The effect of transcranial random noise stimulation on the movement time and components of noise, co-variation, and tolerance in a perceptual-motor task

Abstract

There exist numerous factors that contribute to the amplification of errors and complexity in motor processes, among which variability and noise are particularly noteworthy. Transcranial random noise stimulation (tRNS) has been proposed as a potential means of enhancing motor performance by modulating excitability in the motor cortex. This study aimed to examine the role of the concomitant administration of tRNS with training in enhancing the performance measures of movement time, noise, covariation, and tolerance in the acquisition of a perceptual-motor task. This study enlisted a cohort of 30 healthy male adults (mean age: 22.62 ± 3.83 years) who were randomly assigned to three distinct groups. The participants executed the specified motor task during three sequential phases, namely, the pre-test, intervention, and post-test phases. Statistical analyses showed that training with tRNS has a significant effect on noise cost, co-variation, and movement tolerance (p ≤ 0.05). In addition, tRNS improved the function of the sensorimotor wave (p ≤ 0.05). Moreover, the results indicate that tRNS elicited a significant reduction in both spatial error and movement execution time, (p ≤ 0.05). The study’s findings indicate that a mere three training sessions leveraging tRNS may suffice in diminishing the spatial error; nevertheless, a higher number of training sessions is required to alleviate the temporal error.

Introduction

It has been observed that human beings are incapable of replicating a given movement in a precisely identical manner, despite subsequent attempts to do so^1,2. The terminology utilized by scientists in elucidating this occurrence is “variability.” Training has been shown to lead to a decrease in variability in motor performance³ but it never completely disappears, which is partly because of inherent motor noise⁴. The aforementioned factor has been categorized by researchers into three distinctive components, namely, Tolerance (T), Noise (N), and Covariance (C). This division has been facilitated by employing a novel technique to discover structure in data and better measures of variability. The etiology of variability within the sensory system remains conjectural, however, it is hypothesized that it may stem from processes compromised by noise. Consequently, the observed variability is explained by noise⁵. The variability in the movement of various body parts can be attributed to the existence of noise during the different stages of movement production, ranging from the process of detecting the body’s position to the issuance of movement directives^6–8. The presence of disruptions in the neuromotor system encompasses various components, such as receptors, central neurons, motor neurons, muscle fibers, and even various computations that are applied to all these incoming signals⁹.

Previous studies have assessed the postulation that the amplification of inherent noise, or adding extrinsic noise, may act as a directional cue, guiding the learner towards potential solutions that lie within the manifold of available solutions^10,11. Hence, skill cannot, and probably should not, completely suppress noise. Rather, the emphasis should be on reducing the significance of noise so that it does not impede the successful completion of tasks, as supported by relevant literature^12,13. Based on this and according to the hypothesis of psycho-motor efficiency, modification and facilitation of the communication processes of the cerebral cortex leads to the reduction of the complexity of the motor processes, which reduces variability, prevents the occurrence of factors unrelated to the task (such as noise) and adaptability in motor performance¹⁴. Specifically, among experienced performers, motor skill is characterized by the suppression of task-irrelevant cognitive and motor processes (e.g., reduced neuromotor noise). There is evidence that increased sensory motor rhythm (SMR) power may be associated with superior performance, which is characterized by fewer analytic-verbal processes during performance^15,16. Cheng et al.¹⁵ conducted research on SMR activity and skill level, demonstrating that skilled performers execute movements with lower conscious processing, which is reflected by less cognitive involvement.

The findings of research using the TNC approach (tolerance, noise, covariation) showed that variability is the result of noise reduction, not due to velocity reduction³. Instead of focusing solely on “success” as an outcome measure, the TNC approach focuses on how tasks are performed by individuals. In fact, by utilizing this approach, it is possible to understand which aspects of performance should be improved to cater to individual differences. Abe and Sternad¹² demonstrated the three variables of tolerance, noise, and covariation by examining the Skittles throwing task in a simple way, which shows that this framework is able to reveal the underlying processes related to performance improvement and learning. The present study has presented a method that shows how to shape the performance of subjects to minimize the impact of movement variability on movement outcomes by adjusting TCN-Costs.

Behavioral performance depends on the amount of variability in performance and even neural variability that should be reduced¹³. Changes in neural activity in the motor and premotor cortices prior to movement initiation that accompanies the recruitment of motor units can account for approximately half of the variability in velocity and timing of movement^17,18.

There are various methods to increase the recruitment of motor units in order to improve the execution and performance of motor skills¹⁹. Stimulation of motor neurons in the cerebral cortex using transcranial electrical stimulation is one of these solutions. Battaglini²⁰ has shown that tRNS has more excitability compared to other electrical stimulation methods. tRNS is a form of subthreshold electrical stimulation of cortical neurons that induces neural noise by delivering a low-intensity alternating current at random amplitudes and frequencies²¹. Research shows that tRNS may be the most effective method of electrical stimulation of the brain to increase the excitability of the cerebral cortex and thus bring about behavioral changes^22,23. Stochastic resonance explains this behavioral effect, which describes how signal processing in nonlinear systems can take advantage of added noise²⁴.

The primary motor cortex (M1) is the area of the motor cortex where movements are evoked by the lowest amount of electrical stimulation. C3 (in the left hemisphere) located in M1 is one of the three parts of the motor cortex and is responsible for regulating body movements²⁵. The augmentative influence of transcranial random noise stimulation (tRNS) on the excitability of the M1 has been extensively investigated, specifically about motor-evoked potentials (MEPs) that are elicited through the application of transcranial magnetic stimulation²⁶. Research has shown that by stimulating this area, one can witness the precise movement function of the upper limb²⁷. It has been shown that the increase in SMR wave power in this area indicates a high level of learning and low conscious performance^15,28. This wave has a greater range in the states of relaxation, concentration, and immobility. SMR (12–15 Hz) is one of the main indicators demonstrating the level of attention and concentration²⁹.

Therefore, by measuring this wave during training sessions and also using the TNC approach, it is possible to examine the improvement of the movement process caused by electrical stimulation. As a result, we aim to examine the effect of the concomitant administration of tRNS with training in enhancing the performance measures of movement time, noise, covariation, and tolerance in the acquisition of a perceptual-motor task. We hypothesized that increased training sessions and continued application of tRNS would lead to higher SMR activity at C3. We also hypothesized that due to the increase in SMR wave power at C3, a decrease in motor variability (noise, tolerance, and covariance) became visible.

Methods

Participants

Power analysis with G*Power showed that 27 participants were needed for a medium effect size (d = 0.5) and 80% statistical power (1- beta = 0.8), alpha = 0.05. We recruited 33 participants for possible subject attrition, particularly during the Covid-19 pandemic. Two subjects were withdrawn from the study for their failure to attend the sessions regularly and another due to excessive consumption of cigarettes and caffeine during rest between blocks. Therefore, 30 healthy male students (mean age: 22.62 ± 3.83 years) were randomly assigned to three groups (Group 1: Active tRNS + perceptual-motor task, Group 2: Sham tRNS + perceptual-motor task, Group 3: Perceptual-motor task). All the subjects were right-handed. All participants reported having a corrected-to-normal visual acuity and had no documented neurological impairments. Not using female participants was due to limitations, as research has shown the effect of ovarian hormones on task performance and transcranial magnetic stimulation. These studies have shown that the level of cortical excitability in men and women is the same similar only during the follicular phase of the menstrual cycle when progesterone levels are low and Estrogen levels are high^30–33. This quasi-experimental research had a pre-test, acquisition, and post-test design (Fig. 1). All participants gave written informed consent, and they were asked to avoid all sorts of caffeinated substances and recreational drugs within 24 h before their visits. None of the participants reported any major side effects resulting from the stimulation ethical approval was obtained from the ethics committee of Shahid Chamran University (EE/1401.2.24.221896/scu.ac.ir).

Fig. 1.

Experimental design. Group (1) During the pre-test and post-test sessions, the subjects received sham tRNS for a duration of 20 min subsequent to the EEG recording. Following the application of 20 min of active tRNS during the acquisition sessions, the participants subsequently engaged in a period of rest for a duration of 25 min, after which they completed the task in a sequence of 5 training blocks. Moreover, EEG was recorded at the onset of session 4. Group (2) The same protocol was repeated for the Group 2, with the difference that they received sham tRNS during the all sessions. Group (3) The participants of the Group 3, in the pre-test, post-test, and session 4 after EEG recording, only performed 5 blocks of task every day without receiving any stimulation.

Electroencephalogram (EEG)

The participants took part in the pre-test, 6 acquisition sessions, and post-test, respectively (Fig. 1). The Infiniti Procomp5 neurofeedback device and BioGraph Infiniti software (Thought Company, Montreal, Canada) were used to record brain waves (brain activity levels and absolute SMR wave power) at the C3 of individuals, at the beginning of the pre-test session, in the fourth session, and in the post-test session. For this, an electrode based on the 10–20 system of electrode placements was placed on C3, and two electrodes related to the ground and reference electrodes were placed on the left earlobe and the right earlobe, respectively.

Transcranial random noise stimulation

Stimulation was performed with the battery-driven Neurostim2 (Medina Tebgostar Co., Iran). tRNS was a sham in the pre-test and post-test sessions for Group 1 and also in all sessions for Group 2. Sham conditions consisted of 30-sec stimulation at the beginning. The intervention phase for Group 1 consisted of 20 min of active electrical stimulation during the acquisition sessions (Fig. 1). Thus, C3 was stimulated through conductive carbon electrodes (4 × 4 cm), placed in two squared-shaped saline-soaked (9% sodium chloride wash serum) sponges. Also, the reference electrode was extracephalic and was attached to the participants’ trapezius muscle with a special tape. The duration of the 2-mA high-frequency (100_640 Hz) stimulation and offset value of 0 was 20 min. The findings of Yeh et al.‘s research show that the high-frequency range of tRNS, stimulated cortical neural excitability²³, this occurs possibly through the repeated opening of voltage-gated sodium (Na+) channels²¹, and functional stimulus hemodynamic response³⁴. As a result, the neural signal ratio leads to an increase in noise and neural coordination in the stimulated cortex. For Group 1, after receiving the electrical stimulation, the subjects rested for 25 min, then performed the perceptual-motor task. For Group 2, the instructions for electrical stimulation were similar to those of Fertonani et al.³⁵ and Monastero et al.³⁶, including 20 min of sham electrical stimulation. Group 3 did not receive any electrical stimulation. The purpose of creating this group was to investigate the important and beneficial role of training in comparison to tRNS, as Classen et al.³⁷ and Botfish et al.³⁸ measured the role of training in creating continuous plasticity and strengthening neural network connection patterns in the motor cortex³⁹.

Experimental setup

Experiment protocol

The setup is similar to the one used by Cohen et al. [40; 41]. The participants were presented with a circle template (with a radius of 200 pixels equal to 5.291 cm) projected on a monitor (ASUS X455L) placed in front of them (Fig. 2). A dark paperboard impeded the vision of the hand. The sessions were held in the following order and every other day. Subjects performed 10 trials in the pre-test session. Then they finished each acquisition session, which consisted of 5 blocks. And at the end, they did the post-test, which included 10 trials (Fig. 1). It should be mentioned that each participant made 10 trials in each block (1 trial included drawing 20 circles). Since TNC is examined between and within blocks, the horizontal axis of the graphs is given in block order. Therefore, here we must state which session each block belongs to. Blocks 1–5 are the first session of acquisition, and blocks 6–10, 11–15, 16–20, 21–25, and 26–30 are also the second to sixth sessions of acquisition, respectively.

Fig. 2.

Setup. Diagram illustrating the experimental setup. Each subject was presented with a circle template projected on a monitor in front of him at eye level. A black paperboard occluded the vision of the hand. The subjects executed a drawing of a circle, while seated without the support of either wrist, arm, or elbow, in such a way that the only contact with the tablet was made through the pen.

The perceptual-motor task

The participants executed drawings of a circle, using a Genius X608i graphic pen tablet (Report rates: 100 RPS; Resolution 2560 LPI; digital pen-pressure sensitive:1024 levels). This tablet came bundled with Paint.Net, as well as the Pen ToolBar software they were instructed to execute while seated without the support of their wrists, arms, or elbows. This was to make sure that their only contact with the tablet was through the pen. Subjects were told to look at the target circle (on the monitor) and draw it on the graphic pen tablet counterclockwise as fast and as accurately as possible. Before starting the task, each participant was asked whether the instructions were understood. The small red dot indicated the start of the experiment. During execution, the position of the cursor (indicating the position of the pen tip) was visible on the monitor. The software settings (hand-drawing accuracy software, patent number: 93720) were such that a trial was automatically ended when 20 circles were drawn.

Analysis

Circle analysis

To better analyze the drawn circles, and to avoid over calculations, the circumference of the circle was first reduced to 360 points (pixels). After completing each trial, the software calculated the total number of pixels (TP) drawn in the execution space as well as the number of pixels drawn on the circumference of the pattern circle (Acceptable Pixels (AP)). Other software’s outputs included the number of circles, the percentage of acceptable circles, drawing time (with an accuracy of 0.001 s), drawing velocity for each circle, and the average of these variables for each trial. The number of AP was considered as a factor in measuring the performance accuracy of the subjects and the TP as the distance traveled.

Creation of execution space and solution manifold. To better examine the data, first of all, it was necessary to create an execution space (all patterns drawn based on execution variables). For this, a result variable should be determined and compared with the target result (the desired outcome). In the task of drawing a circle, the AP can be easily compared with the circumference of the target circle (360 pixels), so it was determined as the outcome variable. Two execution variables should also be selected so that the relationship between them can be used to quantify the outcome variable. Cause our task is similar to those described in references^{40] and [41}, we conducted pilot studies to identify the appropriate operational variables. As a result, we selected velocity and time per revolution as the execution variables. This allows for the creation of an execution space based on the various combinations of velocity and time, and also, a solution manifold for the combinations yielding zero discrepancies between the circumference of the target circle (360 pixels) and the given combination. The limits of the execution space (X and Y axes) were chosen for a posteriori following the examination of the dataset and were set to maximum values of 0.960 pixels/ms for velocity, and 6040.909 ms for time. In the next step, the APs, which were calculated using combinations of velocity and duration, were determined. A 6040 × 6040 matrix of APs with different duration and velocity combinations have been chosen. Each obtained value was compared with the template circle (360 pixels). The closer the difference value is to 0, the whiter will be the area of the combinations of execution variables in the execution space diagram.

Tolerance, noise, and covariance‑cost analysis

Three components of T, N, and C are used to investigate movement variability⁵. In a new approach, Cohen and Sternad⁴ calculated these three components of variability as costs related to optimal performance. The T-Cost determines how much the result would be improved if the location of the information was optimal, the N-Cost compares the actual results with the optimal scattering results at the same location, and the C-Cost indicates what improvement would be achieved if the data were optimally co-varied. According to the research of Cohen and Sternad⁴, to extract these three costs from a set of data, 10 consecutive trials (each trial was 20 circles), each with two execution variables (duration and speed) and one result variable (acceptable points) have been described, were analyzed as a set. For the calculation of each component, the data were transformed specifically to create another set with optimal results in terms of one component, while other features of the data set remained unchanged. In the following, we will describe the calculation of each of these 3 costs separately.

C-Cost

C-Cost expresses the cost of running a given data set that does not fully utilize the redundancy in the execution space. To estimate the C-Cost for a dataset, an optimal dataset was generated where the mean and distribution of duration and velocities were preserved, while the individual pairs were recombined to achieve the best possible performance. This idealized data set was found with a greedy hill-climbing algorithm in MATLAB, using the pair-wise matching procedure⁴. To implement this, during every 20 attempts (1 block) first, the pairs of durations, d, and velocities, v, were ranked in order from the best to the worst according to the result variable, APi, with i = 1, 2, 3…20. Then, the duration from the worst performing pair d20 was paired with v19, and d19 was paired with v20, i.e., v20 and v19 were swapped; the mean result of d19 and d20 were determined. If the mean result improved over the original d19 and d20, the swap was accepted. In the next step, v20 was swapped with v19, and the resulting mean of AP18 and AP20 was evaluated. If the mean result improved, the swap was accepted. This procedure continued until d20 was paired with v1, i.e., v20 was swapped with v1. After this, the same procedure was repeated with d19. Hence, the batch consisted of 19 × 19 = 361 comparisons. The number of profitable swaps was recorded for each batch. Then, this entire batch of procedures was repeated on the improved set until there were no more profitable exchanges. The algebraic difference between the mean result of the actual data set and the mean result of the optimally recombined set defined C-Cost.

T-Cost

The best trial with the highest average of AP in the appropriate duration was selected in each training session and the difference in its AP was calculated from each of the 10 trials of the blocks of each session. The algebraic difference between the minimum difference and the average AP of these blocks shows the T-Cost.

N-Cost

The cost N is the difference between the result of the initial set and the optimal set. In the present study, the cost of N was calculated as follows: The best circle (with the most AP in the appropriate time) was identified in each trial and the difference in its AP was calculated from each of the 20 circles of the same trial. The algebraic difference between the minimum difference and the average of the AP of the said trial shows the N-Cost. The next diagrams (Figs. 3, 4 and 5) related to Execution space and solution manifold for Group 1, Group 2 and Group 3, respectively were drawn using MATLAB (R2022a) software.

Fig. 3.

Analyzing T-Cost, N-Cost, and C-Cost in Group 1. The orange points are the real data set and the optimized data set is plotted in blue. The smaller the participant’s error in drawing the circle, or in other words, the more accurate the participant is and the more pixels he draws on the circumference of the circle, the whiter the graph will be. The following data sample is related to one person from Group 1 and shown during three sessions. The graphs in the upper row show the data of the pre-test session (early stage). The middle row is the data from session 4 (intermediate stage) and the bottom row is the post-test session (advanced stage) data. The left column shows the real and data optimized in terms of tolerance. The middle column shows the real and data optimized in terms of noise, and the right column shows the real and data optimized in terms of covariation.

Fig. 4.

Analyze T-Cost, N-Cost, and C-Cost in Group 2. The orange points are the real data set and the optimized data set is plotted in blue.

Fig. 5.

Analyze T-Cost, N-Cost, and C-Cost in Group 3. The orange points are the real data set and the optimized data set is plotted in blue.

Statistics

Descriptive statistics methods such as frequency, mean and standard deviation was used to analyze the data. The results of the Shapiro-Wilk test about the SMR wave showed that in all three groups and all stages, the data have a normal distribution. The results of the Shapiro-Wilk test for the noise component showed that this variable does not have a normal distribution in one of the groups, though the difference was small, and the skewness of the data was between + 1 and − 1. After applying the Box-Cox normalization method, the distribution became normal in the tolerance variable, the data did not have a normal distribution. As for the covariance, the data distribution was normal; therefore, for noise and covariance, within-group analysis of variance and one-way ANOVA were used, and for tolerance, Friedman and Kruskal-Wallis tests were used. A p-value of 0.05 was considered and SPSS version 22 software was used for data analysis.

EEG data processing

MATLAB and EEGlab software were used to process EEG data. Also, by using a low-pass filter with a range of 12–15 Hz, removing city electricity noise (50 Hz), using independent component analysis (ICA) and multiple artifact rejection algorithm (MARA), we tried to extract information and remove (adjust) noises in the best way⁴². Then the absolute power of the SMR wave (13–15 Hz) was extracted and analyzed.

Results

Result variable: AP

The results of the Friedman test showed that there are significant differences between the pre-test, acquisition sessions, and post-test in AP. Descriptive statistics showed that the highest average rank in AP corresponds to blocks 16–20 and post-test (AP average 122.15 and 144.00, respectively) and the lowest AP is related to blocks 1–5 and pre-test (AP average 69.85, 86.58 respectively) (Fig. 6). Also, the results of Levene’s test for the difference in the pre-test between the 3 groups show no difference between the groups in the pre-test (p = 0.403). Also, the results of the Friedman tests showed that there is a significant difference in AP between the pre-test, acquisition sessions, and post-test in Group 1 (K2 = 53.267،p = 0.001). In Groups 2 and 3, there was a significant difference in AP between the pre-test, acquisition sessions, and post-test (K2 = 15.727 ،p = 0.028 and K2 = 18.233 ،p = 0.011) (Fig. 6). The results of Kruskal-Wallis tests for the difference in the pre-test, acquisition sessions, and post-test between the three training groups show that there is no significant difference in the pre-test (p = 0.874) and blocks 1–5 (p = 0.842), 6–10 (p = 0.053), and 11–15 (p = 0.065), but from blocks 16–20 (p = 0.004) onwards until the post-test, there is a significant difference between the three training groups, and this difference is growing increasingly bigger (the significance level for the blocks 21–25, 26–30 and post-test session is 0.014, 0.001, and 0.001 respectively). Comparisons of average rank and average AP showed that Group 1 had more significant progress (from 65/7 in pre-test to 171/3 in post-test) than the other two groups. The biggest difference in the average rank between Group 1 and the other two groups was in the post-test (25.40 vs. 10.10 and 11.00) (Fig. 6).

Fig. 6.

Changes in the Acceptable Pixels (AP). For each block, the data from 200 trials were averaged. Participants performed five blocks of trials per day. The AP for each block for 10 participants of Group 1 is shown by blue line, Group 2 is shown by orange line, and Group 3 is shown by gray line. Error bars represent standard deviation.

Execution variables

Duration (Time)

The results of the Friedman test showed that there was a significant difference between the pre-test, acquisition sessions, and post-tests in the execution time (K2 = 71.442, p = 0.001). Descriptive statistics showed that the highest average rank in the execution time was for the pre-test (average execution time 2412 ms) and the lowest execution time was for the post-test (average execution time 1039 ms) (Fig. 7). The Friedman test was used to check the execution time in each group, which showed that there is a significant difference between the pre-test, acquisition sessions, and post-test in Group 1 (K2 = 50.333, p = 0.0001). As can be seen, descriptive statistics show that the highest average ranking in the execution time was related to the pre-test (average running time 2683 ms) (Fig. 7). and the lowest execution time was related to the post-test (average execution time 725 ms). In Group 2, there was no significant difference between the pre-test, acquisition sessions, and post-test in acceptable points (K2 = 12.290, p = 0.091). The results of Kruskal-Wallis tests for the three training groups show that there was no significant difference in the pre-test (p = 0.636) and all the acquisition sessions (p = 0.371), but there was a significant difference between the three training groups in the post-test (p = 0.005). In Group 3, there was a significant difference between the pre-test, acquisition sessions, and post-test in the execution time (K2 = 29.00, p = 0.001), But this difference was not as big as in Group 1 (p = 0.45).

Fig. 7.

Changes of the duration across blocks of practice. The mean results for 10 participants of Group 1 is shown by blue line, Group 2 is shown by orange line, and Group 3 is shown by gray line. Error bars represent standard deviation.

Velocity

The findings showed no difference between the 3 groups in the velocity pre-test (p = 0.062). However, there was a difference between the 3 groups in the post-test (p = 0.0001). Bonferroni follow-up tests showed that Group 1 improved more in the post-test than in Groups 2 and 3 (p = 0.0001) (Fig. 8). However, there was no difference between Groups 2 and 3 (p = 0.601). In addition, Kruskal Wallis tests were used to compare groups on each day and the least difference was observed in the pre-test (p = 0.613), and the largest difference in the post-test (p = 0.0001). During acquisition sessions, the difference has been increasing. In other words, Group 1 had the most improvement in movement velocity (Blocks 1–5 p = 0.272, Blocks 6–10 p = 0.141, Blocks 11–15 p = 0.024, Blocks 16–20 p = 0.002, Blocks 21–25 p = 0.002, Blocks 26–30 p = 0.001) (Fig. 8).

Fig. 8.

Changes of the velocity across blocks of practice. The mean results for 10 participants of Group 1 is shown by blue line, Group 2 is shown by orange line, and Group 3 is shown by gray line. Error bars represent standard deviation.

Cost quantification

The results of Levene’s test for the difference in the pre-test between the 3 groups show no difference between the groups in the pre-test in the T-Cost, N-Cost and C-Cost (F (2, 89) = 0.65, p = 0.52). T-Cost shows the cost to performance of nonoptimal tolerance. For all three groups, T-Cost was the last component to be exploited (Fig. 9A). T-Cost significantly decreased in Group 1, from the block 1 (52.2) to the post-test (11.1), so if the interventions continued, this component would have been less. Also, in Group 2, from the pre-test (65.5) to the post-test (59), and in Group 3, from the pre-test (64) to post-test (53.7), the decrease in T-Cost continued with a very low slope, and compared to Group 1, the decrease was much lower. An analysis of variance with repeated measures was conducted to examine the trend of changes within each group. It was found that, unlike Group 1, the speed changes were not significant for Groups 2 (P = 0.95) and 3 (P = 0.98) from Block 26 to the post-test. In these blocks, participants reached a plateau in execution velocity during these blocks. For all three groups, C-Cost was the first cost that was optimized in the maximum form and started from much lower values (32.2, 31 and 42 for group 1, 2 and 3 respectively) than T-Cost and N-Cost (Fig. 9B and C). C-Cost decreased quite gradually for Groups 2 (from 31.3 in pre-test to 24.3 in post-test) and 3 (from 42 in pre-test to 24.1 in post-test) in all blocks, but its decrease was slightly higher for Group 1.

Fig. 9.

Cost changes of T, C and N during all sessions (including: pre-test, 6 training sessions and post-test) for A: Group 1, B: Group 2 and C: Group 3.

As it is evident in Fig. 9B, C and N-Cost ranked as the most significant contributor to cost for variability and error in Group 2 and Group 3 from pre-test to post test (p = 0.003). Also, N-Cost (p = 0.03) and T-Cost (p = 0.045) ranked as the most significant contributors to cost for variability and error in Group 1. However, T-Cost in Group 1 from block 15 (25.7) onwards (post-test = 16), was contributed the most to errors (Fig. 9A). N-Cost had the highest value in Group 2 in the block 10 (107.1) and the lowest value in Group 1 in the post-test (11.1). Group 1 had a lower N-Cost (65.8) than Group 2 (103.3) and Group 3 (100.2) in pre-test (Fig. 9C) and continued to improve for a longer period to reach similar T-Cost and C-Cost values. Generally, it can be said that in Group 2 and Group 3, N-Cost was higher than T-Cost and C-Cost (p = 0.03), (Fig. 9), which is inconsistent with findings from previous studies where T-Cost decreased as the first cost.

Discussion

Variability and noise are a natural part of the neuromuscular system and can occur at several levels. To better understand the basic processes in acquisition and control of movements, we showed how the study of variability provides a suitable method to better study this phenomenon³. The ability to ascertain the mode of performing a task may enhance the subjects cognitive and metacognitive awareness regarding specific elements of their performance, thereby affording them the opportunity to refine and modify their execution strategies. It also serves to foster a heightened sense of awareness in study participants regarding previously unrecognized performance patterns, ultimately facilitating an improvement in overall performance. Numerous factors have been posited as influencing performance. However, restricting the analysis to achievement alone as a metric of outcome may curtail the capacity to prognosticate the subject’s performance⁴¹.

In this paper, by using the analysis of the TNC approach, we went beyond “how well the task is performed” by examining the differences in the “how to perform the task” between individuals.

There were three major objectives for this study. The first was to investigate the effectiveness of tRNS along with perceptual-motor training on improving variability components (noise, covariation, and tolerance) and movement time in a circle drawing task. The second objective was to use the concepts of Tolerance, Noise, and Covariance, first proposed by Müller and Sternad² to quantify the skill improvement components and formulate them in terms of costs concerning optimal performance. The third objective was to use the new cost analysis to examine the relative importance of different costs and their changes in the pre-test, 30 practice blocks, and the post-test in which the skill was learned and fine-tuned. Although variability and noise are known as factors that disrupt motor control, from a neurophysiological point of view, adding an optimal amount of noise to the subthreshold signal increases the recall of motor units and improves performance⁴³. A common way to add noise is to add it directly to the sensory stimulus through electrical stimulation⁴⁴. In this paper, we intended to measure the process of neuromotor changes in a circle drawing task by adding external noise to the primary motor cortex through tRNS. The analysis of statistical data showed that all three groups succeeded in increasing the power of the SMR wave, but Group 1 experienced a more significant improvement than the other two groups, and as a result, they improved their motor performance and learning more. Consistent with previous studies, we argue that this significant increase in SMR wave power was due to receiving tRNS¹, ⁴⁵, ⁴⁶; ⁴⁷, ⁴⁸. The improvement in participants performance obtained by increasing the power of the SMR wave can be explained by the theory of psychomotor efficiency. Higher psychomotor efficiency is characterized by less interference in neural processes during motor performance⁴⁹. SMR was used to investigate these processes because SMR can reflect the interference of sensorimotor information processing. Cheng et al. research¹⁵ showed that SMR activity is sensitive to the quality of sport performance. Furthermore, the results show that increased SMR power may be associated with superior performance⁵⁰. Superior performance is characterized by fewer analytic-verbal processes during the performance⁵¹. This finding supports the psychomotor efficiency hypothesis as less complex neural networks are shown to have higher SMR power⁴⁹. Reduced motor interference, reflected by increased SMR power, serves as the key to superior performance¹. Also, the results of the current research (however partial) on the effect of training on improving SMR wave performance, as shown by Dimyan and Cohen⁵², can be justified by explaining the neural plasticity that occurs after training. Motor learning is a complex process that occurs in the brain in response to the practice or experience of a specific skill leading to changes in the central nervous system⁵³.

Besides the aforementioned cross-sectional studies, studies have also shown that less activity in C3 and C4 (in the right hemisphere) is observed in expert shooters after training⁴⁶. Genetic, anatomical, physiological, and psychological factors affect the strength and increase of EEG waves basic levels³⁹. Theoretically, valid research benefits are obtained by controlling these factors. Overall, establishing a training protocol is very important because the nature of sports performance is complex. To expand the scope of the beneficial effects of tRNS, a training protocol that can measure and compare results from one study to another is needed.

The findings showed that Group 1, compared to the other two groups, showed greater progress in the acquisition of the perceptual-motor task; which was shown in this research by increasing the AP. According to the findings of the current research that shows a significant increase in AP and also a significant decrease in N-Cost in Group 1 compared to the other two groups, it can be proposed that the reduced noise because of tRNS is the reason for improving participants performance in acquisition trials. This finding is in line with^{20,35,49,51,54–60}, in which the effect of tRNS on reducing noise and variability components and subsequently improving motor performance and learning has been confirmed.

We believe that the observed alignment is probably because of the application of tRNS, which improves cortical excitability and reduces the excitability threshold of neurons, which causes facilitation and neuroplasticity in the stimulated area^28,43. The importance of improving neuroplasticity is that sensorimotor skill learning occurs through the general mechanism of plasticity^61,62. In addition, amplification of synaptic signaling, stochastic resonance^43,63, activation of sodium channels, and induction of long-term potentiation through modification of the N-Methyl-D-aspartate receptor (NMDAR) efficacy^63,64 is likely responsible for the neuroplasticity effects that follow tRNS administration^65–67. Another mechanism is that tRNS, with repeated subthreshold stimulation, causes the sequential opening of sodium channels, which may lead to the temporary summation of small membrane potentials and depolarization of the nerve membrane because of the increase of the inflow of sodium currents and/or preventing the homeostasis of the system^21,35. This may affect M1 excitability. Finally, the effects of tRNS may also be attributed to the increased synchronization of neural firing through the amplification of subthreshold oscillatory activity, reducing the amount of endogenous noise^24,68. Accordingly, even subthreshold stimulation that induces very weak electric fields in the cerebral cortex can modulate membrane potentials^24,69–71.

Two variables duration, and velocity, determine the path of drawing the circle and thus show the accuracy of the drawing. It is a redundant task and defines the successful solutions of a nonlinear multipath^40,41. Analysis of the experimental results showed that all three components T, C, and N were present and all three decreased during training. Group 1 had the best performance and the changes (reduction) in N-Cost and T-Cost were significant in the fifth acquisition sessions until the post-test. Although C-Cost decreased earlier, these 3 components reached almost the same amount in the post-test. These results showed that the ability to change performance is reduced by three paths: by adjusting tolerance, correlation, and noise in execution. Group 1 outperformed the other two groups in reducing the C-Cost. The absence of a significant decrease in the C-Cost in Groups 2 and 3 shows that covariation decreases later and harder than in the other two components. These findings are similar to Cohen and Sternad⁴, in which C-Cost decreased relatively slowly in all groups and remained unchanged when subjects reached a performance plateau. Since C-Cost is considered as a change of strategy in the execution of the movement⁴⁰, the stability of this component indicates the unwillingness of subjects to change strategy and their failure to find the best pair of two execution variables (velocity and time) to achieve the desired result (The most AP on an individual scale).

The results of statistical data analysis show that the C-Cost decreases earlier than the other two components. It was also found that from the fifth session (blocks 16–20) to the post-test session, the T- Cost is clearly much lower in Group 1, which is a sign of the effect of tRNS, but on these acquisition sessions, no significant difference was observed between Group 2 and Group 3. Since the results of the analysis of the first hypothesis showed that N-Cost in Group 1 had a significant decrease compared to the other two groups during the acquisition sessions, this component had the largest decrease compared to T-Cost and N-Cost in this group. Of the special importance of understanding the role of motor noise in performance, it can be mentioned that the value of N-Cost depends on both T-Cost and C-Cost⁴. Further reduction of N-Cost compared to other components is not consistent with the research results of Cohen & Sternad^4,72, because, in all studies based on the TNC approach, it was T-Cost that was reduced as the first component. On the other hand, the non-continuity of reduction in T-Cost in Groups 2 and 3 during blocks 16–20 to blocks 26–30 is in line with part of the research by Cohen et al.^{4,13,41,72,73}.

Similar to previous studies, the results showed that the subjects did not have a desire to increase exploration during the performance because they did not continue to further decrease T-Cost, so subjects did not want to explore the performance space enough (perhaps because of the fear of failure). The continued non-reduction of T-Cost is not consistent with King et al.⁷⁴. One reason for this inconsistency is the difference in the approaches used in these studies. In King et al. research, the assignment used was a single assignment that was based on receiving points after receiving a better result. Getting scores and feedback between trials can allow for details and refinements for the next trial leading to further exploration and possibly changes in strategy. Another explanation for the difference in findings between King et al.⁷⁴ study and this study is that the subjects in the former received feedback about their performance before doing the task, and they knew that the improvement of their score occurred because of modifying one or both execution variables; consequently, they did not change this variable in the next trials. But in the present study, even if the subjects received continuous visual feedback about their performance, they were not given enough instructions to modify the movement to improve their performance. The only instruction given was to perform the movement as quickly and accurately as possible.

Although sensorimotor noise can inadvertently lead to better movement, exploration can be beneficial because the exploration is aimed at improving performance^75–78, and has the property of learning from it, unlike other sources of variability, such as inevitable sensorimotor noise^77–79. On the other hand, exploration in task-irrelevant dimensions might be disadvantageous because it enhances the complication of the learning problem. As the variability enhances in response to an increment in task relevance, the variability might reflect exploration somewhat rather than sensorimotor noise⁷⁹. Sensorimotor noise arises from noise in the perception of a moving target, noise in the execution of a movement, and noise in the planning of the movement⁸⁰. Even though these sources of variability are not pointed at learning, the nervous system may to learn from other sources of variability, then exploration in specific from planning noise⁷⁹.

In short, the results support the idea that the choice of a movement strategy is determined by the individual’s inherent variability. Besides the choice of strategies, the current approach also confirms the duration and manner of learning and differentiates between the paths that participants can take to optimize their scores. Also, understanding the relationships between components can provide interesting insight into changes in variability across exercise. For instance, performers who have reached their physiological limit to reduce motor noise can reduce the impact of that motor noise on their performance (N-Cost) by continuing to optimize T-Cost and C-Cost². Note that Groups 2 and 3 in the current study reported here did not continue to improve tolerance after the first few days of training, whereas the performance of Group 1 participants showed that further improvement in that component was possible.

As observed, there was no significant difference between Groups 2 and 3 in execution time during acquisition sessions. The subjects of Group 1 were able to reduce their execution time significantly better than the other two groups, and Group 2 could not show a significant reduction during the sessions. In addition, Group 3 had a significant decrease in execution time, but compared to Group 1, it experienced a smaller decrease in movement time. Considering that Group 2 was not successful in reducing their movement time, these findings are not consistent with the results of Maurer et al.⁸¹ because they showed that subjects were able to improve their execution time after 100 Skittles training trials. Among the reasons for this inconsistency, we can mention the type of task used in the two studies; in our case, the continuous task of drawing a circle has a completely different quiddity. Additionally, considering that Group 2 failed to significantly reduce its noise and also failed to reduce its execution time, we can acknowledge the reasons for this inconsistency, as shown in various studies^82,83, is the unreduced noise. The unreduced noise causes significant variability in the movement, which can explain the variability in the velocity and execution time well⁵. A certain dispersion in operational variables with poor covariance (not aligned with the solution manifold) may be detrimental to performance, while the same variance at the same location but with good covariance (aligned with the solution manifold) may provide excellent performance⁴.

Conclusion

In summary, the results in the current research indicated a late decrease in time in the perceptual-motor task implying that the execution time needs more training during consecutive sessions to decrease further, and if the training is accompanied by tRNS, perhaps more favorable results will be observed as in Group 1. Also, the results obtained from Group 1 indicate that this group outperformed the other two groups and employed a more effective strategy to reduce movement variability. Since the covariance for all three groups was subjected to the same conditions from the outset and was lower than the other two components, it can be concluded that tolerance and noise are more critical in the current task. Therefore, enhancing these two components may be the most effective strategy for reducing movement variability. However, the role of tRNS in improving participants’ performance should not be overlooked. As demonstrated in previous studies, the results clearly indicated that stimulation at the C3 point helps to diminish motor noise and enhance hand motor performance^15,27,28.

Furthermore, instructing participants to minimize the use of hand joints and to limit the task to wrist movements positively impacted the reduction of movement noise across all three groups. Among other strategies to decrease movement noise and, consequently, movement variability, we can highlight the importance of not focusing on the executing organ and not relying on visual feedback from this organ, as reliance on proprioception⁸⁴ proved to be more beneficial in this movement perception task, because relying on proprioception was more fruitful in this motor perception task.

It is important to highlight not only our work’s novelty but also the research’s limitations, including the small sample size and the absence of female participants. It should be mentioned that a much larger sample size is usually used in research related to brain stimulation. In the current study, this sample size was one of the limitations. As previously mentioned in Sect. 2.1, to ensure equal levels of cortical excitability between men and women, female participants must be in the follicular phase of their menstrual cycle. This requirement posed a limitation, as the testing process for each participant necessitated 13 days. However, factors such as variability in menstrual cycle length and the challenges associated with accurately identifying the follicular phase often extended this duration beyond 13 days. As a result, we were unable to include women in this research. Furthermore, given that this study was conducted during the midst of the Covid-19 pandemic and faced restrictions related to the female dormitory (such as dormitory closures and challenges in traveling to the laboratory for study participation), we were compelled to exclusively recruit male participants. As a result, it is recommended that future researchers address this constraint by including both male and female participants in similar studies.

As a final comment about the method, it should be noted that the quantification of the components is, to some degree, dependent on the chosen coordinate system, i.e., the space of execution variables. Therefore, in future research, by choosing a different task and different execution variables, the quantification of TNC and the subject’s preference in choosing their strategy to reduce variability can be investigated in another way.

Author contributions

Conceptualization, FS. and MD; methodology, FS, MD. software, FS.; validation, MD and ES; formal analysis, MD; investigation, FS. and MD; data curation, FS.; writing—original draft preparation FS, MD and ES; writing—review and editing, FS, MD, and ES. visualization, FS and MD; supervision, MD; project administration. All authors have read and agreed to the published version of the manuscript.

Funding

This study received no external funding.

Data availability

The datasets used during the current study available from the corresponding author on reasonable request.

Declarations

Ethics approval and consent to participate

The study design was developed based on the Declaration of Helsinki and all experimental protocols were approved by Shahid Chamran University of Ahvaz’s Ethics Committee (Approval Code: EE/1401.2.24.221896/scu.ac.ir; Approval Date: 10.06.2022). Informed consent was obtained from all participants.

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.