Midfrontal theta as moderator between beta oscillations and precision control

Control of movements using visual information is crucial for many daily activities, and such visuomotor control has been revealed to be supported by alpha and beta cortical oscillations. However, it has been remained to be unclear how midfrontal theta and occipital gamma oscillations, which are associated with high-level cognitive functions, would be involved in this process to facilitate performance. Here we addressed this fundamental open question in healthy young adults by measuring high-density cortical activity during a precision force-matching task. We manipulated the amount of error by changing visual feedback gain (low, medium, and high visual gains) and analyzed event-related spectral perturbations. Increasing the visual feedback gain resulted in a decrease in force error and variability. There was an increase in theta synchronization in the midfrontal area and also in beta desynchronization in the sensorimotor and posterior parietal areas with higher visual feedback gains. Gamma de/synchronization was not evident during the task. In addition, we found a moderation effect of midfrontal theta on the positive relationship between the beta oscillations and force error. Subsequent simple slope analysis indicated that the effect of beta oscillations on force error was weaker when midfrontal theta was high. Our findings suggest that the midfrontal area signals the increased need of cognitive control to refine behavior by modulating the visuomotor processing at theta frequencies.


Introduction
Integration of visual information into motor commands is crucial for execution of fine and precise movements or manipulation of tiny objects, and movement errors can be reduced by better use of visual feedback. In laboratory settings, amplification of visual feedback gain has been shown to improve performance by reducing movement errors in various motor tasks ( Chung et al., 2017 ;Sosnoff and Newell, 2005 ;Vaillancourt et al., 2006 ;Watanabe et al., 2020 ). Neuroimaging studies further demonstrated that such reduction in movement errors is associated with activation of the brain's visuomotor system including visual cortex, parietal cortex, motor cortex, premotor cortex, supplemental motor area (SMA), and cerebellum ( Coombes et al., 2010 ;Debaere et al., 2003 ;Vaillancourt et al., 2003 ). Indeed, interfering with these brain regions can disrupt error correction of visually-guided movements ( Della-Maggiore et al., 2004 ;Lee and van Donkelaar, 2006 ;Van Donkelaar et al., 2000 ). Despite clear evidence that this visuomotor system con- Erla et al., 2012 ;Hübner et al., 2018 ;Papadelis et al., 2016 ;Rilk et al., 2011 ). Furthermore, studies manipulating visual feedback gain similarly showed the greater desynchronization in alpha and beta bands with better performance at high than low visual gain ( Chung et al., 2017 ;Rearick et al., 2001 ).
Similar to the alpha and beta bands, gamma oscillatory activity is widely distributed in the cerebral cortex and has been measured with variety of paradigms. Yet, for visual tasks most of the investigations have been performed with particular focus on the visual cortex. For instance, gamma oscillations can synchronize in response to visual stimulation in occipital areas, and characteristics of the response have been demonstrated to depend on properties of visual stimuli ( Adjamian et al., 2004 ;Busch et al., 2004 ;Muthukumaraswamy and Singh, 2013 ;Muthukumaraswamy et al., 2010 ;Perry et al., 2013 ). Furthermore, they have been revealed to be associated with higher cognitive functions, such as attention ( Fries et al., 2001 ;Siegel et al., 2008 ), feature biding ( Fell et al., 2001 ;Tallon-Baudry et al., 1997 ), and stimulus information processing ( Van Der Werf et al., 2008 ;. However, it remains not fully understood to what extent these oscillations contribute to translation of visual information into volitional movement control. Clarifying this aspect could help in better understanding of the role of gamma oscillations in top-down control processes. Another distinct frequency band that has been paid great attention for several decades as one of the physiological makers reflecting the top-down control is theta. It has been continuously demonstrated that theta oscillations especially in the midfrontal brain area are associated with high-level cognitive functions ( Cavanagh and Frank, 2014 ;Clayton et al., 2015 ;Cohen, 2016 ). For example, these oscillations synchronize during working memory tasks requiring maintenance and updating of serial order information ( Jensen and Tesche, 2002 ;Onton et al., 2005 ). Also, the increased theta synchronization can be observed when resolving conflicting response options as well as immediately after making an error during conflict control tasks (e.g., Flanker and Simon tasks) ( Cavanagh et al., 2012 ;Jiang et al., 2015 ;McDermott et al., 2017 ;van Driel et al., 2012 ). From these latter findings, it has been suggested that the midfrontal theta oscillations reflect the action monitoring system of the brain ( Cohen, 2016 ). In spite of their potential link to the ability to monitor one's own action and adjust movements to prevent or correct errors, it is currently unclear whether these oscillations can be identified in the other motor tasks that necessitate this ability. Specifically, as continuous monitoring of actions and errors is required during visuomotor coordination, it was hypothesized that theta oscillations would increase with greater integration of visual information to achieve better performance. Testing this hypothesis will help clarify a link between cognition and action ( Serrien et al., 2007 ).
The purpose of this study was to investigate whether theta and gamma oscillations would be modulated along with task performance by amplification of visual feedback during a visuomotor force-matching task, and also to determine the impact of these oscillations on the wellestablished link between alpha/beta oscillations and visuomotor precision control ( Chung et al., 2017 ;Rearick et al., 2001 ). To this end, we recorded high-density electroencephalography (EEG) during a precision pinch grip task at different visual gains and thereby reported the alterations in event-related spectral perturbations (ERSP) and their association with task performance.

Participants
Seventeen healthy young adults (mean age ± SD = 23.4 ± 2.2; age range: 20-30 years old) participated in this study. Exclusion criteria was previous history of neurological, psychiatric, or orthopedic disorders. They had normal or corrected-to-normal vision and were all righthanded as confirmed by Edinburgh Handedness Inventory. Before start-ing experiment, the subjects were informed about the study and provided informed consent. This study was approved by institutional review boards of Nagoya University and conducted in accordance with Helsinki declaration of 1975/83.

Experimental design
Subjects were seated on chair in dimly lit, electrically shielded room and were instructed to perform pinch grip contractions with their right thumb and index finger. A force transducer (Tech Gihan, Kyoto, Japan) was attached to a table in front of the subjects. They rested the forearm on the table and produced force against the force transducer. The height of the force transducer was arranged to match each subject's table-toindex finger height, excluding as much unnecessary contraction as possible.
Prior to experimental tasks, maximal voluntary force (MVF) of the isometric pinch grip was determined. The force was gradually increased over 3 s and maintained at the maximum for 2 to 3 s. We adopted the highest force over three trials as the MVF.
Each experimental task was composed of contraction and rest periods. We displayed three horizontal parallel bars on a PC monitor (LCD-MF235XDBR, I-O Data, Japan) set 0.6 m in front of the subjects ( Fig. 1 A). Two of them were separated by the length of the smaller side of the bar and stayed at the same position (target bars). The third one moved in real time according to the subject's contraction force level (force bar). The exerted force was low-pass filtered at 20 Hz, converted in Newton, and digitized at 1k Hz with an A/D board (National Instruments, Austin, TX, USA). During the experimental task, color of the target bars changed between green and red. The subjects were instructed to start producing force as soon as the target bars turned green, without making anticipatory responses, and to place the blue force bar between the target bars as accurately and steadily as possible while the target bars were green. They were also instructed to stop producing force as soon as the target bars turned red. The target bars were green for 4 s and red for 4 s, and thus the green-colored period (4 s) included the time to reach the target force and maintain that force in total. The target force level (middle of the target bars) was set at 15% of each subject's MVF. A customized LabVIEW program (National Instruments) was used to display the bars and to collect the force data.
Visual gain was manipulated by changing the height of the force fluctuation on the monitor ( Fig. 1 A), because the distance from the subject's eye to the monitor remained constant. As in previous studies ( Coombes et al., 2010 ;Watanabe et al., 2020Watanabe et al., , 2019, we calculated the visual angle using the following equation: where h is half of the force fluctuation on the monitor, and d is the distance from the subject's eye to the monitor. In this study we used three different visual gains, 0.05°(low), 0.5°(medium), and 3.0°(high), for the following two reasons: 1) changes in force precision have previously been observed between above and below 1° ( Vaillancourt et al., 2006 ), and 2) although performance error reaches an asymptote around 0.5°, change in activity of the visuomotor system (i.e., brain activity) from low visual gain to the asymptote was different from that from the asymptote to high visual gain ( Coombes et al., 2010 ). Each subject completed five blocks of seven contraction trials for each visual gain conditions (35 contraction trials total for each condition). The order of the conditions was randomized among the subjects, and a sufficient rest was provided between conditions.

EEG data acquisition
EEG data were collected with eego TM sports (ANT Neuro, Enschede, Netherlands). We recorded sixty-three EEG signals at a sampling rate of 1k Hz using a standard Waveguard EEG cap with sintered Ag/AgCl electrodes (ANT Neuro) positioned according to the international 10-20 system. The reference and ground electrodes were placed at CPz and AFz, respectively. The electrode impedance was kept below 5 k Ω.

Data analysis
Behavioral and EEG data were analyzed with MATLAB (Mathworks, MA, USA). The force signal was low-pass filtered at 10 Hz (fourth-order Butterworth filter) and converted to the rate of force change (N/s). The movement onset was defined as the first time point at which the rate of force change (increase in force) reached above 10 N/s after the start cue (green). The movement offset was defined as the first time point at which the rate of force change (decrease in force) reached above 10 N/s after the end cue (red). For the subsequent analyses, we removed the following trials: 1) trials with movement onset/offset below 100 ms or above 1000 ms, and 2) trials with the rate of force change above 10 N/s during a time interval of 2000 ms from 2000 to 4000 ms with respect to the start/end cue. These removals were conducted to include only trials in which subjects performed the task as instructed and to exclude trials with anticipatory responses and accidental force deviations.
Behavioral data included mean force, mean force error (MFE) in percent MVF, and coefficient of variation (CV) of force. Considering the transition phase from the movement onset to the time at which the exerted force became stable around the target force level, we calculated these behavioral variables during a period of 2000 ms from 1500 to 3500 ms with respect to the movement onset (force control phase).
Processing of EEG data was performed with EEGLAB ( http://sccn.ucsd.edu/eeglab/ ) ( Delorme and Makeig, 2004 ). EEG data were band-pass filtered between 1 and 100 Hz. Sinusoidal artifacts were cleaned with the CleanLine function within EEGLAB ( Bigdely-Shamlo et al., 2015 ), and bad channels were interpolated using neighboring channels (mean number of interpolated channels ± SD = 1.96 ± 2.33). The EEG data were then re-referenced to the global average. After resampling the data at 250 Hz, EEG epochs were extracted from 2 s before movement onset to 6 s after movement onset. Trials with EEG exceeding ± 500 V were removed from further analysis. Consequently, the mean number of trials per subject used for subsequent analysis (mean ± SD) was 33.24 ± 1.68, 33.94 ± 1.25, and 33.41 ± 1.91, for low, medium, and high visual gain conditions, respectively. The trial number was not significantly different between visual gain conditions ( p > 0.05). The epochs were concatenated for each subject and decomposed into independent components (ICs) using independent component analysis.
Using DIPFIT functions within EEGLAB ( Oostenveld and Oostendorp, 2002 ), each IC was modeled as an equivalent current dipole within a boundary element head model based on the Montreal Neurological Institute (MNI) standard brain. Any ICs whose best-fit equivalent current dipole model accounted for less than 85% of the variance of its scalp map were removed from further analysis, as were any ICs whose equivalent dipole was located outside of the brain. These removals left 333 ICs in total, with an average ± SD of 19.6 ± 4.5 per subject.
For each of the final 333 ICs, we computed ERSP from 3 to 100 Hz using Morlet wavelet transforms with 3 cycles at the lowest frequency and 20 cycles at the highest frequency. ERSP values were normalized with respect to a − 1000 to − 500 pre-movement onset baseline and expressed in decibel (dB) units in 100 log-spaced frequencies and in 200 time points. Next, we performed a cluster analysis using a k -means ( k = 13) clustering algorithm. During the clustering process, ICs with a distance larger than 3 SDs from any of the resulting cluster centroids were excluded as outliers. From the resulting 13 clusters, clusters with less than 70% of the subjects or with centroids located far from the scalp (e.g., subcortical area) were excluded from group analysis. Clusters identified by their dipole locations and scalp maps as comprised of non-brain artifact components (eye movements and muscle activity) were also excluded from group analysis. Five cortical clusters were finally identified as having task-related activation. Fig. 2 shows dipole locations of cluster ICs and clusters centroids visualized in the MNI standard brain. Table 1 provides the cluster information.

Statistical analysis
Condition differences in ERSP data were evaluated within EEGLAB using permutation statistics (2000 permutations) ( Maris and Oostenveld, 2007 ). We report uncorrected p-values of 0.01 and those remained  significant after false discovery rate (FDR) correction with p-value of 0.05 ( Benjamini and Hochberg, 1995 ). Statistical differences in behavioral variables (mean force, MFE, and CV) were examined using R (R Development Core Team) with a significant threshold of 0.05. Depending on normality of the data (assessed by Shapiro Wilk test), either one-way repeated measures analysis of variance (ANOVA) or Friedman rank test was used to examine the effect of visual gain condition on the behavioral variables. For the ANOVA, a Greenhouse-Geisser correction was used when sphericity assumption was not met. Post-hoc pairwise comparison was performed with t -test for normal data and with Wilcoxon test for non-normal data. The multiple comparison was corrected by FDR.
As described in detail below (Results section), we found that higher visual gain resulted in greater theta synchronization in the midfrontal area and greater beta desynchronization in the sensorimotor and posterior parietal areas, along with better visuomotor performance. Based on these findings, we conducted a moderation analysis to assess the impact of theta oscillations on the well-established relationship between beta oscillations and visuomotor task performance (e.g., Chung et al., 2017 ). Since not all subjects contributed to each of the obtained clusters, channel-wise ERSP, which was computed under the same setting as above for each subject after automatic artifact IC rejection using AD-JUST toolbox ( Mognon et al., 2011 ), was used for the following analysis. Average power during the force control phase was calculated for each subject and condition. Based on the cluster centroid locations and scalp maps, the midfrontal area was represented by average of FCz and Cz, and the sensorimotor and posterior parietal areas by average of C3, C4, and POz. A linear mixed model with task performance as a dependent variable, theta-(3-8 Hz) and beta-band (15-30 Hz) power as independent variables, visual gain as a covariate, and subject as a random effect, was fitted using R. Simple slope analysis was subsequently performed to examine the effect of beta-band power on task performance at one SD above/below the mean of theta-band power with jtools package ( https://cran.r-project.org/web/packages/jtools/ ).

Data and code availability
Data and code presented in this study will be made available by contacting the corresponding author by email and with a formal data sharing agreement.

Behavioral performance
Time course of force output during the task is shown in Fig. 1 B. Mean force during the force control phase was 7.71 ± 1.2 N for low, 7.93 ± 1.3 N for medium, and 7.95 ± 1.4 N for high visual gain. The one-way repeated measures ANOVA revealed a significant main effect of visual gain on the mean force (F(2,32) = 6.9, p = 0.017). Post-hoc analysis showed that the mean force was greater at high than low ( p = 0.032) and medium than low visual gain ( p = 0.032). This result is consistent with a previous study ( Coombes et al., 2010 ) and indicates that the target force level was slightly underestimated at the low visual gain. Fig. 3 shows results of the MFE and CV of force. The Friedman rank test revealed significant differences between three visual gains for the MFE (chi-square (2) = 34.0, p < 0.001) and for the CV of force (chi-square (2) = 23.7, p < 0.001). Pairwise Wilcoxon test showed that both the MFE and the CV were smaller at high than medium (MFE: p < 0.001; CV: p = 0.035) and medium than low visual gain (MFE: p < 0.001; CV:  p < 0.001). Also, they were smaller at high than low visual gain (MFE: p < 0.001; CV: p < 0.001).

ERSPs
Clusters of electrocortical sources were spatially localized to the prefrontal area, midfrontal area, left and right sensorimotor areas, and posterior parietal area ( Fig. 2 and Table 1 ). Fig. 4 presents the average ERSP plots for each of the identified clusters in low, medium, and high visual gain conditions. The left and right sensorimotor areas and posterior parietal area showed a clear desynchronization in alpha and beta bands during the force control phase. Also, the midfrontal area showed a clear synchronization in theta band, particularly in medium and high visual gain conditions. In the prefrontal area, there was a slight desynchronization in high alpha and low beta range, particularly in medium and high visual gain conditions. No clear de/synchronization was observed for gamma oscillations. Analysis of condition differences revealed that the magnitude of midfrontal theta synchronization was greater in higher visual gain conditions ( p < 0.05, FDR corrected; see supplementary material for power spectral density). Also, the magnitude of beta desynchronization in the sensorimotor and posterior parietal areas was greater in higher visual gain conditions ( p < 0.01, uncorrected).

Moderation analysis
The moderation analysis revealed a trend of positive relationship between beta-band power and CV of force ( = 0.27, t = 2.87, p = 0.09), but there was no moderation effect of theta-band power on this relationship. There was no significant effect of theta-band power on CV of force. On the other hand, there was a significant positive relationship between beta-band power and MFE ( = 0.26, t = 3.89, p = 0.006) ( Fig. 5 A), and this relationship was significantly moderated by theta-band power, which was reflected by an interaction between beta-and theta-band power ( = − 0.096, t = − 2.74, p = 0.036). Simple slope analysis indicated that higher beta-band power was associated with higher MFE when theta-band power was low ( − 1 SD); however, this association was not significant when theta-band power was high ( + 1 SD) ( Table 2 and Fig. 5 B). There was no significant effect of theta-band power on MFE.

Discussion
Magnification of visual feedback leads to improved motor performance by reducing movement errors during visuomotor tasks. In this study, we investigated how manipulating visual feedback gain influenced neural oscillations of the visuomotor system. We found that the magnitude of theta synchronization in the midfrontal area and also the magnitude of beta desynchronization in the sensorimotor and posterior parietal areas were greater at higher visual gains. Importantly, the midfrontal theta synchronization was larger when actual (not visual) force error was smaller. Furthermore, the theta oscillations were revealed to moderate the positive relationship between the beta oscillations and force error. Our findings extend the current literature by elucidating the importance of midfrontal theta oscillations in highly precise visuomotor coordination.

Theta oscillations in midfrontal area
Theta oscillations in the midfrontal area are thought to be generated by the dorsal anterior cingulate cortex, SMA, and/or pre-SMA ( Cohen, 2011( Cohen, , 2014Hsieh and Ranganath, 2014 ;Onton et al., 2005 ;Tsujimoto et al., 2006 ) and have been suggested to be part of a physiological mechanism signaling the need to enhance cognitive control ( Cavanagh and Frank, 2014 ) as demonstrated in a number of previous studies mostly using conflict control tasks. For instance, theta synchronization is larger for stop trials as compared to go (no-stop) trials in Go/No-go task ( Harper et al., 2014 ;Mückschel et al., 2017 ) as well as when responding to incongruent trials as compared to congruent trials in Simon and Flanker tasks ( Cohen and Donner, 2013 ;Cohen and Ridderinkhof, 2013 ;McDermott et al., 2017 ;Nigbur et al., 2012 ;Pastötter et al., 2013 ). Also, theta synchronization increases following error commissions, and this increase has been demonstrated to be associated with post-error adjustments ( Cohen and van Gaal, 2013 ;Luu and Tucker, 2001 ;Luu et al., 2003 ): post-error responses are more accurate as the error-induced midfrontal theta synchronization becomes larger ( Luft et al., 2013 ;Valadez and Simons, 2018 ;van Driel et al., 2012 ). Furthermore, in a cued conflict control task during which likelihood of conflict is cued, high-conflict-likelihood cues result in greater theta synchronization as compared to low-conflict-likelihood cues ( Ryman et al., 2018 ). In a similar vein, in a task-switching paradigm theta synchronization can be larger when a pre-stimulus cue warns of the need to switch the task ( Cooper et al., 2019( Cooper et al., , 2017. Collectively, these findings indicate that midfrontal theta is involved in reactive (reactions to conflict) and proactive (preparations for conflict) cognitive controls, suggesting that it could serve for different types of cognitive processes and thus is not much informative about what the response should be, as insisted in previous studies ( Cavanagh and Frank, 2014 ;Cohen, 2014 ;Swart et al., 2018 ). In addition to the conflict control tasks, in one study examining EEG activity in a continuous visuomotor tracking task, theta synchronization was found to occur in the midcentral area during reactive compensatory error correction more frequently in high-than low-error trials, although a clear theta synchronization was not observed in averaged ERSP plots ( Huang et al., 2008 ). Contrary to this previous observation, we found that midfrontal theta synchronization was larger when smaller force error was achieved by the use of magnified visual feedback. This finding suggests that the actual level of error is not a factor modulating the theta oscillations, at least in visuomotor precision control: strength of theta oscillations likely depends on the amount of cognitive control allocated to a given task demand. During visuomotor force-matching tasks, it is required to monitor exerted force and watch out for errors from a target. As exerted force is not at the target force level for most of the time, subjects need to continuously detect and correct errors and also prepare for possible large deviations from the target. It appears, therefore, that the magnification of visual feedback has increased the demand of this cognitive process. The most-right plot shows significant differences between conditions. Brown-colored areas indicate significant difference at uncorrected p < 0.01, and white-colored areas indicate significant difference at FDR corrected p < 0.05. The circles indicate data points for all subjects and conditions (17 subjects × 3 conditions = 51 data points). B: Moderation effect of theta power on the relationship between beta power and MFE. Two lines indicate the relationship at two levels of theta power (one standard deviation (SD) below the mean and one SD above the mean). The effect of beta power on MFE was weaker when theta power was high ( Table 2 ). Specifically, since errors or deviations from the target become larger and more apparent on a PC monitor with the magnification of visual feedback, theta synchronization increased likely as a consequence of more frequent error detection and correction (more reactive cognitive control) as well as increased possibility of large deviations (more proactive cognitive control) at higher visual gains. As the midfrontal theta is not much informative about the response, it could have served to signal the increased need of cognitive control to monitor and flexibly adjust performance of on-going activity.
Besides enhanced need of cognitive control, attention to the task may have influenced theta oscillations. Using working memory paradigms, it has been documented that sustained attention and allocation of attention increase midfrontal theta oscillations. For instance, theta-band power was found to be larger when it was required to memorize three words than one word in a word recognition paradigm ( Gomarus et al., 2006 ). Also, a study using a sequential button-pressing task demonstrated that theta-band power was larger with novel button sequence than memorized button sequence ( Sauseng et al., 2007 ). From these and related findings, increased midfrontal theta-band power was suggested to indicate the greater demands for attention associated with working memory process ( Clayton et al., 2015 ;Gomarus et al., 2006 ;Sauseng et al., 2007 ). Meanwhile, Rajan and colleagues ( 2019 ) recently reported that attention-related increase in midfrontal theta-band power can be observed when voluntary attention is made by one's own will (willed attention) but not by external stimuli. The finding was interpreted as reflecting the conflict processing and decision making inherent in willed attention ( Rajan et al., 2019 ). Therefore, although there was no need of working memory process in the visuomotor force matching task used in the present study, theta oscillations could have been modulated by attentional state if the subjects have paid greater attention to visual information on their own will/decision at higher visual gains to monitor their own action and thus to achieve accurate and precise force control performance. However, it is unknown how much attention the subjects actually paid at each visual gain in the present study. Further studies are hence necessitated to examine to what extent attention influences midfrontal theta oscillations during motor tasks.

Beta oscillations in sensorimotor and posterior parietal areas
It is well-established that alpha and beta oscillations desynchronize with movement, movement preparation, or motor imagery, and synchronize with movement termination or relaxation Engel and Fries, 2010 ;Fry et al., 2016 ;Heinrichs-Graham et al., 2017 ;Heinrichs-Graham and Wilson, 2015 ). This oscillatory response has been reported for internally and externally triggered movements and for different peripheral effectors ( Arpin et al., 2017 ;Stancák et al., 2000 ). In terms of brain regions, the movement-related power change is observed typically in bilateral sensorimotor areas ( Bai et al., 2005 ;Rau et al., 2003 ) but also in widespread brain areas Gaetz and Cheyne, 2006 ;Heinrichs-Graham and Wilson, 2015 ;Wilson et al., 2010 ). In line with these previous reports, our results revealed a decrease in alpha-and beta-band power after movement initiation and during force control phase in several different brain areas ( Classen et al., 1998 ;Erla et al., 2012 ;Hübner et al., 2018 ;Papadelis et al., 2016 ;Rilk et al., 2011 ). In addition, we found that beta desynchronization was larger at high than low visual gain in the sensorimotor and posterior parietal areas. This finding is in general agreement with two previous studies that examined the effect of visual gain on neural oscillations and motor control ( Chung et al., 2017 ;Rearick et al., 2001 ).

Midfrontal theta as moderator of beta-performance link
As expected from previous studies ( Archer et al., 2018 ;Chung et al., 2017 ;Coombes et al., 2010 ;Vaillancourt et al., 2006 ;Watanabe et al., 2020 ), MFE and CV of force decreased with magnification of visual gain. However, even though we found the greater theta synchronization at higher visual gains, there was no significant effect of theta oscillations on MFE or CV of force when the effects of visual gain and beta oscillations were controlled for. This finding is in line with a view that the midfrontal theta is uninformative about the response required in a given task and is more reflective of a signal of the increased need for cognitive control ( Cavanagh and Frank, 2014 ;Cohen, 2014 ;Swart et al., 2018 ). On the other hand, there was a significant positive relationship between the beta oscillations and MFE, which was further found to be moderated by the midfrontal theta. Specifically, the effect of beta oscillations on MFE was weaker when the midfrontal theta-band power was high ( Table 2 and Fig. 5 B). One possible explanation for this moderation effect is a change in cognitive top-down control, which, in our task, refers to the regulation of online visuomotor control processes in the lower-level brain system by the higher-level cognitive brain system. At lower midfrontal theta synchronization levels and thus at lower topdown cognitive control, the generation of movements may have been based more on online visuomotor control (reactive response to emerging visual information), and this online visuomotor control could have resulted in the stronger influence of beta oscillations involved in visuomotor processing on performance. Contrarily, at higher midfrontal theta synchronization levels (at higher top-down cognitive control), the top-down control could have served to modulate the online visuomotor control processes to refine behavior as a function of performance outcomes. As described above, the increase in midfrontal theta synchronization has likely led to a more cautious behavior: being attentive and well prepared (proactive) to take control immediately, if necessary, appears to have reduced the amount of online visuomotor control and thus the effect of beta oscillations on performance ( Fig. 5 ). Similarly, in conflict control tasks, decision thresholds can be increased to prevent impulsive responses after commission of errors, and this adjustment in behavior has been shown to be achieved through the midfrontal theta oscillations ( Cavanagh and Frank, 2014 ;Frank et al., 2015 ;Zavala et al., 2014 ). Therefore, the midfrontal cortex monitors the performance and possibly signals the need for behavioral adjustments at theta frequencies. As proposed in previous studies ( Cavanagh and Frank, 2014 ;Cohen, 2014 ;Swart et al., 2018 ), this cortical region may function as a hub, where theta oscillations modulate disparate neural networks, including the visuomotor network.

Future outlook
An ability to control movements using visual information can be impaired by aging and various brain disorders, such as stroke and Parkinson's disease ( Archer et al., 2018 ;Chen et al., 2016 ;Christou, 2011 ;Watanabe et al., 2020Watanabe et al., , 2018aWatanabe et al., , 2018b, and extensive rehabilitation interventions are usually implemented to restore the function, as this ability is pivotal to most activities of daily living. However, the intervention that has been demonstrated to be effective is a repetitive, task-specific exercise ( Bernhardt et al., 2007 ;Lohse et al., 2014 ), which is commonly limited due to cost and availability of physical and occupational therapists. Given that the number of individuals with impaired motor control will further increase as our society ages, more effective and efficient rehabilitation interventions are needed. One of the potential methods is a non-invasive Brain Stimul.ation ( Joundi et al., 2012 ;Miyaguchi et al., 2018 ;Nakazono et al., 2020 ;Nitsche and Paulus, 2000 ;Nojima et al., 2019 ;Oliviero et al., 2011 ;Tsuru et al., 2020 ). Particularly, transcranial alternating current stimulation has been reported to entrain ongoing oscillatory activity depending on parameters used for the stimulation (e.g., frequency and intensity), accompanied possibly by improved performance ( Joundi et al., 2012 ). Therefore, extending the current study to aged population as well as those with brain disorders would provide new insights into factors critical for the intervention.

Limitation
There are several limitations to be acknowledged. First, the number of subjects evaluated in this study was seventeen, which is relatively low for an EEG ERSP investigation, even though a similar sample size was selected in some previous studies (e.g., Chung et al., 2017 ). Smaller condition differences could have been distinguished with a larger sample size. Second, although the number of trials used to compute the ERSP was within the typical range (30-80 trials) reported in a previous study ( Graimann and Pfurtscheller, 2006 ), signal-to-noise ratio could have been enhanced with a higher number of trials. Third, reference and ground electrodes for EEG recording were positioned close to the regions of interest. This may have affected our IC and dipole analyses to some degree.

Conclusion
Alpha and beta oscillations have been continuously demonstrated to contribute to precise and accurate control of movements using visual information. This study extends the current literature by providing evidence that midfrontal theta oscillations, which have been reported to be associated with high-level cognitive control processes, play an important role in the visuomotor coordination. Specifically, these oscillations increase with increased need of visuomotor coordination and further moderate the well-established link between beta oscillations and visuomotor precision control. The midfrontal area may, thus, function as a hub to modulate the visuomotor processing at theta frequencies. Our findings highlight the importance of midfrontal theta in precise control of movements.

Declaration of Competing Interest
None.