

setting (kHz)

2 Frontalis Diplopia Normal 0.5–10

5 Vastus

lateralis and Tibialis anterior

Lumbar pain with radiating paresthesias to L5

Mild subacute L5

radiculopathy 1–10

6 Tensor fascia lata and Tibialis anterior

Lumbar pain with radiating paresthesias to L5

Moderate chronic L5 radiculopathy with relapsed active denervation

1–10

Fig. 9. Screenshot of Keypoint extracted MUPs (A). Three MUP templates of MUP trains extracted by DQEMG from the same EMG signal (B–D). The first of these MUP templates (B) represents the DQEMG extracted MUP train which corresponds to the Keypoint extracted MUPs of the screenshot shown in A. The same MUP train analyzed by the automatic method (traces in red correspond to valid alignment and/or measurement intervals) (E).

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3. RESULTS

3.1. Results from simulated data

The results of Study 1 (Fig. 10A, D) show that the relative error decreases as the level of jitter increases. A large percentage of the estimates had a relative error of less than 10%. In fact, the 5 and 95 percentiles for all the studied simulation jitter values below 125 μs were in this case, and the samples included between percentiles 25 and 75 (i.e. half of the studied trains for each case), had errors below 2%. Finally, as the simulated jitter increased, the number of valid MUPTs and SF-MUP segment pairs decreased dramatically, to values of 35 and 45, respectively, for a jitter level of 125 μs.

In Study 2 (Fig. 10B, E) it is observed that the relative error increases as the number of MFPs increases up to four. A large percentage of the estimates (more than 95%) had a relative error of less than 15%, and the samples included between percentiles 25 and 75, had errors below 5%.

Finally, as the number of MFPs varies from 2 to 5, the number of valid trains increases (from 61 to 78) and the number of SF-MUP segment pairs also increases in a steeper way (from 61 to 148).

In Study 3 (Fig. 10C-F), the relative error is low (below 10% between percentiles 5 and 95 and below 1.5% between percentiles 25 and 75) for 10 MUPs per MUPT or more. For five MUPs per MUPT, the error is larger: the 95 percentile reaches an error of 38%. Besides, for five MUPs, the number of SF-MUP segment pairs and valid trains are 55 and 80, respectively, and raises to around 70 and 100, respectively, for a larger number of MUPs per MUPT.

The results of Study 4 (Fig. 11A, D) show that the relative jitter error increases as the second fiber increases its distance in the Y dimension; it is very low when this fiber is placed in an interval [0.4, 0.5] mm apart from the electrode or closer (percentiles 5 and 95 were within 5%

relative error). When

this fiber is situated in the interval [0.5, 0.6] mm, the error gets larger (percentiles 5 and 95 were within − 20% and 10% relative error).

The number of valid MUPTs and SF-MUP segment pairs, also coincidental in this study, decreases with increasing distance of the second

fiber, with values above 50 for Y locations in the interval [0.4, 0.5] mm or lower, and below 20 in the interval [0.5, 0.6].

In Study 5 (Fig. 11B, E), there is a positive bias (around 1%) when the neuromuscular junction of the second fiber is placed within the [10, 12.5] mm interval (minimum and maximum MFP temporal separation of 0 and 0.625 ms, respectively). The relative jitter error decreases as this interval gets further away up to the interval [17.5, 20] mm (minimum and maximum MFP temporal separation of 1.25 and 2.5 ms, respectively). For all the cases, percentiles 5 and 95 were within − 7%

and 4% relative error and percentiles 25 and 75 were within 2.5% error.

The number of valid MUPTs and SF-MUP segment pairs, coincidental in this study also, were below 30 for the first two intervals, but varied from 90 to 100 for further intervals.

Results of Study 6 (Fig. 11C, F) show very low jitter error values for all the considered noise levels (percentiles 5 and 95 were within − 7%

and 4% relative error). The number of valid MUPTs and SF-MUP segment pairs steadily decreased with the noise level, from more than 80 and 120, respectively, for a noise level of 2.5 μV, to 20 and 21, respectively, for a noise level of 80 μV.

3.2. Results from real data

For each MUP train under test there were one or more MCD measures computed by the Keypoint. They corresponded to the independent peak pairs considered by the Keypoint and were as many as the number of peaks marked in the corresponding screenshot, excluding the reference peak. From the 19 MUP trains used in the analysis, 23 MCD measures were computed by the Keypoint and also 23 MCD measures were computed by the automatic technique. (The same number of MCD measures were obtained by each of these techniques only by coincidence).

Only 15 of the peak pairs detected by the Keypoint actually corresponded (were close in time) to valid interval pairs determined by the automatic method. With these coincidental pairs (MCD measures) a comparative analysis of MCD values obtained by the Keypoint and by the automatic method was performed.

Fig. 10. Results of Study 1 (A, D), Study 2 (B–E) and Study 3 (C–F). Boxplots of relative jitter errors (A–C). The central mark of the box is the median, the box edges mark the 25th and 75th percentiles, the whiskers extend to the most extreme data points not considered outliers, and outliers are plotted individually. To enlarge the view of the central parts of the distributions, plots have been zoomed and some outliers may not appear. Number of SF-MUP segment pairs (upper curve) and number of valid MUPTs (lower curve) (D–F).

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Boxplots of MCD measures are shown in Fig. 12, which include: MCD measures extracted by the Keypoint and by the automatic method; MCD measures extracted by the Keypoint and by the automatic method, but only when they were coincidental in the sense explained above; and the differences between the Keypoint MCD measures and the automatic measures when these measures were coincidental. Statistical figures

corresponding to these variables and boxplots are given in Table 2.

The range and statistical distribution of the MCD values obtained by both techniques were similar with regard to the 25% and 75% percentile intervals, although the range of MCD values obtained by the Keypoint was larger (up to 86.5 μs) than those obtained by the automatic method (up to 53 μs). The distributions of coincidental MCD measurements were very close, regarding the 5%, 25% 75% and 95% percentile intervals as well as the median MCD. For these cases, the MCD differences were low, with a mean value (bias) of 1.3 μs, a median of 0.8 μs and a mean of absolute differences of 2.97 μs.

The dispersion was also low, especially in the 25% and 75%

percentile intervals (− 0.85, 3.82 μs). Four different MUP train examples from the studied set, together with their self-jitter curves are shown in Fig. 13. MCD measurements obtained by the Keypoint and by the automatic method are given. Different situations are present in these examples. In the first example (Fig. 13A-C) the two peaks detected by the Keypoint are close to the two intervals obtained by the automatic method; it is therefore a coincidental case. The MCD values obtained by the two methods (37.6 and 35.5 μs, respectively) are very close. In the second example (Fig. 13D-F) the Keypoint detected two peaks and an MCD measurement was extracted accordingly, but only one valid interval was determined by the automatic method (corresponding to the first of the two peaks) and therefore, no MCD measurement was provided. There may be MUP trains in which not even one interval is obtained by the automatic method and therefore no MCD value will be obtained. Example 3 (Fig. 13G-I) is a polyphasic MUP train. The Key- point detected three peaks and extracted two MCD measurements.

Likewise, the automatic method determined three valid intervals and extracted two MCD measurements, but only one of these was coincidental with one of the Keypoint measurements (i.e., MCD = 11.6 μs taken from p1 and p3 and MCD = 10 μs taken form interval 1 and interval 2). The other two MCD measurements cannot be compared as they do not correspond to pairs of peaks and intervals close in time. Finally, in example 4 (Fig. 13J-L) three peaks (p1, p2 and p3) were detected by the Keypoint and two intervals were determined by the automatic method.

The pair of peaks p1 and p2 is coincidental with the pair of intervals 1 Fig. 11. Results of Study 4 (A, D), Study 5 (B, E) and Study 6 (C, F). Boxplots of relative jitter errors (A–C). The central mark of the box is the median, the box edges mark the 25th and 75th percentiles, the whiskers extend to the most extreme data points not considered outliers, and outliers are plotted individually. To enlarge the view of the central parts of the distributions, plots have been zoomed and some outliers may not appear. Number of SF-MUP segment pairs (upper curve) and number of valid MUPTs (lower curve) (D–F).

Fig. 12. Boxplots of MCD values obtained by the Keypoint system and the automatic method for all the valid measurements and for the coincidental measurements (see text) and of the difference of MCD values by the two methods for the coincidental measurements. In the boxes, the central mark is the median, the edges mark the 25th and 75th percentiles, the whiskers extend to the most extreme data points not considered outliers, and outliers are plotted individually.

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and 2; however, their corresponding MCD values (48.7 and 60.3 μs, respectively) are quite distant.

4. Discussion

Several aspects of the proposed method and the given results deserve further comment:

a) As noted in the Introduction, only two fully automatic techniques for jitter estimation from EMG records have been published so far: the one proposed by M. Abdelmaseeh and D. Stashuk in 2017 [32] and the one proposed by Piasecki et al., in 2021 [33]. Previous techniques were based to a greater or lesser extent on manual selection of

two isolated peaks (supposedly being generated by just one muscle fiber) in the same MUP and calculation of the MCD [1,21]. A comparative study between our algorithm and Abdelmaseeh’s technique was not made because access to the specific algorithms and training data used to implement this technique were not available.

Although the simulation programs and, therefore, the signals used, as well as the evaluation tests and figures of merit of that work were different from those of our study, a review of those figures of merit published in the referenced article can be made. The percentage of estimation error and the so-called “yield” (percentage of times the algorithm is able to provide a jitter estimate), based on two internal parameters of the method, are given. The lowest percentage of error reported is 8.9%, with a yield of 85.3%. Roughly, this mean error Table 2

Statistics on MCD data obtained by the Keypoint system and by the automatic method for all the valid measurements and for the coincidental measurements (see text), and of the difference of MCD values obtained by the two methods for the coincidental measurements.

Num measurements Median (μs) [25th, 75th percentile] (μs) [5th, 95th percentile] (μs) Num outliers

Keypoint 23 26.4 [12.72, 44.8] [6.51, 76.36] 0

Automatic method 23 33.0 [11.97, 41.22] [6.85, 50.4] 0

Keypoint (coincidental) 15 23.5 [11.72, 44.8] [6.07, 58.55] 0

Automatic method (coincidental) 15 27.4 [10.5, 42.95] [5.65, 52] 0

Difference (coincidental) 15 0.8 [-0.85, 3.82] [-3.82, 9.95] 1

Fig. 13. Examples of MUP trains analyzed by the Keypoint, with detected negative peaks marked and obtained MCD values displayed (A, D, G, J). The same MUP trains analyzed by the automatic method, with valid intervals highlighted and MCD values displayed (B, E, H, K). Corresponding self-jitter curves (C, F, I, L).

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value is higher or at most equivalent to most of the cases in our seven simulation studies. On the other hand, our algorithm was able to provide a greater number of jitter estimates in many of the cases studied (number of valid pairs larger than 85.3 in Fig. 10D-F and Fig. 11D-F). On the other side, the results of Piasecki’s method reported in Ref. [33] do not include direct assessment of jitter estimation errors and thus are not comparable to the ones given in here.

b) Although the IPI SD has been used as an internal procedure in the proposed method for the simulation studies, MCD has been applied in the test with real EMG data. Both measurements are strongly related. In fact, if the IPIs of a couple of SF-MUPs within a MUPT are considered to be samples of an independent and stationary random variable with a Gaussian distribution [35,36], both IPI SD and MCD are statistics that measure the dispersion of this distribution and their expectations (E) are directly related to each other as [22]:

E{MCD(IPI)} = 2

̅̅̅π

√ E{SD(IPI)} (19)

c) There are a number of internal parameters in the algorithm. The most important are:

j. 1- Those related with the width of the alignment and matching segments;

j. 2- Thresholds for jitter level, segment duration, inter-segment temporal separation and SPJV, according to which a certain sample in the local jitter scan will be considered to belong to a SF- MUP segment, and a given SF-MUP segment or pair of SF-MUP segments will be considered valid for jitter estimation.

The set of parameters in (j.1) have been established empirically such that the ranges of estimated jitter values obtained are physiologically plausible.

Parameters in (j.2) have also been determined empirically. They set up a compromise between jitter estimation error and the number of valid jitter estimates obtained from a MUPT. For example, as the SF-MUP segment duration threshold is increased, a segment will have to be longer to be considered a SF-MUP segment. Therefore, jitter estimation error will probably decrease, while the number of SF-MUP segment pairs (equivalent to the number of jitter estimates) will decrease, as the cri- terion for selecting SF-MUP segments is made more demanding.

d) As stated above, for N valid SF-MUP segments, there are ^{N⋅(N− 1)}₂ different SF-MUP segment pairs, but only N-1 independent pairs are to be chosen. This issue has also been contemplated by Stalberg et al.

when measuring jitter in MUPs with multiple peaks [28,37]. Their strategy is first to take a triggering peak (equivalent to our alignment segment) among the set of N peaks and then measure the jitter in the remaining N-1 peaks and sum them all. This process is to be repeated for the N possible triggering peaks, but only one triggering peak will be selected, particularly the one from which the minimum summed jitter results. Finally, several jitter estimates will be output by using the selected triggering point and measuring the jitter in all the remaining peaks. The rationale for this strategy is that the higher the jitter in the triggering peak, the larger the error. This general and somehow arbitrary principle is not used in the proposed algorithm, instead the more specific indicator of jitter measurement reliability given in (16) is used.

e) The practical utility of the proposed algorithm is considerable, since the jitter measurement is, as stated above, a very manual technique and, therefore, subject to the experience, skill and subjectivity of the electromyographer. As explained in the Introduction, the jitter has traditionally been computed from potentials recorded with SF electrodes. The small dimensions of the active tip of these electrodes allow recording MUPs, which are composed of very few significant MFPs, rarely more than two. When recorded MUPs appear as two

significant MFPs sufficiently separated in time, the jitter is computed. Due to the high price, the difficulty of handling them and the potential problems of infection associated with their reuse, SF electrodes are increasingly being replaced by concentric needle electrodes. Concentric needle electrodes have much larger detection surface areas and their recorded MUPs contain contributions from significantly larger numbers of MFPs, sometimes tens or more, although the most significant contributions are from a smaller number of fibers, usually from one to five. In addition, the contributions of these fibers to the MUP tend to temporally overlap, such that the manual determination of suitable peaks or other reference points for jitter measurement is complicated. This calls for automatic methods such as that proposed by Abdelmaseeh or the one presented here, not only for better accuracy and consistency (elimination of subjectivity), but also to reduce the time required to complete an EMG examination of NMJ transmission stability.

f) In the first simulated study (Study 1), the jitter error did not significantly vary as the simulated jitter value increased (Fig. 10A), but the number of SF-MUP segment pairs and valid trains decreased significantly, yielding very low values for a simulated jitter of 125 μs (Fig. 10D). Even well separated MFPs, as depicted in the example of Fig. 14, may become widely overlapping with this high level of jitter.

(Note the second and third positive peaks).

g) As the number of fibers increases, the relative jitter error also increases and so does the number of SF-MUP segment pairs and trains (Fig. 10B, E). This establishes a compromise for the electromyographer’s manual MUP search, as picking up MUPs with a low number of main components (i.e., two or three MFPs) will render more precise jitter measurements, but lower number of estimates compared to MUPs with more components.

h) The core of jitter estimation is the variability measurement of the estimated temporal offsets between SF-MUP segments across the MUPT. As the number of MUPs in the train decreases, the variability in the jitter estimation provided by that IPI SD or the MCD increases.

That is the reason for the high relative jitter error when the number of MUPs in the MUPT is as low as five, reaching 40% for the 95th percentile (Fig. 10C). For ten or more MUPs in a train, the errors come to a low and steady level. This issue should be taken into consid- eration in situations in which the number of MUPs per train may be small, for example, when poor cooperation or severe fatigue from the patient impedes a sustained contraction.

i) In Study 4, MUPs were composed of only two MFPs and the spatial positions of their generating fibers in the Y dimension were varied to study the impact on jitter estimation. The accuracy and reliability of the jitter estimates were only compromised when the two fibers were maximally separated (the first fiber’s Y coordinate was in the [0.1, 0.2 mm] interval and the second fiber was in the [0.5, 0.6 mm] interval). In this case, the first MFP was considerably larger than the second, and the jitter error was significantly higher (Fig. 11A) and the number of estimates was lower (Fig. 11D) than in other situations where the two fibers where closer. When a small MFP (generated by a distant fiber) is eclipsed by a much larger MFP (generated by a closer fiber) its mere detection and subsequent jitter estimation will be more troublesome compared to the case of a MUP with two MPFs of similar amplitude. These results are congruent with those of Rodriguez et al. [26,38] who studied the rise time and rise time variability of MUPs composed of two MPFs in several scenarios.

They showed how rise time and rise time variability and, in general, the variability in MUP waveforms were very much un- affected by jitter when the fiber-to-electrode distances of the two fibers were very different. This indicates that jitter estimation under these conditions is very unreliable, as it was in this study.

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j) In Study 5, when the neuromuscular junctions of both fibers were placed in the same axial interval [10, 12.5 mm] from the electrode (minimum and maximum MFP temporal separation of 0 and 0.625 ms, respectively), the number of valid estimations was only two (Fig. 11E). It seems that the generated MFPs were too close together in time and temporally overlapped so much that it was almost impossible to find two SF-MUP segments. As the two fibers were placed further axially apart, the number of jitter estimates increased and the jitter estimation error decreased steadily, reaching a stable situation between 90 and 100 valid estimates, when the neuromuscular junction of the second fiber was in the [17.5, 20] mm interval (minimum and maximum MFP temporal separation of 1.25 and 2.5 ms, respectively) or further (Fig. 11B, E). However, jitter estimation is already observable when end-plates zones of different fibers of the same MU are axially separated by 2.5 mm. Considering a fiber conduction velocity of 4 m/s, this means a time gap of 0.625 ms between potentials, which is comparable to the 500 μs expressed by Navallas et al., as the minimum temporal separation required between two MPFs composing a MUP for valid jitter measurement [22].

k) In Study 6, it can be seen that the estimation error is very low and not greatly affected by the noise level (Fig. 11C). However, when the noise level SD is of 40 μV or higher, the number of valid estimates for a MUPT is low (40% or lower) (Fig. 11F). So, the method is increasingly inefficient as noise level increases, i.e., more EMG recordings would be necessary to reach a certain level of reliability in overall jitter measurement.

l) These real signal evaluations provide only an overview of the capabilities of the presented algorithm for measuring jitter in real EMG signals and compliment the simulation studies. The number

of signals and subjects tested is too small to grasp in detail the behavior of the technique, its subtleties and limitations. To obtain a more robust characterization, a more profound and extensive study is required.

m) Although most jitter studies are performed on small muscles (i.e., frontalis) aimed at confirming or ruling out neuromuscular junction diseases like myasthenia gravis, we have also included larger muscles (i.e., deltoid, vastus lateralis, tibialis anterior, etc.), as jitter evaluation in these muscles can also be of value to assess the degree of active reinnervation.

n) The interpretation of the results is intrinsically problematic with real signals, as with these signals (unlike with simulated signals) there is no “ground truth” of the neurophysiological jitter present in the signals. The Keypoint MCD measurements may not accurately represent the “ground truth” for comparison with the automatic method or other methods, as it is just a possible procedure (partly manual, in fact) for assessing the time variability of the activation times of the fibers comprising a MU. In any case, some general comments about the results obtained by both techniques are provided next.

o) The upper part (including the maximum) of the distribution of Keypoint MCD values (Fig. 12, first box) is clearly higher than the automatic distribution (Fig. 12, second box), but this is only due to a single MUP train. The outlier seen in the fifth box of the figure corresponds to the same MUP train. Apart from this, as previously pointed out, the distribution of MCD values by the two methods, especially for the coincidental pairs, are close.

p) The high discrepancy between the two coincidental MCD values in the MUP train referred in the previous paragraph and pointed out in the results section (example 4, Fig. 13J-L) may well be Fig. 14. Three MFPs (A); composed MUP (B); MUPT with elevated jitter (C).