Case Study: Intra- and Interpersonal Coherence of Muscle and Brain Activity of Two Coupled Persons during Pushing and Holding Isometric Muscle Action

Inter-brain synchronization is primarily investigated during social interactions but had not been examined during coupled muscle action between two persons until now. It was previously shown that mechanical muscle oscillations can develop coherent behavior between two isometrically interacting persons. This case study investigated if inter-brain synchronization appears thereby, and if differences of inter- and intrapersonal muscle and brain coherence exist regarding two different types of isometric muscle action. Electroencephalography (EEG) and mechanomyography/mechanotendography (MMG/MTG) of right elbow extensors were recorded during six fatiguing trials of two coupled isometrically interacting participants (70% MVIC). One partner performed holding and one pushing isometric muscle action (HIMA/PIMA; tasks changed). The wavelet coherence of all signals (EEG, MMG/MTG, force, ACC) were analyzed intra- and interpersonally. The five longest coherence patches in 8–15 Hz and their weighted frequency were compared between real vs. random pairs and between HIMA vs. PIMA. Real vs. random pairs showed significantly higher coherence for intra-muscle, intra-brain, and inter-muscle-brain activity (p < 0.001 to 0.019). Inter-brain coherence was significantly higher for real vs. random pairs for EEG of right and central areas and for sub-regions of EEG left (p = 0.002 to 0.025). Interpersonal muscle-brain synchronization was significantly higher than intrapersonal one, whereby it was significantly higher for HIMA vs. PIMA. These preliminary findings indicate that inter-brain synchronization can arise during muscular interaction. It is hypothesized both partners merge into one oscillating neuromuscular system. The results reinforce the hypothesis that HIMA is characterized by more complex control strategies than PIMA. The pilot study suggests investigating the topic further to verify these results on a larger sample size. Findings could contribute to the basic understanding of motor control and is relevant for functional diagnostics such as the manual muscle test which is applied in several disciplines, e.g., neurology, physiotherapy.


Setting
The setting (Figure 1a) was related to the one reported in Schaefer and Bittmann [30]. The subjects were sitting opposite but shifted in a way, so that the measured dominant vertically positioned forearms were directly towards each other. The angles between leg and trunk, arm and trunk, as well as the elbow angle measured~90 • . An interface proximal to the ulnar styloid processes connected the subjects. It consisted of two shells of a thermic deformable polymer material shaped according to the contour of forearms. A strain gauge was located between the shells (model: ML MZ 2000 N 36, incl. amplifier; modified by Co. Biovision, Wehrheim, Germany) in order to record and control the reaction force between the subjects. An acceleration sensor (ACC) incl. amplifier (Co. Biovision, Wehrheim, Germany) was fixed on the strain gauge to detect the accelerations along the longitudinal acting force vector.

Mechanomyographic and Mechanotendographic Recordings
The mechanical muscular oscillations of the lateral head of the triceps brachii muscle (MMGtri) and its tendon (MTGtri) as well as the ipsilateral abdominal external oblique muscle (MMGobl) were recorded using a piezoelectric based measurement system. This included pick-ups for clarinets (MMG-sensors; model: Shadow SH 4001, Co. shadow electronics, Erlangen, Germany) and amplifiers for guitars (Nobels preamp booster pre-1, Co. Nobels, Hamburg, Germany), which turned out to be especially suitable to measure MMG and MTG [63]. The piezo-sensors (sensor head) were fixed using tape (usually applied for adhering electrodes of electrocardiography) on the skin above the muscle bellies (greatest protrusion of the muscle during activity in the setting) and above the tendon at the olecranon fossa. Additionally, adhesive tape was used to attach the cable directly behind the sensor head to avoid probably disturbing cable motions. All MMGs, force, and ACC signals were conducted across an analog to digital converter (14-bit; Co. Biovision, Wehrheim, Germany) and were recorded by the software NI DIAdem 10.2 (Co. National Instruments, Austin, TX, USA) on a measurement notebook (Sony Vaio: PCG-61111M, Co. Sony, Tokio, Japan; Windows 7, Co. Microsoft, Redmond, WA, USA). Sampling rate was 1 kHz.
Brain Sci. 2022, 12, 703 4 of 27 strain gauge was located between the shells (model: ML MZ 2000 N 36, incl. amplifier; modified by Co. Biovision, Wehrheim, Germany) in order to record and control the reaction force between the subjects. An acceleration sensor (ACC) incl. amplifier (Co. Biovision, Wehrheim, Germany) was fixed on the strain gauge to detect the accelerations along the longitudinal acting force vector.

Electroencephalographic Recordings
Two 64-channel EEG-systems (eego™; noise < 1.0 µV rms, resolution 24-bit; Co. ANTneuro, Hengelo, The Netherlands) including a DC amplifier (2 kHz; Co. ANTneuro, Hengelo, The Netherlands) were used to record the EEG of each partner. Waveguard™ original caps (Co. ANTneuro, Hengelo, The Netherlands) with 64 Ag/AgCl electrodes positioned according to the 10/20 international EEG system were fixed on the scalp of the participants (Figure 1b). The ground electrode was CPz. Skin impedances were kept below 10 kΩ and the sampling rate was 1 kHz. The EEG signals were recorded by the eegoTM mylab software package (Co. ANTneuro, Hengelo, The Netherlands). No online pre-processing was applied (data processing see below).
To synchronize the signals recorded with NI DIAdem (MMGs, force, ACC) and the EEG signals, a single button response box was utilized to send a trigger ( Figure 1a) to both recording softwares to mark three time points: start of measurement (trigger 1; prior to force application), start (trigger 2), and end (trigger 3) of the isometric plateau.

Measuring Procedure
The measurements took place at a single appointment in the neuromechanics laboratory of the University of Potsdam (Potsdam, Germany). Both participants were introduced to the setting and procedure and gave their written informed consent. Subsequently, EEG, MMG, and MTG sensors were fixed. Afterwards, each participant performed two MVIC measurements separately. For that, they had to push (PIMA) in the later used measurement position against a strain gauge, which was fixed at a stable abutment. The MVIC of the weaker subject (highest value of two trials) was used to calculate the intensity of 70% of the MVIC for the subsequent interpersonal trials. Measurements without motor task followed, one with opened and one with closed eyes. They were executed simultaneously for both subjects in order to control the EEG signals. Then, the PIMA-HIMA trials were performed. Basically, the subjects adjusted an interpersonal isometric muscle action with their forearms at 70% of the MVIC of the weaker subject and maintained this for as long as possible. Six fatiguing trials were performed. The tasks PIMA and HIMA changed Brain Sci. 2022, 12, 703 5 of 27 alternatingly, whereby partner A started with PIMA and B with HIMA (assigned by coin toss). The partner performing PIMA had to actively generate the force by pushing against the partner's resistance and control the force level via biofeedback (dial instrument). The holding partner should provide a stable resistance ("wall") and should just react to the applied force of his partner in an isometric holding manner (HIMA). He received no visual or acoustic feedback. The fatiguing trials ended either if one partner suddenly stopped the resistance (decline in force) or if the forearms deviated more than 7 • from the starting position. Three trials in which A performed PIMA and B HIMA (A-PIMA_B-HIMA) as well as three trials in which B performed PIMA and A HIMA (B-PIMA_A-HIMA) were executed in an alternating manner. Resting time between the trials was 120 s. The six fatiguing, the MVIC, and the opened eyes trials were considered for evaluation.

Data Processing
All raw data (EEG, MMGs, force, ACC) of the fatiguing PIMA-HIMA trials were cut from trigger 2 to trigger 3, which refers to the isometric plateau at 70% of the MVIC. The cut EEG raw data were transferred to NI DIAdem to unite the EEG signals with the other ones in one data set for further processing. All signals were checked for quality. The signal-to-noise ratio (SNR) is excellent for MMGs and ACC signals-as always seen by utilizing the above-mentioned measurement system. The unfiltered EEG signals showed a very low SNR, which seems to be usual for EEG [64][65][66]. Therefore, the online filtering is commonly applied. Nevertheless, firstly, the unfiltered EEG signals were visually investigated concerning possible faulty signals, which were never present. Independent component analysis (ICA) was not applied due to the known uncertainty of ICA, which may "influence the underlying EEG signal with a real data set" [67]. Artifacts as eye-blinks were seldomly present only in a few EEG channels. The duration of trials used for coherence analysis was considerably long so that those artifacts would not have a major effect on the outcome of coherence regarding the entire trial. Since eye-blinks did not appear simultaneously between the partners the interpersonal coherence would have been even worse. Moreover, the EEG signals were averaged (see below) and, therefore, the minor occurred artifacts were levelled. The signals of the used MMG measuring system usually do not need pre-processing. Since this investigation considered, inter alia, MMG-EEG coherence, all signals had to be processed identically. Therefore, the common filtering approach for EEG was applied for each signal. Hence, all signals (EEG, MMGs, ACC, force) were filtered using a Notch-Filter (49-51 Hz) and a bandpass filter (Butterworth, Hamming window, window width 25) from 0.016 to 256 Hz according to [68]. Furthermore, the signals were down-sampled from 1000 Hz to 250 Hz. Subsequently, the drift was removed by subtracting the highly filtered signals (Butterworth, filter degree 10, cutoff frequency 1 Hz) from the previously filtered signals. In doing so, the signals were pulled down oscillating around zero. This is necessary for wavelet coherence analysis to avoid leakage effect. Other filtrations were not applied since for wavelet coherence analyses, ideally raw signals should be used. Regarding EEG, there are different partly complex approaches for channel selection depending on the application [69]. Since the present investigation differs clearly from common ones, we decided to basically use an approach suggested by Ernst [70]. She averaged different EEG channels according to 17 anatomical brain regions [70]. We defined ten brain regions (Table 1, named sub-regions in the following). For that, the channel selection was supported by examining the coherence wavelet of each of two different adjacent channels (intrapersonally). Thus, the brain sub-regions were grouped by considering the intensity of coherence of those channels. In case they showed high coherence over the whole duration, they were combined. In case of lower coherence, the channel was excluded from the sub-region and another sub-region was defined. The EEG channels were then averaged according to those ten defined sub-regions (Table 1). The isometric plateau of the signals of MVIC trials was cut, too. In case it was shorter than 3 s, the starting point was shifted to the force increase, so that at least a duration of 3 s was gained. This is necessary for the wavelet coherence analysis. The data processing was identical to the above-mentioned one. The same applies for the opened eyes trials (OpEy), in which the whole duration was used.
For wavelet coherence analysis, the ten EEG sub-regions, the six MMGs as well as the force and ACC signals were included. Exemplary signals are given as Supplementary Materials ( Figure S1).

Wavelet Coherence Analysis
The wavelet coherence analysis was performed using a script programmed in Python (Python Software Foundation, Beaverton, OR, USA), which was compiled in cooperation with the Department of Applied Mathematics, University of Potsdam (Prof. Matthias Holschneider, Dr. Hannes Matuschek) and was used previously [30]. The wavelet coherence enables statements about two non-stationary signals and shows the degree of coherence in specific frequency bands in the course of time [30,31]. This was utilized here to estimate the interaction of the respective signals intra-and interpersonally (EEG sub-regions, MMGs, ACC, force).
The wavelet coherence Coh g [s x , s y ] [71] of two time series s x and s y was estimated by where CS stands for the cross spectrum defined by  [31]. The variance of the cross-wavelet estimator and, therefore, also the coherence wavelet estimator can only be reduced on the cost of increasing bias [73]. In order to separate 7 of 27 spurious from significant coherence patterns, a point-wise significance test using surrogate data was implemented in the Python script. A detailed description of the algorithm can be found in Maraun et al. [73]. The frequency borders were defined from 3 to 30 Hz.
For two time series, always one Excel (IBM Microsoft Office, Co. Microsoft, Redmond, WA, USA) and one png file resulted from the wavelet coherence analysis. The Python script bordered the significant coherence patches in the plot (α = 0.05) and extracted the following values in an Excel file: (1) duration of the whole time series (s); (2) number of patches (n); (3) minimal and maximal time points of each patch (s) (refers to the start and the end of each patch); (4) total duration of each patch (s); (5) minimal and maximal frequency of each patch (Hz); and (6) frequency range of each patch (Hz).

Coherence Parameters of Wavelet Coherence Analysis Used for Statistical Evaluation
A second Python script was programmed to extract the following parameters of the Excel files which resulted from the wavelet coherence analysis: 1.
Sum5PaD (%): The duration (s) of the five longest significant coherence patches in the frequency range of 8 to 15 Hz were added and this sum was related to the whole duration time (s). Hence, this parameter stands for the ratio (%) of the summed duration of the five longest coherent patches to the total duration time in the respective frequency range. The frequency band of 8-15 Hz was chosen since muscular oscillations are known to be located at~10 Hz. A value >100% could appear due to the summation of the duration of the five longest significant patches, which might overlap because of different frequencies.

2.
WFreq (Hz): This parameter refers to the time-weighted average of the frequency of the five longest significant patches in the frequency range of 8-15 Hz. It should give an impression of the frequencies in which the patches were located. Some considerations included additionally the WFreq of the five longest coherence patches in the frequency range of 3 to 25 Hz.
The frequencies are located in the classical alpha band (~8-14 Hz). However, according to Pfurtscheller and Lopes da Silva [74], we suggest not clearly distinguishing between the bands because clear overlaps arose.

Statistical Comparisons
Statistical comparisons were, inter alia, performed between real vs. randomly matched signal pairs. This is necessary because randomly matched signal pairs also show significant coherence patches and it is not clear if the patches of real pairs are based on true coherence resulting from the interaction [30]. For the randomly matched signal pairs, the wavelet coherence was also calculated as described above. Thus, two signals were randomly selected out of different measurements. Hence, each possible signal pair (in total 378, see above) was gathered out of different measurements for random pairs.

Real vs. Randomly Matched Pairs
For the statistical comparisons, firstly, the real (AB_IMA) and the randomly matched pairs (rand) were examined regarding possible differences concerning both coherence parameters (Sum5PaD, WFreq) without the consideration of the motor tasks (PIMA vs. HIMA). The applied statistical tests are given below. In general, the EEG sub-regions were combined into three regions: EEG central (EEGcen), EEG left (EEGle), and EEG right (EEGri) for statistics ( Table 1). The values for statistical comparisons were obtained as described in the following (concrete examples are given in Appendix A).
Intrapersonal. For intrapersonal considerations, the values of Sum5PaD or WFreq of all signal pairs of each partner were considered intrapersonally (MMGs, EEG sub-regions).
For that, the values of the respective parameter of one participant of all trials of each configuration (A-PIMA_B-HIMA and B-PIMA_A-HIMA) were averaged. The obtained values of A and B were averaged again (AB_IMA). Hence, all values of A and B regarding one intrapersonal region combination were averaged to receive the respective arithmetic means (M) for statistical comparison (for example, see Appendix A). This was done for each of the ten region combinations (intra-MMGs, intra-EEGcen, intra-EEGle, intra-EEGri, intra-EEGcen-EEGle, intra-EEGcen-EEGri, intra-EEGle-EEGri, intra-MMGs-EEGcen, intra-MMGs-EEGle, and intra-MMGs-EEGri). Additionally, the coefficients of variation (CV) of the averaged values of each region combination were calculated by dividing M by the standard deviation (SD).
For force and ACC signals, the parameters Sum5PaD or WFreq were averaged similarly over the three trials, but separately for A and B. Thus, the values of A and B were not averaged again but considered together in one group because of the otherwise resulting low sample sizes of n = 3 or 4.
Interpersonal. A similar procedure was applied for interpersonal region combinations. The values of Sum5PaD or WFreq of all interpersonal signal pairs (MMGs, EEG sub-regions) were considered. For each possible region combination (Table A1), the values of the three trials of A-PIMA_B-HIMA and of B-PIMA_A-HIMA were averaged. Subsequently, the M of those two averaged values were calculated (for example, see Appendix A). Those were used for statistical comparisons between real and random pairs classified according to the ten-region combination (inter-MMGs-MMGs, inter-MMGs-EEGcen, inter-MMGs-EEGle, inter-MMGs-EEGri, inter-EEGcen-EEGcen, inter-EEGle-EEGle, inter-EEGri-EEGri, inter-EEGcen-EEGle, inter-EEGcen-EEGri, and inter-EEGle-EEGri). In the following, the coherence parameters of same region comparisons will be named MMGs (=MMGs-MMGs), EEGcen (=EEGcen-EEGcen); analogues for EEGle and EEGri. Additionally, the CVs of the averaged values of each region combination were calculated.
Further comparisons. The same procedure was used for the parameters Sum5PaD and WFreq comparing the real AB_IMA vs. MVIC trials, which were performed during single measurements by pushing against a stable resistance (PIMA). Therefore, the intrapersonal coherence of MVIC measurements were based on real comparisons. In contrast, the interpersonal comparisons of MVIC reflect randomly matched trials. They include the same motor task, but without coupling between the partners. This consideration was performed to get an impression of whether inter-brain coherence during real coupled interpersonal measurements differed from non-coupled measurements with motor task.
The Sum5PaD of interpersonal EEG-regions were furthermore compared between the measurements with real isometric muscle interaction (AB_IMA) and the trial with opened eyes without muscular action (OpEy). This was considered because it seems to be conceivable that EEG activity might regularly show coherent phases during any kind of muscular activity. That is why the task of muscular activity should be eliminated for regarding the coherence of interpersonal EEGs.
Normal distribution of all data sets was checked by the Shapiro-Wilk test. The group comparisons between real vs. random (AB_IMA vs. rand), real vs. MVIC, and real vs. OpEy were performed by t-test for paired samples for parametric data and by Wilcoxon signed rank test for non-parametric data. The effect size was determined by Cohen's d z = |MD| SD MD for paired t-test, where MD is the mean difference of the respective values of each group and SD MD its standard deviation. The effect sizes were interpreted as small (0.2), moderate (0.5), large (0.80), or very large (1.3) [75,76]. For the Wilcoxon test, the effect size was calculated by r = z √ n .

Comparisons between Pushing (PIMA) vs. Holding Isometric Muscle Action (HIMA)
The second objective of the pilot study focused on the investigation of the motor tasks PIMA and HIMA. The parameters Sum5PaD and WFreq were compared between PIMA and HIMA by uniting the data of the trials of both partners, in which the partners performed either PIMA or HIMA. For that, the M of the three trials were calculated for Brain Sci. 2022, 12, 703 9 of 27 A and B, respectively. For intrapersonal comparisons or for comparisons including ACC or force, the signals of the partner either performing PIMA or HIMA could be clearly distinguished and, therefore, a clear differentiation between HIMA and PIMA was possible. For interpersonal comparisons, a problem arose since in each trial either partner A or B performed PIMA or HIMA, respectively. Hence, each motor task was present concerning the coherence of the signal pairs. To sharpen the comparisons of the data sets, the M of the values of the respective parameters were calculated by the combination of the signal regions of A (or B) towards all signal regions of B (or A) (for a concrete example, see Appendix A).
The data sets of PIMA and HIMA were checked for normal distribution utilizing the Shapiro-Wilk test. In case of normal distribution, a t-test for paired samples was executed for interpersonal comparisons; for non-parametric data, the related samples Wilcoxon signed rank test was performed. Effect sizes were calculated as described above. For intrapersonal comparisons, the group of MVIC was included into statistical comparisons since they also reflect a PIMA. Therefore, an ANOVA for repeated measurements (RM ANOVA) was executed. In case, Mauchly's sphericity was not fulfilled, the Greenhouse Geisser correction (F Green ) was applied. The effect size of RM ANOVA was given by eta-squared (η 2 ).
All statistical comparisons were performed in IBM SPSS Statistics 27 (IBM, Armonk, New York, USA). The significance level was α = 0.05. A large number of comparisons resulted. Due to the explorative character of this preliminary study, we accepted the problem of multiple testing as was suggested by several authors [77][78][79].

Real vs. Randomly Matched Pairs
As the exemplary plots illustrate (Figure 2), the real in contrast to random signal pairs showed large significant patches with high coherence, except for MMGtri_B-TLle_B. The latter also exhibited a large number of significant patches with high coherence, but they were rather short. The different time axes in Figures 2 and 3 for real and random pairs resulted because evaluating the wavelet coherence for random pairs required the same durations of the trials. Therefore, all trials had to be cut to the shortest measurement (~19 s).

Discussion
This preliminary pilot study investigated the wavelet coherence of electrophysiological brain and mechanical muscle activity intra-and interpersonally during muscular interaction of two persons. To the authors' knowledge, it was the first investigation on this topic. The major objectives were, firstly, to examine if real interpersonal synchronization can basically arise (real vs. random pairs); secondly, if differences between two isometric motor tasks HIMA and PIMA occur. Due to the small sample size, the results have to be interpreted with caution and it is naturally not sure if those will be verified in a larger sample size. Nevertheless, the provided data of this case study should give first hints on the topic of interpersonal muscle-brain-coupling during muscular interaction.

Limitations
The major limitations are the sample size (n = 2) and the number of statistical comparisons. Due to the explorative character, we accepted the latter without adjustments according to [77][78][79]. Especially the inter-muscle-brain and intrapersonal coherences showed high significances comparing real vs. random pairs with very large effect sizes so that a multiple testing effect seems not to be likely. However, the large effect sizes are presumably resulting from the small sample size and cannot lead to meaningful conclusions. Therefore, the results can only be interpreted as first indications at this point.
The data processing might show limiting factors. Regarding methodological considerations, the approach of averaging adjacent channels seems to be appropriate. The Sum5PaD and WFreq values were averaged again which resulted in three EEG-regions for statistical comparisons. Thereby, potential effects might have been obscured. The non-existence of clear patterns regarding the coherence of EEG sub-regions (except for above-mentioned ones) might reflect a highly variable inter-and intraindividual EEG expression. Moreover, for MMGs, it might be advisable to separate the MMG of abdominal external oblique muscle from the MMG/MTG of triceps muscle and tendon, since they showed clearly different coherence patterns.
Another limitation has to be mentioned regarding MVIC vs. AB_IMA comparisons, which are based on different force states and intensities, which might have influenced the coherence characteristics.
The findings must be interpreted as preliminary. However, they justify further examinations based on a larger sample size. Some results were so clear and consistent that we interpret them as non-coincidental. However, it is naturally not clear if they will be verified in a larger sample size. Based on the assumption they would be verified in a larger sample size, first neurophysiological consideration on that topic should nevertheless be presented in the subsequent discussion.

Advantages and Disadvantages of Electroencephalography
EEG is a commonly used method for assessing brain activity because of the high temporal resolution, non-invasive, ease of use, and safety [64][65][66]. Disadvantages are a low SNR, low spatial resolution, and the sensitivity regarding muscular activity in the head region as well as concerning heart rate and power line interfaces [64][65][66]. The low spatial resolution is considered as the main disadvantage [80]. The received signal is "the sum of the electric field (in the direction perpendicular to the scalp) that is produced by a large population of neurons" [64]. Therefore, EEG "does not allow researchers to distinguish between activities originating in different but closely adjacent locations" [64]. The EEG is considered to show "spatial blurring" and is regarded as a "low spatial filtering of the cortical potential distribution" [80]. High resolution EEG enhances the spatial resolution [80]. However, due to this limitation of EEG, the interpretation of brain activity in specific locations seems to be difficult. Therefore, the approach of averaging adjacent channels seems to be appropriate.

Corticomuscular Coherence during Coupled Isometric Interaction
Intra-and interpersonal muscle-to-muscle coherence of mechanical oscillations during isometric interaction of two partners was shown previously [30][31][32]. The presented results support those findings: all MMG comparisons between real vs. random pairs differed significantly with very large effect sizes (d z = 1.5-10.5). The large coherence patches are interpreted as synchronization of the myotendinous oscillations during personal interaction, which can only arise if both neuromuscular systems are able to adapt to each other. This coupling must be controlled by central processes; therefore, a coherence of inter-musclebrain and inter-brain activity is conceivable. This case study should especially provide a first impression of inter-brain and inter-muscle-brain coherence in such a setting of two muscularly interacting persons. It should again be stated that the discussion has to be interpreted with caution having in mind that only two persons were investigated. However, the results were very clear for inter-muscle-brain coherence comparing real vs. random pairs (d z > 2.31). This indicated the brain of one partner was able to synchronize to the partner's mechanical myotendinous oscillations in the sense of coherent behavior. We suggest that this inter-muscle-brain synchronization reflects a specific facet of sensorimotor control during interaction with another oscillatory neuromuscular system. The brain of partner A (or B) is receiving and reacting to the sensorimotor input of partner B (or A). This finding was further supported by the significantly higher coherence of force/ACC vs. EEG for real vs. random pairs (d z = 1.31-3.68, r = 0.81).
Worth highlighting is the significantly higher inter-vs. intrapersonal coherence of corticomuscular activity ( Figure 6). The 95%-CIs were clearly disjointed for all regions. This was not expected since the muscle and brain of one person belong to one neuromuscular system. However, the intense coherence between both partners indicates for this case example that both systems can unite to one joint system during interpersonal motor task with a high connectivity between the partners' muscles and brains. This reflects a higher demand of sensorimotor control for interpersonal than intrapersonal muscle-braininteraction. The significances and effect sizes of Sum5PaD and its CV between real and random pairs were very clear reflecting a substantial difference, which is interpreted as non-coincidental despite the case study character. case example that both systems can unite to one joint system during interpersonal motor task with a high connectivity between the partners' muscles and brains. This reflects a higher demand of sensorimotor control for interpersonal than intrapersonal muscle-braininteraction. The significances and effect sizes of Sum5PaD and its CV between real and random pairs were very clear reflecting a substantial difference, which is interpreted as non-coincidental despite the case study character. Due to the novel approach, investigations of other researchers do not exist to our knowledge. Some studies considering only one person are related. The beta band activity of brain areas (EEG/MEG) were connected to voluntary motor activity (EMG) [9,[19][20][21][22][23][24][25][26][27][28]. The present findings of corticomuscular coherence intra-and especially interpersonally suggest that motor activity is also strongly characterized by lower frequencies (alpha band). Salenius and Hari suggested that a "sensory feedback loop is not necessary for the generation of corticomuscular coherence" [25]. Our results, nevertheless, showed enhanced corticomuscular coherence under the condition of interpersonal interaction. It must be accompanied by intense sensory inputs during the adjustment to the motor action Due to the novel approach, investigations of other researchers do not exist to our knowledge. Some studies considering only one person are related. The beta band activity of brain areas (EEG/MEG) were connected to voluntary motor activity (EMG) [9,[19][20][21][22][23][24][25][26][27][28]. The present findings of corticomuscular coherence intra-and especially interpersonally suggest that motor activity is also strongly characterized by lower frequencies (alpha band). Salenius and Hari suggested that a "sensory feedback loop is not necessary for the generation of corticomuscular coherence" [25]. Our results, nevertheless, showed enhanced corticomuscular coherence under the condition of interpersonal interaction. It must be accompanied by intense sensory inputs during the adjustment to the motor action of the counterpart, especially during the holding task, since the participant must react and adapt to the force input of the partner performing PIMA.
We assume the significantly higher inter-muscle-brain vs. intra-muscle-brain coherence might be a result of this sensorimotor regulation and the complex control mechanisms during muscular interaction of two persons, indicating that there is a higher amount of inter-muscle-brain than intra-muscle-brain coordination during personal interaction. The joint rhythm can only arise with a kind of clock generator, which has to be located in central structures. The olivocerebellar circuitry was suggested to undertake a decisive role in temporal-spatial processing, whereby the cerebellum is considered as the most relevant sensorimotor structure [81][82][83][84][85]. Furthermore, the supplementary motor area and the premotor cortex are involved in temporal processing of motor activity [86][87][88]. We assume that other central structures, such as the thalamus, the cingulate cortex, and the basal ganglia [85,[89][90][91][92][93][94][95][96][97], are participating during the execution of such a complex interpersonal motor task. Intrapersonal corticomuscular coherence already has to be based on complex control processes; an interpersonal one must entail even higher regulatory demands. The ability of both neuromuscular systems to generate a mutual rhythm of mechanical muscle and electrophysiological brain oscillations in this case reflects the tremendous capacity of neuromuscular systems regarding their dynamic adaptability. Such interactions actually require two properly functioning regulatory systems. In turn, it seems to be conceivable that such a fragile oscillating dynamic equilibrium could easily be interfered with by impairing influences. It was previously shown that during muscular interaction in the sense of the Adaptive Force (AF) assessed by a manual muscle test (MMT), which tests the holding capacity of a person, mutual oscillations appear in stable neuromuscular systems, whereas in impaired ones, oscillations are missing [51][52][53]. This might reflect the oscillatory coherence in undisturbed interacting neuromuscular systems. During MMT, the participant has to adapt in an isometric holding manner to an external increasing force application of the examiner (PIMA) [50][51][52]. Hence, a similar task exists compared to the here presented one. Gaining information on brain activity during such muscular interactions between two persons might help understanding the underlying neuromuscular control processes in case of an impaired holding capacity. Furthermore, Parkinson patients showed altered patterns of mechanical muscle oscillations already in premotor stages, especially by pushing the hands against each other, thus interacting with oneself [98,99]. It can only be assumed how a personal muscular interaction would be characterized in such cases.

Comparison of Holding and Pushing Isometric Motor Tasks (HIMA vs. PIMA)
Regarding intrapersonal coherence, only partner B showed significantly higher coherence during HIMA vs. PIMA for MMG-EEGle (d z = 1.95), MMG-EEGri was close to significance (p = 0.079). If there are generally intrapersonal differences or if this might be a sign that partner B executed the motor tasks in a better way than A remains open. It could still reflect an incidental finding but is assumed to be an actual effect because of the high effect size and the appearance of the finding regarding EEGle. EEGle should reflect the motor task with the right arm more pronounced than EEGri. Regarding the sub-regions, it was visible that Sum5PaD of intra-AFle-POle was higher during HIMA vs. PIMA in both participants (63.08 ± 10.98% vs. 38.88 ± 17.00%). If this would hold true in a larger sample size, it could indicate that HIMA needs a higher amount of synchronization in specific brain areas.
The inter-muscle-brain synchronization (MMG-EEGcen; MMG-EEGle) was significantly higher during HIMA vs. PIMA. MMG-EEGri showed no significant difference between both tasks. The highest significance was present for MMGs-EEGle, which again might reflect the motor task performance with the right arm [100]. Nevertheless, EEGri seems to occupy a special role during this personal interaction due to the higher interbrain coherence comparing real vs. random pairs. Still, this might not characterize the HIMA-PIMA tasks, but the interpersonal muscle action in general.
The higher coherence for inter-muscle-brain during HIMA vs. PIMA, but not for inter-brain or intra-muscle-brain in this case example might indicate that HIMA probably requires higher sensorimotor control processes between the brain of one partner and the muscles of the other one during such a coupled motor task. During PIMA, the participants initiated the force application but did not have to react as intensely to the partner's input as during HIMA. It was hypothesized previously that HIMA might involve control strategies related to eccentric muscle action and PIMA rather those of concentric contractions [60][61][62]. The higher requirements for motor control processes during eccentric muscle action are secured [101][102][103][104]. The presented findings of a higher inter-muscle-brain coherence might support the hypothesis that control strategies during HIMA are more complex and, therefore, are probably related to neural processes during eccentric actions. That HIMA might be controlled by more complex neuronal control processes is furthermore supported by findings concerning the AF. The execution of AF is based on HIMA in reaction to a varying external load. It reflects the adaptive holding capacity of the neuromuscular system. In previous studies, the AF was assessed by the above-mentioned MMT. The maximal isometric AF was reduced by perceiving negative stimuli as unpleasant food imaginations or odors and, hence, was interpreted to be more vulnerable than PIMA [51][52][53]. This might reflect the more complex control circuitries in central structures during HIMA vs. PIMA, in which other inputs are also processed, e.g., emotions. It is known that central structures processing emotions are also relevant for motor control [85,90,91,96,105,106] and, hence, emotions can influence the motor output [96]. HIMA might be especially suitable to investigate the effect of negative stimuli (e.g., emotions, nociception) on the motor output. The higher coherence of inter-muscle-brain coherence during HIMA vs. PIMA in this case example might be a first neuroscientific hint for a more complex adjustment of muscle and brain activity during holding actions.
The significantly lower WFreq in 3-25 Hz of inter-brain coherence (EEGle-EEGcen, EEGri-EEGcen) during HIMA vs. PIMA (d z = 4.71, d z = 1.10) might also reflect further possible differences between both motor tasks for inter-brain synchronization. It was not expected to find significant differences regarding the frequency between HIMA and PIMA since they were missing in previous studies regarding muscular activity. The amplitude variation, frequency, and power distribution rather showed differences [58,60,61]. Investigating those parameters for EEG could lead to further insights regarding both motor tasks. However, the frequency might be an important parameter investigating inter-brain synchronization comparing HIMA vs. PIMA. Indeed, the findings of this case study are not appropriate to make any conclusions on this topic, but they might point out that it could be worthful to include the frequency consideration in further examinations.

Inter-Brain Synchronization as an Epiphenomenon?
As mentioned in the introduction, inter-brain synchronization is especially investigated during joint guitar playing [44][45][46] or social interactions [33][34][35]49]. During joint guitar playing, each subject perceives the same acoustic input [44,46,107]. Inter-brain couplings were also present if one participant played guitar and the other one listened, indicating the acoustic input already provokes an inter-brain synchronization [46]. Furthermore, proprioceptive and tactile inputs as well as motor action happen simultaneously during guitar playing, which could trigger mutual EEG patterns. Therefore, the reasonable criticism arose if inter-brain synchronization in such settings just occurs due to the perception of the same stimuli and, hence, reflects an epiphenomenon [47,48]. From our point of view, the here performed comparison of real vs. random pairs could be useful to investigate whether or not inter-brain synchronization is related to an epiphenomenon.
Although logically conceivable that due to the remarkable inter-muscle-brain coherence, inter-brain synchronization would also be present, the results were not as clear as expected. The inter-EEGcen and inter-EEGri of both partners showed significantly higher coherence comparing real vs. random pairs (d z = 1.00-1.29); however, inter-EEGle did not show this behavior. The coherence of same sub-regions of both partners (AFle_A-AFle_B, TLle_A-TLle_B and POle_A-POle_B) was also high for random pairs. By excluding them, the interpersonal coherence of EEGle was significantly higher for real vs. random pairs with a very large effect size (d z = 8.87). Thereby, the Sum5PaD for random pairs was similarly low as for non-coupled non-motor tasks. Hence, for this case example, inter-brain synchronization seems not only to be based on an epiphenomenon resulting from the performed motor task; specific brain regions could reflect 'real' inter-brain synchronization which is assumed to be based on the synergy type of neuronal coupling according to Hasson and Frith [49]. The partly high coherence for random pairs might have occurred since random pairs were taken from the real coupled trials only by matching different measurements. It is assumed that central activities during isometric tasks are generally similar. This is supported by the significantly lower inter-brain-coherence of uncoupled non-motor (OpEy) vs. real pairs for all brain regions (d z = 1.01-2.05, r > 0.78). This indicates that without a motor task or any other interaction, the partners' brains show rather spurious Sum5PaD of 12%. The findings of significantly higher inter-EEGri and inter-EEGcen coherence in real pairs rather speaks for a 'real' inter-brain synchronization for this case example. On the one hand, it could still be a random finding due to multiple testing and the low sample size; on the other hand, it cannot be ruled out that central and right brain areas might undertake specific functions in the present complex interpersonal motor task. Since the right arms executed the motor action, a stronger inter-brain synchronization was expected for left areas. However, the significant presence of inter-brain-coherence for EEGri and EEGcen in this case example might reveal first hints that those brain areas occupy a specific function during the regulation and control of complex interpersonal motor tasks. The EEGle might rather represent the general execution of the sensorimotor task with the right arm, which is supported by the high inter-MMG-EEGle coherence. This could explain why the random pairs also showed a considerably high interpersonal coherence for EEGle, especially regarding same sub-regions. Another parameter speaking for a real inter-brain synchronization is the significantly lower CV in real vs. random pairs (d z = 1.75). This points out that the coherence seems to be more consistent for real than random pairs at least in this case example.
It is concluded that a mixture of real inter-brain connectivity and the appearance of an epiphenomenon was present regarding the here investigated pair of participants. An external stimulus, such as the acoustic one mentioned above, did not exist here, but there were proprioceptive and tactile inputs from the counterpart and, of course, both partners were muscularly active. However, the significant differences of Sum5PaD for inter-EEGri, inter-EEGcen, and for some sub-regions of inter-EEGle as well as the differences in CV might be interpreted as possible signs for 'real' inter-brain coupling rather than an epiphenomenon during muscular interaction at least regarding the two participants of this case example.

Conclusions
To our knowledge, the presented case study was the first investigating inter-brain and inter-muscle-brain synchronization during a coupled isometric motor task. Having in mind that only one pair of two interacting participants was investigated, the findings can only be considered as preliminary, providing first hints on the topic. If they will be verified in a larger sample size remain open. Consistent with previous findings, an inter-muscle synchronization was present indicating that both neuromuscular systems were able to agree to a mutual rhythm. The novel finding was that an inter-muscle-brain synchronization arose between both participants which differed significantly from random pairs for all brain regions. The inter-brain synchronization was not that clear, however, showing significant differences to random pairs regarding right and central brain areas and also for sub-regions of the left hemisphere. Furthermore, the CVs were significantly lower for real vs. random pairs. It is hypothesized therefore that inter-brain synchronization might be partly based on 'real' synchronization and partly on an epiphenomenon due to the motor action. This indicates, at least for this pair of participants, that their neuromuscular systems were not only able to adjust their own activities between muscles and/or brain intrapersonally, but also that it is in principle possible that a neuromuscular system is able to adjust and synchronize to another coupled neuromuscular system in low frequency areas. Due to the found lower intra-than interpersonal muscle-brain coherence, it is assumed that the systems of both partners merge into one united neuromuscular system during muscular interaction. Thereby, the brain of the holding partner seems to couple more strongly to the muscular oscillations of the partner than to the own ones. This could be a possible first hint that during HIMA, the brain probably processes more complex information than during PIMA. It is assumed that this might be the results from the reaction and adaptation during HIMA to the force input of the partner. A higher involvement of the somatosensory areas can be expected by this. Hence, higher requirements regarding control processes are presumed for HIMA vs. PIMA, which supports the current hypothesis.
The findings can only be considered as preliminary results since only one couple was investigated. Since some results appeared consistently and clear, we assume that it is unlikely those are related to incidental findings. At least the results justify further examinations, which will show if the inter-brain synchronization is based on random effects or on true connectivity. The next step will be to investigate the topic on a larger sample size.
These preliminary findings might provide first novel indications on motor control during a complex task of interpersonal muscular actions, which could be relevant for sport and training sciences, kinesiology, and neurosciences. It could also be of interest for functional diagnostic approaches as the manual muscle test measured by the Adaptive Force. This adaptive holding capacity, which is based on HIMA, was recently suggested to be especially vulnerable to interfering stimuli, which might probably be explained by the required high complex control processes.