Neuro-Muscular Responses Adaptation to Dynamic Changes in Grip Strength

Precise control of strength is of significant importance in upper limb functional rehabilitation. Understanding the neuro-muscular response in strength regulation can help optimize the rehabilitation prescriptions and facilitate the relative training process for recovery control. This study aimed to investigate the inherent characteristics of neural-muscular activity during dynamic hand strength adjustment. Four dynamic grip force tracking modes were set by manipulating different magnitude and speed of force variations, and thirteen healthy young individuals took participation in the experiment. Electroencephalography were recorded in the contralateral sensorimotor cortex area, as well as the electromyography from the first dorsal interosseous muscle were collected synchronously. The metrics of the Event-related desynchronization, the electromyography stability index, and the force variation, were used to represent the corresponding cortical neural responses, muscle contraction activities, and the level of strength regulation, respectively; and further neuro-muscular coupling between the sensorimotor cortex and the first dorsal interosseous muscle was investigated by transfer entropy analysis. The results indicated a strong relationship that the increase of force regulation demand would result in a force variation increase as well as a stability reduction in muscle motor unit output. Meanwhile, the intensity of neural response increased in both the <inline-formula> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$\beta $ </tex-math></inline-formula> frequency bands. As the force regulation demand increased, the strength of bidirectional transfer entropy showed a clear shift from <inline-formula> <tex-math notation="LaTeX">$\beta $ </tex-math></inline-formula> to the <inline-formula> <tex-math notation="LaTeX">$\gamma $ </tex-math></inline-formula> frequency band, which facilitate rapid integration of dynamic strength compensation to adapt to motor task changes.


I. INTRODUCTION
S TROKE is a condition with a high incidence and disability rate, often resulting in sequelae such as hemiplegia [1] with upper and lower limb sensory and motor functional impairment [2].Post-stroke rehabilitation of upper limb requires hand training [3], which can be categorized into strength training [4] and motor control training [5].The theory of neuroplasticity [1], [6], suggests that the recovery progression and its relative effectiveness are dynamically modulated via the neural responses induced by motor training [6], [7].Evidences have been accumulated through various previous studies, indicating that dynamic strength production requires complex neural and muscular activity [8], [9], [10], [11].Nevertheless, further investigation is required to determine how nerves and muscles respond to meet the demands of force change.It can help physiatrists optimize the strength control for personalized rehabilitation training prescriptions in order to enhance the recovery effectiveness and efficiency in functional rehabilitation.
During hand-grip exercises, there is continuous information exchange between the central and peripheral nervous system [12].The cortex sends out commands to control muscle contractions, while afferent feedbacks also trigger adaptive responses in the corresponding brain regions [13].Therefore, a fundamental neuro-muscular closed-loop for neural information transmission is generally established during the force production.Early studies on primates have showed that different levels of force production are associated with distinct oscillatory rhythmic activities in the sensorimotor system [14].Through physiological electrical activity recording from both cortex [8], [15], [16], [17], [18] and muscles [19], [20], it was found that hand movements induce cortical activation, which is related to muscle contraction intensity [21], [22].
Fetz [23] demonstrated a correlation between the output of different hand forces and the oscillatory activity of the entire sensorimotor system.Efforts demonstrated that the oscillatory activity in the β-band is significantly affected by factors such as the level of force [24] and task complexity [9], and the result has also been applied to the MI-BCI field [25].Omlor et al. [10] observed that the synchronized oscillation shifted toward higher frequencies (γ -band) during a dynamic task compared with a constant force task.Various experiments were designed under different force levels, linear force variations, and contrasting constant force and fixed variation patterns.However, for dynamic tasks such as adaptive force tracking, limited research has focused on the effects of temporal and condition changes on synchronized oscillatory activity.Subsequent studies analyzed the directional characteristics of the synchronous oscillation and found that there is a bidirectional coupling characteristic between the brain and muscle during movement [26].Some studies have pointed out that the synchronous oscillation from EEG to EMG reflects the transmission of motor control commands [13], while EMGto-EEG oscillation describes sensory afferent feedback [12].The neural signal characteristics and the corresponding myoelectric activities are capable to provide intrinsic insights into the neural adaption processes of force control, respectively.Studies have indicated that the αand β-band power spectrum of electroencephalography(EEG) signals are significantly correlated to grip force activities [27], [28].Specifically, the αband component reflects the level of attentional demands [29], while β-band component relates to the adaptability of motor tasks [9].Erbil and Ungan [28] showed the intensity of the β-band EEG power spectrum was correlated to the precision and difficulty level of motor tasks.Meanwhile, the neural system evidently synchronizes at low-γ -band in the complex but predictable tasks for rapid information integration [30], [31].Moreover, research have observed a notable lack of γband synchronized oscillations in stroke patients [32], which potentially indicates that dynamic fine control training may introduce the neuro-muscular responses critical for rehabilitation.Considering the correlation between the intensity of sensory input and EMG amplitude [21], [31], the sensory input during grasping movements is able to affect the EMG intensity and functionally important in feedback for force control [22], [33].The Surface Electromyogram (sEMG) records electrical activities of superficial nerve branches and muscle fiber groups [19], [20], which can partially express the control information from the cortical neurons and the incoming feedback from the peripheral nervous system.In summary, the control of force change requires coupling of neuro-muscular information.The adjustment of force is controlled by muscle contraction, which is driven by neural commands and also affects the nervous system through feedback information.Therefore, it is imperative to investigate the activation characteristics of cortex, the contraction activity of the muscles and the neuro-muscular coupling mechanism, which can improve the beneficial neuro-muscular responses in hand rehabilitation and further optimize the prescription for upper limb functional impairments.
The neuro-muscular information exchange can be measured as Cortical Muscle Coupling (CMC) [13].The CMC is capable of representing the synchronization of neural oscillations for muscle motor units, which serves as an important tool for quantifying effective motor control.Previous research has acknowledged the CMC in the βand γ -band as effective metrics to evaluate the brain-to-muscle communication corresponding to force control [34], [35].Various methods have been developed for further neuro-muscular coupling investigation, including coherence analysis [11], Granger Causality (GC) analysis [36], Mutual Information (MI) [37], Directed Transfer Function (DTF) [38], [39], and Transfer Entropy (TE) [40], [41], [42].However, the coherence analysis can only explore the unidirectional transmission characteristics between the brain and muscles, while both GC and DTF are not effective for the nonlinear characteristics assessments of the sensory-motor system.The MI method cannot reflect the direction of information flow within the CMC and cannot exclude the influence of common signal sources [43], [44].TE is capable of capturing nonlinear coupling effects and directionality, making it a popular choice for the cortico-muscular coupling characteristics analysis.In response to the evolving research needs, researchers have developed a range of innovative computational methods.Chen et al. [45] extended the TE method to the frequency domain and proposed transfer spectral entropy.The Event Related Desynchronization (ERD) [46], [47] is commonly used for characterizing the cortical responses of hand sensory-motor functions.It can reflect the time differentiation of hand postures in motor planning process or the variation of proprioception resulting from hand movements, rather than the motor command generated in the down stream, which recruits a group of motor neurons [48].Kun et al. [49] found in the field of MI-BCI that load (imagined) can regulate EEG oscillations, with significantly higher ERD under high load compared to low load.In terms of muscular responses, the linear relationship between EMG amplitude during contractions and muscle force has been widely acknowledged [50], [51].Furthermore, the stability index of EMG amplitude can describe the stability of muscle contraction [52], [53], which is correlated with the recruitment of motor units and discharge frequency.In summary, this paper has designed a grip force tracking task with different amplitudes and frequencies of change and used EMG stability, ERD and TE to elucidate the interactions and characteristics between force regulation demands and muscle contraction, cortical activation and neuro-muscular coupling.
Grasping training is a crucial part of hand rehabilitation.Targeted training can selectively activate neurons to promote effectiveness of rehabilitation.However, how to optimize the training protocols to activate the proper neural responses according to personalized conditions is still an open question.The generation of strength is triggered by the excitation of primary motor cortex neurons, which transmit motor signals to muscles to complete muscle contraction or relaxation.The motor cortex controls and regulates muscle activity to adjust the power of gripping through sensorimotor integration, which involves continuous processing of sensory inputs for movement preparation and performance improvement during dynamic force follow-up task.And increased demands for force regulation increase the neuro-muscular load on both feedforward and feedback mechanisms.Some studies have found that as the level of grip strength increases, the intensity of cortical activation increases [27], and the cortical-spinal oscillation pattern of the sensory-motor system would shift to higher frequencies [54].Regarding dynamic variations in force, the neuro-muscular system may produce a similar response.Therefore, we assume that in order to meet the demands of force regulation, the neuro-muscular system enhances muscle response efficiency and optimizes force output and motor control by adjusting the frequency and intensity of neural impulses and information transmission, which is directly reflected in muscle contraction and cortical activation.Thus, this study conducts a grip force tracking experiment with different change amplitudes and frequencies, analyzed neuro-muscular characteristics such as ERD, EMG stability, and CMC.Additionally, the level of force control is represented by a pre-defined Performance Index (i.e.Force Variation, FV), in order to explore the intrinsic regulatory mechanism of neuro-muscular during grip force changes.

II. METHOD A. Subject
Sixteen healthy right-handed young adults (10 males, 6 females) with an average age of 24 ± 3 years, height of 170 ± 7.21 cm, and weight of 60.893 ± 7.69 kg, participated in the experiment.All participants had confirmed normal or corrected-to-normal vision and had no history of cardiovascular, neurological, or musculoskeletal disorders.The Ethics Committee of the Affiliated Three Gorges Hospital of Chongqing University (No. Res.2021-20) approved this study.Informed consent were provided to all participants before the experiment.

B. Experimental Setup and Protocol
In this study, grip tracking a target force was selected as the dynamic force production task, which denoted as the parameter in force amplitude (A in Maximum Voluntary Contraction (MVC)%) and change rate (F in Hz).The task mode included four settings: A1F1 (A = 3%MVC, F = 0.25), A1F2 (A = 3%MVC, F = 0.5), A2F1 (A = 5%MVC, F = 0.25), and A2F2 (A = 5%MVC, F = 0.5), as shown in Table I and Fig. 1.
The experiment platform included: 1) a custom-built dynamic grip force tracking platform, 2) a multi-channel physiological signal acquisition device (Cerebus, Blackrock Microsystems, USA), and 3) an EMG acquisition device (Octopus-Pro, Shanghai OYMotion Information Technology Co., Ltd., Shanghai, China).The dynamic grip force tracking platform was designed for data recording and display.The platform was powered by a switch power supply (LRS-150-24, Mean Well, Taiwan, China), which converted 220V AC power to 24V DC power for the platform.A high-frequency pressure transducer (CJGP-15, Xi'an Chuangjin Electronic Technology Co., Ltd., Xi'an) was used to convert pressure changes in the airbag to voltage changes, and the pressure signal was detected with a data acquisition card (DAM1066, Juying Electronics, Beijing).A computer was used to record the grip force signal, and provide online visual feedback to participants in the form of a sliding block.The multi-channel physiological signal acquisition device was used to record 46-channel EEG signals at a sampling frequency of 1000Hz, with a 150Hz low-pass filter setting.Meanwhile, the EMG acquisition device acquired the sEMG signals of the first dorsal interosseous muscle.The sampling frequency was set at 1000Hz.
The real-time force production was visually provided as colored bar to participants on screen during experiments, in the purpose of help the participants to adjust their grip outputs with their best accuracy.The height of bar denoted the dynamic strength detected via sensors, and the color represented the corresponding adjustment indication (green as correct, and yellow as error).A considerable performance error was set as 3%MVC and the displayed slider would turn yellow when the force production out of range; hence, the participants were able to artificially estimate the performance errors by adjusting the height of the yellow block to approach the target height.The experiment took place in the shielding room of the College of Bioengineering at Chongqing University.

C. Experiment Procedure
Before experiment, the personal MVC were obtained using the grip force collection system.For each participant, the MVC was repeatedly measured three times, and the averaged peak value was calculated and used to normalized the individual differences.A target force of 15% of the MVC was selected as the control test mode (denoted as A0F0).
During the experiment, participants completed five motion modes in a random order.Each motion mode consisted of 36 trials.Every trial included 3 seconds of preparation, 8 seconds of task execution, and 5 seconds of rest.The experimental scene displayed in Fig 2(B).Participants were required to seat and follow instructions to grip the airbag on the table using

D. Data Processing
Data processing and feature extraction were performed in the MATLAB2019b environment (MathWorks, Natick, MA).
1) Preprocessing: The grip force signals were initially smoothed and segmented according to the trials.Data verification were conducted, trials with data out of range were identified and excluded, while the qualified data were then re-segmented.
The EEG signals were filtered using a Butterworth band-pass filter with a range of 2 to 150Hz (EEGLAB, Natick, MA) to eliminate unnecessary interference in the frequency domain.Further components such as ocular, muscular, and cardiac noise were removed by Independent Component Analysis (ICA) algorithm.Then the EEG signal was downsampled to 200Hz.
The baseline wander of sEMG signals was removed using the average reference method.Then, a second-order band-pass Butterworth filter from 4 to 150Hz was applied followed by a 50Hz notch filter for noise removement.
2) EEG Data Analysis: Oscillations in the αand β-bands of the EEG are closely associated with grip force movements.The ERD within the αand βbands of C3 were selected to evaluate cortical activity during movement, as the C3 electrode corresponds to the primary somatosensory cortex for the right upper limb.The Event-Related Spectral Perturbation (ERSP) of the EEG signals in the time-frequency domain was quantified to calculate ERD: where F k (f,t) is the spectral estimation of the n-th trial at the frequency f and time t.The average ERD values in the α-band (8-14Hz) and β-band (15-30Hz) were computed during the movement task (3-11s): where µ B ( f ) is the mean of the power during the baseline(0s < t < 3s) at frequency f across all trials, where f1 and f2 represented the frequency band range where ERD occurs.K is the number of the time-frequency bins during the movement phase(3s < t < 11s).
3) Motor Performance Data Analysis: The motor performance in different patterns of target force variation were investigated through the aspects of muscle contraction and strength output.For muscle activity during the force adjustment, the coefficient of variation of the EMG amplitude in the first dorsal interosseous muscle was calculated, denoted as EMG stability [24].This metric provided a qualitative assessment to the stability of muscle activity during performance modulation [17], [32].
For force production investigation, the Force Variation (FV) during the movement task from 3 to 11 seconds was calculated to assess the variation level of force.FV was defined as the absolute average of the grip force differential signal.
Where N represented the number of sampled grip force signal, and x(i) denoted the i-th actual grip force signal.4) Neuro-muscular Coupling Analysis: The βand lowγ -band information was decomposed from both EEG and sEMG signals using wavelet transformation, while TE was calculated to quantify the coupling strength and directional information between muscles and brain during movement.Given time sequences M = m1,m2,. . .,ml and N = n1,n2,. . .,nl with a length of l, the TE from m to n can be accessed by: where the joint probability of occurrence of n i ,n i−t , and m i−τ was represented by ρ(n i ,n i−t ,m i−τ ), and the time lag within n and m was represented by t and τ respectively.Previous research has shown that a 25-milliseconds neural information transfer delay between brain and muscle [58].
To avoid spurious correlations in time sequence computation, the time-domain signals of EEG and sEMG in each functional band were randomly shuffled, followed by probability density function estimation.Finally, the normalized TE based on numerical ratios were accessed [60]:

E. Statistical Analysis
The statistical analysis were conducted using SPSS (version 22.0.0.0 SPSS Inc).The two-way repeated ANOVA was used to investigate the force variation impact (amplitude and frequency) on the neural response, muscle contraction activity, and neuro-muscular coupling.Mauchly's test of sphericity was applied.The Huynh-Feldt correction was performed when assumption of sphericity was violated.We also performed post hoc pairwise comparisons using the Least Significant Difference (LSD) correction.Statistical significance was established at p < 0.05.

III. RESULT
In the process of strength training, the central nervous system is activated and transmits the motion control information to the relevant muscles through neural oscillation, which will be reflected in the bioelectric signal and motor performance.Therefore, this paper proposed FV, EMG stability , ERD and TE to analyze the level of force regulation, the output state of muscles, activation level in the cortex and the characteristics of functional cortical-muscular coupling under different amplitude and frequency of target force variation.Data from three participants were excluded from further analysis due to recording issues.Furthermore, we excluded data with inadequate training performance based on the average relative error between the actual grip strength signal and the target grip strength curve.

A. The Impact of Different Variation Modes on Force Regulation and Muscle Response
Fig 3(A) illustrated the impact of the amplitude and frequency of target force variation on actual FV of the 13 participants.The amplitude (F(1, 12) = 273.318,p < 0.001) and the frequency (F(1, 12) = 597.729,p < 0.001) of target force variation both significantly affected the FV.Post-hoc tests showed that FV increased as the amplitude ( p < 0.001) and frequency ( p < 0.001) of target force variation increased ( p < 0.001), indicating a higher level of self-regulation in force control.Fig 3(B) showed the EMG stability at different amplitude and frequency variations.The two-way repeatedmeasures ANOVA demonstrated significant effects of the amplitude (F(1, 12) = 38.781,p < 0.001) and frequency (F(1, 12) = 28.782,p < 0.001) of target force variation across the modes, with no significant interaction between the two factors.According to Post-hoc analysis, the EMG stability in mode with smaller amplitude of target force variation overpassed in mode of larger changes( p < 0.001).Furthermore, the EMG stability was also higher in mode with low-frequency change than the faster changing mode ( p < 0.001).

B. The Impact of Different Variance Patterns on Levels of Cortical Activation
The averaged ERD intensity was used to describe the level of cortical neural activation.Significant differences in the ERD intensity in the αand β-bands were observed among different patterns.The absolute average intensity of ERD (task period: 3-11s) was summarized in Table II.The average ERDs of αand β-bands for the contralateral sensorimotor cortex during task under different target force variation were illustrated in Fig 4 .The two-way repeated ANOVA indicated that frequency of target force variation significantly impacted the α-band ERD in the contralateral sensorimotor area (F(1, 12) = 7.442, p = 0.018), while the amplitude did not (F(1, 12) = 0.688, p = 0.423), and no significant interaction effects were found between factors.In contrast in β-band, the amplitude of target force variation showed significant influences (F(1, 12) = 9.808, p = 0.009) compare to that induced by frequency of target force variation(F(1, 12) = 0.074, p = 0.791).Post-hoc analysis demonstrated that the average ERD was significantly lower in constant force mode than in the dynamic mode regardless the frequency band.Moreover, the task-related α-band ERD was significantly higher under high-frequency patterns than low-frequency patterns (p = 0.018).The α-band ERD also tended to increase as amplitude of target force variation increased, though without statistical significance.On the contrary, in β-band, the average ERD was significantly greater under large-amplitude patterns over the patterns with small amplitude of target force variation (p = 0.009).Also the amplitude and frequency of target force variation increases would cause observable but not significant stronger β-band ERD changes.

C. The Impact of Different Variance Patterns on the Direction and Intensity of Neuro-Muscular Coupling
Significant differences were found between different modes (F(4, 21) = 245.281,p < 0.001) and across different frequency bands (F(1, 24) = 857.861,p < 0.001), regarding the ratio of TE.Post-hoc tests showed in β-band, the constant force mode A0F0 exhibited significantly lower dTE EMG−EEG compared to the dynamic modes A1F1, A1F2, A2F1 and A2F2 ( p < 0.001).The amplitude (F(1, 12) = 4.851, p = 0.048) and frequency (F(1, 12) = 25.139,p < 0.001) of target force variation significantly affected dTE EMG−EEG in the β-band.Post-hoc analysis indicated that low-frequency variation can induce significantly higher dTE EMG−EEG in β-band compared to high-frequency force change ( p < 0.001); while greater amplitude variation resulted significantly lower dTE EMG−EEG in β-band compared to modes with smaller changes ( p < 0.05).In low γ -band, the constant force mode A0F0 showed significantly higher dTE EMG−EEG over all dynamic modes A1F1, A1F2, A2F1 and A2F2 ( p < 0.001).The mode with a change amplitude of 5%MVC exhibited significantly higher dTE EMG−EEG in the low γ -band compared to the mode with a variation of 3%MVC ( p < 0.001).In the meantime, highfrequency modes showed significantly higher dTE EMG−EEG in the low γ -band compared to that of the low-frequency variations ( p < 0.001).
The relationship between the FV and dTE EMG−EEG was shown in Post-hoc analysis indicated that in EEG-sEMG direction, the TE was significantly lower for high frequency ( p < 0.001).In the β-band, both the bidirectional coupling strength decreased significantly according to the amplitude and frequency of target force variation increase.In addition, considering the inherent individual differences, correlation analysis between FV and TE from all trials were conducted for all participants.Table III showed the majority of participants (11 out of 13) exhibited a similar trend in bidirectional coupling strength in the βand γ -bands with respect to force variation.Specifically, as the FV increased, the TE decreased in β-band while increased in γ -band as well.
Fig 9 illustrates the linear relationship of TE EMG−sEMG with both FV and EMG stability within βand γ -band respectively.In the β-band, the FV(r = −0.581,p < 0.001) showed significantly stronger correlation with TE EMG−sEMG compared to the EMG stability (r = 0.399, p = 0.003).The similar

IV. DISCUSSION
Data analysis revealed that, as the target force variation increases, the human body will produce corresponding physiological responses to achieve rapid adjustment of force production.These responses are manifested as increased cortical activation, decreased stability of muscle output, and transfer of cortical muscle coupling from β-band to low-γband.We further investigated the correlation between these characteristics and the FV, and analyzed possible underlying reasons.

A. Increasing the Rate and Amplitude of Target Force Variation Will Reduce Muscle Stability While Increase the Level of Force Regulation
When perform tasks with force variations, dynamic regulations were required for appropriate adaption.During the force regulation, the cerebral cortex continuously transmits information downward to control the recruitment of motor units and relative discharge rates according to movement requirements.This regulation would not only be applied to the force performance, but also be reflected in the performance of muscle contraction.Therefore, the presented study investigated the dynamic muscle control mechanism from two perspectives.The significant linear relationship exists between FV and EMG stability indicated a negative correlation between the force regulation level and the stability of muscle output.Fig 3 further illustrated the increased FV with decreased muscular stability attributed to the increase of the amplitude and frequency of target force variation.In dynamic tasks with force variation, the increase of amplitude of target force variation can induce relative increases in fiber length and tension of muscle; meanwhile it can accelerate the changing in muscle fiber length and alter the corresponding proprioceptive feedback.The results suggested that, compared to constant force patterns, the dynamic patterns can modulate the stability of motor unit output through manipulate the amplitude and frequency of target force variation.As the proprioceptive feedback generally changes according to dynamic task requirements, proper adaption may sequentially adjust the motor recruitment units and corresponding discharge frequency.In the meantime, the relative error increase in dynamic pattern would induce corresponding regulation of force production through feedforward and feedback mechanisms, which may also contribute to the observed variability increase in Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
force output.Previous research have documented that dynamic tracking tasks with variable force might induce cortical neural activation and muscle contraction to avoid decision errors [55], which suggested that the different performance according to different dynamic tasks may attribute to more complex neural control processes.The subsequent research results presented by our study may provide further evidences.
B. The α-band ERD Increases as the Frequency of Target Force Variation Increases, While the β-band ERD Increases as the Amplitude of Target Force Variation Increases The research suggested that the changing rate of force variation has a greater impact on the contralateral motor cortical responses in the α-band, where the averaged αband ERD increase as the frequency of target force variation increases.The frequency of target force variation was directly correlated to the performance precision which was considered to play an important role on human cognition.The α-band ERD was recognized to reflect attentional demands such as vigilance and anticipation [29], [48].The real-time force production requirements can excite participants to accelerate necessary cognitive process to meet the dynamic task changes, which consequently requires increased attentional resources for precise force modulation and the complex dynamic information integration from multiple sources such as visual and somatosensory inputs.Thus, the α-band ERD exhibited to be the positive correlation with the frequency of target force variation.On the other hand, the amplitude of target force variation showed significant relationship with the contralateral motor cortical activation in the β-band, where stronger average β-band ERD were generally observed as the amplitude of target force variation increases.As the production of grip force are positively correlated with ERD intensity [30], it was reasonable that the amplitude of target force variation potentially affect the β-band ERD as well.Previous research have reported the influence of the performance precision [28] and task difficulty level [15] on intensity of β-band EEG power spectrum.Increasing the amplitude of target force variation can somehow elevate the tracking difficulty followed with the increasing control requirements of fine force modulation, which may considerably contribute to the observed effect on β-band ERD.ERD intensity is related to cortical excitability and neural activation, and have been widely acknowledge as an useful metric to represent the cortical oscillations and commonly applied to cortical sensorimotor and cognitive analysis [10].Our results demonstrated different target force variation impacted the ERD in different frequency domain, as the frequency mainly effected on α-band ERD while the amplitude preferably change the β-band ERD.Considering the effectiveness and efficiency of stroke rehabilitations highly related to the cortical neural response during recovery training which demonstrated to be a long-term dynamic procedure, our study may provide fundamental evidences for developing adaptable rehabilitation prescription optimization in force aspect.As acknowledged, the cerebral cortex transmits information downward to control the motor unit recruitment and its relative discharge rates in order to fulfill movements, which is considered as a nonlinear process.Both the descending corticospinal pathway and the ascending sensory feedback pathway contribute to the cortical-muscular coherence in the β-band [14], [56], [57], [58], [59], [60], [61], [62].This study focused on the information transmission characteristics in both descending and ascending pathways.According to our results, all the cortical-muscular coupling exhibited the characteristics of bidirectionality, regardless of force task patterns (Fig 5).Therefore, during task executions, continuous information transmission between the cortex and muscles follows both the feedforward and feedback mechanisms, which requires information interactions between two rhythms in the sensorimotor system to fulfill movement adaptations.This is in accordance with the conclusion of Witham et al. [58] that "oscillations are transmitted bidirectionally between the sensorimotor cortex and responding muscles during stable muscle contraction."Additionally, our results also illustrated the contribution of downward pathways in the upward and downward information transmission during dynamic grip force tracking(Fig 5).In both the βand γ -bands, the strength of information transmission in the downward pathway consistently exceeds that of the upward pathway.In the β-band, the dTE EMG−EEG decreases as the frequency and amplitude of target force variation increase, indicating the increased transmission of sensory feedback information in the upward pathway according to requirements of force regulation increase.Contrarily in the γ -band, the dTE EMG−EEG increases as the amplitude and frequency of target force variation increase, which potentially denoted a shift in downward information transmission from the βto γ -band caused by the increased force fluctuations.
Both the amplitude and frequency of target force variation can impact the FV which was defined to represent the level of force regulation during the experimental dynamic tasks.The linear relationship analysis showed positive correlation between dT EEMG−EEG in both βand γ -bands and FV(Fig 6).In other words, the proportion of information transmitted in the downward pathway increases as demand for the level of force regulation increases, as the central nervous system continuously sends descending information flow to meet the ongoing demands for force adjustments.Meanwhile, the afferent feedback from the peripheral nervous system to the central nervous system is also proliferated along with dynamic training, which sequentially increased corresponding demand for sensory-motor processing and the relative corrective responses caused by growing prediction errors from feedforward mechanism as well.The results also showed the βto γ -band shift of information in the descending cortical-spinal pathway as the demand for force regulation increases, which might be attribute to the demands of force regulation required much more abundant information transmitting for dynamic fine movement controls (Fig7).

D. As the Frequency and Amplitude of Target Force Variation Increases, the β-band Coupling Strength Decreases Bidirectionally While the γ -band Coupling Strength Increases
This study employed normalization method [57] to describe the changing characteristics of overall information flow, and the variations TE was analyzed across different frequency bands and directions.The results showed similar bidirectional changing trends in TE across different force training patterns, regardless of frequency bands(Fig 8).Previous research have recorded the β-band cortical-muscular coupling correlated with the mild to moderate isometric muscle contractions [58], whereas γ -band tended to relate to stronger muscle force production control and dynamic motor strategies [59].Therefore, the cortical-muscular coupling shifts from the βto γ -bands as the amplitude and frequency of target force variation increases.Higher frequency oscillation of the cortical-spinal network is able to facilitate the rapid integration of multiple information from tactile, proprioceptive, visual and cognitive etc. for  dynamic force adaption requirements.The change in EMG stability then suggested the improvement in neural control of muscle activity.
Our results also described the change of TE in bi-directions and different frequency bands as FV increases (Table III).As force regulation demands increase, the decrease in bidirectional TE in the β-band indicated a shift to higher frequencies to meet more complex fluctuating task requirements.Meanwhile, the incoming dynamic motion information processing with focused attention probably increase the bidirectional TE in the γ -band as well [62].Moreover, the β-band in the efferent EEG-sEMG direction descended faster than the opposite sEMG-EEG way, while the γ -band ascended in the EEG-sEMG direction faster than in sEMG-EEG.This somehow agreed to the positive correlation between dTE EMG−EEG in both βand γ -bands and FV discussed above (Fig 6 (A)).Studies have highlighted the significant absence of cortical-muscular coupling in γ -band in stroke patients [63].Our findings could potentially serve for the dynamic motor rehabilitation program design by targeting the missing cortical-muscular coupling in relevant frequency bands.
Furthermore, the EMG stability [17], [48] has been considered to be reliable for motor performance assessment.This study introduced the metric of FV for quantified performance estimation.According to our results across five different force tracking tasks, the introduced metric of FV exhibited better discriminative ability of over traditional EMG stability in dynamic patterns.Moreover, comparing the slopes of linear regression between the two metrics and transfer entropy, the FV was also more sensitive to the TE changes than EMG stability.This may suggest FV as a potential useful indicator to provide evaluation of cortical-muscular coupling.
The mechanisms of neuro-muscular activity in regulating dynamic hand strength is a crucial aspect of motor function rehabilitation.This study investigated the effects of target force variation on level of force regulation, muscle contraction, brain activation, and cortical-muscular coupling to explore the intrinsic physiological response mechanisms of the human when faced with the demand of grip force variation.The research results indicate that as the regulatory demand increases, the muscle stability decreases and is significantly negatively correlated with the level of force regulation.The ERD increases significantly, the rate of force change mainly affects α-band ERD, and the amplitude of force change mainly affects the β-band ERD.And the coupling strength in the β-band decreases while the coupling strength in the γ band increases, showing a coupling characteristic that transfer from low-frequency to high-frequency.The findings of this study may guide the design of training strategies to optimize efficiency and effectiveness, enhance beneficial cortical activation, and induce key cortical-muscular coupling in the missing frequency bands during rehabilitation.Although the article only presents preliminary data on healthy subjects, future research will investigate stroke patients with upper limb motor dysfunction.
their dominant hand.Meanwhile, the non-dominant hands rested on the table.

TABLE II ERD
IN THE CONTRALATERAL SENSORIMOTOR CORTEX DURING THE MOTOR TASK (0-8s)