Temporal cascade of frontal, motor and muscle processes underlying human action-stopping

1The ability to control one’s actions and thoughts is important for our daily lives; for example: changing gait when there is an obstacle in the path, resisting the temptation to eat when on a diet, and overcoming the tendency to say something hurtful. While many processes contribute to such forms of control, one important process is response inhibition – the prefrontal (top-down) stopping of initiated response tendencies. In the laboratory, response inhibition is often studied with the stop-signal task. On each trial, the participant initiates a motor response, and then, when a subsequent Stop signal occurs, tries to stop. From the behavioral data one can estimate a latent variable; the latency of stopping known as Stop Signal Reaction Time (SSRT), which is typically 200–250 ms in healthy adults. SSRT has been useful in neuropsychiatry where it is often longer for patients vs. controls. The task has also provided a rich test-bed, across species, for mapping out a putative neural architecture of prefrontal-basal-ganglia-regions for rapidly suppressing motor output areas. Given this rich literature, this task is one of the few paradigms included in the longitudinal Adolescent Brain Cognitive Development study of 10,000 adolescents over 10 years.

2Against this background, a puzzle is that the relation between SSRT and ‘real-world’ self-reported impulsivity is often weak. One explanation is that SSRT may not accurately index the brain’s true stopping latency. Indeed, recent mathematical modelling of behavior during the stop-signal task suggests that standard calculations of SSRT may overestimate the brain’s stopping latency by ~100 ms (; also see ). Further, in a recent study, electromyographic (EMG) recordings revealed an initial increase in EMG activity in response to the Go cue, followed by a sudden decline at ~150 ms after the Stop signal. This decline in EMG could be because of the Stop process ‘kicking in’ to cancel motor output – but the striking thing is that this was 50 ms before the SSRT of 200 ms. This timing is also consistent with experiments using transcranial magnetic stimulation (TMS) to measure the motor evoked potential (MEP) during the stop-signal task (the MEP indexes the excitability of the pathways from motor cortex to muscle). The MEP in the muscle that was-to-be-stopped reduced at ~150 ms. Further, other studies that measured the MEP from muscles that were not needed for the task, show there is ‘global suppression’ also at ~150 ms (i.e. corticospinal activity was suppressed for the broader skeletomotor system). This ‘global MEP suppression’ has been linked to activation of the subthalamic nucleus of the basal-ganglia, which is thought to be critical for stopping, and might broadly inhibit thalamocortical drive.

3The potential overestimation of the brain’s true stopping latency by SSRT could arise for several reasons. First, the race model assumes that the Stop process is ‘triggered’ on every trial. But recent research shows that this is not the case, and that failing to account for ‘trigger failures’ inflates SSRT. Second, while the standard ‘race model’ assumes that the Go and Stop processes are independent, recent research show that violations of this independence underestimates SSRT. Finally, the standard ways of computing SSRT likely do not account for electromechanical delays between muscle activity and the response. In any event, overestimating the brain’s stopping latency would add variance to SSRT which could potentially weaken the above-mentioned across-participant associations between stopping latency and self-report scores. Furthermore, if the true stopping latency is ~150 ms, the timing of activation of nodes in the putative response inhibition network should precede this time-point for those nodes to play a causal role in action stopping – and this is important for the interpretation of neuroscience studies. For instance, in electrocorticography, electroencephalography (EEG), and magnetoencephalography (MEG) studies, successful stopping elicits increased beta band power over right frontal cortex in the time period between the Stop signal and SSRT. Whether this, and other, neurophysiological markers of the Stop process occur sufficiently early to directly contribute to action-stopping (if SSRT is overestimated) is unknown; yet this is fundamental to our understanding of brain networks underlying response inhibition.

4Here we leveraged the insight from the above-mentioned study which used EMG of the task relevant muscles. We now tested whether we could derive a single trial estimate of stopping latency from EMG (referred to as CancelTime). More specifically, we hypothesized that ‘partial’ EMG bursts on the Successful Stop trials (i.e. small EMG responses that begin but do not reach a sufficient amplitude to lead to an overt response) would carry information about the latency of stopping. We tested this in two studies. In a third study we tested if CancelTime would correspond with the measure of putative basal ganglia-mediated global motor suppression, measured with single-pulse TMS. In studies four and five we turned to the cortical process thought to initiate action–stopping, using the above-mentioned proxy of right frontal beta. We measured scalp EEG, derived a right frontal spatial filter in each participant, and then extracted beta bursts in the time period between the Stop signal and SSRT. We tested how the timing of these beta bursts related to CancelTime.

510 participants performed the stop-signal task (Figure 1a). On each trial they initiated a manual response when a Go cue occurred, and then had to try to stop when a Stop signal suddenly appeared on a minority of trials. Depending on the stop signal delay, SSD, participants succeeded or failed to stop, each ~50% of the time). We measured EMG from the responding right index and little fingers (Figure 1b inset). Behavioral performance was typical, with SSRT (referred to as SSRTBeh) of 216 ± 8 ms, and action-stopping on 51 ± 1% of Stop trials (Table 1). EMG analysis was performed on the trial-by-trial root-mean-squared EMG (EMGRMS; Figure 1b). On 53 ± 6% of Successful Stop trials (i.e. where no keypress was made) there was a small but detectible EMG response (Partial EMG trials; see Figure 1—figure supplement 1 for RTEMG-RTBeh correlation), while on the remainder of Successful Stop trials there was no detectible EMG response (No EMG trials). The amplitude of EMG responses (mean peak EMG voltage) in the Partial EMG trials was 48 ± 3% smaller than in trials with a keypress (Figure 2a).

6We hypothesized that the time when the Partial EMG response starts declining after the Stop signal is a readout of the time when the Stop process is implemented in the muscle (hereafter ‘CancelTime’). We observed that, first, CancelTime is much earlier than SSRTBeh (see Figure 2c (left) for all CancelTimes in an exemplar participant; mean CancelTime = 146 ± 3 ms, SSRTBeh = 203 ms); and second, across participants, CancelTime was positively correlated with SSRTBeh (Figure 2d; study 1: mean CancelTime = 152 ± 11 ms, mean SSRTBeh = 216 ± 8 ms; r = 0.71, p=0.020, BF10 = 3.6). This suggests that CancelTime might index the time when stopping is implemented at the muscle.

7We then ran a new sample (n = 32; see Table 1 for behavioral results). Again, we observed partial EMG responses on 49 ± 2% of Successful Stop trials; where the EMG amplitude was 54 ± 1% smaller than the amplitude in trials with a keypress (Figure 2b). Figure 2c (right) shows the distribution of CancelTimes in an exemplar participant (mean CancelTime = 156 ± 4 ms, SSRTBeh = 218 ms). Again, across participants, mean CancelTime was positively correlated with SSRTBeh (Figure 2d; mean CancelTime = 146 ± 4 ms, mean SSRTBeh = 204 ± 4 ms; r = 0.59, p<0.001, BF10 = 71.7). Intriguingly, in each study, CancelTime was ~ 60 ms less than SSRTBeh. To further explore this, we pooled the data across the two studies.

8Mean CancelTime (147±5 ms) was 60±3 ms shorter than SSRTBeh (t(41) = 18.4, p < 0.001, d = 2.5, BF10 > 100; r = 0.62, p < 0.001, BF10 > 100). However, one must note that the criterion for estimating the stopping latency is different for the two measures, CancelTime uses EMG responses, while SSRTBeh uses the keypress responses. Hence, inherent differences in latencies between the two responses might lead to these incompatible measures of stopping latency. We hypothesized that the difference between SSRTBeh and the time of EMG cancellation (CancelTime) is due to an inherent “ballistic stage” in movements and once the muscle activity crosses the point-of-no-return they can no longer be stopped and a movement is inevitable. [The duration of such ballistic stages has been estimated to be ~15 ms in saccades in non-human primates and ~50 ms for reaching movements in humans]. In other words, the time of EMG cancellation on partial trials reflects a time just before the point-of-no-return, whereby if EMG activity is allowed to continue develop beyond this point it will exceed a critical threshold such that a button press necessarily ensues (we presume this threshold reflects the point at which the inertia of the finger is overcome). In this respect, what is being tracked by the SSD staircasing procedure is the probability of crossing that EMG threshold, but since SSRT is calculated based on button press response times, it inevitably incorporates the ballistic stage that follows the crossing of this threshold. Hence, although our study was not designed to track the SSD staircase based on EMG, we calculated SSRT using the presence of EMG responses (SSRTEMG) instead of the keypress responses (SSRTBeh). The purpose of the SSRTEMG estimation was to test the idea of a ballistic phase by removing the influence of electromechanical delays and inertia in the neuromuscular system and response device, which likely make-up the ballistic stage, on the estimated stopping latency. We thus considered Partial EMG trials as Failed Stop trials and used EMG onset time (RTEMG) on Correct Go trials to recalculate SSRT (i.e. instead of using P(Respond|Stop) from behavior and Go RTBeh as is typical for SSRTBeh calculations; see Materials and methods; see Figure 3a for an exemplar participant). We then performed 1-way repeated measures ANOVA with 'Stop Time' as the dependent measure and the method of estimation as a factor (SSRTEMG, SSRTBeh, and CancelTime). There was a significant main effect of the estimation method on 'Stop Time' (FGG(1.4, 56.1) = 66.3, p < 0.001, = 0.6). Pairwise comparisons showed that SSRTEMG (157±7 ms) was significantly faster than SSRTBeh (207±3 ms) (Figure 3b; t(41) = 8.2, pBon < 0.001, d = 1.3, BF10 > 100), but importantly, not significantly different from mean CancelTime (t(41) = 1.5, pBon = 0.270, d = 0.2, BF10 = 0.5). This suggests that SSRTBeh might be protracted by a peripheral delay and that CancelTime might be a better metric of the time of implementation of the Stop process. [Our simulations using a previously described modelling framework also lead credence to this idea, demonstrating that the duration of the ballistic stage might be ~35 ms or longer (see Figure 3—figure supplement 1 and Appendix 1)].

9Next, we examined in more detail the EMG profile on Partial EMG trials. Across all participants, the EMG response in the Partial EMG trials (when aligned to the EMG onset) had a profile similar to the EMG response in the Correct Go and Failed Stop trials, but diverged ~55 ms after EMG onset (55 ms compared to Correct Go, and 56 ms compared to Failed Stop trials, Figure 3c). We surmised that if the Partial EMG trials reflect responses that have been actively cancelled at the muscle-level, then the amplitude of these responses should increase with SSD. The rationale was that, at shorter SSDs, the Go process will have been active for a shorter duration, meaning EMG activity will not have increased much before being inhibited, while at longer SSD, the Go process will have been active for a longer duration, meaning EMG activity will have increased much more before being inhibited. Indeed, the amplitude of the Partial EMG responses increased with SSD (Figure 3—figure supplement 2). A 1-way repeated measures ANOVA with amplitude as the dependent variable and the SSD as the independent variable showed significant effect of SSD on amplitude (F(4,24) = 3.7, p = 0.018, = 0.4) (also see ). This suggests that the Partial EMG trials represent inhibited Go responses and not merely a weak Go process (which would presumably not increase across SSDs). In other words, the partial EMG response does not simply reflect a weak Go response, where the individual intended to execute a response but failed to produce sufficient muscle activity to fully depress the button, since the amplitude of such responses would presumably not vary as a function of SSD.

10To further validate CancelTime, we modelled the behavior using BEESTS (Bayesian Estimation of Ex-gaussian STop-Signal reaction time distributions; see Table 2 for model estimates). While SSRTBeh produces a single estimate per person, BEESTS uses a Bayesian parametric approach to estimate the distribution of SSRTs. Also, for each participant, it provides an estimate of the probability of trigger failures (i.e. stop trials where the stopping process was not initiated ). Across participants, mean CancelTime was positively correlated with the mean SSRTBEESTS (205 ± 3 ms; r = 0.54, p<0.001, BF10 > 100; Figure 3d). More interestingly, the SD of CancelTime (33 ± 2 ms) was positively correlated with the SD of SSRTBEESTS (48 ± 5 ms; r = 0.42, p=0.005, BF10 = 6.9; Figure 3e). Further, the percentage of trigger failures (4 ± 1%) was positive correlated with mean CancelTime (ρ = 0.57, p<0.001, BF10 > 100) suggesting that participants who fail to ‘trigger’ the Stop process more often, are also likely to have longer stopping latency, indicating that there might exist a dependency between the triggering and the implementation of the Stop process (Figure 3f). These relationships between CancelTime and model estimates give further credence to our interpretation that CancelTime on Partial EMG trials reflects a single-trial measure of the time of implementation of the Stop process.

11To further validate CancelTime and relate it to brain processes we turned to a different method – single-pulse TMS over a task-irrelevant muscle representation in the brain. As mentioned above, the reduction of MEPs from task-irrelevant muscles on Successful Stop trials, is thought to reflect a basal ganglia-mediated global suppression. Seventeen new participants (see Table 1 for behavioral results) now performed the task with their left hand, while TMS was delivered over the left motor cortex and MEPs were recorded from a task-irrelevant, right forearm muscle. MEPs were recorded at different times after the Stop signal on different trials: 100–180 ms in 20 ms intervals, as well as during the inter-trial interval which served as a baseline. Concurrently, we recorded EMG from the task-relevant left-hand muscles as in studies 1 and 2 above (Figure 4a).

12The key TMS finding, in keeping with earlier studies, was of suppression of MEPs in the task-irrelevant forearm, indicating global motor system suppression, beginning ~ 140 ms following the Stop signal in Successful Stop trials (Figure 4b; see Figure 4—figure supplement 1 for MEP amplitudes for Partial EMG and No EMG trials separately). A 2-way repeated measures ANOVA with MEP amplitude as the dependent measure and the factors of trial-type (Correct Go, Successful Stop, Failed Stop) and time (100, 120, 140, 160, 180 ms after the Stop signal) showed main effects of both trial-type (F(2,32) = 7.2, p=0.003, ηp2 = 0.3) and time (FGG(2.5, 40.7)=4.8, p=0.008, ηp2 = 0.2), as well as an interaction of trial-type by time (F(8, 128)=3.4, p=0.002, ηp2 = 0.2). Post hoc t-tests across Successful Stop and Correct Go trials showed no difference at 100 ms (t(16) = 0.7, pBon = 1.0, BF10 = 0.3), 120 ms (t(16) = 2.5, pBon = 0.066, BF10 = 2.8), and 160 ms (t(16) = 2.1, pBon = 0.159, BF10 = 1.4). However, MEP amplitudes were significantly suppressed on Successful Stop trials at 140 ms (t(16) = 4.1, pBon = 0.003, BF10 = 39.8) and 180 ms (t(16) = 4.4, pBon < 0.001, BF10 = 65.2) after the Stop signal. Therefore, we estimate the onset of the global motor suppression to be ~ 140 ms after the Stop signal, which places it ~ 20 ms prior to the mean CancelTime (160 ± 9 ms). There were no significant differences in MEP amplitudes between Failed Stop and Correct Go trials at any time point, though MEP amplitudes on Successful Stop trials were also suppressed compared to Failed Stop trials at 160 ms (t(16) = 2.9, pBon = 0.033, BF10 = 4.9).

13It makes sense that global motor suppression occurs before CancelTime as motor cortical output takes time to be transmitted along the corticospinal pathway to the muscles. To verify whether the ~20 ms discrepancy in timings could be accounted for by corticospinal conduction delays, we estimated this corticospinal conduction time in a separate phase of the current study by delivering TMS over the hand representation to evoke MEPs in the left, task-relevant, FDI muscle (Figure 4c). This was 23 ± 0.3 ms. Thus, a decline in muscle activity would be expected to be preceded by a reduction in motor cortical output by ~23 ms, which is very similar to the ~20 ms difference between global motor suppression and CancelTime. Note, however, that the onset latency of the TMS-evoked MEP is likely an under-estimate of the mean conduction time of all pathways involved in voluntary movement, because TMS is biased towards recruiting fast conducting corticospinal neurons with mono-synaptic connections to the spinal motorneurons. Therefore, the mean latency at which changes in motor cortical output are observable as changes in EMG activity is probably longer than 23 ms by several milliseconds.

14To further elaborate the temporal relationship between global motor suppression and CancelTime, we performed a trial-by-trial analysis whereby MEP amplitudes were sorted according to the time at which TMS was delivered, relative to the time at which EMG decreased on Successful Stop, Failed Stop and Correct Go trials (Figure 4d). The suppression of MEPs in Successful Stop trials compared to Correct Go trials began in the 30 ms prior to the EMG decline (−30 to 0 ms: Z = 3.12, pBon = 0.005; 0 to 30 ms: Z = 4.48, pBon <0.001; 30 to 60 ms: Z = 2.45, pBon = 0.045). This lag in the time of EMG decrease relative to the time of the MEP suppression on Successful Stop trials can again be accounted for by the corticospinal conduction time. Thus, these results imply that the brain output to task-relevant muscles declines at approximately the same time as the global motor suppression begins. We note too, that MEPs were also suppressed in Failed Stop versus Correct Go trials, but at some delay relative to Successful Stops and the time of EMG cancellation (Figure 4d). This is consistent with the idea that the Stop process is initiated even in Failed Stop trials, and that part of the reason for the failure to stop is that the Stop process is initiated/implemented later in these trials (the other reason being that the Go process might have been completed particularly quickly).

15Having established that CancelTime reflects the time of an active stopping process at the muscle (studies 1 and 2, EMG/behavior), which also related tightly with the timing of global motor suppression (study 3, TMS), we then tested whether this EMG measure was also related to the timing of a prefrontal correlate of action-stopping, specifically the increase of beta power (13–30 Hz) before SSRTBeh at right frontal electrode sites. We now measured scalp EEG as well as EMG from the hand, in 11 participants (see Table 1 for behavioral results). We derived beta bursts rather than beta power per se, as bursts have richer features also see;, such as burst timing and duration.

16To identify right frontal electrodes of interest in each participant (i.e. a spatial filter), we used Independent Components Analysis (; see; ). We selected a participant-specific independent component (IC) based on two criteria; First, the scalp topography (right-frontal, and if not present, frontal); and Second, an increase in beta power on Successful Stop trials (from Stop signal to SSRTBeh; StopWin) compared to activity prior to the Go cue [−1000 to −500 ms aligned to the Stop signal; see Materials and methods; Figure 5—figure supplement 1]. The average scalp topography across all participants is shown in Figure 5b, inset (see Figure 5—figure supplement 2 for average dipoles). For each participant, we estimated beta bursts; First, by filtering the data at the peak beta frequency; and Second, by defining a burst threshold based on the beta amplitude in a baseline period after the Stop signal (500–1000 ms after Stop signal in the Stop trials, and 500–1000 ms after the mean SSD in the Correct Go trials) (see Materials and methods; Figure 5—figure supplement 3).

17In an exemplar participant, the burst % increased for Successful Stop compared to both Failed Stop and Correct Go trials prior to SSRTBeh (Figure 5a). To quantify this across participants, we compared the mean burst % among the three trial-types, and for the time window from the Stop signal to the SSRTBeh of a participant (StopWin) and the baseline period before the Stop signal (BaseWin; Go to Stop signal in Stop trials and Go to mean SSD in Correct Go trials). We performed a 2-way repeated measures ANOVA with mean burst % as the dependent measure, with trial-type (Successful, Failed Stop, and Correct Go trials) and time-window (StopWin and BaseWin) as factors. There was a significant main effect of trial-type (F(2,20) = 4.5, p=0.025, ηp2 = 0.3) and a trial-type by time-window interaction (F(2,20) = 4.0, p=0.034, ηp2 = 0.3), but no main effect of time-window (F(1,10) = 3.8, p=0.088, ηp2 = 0.3). Post hoc t-tests showed that in the StopWin there was a significant increase in burst % for Successful Stop (14.6 ± 1.7%) compared to both its baseline (9.9 ± 1.7%; t(10) = 3.3, pBon = 0.022, BF10 = 7.6), and Correct Go (9.6 ± 1.3%; t(10) = 3.7, pBon = 0.015, BF10 = 11.8), but not to Failed Stop (10.3 ± 1.6%; t(10) = 2.1, pBon = 0.198, BF10 = 1.2) (Figure 5b). Thus, burst % increased for the Successful Stop trials which could not be attributed to post-movement beta rebound (see Figure 5—figure supplement 4).

18To further clarify the temporal relationship between beta activity and the current EMG measure of action-stopping, we quantified the mean burst time (BurstTime in the StopWin) for each participant. Across participants, the mean BurstTime (115 ± 6 ms) was significantly shorter than mean CancelTime (169 ± 10 ms; t(10) = 8.2, p<0.001, BF10 > 100) and there was also a strong positive relationship between them (ρ = 0.76, p=0.006, BF10 = 10.6; Figure 5d; see Figure 5—figure supplement 5 for correlation between CancelTime and other burst parameters). Further, we show that the observed correlation was not merely an artifact of varying StopWin across participants (permutation test, p<0.05; see Materials and methods). Thus, these results show that participants with an early frontal beta burst also had an early CancelTime.

19We ran a new sample of 13 participants (see Table 1 for behavioral results). As above a right frontal IC was extracted for each participant (average topography Figure 5c inset) and the burst % was compared for the three trial-types (Successful Stop, Failed Stop, and Correct Go) in the two time-windows (StopWin and BaseWin). Again, a 2-way repeated measures ANOVA with burst % as the dependent measure revealed that there was a significant main effect of trial-type (F(2,24) = 6.9, p=0.004, ηp2 = 0.4) and a trial-type by time-window interaction (F(1,12) = 5.8, p=0.009, ηp2 = 0.3; Figure 5c). Here there was also a significant effect of time-window on burst % (F(1,12) = 16.1, p=0.002, ηp2 = 0.6). Post-hoc t-tests confirmed that the burst % was greater for Successful Stop (16.2 ± 2.2%) compared to its baseline (11.3 ± 1.4%; t(12) = 3.3, pBon = 0.021, BF10 = 7.6), and Correct Go (12.0 ± 1.4%; t(12) = 3.0, pBon = 0.030, BF10 = 5.3) but not compared to Failed Stop (15.4 ± 1.4%; t(12) = 1.0, pBon = 0.957, BF10 = 0.34). Across participants, the mean BurstTime (129 ± 7 ms) was again significantly shorter than CancelTime (166 ± 8 ms; t(10) = 5.0, p<0.001, BF10 > 100) and there was a significant positive relationship (ρ = 0.57, p=0.045, BF10 = 1.9; Figure 5d). Again, a permutation test suggested that this correlation was unlikely to result from mere variation in the length of StopWin across participants (p<0.05). Combining data from studies 4 and 5 confirms the strong relationship between right frontal beta BurstTime and CancelTime (ρ = 0.66, p<0.001, BF10 = 29.4).

20This set of studies provides detailed information about the timing of subprocesses in human action-stopping. We started with the recently published observations that the standard behavioral measure of action-stopping (SSRT) is, an over-estimate of stopping latency. To more precisely delve into this, we validated a trial-by-trial method for estimating stopping latency from EMG. We focused on Successful Stop trials with small impulses (partial bursts) in EMG activity. The amplitude of such partial EMG activity was ~ 50% of the amplitude of EMG activity for outright keypresses, and this decreased at ~160 ms after the Stop signal (CancelTime), which is similar to other studies. While, one interpretation of this partial EMG activity is that it merely reflects ‘weak’ Go activation that did not run to completion, several lines of evidence strongly suggest it is a muscle manifestation of the stopped response. First, CancelTime was positively correlated with SSRTBeh, similar to recent studies. Second, the variability of CancelTime was positively correlated with the variability of SSRT estimated from the BEESTS modeling framework. Third, the partial EMG activity had a profile which was initially similar to the EMG profile seen when actual keypresses were made, and only diverged at ~55 ms after EMG onset. This initial similarity would not be expected if it were a weak Go activation – since previous research has demonstrated that weak and strong muscle activations have distinct profiles that diverge soon after onset. Fourth, our TMS experiment demonstrated that CancelTime coincided well with the timing of a putative basal ganglia-mediated global motor suppression. This implies that the smaller amplitude and earlier decline of the partial EMG activity on Successful Stop was due to an active suppression of motor output. Fifth, across participants, on Successful Stop trials, CancelTime correlated strongly with the time of right frontal beta bursts (BurstTime) from scalp EEG. This is consistent with response inhibition being implemented via right prefrontal cortex, and with previous research showing an increase of beta at right frontal electrode sites before SSRTBeh.

21Due to the poor spatial resolution of EEG it is not possible to pin down the origin of the bursts recorded on the scalp to any particular frontal cortical area (see Figure 5—figure supplement 2) – these bursts could relate to the rIFC or the presupplementary motor area, preSMA, or both [the rIFC and preSMA are connected via the aslant tract]. We note again that two studies with intracranial EEG showed increases of right frontal beta for rIFC and also that a recent study using source reconstruction of MEG signals based on fMRI in the same subjects showed an especially strong beta power increase for rIFC, that began ~ 140 ms after the Stop-signal, consistent with our results.

22We also acknowledge that the burst % was quite low on Successful Stop trials (~15%) and that CancelTimes on trials with and without bursts were not different (Study 5: CancelTimeWith Burst = 164 ± 9 ms; CancelTimeNo Burst = 165 ± 9 ms, t(12) = 0.6, p=0.58, d = 0.2, BF10 = 0.3; Study 4: too few trials for meaningful comparisons). While this might indicate that bursts are not necessary or sufficient for action-stopping, we think that the poor signal-to-noise of EEG could explain the low burst %. Further research is needed to test if beta bursts are causal to stopping. On a related point, the presence of beta on Go trials was also interesting. It is possible that beta bursts on Go trials reflected the (partly) spontaneous events that occur periodically (but have some functional consequence), or the bursts might have had a role in proactive slowing on Go trials (as the task, after all, required participants to prepare to stop their response).

23While several scalp EEG, intracranial EEG, and MEG studies showed increased right frontal beta power for stopping, a recent scalp EEG study focused on the spatial and temporal dynamics of beta bursts. That study saw that burst probability increased for likely dorsomedial frontal cortex (electrode FCz) rather than right frontal cortex, as we do. This discrepancy could be explained by our use of a spatial filter approach whereas that study analyzed the data in channel space. A further observation of was that bursts increased over bilateral sensorimotor cortex ~ 25 ms after the frontal area; and this was interpreted as inhibition of the motor system. This fits our observation of a decrease in corticospinal excitability within ~ 20 ms of right frontal bursts. Putting aside methodological differences, these studies together implicate beta bursts in action-stopping.

24A puzzle in our results was that CancelTime was ~ 60 ms earlier than SSRTBeh. To better understand this discrepancy, we calculated SSRT based on the EMG response rather than behavior. We saw that SSRTEMG better matched CancelTime than did SSRTBeh. Thus, SSRTBeh could be an over-estimation of the duration of the Stop process in the brain. This extra time in SSRTBeh probably reflects a ‘ballistic stage’ in generation of the button press. We suggest that the maximum CancelTime reflects the last point at which a Stop process can intervene to prevent responses. We note that CancelTime (a muscle measurement) is an overestimation of the brain’s stopping latency since it does not include the corticospinal conduction time, which we estimated as ~ 20 ms, and does not include the stopping latencies of the No EMG trials, which presumably reflect the fastest stopping latencies where the Stop process was fast enough to cancel the impending response before it reaches the muscle. Indeed, our TMS results show that global motor suppression, which we take as the time at which motor areas of the brain are suppressed, is ~ 140 ms (which is ~ 20 ms less than CancelTime). One important consequence of our observation that the brain’s stopping latency is ~ 140 ms is that neural events that mediate stopping need to occur before this time. Indeed, we found that right frontal beta activity increased ~ 120 ms after the Stop signal on Successful Stop trials, and also that, across participants, there was a strong positive relationship between mean BurstTime and mean CancelTime.

25Taken together, these studies motivate a relatively detailed model of the temporal events of action-stopping (Figure 6; Video 1). First, we suppose the right frontal beta bursts relate to activity of right inferior frontal gyrus, and this happens in ~ 120 ms, which then leads via basal ganglia to global suppression of the primary motor cortex at ~140 ms. After a corticospinal conduction delay of ~ 20 ms, this suppression of motor output is then reflected at ~160 ms as a decline in muscle activity (CancelTime). Finally, SSRTBeh occurs at ~220 ms, after, what we suppose is an electromechanical delay of ~ 60 ms. Thus, CancelTime narrows the time window for the causal manipulation of neural structures involved in action-stopping. This is in contrast to previous studies that have proposed that the onset of intramuscularly-recorded antagonist EMG responses (which is longer than SSRT) can be used as an alternative for estimating the stopping latency.

26We acknowledge that the timings in this model are approximations that are dependent on a range of factors (such as averaging across participants, running different experiments, and the particular parameters of detection algorithms). However, we note a striking convergence of timings across the current experiments and in other studies, for example CancelTime, time of MEP suppression, corticospinal conduction time, BurstTimes, and the ballistic stage. Together, these all provide support for our model.

27This model specifies the possible chronometrics of stopping in more detail than extant human models, and, more generally, raises questions about the timing reported in some other studies where the neural change appears late. For example, movement neurons in monkey Frontal Eye Field decrease activity in less than 10 ms before SSRT, dopaminergic neurons in rodent substantia nigra and striatum increase activity only 12 ms before SSRT, TMS at ~ 25 ms before SSRT over human Intraparietal Sulcus prolongs SSRT, and P300 human EEG activity ~ 300 ms after the Stop signal relates to the stopping latency. Whereas the rather late timing of some of these results might be related to processes such as monitoring and feedback as has been ascribed to brain signatures that modulate after SSRT, our earlier latencies for prefrontal bursts, TMS-MEP and muscle CancelTime are more indicative of a role in stopping itself.

28While our study specifically looked at the chronometrics of the Stop process, and tried to better characterize the physiological model underlying action-stopping, we also now speculate how our results relate to computational models of action-stopping (specifically, the independent race model, the interactive race model, the BEESTS model, and the blocked-input model, and the). First, our results are not compatible with a strictly independent model (of the Go and the Stop processes) since we see active inhibition of M1 (the Go process) already some time before SSRT. Second, our results are compatible with the interactive race model which suggests that the Stop process begins late, but implementation is quick (i.e. within the last 1/3th of the stopping latency). Indeed, we observed beta bursts in frontal areas ~ 120 ms after the stop signal followed by rapid cancellation at the muscle within ~ 40 ms. Third, our results are also compatible with the BEESTS model insofar as they point to a trigger process that has a duration of about 80–120 ms. Finally, the interactive-race model and blocked-input model are very similar, so our results do not disambiguate them.

29Our results have several important implications. First, whereas several earlier studies of action-stopping recorded partial EMG for various purposes, some more recent ones specifically interpreted the time of the partial EMG as related to stopping. Our results strongly affirm that partial EMG can be used to estimate the latency of stopping reflected in the muscle. Second, as just noted, they provide temporal constraints on neuroscience studies of stopping in the brain. They suggest that methods with high temporal resolution need to focus on the time after the Stop signal and before CancelTime (indeed CancelTime minus conduction time) rather than before SSRTBeh, and the current study points to the potential of CancelTime as single-trial metric of stopping (please see our recent pre-print; ). Third, our results have clinical implications. Whereas meta-analysis shows that SSRTBeh is longer for patients (e.g. ADHD, OCD, and substance use disorder) vs. controls, not all such studies show differences. We predict that CancelTime will be more sensitive than SSRTBeh. Furthermore, future studies can easily estimate within-subject variability in CancelTime, which will likely discriminate patients from controls. Fourth, our results provide insight into why SSRTBeh might only have a modest relationship with more ‘real-world’ measures of impulsivity. As we show, SSRTBeh includes not only CancelTime but an extra, and variable, 60 ms ballistic stage. We expect that future studies may show stronger correlations between CancelTime and self-report than that seen between SSRTBeh and self-report (also see ); likewise we predict that right frontal beta burst time might also correlate more tightly with self-report measures. More generally, the detailed timing information of frontal beta at ~ 120 ms, global motor suppression at ~ 140 ms, and CancelTime at ~ 160 ms points to subprocesses of action-stopping that provide potential biomarkers that could better explain individual differences in impulse control.

30In conclusion, we propose a detailed timing model of action-stopping that partitions it into subprocesses that are isolable to different nodes and are more precise than the behavioral latency of stopping. At the core of this timing model is a method of measuring the latency of stopping from the muscles. This offers a potential single-trial estimate of stopping latency that could be easily measured with minimal equipment in any lab that studies human participants.

31All were adult, healthy, human volunteers provided written informed consent and were compensated at $20/hour. The studies were approved by the UCSD Institutional Review Board (protocol #171285).

32Study 1. Ten participants (four females; age 22 ± 1 years; all right-handed).

33Study 2. Thirty-six participants (19 females; age 19 ± 0.4 years; all right-handed). Two were excluded for bad behavior (violating the assumptions of the independent race model - Failed Stop RTBeh < Correct Go RTBeh, and P(Stop) increasing monotonically as a function of SSD), and two were excluded for noisy EMG data.

34Study 3 (TMS): Eighteen participants (11 females; age 19 ± 0.4 years; 15 right-handed, 2 left-handed) with no contraindications to TMS. One was excluded for bad behavior.

35Study 4 (EEG). Eleven participants (six females, age 19 ± 0.4 years, all right-handed).

36Study 5 (EEG): Fifteen participants (nine females, age 21 ± 0.4 years, all right-handed). Two were excluded from analysis, one for misaligned EEG markers due to a technical issue, while the other lacked a right frontal brain IC, based on our standard method.

37This was run with MATLAB 2014b (Mathworks, USA) and Psychtoolbox. Each trial began with a white square appearing at the center of the screen for 500 ± 50 ms. Then a right or left white arrow appeared at the center. When the left arrow appeared, participants had to press a key on a vertically oriented keypad using their index finger, while for a right arrow they had to press down on a key on a horizontally oriented keypad with their pinky finger (Figure 1b inset), as fast and as accurately as possible (Go trials). The stimuli remained on the screen for 1 s. If participants did not respond within this time, the trial aborted, and ‘Too Slow’ was presented. On 25% of the trials, the arrow turned red after a Stop Signal Delay (SSD), and participants tried to stop the response (Stop trials). The SSD was adjusted using two independent staircases (for right and left directions), where the SSD increased and decreased by 50 ms following a Successful Stop and Failed Stop respectively. Each trial was followed by an inter-trial interval (ITI) and the entire duration of each trial including the ITI was 2.5 s (Figure 1a).

38Study 1 and 2. Participants performed the task with their right hand. They performed 40 practice trials before the actual experiment, where their baseline SSD was determined and was subsequently used as the starting SSD in the main experiment. In study 1 and 2, the experiment had 600 trials divided in 15 blocks, such that each block had 40 trials (450 Go trial and 150 Stop trials). At the end of each block the participants were presented a figure showing their mean reaction times (RT) in each block. Participants were verbally encouraged to maintain their mean reaction time constant across the different blocks and between 0.4–0.6 s.

39Study 3. Participants performed the task with their left hand. Following 48 practice trials without TMS, participants performed 12 blocks of the experiment with TMS, with each block consisting of 96 trials each (72 Go trials and 24 Stop trials).

40Study 4. Participants performed the task with their right hand. Following 160 practice trials, participants performed 4 blocks of 80 trials (240 Go trials and 80 Stop trials).

41Study 5. Participants performed the task with their right hand. Following 80 practice trials, participants 24 blocks of 80 trials each (1440 Go trials and 480 Stop trials).

42EMG data were acquired using a Grass QP511 AC amplifier (Glass Technologies, West Warwick, RI) with a frequency cut-off between 30 and 1000 Hz. A CED Micro 1401 mk II acquisition system sampled the data at 2 kHz. The EMG data were acquired by CED Signal v4 software (Cambridge Electronic Design Limited, Cambridge, UK) for 2 s following the fixation cue. The data acquisition was triggered from MATLAB using a USB-1208FS DAQ card (Measuring Computing, Norton, MA). In all five experiments, surface EMG was recorded from both the first dorsal interossei (FDI) and the abductor digiti minimi (ADM) muscles of the hand (Figure 1b inset). In the TMS experiment, surface EMG was also recorded from the task-irrelevant right extensor carpi radialis (ECR) muscle (Figure 4a).

43MEPs were evoked using a TMS device (PowerMag Lab 100, MAG and More GMBH, Munich, Germany) delivering full sine wave pulses, and connected to a figure-of-eight coil (70 mm diameter, Double coil PMD70-pCool; MAG and More GMBH, Munich, Germany). During the task, the coil was positioned on the scalp over the left primary motor cortex representation of the ECR muscle and oriented so that the coil handle was approximately perpendicular to the central sulcus, that is at ~45° to the mid-sagittal line, and the initial phase of current induced in the brain was posterior-to-anterior across the central sulcus. Prior to the experiment, the motor hot spot was determined as the position on the scalp where slightly supra-threshold stimuli produced the largest and most consistent MEPs in ECR. The position was marked on a cap worn by the participants. Resting motor threshold (RMT) was defined as the lowest intensity to evoke an MEP of at least 0.05 mV in 5 of 10 consecutive trials while participants were at rest. We then established the test stimulus intensity to be used during task, which was set to produce a mean MEP amplitude of approximately 0.2–0.5 mV whilst the participant was at rest.

44MEPs were also evoked in the left FDI muscle prior to beginning the main experiment for the purpose of recording the corticospinal conduction time. The motor hot spot for the FDI was defined in a manner similar to that for the ECR. The active motor threshold (AMT) was defined as the lowest intensity to evoke a discernible MEP in 5 of 10 consecutive trials, while participants maintained slight voluntary contraction (~10% of maximum voluntary EMG amplitude during isometric finger abduction). Then, 10 stimuli were delivered at 150% AMT during slight voluntary contraction (again 10% of maximum), with the coil oriented to induce lateral-medial current in the brain in order to obtain estimates of corticospinal conduction time.

45During the task, TMS stimuli were delivered on every Stop trial and on 50% of Go trials. On every Stop trial, a single TMS stimulus at the test stimulus intensity was delivered at one of six time points: inter-trial interval (100 ms prior to fixation; ITI), 100 ms, 120 ms, 140 ms, 160 ms and 180 ms after the Stop signal (Figure 4a). On the Go trials, TMS stimuli were yoked to the time of the Stop signal on the previous Stop trial. Thus, there were 48 trials per TMS time point on Stop trials and 96 trials per time point on Go trials.

4664 channel EEG (Easycap, Brainvision LLC) was recorded in the standard 10/20 configuration at 1 kHz using BrainVision actiChamps amplifier (Brain Products GMBH, Gilching, Germany) and BrainVision Pycorder (Brain Products GMBH, Germany).

47All analyses were performed using MATLAB (R2016b, R2018b, R2019a).

48SSRT from the behavioral responses (SSRTBeh) was determined using the integration method. When calculating SSRT using the EMG responses, SSRTEMG, as the P(Respond|Stop) was often much more than 0.5, we calculated the SSRT individually for all SSDs and then averaged it.

49EMG data were filtered using a 4th order Butterworth filter (roll-off 24 dB/octave) to remove 60 Hz noise and its harmonics at 120, and 180 Hz. EMG data were full-wave rectified and the root-mean square (RMS) of the signal was computed using a centered window of 50 ms. Any EMG activity which was greater than 8 SD of the mean EMG activity in the baseline period (Fixation to Go cue) was marked, on a trial-by-trial basis. Starting from the peak of that EMG activity, we backtracked and marked the onset at the point where the activity dropped below 20% of the peak for five consecutive ms. This method of adjusting the threshold based on the peak EMG activity, allowed better onset detection than a fixed threshold, especially when the amplitude of the EMG activity was small. The time when EMG started to decline was determined as the time when, following the peak EMG, the activity decreased for five consecutive ms. Visual inspection of individual trials showed that this method provided a reliable detection of both EMG onsets (see Figure 1—figure supplement 1a,b for RTEMG vs. RTBeh correlation) and decline. Any detected EMG timing which was beyond 1.5 times the inter-quartile range (IQR) of the first and third quartile (Q3) of that particular timing distribution was deemed an outlier. This removed < 4% trials. CancelTime was marked as the time of the EMG decline following the Stop signal. For outlier rejection, CancelTimes had a lower cutoff of 50 ms and higher cutoff of Q3+1.5 × IQR. This removed < 3% trials.

50As the peak EMG amplitude for the FDI and ADM muscle were quite distinct, before averaging the two EMG activities, we normalized the muscle activity by the peak activity in that particular muscle (VoltageNorm in Figures 2a, b and 3c, Figure 3—figure supplement 2).

51MEP amplitudes were measured on a trial-by-trial basis. Data were included for analysis if the following criteria were met: (i) the amplitude of the ECR EMG signal in a 90 ms period prior to the TMS stimulus was < 0.05 mV; (ii) the amplitude of the MEP fell within the mean±1.5× IQR of values for the same time point and trial type (Correct Go, Failed Stop, Successful Stop). Thereafter, MEP amplitudes measured at the ITI were collapsed across trial type (Correct Go, Failed Stop and Successful Stop), averaged and used as a baseline against which to compare other TMS time points. For each of the other TMS time points (100, 120, 140, 160, 180 ms following the Stop signal), data were averaged within each trial type (Correct Go, Failed stop, Successful Stop) and expressed as a percentage of the mean ITI MEP amplitude.

52Corticospinal conduction time was determined by delivering TMS over the hand representation of left FDI and measuring MEP from the muscle (Figure 4c). The earliest MEP onset latency across 10 trials was identified by visual inspection of the EMG traces.

53To compare the temporal association between the EMG decline and MEP suppression, we performed a trial-by-trial analysis of Stop-signal task data only on trials where an EMG burst was detected. We first normalized the time of TMS on a given trial by subtracting the time of EMG decline from the time of the TMS pulse. Hence, negative values mean that TMS was delivered before the EMG decline and positive values mean that TMS was delivered after. We then plotted MEP amplitudes for each of the three response types (Correct Go, Failed Stop, and Successful Stop) against the normalized times binned into 30 ms windows. This analysis meant that for a given individual there were relatively few trials per time bin, and some bins would occasionally contain no data. Therefore, we combined data across all individuals. Prior to this, MEP amplitudes for each individual were normalized to the mean MEP amplitude at the inter-trial interval, to account for inter-individual variability in absolute MEP amplitudes at baseline. We restricted our analysis to time bins that contained at least 50 trials, which resulted in time range −90 ms to 60 ms.

54We used EEGLAB and custom-made scripts to analyze the data. The data were downsampled to 512 Hz and band-pass filtered between 2–100 Hz. A 60 Hz and 180 Hz FIR notch filter were applied to remove line noise and its harmonics. EEG data were then re-referenced to the average. The continuous data were visually inspected to remove bad channels and noisy stretches.

55The noise-rejected data were then subjected to logistic Infomax ICA to isolate independent components (ICs) for each participant separately. We then computed the best-fitting single equivalent dipole matched to the scalp projection for each IC using the DIPFIT toolbox in EEGLAB. ICs representing non-brain activity related to eye movements, muscle, and other sources were first identified using the frequency spectrum (increased power at high frequencies), scalp maps (activity outside the brain) and the residual variance of the dipole (greater than 15%) and then, subtracted from the data. A putative right frontal IC was then identified from the scalp maps (if not present then we used frontal topography) and the channel data were projected onto the corresponding right frontal IC. The data on Successful Stop trials were then epoched from −1.5 s to 1.5 s aligned to the Stop signal. We estimated the time-frequency maps from 4 to 30 Hz, and −100 to 400 ms using Morlet wavelets with three cycles at low frequencies linearly increasing by 0.5 at higher frequencies. The IC was selected only if there was a beta power (13 to 30 Hz) increase in the window between the Stop signal and SSRTBeh compared to a time-window prior to the Go cue (−1000 to −500 ms aligned to Stop signal). In each participant, the beta frequency which had the maximum power in this time window was used in the beta bursts computation (Figure 5—figure supplement 1).

56To estimate the beta bursts, the epoched data were first filtered at the peak beta frequency using a frequency domain Gaussian window with full-width half-maximum of 5 Hz. The complex analytic envelope was then obtained by Hilbert transform, and its absolute value provided the power estimate. In each participant, to define the burst threshold, the beta amplitude within a period of 500 to 1000 ms (i.e. after the Stop signal in the Stop trials, and after the mean SSD in the Correct Go trials) was pooled across all trials [Note that compared to the ICA analysis here we picked a different time-window to estimate the burst threshold to keep the analysis unbiased. However, picking the same time-window also yielded similar results]. The threshold was set as the median + 1.5 SD of the beta amplitude distribution (Figure 5—figure supplement 3). Once the burst was detected, the burst width threshold was set as the median + 1 SD. We binary-coded each time point where the beta amplitude crossed the burst width threshold to compute the burst % across trials. For each detected burst, the time of the peak beta amplitude was marked as the BurstTime.

57For pairwise comparisons, the data were first checked for normality using Lilliefors test, and if normally distributed a two-tailed t-test (t-statistic) was performed, else a Wilcoxon signed rank test (Z-statistic) was performed. We interpret the effect sizes as small (Cohen’s d: 0.2–0.5; Bayes Factor in favor of the alternate hypothesis, BF10: 1–3), medium (d: 0.5–0.8; BF10: 3–10), large (d > 0.8; BF10 > 10). For comparisons across multiple levels, repeated-measures ANOVA was used, followed by Bonferroni corrected t-tests for pairwise comparisons (Bonferroni corrected p-value: pBon). The Greenhouse-Geisser correction was applied where the assumption of sphericity in ANOVA was violated (corrected F-statistic: FGG). Effect sizes for ANOVAs were interpreted as small (partial eta-squared, ηp2: 0.01–0.06), medium (ηp2: 0.06–0.14), and large (ηp2: 0.14). For correlational analyses, Pearson’s correlation coefficient (r) was usually used, but Spearman’s correlation coefficient (ρ) was used when the data was bounded in a closed interval. All data are presented as mean ± s.e.m.

58In testing the relationship between BurstTime and CancelTime, we performed a permutation test. We sampled BurstTimes randomly from a uniform distribution between 0 and SSRTBeh for a given participant for 3000 iterations. For each iteration, we then computed the correlation (r) between the mean BurstTime and the mean CancelTime across participants. This generated a distribution of r ranging between −1 and 1. The p-value for our analysis was determined as the P(r ≥ rObs|H0) in the permuted data.

59We used the BEESTS model developed by Dora Matzke and colleagues (run in R Studio 1.1.463) which assumes a race between two stochastically independent process, a Go and a Stop processes. This model estimates the distribution of the SSRT by using the participant’s Go RTBeh distribution, and by considering the Failed Stop RTBeh as a censored Go RTBeh distribution. The censoring points are sampled randomly from the SSRT distribution on each Stop trial. The RTBeh distributions underlying the Go and Stop processes are assumed to have a Gaussian and an exponential component and is described by three parameters (μGo, σGo, τGo and μStop, σStop, τStop). For such ex-Gaussian distributions, the mean and variance of the RTBeh distributions are determined as μ + τ and μ2 + τ2, respectively. The model also estimates the probability of trigger failures for each participant. The model uses Bayesian Parametric Method (BPE) to estimate the parameters of the distributions. We used a hierarchical BPE, where individual subject parameters are modeled with the group-level distributions. This approach is thought to be more accurate than fitting individual participants and is effective when there is less data per participant. We pooled the subjects across both study 1 and 2 to estimate the individual parameters. The priors were bounded uniform distributions (μGo, μStop: U(0,2); σGo, σStop: U(0,0.5) τGo, τStop: U(0,0.5); pTF: U(0,1)). The posterior distributions were estimated using the Metropolis-within-Gibbs sampling and we ran multiple chains. We ran the model for 5000 samples with a thinning of 5. The Gelman-Rubin (R̂) statistic was used to estimate the convergence of the chain. Chains were considered converged if R̂<1.1.

60A core element of this paper is a novel method of calculating single-trial stopping latency from EMG. Accordingly, we provide the EMG and behavioral data from all participants in study 1 and 2, along with analysis scripts, and a brief description of how to execute the scripts (https://osf.io/b2ng5/). All other EMG, TMS-MEP and EEG data and scripts are also provided at the above link.