Relationship between firing rate and recruitment threshold of motoneurons in voluntary isometric contractions

Abstract

We used surface EMG signal decomposition technology to study the control properties of numerous simultaneously active motor units. Six healthy human subjects of comparable age (21 +/- 0.63 yr) and physical fitness were recruited to perform isometric contractions of the vastus lateralis (VL), first dorsal interosseous (FDI), and tibialis anterior (TA) muscles at the 20, 50, 80, and 100% maximum voluntary contraction force levels. EMG signals were collected with a five-pin surface array sensor that provided four channels of data. They were decomposed into the constituent action potentials with a new decomposition algorithm. The firings of a total of 1,273 motor unit action potential trains, 20-30 per contraction, were obtained. The recruitment thresholds and mean firing rates of the motor units were calculated, and mathematical equations were derived. The results describe a hierarchical inverse relationship between the recruitment thresholds and the firing rates, including the first and second derivatives, i.e., the velocity and the acceleration of the firing rates. This relationship describes an "operating point" for the motoneuron pool that remains consistent at all force levels and is modulated by the excitation. This relationship differs only slightly between subjects and more distinctly across muscles. These results support the "onion skin" property that suggests a basic control scheme encoded in the physical properties of motoneurons that responds consistently to a "common drive" to the motoneuron pool.

Figures

Fig. 1.

A: example of the incidences of firing of 21 motor units decomposed from the surface EMG signal obtained from the first dorsal interosseous muscle (FDI). Each bar represents the firing time of an action potential. The dark solid line represents the force output of the FDI muscle. The force in percentage of maximal voluntary contraction (MVC) level is scaled on the right and the motor unit number in order of recruitment order is listed on the left. B: these are the averaged time-varying firing rates for each of the 21 motor units calculated from the timing data above. Note the hierarchical relationship of the firing rates of each motor unit. The earlier recruited motor units (lower-threshold) have greater firing rates. Note that the firing rate values at recruitment and de-recruitment are influenced by the filter used to smoothen the firing rate values.

Fig. 2.

Average value of the motor unit firing rates plotted as functions of recruitment threshold—separately for contractions sustained at 20, 50, 80, and 100% MVC. The data are representative of different subjects and different muscles (the vastus lateralis, the FDI, and the tibialis anterior). The regression lines are drawn through the data from individual contractions, with each data point representing an individual motor unit. The average R2 values are provided in Table 2.

Fig. 3.

Average value of the motor unit firing rates plotted as functions of recruitment threshold. Data are from all analyzed contractions from the vastus lateralis (VL), FDI, and tibialis anterior (TA) for contractions sustained at 20, 50, 80, and 100% MVC. The regression lines are drawn through the data from all the contractions at each force level, with each data point representing an individual motor unit. As expected, the regression lines for the greater contractions have higher values. Note that the data scatter is greater in these grouped data than in the data for the individual subjects. The R2 values are provided in Table 2.

Fig. 4.

Motor unit firing rates and recruitment threshold from the FDI muscle from an additional subject under the reverse protocol. Contractions performed at 100, 50, and 20% MVC are shown.

Fig. 5.

Relationship between recruitment threshold and de-recruitment threshold is shown. The data from the VL, FDI, and TA are shown. The data from all force levels were grouped together. The lines represent the regression analysis for the data from each subject. Note that the relationship varies slightly in slope for all the subjects in each muscle. In the FDI muscle, all the data points lie above the unity line, indicating that the de-recruitment threshold is always greater than the recruitment threshold. In the VL, a few motor units from 2 subjects lie below the unity line in the range below 50% MVC. In the TA, the shift from the unity line is less well organized.

Fig. 6.

A: regression slopes for grouped data, as functions of excitation. Data points consist of the 4 slopes of the mean firing rate vs. recruitment threshold regressions for each of the 3 muscles. Data points are taken from slopes of Fig. 3. An exponential equation was used to fit the data. B: The y-intercept values for the grouped data are plotted as a function of excitation. Data points consist of the 4 values of the mean firing rate for each of the 3 muscles. Data points are taken from slopes of Fig. 3. A linear equation was used to fit the data.

Fig. 7.

A: projected firing rates of motor units in the VL muscle calculated from Eq. 4. The firing rates of motor units recruited between 10 and 90% MVC at intervals of 10% MVC are shown. The curves are limited to this range because the empirical data were so limited. B: projected velocity of the firing rates of motor units in the VL muscle calculated from Eq. 5. The firing rates of motor units recruited between 10 and 90% MVC at intervals of 10% MVC are shown. The curves are limited to this range because the empirical data were so limited.

Fig. 8.

Example of the 4 channels of surface electromyographic (sEMG) signals obtained by the sEMG sensor. A 100-ms epoch is expanded to display the complexity of the signal that is to be decomposed. The firing instances of the identified motor units are located below. The action potential of each train is presented to the left of the motor unit train.

Fig. 9.

A schematic diagram of the decompose-synthesize-decompose-compare test. The sEMG signal, s(n), is decomposed, and the action potentials are used to reconstruct a synthetic signal, y(n), which in turn is decomposed. The number of motor units is identified, and the shapes and firing times of the action potentials are compared. The comparison provides a metric for the accuracy of the decomposition algorithms. (This figure is modified from one that appears in Nawab et al. 2010.)

Fig. 10.

Comparison of the decomposition of the original sEMG signal and that of the synthesized signal. Top: the action potential shapes of the 28 motor unit action potential (MUAPs) that were identified in both the original sEMG signal and the synthesized signal. Note the similarity in the shapes of each individual motor unit recognized in both decompositions. Bottom: a short epoch of the firings of the 28 motor unit action potential trains (MUAPTs). The bar represents the firing instances from the decomposition of the original sEMG signal; the X indicates those from the decomposition of the synthesized signal. Note that in those firings where the two instances are not superimposed, the location of the X remains in the same motor unit. In other words, there may be some misalignment resulting from 1 of the 2 decompositions (unpaired events), but identification errors were rare. Seventeen are identified in the figure.