A computational approach for generating continuous estimates of motor unit discharge rates and visualizing population discharge characteristics

Abstract

Objective. Successive improvements in high density surface electromyography and decomposition techniques have facilitated an increasing yield in decomposed motor unit (MU) spike times. Though these advancements enhance the generalizability of findings and promote the application of MU discharge characteristics to inform the neural control of motor output, limitations remain. Specifically, (1) common approaches for generating smooth estimates of MU discharge rates introduce artifacts in quantification, which may bias findings, and (2) discharge characteristics of large MU populations are often difficult to visualize.Approach. In the present study, we propose support vector regression (SVR) as an improved approach for generating smooth continuous estimates of discharge rate and compare the fit characteristics of SVR to traditionally used methods, including Hanning window filtering and polynomial regression. Furthermore, we introduce ensembles as a method to visualize the discharge characteristics of large MU populations. We define ensembles as the average discharge profile of a subpopulation of MUs, composed of a time normalized ensemble average of all units within this subpopulation. Analysis was conducted with MUs decomposed from the tibialis anterior (N= 2128), medial gastrocnemius (N= 2673), and soleus (N= 1190) during isometric plantarflexion and dorsiflexion contractions.Main result. Compared to traditional approaches, we found SVR to alleviate commonly observed inaccuracies and produce significantly less absolute fit error in the initial phase of MU discharge and throughout the entire duration of discharge. Additionally, we found the visualization of MU populations as ensembles to intuitively represent population discharge characteristics with appropriate accuracy for visualization.Significance. The results and methods outlined here provide an improved method for generating estimates of MU discharge rate with SVR and present a unique approach to visualizing MU populations with ensembles. In combination, the use of SVR and generation of ensembles represent an efficient method for rendering population discharge characteristics.

Keywords: data visualization; high-density surface EMG; motoneuron; motor unit visualization; support vector regression.

Figure 1.

Overview of ensemble construction. Populations of estimated motor unit discharge profiles were subdivided into cohorts based upon a metric of interest (four groups on left), filtered or fit with an estimating function with the time axis (x-axis) normalized such that motor units within a subdivision align from onset to offset, and ensemble averaged (four traces on right). (pps: pulses per second; s: second).

Figure 2.

Normalization in ensemble construction. Shown above is the ensemble construction process for all decomposed TA motor units (N = 2128). Units are first separated into ten cohorts based upon their recruitment threshold, with the color bar indicating the recruitment range of this group normalized to individual participants’ MVT and the black triangular trace representing the average torque across all trials and participants. Smoothed continuous estimates of MU discharge rate are then created with support vector regression (A), and projected onto time vectors of identical length (B). These normalized estimates are then ensemble averaged to generate the overlying black traces. These ensemble traces in black are shown overlying the normalized and non-normalized estimates for comparison. (pps: pulses per second; s: second).

Figure 3.

Effects of fit method on smoothed estimates of discharge for a single motor unit. A single decomposed medial gastrocnemius (MG) motor unit from a plantarflexion trial is shown with its estimated instantaneous discharge rate (IDR) in pulses per second (pps) and orange. The discharge rate at recruitment and derecruitment are shown outlined in black. The smooth estimates of discharge rate generated through each investigated approach are shown in solid lines. This includes (A) support vector regression (SVR), (B) Hanning (Hann) window filtering, and polynomial regression with either a (C) 5th or (D) 6th degree polynomial. Plantarflexion torque about the ankle is shown in black, normalized to maximum voluntary torque (MVT).

Figure 4.

Absolute fit error for each fit method across motor unit duration. The absolute difference between the estimated discharge rate (ŷ) and instantaneous discharge rate (y) is shown as a function of motor unit duration from recruitment (0%) to derecruitment (100%) for each fit method in pulses per second (pps). Fit methods included support vector regression (SVR), Hanning (Hann) window filtering, and polynomial regression with either a 5th or 6th degree polynomial. Colored dots indicate individual discharge instances and the solid lines represent a moving average with width corresponding to a 6% unit duration. The inset displays the absolute error as a function of the number of discharge instances from recruitment, for the first five discharges for all motor units (μ ± SE). This is shown for the tibialis anterior (TA, N = 2128), medial gastrocnemius (MG, N = 2673), and soleus (SOL, N = 1190).

Figure 5.

Average absolute error across the fit methods. The average absolute difference between the estimated discharge rate (ŷ) and instantaneous discharge rate (y) is shown for each fit method in pulses per second (pps) for the first five motor unit discharges (A) and entire duration of discharge (B). Each data point represents an individual motor unit with the corresponding probability density generated by a gaussian kernel. Individual colors represent the various fit methods and include support vector regression (SVR), Hanning (Hann) window filtering, and polynomial regression with either a 5th or 6th degree polynomial. This is shown for the tibialis anterior (TA, N = 2128, left), medial gastrocnemius (MG, N = 2673, middle), and soleus (SOL, N = 1190, right).

Figure 6.

Ensembles for each fit method. Each quadrant represents one of the investigated fitting schemes and corresponds to (A) support vector regression (SVR), (B) Hanning (Hann) window filtering, and polynomial regression with either a (C) 5th or (D) 6th degree polynomial. Within each quadrant, the top plot depicts the average torque in black, the cumulative spike train (CST) across all units in green, and the average moving root mean squared EMG for all trials in dashed purple. Torque is shown as percent of maximum voluntary torque (MVT), the CSTs are shown in pulses per second (pps), and peak EMG is shown equivalent to maximum torque. The bottom plot within each quadrant houses the ensembles, color coordinated in accordance with the color bar, and the CST for reference. The light gray line across plots indicates the time of peak torque. (Ensemble cohorts: N = 240, 215, 202, 232, 232, 229, 210, 259, 202, 107).

Figure 7.

SVR ensembles across muscles. Shown are the ensemble traces for each muscle, generated from motor unit discharge rates estimated with support vector regression (SVR). For each muscle, the top plot depicts the average torque in black, the cumulative spike train (CST) across all units in green, and the average moving root mean squared EMG for all trials in dashed purple. Torque is shown as percent of maximum voluntary torque (MVT), the CSTs are shown in pulses per second (pps), and peak EMG is shown equivalent to maximum torque. The bottom plot for each muscle houses the ensembles, color coordinated in accordance with the color bar, and the CST for reference. The light gray line across plots indicates the time of peak torque. (Ensemble cohorts: [TA: N = 240, 215, 202, 232, 232, 229, 210, 259, 202, 107]; [MG: N = 221, 261, 299, 310, 373, 383, 304, 287, 160, 75]; [SOL: N = 154, 146, 142, 171, 136, 150, 110, 97, 54, 30]).

Figure 8.

Ensemble accuracy. Shown above are the results of the Monte Carlo simulation, treating the construction of ensembles as a process. This is shown for five parameters of interest, including discharge rate at recruitment (A, left), derecruitment (A, right), and peak (B) as well as time from recruitment to peak discharge rate (C) and ΔF (D). Within each quadrant, the bottom plot depicts the ensemble estimate of a given parameter against the average of that parameter estimate for all individual motor units. This is separated into ensemble cohorts according to the color bar, with a data point for each iteration (N = 1000). The dashed red line depicts a theoretical 100% agreement between the ensemble estimates and the population average for a random sample. The probability density for each ensemble and parameter are displayed in the top row of each quadrant and follow an identical color scheme. Distributions outlined in purple on the top row correspond to population averages of the sample with those on the bottom row outlined in blue corresponding to the ensemble estimates. Motor units were sampled from the decomposed population of tibialis anterior units (N = 2128).