Yank-related changes in corticospinal recruitment gain in humans

Abstract

The generation of muscle force is a key component of movement. Force is generated by increasing the number and firing rates of motor units (MU), but limited information is available on the corticospinal (CS) recruitment gain across the spectrum of magnitude and rate of force (yank). To assess the effects of force magnitude and yank on motor outputs, we recorded force (motor evoked twitches, METs) and EMG (motor evoked potentials, MEPs) in response to transcranial magnetic stimulation (TMS) during nearly isometric hand gripping tasks in 20 healthy subjects. Motor cortex TMS was applied during force ramps at different levels of voluntary force magnitude and yank. Yank robustly facilitated METs, maximally at lowest magnitudes of voluntary force, but this facilitation saturated at forces >50% of the maximal voluntary contraction (MVC). At each level of force magnitude there was a linear relationship between the yank of voluntary force and MET amplitude. The slope of this relationship, representing the CS recruitment gain, decayed exponentially with increasing magnitude of force. Changes in CS recruitment gain associated with force magnitude and yank were better explained by METs than by MEPs. A positive yank resulted in larger estimated maximal MET at 0% force compared to static contractions. These results suggest that METs capture a robust yank-related increase in CS recruitment gain, which is blunted by limited MU availability at high force magnitude. We showed that the estimation of maximal motor outputs is optimally achieved in tasks in which force production is achieved with high yank.

Graphical Abstract

1. Introduction

The generation and gradation of muscle force is, arguably, the main function of mammalian motor systems. The first time derivative of force, also referred to as the rate of force development or ’yank’ (Lin et al., 2019), describes the change in the magnitude of muscular force over time (dynamic force) achieved through two mechanisms of motor unit (MU) activation: an increase in the number of firing MUs (population coding or recruitment) and an increase in their firing rates (rate coding) (Adrian and Bronk, 1929). While muscular force is encoded in the firing patterns of MUs excited above threshold (Baldissera and Campadelli, 1977), existing data on MU activation during ramp-up contractions indicates that there is no linear relationship between their firing rate and the output force and that the relative importance of recruitment versus rate coding vary across the force spectrum (Milner-Brown et al., 1973b; Tanji and Kato, 1973; Büdingen and Freund, 1976; Enoka and Duchateau, 2017). In fact, both the recruitment and firing rate modulation represent the output response of a fraction of MUs, with motor commands having simultaneous wider subthreshold synaptic effects on the motoneuronal pools. Those subthreshold synaptic effects facilitate MU activation in response to additional excitatory inputs (i.e., increase the MU recruitment gain) (Kernell and Hultborn, 1990). Modulation of MU recruitment gain for the physiological control of motor outputs has been suggested to be a fundamental property of voluntary control (Nielsen et al., 2019). While studies of MU activity provide a granular picture of the net MU activation resulting from multiple excitatory inputs, they leave unexamined the gain changes that occur across the whole corticospinal (CS) axis during force generation.

During the execution of movement, the facilitation of motor-evoked potential (MEP) or twitch (MET) in response to transcranial magnetic stimulation (TMS) reflects the increased recruitment gain of neurons contributing to the task, at both cortical and spinal levels, hereafter referred as CS recruitment gain (Devanne et al., 1997; Sekiguchi et al., 2003). Experimental paradigms demonstrating increased CS recruitment gain typically use static contractions, in which TMS is administered while maintaining a constant submaximal force (Mazzocchio et al., 1994; Kiers et al., 1995; Devanne et al., 1997; Di Lazzaro et al., 1998; Todd et al., 2003). However, the CS contribution to voluntary movement is maximized when changes in movement parameters are required, rather than with static tasks (Shalit et al., 2012; Zinger et al., 2013). Thus, testing during static contractions may favor the elucidation of anatomical connectivity over function, masking changes in CS recruitment gain associated with changing force. In fact, the limited data available suggest that the METs obtained during dynamic tasks bear limited relation to the magnitude of voluntary force at which they are obtained (Latash et al., 2003), differ depending on the type of contraction (Sekiguchi et al., 2003), are significantly larger than those obtained during static tasks (Cros et al., 2007), and that yank is selectively replicated in the outputs (Soto and Cros, 2011).

Here, we systematically examine the influence of the voluntary force magnitude and yank on the motor outputs to TMS during execution of a hand gripping task, aiming at describing the input-output relationship in humans. This relationship describes the cortical and spinal excitation changes (CS recruitment gain) associated with force generation and depends on the number of MUs available for recruitment. We show that voluntary force magnitude, yank, and their interaction explain most of the variance in the outputs. Notably, MET amplitude was positively correlated with yank at low force magnitude. However, as force magnitude increases, the influence of yank is reduced. We address this interaction by modeling our experimental human subject data.

2. Materials and Methods

2.1. Ethical approval

All protocols were approved by the Institutional Review Board at Tufts Medical Center (STUDY 13277) and all research was carried out in accordance with the standards established by the Declarations of Helsinki. A total of 20 individuals (25±.8 10.2 years, 11 males, and 9 females) participated in the study after providing their written informed consent. All subjects self-reported right-hand dominance, were free of neurological or orthopedic conditions that could interfere with the experiment, and met inclusion/exclusion criteria for receiving TMS (Rossi et al., 2009).

2.2. Experimental Design

2.2.1. Hand Grip Pressure Recording Device

Hand grip force was recorded using a custom-built recording device. A pressure transducer PX-119-100GI (OMEGA Engineering, Norwalk, CT) with a dynamic range of 0-100 psi and a response time of 1 ms was secured to a semi-flexible tube (30 cm) that terminated in a rubber sphygmomanometer bulb filled with water The bulb was pressurized to prevent deformability during contraction, and care was taken to remove all air bubbles from the system (Figure 1, a). The pressure signal was acquired at 1 kHz using a NI USB-6341 data acquisition (DAQ) board (National Instruments, Austin, TX). The entire system could be described as measuring nearly isometric hand grip forces, as there was a small deformation of the bulb at high forces. The pressure transducer was calibrated by adding known weights to the sphygmomanometer bulb and recording the corresponding output voltages. Linear regression of voltage versus applied weight was used to determine the calibration (1 N = 1.83 psi).

Figure 1:

a, Experimental setup, showing hand grip force exerted on water filled bulb. Real-time force changes were displayed on a monitor in front of the participant, with force increase causing an upward vertical displacement of the cursor as it moves from left to right at constant speed. Subjects were instructed to track presented trajectories displayed in black. At predetermined times (unknown to the participant) the contralateral motor cortex was stimulated non-focally with a large circular coil centered at vertex. b, Trial structure for dynamic contractions, showing different ramps presented and force magnitudes at which TMS was automatically triggered (inset). Main figure shows a voluntarily exerted force trajectory (thick dark grey line) tracking the instructed trajectory (light grey), TMS pulse time (vertical red line) is given at a time when a predetermined voluntary force threshold (Force at TMS) is reached (%MVC). The first time derivative of voluntary contraction (dF/dt, %MVC/s) is calculated in the 20 ms preceding TMS (Yank), and MET Amplitude (%MVC), is calculated from onset to peak.

2.2.2. Surface Electromyography (EMG)

Electromyography (EMG) was recorded from six muscles using preamplified bipolar surface EMG electrodes (circular bar, 12mm diameter) with a 17mm inter-electrode distance (Z03, Motion Lab Systems, Baton Rouge, LA). The electrodes were run through a six-channel amplifier (BL Engineering, Santa Ana, CA) and digitized at 1 kHz with the same NI USB-6341DAQ used to acquire the pressure transducer ensuring synchronous data streams. EMG signals were recorded from six muscles participating in the hand grip force task: abductor pollicis brevis (APB), first dorsal interosseous (FDI), flexor digitorum superficialis (FDS), flexor carpi radialis (FCR), flexor digitorum profundus to digits 4-5 (FDP), and extensor digitorum communis (EDC). The skin at the electrode sites was cleaned with alcohol wipes prior to electrode application. The electrodes were held in place with a Tegaderm dressing and secured with Coban wrap around the arm. The signal background noise level was visually checked when the arm was relaxed.

2.2.3. Transcranial Magnetic Stimulation (TMS)

A Magstim 200² (Magstim Co, Whitland, UK) with a standard 90 mm circular coil was used to deliver the TMS. The center of the coil was positioned over the Cz, and side A up in order to induce a posterior to anterior current at the motor cortex contralateral to the participant’s right upper limb. Muscle responses to TMS were described by the amplitude of the MEP, quantified as the peak-to-peak amplitude of the EMG signal during a window from 10 to 40 ms following the TMS pulse. The resting motor threshold (RMT) of the FDI muscle was determined as the minimum intensity required to elicit MEPs >50μV in the FDI muscle on 3 of 6 consecutive trials (Butler et al., 2005; Yarossi et al., 2019). TMS was delivered at 130% of RMT during all subsequent experimental trials.

2.2.4. Maximum Voluntary Contraction Recording

The participant was seated comfortably in a chair with their right arm resting on the armrest and their hand in a neutral, relaxed position. The pressure device was placed in the palm of the participant’s right hand. The palm and finger apposition to the bulb was passively maintained by strapping the hand with self-adherent Coban wrap applied with minimal pressure to prevent bulb release between trials. Subjects were told to remain completely relaxed between trials. The forearm was stabilized to the armrest with a strap. Each subject’s maximum voluntary contraction (MVC) was recorded with the pressure device. Subjects were cued by the experimenter to squeeze the pressure bulb as hard as they could and hold at maximum force for one second and then relax. This process was repeated three times, and the highest MVC value of the trials was averaged. As these recordings were obtained with the wrist and hand grip in a neutral position and were virtually isometric, mechanical effects derived from changes in muscle elongation or force-velocity relationships are considered negligible.

2.2.5. Data Acquisition and Experimental Paradigms

A custom MATLAB-based data acquisition platform (MathWorks, Natick, MA) was used to collect data, present prompts to the participant, and monitor EMG and force traces. In each trial, an on-screen black line showed the instructed force trajectory on a white background. Real-time feedback of magnitude of exerted force was displayed as vertical movement of a red cursor on the screen. The instructed line and cursor for resting were aligned at the bottom of the screen. The cursor moved at constant speed from left to right across the screen for 6 seconds. Force and EMG signals were recorded in three experimental paradigms as defined by the magnitude and the yank of the voluntary force exerted: resting (magnitude = 0, yank = 0), static contraction (magnitude > 0, yank = 0), and dynamic contraction (magnitude > 0, yank > 0). Each subject performed 250 dynamic (10 for each force level and ramp combination), 50 static (10 for each force level), and 10 resting trials. For resting trials, the instructed trajectory was a flat line at 0 force level. For static contractions, a rectangular force trajectory was presented, consisting of 2 seconds at 0 force, 2 seconds at the target force, and then 2 more seconds at 0 force. For dynamic contractions, a ramp-and-hold trapezoidal force trajectory was presented after 2 seconds at 0 force, with target force equal to MVC (Figure 1, b). Five different magnitudes of submaximal voluntary force were used: 5, 10, 20, 50, and 75 %MVC. Five different ramp slopes of 50, 70, 110, 330 and 1000% MVC/s, were used to manipulate the contraction yank. These slopes were selected for maximum ease of visual discrimination by subjects and hereafter are referred to as ramps 1-5, respectively. For resting contractions, TMS was applied at mid trial time; for static contractions, TMS was applied once a stable contraction at target level was achieved for 0.5 s; for dynamic contractions, TMS was applied when the required force magnitude was reached within a small tolerance window for 50 ms (between 80% and 1 psi greater than target magnitude). The actual force at TMS values varied due to this tolerance window. Therefore, we treated Force at TMS as a continuous variable rather than a categorical variable with 5 force levels (i.e., 0-5, >5-10, >10-20, >20-40, >40-60, and >60% MVC). During ramp contractions subjects remained unaware of the required voluntary force magnitude that would automatically trigger the TMS.

2.2.6. Data analysis

All data were processed using custom scripts in MATLAB (2020a, MathWorks, Natick, MA). MEP and MET data were visually inspected prior to analysis. EMG data was highpass filtered (20 Hz, 4th-order Butterworth). MEP amplitude was normalized to the maximal MEP per muscle across all trials. Force data was lowpass filtered (20 Hz, 4th-order Butterworth). MET onset was detected as the maximum of the double derivative of the force in a window from 10 and 60 ms after TMS. The end of the twitch was obtained using the same double derivative method as the onset in a window between the peak of the twitch and 130 ms after TMS. The amplitude of the MET was obtained by subtracting the force value at twitch onset from the peak force value of the twitch. For subsequent analyses, MET amplitudes were normalized to MVC. Voluntary force magnitude (’Force at TMS’) was defined as the recorded force at the time when TMS was triggered. For the dynamic condition, force slopes were fitted to estimate the yank (%MVC/s) in the 20 ms window preceding TMS time (Figure 1, b). We estimated MET amplitude at 0% MVC force by fitting a linear regression of MET and voluntary force magnitude at which TMS was delivered for each participant. In this analysis, we included either all levels of voluntary force magnitude or only those over 40% MVC, similar to the approach of (Todd et al., 2003). MET at 0% MVC was estimated for static and dynamic conditions (6 yank levels). Lastly, we calculated maximum yank within MET in the window between the start and peak of MET across the static, dynamic, and resting conditions.

2.3. Statistical analysis

Statistical analyses were performed in R (version 4.4.1). We treated force at TMS and yank as continuous variables to determine their ability to predict outcome variables. We used linear mixed models (lmerTest package, (Kuznetsova et al., 2017)) with restricted maximum likelihood to estimate the differences in MET data. The model included yank, force at TMS and their interaction as fixed effects and a random intercept for subject to account for within-subject variability. The low collinearity, normality of random effects, and linearity were confirmed for the model. There were no extreme outliers in the MET data. We used the fixed effects in the model to predict 10,000 MET estimates. A linear mixed model with the same fixed and random effects were used to analyze the MEP data for each of the 6 muscles separately. We added condition as a fixed effect to compare static and dynamic conditions in a separate linear mixed model. A repeated-measures ANOVA was used to evaluate the differences in estimated MET at 0% force (%MVC) across static and dynamic conditions (n=19). The normality of data (Shapiro Wilk) and homogeneity of variances (Levene) were confirmed. Bonferroni correction was applied to adjust p values for paired comparisons.

The relationship between the variables was quantified using repeated measures (RM) correlation (rmcorr library; (Bakdash and Marusich, 2017)). RM correlation determines the common within-individual association and estimates the correlation coefficient shared among individuals (common regression slope). We reported the number of trials for dynamic condition and categorized force (0-5, >5-10, >10-20, >20-40, >40-60, >60 %MVC) and yank (0-50, >50-100, >100-150, >150-250, >250-350, >350 %MVC/s) values into 6 levels when appropriate. Statistical significance was set to 0.05 for all statistical analyses.

3. Results

3.1. The type and magnitude of voluntary force exerted have a marked effect on MET amplitude

In agreement with previous observations (Cros et al., 2007), our data confirm that dynamic contractions had both a robust facilitatory effect on METs compared to static contractions (p < 0.0001) (Figures 3 and 4) and a robust facilitation of METs during active contractions of both types compared to those recorded at rest (Figure 4). For static and dynamic conditions, the MET amplitude changed as a function of voluntary force magnitude at which TMS is delivered (Figure 5). For static contractions, there was no correlation between voluntary force magnitude (Force at TMS) and MET amplitude (r = −0.2) (panel c), likely due to the non-linear relationship between static force measured across full range and METs. Figure 5, panel c, shows the known curvilinear distribution of MET as a function of static voluntary force magnitude (initial increase at low force level followed by decrease at high force (Kiers et al., 1995; Todd et al., 2016). However, when only forces ≥40% MVC were included, the correlation was significant (r = −0.51; p < 0.0001), as previously demonstrated by other researchers (Todd et al., 2003; Todd et al., 2016). For dynamic contractions, after categorization of yank into 6 levels based on the number of dynamic trials (panel a), we found a negative correlation between MET and the magnitude of voluntary force. The strength of this correlation increased with yank and saturated after 50-100% MVC/s (r = −0.35 to −0.79) (panel b). RM correlation coefficients and their 95% confidence intervals for MET and force are reported in panels c (static) and d (dynamic). The negative correlation coefficients observed in dynamic conditions indicate that larger METs were obtained at low force levels, and the METs were similar in amplitude to those under static conditions at force levels >50% MVC.

Figure 3:

Voluntary force trajectories and METs obtained in a single subject, under static and dynamic conditions, with TMS applied at 5% (left panel) and 50% MVC (right panel). Traces show force levels (%MVC; mean and standard error). The vertical dashed line indicates the time point at which TMS was delivered. At the lower force level the modulation of MET amplitude with increasing yank (ramp 1 to ramp 5) was more conspicuous than that seen at the higher force level.

Figure 4:

Left panels show MET amplitude (%MVC) for the dynamic condition (top panel; color coded for different yank levels) and static and resting (bottom panel, gray and black, respectively) conditions, as a function of force at which TMS was delivered. Each data point indicates a single trial. Right panels show contour plots of all trials. Both dynamic and static trials resulted in significant facilitation of METs compared to resting. For the dynamic condition, MET amplitude was affected by both the force magnitude at TMS (%MVC) and the yank (%MVC/s). In contrast, for the static condition, the effect of force magnitude at TMS on MET amplitude was less evident.

Figure 5:

MET amplitude (%MVC) as a function of force at TMS (%MVC) for static and dynamic conditions. a) Number of dynamic condition trials across yanks (%MVC/s). b) Repeated-measures (RM) correlation coefficients (mean and 95% CI) between MET amplitude and force at TMS for static and dynamic conditions. Dynamic conditions were categorized based on yank (e.g., 0-50 %MVC/s). c) RM correlation between MET amplitude and force at TMS for static condition. Within-subject RM correlation fits are color coded by subject. Each dot represents one trial of a subject. d) Same as in c but for the dynamic condition across yanks. The RM correlation coefficients and the 95% CI are shown in each panel.

3.2. Voluntary yank and MET amplitude are linearly related and their relationship declines exponentially with increasing voluntary force magnitude

In dynamic conditions, the input-output relationship between the attributes of voluntary force, obtained in a range of force and yank levels, and MET amplitude, confirmed the existence of a robust effect of voluntary yank on MET amplitude (Figure 6) (Cros et al., 2007). Furthermore, individual participant data showed a linear relationship between MET amplitude and voluntary yank (Figure 6, panel b), and a significant effect of voluntary force magnitude (p < 0.0001) on the steepness of the slopes describing the MET/yank relationship (0-5% MVC = 0.15 s; 5-10% MVC = 0.06 s; 10-20% MVC = 0.03 s; 20-40% MVC = 0.01 s; 40-60% MVC = −0.002 s; >60% MVC = −0.003 s), which decayed exponentially with increasing force magnitude (Figure 6, panel c). This decay resulted in significant differences in slopes being present only for low levels of force (p < 0.05), but not for those above 20% MVC (20-40% vs 40-60% MVC (p = 0.31), 20-40% vs >60% MVC (p = 0.12), and 40-60% vs >60% MVC (p = 1) (data of 12 subjects in whom available data allowed for satisfactory calculation of MET/Yank slopes in each category of force magnitude ). The progressive decrease in the strength of the within-participant association between MET and yank with increasing magnitude of voluntary force is further shown by the progressive decline of the RM correlation coefficients with increasing force (Figure 6, panel d).

Figure 6:

MET amplitude (%MVC) as a function of yank (%MVC/s) for dynamic condition. a) Number of dynamic condition trials across force magnitude (%MVC) at which TMS was delivered. The force magnitude at TMS was categorized into 6 levels (shown in different colors). b) Single subject example of the linear relationship between MET amplitude and yank across the 6 force levels (same color-coding as in panel a). c) Linear regression slopes (mean ± SE) for MET amplitude and yank across the force levels. d) RM correlation between MET amplitude and yank across the 6 force categories. Within-subject RM correlation fits are color-coded by subject. Each dot represents one trial of a subject. The RM correlation coefficients and the 95% CI are shown in each panel.

The linear mixed model of the data obtained under dynamic conditions revealed a significant effect of voluntary force at TMS (r² = 0.46; p < 0.0001), yank (r² = 0.54; p < 0.0001), and their interaction (r² = 0.71; p < 0.0001) on MET amplitude. The overall model explained 76% of the variance in MET. Figure 7 demonstrates the input-output relationships between force attributes (magnitude and yank) and MET amplitude for the hand gripping task in humans. The model summarizes three major observations of this research: a) the 54% of variance explained by yank is concentrated at force magnitudes below 50% MVC; b) force magnitude, which explains 46% of variance, has a limited effect on MET amplitude in the absence of yank (i.e., static contraction), and c) at force levels > 50% MVC, yank may even be detrimental for MET amplitude.

Figure 7:

MET amplitude (%MVC) was predicted using the experimental data (dynamic condition trials only) fitted with linear mixed model. Yank (%MVC/s), force at TMS (%MVC), and their interaction were included as fixed effects, while subject was a random effect. The model explained 76% of the variance in MET. MET increased with yank at forces below 50% MVC, more robustly the weaker the contraction. The facilitation of MET decayed with increasing level of voluntary force magnitude. When force was >50% MVC, the relationship between MET and yank trends towards 0 and negative values. The blank region (top right corner) indicates the absence of positive MET values for the corresponding force and yank levels.

3.3. Static conditions underestimate maximal force outputs of the motor system

We observed that dynamic contractions resulted in a significant excess facilitation of METs over static contractions (Figures 4 and 5). A linear regression model for the entire force range (Figure 8) allowed us to estimate MET at 0% MVC for static and dynamic conditions and study the effect of yank levels. Repeated-measures ANOVA showed that the estimated MET at 0% MVC was higher during dynamic contraction than during static contraction (p < 0.0001). In addition, for dynamic contractions, the estimated MET at 0% MVC increased with yank. Importantly, our analysis included METs obtained in the entire range of voluntary force magnitude (Figure 8, panel a), as well as only those over 40% MVC as was suggested by (Todd et al., 2003)(Figure 8, panel b). Importantly, regardless of the approach to the analysis, static contractions underestimated the estimated maximum MET.

Figure 8:

Estimated MET at 0% MVC (mean ± SE) for static and dynamic conditions (6 yank levels). Each data point is an estimated MET for one subject (n = 19). Horizontal bars indicate statistical significance. We calculated estimated MET by fitting a linear regression model to predict the MET at 0 force. The linear models included METs obtained either across the entire force range for each participant (a) or only at forces ≥40% MVC (b). The insets (top left) show examples of linear model fit (blue line) and estimated MET (red circle).

3.4. MEPs and METs capture corticospinal recruitment gain differently.

The linear mixed model of MEP data showed that all main effects and interactions are statistically significant (p < 0.001) and that magnitude of voluntary force (Force at TMS) was the strongest predictor of MEP size across all muscles, with significantly lower contribution of Yank. There was significant variability among different muscles, with hand and long forearm finger flexors (FDI, FDP, and FDS) showing high conditional r² values, indicating that the full model explains a large portion of variability in MEP amplitude. Of those, FDP and FDS showed consistently elevated marginal r² values, showing significant contribution by the fixed effects alone. Overall, we found that in the six muscles recorded, the predictive power of voluntary force magnitude and yank was comparatively lower in estimating MEPs r² conditional = 0.35 – 0.56; p < 0.001) than in estimating METs (Table 1) as compared to data presented in 3.2. Significantly, among the muscles exhibiting lowest MEP predictive power was EDC, the only antagonist recorded, confirming that METs arise largely from action of flexor muscles with agonist role to the task. Regarding METs, we found a strong linear relationship between the maximal yank of forces composing the MET (’Max yank within MET’) and its amplitude (r = 0.92, 95% CI = [0.916 0.924], p < 0.0001), as shown in Figure 9. Since voluntary yank is linearly related to MET amplitude (see 3.2), this finding indicates there is a relation between the voluntary Yank and the yank within the MET which ultimately specifies its amplitude.

Table 1:

Summary of statistics for the normalized peak to peak MEP data.

Main Effect	β	SE	p	R2 (Conditional vs. Marginal)
Abductor pollicis brevis (APB)
Force at TMS	0.256	0.0145	<0.001	0.52 0.41
Yank	0.0354	0.00315	<0.001
Interaction	−0.0007	0.00008	<0.001
First dorsal interosseous (FDI)
Force at TMS	0.142	0.013	<0.001	0.56 0.18
Yank	0.0176	0.00284	<0.001
Interaction	−0.0003	0.00007	<0.001
Flexor digitorum superficialis (FDS)
Force at TMS	0.274	0.0137	<0.001	0.50 0.68
Yank	0.0298	0.00297	<0.001
Interaction	−0.0005	0.00007	<0.001
Flexor carpi radialis (FCR)
Force at TMS	0.201	0.0151	<0.001	0.35 0.37
Yank	0.0239	0.00329	<0.001
Interaction	−0.0004	0.00008	<0.001
Flexor digitorum profundus (FDP)
Force at TMS	0.283	0.014	<0.001	0.43 0.88
Yank	0.0357	0.00305	<0.001
Interaction	−0.0005	0.00007	<0.001
Extensor digitorum communis (EDC)
Force at TMS	0.17	0.0135	<0.001	0.35 0.44
Yank	0.0211	0.00294	<0.001
Interaction	−0.0002	0.00007	<0.001

β: Fixed effect coefficient for linear mixed model; SE: Standard error of the coefficient; R² conditional: Coefficient of determination accounting for both random and fixed effects; R² marginal: Coefficient of determination accounting for fixed effects only.

Figure 9:

Maximum yank within MET predicts its amplitude. a) Two sample METs evoked by TMS (vertical dashed line). Maximum yank (dF/dt) was calculated within the window between the start and peak of MET, as shown by the red trace in the inset. The MET with the magnitude of 20.6% MVC (black) had a maximum yank value of 784% MVC/s, while MET with the magnitude of 11.9% MVC (gray) had a maximum yank value of 427% MVC/s, showing that the change in maximum yank was proportional to the change in MET amplitude. b) Single subject example of the linear relationship between MET amplitude and maximum yank within MET. c) Repeated-measures (RM) correlation coefficients (mean and 95% CI) between MET amplitude and maximum yank within MET. METs from static, dynamic, and resting conditions were included in the analysis. Within-subject RM correlation fits (color-coded) as well as an overall slope (black dashed line; simple regression) are plotted. Each dot represents one trial of a subject. Linear regression model fit results are shown on the bottom right portion of the panel.

4. Discussion

The main finding of this study was that the MET size is yank dependent, and that this relationship is modulated by the level of the voluntary force. The robust yank-dependent modulation of outputs is limited by finite MU availability. Maximal force output estimates of the motor system are optimally estimated during contractions with high yank, and the neural substrates for yank-related MET facilitation and ballistic contractions are similar.

4.1. MET modulation with voluntary contraction.

We demonstrate that both the modality of voluntary force production (static vs. dynamic) and its magnitude exert a significant influence on MET amplitude. At the MU level, these results raise key mechanistic questions: To what extent does the differential force-generating capacity of recruited MUs modulate MET amplitude? And, are METs elicited during voluntary contraction predominantly mediated by the recruitment of additional MUs, or by modulation of discharge rates in already active MUs? Unless the MET capture different portions of the MU pools at different force levels, the orderly MU recruitment would predict larger METs at higher levels of voluntary force magnitude, due to higher force capacity of those MUs (Milner-Brown et al., 1973b; Fuglevand, 2011). However, with dynamic contractions, METs were larger at the lowest force levels, suggesting that differences in the force capacity of individual MUs are not highly relevant in predicting MET amplitude. Alternatively, the activation history of MUs may affect the MET amplitude both through firing rate effects on the mechanical summation of single muscle fiber twitches, and through activity-related changes in MU responsiveness. Physiologically, MU firing rates increase monotonically, but not linearly, with increasing voluntary force (Oya et al., 2009; Hu et al., 2014; Fuglevand et al., 2015; Enoka and Duchateau, 2017). Short interspike intervals result in increased force outputs due to optimal mechanical force fusion (Burke et al., 1976), suggesting rate-based facilitation (extra firing of active MUs in response to TMS) to be potentially advantageous. However, this effect is likely limited by spike-frequency adaptation (Calvin and Schwindt, 1972; Baldissera and Gustafsson, 1974; Jones and Bawa, 1999; Matthews, 1999). While input output function to TMS may be muscle-dependent (Koponen et al., 2024), available experimental data indicates that TMS does not have the capacity to produce considerable, repeated MU firing (Z’Graggen et al., 2005; Skarabot et al., 2023), overall suggesting a limited effect of MU activation history on MET amplitude. Alternatively, MU availability for recruitment is likely a critical factor in determining the amplitude of METs. In human arm muscles full MU recruitment is reached at 30-78% of MVC (Gydikov and Kosarov, 1974; Kukulka and Clamann, 1981; Zijdewind and Thomas, 2003; Klass et al., 2008). Thus, in our setup with forces above 50% MVC the number of MUs available for recruitment is very limited or non-existent, while recruited MUs are firing at high rates with reduced responsiveness, as discussed above. Thus, the comparative reduction of MET amplitude with voluntary force magnitude of >50% MVC likely reveals the limitations of rate-based MET facilitation to compensate for the reduced availability of MUs, and suggests that the theoretical advantage of inducing extra MU discharges by TMS (Burke et al., 1976) did not make a significant difference in outputs (Figure 4 and 5). This framework suggests a critical role for excitability modulation of not-yet-recruited MUs during ramp force increase in the MET amplitude.

The output of a MU pool depends on both the excitatory synaptic drive and the motoneuronal intrinsic properties, both of which are non-uniformly distributed across the pool (Heckman, 1994; Binder et al., 2002; Ruggiero and Gruber, 2024). Thus, with any prescribed level of voluntary force magnitude, a proportion of MUs are excited below threshold while others are firing and generating motor outputs (Denny-Brown and Sherrington, 1928; Lorente de Nó, 1935; Lloyd, 1945; Hultborn et al., 2003). Experimental setups like ours have shown subthreshold excitation to contribute to MEPs (Pereon et al., 1995; Baldissera et al., 2002). Furthermore, we previously showed that in a dynamic task, the kinematic aspects of voluntary yank are selectively and robustly replicated by TMS and bear no relationship with the magnitude of contributing forces to the task, strongly suggesting capture of neurons that are excited below threshold (Soto and Cros, 2011; Rothwell and Hannah, 2024). Since TMS outputs capture MUs according to the size principle (Bawa and Lemon, 1993), their linear relationship with voluntary yank suggests yank determined the proportion of MUs captured in the response to TMS. Due to the different force capacity of MUs, there is no 1:1 relationship in the number of MUs responsible for MET amplitude at different force levels, but the recorded force appear to replicate the linear relationship present physiologically between the force capacity of individual MUs and total force output (Milner-Brown et al., 1973a; Fuglevand et al., 1993). Along this framework during voluntary force generation, the fraction of MUs next-in-line to be recruited receives subthreshold excitation, is captured in the MET, and the force output of that fraction is linearly related to voluntary yank. The progressive decline of slope steepness with increasing force magnitude is a predictable consequence of the progressive reduction of MU availability for recruitment (i.e., saturation of recruitment-based facilitation), with any facilitation necessarily requiring a rate-based mechanism. Since at high force levels MUs are firing at higher rates, they exhibit unresponsiveness to TMS and METs cannot be further facilitated.

4.2. Recruitment-dependent facilitation and maximal force capacity of the motor system

Modeling studies of MU pools receiving an excitatory input of constant magnitude (’steady state activation’) show magnitude modulation of force outputs evoked by an excitatory transient (Heckman, 1994). Notably, in those studies there was a decreasing gain with high force, consistent with our results of the static and dynamic force protocol. Interestingly, our data also align with the force outputs observed in a simulation model using a ’narrow’ recruitment constraints (full recruitment at 50% MVC) (Fuglevand et al., 1993). To date, the available simulation or empirical data for dynamic force paradigms remains scant. The few existing studies indicate that the dynamics of the contraction impact the recruitment gain. Studies of ballistic contractions (i.e., requiring maximal yank) indicate an important effect on voluntary force magnitude of the rate of MU recruitment at the onset of contractions (Del Vecchio et al., 2019). A recent modeling study confirmed a higher dependence of the force magnitude of outputs on the rate of MU recruitment rather than rate coding (Dideriksen et al., 2020). To our knowledge, there are no modeling studies available that describe the input-output function of MU activation across a wide range of force magnitudes and yanks, but our data supports incorporating yank-related increased gain at the lowest level of force range and yank-related modelling of subthreshold excitation at both cortical and spinal levels (Kernell and Hultborn, 1990; Hultborn et al., 2004; Nielsen et al., 2019). Furthermore, yank-dependent increases in CS recruitment gain might be a central physiological mechanism maximizing voluntary force (Ruggiero and Gruber, 2024). Using static contractions, other researchers have used METs to estimate, by linear extrapolation to rest (0% MVC), a theoretical maximal force capacity of the motor system, labeled ’estimated maximum twitch’ (EMT). The difference existing between the EMT (corresponding to the estimated MET amplitude at 0% MVC in our setup) and the actual force exerted during maximal voluntary contraction is suggested to reflect incomplete central activation (Todd et al., 2003). According to our data static contractions underestimate the EMT, but we also found the EMT to be yank-dependent. Our analysis included either METs obtained in the entire range of voluntary force magnitude or only at forces ≥40% MVC. Importantly, in both cases, static contractions underestimated the EMT. Our data suggest that the maximal force capacities of motor systems are reached during the generation of dynamic forces and are yank-dependent. Available data indicates that behavioral engagement can help focusing on the outputs and that intent is a prime driver of maximal yank (Gandevia and Rothwell, 1987; Behm and Sale, 1993).

4.3. Motor cortex commands’ role in yank-related gain changes

The yank-dependency of METs may reflect modulation of excitability at both motor cortex and spinal levels, hence labeling this process as CS recruitment gain. Several descending pathways transmit signals to MUs, most importantly CS and reticulospinal (RS) pathways (Lemon, 2008; Ruggiero and Gruber, 2024). While RS commands exert a robust effect in MU recruitment gain associated with force magnitude (Glover and Baker, 2020), the relationship between RS neuron firing patterns and muscle force magnitude is monotonic and uniform, whereas motor cortical neurons play a more complex and heterogeneous role in force generation (Evarts, 1968; Humphrey et al., 1970; Cheney and Fetz, 1980; Glover and Baker, 2022). Indeed, CS pathways are more relevant in the transmission of phasic signals correlating with changes in motor parameters (such as muscular force or direction)(Shalit et al., 2012). In force space, this functional organization supports that MC signals have a preferential role in control of yank, as suggested from single-cell recordings in primate motor cortex (Georgopoulos et al., 1992), human TMS studies (Soto and Cros, 2011), and yank-related changes in MC beta oscillatory activity (Uehara et al., 2023). Trans-synaptic excitation of output cortical neurons with TMS intensities at or close to RMT (Day et al., 1989a; Burke et al., 1993; Berardelli et al., 1994; Fujiki et al., 1996; Rothwell, 1997; Aberra et al., 2021; Wang et al., 2024) allows capturing changes in excitability occurring at the cortical level during force generation (Mills et al., 1987; Datta et al., 1989; Nielsen et al., 1993; Di Lazzaro et al., 1998). However, with the suprathreshold TMS intensity used in our experiments, causing direct excitation of CS axons, it is likely that modulation of MU excitability by supraspinal and segmental inputs contributed more markedly to the observed effects (Taylor, 2006; Wang et al., 2024). Spinal mechanisms that facilitate contractions include fusimotor drive to primary and secondary spindle afferents that may exist under isometric conditions, inputs from flexor reflex afferent and cutaneomuscular responses, and suppression of inhibitory pathways (reviewed in (Pierrot-Deseilligny and Burke, 2012)). While spinal contributions are likely to be present, previous data showing a robust selectivity of METs according to yank suggest that afferent feedback has a secondary role relative to supraspinal inputs in the specification of the yank related increase in CS recruitment gain (Soto and Cros, 2011). TMS-evoked outputs are strongly biased towards fast CS connections, a large proportion of which have direct synaptic contact with MUs (Morecraft et al., 2013; Innocenti et al., 2019). These monosynaptic connections are highly relevant functionally (Lemon et al., 1986; Lemon, 2008) and contribute to the initial part of cortically-evoked outputs (Burke et al., 1994). Consequently, the rising force epoch of METs is likely to be strongly influenced by direct CS connections, and the maximal yank within the MET to depend on the strength of these connections. Studies on the physiological underpinnings of fastest voluntary contractions suggest a speed control strategy as a simple mechanism to control amplitude of motor outputs with minimal computational burden (Enoka, 1983; Bellumori et al., 2011; Folland et al., 2014; Maffiuletti et al., 2016). We found that the MET represents a type of response similar to voluntarily generated force pulses in which the maximum yank during the force pulse is linearly related to its force amplitude (Freund and Budingen, 1978; Ghez and Vicario, 1978). Our data, showing artificially generated TMS force pulses to mirror control of amplitude scaling of voluntary pulses, suggests leveraging of same neural substrates.

4.4. MET vs MEP

In contrast to MEPs, METs have received the attention of a limited number of studies. MEPs are a myoelectrical signal representing the algebraic sum of single, relatively synchronous, muscle fiber action potentials. In contrast, in METs, the net force output results from a nearly linear summation of the force of individual muscle fibers, in which there are negligible effects from the viscoelastic properties of the muscle (Sandercock, 2005). Our MET recordings used a nearly isometric device indicating METs were not significantly affected by length-tension muscular relationships. Thus, METs are exclusively shaped by neural (MU) activation patterns in response to TMS, free from viscoelastic/biomechanical effects. Since TMS outputs are always followed by a period of electrical silence (cortical silent period)(Figure 2), there is no concern of METs being contributed by lingering voluntary activation (Day et al., 1989b), eliminating the need to control for voluntary yank levels as might be necessary with twitches evoked with peripheral stimulation (Babault et al., 2001). Comparing MEPs and METs, we found that in the six muscles recorded, the predictive power of voluntary force magnitude and yank was comparatively lower in estimating MEP (r² conditional = 0.35 – 0.56; p < 0.001) than MET size (Table 1). This discrepancy is likely due to phase cancellation of myoelectric signals contributing to MEPs (Kiers et al., 1995; Spampinato et al., 2023), while METs efficiently capture summation of individual muscle fiber twitches.

Figure 2:

Representative single trial data over a 0.5 s epoch, for force and 6-channel EMG recordings of APB, FDI, FDS, FCR, FDP, and EDC muscles. Note the alignment of MEPs (vertical red line) immediately preceding the MET onset, and the complete EMG suppression (cortical silent period) during the MET phase. TMS was applied at 0 ms.

4.5. Limitations

We did not control muscle fatigue across the trial blocks, and it can be hypothesized that yank-dependent facilitation might be an index of central fatigue. While the order of trials was randomized to minimize possible effects of fatigue, it is possible that fatigue may have contributed to the limited number of trials combining high force and high yank in our recordings. The assessment of yank-dependent changes in MU recruitment thresholds to TMS can be optimally verified with single MU recordings, which we did not perform. We did not explicitly control hand posture and joint angle that may have differed across participants depending on hand size and gripping strategy. Thus, differences in yank-related changes in CS transmission related to muscle size, muscle length, and hand posture, could not be accounted in the current study.

Highlights.

• We capture the facilitation of mechanical motor cortical outputs across a range of force attributes (magnitude and yank).

• Robust state-dependent increases in recruitment gain occur during force generation compared to force maintenance.

• Recruitment gain is linearly dependent on the intensity of yank and constrained by finite motoneuron availability.

• Recruitment gain changes with dynamic contractions optimize the estimation of maximal force capacity of the motor system.

• This novel approach enables estimation of motoneuronal availability and neural drive in health and diseased states.

Data availability.

Data will be available upon reasonable request.