Task performance

The subjects’ performance in the delayed-reach task reached a plateau relatively quickly, with the average performance in terms of % correct trials being above 90% after the first four blocks (Fig. 2a). Therefore, the first four blocks of trials were deemed familiarisation blocks and were not included in subsequent statistical analyses. Although the subjects generally performed well at the task, each subject occasionally initiated movements before receiving the ‘Go’ cue (2.6 ± 2.3% of all trials), a phenomenon mainly observed during the longest preparatory delays, i.e., 450–500 ms with a total of 90 and 233 ‘false starts’, respectively (Fig. 2b). For each participant and each preparatory delay, there were two targets, two loads and two perturbations repeated for 13 or 18 blocks (a total of 2 × 2 × 2 × 13 = 104 or 2 × 2 × 2 × 18 = 144 trials). Summing across all subjects, there was a total of 2104 trials for each preparatory delay. Thus, there were, on average, 4% and 11% false starts at the 450- and 500-ms preparatory delays. For the shorter preparatory delays, most false starts occurred during the familiarisation blocks (Fig. 2b). Although infrequent overall, these false starts persisted despite repeated instructions to wait for the ‘Go’ cue. That is, the experimenter provided relevant instructions before data collection began and repeatedly after false starts, but interestingly, a relatively small number of such trials often persisted throughout the experiment. ‘False-start’ trials were removed from further analyses (see “Methods” for more details).

Fig. 2

Reach performance and premature movement initiation. a The subjects’ performance at the task, in terms of % correct trials in each block of trials. A correct trial involved reaching the cued target within a certain time interval (see main text for more details). Performance reached a high and relatively stable plateau after the first four blocks, which were deemed familiarisation blocks and not included in subsequent analyses (grey background rectangle). b Each subject occasionally initiated movements prematurely, i.e., before the ‘Go’ cue (2.6 ± 2.3% of all trials), mainly during the longest preparatory delays. These “false starts” occurred even though the subjects were repeatedly instructed to wait for the ‘Go’ cue. The vertical dotted line represents the final block of familiarisation

Goal-directed modulation of stretch reflex responses

All data in the following results pertain to stretch reflex responses, i.e., we focused on trials where the hand was perturbed in the direction of homonymous muscle stretch. The median z-scored EMG activity (across subjects) for the unloaded and loaded pectoralis major, anterior deltoid, and posterior deltoid muscles for all preparatory delays is shown in Fig. 3. As indicated in this figure, goal-directed EMG activity, i.e., the difference between the red and blue curves for the unloaded (loaded) traces, seemed to vary overall as a function of preparatory delay.

Fig. 3

The median z-scored EMG activity across subjects (n = 16) for the unloaded and loaded pectoralis major, anterior deltoid, and posterior deltoid muscles. The conditions are specified by the cued targets (red and blue lines/dots), the load direction before perturbation (purple arrow), and the kinematic perturbation direction (black arrow). Throughout this figure, the data represent trials where the hand was perturbed along the direction of homonymous muscle stretch, whereas “loaded” and “unloaded” refer to the direction of muscle loading that was applied before the kinematic perturbation. The black vertical line at time ‘0’ represents perturbation onset. Curve shading denotes ± 1 SE

Goal-directed modulation of stretch reflex responses—pectoralis major

A representative example of hand positions, forces, and median z-scored pectoralis EMG activity (across subjects) with a 400 ms preparatory delay is also illustrated in Fig. 1d–e: a preparatory delay of 400 ms appears sufficient for inducing goal-directed tuning of the SLR response when the homonymous muscle is unloaded, i.e., reflected by the differentiation of the EMG curves (red vs. blue) within the SLR epoch when the pectoralis is unloaded. On the other hand, there is goal-directed tuning of the long-latency stretch reflexes (LLRe and LLRl) regardless of background load condition.

For the unloaded pectoralis SLR, Wilcoxon tests indicated significant goal-directed tuning (i.e., goal-directed difference values > 0) at all preparatory delays except 250 and 300 ms (Fig. 4, top; N = 16 subjects; 250 ms: W = 47, p = 0.511, rrb =  − 0.31; 300 ms: W = 98, p = 0.311, rrb = 0.44; 350 ms: W = 115, p = 0.039, rrb = 0.69; 400 ms: W = 127, p = 0.006, rrb = 0.87; 450 ms: W = 116, p = 0.039, rrb = 0.71; 500 ms: W = 129, p = 0.006, rrb = 0.90). A Friedman test indicated no significant differences in goal-directed SLR responses among the preparatory delays of 300–500 ms (χ24 = 14.6, p = 0.211). In accordance with previous findings, Wilcoxon tests indicated no significant goal-directed tuning of the SLR when the pectoralis muscle was loaded, at all preparatory delays (all p > 0.462). A direct comparison of pectoralis SLR tuning magnitudes between the unloaded and loaded conditions for (350 to 500 ms preparation delays) did not reach statistical significance (N = 16 subjects, 350 ms: W = 100, p = 0.193; 400 ms: W = 88, p = 0.215; 450 ms: W = 94, p = 0.193; 500 ms: W = 84, p = 0.217).

Fig. 4

Goal-directed differences in pectoralis EMG for the SLR, LLRe, and LLRl epochs. Grey circles represent the median single-subject EMG values of the group performing 18 blocks of trials, whereas the black circles represent the values of the group performing 13 blocks. Grey background rectangles represent upper and lower quartiles, and thin vertical lines represent the 95% data range. Solid red lines represent the group-level median values. *p < 0.05, **p < 0.01, ***p < 0.001 denote significant difference from zero

Concerning the early long-latency reflex response (LLRe) of the pectoralis, Wilcoxon tests indicated significant goal-directed modulation across both load conditions at all preparatory delays (Fig. 4, middle; N = 16 subjects; Unloaded pectoralis, 250 ms: W = 122, p = 0.003, rrb = 0.80; 300 ms: W = 131, p < 10−3, rrb = 0.93; 350 ms: W = 133, p < 10−3, rrb = 0.96; 400 ms: W = 136, p < 10−3, rrb = 1.00; 450 ms: W = 135, p < 10−3, rrb = 0.99; 500 ms: W = 135, p < 10–3, rrb = 0.99; Loaded pectoralis, 250 ms: W = 123, p = 0.003, rrb = 0.81; 300 ms: W = 136, p < 10−3, rrb = 1.00; 350 ms: W = 136, p < 10−3, rrb = 1.00; 400 ms: W = 133, p < 10−3, rrb = 0.96; 450 ms: W = 125, p = 0.002, rrb = 0.84; 500 ms: W = 127, p = 0.001, rrb = 0.87). However, Friedman tests indicated no significant differences in goal-directed tuning of the pectoralis LLRe among the different preparatory delays, under any load condition (Unloaded: χ24 = 20.1, p = 0.090; Loaded: χ24 = 5.4, p = 0.708).

The late long-latency reflex responses (LLRl) of the pectoralis also showed strong goal-directed tuning across the board, with all relevant Wilcoxon tests yielding W = 136, p < 10−4 and rrb = 1.00 for all preparatory delays under either load condition (see also Fig. 4, bottom). For the LLRl of the unloaded pectoralis, a Friedman test also indicated a significant impact of preparatory delay (Unloaded: χ24 = 27.1, p = 0.028; Loaded: χ24 = 24.5, p = 0.044), with Dunn–Šidák–adjusted post-hoc test indicating a significant difference between the 300 vs. 400 ms delay (p = 0.036) when the muscle was unloaded, and a significant difference between the 300 vs 500 ms delays when the muscle was loaded (p = 0.036). Note that data on the 250-ms delay were not included in these analyses, as elaborated in the Methods section.

Goal-directed modulation of the stretch reflex responses – Anterior deltoid

In contrast to the case of its synergist (pectoralis), Wilcoxon tests indicated no significant goal-directed modulation of the anterior deltoid SLR, at any preparatory delay, regardless of load condition (all p > 0.853; Fig. 5, top). However, significant goal-directed tuning of reflex responses was observed at the long latency epochs. Specifically, when the anterior deltoid was unloaded, there was goal-directed tuning of LLRe responses at all preparatory delays except for 250 and 300 ms (N = 16 subjects; 250 ms: W = 92, p = 0.231, rrb = 0.35; 300 ms: W = 105, p = 0.069, rrb = 0.54; 350 ms: W = 136, p < 10−4, rrb = 1.00; 400 ms: W = 135, p < 10−4, rrb = 0.99; 450 ms: W = 136, p < 10−4, rrb = 1.00; 500 ms: W = 136, p < 10−4, rrb = 1.00). The Friedman test indicated a significant impact of preparatory delay on LLRe responses of the unloaded anterior deltoid (χ24 = 42.5, p = 0.002), with Dunn–Šidák–adjusted post-hoc test indicating a significant difference between the 300 vs. 400 ms delay (p = 0.036), and a significant difference between the 300 vs. 500 ms delay (p = 0.002; Fig. 5, middle). Inspection of Fig. 5 (middle row) indicates a relatively suppressed goal-directed tuning of the LLRe response at the 300-ms delay. For the loaded anterior deltoid muscle, there was goal-directed tuning of the LLRe at all preparatory delays except 250 ms (N = 16 subjects; 250 ms: W = 98, p = 0.141, rrb = 0.44; 300 ms: W = 132, p < 10−3, rrb = 0.94; 350 ms: W = 136, p < 10−4, rrb = 1.00; 400 ms: W = 135, p < 10−3, rrb = 0.99; 450 ms: W = 111, p = 0.033, rrb = 0.63; 500 ms: W = 121, p = 0.006, rrb = 0.78). For the loaded anterior deltoid, however, the Friedman test indicated no difference in the magnitude of goal-directed LLRe among the 300–500 ms preparatory delays (χ24 = 3.9, p = 0.818). A direct comparison of anterior deltoid LLRe tuning magnitudes between the loaded and unloaded conditions for the 300 ms preparation delays did reach statistical significance (N = 16 subjects, W = 111, p = 0.012).

Fig. 5

Goal-directed differences in anterior deltoid EMG for the SLR, LLRe, and LLRl epochs. Grey circles represent the median single-subject EMG values of the group performing 18 blocks, whereas the black circles represent the values of the group performing 13 blocks. Grey background rectangles represent upper and lower quartiles, and thin vertical lines represent the 95% data range. Solid red lines represent the group-level median values. *p < 0.05, **p < 0.01, ***p < 0.001 denote significant difference from zero

Similar to the pectoralis, the LLRl response of the anterior deltoid showed goal-directed tuning across the board, with Wilcoxon tests yielding statistical significance for all preparatory delays under both load conditions (N = 16 subjects; Unloaded anterior deltoid, 250 ms: W = 130, p < 10−3, rrb = 0.91; 300 ms: W = 121, p = 0.004, rrb = 0.78; 350 ms: W = 128, p < 10−3, rrb = 0.88; 400 ms: W = 131, p < 10−3, rrb = 0.93; 450 ms: W = 136, p < 10−4, rrb = 1.00; 500 ms: W = 134, p < 10−3, rrb = 0.97; Loaded anterior deltoid, 250 ms: W = 130, p < 10−3, rrb = 0.91; 300 ms: W = 135, p < 10−3, rrb = 0.99; 350 ms: W = 136, p < 10−4, rrb = 1.00; 400 ms: W = 134, p < 10−3, rrb = 0.97; 450 ms: W = 136, p < 10−4, rrb = 1.00; 500 ms: W = 136, p < 10−4, rrb = 1.00). For the loaded anterior deltoid, the Friedman test indicated no significant differences in goal-directed modulation of the LLRl as a function of preparatory delay (300–500 ms: χ24 = 15.6, p = 0.181). But there was such an effect when the muscle was unloaded (χ24 = 75.9, p < 10−4), with post-hoc analysis indicating significant differences between 300 vs 400 ms delay (p = 0.005), 300 vs 450 ms delay (p < 10−4), 300 vs 500 ms delay (p = 0.012), as well as between 350 vs 450 ms (p = 0.002). Inspection of Fig. 5 (bottom row) highlights that the above primarily reflects a diminished goal-directed tuning of the anterior deltoid LLRl when the preparatory delay was 300 ms.

Goal-directed modulation of stretch reflex responses – Posterior deltoid

For the SLR response of the unloaded posterior deltoid (Fig. 6, top), Wilcoxon tests indicated significant goal-directed tuning at all preparatory delays except for 250 ms (N = 16 subjects; 250 ms: W = 107, p = 0.067, rrb = 0.57; 300 ms: W = 113, p = 0.044, rrb = 0.66; 350 ms: W = 132, p < 10−3, rrb = 0.94; 400 ms: W = 136, p < 10−3, rrb = 1.00; 450 ms: W = 118, p = 0.023, rrb = 0.74; 500 ms: W = 110, p = 0.050, rrb = 0.62). A Friedman test indicated significant differences in goal-directed SLR responses among the preparatory delays of 300–500 ms (χ24 = 38.5, p = 0.004) with post-hoc comparisons indicating a significant difference in goal-directed SLR between the 350 and 450 ms delay (p = 0.036), as well as the 400 vs 450 ms delay (p = 0.036). In contrast to previous findings and the current case of the loaded pectoralis and anterior deltoid muscles, Wilcoxon tests indicated a significant difference in goal-directed tuning of the posterior deltoid SLR, when the muscle was loaded and preparatory delays was 300 ms (W = 136, p < 10−3, rrb = 1.00) or 350 ms (W = 110, p = 0.050, rrb = 0.62). The goal-directed modulation of the SLR at the other preparatory delays was not statistically significant (all p > 0.077). A Friedman test indicated no significant and systematic impact of preparatory duration on the loaded posterior deltoid SLR across the 300–500 ms delays (χ24 = 11.1, p = 0.349). A direct comparison of posterior deltoid SLR tuning magnitudes between the unloaded and loaded conditions for (400 to 500 ms preparation delays) did not reach statistical significance (N = 16 subjects, 400 ms: W = 91, p = 0.189; 450 ms: W = 64, p = 0.590; 500 ms: W = 92, p = 0.189).

Fig. 6

Goal-directed differences in posterior deltoid EMG for the SLR, LLRe, and LLRl epochs. Grey circles represent the median single-subject EMG values of the group performing 18 blocks, whereas the black circles represent the values of the group performing 13 blocks. Grey background rectangles represent upper and lower quartiles, and thin vertical lines represent the 95% data range. Solid red lines represent the group-level median values. *p < 0.05, **p < 0.01, ***p < 0.001 denote significant difference from zero

The posterior deltoid LLRe (Fig. 6, middle row) showed strong goal-directed tuning across the board, with all relevant Wilcoxon tests yielding W > 134, p < 10−4 and rrb > 0.98 for all preparatory delays under either load condition. The Friedman test indicated a significant impact of preparatory delay on posterior deltoid LLRe when this muscle was unloaded (χ24 = 45.9, p = 0.001). The Dunn–Šidák–adjusted post-hoc test indicated a significant difference between the 300 vs. 350 ms delay (p = 0.008), between the 300 vs. 400 ms delay (p = 0.002) and between the 300 vs. 500 ms delay (p = 0.012). Again, visual inspection of Fig. 6 indicates relatively diminished goal-directed tuning of the LLRe when the preparatory delay is 300 ms or shorter. However, when the posterior deltoid was loaded, no significant effect on the LLRe response was found (χ24 = 6.6, p = 0.618).

The LLRl response of the posterior deltoid (Fig. 6, bottom row) also displayed strong goal-directed tuning across all preparatory delays and load conditions, with all relevant Wilcoxon tests yielding W = 136, p < 10−4 and rrb = 1.00. As the case for this muscle’s LLRe, the Friedman test indicated a significant impact of preparatory delay on the unloaded posterior deltoid LLRl response (χ24 = 35.1 and p = 0.007), with post-hoc analyses indicating a significant difference between the 300 ms delay vs. 350 and 500 ms delays (p = 0.036 and p = 0.012, respectively). Again, as the LLRe response, however, the Friedman test indicated no systematic difference in goal-directed tuning of the LLRl when the posterior deltoid was loaded (χ24 = 7.2, p = 0.575).

In summary, Table 1 presents the results for the pectoralis major, anterior deltoid, and posterior deltoid muscles, regarding the minimum observed preparatory delays associated with goal-directed tuning of responses at the three stretch reflex epochs.

Table 1 Shortest preparatory delays where goal-directed tuning of stretch reflexes occurred and facilitation of such tuning with increased preparationOnset of the goal-directed modulation of stretch reflex responses

For the two muscles (pectoralis and posterior deltoid) showing goal-directed tuning of the SLR, we also investigated the onset time of goal-directed discrimination in the unloaded and loaded EMG signals using a sliding ROC analysis (Fig. 7). In addition to onset time, we also investigated the time point at which an ideal observer could discriminate the target position based on the EMG signals. Examples of the AUC values and dog leg fits for the unloaded and loaded (pectoralis and posterior deltoid) muscles with a 400 ms preparatory delay are shown in Fig. 7a–b. From these dog-leg fits, the onset time can be extracted (Fig. 7b), along with the discrimination times for the unloaded and loaded muscles.

Fig. 7

The time onset of SLR modulation with a 400 ms preparatory delay for the pectoralis and posterior deltoid muscles. a The area under the curve (AUC) for the ROC values regarding the unloaded (black solid line) and loaded pectoralis (grey solid line) SLR tuning as a function of target direction. The red solid and dotted lines represent the dog leg fits for the unloaded and loaded pectoralis muscle conditions. b Same as in (a) but for the posterior deltoid muscle. The onset and discrimination times are shown for the unloaded (red solid arrows) and loaded (red dotted arrows) conditions

For the unloaded pectoralis muscle, the onset and discrimination times for the 250–300 ms preparation delays (41–52 ms and 66 ms) appeared later than the 350–500 ms preparation delays (33–36 ms and 57–61 ms) (Fig. 8a). For the loaded pectoralis, there was no such trend, with onset and discrimination times ranging from 45 to 58 ms and 59 to 66 ms, respectively. By taking into consideration the time difference of the onset and discrimination times between the unloaded and loaded conditions, it is evident that for the 350–500 ms preparation delays, both onset and discrimination times are shorter for the unloaded compared to the loaded pectoralis muscle (denoted ‘ ++  ’ in Fig. 8b). In contrast, for the 250–300 ms preparation delays, either onset or discrimination time is longer. Thus, our findings provide support for the goal-directed tuning observed in the top row of Fig. 4 for the 350–500 ms preparation delays.

Fig. 8

The onset and discrimination times for the pectoralis (a–b) and posterior deltoid muscles (c–d). In the top row, the actual times are shown for both the unloaded and loaded muscles. In the bottom row, the time differences (loaded-unloaded) are shown, where ‘ ++ ’ represents when both the onset and discrimination times of the unloaded muscle are shorter than the loaded muscle. In contrast, ‘- -’ represents when both the onset and discrimination times of the unloaded muscle are longer than those of the loaded muscle

In contrast to the pectoralis muscle, the posterior deltoid muscle showed a different trend for the onset and discrimination times (Fig. 8c). For the unloaded muscle, the onset times were 21–39 ms, whereas the discrimination times were 46–60 ms. For the loaded muscle, the onset times were 18–47 ms, whereas the discrimination times were 43–63 ms. The time difference of the onset and discrimination times between the unloaded and loaded conditions revealed that for 300 ms preparatory delay, both onset and discrimination times are longer for the unloaded compared to the loaded pectoralis muscle (denoted ‘- -’ in Fig. 8d). In contrast, for the 350, 400, and 500 ms preparation delays, both onset and discrimination times are shorter for the unloaded compared to the loaded pectoralis muscle (denoted ‘ ++  ’ in Fig. 8d). Thus, these findings for the posterior deltoid muscle provide support for the goal-directed tuning observed in Fig. 6 top row for the 300–500 ms preparation delays.