Effect of changing data collection parameters on statistical motor unit number estimates

The effect of number of samples and selection of data for analysis on the calculation of surface motor unit potential (SMUP) size in the statistical method of motor unit number estimates (MUNE) was determined in 10 normal subjects and 10 with amyotrophic lateral sclerosis (ALS). We recorded 500 sequential compound muscle action potentials (CMAPs) at three different stable stimulus intensities (10–50% of maximal CMAP). Estimated mean SMUP sizes were calculated using Poisson statistical assumptions from the variance of 500 sequential CMAP obtained at each stimulus intensity. The results with the 500 data points were compared with smaller subsets from the same data set. The results using a range of 50–80% of the 500 data points were compared with the full 500. The effect of restricting analysis to data between 5–20% of the CMAP and to standard deviation limits was also assessed. No differences in mean SMUP size were found with stimulus intensity or use of different ranges of data. Consistency was improved with a greater sample number. Data within 5% of CMAP size gave both increased consistency and reduced mean SMUP size in many subjects, but excluded valid responses present at that stimulus intensity. These changes were more prominent in ALS patients in whom the presence of isolated SMUP responses was a striking difference from normal subjects. Noise, spurious data, and large SMUP limited the Poisson assumptions. When these factors are considered, consistent statistical MUNE can be calculated from a continuous sequence of data points. A 2 to 2.5 SD or 10% window are reasonable methods of limiting data for analysis. Muscle Nerve 27: 320–331, 2003

The stimulus-response curve and motor unit variability in normal subjects and subjects with amyotrophic lateral sclerosis

The behavior and stability of motor units (MUs) in response to electrical stimulation of different intensities can be assessed with the stimulus-response curve, which is a graphical representation of the size of the compound muscle action potential (CMAP) in relation to stimulus intensity. To examine MU characteristics across the whole stimulus range, the variability of CMAP responses to electrical stimulation, and the differences that occur between normal and disease states, the curve was studied in 11 normal subjects and 16 subjects with amyotrophic lateral sclerosis (ALS). In normal subjects, the curve showed a gradual increase in CMAP size with increasing stimulus intensity, although one or two discrete steps were sometimes observed in the upper half of the curve, indicating the activation of large MUs at higher intensities. In ALS subjects, large discrete steps, due to loss of MUs and collateral sprouting, were frequently present. Variability of the CMAP responses was greater than baseline variability, indicating variability of MU responses, and at certain levels this variability was up to 100 mu Vms. The stimulus-response curve shows differences between normal and ALS subjects and provides information on MU activation and variability throughout the curve.

Motor unit number estimation - A Bayesian approach

All muscle contractions are dependent on the functioning of motor units. In diseases such as amyotrophic lateral sclerosis (ALS), progressive loss of motor units leads to gradual paralysis. A major difficulty in the search for a treatment for these diseases has been the lack of a reliable measure of disease progression. One possible measure would be an estimate of the number of surviving motor units. Despite over 30 years of motor unit number estimation (MUNE), all proposed methods have been met with practical and theoretical objections. Our aim is to develop a method of MUNE that overcomes these objections. We record the compound muscle action potential (CMAP) from a selected muscle in response to a graded electrical stimulation applied to the nerve. As the stimulus increases, the threshold of each motor unit is exceeded, and the size of the CMAP increases until a maximum response is obtained. However, the threshold potential required to excite an axon is not a precise value but fluctuates over a small range leading to probabilistic activation of motor units in response to a given stimulus. When the threshold ranges of motor units overlap, there may be alternation where the number of motor units that fire in response to the stimulus is variable. This means that increments in the value of the CMAP correspond to the firing of different combinations of motor units. At a fixed stimulus, variability in the CMAP, measured as variance, can be used to conduct MUNE using the "statistical" or the "Poisson" method. However, this method relies on the assumptions that the numbers of motor units that are firing probabilistically have the Poisson distribution and that all single motor unit action potentials (MUAP) have a fixed and identical size. These assumptions are not necessarily correct. We propose to develop a Bayesian statistical methodology to analyze electrophysiological data to provide an estimate of motor unit numbers. Our method of MUNE incorporates the variability of the threshold, the variability between and within single MUAPs, and baseline variability. Our model not only gives the most probable number of motor units but also provides information about both the population of units and individual units. We use Markov chain Monte Carlo to obtain information about the characteristics of individual motor units and about the population of motor units and the Bayesian information criterion for MUNE. We test our method of MUNE on three subjects. Our method provides a reproducible estimate for a patient with stable but severe ALS. In a serial study, we demonstrate a decline in the number of motor unit numbers with a patient with rapidly advancing disease. Finally, with our last patient, we show that our method has the capacity to estimate a larger number of motor units.

Quantitative motor unit action potential analysis in 2 paraspinal neck muscles in adult Royal Dutch Sport horses

BACKGROUND: Reference values for quantitative electromyography (QEMG) in neck muscles of Royal Dutch Sport horses are lacking. OBJECTIVE: Determine normative data on quantitative motor unit action potential (QMUP) analysis of serratus ventralis cervicis (SV) and brachiocephalicus (BC) muscle. ANIMALS: Seven adult normal horses (mean age 9.5 standard deviation [SD] +/- 2.3 years, mean height 1.64 SD +/- 4.5 cm, and mean rectal temperature 37.6 SD +/- 0.3 degrees C). METHODS: An observational study on QMUP analysis in 6 segments of each muscle was performed with commercial electromyography equipment. Measurements were made according to formerly published methods. Natural logarithm transformed data were tested with ANOVA and posthoc testing according to Bonferroni. RESULTS: Mean duration, amplitude, phases, turns, area, and size index (SI) did not differ significantly among the 6 segments in each muscle. Mean amplitude, number of phases, and SI were significantly (P < .002) higher in SV than BC, 520 versus 448 muV, 3.0 versus 2.8 muV, and 0.48 versus 0.30 muV, respectively. In SV 95% confidence intervals (CI) for amplitude, duration, number of phases, turns, polyphasia area, and SI were 488-551 muV, 4.3-4.6 ms, 2.9-3.0, 2.4-2.6, 7-12%, 382-448, and 0.26-0.70, respectively; in BC this was 412-483 muV, 4.3-4.7 ms, 2.7-2.8, 2.4-2.6, 4-7%, 393-469, and 0.27-0.34, respectively. Maximal voluntary activity expressed by turns/second did not differ significantly between SV and BC with a 95% CI of 132-173 and 137-198, respectively. CONCLUSIONS AND CLINICAL IMPORTANCE: The establishment of normative data makes objective QEMG of paraspinal muscles in horses suspected of cervical neurogenic disorders possible. Differences between muscles should be taken into account.

Twitch potentia induced by two different modalities of neuromuscular electrical stimulation: implications for motor unit recruitment.

INTRODUCTION: We tested the hypothesis that twitch potentiation would be greater following conventional (CONV) neuromuscular electrical stimulation (50-µs pulse width and 25-Hz frequency) compared with wide-pulse high-frequency (WPHF) neuromuscular electrical stimulation (1-ms, 100-Hz) and voluntary (VOL) contractions, because of specificities in motor unit recruitment (random in CONV vs. random and orderly in WPHF vs. orderly in VOL). METHODS: A single twitch was evoked by means of tibial nerve stimulation before and 2 s after CONV, WPHF, and VOL conditioning contractions of the plantar flexors (intensity: 10% maximal voluntary contraction; duration: 10 s) in 13 young healthy subjects. RESULTS: Peak twitch increased (P<0.05) after CONV (+4.5±4.0%) and WPHF (+3.3±5.9%), with no difference between the 2 modalities, whereas no changes were observed after VOL (+0.8±2.6%). CONCLUSIONS: Our results demonstrate that presumed differences in motor unit recruitment between WPHF and CONV do not seem to influence twitch potentiation results.

Effects of muscle fibre shortening on the characteristics of surface motor unit potentials.

Traditionally, studies dealing with muscle shortening have concentrated on assessing its impact on conduction velocity, and to this end, electrodes have been located between the end-plate and tendon regions. Possible morphologic changes in surface motor unit potentials (MUPs) as a result of muscle shortening have not, as yet, been evaluated or characterized. Using a convolutional MUP model, we investigated the effects of muscle shortening on the shape, amplitude, and duration characteristics of MUPs for different electrode positions relative to the fibre-tendon junction and for different depths of the MU in the muscle (MU-to-electrode distance). It was found that the effects of muscle shortening on MUP morphology depended not only on whether the electrodes were between the end-plate and the tendon junction or beyond the tendon junction, but also on the specific distance to this junction. When the electrodes lie between the end-plate and tendon junction, it was found that (1) the muscle shortening effect is not important for superficial MUs, (2) the sensitivity of MUP amplitude to muscle shortening increases with MU-to-electrode distance, and (3) the amplitude of the MUP negative phase is not affected by muscle shortening. This study provides a basis for the interpretation of the changes in MUP characteristics in experiments where both physiological and geometrical aspects of the muscle are varied.

Decreased motor unit firing rate in the potentiated tibialis anterior in humans

With repeated activity, force production, rate of force production, and relaxation time are impaired. These are characteristics ofa fatigued muscle (Vandenboom, 2004). However, brief bouts of near maximal to maximal activity results in the increased ability of the muscle to generate force, termed post activation potentiation (P AP)(V andervoort et aI., 1983). The purpose of the present study was to characterize motor unit firing rate (MUFR) in the unfatigued, potentiated tibialis anterior (TA). Using a quadrifilar needle electrode, MUFR was measured during a 5s 50% MVC in which the TA was either potentiated or unpotentiated; monopolar electrodes measured surface parameters. A lOs MVC was used to potentiate the muscle. Firing rate decreased significantly from 20.15±2.9Opps to 18.27±2.99pps, while mean power frequency decreased significantly from 60. 13±7.75 Hz to 53.62±8.56 Hz. No change in root mean square (RMS) was observed. Therefore, in the present study, MUFR decreases in response to a potentiated TA.

Condition number estimates for combined potential boundary integral operators in acoustic scattering

We study the classical combined field integral equation formulations for time-harmonic acoustic scattering by a sound soft bounded obstacle, namely the indirect formulation due to Brakhage-Werner/Leis/Panic, and the direct formulation associated with the names of Burton and Miller. We obtain lower and upper bounds on the condition numbers for these formulations, emphasising dependence on the frequency, the geometry of the scatterer, and the coupling parameter. Of independent interest we also obtain upper and lower bounds on the norms of two oscillatory integral operators, namely the classical acoustic single- and double-layer potential operators.

Determining feature relevance for the grouping of motor unit action potentials through generative topographic mapping

The study of motor unit action potential (MUAP) activity from electrornyographic signals is an important stage on neurological investigations that aim to understand the state of the neuromuscular system. In this context, the identification and clustering of MUAPs that exhibit common characteristics, and the assessment of which data features are most relevant for the definition of such cluster structure are central issues. In this paper, we propose the application of an unsupervised Feature Relevance Determination (FRD) method to the analysis of experimental MUAPs obtained from healthy human subjects. In contrast to approaches that require the knowledge of a priori information from the data, this FRD method is embedded on a constrained mixture model, known as Generative Topographic Mapping, which simultaneously performs clustering and visualization of MUAPs. The experimental results of the analysis of a data set consisting of MUAPs measured from the surface of the First Dorsal Interosseous, a hand muscle, indicate that the MUAP features corresponding to the hyperpolarization period in the physisiological process of generation of muscle fibre action potentials are consistently estimated as the most relevant and, therefore, as those that should be paid preferential attention for the interpretation of the MUAP groupings.

Generative topographic mapping applied to clustering and visualization of motor unit action potentials

The identification and visualization of clusters formed by motor unit action potentials (MUAPs) is an essential step in investigations seeking to explain the control of the neuromuscular system. This work introduces the generative topographic mapping (GTM), a novel machine learning tool, for clustering of MUAPs, and also it extends the GTM technique to provide a way of visualizing MUAPs. The performance of GTM was compared to that of three other clustering methods: the self-organizing map (SOM), a Gaussian mixture model (GMM), and the neural-gas network (NGN). The results, based on the study of experimental MUAPs, showed that the rate of success of both GTM and SOM outperformed that of GMM and NGN, and also that GTM may in practice be used as a principled alternative to the SOM in the study of MUAPs. A visualization tool, which we called GTM grid, was devised for visualization of MUAPs lying in a high-dimensional space. The visualization provided by the GTM grid was compared to that obtained from principal component analysis (PCA). (c) 2005 Elsevier Ireland Ltd. All rights reserved.

Condition number estimates for combined potential integral operators in acoustics and their boundary element discretisation

We consider the classical coupled, combined-field integral equation formulations for time-harmonic acoustic scattering by a sound soft bounded obstacle. In recent work, we have proved lower and upper bounds on the $L^2$ condition numbers for these formulations, and also on the norms of the classical acoustic single- and double-layer potential operators. These bounds to some extent make explicit the dependence of condition numbers on the wave number $k$, the geometry of the scatterer, and the coupling parameter. For example, with the usual choice of coupling parameter they show that, while the condition number grows like $k^{1/3}$ as $k\to\infty$, when the scatterer is a circle or sphere, it can grow as fast as $k^{7/5}$ for a class of `trapping' obstacles. In this paper we prove further bounds, sharpening and extending our previous results. In particular we show that there exist trapping obstacles for which the condition numbers grow as fast as $\exp(\gamma k)$, for some $\gamma>0$, as $k\to\infty$ through some sequence. This result depends on exponential localisation bounds on Laplace eigenfunctions in an ellipse that we prove in the appendix. We also clarify the correct choice of coupling parameter in 2D for low $k$. In the second part of the paper we focus on the boundary element discretisation of these operators. We discuss the extent to which the bounds on the continuous operators are also satisfied by their discrete counterparts and, via numerical experiments, we provide supporting evidence for some of the theoretical results, both quantitative and asymptotic, indicating further which of the upper and lower bounds may be sharper.