Supplementary material associated with "Rigid Control of Motor Unit Firing Rates in the Human Tibialis Anterior Muscle Persists during Neurofeedback"

Supplementary material associated with the ar4cle Rigid Control of Motor Unit Firing Rates in the Human Tibialis Anterior Muscle Persists during Neurofeedback Meng-Jung Lee1,2, Patrick Ofner1,2, Hsien-Yung Huang3, Joris Mulder4, Jaime Ibanez5,6, Dario Farina7, Carsten Mehring1,2,8 1 Bernstein Center Freiburg, University of Freiburg, Freiburg im Breisgau, Germany 2 Faculty of Biology, University of Freiburg, Freiburg im Breisgau, Germany 3 Department of Engineering and Design, University of Sussex, Brighton, United Kingdom 4 Department of Methodology and StaFsFcs, Tilburg University, Tilburg, Netherland 5 Centro de InvesFgacion Biomedica en Red en Bioingeniera, Biomateriales y Nanomedicina, CIBER, Zaragoza, Spain 6 BSICoS, I3A and IIS Aragón, Universidad de Zaragoza, Zaragoza, Spain 7 Department of Bioengineering, Imperial College London, London, United Kingdom 8 BrainLinks-BrainTools, University of Freiburg, Freiburg im Breisgau, Germany Supplementary material BF20 BF21 BF10 T1 B1 18 16 1 B2 2.8 10.9 0.26 B3 58 18 2.6 B4 12 44 0.27 B5 97 190 0.5 T2 B1 1.2 x 104 2.3 x 103 5.4 B2 5.4 x 103 71 75 B3 1.4 x 107 93 1.5 x 105 B4 5 x 103 24 210 B5 1.3 x 106 78 1.7 x 104 T3 B1 154 83 1.85 B2 1.5 9.8 0.16 B3 1.7 17 0.09 B4 11 6 1.86 B5 2.2 10 0.22 T4 B1 57 22 2.6 B2 54 2.99 18 B3 97 0.4 230 B4 10.4 2.1 4.9 B5 31 1.9 16 Supplementary Table 1. Bayes factors for the displacement experiment for individual targets and blocks. Supplementary Table 2: Bayes factors for individual participants and targets. See methods section for a more detailed explanation of the interpretation of BF. Evidence for target reach include P23(T2 and T4), P24(T2), P25(T4), P26(T1), P28(T1) and P31(T3). Participant P28 was excluded from the main results analysis due to instability in MU decomposition. Real time difference control with motor unit activities: experimental design and performance evaluation In this experiment, participants were told to play a food delivery game by first moving the cursor in cartoon hand shape over the baseline area (Fig. S1a, white open circle) and hold it there for 1 second (baseline phase) to pick up the delivery (Fig. S1a1). During this phase, the horizontal cursor position was fixed. After the delivery was picked up, the cursor turned from hand to delivery icon, and the trial entered the action phase, during which the cursor was free to move horizontally and vertically. A delivery item was randomly selected in each trial from a pool of six options: cheese, a basket of apples, milk, apple juice, ice cream, and an apple pie. The varied selection of items was used to increase participant engagement. The delivery was only successful if the cursor was held at the target house for 3 consecutive seconds within 30 seconds after the delivery was picked up (Fig. S1a2). Participants were asked to keep both motor units active throughout the trial and keep the cursor around the same vertical position (to not make a drastic change in the exerted force level). Activation of the MUs appeared as two traffic lights on the screen (Fig. S1a; green for active, grey for inactive). The trial ended if both MUs were de-recruited at the same time. In this experiment, rather than altering motor unit firing rates in opposing directions, participants were only required to generate a difference in the firing rates to move the cursor towards the targets (Fig. S1b). Figure S1c shows the activity map of the two control MUs from the same example trial as in Fig. 7c-d in the main text. For the purpose of the analysis, the two MUs were numbered such that MU1 had a lower recruitment threshold than MU2 (see Methods). There was no evidence for a trend of the measured forces across blocks (Fig. S1d, trend-BF10 = 0.5). We employed two metrics to assess performance: success rate and latency. Success rate was computed as the percentage of successful trials within each block. Latency was defined by the time from the beginning of the action phase until successful target reach (cursor hold on target area for 3 consecutive seconds) and thus only computed for successful trials. Our results showed an increase of the success rate from 49% in the first block to 68% in the last block (Fig. 7f in the main text, trend-BF10 >100) in parallel to a decrease in latency from 14 s in the first to 11 s in the last block (Fig. S1e, trend-BF10 = 20). There was strong evidence for a change of the success rate and latency across blocks for T2 but not for T1 (Fig. 7f in the main text for success rate, Fig. S1f, trend-BF10 =0.4 and 76 for T1 and T2), however, there was only anecdotal evidence for a difference in the trends of the success rates (Fig. 7f right in the main text , Bayesian Wilcoxon signed-rank test for trend-BF10 =1.6) and moderate evidence for a difference in the trends of the latencies (Fig. S1f, Bayesian Wilcoxon signed-rank test for trend-BF10 = 8) between the targets. The delivery item had no impact on the success rate (Bayesian repeated measures ANOVA, BFinclusion = 0.26 for delivery item). Supplementary Figure S1. (a) Screen images of the experiment. Participants first controlled the movement of a cartoon hand-shaped cursor moving only along the y-axis to pick up the delivery item (cheese) in the baseline area indicated by a white circle (a1). Participants then had to move the delivery to the target house (a2). (b) Schematic diagram of firing rates of control-MUs during the experiment. Black dots show typical correlated firing patterns observed during force modulation when both control-MUs are active. Firing rates of control-MUs were re-scaled to a similar level so that the activity observed during isometric contraction lied approximately on the diagonal. (c) Firing rate distribution from an example trial. Probability of the activities of the controlled-MUs in one trial using a bin width of 0.6 Hz. (d-e) Force (d) and target reach latency (e) across the 5 blocks (individual participants in gray; mean across participants in red). (f) Same as (e) but separately for targets T1 (left) and T2 (right) (individual participants in gray; mean across participants in color). In (d)-(f) the dash-dotted line reflects the participant whose neural data was excluded (see Methods for details). Modulation of firing rates differences across blocks in the difference control task We examined the firing rates during the baseline and action phases. Note that the firing rates here were adjusted with the gain values. We separately analyzed the sum of the firing rates of the two MUs as well as the difference (𝐹𝑅1−𝐹𝑅2) between their firing rates. In the experiment, the firing rate sum controlled the horizontal cursor position while the firing rate difference controlled the vertical cursor velocity. The firing rate difference, thus, needs to be modulated to move the cursor to the targets. All analyses were carried out separately using the MU firing rates during the baseline and the action phases, as well as the rates during the action phase after subtracting the baseline rates. We found no evidence (beyond anecdotal) for a difference in the sum of the firing rates between the two targets, neither for the action phase nor for the baseline phase nor for the action phase rates after subtracting the baseline rates (Fig. S2, a left: Bayesian Wilcoxon signed-rank test BF10 = 0.84; f left: Bayesian Wilcoxon signed-rank test BF10 = 0.33; k left: Bayesian Wilcoxon signed-rank test BF10 = 1.2). This remained to be the case when analyzing the summed firing rates across blocks (Fig. S2, b: Bayesian repeated measures ANOVA, BFinclusion = 1, 0.13 and 1.2 for target, block and target – block interaction; c: trend-BF10 = 1.3; g: Bayesian repeated measures ANOVA, BFinclusion = 0.4, 0.3 and 0.5 for target, block and target – block interaction; h: trend-BF10 = 0.43; l: Bayesian repeated measures ANOVA, BFinclusion = 0.95, 0.11 and 0.42 for target, block and target – block interaction; m: trend-BF10 = 1.2). For the firing rate difference, there was no evidence for target specificity during the baseline phase (Fig. S2, f right: Bayesian Wilcoxon signed-rank test BF10 = 0.46; i: Bayesian repeated measures ANOVA, BFinclusion = 0.4, 0.6 and 0.3 for target, block and target – block interaction; j: trend-BF10 = 0.3). During the action phase, the firing rate differences were target specific (Fig. S2a right, Bayesian Wilcoxon signed-rank test BF10 = 14.7) and the target specificity increased slightly across blocks (Fig. S2e, trend-BF10 = 40; Fig. S2d, Bayesian repeated measures ANOVA, BFinclusion = 10, 2 and >100 for target, block and target – block interaction) in parallel to the increasing performance (Fig. 7f and Fig. S1f). After subtracting the baseline rates, the firing rate differences remained different between the two targets (Fig. S2k right: Bayesian Wilcoxon signed-rank test BF10 >100) and the target specificity continued to increase across blocks (Fig. S2o, trend-BF10 = 21; Fig. 2n, Bayesian repeated measures ANOVA, BFinclusion = 8.9, 0.25, 2.8 for target, block and target – block interaction). Yet, visually the changes of the rate differences for T1 and T2 across blocks during the action phase (Fig. S2d) are affected by the subtraction of the baseline phase (Fig. S2n). Taken together, these results show that the difference but not the sum of the firing rates of the two MUs was target specific. The target specificity of the firing rate differences increased across blocks in parallel to the performance. Supplementary Figure S2. (a) Difference of firing rate sum (left) and differences (right) between T1 and T2 during action phase. Each filled dot depicts one participant. White dots depict the mean; horizontal lines the median. (b-e) Firing rate sum (b) and differences (d) across 5 blocks for T1 (left) and T2 (right) trials during the action phase. Differences between the targets across blocks for firing rate sum (c) and difference (e). Individual participants in gray; mean across participants in color. Dashed lines depict zero. (f-j) same as a-e but for baseline phase. (k-o) same as in a-e but after subtraction of baseline rates. Supplementary Figure S3. Averaged 𝛥𝐹𝑅1 and 𝛥𝐹𝑅2 separately for each block for the difference control task (dots: individual participants; +: mean across participants). BF20 BF21 BF10 T1 B1 1.1 0.7 1.5 B2 2.5 1.3 2 B3 1.9 1.7 1.1 B4 2.4 0.5 4.4 B5 3.8 0.7 5.2 T2 B1 1 13 0.07 B2 0.16 0.7 0.24 B3 0.19 2.1 0.09 B4 0.14 0.7 0.2 B5 0.18 1.7 0.1 Supplementary Table 3. Bayes factors for difference control experiment for individual targets and blocks. Supplementary Figure S4. Recruitment threshold difference from the two MUs during ramp task and control trials. The filled circles with black edges at the very beginning and end represent the recruitment threshold differences from the ramp tasks conducted before (left) and after (right) the control tasks. The filled circles without edges depict the recruitment threshold differences observed during each trial. Missing data points may be due to either unrecorded data (P8) or the units being already active before the trial began. Robustness Check The robustness of the neuronal analyses was assessed with regard to the exclusion of participants, the removal of data around derecruitment, the recruitment thresholds, and the time window during the action phase. The results from these robustness checks are presented in the next paragraphs. None of these analyses yielded results supporting successful target reach. Inclusion of data from all participants Repeating the analysis of firing rate differences including the data from all participants yielded qualitatively the same conclusions as the results from the selected participants for both the displacement and the difference control tasks. (Supplementary Figure S5, Supplementary Tables 4 and 5). Supplementary Figure S5. 𝛥𝐹𝑅1 and 𝛥𝐹𝑅2 averaged across all blocks from all participants (dots: individual participants; +: mean across participants). Left: displacement control task experiment. Right: difference control task experiment. BF20 BF21 BF10 T1 263 90 2.9 T2 5.9 x 105 266 2231 T3 52 34 1.6 T4 560 12.9 43 Supplementary Table 4. Bayes factors for the displacement experiment including all participants. BF20 BF21 BF10 T1 24.8 1.5 16.7 T2 0.3 3 0.1 Supplementary Table 5. Bayes factors for the difference control experiment including all participants. Rearrangement of 𝑴𝑼𝟏 and 𝑴𝑼𝟐 S2n FR difference across blocks by target during action-baseline BFinclusion= 8.9 for target BFinclusion= 0.25 for block BFinclusion= 2.8 for targetblock interaction BFinclusion= 8.9 for target BFinclusion= 0.15 for block BFinclusion= 2.4 for targetblock interaction BFinclusion= 8.6 for target BFinclusion= 0.07 for block BFinclusion= 1.8 for targetblock interaction S2n T1 / T2 trend-BF10 = 1 / 0.3 trend-BF10 = 0.98 / 0.2 trend-BF10 = 0.8/ 0.18 S2o FR difference T1-T2 across blocks during action-baseline trend-BF10 = 21 trend-BF10 = 18 trend-BF10 = 17 - Delivery items success rate trend-BFinclusion= 0.26 for item trend-BFinclusion= 0.14 for item trend-BFinclusion= 0.06 for item Supplementary Table 11. Bayes factor robustness check with various Cauchy prior scales. For the Bayesian Wilcoxon signed-rank sum test, the prior scales used were: default (𝑟 = 1 √2), wide (γ = 1), and ultra-wide (γ = √2). For the Bayesian repeated measures ANOVA, the priors scales used were: default (γ = 0.5), wide (𝑟 = 1 √2), and ultra-wide (γ = 1) for the fixed effects with the prior scale for random effects set to twice that of the fixed effects. Post Hoc comparison -Target Prior Odds Posterior Odds BF10, U T1 T2 0.414 1.511 3.647 T3 0.414 7118.624 17185.879 T4 0.414 1255.354 3030.692 T2 T3 0.414 711.487 1717.681 T4 0.414 4439.311 10717.446 T3 T4 0.414 0.135 0.326 Post Hoc comparison -Phase Prior Odds Posterior Odds BF10, U Baseline Action 1.000 0.212 0.212 Supplementary Table 12. Post hoc tests from Fig. 3c were conducted in JASP. The posterior odds have been corrected for multiple testing by fixing the prior probability that the null hypothesis holds across all comparisons according to Westfall1. Individual comparisons are based on the Bayesian ttest with a Cauchy prior with 𝑟 = 1 √2. The "U" in the Bayes factor denotes that it is uncorrected. 1 Westfall, P.H., Multiple testing of general contrasts using logical constraints and correlations. Journal of the American Statistical Association, 1997. 92(437): p. 299-306. Supplementary Figures S10–S40 present the decomposition stability analysis for the two control MUs of each participant. Supplementary figures S10–S28 present participants with stable decomposition that were included in the main analysis: S10-19 from the difference control task and S20–S28 from the displacement control task. Supplementary figures S29–S39 present participants from the difference control task that were excluded from the main analysis, and S40 presents the participant from the displacement control task that was excluded from the main analysis. Each figure follows the same format as Supplementary Figure S9, with panels (a–d) displaying data from 𝑀𝑈1 and panels (e–h) from 𝑀𝑈2. A detailed explanation of each subplot can be found in the caption of Supplementary Figure S8. Included participants-difference control b ca d f ge h Supplementary Figure S10 b ca d f ge h Supplementary Figure S11 b ca d f ge h Supplementary Figure S12 b ca d f ge h Supplementary Figure S13 b ca d f ge h Supplementary Figure S14 b ca d f ge h Supplementary Figure S15 b ca d f ge h Supplementary Figure S16 b ca d h fg e Supplementary Figure S22 b ca d h fg e Supplementary Figure S23 b ca d h fg e Supplementary Figure S24 b ca d h fg e Supplementary Figure S25 b ca d h fg e Supplementary Figure S26 b ca d h fg e Supplementary Figure S27 b ca d h fg e Supplementary Figure S28 Excluded participants-difference control b ca d f ge h Supplementary Figure S29 b ca d f ge h Supplementary Figure S30 b ca d f ge h Supplementary Figure S37 b ca d f ge h Supplementary Figure S38 b ca d f ge h Supplementary Figure S39 Excluded participantsdisplacement control b ca d h fg e Supplementary Figure S40