Fig 1.
Experimental designs used to investigate the response delay.
A: [7]. Bimanual anticipatory response inhibition task. On a Partial trial, one bar unexpectedly stopped rising before the target, cueing cancellation of the corresponding hand. TMS was applied to the right primary motor cortex and motor evoked potentials (MEPs) were recorded from the task-relevant left FDI muscle. Mean response times (ms) are relative to the target positioned at 800 ms. B: [13]. In the foreknowledge stop-signal task, text was displayed to bias stopping expectations followed two seconds later by the imperative. Participants made a synchronous bimanual choice reaction time (RT) response with both index or both little fingers. On Partial trials, a central stop signal appeared after a stop signal delay (SSD) and the stopping rule held in working memory was implemented. MEPs were recorded from the task-irrelevant tibialis anterior muscle. C: [15]. In the dual-task version of the stop-signal task, participants always responded with their foot and performed a choice RT task, responding with the hand that corresponded to the direction of the arrow (imperative). On Partial trials, the arrow turned red (or the hand was vibrated) after a SSD and no hand response was required. RTs are relative to the imperative in B and C. RH: right hand, LH: left hand, RF: right foot, RT: reaction time, Vib: vibration.
Fig 2.
Experimental data used in the activation threshold and horse-race models.
Graphic depiction of the experimental data from Go and GS trials in [7] and how the data is used in the activation threshold model (ATM) and horse-race model (HRM). A: Experimental results showing modulation of left first dorsal interosseous MEP amplitudes during Go (GG) and Partial (GS) trials. Stop signal was given at −250 ms on GS trials. Values are mean ± standard error. #P < 0.05; ##P < 0.001 represent significant increases relative to baseline during GG trials. †P = 0.052 denote trends. *P < 0.05; **P < 0.01 represent significant differences during GS trials. Reproduced from [7]. B: Model parameters for facilitation and inhibition curves in the ATM (equivalent Go and Stop processes in the HRM) were simultaneously fitted to motor evoked potential (MEP) amplitude data collected 150 (1), 125 (2) and 100 ms (3) before the target, and electromyography (EMG) onset (4) and offset (5) times. C: Model parameters for the Stop process on GS trials of the HRM were simultaneously fitted to MEP amplitudes 75 (1′), 50 (2′) and 25 ms (3′) before the target, as well as EMG onset times (4′) and rates of onset (5′). D: Model parameters for the increased inhibition and secondary facilitatory input were fitted to MEP amplitudes 75 (1′), 50 (2′) and 25 ms (3′) before the target, EMG onset times (4′) and rates of onset (5′). Note that the underlying facilitation process is equivalent for B–D which all illustrate the left hand response.
Fig 3.
Program flow for both models. Means and standard deviations (SD) were estimated for facilitatory and inhibitory function parameters to account for physiological variability. MEP: motor evoked potential; EMG: electromyography.
Fig 4.
Theoretical comparison between model predictions for the suppressed finger on Partial trials.
A: The horse-race model would predict that no response is generated when the Stop process reaches the decision threshold before the Go process. B: In contrast, the activation threshold model would predict that no response is generated when inhibition is raised to a level that cannot be reached by the preplanned Go response (facilitation curve). Both models predict the same behaviour resulting from distinct underlying mechanisms. Note that these mechanisms would also apply to both fingers on successful Stop Both trials when no response is generated with either finger.
Table 1.
Output from the horse-race and activation threshold models for Go trials of the anticipatory response inhibition task.
Fig 5.
Model results for Go and GS trials.
100 simulated Go (A–C) and GS (D–F) trials using best fitting parameters produced by the activation threshold model (ATM; bottom four panels) and horse-race model (HRM; top two panels). A: The HRM captures MEP amplitude and EMG data from the anticipatory response inhibition (ARI) task. A single decision threshold is set at 1.659. B: The ATM is able to capture MEP and EMG data from the ARI task and necessitates a relatively narrow distribution of facilitatory drive. C: Using the ATM, bimanual Go reaction times in the stop-signal task are captured with a much wider distribution of facilitatory drive. D: The addition of inhibitory input to the HRM adequately captures modulation of corticomotor excitability but struggles to capture delayed EMG onset times and increased EMG onset rates that are empirically observed in the ARI task. E: The ATM demonstrates that facilitatory input for the Go response on ARI trials is unable to surpass the elevated activation threshold following nonselective inhibition of the bimanual response. F: A secondary facilitatory input is required to summate excitatory drive in the ATM to pass the elevated threshold and generate a unimanual left hand response. Red: inhibitory input (activation threshold); black: facilitatory input; blue: decision threshold.
Table 2.
Output from the horse-race and activation threshold models for Partial trials of the anticipatory response inhibition task.
Fig 6.
Average model simulations on GS trials.
Average best-fitting facilitatory and inhibitory inputs simulated by the horse-race model (A) and activation threshold model (B). Facilitatory input surpassing the elevated activation threshold represents summation of the preplanned Go response (green) and reprogrammed unimanual movement (green dashed). Compare with model predictions in Fig 2C&2D. Red: inhibitory input (activation threshold); black: facilitatory input; green: facilitatory input for preplanned Go response; dashed green: facilitatory input for reprogrammed unimanual response; blue: decision threshold.
Table 3.
Model output for Go trials of the stop-signal task.