Response inhibition is a key feature of executive function most commonly assessed using the stop-signal task (Verbruggen et al., 2019). The standard stop-signal task requires rapid choice responses (e.g., a left or right button press) to a “go” stimulus (e.g., a left or right pointing arrow), that on some trials must be cancelled when a second stimulus occurs some time later (the stop-signal delay, SSD; Table 1 lists the acronyms used in this article). Assuming a simple independent race between processes or “runners” with variable speeds triggered by the go and stop signals (Logan & Cowan, 1984), the standard task affords a key index of executive control, the running time of the inhibitory process. Go response time (RT) is much slower than the running time of the inhibitory process, which is called stop-signal reaction time (SSRT), consistent with stopping being meditated by a specialised fronto-basal ganglia network (Sebastian, Forstmann, & Matzke, 2018).

Although the standard task is widely used (Matzke, Verbruggen, & Logan, 2018), more complex response-selective inhibition tasks—where only some components of a multi-component action are cancelled, with the remaining components being executed as quickly as possible—may be more relevant to inhibition in the real-world (Aron & Verbruggen, 2008), and to executive-function disorders (Aron, 2011). A common example occurs when initiating a manual gear change, braking with one foot and pressing the clutch with the other. When a dangerous change in road conditions occurs, clutching is aborted while still braking. In the laboratory analogue, participants simultaneously press a button with each hand in response to the go signal (e.g., a pair of left and right pointing green arrows). If a selective stop signal occurs (e.g., one arrow turns red) the corresponding button press is withheld but the other still made.

Here we show that the traditional explanation of selective stopping, as instantiated in the Activation-Threshold Model (ATM, see Fig. 1A: MacDonald et al., 2014, MacDonald et al., 2017), is inconsistent with electromyographic (EMG) activity in a task mixing two types of stopping trials, selective stopping and standard stopping (i.e., both arrows turn red and no response should be produced). We then propose a new model, called simultaneously inhibit and start (SIS, see Fig. 1B), which provides a unified explanation of both standard selective stopping trials as well as go trials (i.e., trials with no stop signal). We show that SIS accurately characterises both EMG and all aspects of behaviour, including the probability of stopping and the full distribution of RT in any case where responses do occur.

The traditional approach assumes a global inhibitory process is triggered by both standard and selective stop trials, with a subsequent “restart” process required to produce a unimanual response on selective-stop trials. The need to globally stop and then subsequently restart has been used to explain why, when selective stopping is successful, the unimanual response is delayed relative to the bimanual response on trials without a stop signal, typically by 100–200 ms (Coxon, Stinear, & Byblow, 2007). The ATM explains the common finding that unimanual EMG amplitudes are larger than bimanual EMG amplitudes by the restart needing to exceed a higher activation threshold caused by the global inhibition. More specifically, the ATM was developed based on variations in cortico-motor excitability observed during unimanual stop trials that were taken to suggest a series of three distinct processing stages, (i) a go stage: the go signal triggers preparation and activation of a synchronous two-component (“bimanual”) response via neuronal coupling of effector representations; (ii) a stopping stage: if the stop signal arrives before EMG amplitude is sufficient to cause execution of a bimanual response, the threshold activation required to do so is raised; (iii) a restart stage: a new one-component (unimanual) response is then prepared and activation boosted sufficiently to overcome the higher threshold and trigger a unimanual response. Simulations performed by MacDonald et al. (2017) show that the delay between the onset of the second stage, which causes the activation threshold to increase exponentially towards a higher level, and third stage, which causes activation to increase exponentially towards an even higher level, is usually quite substantial. Their Fig. 5F shows the delay is at the very least 60 milliseconds (ms) and usually much longer.

SIS instead explains selective stopping by an extension of the race-model architecture applied to the standard stop-signal task, where the selective-stop signal simultaneously inhibits the bimanual response and starts a new unimanual response. SIS and ATM differ in three key ways, (i) rather than the second and third stages occurring in series, they occur in parallel, (ii) rather than the third stage being a restart, it is constituted of an entirely new selective-response process; (iii) rather than being global, the action of the stopping process is specific to the bimanual runner. If the same type of inhibitory mechanism is used in the standard and selective stop-signal tasks, SIS must assume its stopping process will be much faster than any go process. This predicts that successful stopping will typically rely on the stop runner being quick enough to overtake the bimanual runner. The selective process then triggers a corresponding response some time later. Unimanual responses are delayed relative to the bimanual responses simply because the onset of the selective process is delayed by the SSD. This predicts that the unimanual vs. manual delay is a function of the SSD, although it could be shorter than the SSD if the unimanual runner is faster than the bimanual runner as indicated by EMG amplitudes. However, under the unified account proposed by SIS, the go runners should rely on the same neural mechanisms, and so the unimanual runner should not be much faster. Similarly, if standard and selective stopping rely on the same neural mechanisms, the stop runner should be much faster than either type of go runner in selective stopping.

Importantly the two theories make clearly contrasting predictions about the time course of “partial” responses—EMG bursts insufficient to cause a response—that sometimes occur in both hands on successful selective-stop trials which later have a single response-generating burst in one hand. ATM predicts a gap between partial responses and the unimanual response due to the need to restart. A partial response occurs when EMG activity increases as activation approaches but does not reach the response threshold before the stopping process elevates the threshold, causing EMG activity to decline before it is sufficient to trigger a response. There is then necessarily a delay before the restart process can boost activation sufficiently to cross the new higher threshold. SIS, in contrast, predicts that partial bursts can occur any time up to just before the unimanual response depending on the margin between the finishing times of inhibitory, bimanual, and unimanual runners. That is, if the stop runner arrives before a sufficient amplitude is generated to trigger a bimanual response and causes EMG in both hands to start to decrease it is still possible that a fast unimanual runner might arrive very soon after, causing EMG to increase in the corresponding hand while it continues to decrease in the other hand.

If running times are as variable in selective stopping as they are known to be in the standard paradigm (Matzke et al., 2013), such “blending” of partial and response-generating bursts should be sufficiently common to be detectable. To enhance measurement of partial bursts and our ability to detect any gap we used both stiff and conventional compliant response buttons in our experiment. To foreshadow our results, for both button types, our EMG analysis found no evidence for a gap, leading us to propose the SIS model. The simple structure of SIS allowed us to implement it as a quantitative cognitive model and extend the Bayesian hierarchical methods that have been successfully used to estimate the distribution of SSRT in the standard paradigm (Matzke, Love et al., 2017, Matzke et al., 2013) to estimate both SSRT and unimanual runner finishing time distributions in selective stopping. We simultaneously fit the SIS model to response probabilities and the distributions of RTs for bimanual and unimanual responses to determine whether it provides an accurate quantitative account of the data. We also test the predictions that the unimanual runner is faster than the bimanual runner but the stop runner is faster than both.