Abstract
Although premovement beta-band event-related desynchronization (β-ERD; 13–30 Hz) from sensorimotor regions is modulated by movement speed, current evidence does not support a strict monotonic association between the two. Given that β-ERD is thought to increase information encoding capacity, we tested the hypothesis that it might be related to the expected neurocomputational cost of movement, here referred to as action cost. Critically, action cost is greater both for slow and fast movements compared with a medium or “preferred” speed. Thirty-one right-handed participants performed a speed-controlled reaching task while recording their EEG. Results revealed potent modulations of beta power as a function of speed, with β-ERD being significantly greater both for movements performed at high and low speeds compared with medium speed. Interestingly, medium-speed movements were more often chosen by participants than low-speed and high-speed movements, suggesting that they were evaluated as less costly. In line with this, modeling of action cost revealed a pattern of modulation across speed conditions that strikingly resembled the one found for β-ERD. Indeed, linear mixed models showed that estimated action cost predicted variations of β-ERD significantly better than speed. This relationship with action cost was specific to beta power, as it was not found when averaging activity in the mu band (8–12 Hz) and gamma band (31–49 Hz) bands. These results demonstrate that increasing β-ERD may not merely speed up movements, but instead facilitate the preparation of high-speed and low-speed movements through the allocation of additional neural resources, thereby enabling flexible motor control.
SIGNIFICANCE STATEMENT Heightened beta activity has been associated with movement slowing in Parkinson's disease, and modulations of beta activity are commonly used to decode movement parameters in brain–computer interfaces. Here we show that premovement beta activity is better explained by the neurocomputational cost of the action rather than its speed. Instead of being interpreted as a mere reflection of changes in movement speed, premovement changes in beta activity might therefore be used to infer the amount of neural resources that are allocated for motor planning.
Introduction
Unveiling the neurophysiological basis and functional role of brain activity in the beta band (13–30 Hz) is of particular interest to basic motor control scientists as well as clinicians because of its characteristic pattern of modulation with movement, described as event-related desynchronization (ERD; Pfurtscheller and Lopes da Silva, 1999), and its specific alteration in neurologic disorders such as Parkinson's disease (PD; Jenkinson and Brown, 2011). Although numerous studies have attempted to link these movement-related changes in beta power to behavior, the evidence so far has been inconsistent, making its functional interpretation still an area of active debate (Engel and Fries, 2010; Brittain and Brown, 2014; Spitzer and Haegens, 2017).
Beta power has often been related to motor activity: the amplitude of beta-band ERD (β-ERD) has been positively correlated with corticospinal excitability (Takemi et al., 2013) and with the activation level of the sensorimotor cortex (Yuan et al., 2010), and beta power from local field potentials of the subthalamic nucleus has been related to the encoding of motor effort (Tan et al., 2015). Furthermore, noninvasive neurostimulation studies have shown that specifically increasing beta-band activity tends to decrease movement speed (Pogosyan et al., 2009; Wach et al., 2013). The most striking evidence of a significant association between beta power and movement speed comes from patients with PD. PD is notably characterized by motor symptoms such as bradykinesia (i.e., movement slowing; Bloem et al., 2021). Beta power is increased in PD and can be attenuated with treatments (Kühn et al., 2006; Ray et al., 2008). The greater the decrease in beta power, the greater the improvement in bradykinesia (Jenkinson and Brown, 2011), making beta power a promising therapeutic target. Although PD treatment most often targets beta power at the subcortical level, there is evidence of abnormalities in cortical beta power as well, such as an attenuation of premovement β-ERD (Heinrichs-Graham et al., 2014). Still, the relationship between beta power and movement speed does not appear monotonic, as several studies have reported no significant difference in β-ERD between slow and fast movements (Stancák and Pfurtscheller, 1995; Zhang et al., 2020; for review, see Kilavik et al., 2013).
From a functional perspective, several studies have provided evidence in favor of a specific role of beta activity in regulating computational power through synchronization/desynchronization of neuronal populations within sensorimotor regions (Brittain et al., 2014), being proposed to be related to top-down interactions (Fries, 2015) and expressing the influence of priors on newly formed neuronal assemblies (Betti et al., 2021). Put another way, beta power would decrease to augment the neurocomputational power required for information processing (Brittain and Brown, 2014), as exemplified by greater β-ERD when increasing cognitive demand during motor planning (Grent-'t-Jong et al., 2013; Wiesman et al., 2020). One intriguing conjecture is that β-ERD amplitude may increase as a function of the neurocomputational cost of the movement being prepared, referred to herein as “action cost.” Action cost can be represented as the sum of a biomechanical cost, which increases with movement speed, and a temporal cost, which decreases with movement speed (Berret and Jean, 2016; Shadmehr et al., 2016). This leads to a u-shaped action cost function, the minimal value of which has been shown to predict the preferred (Pref) speed of participants in various motor contexts (Berret and Jean, 2016). According to this hypothesis, β-ERD amplitude would thus vary nonmonotonically with movement speed, being greater both for slow and fast movements compared with movements performed at medium (i.e., near-preferred) speed.
We tested this hypothesis by using a speed-controlled reaching paradigm while applying computational modeling to estimate the associated action cost. Results revealed that β-ERD amplitude varied nonmonotonically with movement speed, in a manner that was strikingly well predicted by estimated action cost. These results invite rethinking of the interpretation of beta power as a marker of cortical resources allocated for movement instead of a mere correlate of movement kinematics such as speed.
Materials and Methods
Participants
Thirty-one participants (15 females; mean ± SD age, 23 ± 3 years) were recruited for this study. All of them were right handed based on self-report. They had normal or corrected-to-normal vision and were free of any known neurologic or psychiatric condition. All participants gave their informed written consent and received a 30$ Canadian compensation. All procedures were approved by the local ethics committee. The experiment conformed to the standards set by the 1964 Declaration of Helsinki.
Experimental task
Setup.
The experimental setup consisted of a table supporting a 20 inch computer monitor that projected visual stimuli onto a mirror positioned horizontally in front of the participants. The monitor (model P1130 monitor, Dell; 20 inch; resolution, 1024 × 768; refresh rate, 150 Hz) was mounted face down 29 cm above the mirror with the latter positioned 29 cm above the table surface. Participants' movements were recorded with an acquisition frequency of 100 Hz, using a two-joint manipulandum composed of two lightweight metal rods with a potentiometer at the hinges of the manipulandum. Participants performed their movements by grasping a handle located at the mobile end of the manipulandum with their right hand and sliding it over the table. The position of the handle (and thus participants' hands) was shown to participants using a cursor on the monitor. This provided constant visual feedback of participants' hand positions, similar to a computer mouse. A 64-electrode actiCAP extended 10/20 system (Brain Products) was positioned on participants' heads to record scalp electroencephalography (EEG). This was done by measuring the head dimensions in the sagittal and frontal planes to localize the vertex and positioning the reference electrode (FCz) over it. The EEG data were acquired using the BrainVision Recorder software 2.0 (Brain Products) with a sampling rate of 500 Hz.
Overview.
Participants were seated in front of the table and asked to reach a visual target (cyan-filled circle, diameter, 3 cm) with their right hand. Visual stimuli were presented using Psychtoolbox on MATLAB (MathWorks). Trials were initiated by placing the cursor (white filled circle; diameter, 0.6 cm) on a starting point (light gray filled circle; diameter, 0.6 cm) located at the center of the screen. Participants were told to place their chin on a small support, to keep their right arm in contact with the surface of the table, and to minimize postural changes during the experiment. The target was presented either on the right side of the screen (Rt; 60°) at a distance of 10 cm from the starting point or on the left side of the screen (Lt; 150°) at a distance of 6 cm from the starting point. These positions were chosen to ensure that the maximal peak velocity participants could reach was significantly different for each target. Indeed, maximal peak velocity increases with distance (Gottlieb et al., 1989) as well as with the biomechanical constraints of the movement (Gordon et al., 1994). The biomechanical constraints of a reaching movement depend on movement direction and can be represented as an ellipse of mobility of the arm, because of changes in its effective mass because of its inertial properties (Shadmehr et al., 2016). The major axis of the ellipse of mobility corresponds to the directions associated with the lowest effective mass of the arm, and thus the easiest and fastest to reach. Conversely, the minor axis of the ellipse corresponds to the directions in which the effective mass of the arm is the highest, resulting in more difficult and slower movements. In the present task, Rt was located on the major axis, and Lt on the minor axis. Hence, maximal velocity was expected to be significantly higher for movements oriented toward Rt than Lt.
Trial timeline.
Trial timeline is illustrated on Figure 1A. Trials started with the display of a white fixation cross (1.1 × 1.1 cm) 4 cm above the starting point on the screen. Once the cursor was placed on the starting point, participants were required to keep their gaze on the fixation cross for the entire trial duration. They were also asked to minimize eye blinks until they reached the target to avoid artifacts in the EEG signal during the period of interest. After a 2 s delay, the target appeared on the screen. A gauge (6.6 × 1.3 cm) centered on the fixation cross appeared simultaneously to the target. The filling level of the gauge was informative of the speed at which participants would have to perform their movement toward the target: one-quarter filling indicated a slow speed (Low); half filling indicated a medium speed (Med); and three-quarter filling indicated a fast speed (High; Fig. 1B; for details about speed requirements, see subsection Experimental conditions and their related hypotheses). An auditory go cue occurred 2 s after target and gauge appearance, signaling that the movement could be initiated. Participants were asked to start their movement quickly after they heard the go cue. If participants initiated their movement before the go cue, an error message was displayed for 1 s (“false start”), and the trial was automatically rerun. Once the movement ended, all stimuli disappeared and were replaced by visual feedback on whether the speed criterion was reached or not in the form of a message (“well done!”, if the speed criterion was attained; or the difference in centimeters per second between the peak velocity reached during the trial and the speed criterion if it was not attained). Movements were required to end inside the chosen target to ensure accuracy and thus comparability of trials across conditions. In case the target was missed, an error message was displayed for 1 s (“target missed”) and the trial was rerun. Whatever the visual feedback, it was replaced after 1 s by the appearance of the white fixation cross with the starting point and the cursor. The next trial started when the cursor was placed inside of the starting point. Participants were encouraged to take a break between trials by not immediately replacing the cursor inside of the starting point if they felt the need to move their eyes, head, or body, or if they wanted to rest for a few seconds. The experiment was organized in four blocks of 60 trials, which comprised two blocks of trials requiring movements toward Rt, and two blocks of movements directed to Lt. The speed conditions varied pseudorandomly throughout trials in one block, so that a same speed condition was not presented twice in a row and each block comprised 20 trials for each speed condition.
Participants familiarized with the experimental task and their maximal speeds were estimated before performing the trials described above. Participants first performed 10 movements toward each target at a comfortable pace, organized in blocks of five trials presented in an alternating order (five Rt trials, five Lt trials, five Rt trials, and five Lt trials) to familiarize them with the setup. Then, they performed 60 trials in which they were asked to reach the presented target as fast as possible (30 Rt trials followed by 30 Lt trials) to estimate their maximal speeds. Rt and Lt trials were separated by a short break that ended when participants felt rested, to avoid an effect of physical fatigue on motor performance (although fatigue was also minimized on a single-trial basis by allowing participants to delay the start of the next trial by not immediately placing their cursor inside of the starting point as previously explained). Finally, participants familiarized themselves with the different speed criteria by performing trials in each speed condition. More precisely, trials from a given speed condition were repeated until achieving the correct speed five times (not necessarily back-to-back). All of these familiarization and “maximal speed” trials were organized the same way as those in the main experiment, except that no gauge was displayed in the first familiarization and maximal speed trials.
Experimental conditions and their related hypotheses.
Speed criteria were defined to create conditions requiring different peak velocities but similar relative effort (i.e., difference from maximal peak velocity). Six velocity criteria (two Targets × three Gauges) were used in total: for movements toward Rt 120 cm/s when the gauge was three-quarter filled (HighRt), 95 cm/s when the gauge was half filled (MedRt), and 70 cm/s when the gauge was one-quarter filled (LowRt); for movements toward Lt 60 cm/s when the gauge was three-quarter filled (HighLt), 40 cm/s when the gauge was half filled (MedLt), and 20 cm/s when the gauge was one-quarter filled (LowLt; Fig. 1B). During trials, these speed criteria were considered to have been attained if the peak velocity of the movement was within an interval of ±5 cm/s centered on the speed criterion of the corresponding condition. In addition, to ensure significant differences in movement speed across conditions, these criteria were set so that the High speed criteria were to be close to the maximum that speed participants could reach for each target considering differences in amplitude and inertial anisotropy (Gordon et al., 1994; Shadmehr et al., 2016). To verify this assumption, participants were first asked to perform 30 reaching movements toward each target as fast as possible (“maximal speed” trials defined before), and the average maximal peak velocity was then compared with the average peak velocity in High trials a posteriori (see Results). Therefore, the present design allowed the testing of the respective influences of speed and effort on beta power. Indeed, if beta power is influenced by absolute movement speed, then both an effect of Gauge and Target should be expected considering that the two factors significantly influence peak velocities (Fig. 1C, left); whereas if beta power is influenced by the movement speed relative to its maximal value as a measure of expected effort (Tan et al., 2015), then only a significant effect of Gauge should be found despite the significantly different speed ranges reached for each target (Fig. 1C, middle). Finally, modeling work has demonstrated that optimal/preferred movement speed could be selected based on the joint minimization of a trajectory or metabolic cost that increases as movement speed increases, and of a cost of time that increases as movement speed decreases (Berret and Jean, 2016). Based on this model, the relationship between movement speed and action cost is not linear but instead follows a u-shaped curve. As a consequence, beta power may vary nonlinearly with speed, and therefore decrease in High and Low conditions compared with Med (Fig. 1C, right).
Data analysis
Behavior.
Hand position was estimated in real time with the coordinates of the cursor recorded with the two potentiometers located on the manipulandum. Recorded signals were sampled at 100 Hz and were low-pass filtered at 10 Hz using a second-order Butterworth filter. Real-time velocities were determined for each trial using numerical differentiation. The maximal value of these real-time velocities was considered as the peak velocity. Movement onset was defined as the first time point at which velocity exceeded 5% of the peak velocity, and movement end as the first time point at which velocity fell to <5% of this same peak velocity (Berret and Jean, 2016). Reaction times (RTs) were calculated as the latency separating the auditory go cue and movement onset, and movement times (MTs) as the latency separating movement onset and movement end. Trials in which the cursor was located outside of the presented target at the time of movement end were considered as missed-target trials and were not included in the analysis (representing 2.35% trials). In the same vein, trials in which participants initiated their movement before the go cue occurred were removed from the analysis (representing 1.06% trials). Note that removing those trials did not affect the number of trials per condition included in the analysis because, as previously mentioned, any missed target or false start was automatically rerun during the experiment.
EEG
All EEG data were processed offline using custom MATLAB codes and functions from EEGLAB (Delorme and Makeig, 2004) and Fieldtrip (Oostenveld et al., 2011). First, a bandpass filter between 1 and 80 Hz was applied on raw EEG data, with a 59–61 Hz notch filter to attenuate electrical noise. The signal was rereferenced to the average scalp potential. The data were then segmented into epochs of 4.5 s duration locked around the occurrence of the auditory go cue (3 s before to 1.5 s after go cue). The period of interest corresponded to the 2 s delay separating stimuli onset (i.e., target and gauge appearance) and the go cue. Independent component analysis was applied to EEG data using the runica algorithm from the EEGLAB toolbox to remove artifactual EEG activity associated with eye and head movements and other sources of noise (Jung et al., 2000). A surface Laplacian transform was applied on the EEG data with artifactual components removed, using the erplab plugin from EEGLAB. The EEG signal was then downsampled to 125 Hz to reduce computation time for time–frequency decomposition. The latter was performed afterward, using Morlet wavelets (4–45 Hz with 1 Hz steps). The wavelet cycles were increased at each frequency in 0.1 steps (starting from 3–10.6 cycles) to ensure a balance between sufficient temporal resolution at lower frequencies and frequency resolution at higher frequencies. Finally, the data were normalized for each condition by measuring the absolute change from the average power during the 500 ms preceding the delay period (0.5–1 s of the total epoch). The amplitude of β-ERD was quantified as the absolute value of average beta power recorded during the delay period separating the stimulus onset and the auditory go cue.
Action cost modeling.
Action costs were computed from the sum of the estimated trajectory cost and the cost of time following the method of Berret and Jean (2016). In short, the trajectory cost was based on the distance to the target, the joint torque, and the hand jerk. It thus reflects accuracy, smoothness, and effort aspects of the reaching movement, and depends on task parameters (e.g., angle and amplitude of the presented target, anthropometry, starting position of the arm). In contrast, the cost of time rests on the quantification of the affine relationship between movement amplitude and duration that is characteristic of self-paced reaching movements and hence can be inferred from experimental data (Berret and Jean, 2016, details in their Methods section). Therefore, the model enables the computation of action cost as a function of movement duration. The “optimal” MT (i.e., the one associated with the lowest action cost) is supposed to predict the average MT in a context where participants perform self-paced movements, corresponding to their “preferred” MT. Here, because there was no self-paced reaching condition, the slope of this relationship was retrieved from the data in the study by Young et al. (2009), who used a similar reaching task with high temporal constraints. The intercept was adjusted to predict the average MT found in Med, separately for movements directed to Rt and Lt. In other words, the cost of time was set based on a movement duration–amplitude relationship that predicted MTs corresponding to the ones found in Med at the amplitude used in the present experimental task. Average MTs in Med were selected because analysis of participants' speed distributions in the task showed that average speeds that were the most often chosen (thereby the closest estimates of “preferred” speeds) were not significantly different from average speeds in Med, both for movements directed to Rt and Lt (see Results). Peak velocities associated with MTs toward each target were computed from the predicted optimal velocity profiles, which were bell shaped, similar to minimum jerk profiles (Flash and Hogan, 1985; Shadmehr et al., 2016). Action costs were therefore estimated both as a function of MTs and their associated peak velocities, and then normalized between 0 and 1 across velocity ranges centered on the minimal value of the cost functions (i.e., estimated preferred/optimal peak velocity), separately for movements directed to Lt and Rt. These velocity ranges were set to include all measured peak velocity values toward each target.
Experimental design and statistical analyses.
An intraparticipant design was used, so that all the factors included in the statistical analyses were within participant. The 2 × 3 repeated-measures ANOVAs were performed using Target (Rt, Lt) and Gauge (Low, Med, High) as factors on peak velocities, RTs, MTs, absolute error (i.e., average distance between movement endpoint and target center), SD of the absolute error, probability of reaching the speed criterion, as well as beta, mu, and gamma power and estimated action costs. Additional analyses with ANOVAs including Target, Gauge, and Block (1 and 2) as factors were conducted to assess whether the main results remained throughout blocks of trials. Action costs were estimated based on average peak velocities across participants and conditions (Gauge), separately for the two target positions (Target) that were used because a distinct model was fitted to each of them (see EEG subsection), considering that maximal and preferred speeds differed across targets (see Results). t Tests were used for post hoc analysis, with a Bonferroni correction applied to p-values for multiple comparisons. Effect sizes are reported as partial η2 (η2p) for ANOVAs and Cohen's d (d) for t tests. Cluster-based permutation tests were performed to identify electrodes associated with significant modulations of beta, mu, and gamma power across experimental conditions using functions from Fieldtrip (Oostenveld et al., 2011). Monte Carlo permutations (n = 1000) were used to determine p-values for each cluster. A cluster-level correction was set to control for multiple comparisons, using the sum of t-values. A cluster was defined as at least two neighboring electrodes (located <4 cm from each other) showing statistically significant t-values. General linear mixed models (GLMMs) were used to evaluate which of peak velocity or estimated action cost best explained the variance in beta power. Probability density functions of distributions of peak velocities were estimated using kernel distributions [ksdensity() command in MATLAB], separately for each target and participant. Kernel distributions are nonparametric representations of probability density distributions and are thus suited to estimate probability density distributions from multimodal distributions such as the ones that were expected from the experimental manipulation of peak velocities in the present task. Average estimated preferred peak velocities were computed as the mean of the peak velocities corresponding to the maximal probability density functions across participants, separately for each target.
All statistical tests were computed using Jamovi version 1.2.27 (https://www.jamovi.org), a software that implements R statistical language (a language and environment for statistical computing; https://www.cran.r-project.org/).
Results
Briefly, the experimental task consisted of presenting a Target along with a Gauge, indicating where to reach and at which speed. The visual stimuli appearance was followed by a delay period before the occurrence of an auditory go cue (Fig. 1A). Two different target positions (Target: Rt, Lt) and three different filling levels of the gauge (Gauge: Low, Med, High) were used across trials. Critically, each filling level of the gauge was associated with a different speed criterion based on peak velocity values. These speed criteria were set so that the speed required for the highest filling of the Gauge (High) was close to the maximal speed participants could reach for movements directed to each Target separately (Fig. 1B, summary of the experimental conditions and their associated speed criteria; for details, see Materials and Methods). This experimental design allowed to test three main hypotheses about the association between β-ERD and speed: if β-ERD is modulated as a function of absolute speed, then main effects of both Target and Gauge should be expected considering the distinct speeds reached across conditions (Fig. 1C, left). Alternatively, if β-ERD is modulated as a function of speed relative to its maximum, only a main effect of Gauge should be observed (Fig. 1C, middle). Finally, if β-ERD is modulated by action cost instead of speed, only a main effect of Gauge should be expected and β-ERD should be increased in both Low and High compared with Med given that increasing and decreasing speed represents an additional cost (Fig. 1C, right; for details, see Materials and Methods).
Methods. A, Schematic representation of a trial timeline. The content of each dark gray rectangle illustrates stimuli that were displayed on the screen in front of participants. The trial started with the appearance of a white fixation cross at the center of the screen and the starting base (light gray circle; bottom rectangle). Once participants had kept the cursor (white circle) inside of the starting base for 2 s, the target (blue circle) and the gauge appeared on the screen. Participants were asked to reach the target once they heard the go cue, which occurred 2 s after the appearance of the gauge and the target on the screen. Once the target was hit, it turned green. Written feedback was then given to participants about whether their movement reached the speed criterion. B, Summary of the speed criteria across conditions. The table indicates the intervals of peak velocities (PV) that participants were asked to reach according to the position of the presented target (columns) and the filling level of the gauge (rows). C, Working hypotheses of what patterns of β-ERD across conditions could be expected from modulations of movement speed. Conditions including movements directed to Rt are represented in red, and conditions including movements toward Lt are in blue.
Movement speed
The first part of the analysis consisted in verifying that movement speed was effectively modulated in the present task. Peak velocities were indeed strongly influenced both by Target (F(1,30) = 2264, p < 10−10, η2p = 0.99) and Gauge (F(2,60) = 843, p < 10−10, η2p = 0.97) with a significant interaction between the two (F(2,60) = 140, p < 10−10, η2p = 0.82). Post hoc analysis showed that peak velocities were significantly increased when comparing MedRt to LowRt (t(30) = 25.7, p < 10−10, d = 4.62) and HighRt to MedRt (t(30) = 18.0, p < 10−10, d = 3.23), as well as when comparing MedLt to LowLt (t(30) = 27.0, p < 10−10, d = 4.85) and HighLt to MedLt (t(30) = 17.8, p < 10−10, d = 3.20). The effect of Target on peak velocities was also strong, with significant increases found when comparing LowRt to LowLt (t(30) = 34.6, p < 10−10, d = 6.22), MedRt to MedLt (t(30) = 39.1, p < 10−10, d = 7.02), and HighRt to HighLt (t(30) = 51.2, p < 10−10, d = 9.20). The average peak velocities were as follows: LowRt, 71.0 ± 8.0 cm/s; MedRt, 97.0 ± 8.1 cm/s; HighRt, 124.4 ± 9.4 cm/s; LowLt, 24.0 ± 8.0 cm/s; MedLt, 42.4 ± 6.3 cm/s; and HighLt, 58.4 ± 6.2 cm/s (Fig. 2A,B).
Behavioral results. Red and blue lines/dots refer to Rt and Lt, respectively. A, Average normalized velocity profiles across conditions. Solid lines refer to High, large dotted lines refer to Med, and small dotted lines refer to Low conditions. B–D, Average peak velocities, MTs, and RTs across conditions. Error bars indicate 95% CIs around the mean. ***p < 0.001.
Separating data across blocks (two levels: Block 1 and Block 2) does not significantly change this result. Indeed, this additional analysis showed significant effects of Target (F(1,30) = 2264.4, p < 10−15, η2p = 0.99) and Gauge (F(1,30) = 842.9, p < 10−15, η2p = 0.97), but not of Block (F(1,30) = 0.0, p = 0.862, η2p = 0.00). Significant interactions were found between Target and Gauge (F(2,60) = 139.9, p < 10−15, η2p = 0.82) as well as Gauge and Block (F(2,60) = 7.5, p = 0.001, η2p = 0.20), but no interaction was found between Target and Block (F(1,30) = 0.2, p = 0.662, η2p = 0.01), or among Target, Gauge and Block (F(2,60) = 2.4, p = 0.100, η2p = 0.07). Post hoc analysis of the interaction between Gauge and Block revealed that peak velocity was slightly increased in High in Block 2 compared with Block 1 (t(30) = 3.2, p = 0.010, d = 0.57) by 1.89 ± 1.21 cm/s [mean ± 95% confidence interval (CI)]. No significant difference in peak velocity between Block 1 and Block 2 was found in Med (t(30) = 0.7, p = 1.00, d = 0.12) or in Low (t(30) = 2.2, p = 0.117, d = 0.39). Although participants appear to have increased their speed in High in Block 2 compared with Block 1, this effect appeared relatively modest considering the speed difference induced (<2 cm/s) compared with the speed difference between conditions (∼10 times greater; mean difference between Low and Med, 22.2 cm/s; mean difference between Med and High, 21.7 cm/s).
The probability of performing the movement within the speed criteria was strongly impacted by Target (F(1,30) = 68.9, p = 10−9, η2p = 0.70) and to a lesser extent by Gauge (F(2,60) = 4.9, p = 0.011, η2p = 0.14), and there was no significant interaction between the two (F(2,60) = 2.6, p = 0.085, η2p = 0.08). Post hoc analysis revealed that the probability of reaching the speed criterion was higher for movements directed to Lt than to Rt (t(30) = 8.3, p = 10−9, d = 1.49) and for movements performed in High rather than Low, though with a lower effect size (t(30) = 2.7, p = 0.030, d = 0.49). No significant difference in the probability of achieving the speed criteria was found between Low and Med (t(30) = 1.6, p = 0.369, d = 0.29), or between Med and High (t(30) = 1.8, p = 0.240, d = 0.33).
Participants were first asked to perform their movements at maximal speed to ensure that their average maximal speeds for movements directed to each target were close to the speed criteria used in High conditions (for details see, Materials and Methods). The analysis of these trials confirmed that maximal peak velocities were significantly greater for movements directed to Rt compared with movements directed to Lt (t(30) = 23.5, p < 10−10, d = 4.23). The average maximal peak velocity found for movements directed to Lt was not significantly different from the average peak velocity in HighLt (t(30) = 0.2, p = 1.0, d = 0.04; mean difference = 0.2 cm/s; BF10 = 0.20 ± 0.03, moderate evidence for H0). However, the average maximal peak velocity found for movements toward Rt were slightly but significantly lower than the average velocity in HighRt (t(30) = −3.0, p = 0.010; d = −0.54; mean difference = −8.8 cm/s; BF10 = 7.80 ± 1.42e-6, moderate evidence for H1). This suggests that the velocity criteria used in HighRt and HighLt were close to the maximal speed participants could reach for movements directed toward those targets but might have been more challenging for HighRt because its velocity criterion slightly exceeded the maximal speed expressed by participants.
As could be expected from these results, overall response time was significantly impacted by manipulations of peak velocities. Indeed, a significant influence of Target was found on MTs (F(1,30) = 123.8, p < 10−10, η2p = 0.80), as well as a significant influence of Gauge (F(2,60) = 164.2, p < 10−10, η2p = 0.85) and an interaction between the two (F(2,60) = 64.3, p < 10−10, η2p = 0.68). Post hoc analysis showed results similar to those for peak velocities with increased MTs in LowRt compared with MedRt (t(30) = 16.9, p < 10−10, d = 3.03) and in MedRt compared with HighRt (t(30) = 12.0, p < 10−10, d = 2.16), as well as in LowLt compared with MedLt (t(30) = 10.1, p = 10−10, d = 1.81) and in MedLt compared with HighLt (t(30) = 13.5, p < 10−10, d = 2.43). MTs were also significantly increased in LowLt compared with LowRt (t(30) = 9.4, p < 10−9, d = 1.69), in MedLt compared with MedRt (t(30) = 13.1, p < 10−10, d = 2.35), and in HighLt compared with HighRt (t(30) = 11.6, p < 10−10, d = 2.08; Fig. 2C).
In contrast, RTs were not significantly impacted by Target (F(1,30) = 0.1, p = 0.794, η2p = 0.00) but were impacted by Gauge (F(2,60) = 17.0, p = 10−6, η2p = 0.36) with a significant interaction between the two (F(2,60) = 6.4, p = 0.003, η2p = 0.18). Post hoc analysis showed that RTs were significantly increased in Low compared with High (t(30) = 4.4, p = 10−4, d = 0.79) and Med (t(30) = 3.1, p = 0.014, d = 0.55), and in Med compared with High (t(30) = 5.9, p = 10−5, d = 1.06). The interaction effect comes from the fact that the difference in RTs between movements directed to Rt and Lt tended to change with the filling of the gauge but remained nonsignificantly different across Gauge levels (LowRt vs LowLt: t(30) = −1.8, p = 0.258, d = −0.32; MedRt vs MedLt: t(30) = 1.2, p = 0.771, d = 0.21; HighRt vs HighLt: t(30) = 0.3, p = 1.0, d = 0.05; Fig. 2D).
Finally, the absolute error (i.e., the average distance between movement endpoint and target center) was significantly higher for movements directed to Rt compared with movements directed to Lt (main effect: F(1,30) = 33.4, p = 10−6, η2p = 0.53; post hoc: t(30) = 5.8, p = 10−6, d = 1.04) and was increased in High compared with both Med and Low (main effect: F(2,60) = 25.4, p = 10−8, η2p = 0.46; post hoc: High vs Low: t(30) = 5.7, p = 10−5, d = 1.03; High vs Med: t(30) = 6.0, p = 10−5, d = 1.07; Med vs Low: t(30) = 1.7, p = 0.318, d = 0.30) without significant interaction between Target and Gauge (F(2,60) = 1.5, p = 0.225, η2p = 0.05). The SD of the absolute error showed similar trends by monotonically increasing with speed (Target/main effect: F(1,30) = 40.9, p = 10−7, η2p = 0.58; Target/post hoc: Rt vs Lt: t(30) = 6.4, p = 10−7, d = 1.15; Gauge/main effect: F(2,60) = 28.9, p = 10−9, η2p = 0.49; Gauge/post hoc: High vs Low: t(30) = 8.2, p = 10−8, d = 1.47; High vs Med: t(30) = 3.4, p = 0.006, d = 0.61; Med vs Low: t(30) = 4.1, p = 0.001, d = 0.73; Target * Gauge: F(2,60) = 0.2, p = 0.853, η2p = 0.01). Critically, these differences in movement accuracy had little impact on task performance as the diameter of the target was set relatively large (3 cm), so that participants failed to end their movements inside of the target in only 2.35% of trials, which were removed from the analysis and rerun (for details, see Materials and Methods).
Beta power
Cluster-based permutation tests comparing the fastest (HighRt) to the slowest (LowLt) conditions revealed a significant negative cluster (tsum = −4478.5, p = 0.001) 1.4 to 0 s before the go cue. As can be seen in Figure 3A, the cluster appeared over the left frontocentral scalp sites, centered around electrodes C3, C1, FC3, and FC1. Given that motor β-ERD is commonly quantified around these electrodes (Fischer et al., 2018; Haddix et al., 2021; Chen and Kwak, 2022), as they overlay motor/premotor regions (Scrivener and Reader, 2022), β-ERD was computed as the mean signal from those four electrodes. The visual depiction of the time course of beta power indeed showed distinct modulations across conditions during the delay period preceding the go cue (Fig. 3B). Conducting similar cluster-based permutation tests on mu (8–12 Hz) and gamma (31–49 Hz) power revealed a significant negative cluster for mu power (tsum = −4478.5, p = 0.001) centered around electrodes similar to those for beta power, though larger in size (CPz, CP1, CP3, Cz, C1, C3, FCz, FC1, FC3), but no significant cluster was found for gamma power (tsum < 221.5, p > 0.084).
Modulations of beta power across conditions. A, Illustration of the results from cluster-based permutation tests. Each topographical plot represents the average difference in beta power between conditions requiring the slowest (LowLt) and the fastest (HighRt) movements in 500 ms windows, time locked to the occurrence of the go cue. Hot colors indicate an increase and cold colors a decrease in beta power. White dots indicate electrodes belonging to a significant cluster. B, Time course of average beta power change from baseline throughout a trial. C, Average β-ERD amplitude during the delay period (2 s preceding go cue). Red and blue lines/dots indicate results from movements directed to Rt and Lt, respectively. D, Similar representations to C, with beta power averaged in 500 ms windows encompassing the delay period. Error bars indicate 95% CIs around the mean. **p < 0.01, *p < 0.05. n.s. = not significant.
These modulations were first quantified by averaging β-ERD over the entire delay period (−2 to 0 s before go cue). The analysis revealed that the amplitude of β-ERD during the delay period was significantly influenced by Gauge (F(2,60) = 7.7, p = 0.001, η2p = 0.20) but not by Target (F(1,30) = 0.8, p = 0.368, η2p = 0.03), without any significant interaction between the two factors (F(2,60) = 1.4, p = 0.265, η2p = 0.04). Post hoc analysis revealed that the amplitude of β-ERD was significantly smaller for Med compared with both Low (t(30) = −3.1, p = 0.014, d = −0.55) and High (t(30) = −3.4, p = 0.006, d = −0.61), but was not significantly different between Low and High (t(30) = −1.0, p = 1.0, d = −0.17; Fig. 3C, left). Note that β-ERD was computed by simply subtracting the average beta power during a precue baseline period (for details, see Materials and Methods) to minimize the transformation of the EEG signal, but other baseline corrections, such as the percentage signal change as proposed by Pfurtscheller and Lopes da Silva (1999), led to similar results (main effect of Target: F(1,30) = 1.5, p = 0.225, η2p = 0.05; main effect of Gauge: F(2,60) = 18.6, p = 10−6, η2p = 0.38; interaction effect Target * Gauge: F(2,60) = 1.3, p = 0.276, η2p = 0.04).
Interestingly, this Gauge effect was specific to modulations of beta power as it was not found for mu power (Target: F(1,30) = 0.1, p = 0.718, η2p = 0.00; Gauge: F(2,60) = 2.7, p = 0.078, η2p = 0.08; Target * Gauge: F(2,60) = 0.5, p = 0.621, η2p = 0.02), or for gamma power (Target: F(1,30) = 0.9, p = 0.355, η2p = 0.03; Gauge: F(2,60) = 1.8, p = 0.181, η2p = 0.06; Target * Gauge: F(2,60) = 2.0, p = 0.141, η2p = 0.06).
As the modulations of beta power could have evolved differently across conditions throughout a trial, a second analysis was run on the amplitude of β-ERD averaged over 500 ms temporal windows, ranging from 2 to 0 s before go cue, therefore adding a Time factor to the analysis. Consistent with the first analysis, neither a significant effect of Target (F(1,30) = 0.8, p = 0.367, η2p = 0.03), nor interactions between Target and Gauge (F(2,60) = 1.3, p = 0.270, η2p = 0.04), Target and Time (F(3,90) = 1.0, p = 0.412, η2p = 0.03), and Target, Gauge and Time (F(6,180) = 1.6, p = 0.141, η2p = 0.05) were detected. However, consistent with the first analysis, significant effects of Gauge (F(2,60) = 7.6, p = 0.001, η2p = 0.20), Time (F(3,90) = 25.6, p < 10−10, η2p = 0.46), and an interaction between Gauge and Time ((F(6,180) = 5.9, p = 10−5, η2p = 0.16) were observed. Bonferroni-corrected t tests conducted across Gauge and Time factors (12 comparisons) revealed the same pattern as in the first analysis, with significantly lower β-ERD in Med compared with Low and High, as early as 1.5 s before the go cue (Fig. 3C, right, Table 1).
Results from post hoc analysis on beta power across speed conditions and time bins
Finally, β-ERD could also have differently evolved throughout blocks. Additional analysis including a block factor showed a significant effect of Speed on β-ERD (F(2,60) = 7.7, p = 0.001; η2p = 0.20), but neither a significant effect of Target (F(1,30) = 0.8, p = 0.367, η2p = 0.03) nor Block (F(1,30) = 0.2, p = 0.648, η2p = 0.01). The analysis showed no significant interaction with any of these factors (F < 1.5, p > 0.234, η2p <0.05). Therefore, β-ERD does not appear to have been differentially modulated across blocks.
Action cost model
Considering the pattern of β-ERD found, we hypothesized that premovement modulations of beta power might be best explained by changes in expected overall action cost, including both trajectory and temporal costs (Fig. 1C, right; for details, see Materials and Methods). This hypothesis assumed that action cost was lower in Med than in High and Low conditions. Although at first glance the speed instructions of the present paradigm prevented participants from moving at the speed they preferred (i.e., that associated with the lowest cost), peak velocity distributions still revealed biases in participants' chosen speeds. Indeed, despite the very different average speeds reached across conditions (see behavioral results), most participants did not show trimodal distributions of peak velocities as would have been expected from the three nonoverlapping peak velocity criteria used for each target. Instead, they oftentimes presented near-normal distributions, suggesting that their movement speeds were biased toward certain values. Indeed, although speed instructions led to significantly different average speeds across conditions (Fig. 2B), participants failed to perform their movements in the required criteria in a large proportion of trials (mean ± SD = 66.5 ± 8.2%). Speed criteria were voluntarily strict enough to encourage participants to keep their speeds close to the speed criteria and therefore maximize speed differences across conditions. Still, we reasoned that intertrial variability in movement speed could be exploited to estimate their speed preferences, especially considering that speed distributions appeared biased toward certain values for most participants. Hence, the peak velocity corresponding to the maximal value of probability density functions estimated from these distributions (based on kernel smoothing function for nonparametric distributions; for details, see Materials and Methods) was used to estimate participants' preferred speed. The average estimated preferred peak velocity of movements toward Rt was 94.8 ± 13.7 cm/s. This value was significantly lower than peak velocities found at HighRt (t(30) = −11.0, p < 10−10, d = −1.97) and higher than peak velocities found at LowRt (t(30) = 11.9, p < 10−10, d = 2.15), but was not, interestingly, significantly different from peak velocities at MedRt (t(30) = −1.4, p = 0.178, d = −0.25; Fig. 4B, top). Likewise, estimated preferred peak velocities toward Lt were significantly lower than peak velocities found at HighLt (t(30) = −8.0, p = 10−8, d = −1.44) and higher than peak velocities found at LowLt (t(30) = 11.2, p < 10−10, d = 2.01), but not significantly different from peak velocities at MedLt (t(30) = 0.4, p = 0.688, d = 0.07; Fig. 4B, bottom). The average estimated preferred peak velocity of movements toward Lt was 43.0 ± 10.0 cm/s. Together, these data indirectly confirm that although participants' preferred speed was not formally measured, it would have been close to the medium speed used here.
Peak velocity distributions and probability density functions across participants. A, Peak velocity distributions. Red histograms represent peak velocities of movements toward Rt, and blue histograms represent peak velocities of movements toward Lt. Each histogram represents data from one participant. The y-axis indicates the normalized proportion of trials (from 0 to 1), and the x-axis indicates the peak velocities. The solid black curve represents an estimate of the probability density function of each distribution. B, Comparison of the average estimated preferred peak velocity (PrefRt and PrefLt; determined using the maximum of probability density functions illustrated in A) to the average peak velocities of the different experimental conditions. Red and blue dots refer to Rt and Lt, respectively. Error bars indicate 95% confidence intervals around the mean. ***p < 0.001. n.s. = not significant.
The cost functions of movements directed toward Rt and Lt were estimated based on a model of action cost developed and applied to experimental data including reaching movements in previous work (Berret and Jean, 2016). This action cost model uses the combination of a trajectory cost, which increases with movement speed and can be estimated based on task biomechanical constraints (e.g., angle and amplitude of the presented target, anthropometry, starting position of the arm), and a cost of time, which decreases with movement speed and is estimated based on participants' preferred movement duration for a given amplitude. Because previous analysis of speed distributions showed that preferred speed estimates were not significantly different from the average speeds found in Med, average MTs in MedRt and MedLt were set as preferred movement durations in action cost models of movements directed to Rt and Lt, respectively (Fig. 5A, illustration; for details, see Materials and Methods). Estimation of peak velocity from the models appeared to fit the present data as the cost function of movements directed to Rt predicted optimal peak velocities (i.e., peak velocities corresponding to the minimum of the cost function; PrefRt) that were not significantly different from the average peak velocities found in MedRt (t(30) = −1.1, p = 0.269, d = −0.20, mean difference = −1.6 cm/s). Likewise, the cost function of movements directed to Lt predicted optimal peak velocities (PrefLt) that were not significantly different from average peak velocities found in MedLt (t(30) = −0.3, p = 0.737, d = −0.06, mean difference = −0.4 cm/s).
Results from the modeling of action cost. A, Representation of the estimated cost computed by the model as a function of peak velocity. The left panel (red curve) and the right panel (blue curve) illustrate the cost of movements directed to Rt and Lt respectively. B, Estimated costs of movements directed to Rt (red) and Lt (blue) across speed conditions. C, Representation of the correlation between β-ERD amplitude and normalized estimated cost (left) and peak velocity (right) based on the estimated marginal means computed by the GLMM. Error bars (B) or shaded areas (C) indicate 95% confidence intervals. **p < 0.01, ***p < 0.001.
Critically, action cost predicted by the model followed a pattern close to the one found for β-ERD across conditions (Fig. 5B). Once applied to the individual average peak velocity values found across conditions, estimated action cost from the model appeared significantly modulated by Target (F(1,30) = 8.2, p = 0.008, η2p = 0.21) to a smaller extent than by Gauge (F(2,60) = 38.6, p < 10−10, η2p = 0.56), with a significant interaction between the two factors (F(2,60) = 15.9, p = 10−6, η2p = 0.35). Post hoc analysis revealed a significantly lower estimated action cost in MedRt compared with LowRt (t(30) = −10.2, p = 10−10, d = −1.83) and to HighRt (t(30) = −7.2, p = 10−7, d = −1.30), as well as in HighRt compared with LowRt (t(30) = −4.3, p = 0.001, d = 0.78). Likewise, the estimated action cost was significantly lower in MedLt compared with LowLt (t(30) = −9.4, p = 10−9, d = −1.69) and HighLt (t(30) = −7.0, p = 10−6, d = −1.26), but not significantly different between HighLt and LowLt (t(30) = 2.3, p = 0.268, d = 0.41). Additionally, estimated action cost was significantly lower in HighLt compared with HighRt (t(30) = 3.7, p = 0.007, d = 0.67), but no significant difference was found when comparing MedLt to MedRt (t(30) = 0.5, p = 1.0, d = 0.09) and LowLt to LowRt (t(30) = 0.3, p = 1.0, d = 0.06).
Finally, a GLMM was performed to test whether peak velocity and estimated action cost explained a significant proportion of the variance in β-ERD. The model showed a significant influence of action cost (F(1,154) = 8.5, p = 0.004) but not of peak velocity (F(1,153) = 0.1, p = 0.823) on β-ERD (Fig. 5C). The results were similar when including RTs in the model, with a significant influence of action cost on β-ERD (F(1,153) = 8.3, p = 0.004), but not of peak velocity (F(1,154) = 0.2, p = 0.659) or RTs (F(1,179) = 1.5, p = 0.223). Therefore, modulations of premovement β-ERD across conditions appeared overall to be better explained by changes in action cost rather than by the speed of movement initiation and execution.
Discussion
Using a speed-controlled reaching paradigm, the present study aimed to dissociate movement speed and action cost to determine which of these variables best explains changes in premovement β-ERD. Results showed that β-ERD was nonmonotonically modulated by movement speed as its amplitude was greater both for slow and fast movements compared with movements performed at medium speed, following a u-shaped pattern. This pattern was observed for both targets despite very different ranges of speeds (∼50–60 cm/s difference) and appeared specific to beta power as it was not found when averaging activity in the mu and gamma bands. Additionally, these modulations of β-ERD are unlikely to be explained by changes in movement accuracy or success in achieving the speed criteria considering that the two monotonically decreased with movement speed. Interestingly, GLMMs showed that β-ERD amplitude was better predicted by estimated action cost than by movement peak velocity or RT. As predicted by the model, the further the instructed speed from the optimal/preferred speed (i.e., speed associated with the lowest action cost), the greater the β-ERD. These results demonstrate that β-ERD constitutes a potential noninvasive marker of estimated action cost during motor planning.
To the best of our knowledge, this is the first report of a u-shaped association between β-ERD and movement speed. Indeed, β-ERD was attenuated at medium speeds but was comparatively larger both for slow and fast movements. While this observation appears somewhat incongruous with the association between beta power and movement speed found in healthy individuals (Pogosyan et al., 2009) and in those with PD (Jenkinson and Brown, 2011), it is still consistent with some previous work that has reported no significant difference in β-ERD between slow and fast movements (Stancák and Pfurtscheller, 1995; Zhang et al., 2020; for review, see Kilavik et al., 2013). The notion that beta reflects costs may offer an alternative view reconciling the two. Namely, the amplitude of β-ERD might be modulated as a function of action cost, therefore increasing both with movement time and effort considering that the two are responsible for the devaluation of action (Berret and Jean, 2016; Shadmehr et al., 2016). Consequently, greater β-ERD may facilitate the preparation of both slow and fast movements, improving overall motor flexibility. Evidence for decreased speed when increasing beta power (Pogosyan et al., 2009) and increased speed when decreasing beta power (Jenkinson and Brown, 2011) in the context of movements performed at maximal speed supports this hypothesis, but facilitation of slow (i.e., slower than self-paced) movements does not appear to have been tested yet. Furthermore, this assumption is consistent with the influential hypothesis that beta power favors the maintenance of the pre-existing neural state (Engel and Fries, 2010) as well as with force production tasks, which typically reveal nonlinear modulations of beta power as a function of exerted force (Tan et al., 2015; Fischer et al., 2019; Haddix et al., 2021). It also links the attenuated β-ERD (Heinrichs-Graham et al., 2014) to the restricted motor repertoire observed in PD (Baraduc et al., 2013; Sorrentino et al., 2021). From a neural perspective, this hypothesis is supported by the known influence of beta power on the flexibility of neuronal activity, beta power being considered as a marker of the excitation/inhibition balance in the primary motor cortex (M1; McAllister et al., 2013; Rossiter et al., 2014). Furthermore, the motor symptoms observed in PD have been related to reduced plasticity in M1 (Bologna et al., 2018). This alteration of motor flexibility and its associated beta power increase might be linked to dopamine depletion (Jenkinson and Brown, 2011), the action of dopamine being considered central in ensuring behavioral flexibility (Jahanshahi et al., 2015; Cools, 2019).
The phasic dopaminergic activation preceding movement is modulated according to expected action value to assess how much neural resources are worth allocating for an upcoming movement (Hamid et al., 2016; Berke, 2018). Dopamine is thought to attenuate signal-dependent noise, thereby allowing the formation of a more precise motor representation (Manohar et al., 2015). This noise reduction process arguably requires additional neural computational power, which could be achieved through neuronal desynchronization. Indeed, β-ERD has been proposed as a mechanism allowing an increase in entropy of neuronal firing rates, resulting in an increase in their information coding capacity (Hanslmayr et al., 2012; Brittain and Brown, 2014). Beyond explaining the present results, the proposition of β-ERD as a marker of the allocation of neural resources unifies several lines of evidence. First, reward expectation is accompanied by an increase in β-ERD (Meyniel and Pessiglione, 2014; Savoie et al., 2019; Chen and Kwak, 2022). Given that reward is known to shift the speed–accuracy trade-off of movements by increasing speed without penalizing accuracy (Manohar et al., 2015; Summerside et al., 2018), the greater β-ERD might reflect the allocation of additional neural resources to support the increase in speed. In this framework, the attenuation of β-ERD observed in PD might be linked to a deficit in action valuation. This is supported by evidence of an alteration of effort-based decision-making and apathy in PD (Le Bouc et al., 2016). Second, motor learning has been associated with reduced sensorimotor activation over the course of practice, interpreted as a decrease in the mobilization of neural resources because of increased neural efficiency in the network (Karni et al., 1995; Kelly and Garavan, 2005). The amplitude of β-ERD has been shown to decrease with practice accordingly (Pollok et al., 2014; Gehringer et al., 2018). Third, this hypothesis also fits with the mounting evidence of beta activity being modulated as a function of existing priors about stimuli and actions (Betti et al., 2021) because it may reflect the endogenous reactivation of these priors (Spitzer and Haegens, 2017). β-ERD might be attenuated when preparing movements at habitual speeds because of a stronger prior, which echoes the decrease in the amplitude of β-ERD found with learning.
The present results also offer a potential explanation for the cost of time implemented in models of action cost. Indeed, while the cost associated with fast movements can easily be justified by an increase of the net metabolic rate of movements with speed (Shadmehr et al., 2016), what makes slow movements effortful is less clear (Berret and Jean, 2016). Nonetheless, action selection can hardly be predicted from an energy minimization principle alone: behavioral work has shown that movement duration impacts action choices independently from changes in energy expenditure (Morel et al., 2017; Berret and Baud-Bovy, 2022). This influence of movement duration on action selection has mostly been interpreted as the temporal discounting of the rewarding value associated with the motor goal (Shadmehr et al., 2010; Choi et al., 2014). Still, a temporal discounting of reward appears unlikely in the present task, given that the reward consisted in reaching the speed criterion and was therefore intrinsically associated with the slowing of movements. Furthermore, the positive correlation often reported between the amplitude of β-ERD and expected reward (Meyniel and Pessiglione, 2014; Savoie et al., 2019; Chen and Kwak, 2022) is inconsistent with a reduction of expected reward with movement slowing in the present results. β-ERD amplitude at low speed was indeed significantly greater than for medium speed, but not significantly different than for high speed. Alternatively, in relation to the previous paragraph, this cost of time could be because of increased neurocomputational demands or “neural effort” to perform slow movements. Indeed, slowing down movements has been associated with an accumulation of constant noise (van Beers, 2008). Conversely, slow movements could be more costly simply because they are performed less often. Movements at preferred speeds could be seen as a habitual form of control, which is associated with lower computational cost because of an increased contribution of lower-order brain regions (Schneider and Chein, 2003; Jahanshahi et al., 2015). In support, the motor cortex has been shown to be less involved in habitual actions because of a preponderant role of the basal ganglia (Kawai et al., 2015; Dhawale et al., 2021). Therefore, the magnitude of β-ERD could be attenuated when preparing movements at preferred speeds because they require less neocortical resources to be produced. This is consistent with evidence of spontaneous choices of muscle coordination patterns favoring habits or less information encoding at the expense of muscular effort or movement accuracy (de Rugy et al., 2012; Dounskaia and Shimansky, 2016). However, preferred speeds were only approximated from distributions of speed values in the present experiment because specific speed instructions were used to dissociate movement speed from action cost. Additional studies measuring individualized preferred speeds in a context of self-paced movements will be needed to confirm the existence of specific modulation of β-ERD as a function of action cost.
In summary, the present results reconcile discrepancies concerning the relationship between β-ERD and movement speed, and suggest that reducing beta power facilitates the preparation and execution of both fast and slow movements, by enhancing motor flexibility through the allocation of additional neural resources. This encourages exploration of the impact of beta power reduction in PD not only on movement speed, but also on action selection.
Footnotes
This work was supported by the Natural Sciences and Engineering Research Council of Canada Grant 418589. We thank François Thénault for his help in developing the scripts used for the experiment, and Dominique Delisle-Godin for her help in collecting data.
The authors declare no competing financial interests.
- Correspondence should be addressed to Emeline Pierrieau at emeline.pierrieau{at}u-bordeaux.fr
