Effect of force adjustment modalities on characteristics for force generation and relaxation

Abstract

BACKGROUND:

The systematic characteristics of force generation and relaxation have been investigated using a graded isometric task for several target levels and magnitudes in the upper and lower limb. However, whether a relaxation modality affects the accuracy or speed of grading remains unclear. In addition, speed characteristics are still unclear in both force generation and relaxation modalities.

OBJECTIVE:

To investigate the effect of force adjustment modalities on force generation and relaxation characteristics.

METHODS:

Participants were instructed to match a target force level as quickly and as accurately as possible under peak and keep adjustment modalities. The force generation task was increased from 10% to 30%, 50%, and 70% of the maximum voluntary force (MVF). The force relaxation task was decreased from 70% to 50%, 30%, and 10% MVF. The recorded force was analyzed. Errors in reproduction were computed in both modalities and target levels of force.

RESULTS:

The errors of the peak adjustment modality were greater than those of the keep adjustment modality in both tasks. The reaction time was longer with the peak adjustment modality than with the keep adjustment modality in both tasks.

CONCLUSION:

Speed was affected by the choice of adjustment modality.

Keywords

Accuracy motor control speed

1. Introduction

An individual’s movements are controlled in various conditions based on subjective sensorimotor parameters. Accuracy in precisely controlling one’s movements according to the purpose and situation by adjusting the direction, velocity, and magnitude of the force plays a vital role in motor control. With an emphasis on the direction of the force, it is also important to ensure well-coordinated control of both force generation (muscle contraction) and relaxation (muscle relaxation). However, in situations requiring fine motor control, such as engaging in a sports activity and playing a musical instrument, it is difficult to control accuracy and smoothness as intended, especially during muscle relaxation [1, 2, 3].

Comparisons of functional magnetic resonance imaging results [4] or transcranial magnetic stimulation [5] for force relaxation and force generation have revealed different neural mechanisms. Neural substrates are activated for muscle contraction and relaxation. The neurophysiology of the muscle contraction mechanism has been explained by the well-known Henneman’s size principle [6], which describes the relationship between the size and recruitment of motor units (MUs). MUs are recruited from the smallest to the largest MUs to generate a force. For force relaxation, MUs are de-recruited in reverse order [7]. According to this principle, the accuracy of force relaxation may be lower than that of force generation, as the early de-recruitment of large MUs does not induce accurate adjustments. Furthermore, a study evaluating the discharge rate of multiple MU activities showed a greater force variability during force relaxation than during force generation [8]. Regarding the ability to control muscle generation and relaxation of force, as intended relative to the target level, previous studies have discussed the accuracy of forces and suggested that force relaxation is more difficult to control accurately than force generation [9, 10, 11, 12, 13, 14].

The systematic characteristics of force generation and relaxation have been investigated using a graded isometric task for several target levels and magnitudes in the upper limb [15] and lower limb [16]; with this method, the reasons for the increased difficulty associated with accurately controlling force relaxation compared with generation were noted. The results of the aforementioned studies showed that for the accurate control of forces, the magnitude of error was greater in force relaxation than in force generation, especially under conditions of a low magnitude of force. With respect to speed, the timing of force adjustments depended on the magnitude of the target force level for force generation and relaxation in both limbs; however, the reaction time was consistently shorter for force relaxation than for force generation in only the lower limbs. The different strategies showed the increased difficulty in controlling force relaxation compared with force generation, such as the need to control both the timing and peak rate of force development (RFD) in force relaxation. These reports show that the basic characteristics of force relaxation and generation were compared and clarified using graded tasks.

In previous studies, only ballistic control, that is peak adjustment, periodic [9, 10, 11] or discrete [12, 15, 16], have been considered for force control. However, only ballistic control should not be considered. Slow, or holding, constant force and various other adjustment modalities are also applicable. Performance characteristics, such as accuracy and speed, may vary depending on the adjustment modality (i.e., how the force is controlled) in both force generation and force relaxation.

A recent study on force generation focused on how contraction types, such as ballistic or tonic, affect grading characteristics [17]. This study utilized isometric force grading tasks at specific maximum voluntary contraction percentages (20%, 40%, 60%, and 80%) under two contraction types and showed control accuracy by evaluating the error between the intended force (subjective estimation of force) and the actual output force and assessing the force reproducibility using the coefficient of variance (CV). Consequently, the actual force of tonic contraction was significantly less than that of the ballistic contraction, and integrated electromyography and CV were larger under the ballistic contraction than under the tonic contraction, even at similar force levels. Thus, these findings suggest that characteristics depend on contraction types and that the accuracy for the requested contraction level was greater under the tonic contraction than under the ballistic one.

In contrast, only peak adjustment tasks, periodic [9, 10, 11] or discrete [15, 16], have been considered previously for force relaxation. However, it is still unclear whether the adjustment modality (i.e., how the force and the outcome of muscle activity are controlled) affects the characteristics of accuracy or speed in force relaxation. In addition, characteristics of speed are still unclear in both the force generation and relaxation modalities.

Based on the aforementioned study [17], we investigated two different adjustment modalities: (1) the peak adjustment modality, to control force under ballistic contraction/relaxation and (2) the keep adjustment modality, to control force under tonic contraction/relaxation. In this study, we have defined force “control” as the outcome of muscle activity.

This study aimed to investigate the differences in force control characteristics between peak and keep adjustment modalities during force generation and relaxation tasks, with an emphasis on studying force relaxation control characteristics. Force relaxation characteristics may also be dependent on adjustment modalities. The following hypotheses related to differences between adjustment modalities were considered based on previous studies.

In this study we have hypothesized that the reaction time will be constant regardless of the adjustment modalities. However, the adjustment time will be affected by the adjustment modalities; the adjustment time of the keep adjustment modality may be longer than that of the peak adjustment modality both in terms of force generation and relaxation. Moreover, The errors of the peak adjustment modality will be greater than those of the keep adjustment modality in force relaxation and force generation.

This study utilized part of the data from a previous study [18] regarding the peak adjustment modality in force generation. That study elucidated the effect of the force level condition before adjustment. On the other hand, the present study aimed to clarify the difference in force control characteristics by the adjustment modalities; therefore, the point of view in this study is novel and different from the previous study. To assess the above hypotheses in the terms of speed and accuracy, we applied two-way analysis of variance (modality $\times$ magnitude) in force generation and relaxation, respectively. Furthermore, as one possible strategy of force control, we proceeded from the perspective of the speed-accuracy trade-off.

2. Methods

2.1 Participants

Fifteen healthy, right dominant-footed women aged 21.7 $\pm$ 1.3 were enrolled in this study. All participants were right dominant-footed according to the criteria of the foot-preference inventory [19]. All procedures were approved by the Academic Ethics Committee of Nara Women’s University, Japan (Approval Number: 17–27) and conformed with the tenets of the Declaration of Helsinki. Prior to enrollment, all participants were fully informed about the purpose of the study and its procedures, and written informed consent was obtained.

Figure 1.

Experimental setup from the side.

2.2 Apparatus and experimental protocol

Figure 1 is a side view of the experimental setup. The output force of the participants was measured using a force-measuring device (Takei Scientific Instrument Co., Ltd., Japan) [16]. Participants were seated in the force-measuring device, with the right leg placed on the force plate and the knee joint fixed at 120 ${}^{\circ}$ of extension (180 ${}^{\circ}$ is full knee extension); this knee angle was selected based on a previous study that reported the highest magnitude of maximal isometric voluntary contractions at approximately 120 ${}^{\circ}$ of knee extension [20]. The left leg was straightened and positioned on the cylindrical pole. Both arms remained on each side of the body. The output of the force plate and the target line of the force level were displayed on a personal computer (NEC, VJ22LL-D). The target force level line, along with three light-emitting diode lights, controlled by a time programmer (Takei Scientific Instrument Co., Ltd.), were placed approximately 1.5 m from participants’ eyes to act as a visual stimulus.

2.3 Experimental tasks

Participants were instructed to produce an isometric knee extension force to match the target force level as quickly and accurately as possible using their right leg. They were asked to perform two discrete tasks: (1) the force generation task (to increase their force) and (2) the force relaxation task (to decrease their force). Given the target force levels of 10%, 30%, 50%, and 70% of the maximum voluntary force (MVF), they were asked to perform three magnitudes (three target force levels in each task; e.g., 20% magnitude for an increase from 10% to 30% MVF) of force control repetitions.

2.4 Adjustment modality

Moreover, the participants performed two tasks under the following two adjustment modalities (Fig. 2), with each modality performed on a different date.

Figure 2.

Measurement of force in peak (a) and keep (b) modalities.

2.4.1 Peak adjustment modality

The participants were instructed to instantly adjust the target force level during both tasks. During the force generation task, participants were instructed to reduce their force as soon as they achieved the target force level. In contrast to the generation task, after the target force level was adjusted instantly, the participants subsequently increased their voluntary force level during the force relaxation task.

2.4.2 Keep adjustment modality

The participants were instructed to quickly adjust the target force level and maintain their force for 1 s during both tasks [21]. Subsequently, participants were instructed to relax their force.

The participants performed the task under a simple reaction condition. Each trial began with a 500-ms visual warning signal, and the subsequent “go” signal was presented for 500 ms. The foreperiod, the interval between the warning signal and the “go” signal, was 2.0 s. They were informed of the magnitude before each trial along with a visual warning signal and were instructed to control their force following the “go” signal. Participants were instructed to maintain a start force level of 10% MVF (for the generation task) or 70% MVF (for the relaxation task) prior to the warning signal, with a visual presentation feedback of the force level. After maintaining the start force level for 1.0 s, the participants were informed to turn their eyes toward the warning signal, the warning signal was presented for 500 ms, and the subsequent “go” signal was presented for 500 ms [12].

The generation task data in the peak adjustment modality were obtained from a previous study [18].

2.5 Procedure

Participants were initially instructed to produce an isometric force with a maximum effort for 1 s three separate times. The maximum force value of the three trials was set as each participant’s MVF. Participants then practiced controlling their force to the target level, with visual feedback provided to facilitate learning [10]. Up to 10 trials were offered at each target force level. Once participants could accurately control their force output, one practice session using the warning and “go” signals was conducted.

For the test conditions, the target force level was explained to the participants prior to each trial. Participants did not receive visual feedback on their performance during the trials, but they did receive information regarding their performance using a summary of their force after completing the 10 trials. A 1-min rest period was provided between each force level, with a 5-min rest interval between the two tasks (force generation and force relaxation). The order of the tasks was counterbalanced. Regarding force magnitude, we used a blocked randomized design, with the 10 trials at a given level as one block and the order of the “force level” blocks randomized across participants. After completing the test conditions, participants again produced three MVFs to exclude the effects of fatigue. The order of the adjustment modalities was counterbalanced.

2.6 Data collection and performance measures

The produced force was recorded. All recordings were digitized at 1,000 Hz using a Biopac MP150 data acquisition system (Biopac Systems, CA, USA). The data of trials that exceeded $\pm$ 2 standard deviations of the reaction time were excluded, and the number of trials among all magnitudes was unified; eight trials were randomly selected for analysis from each set of 10 trials at each magnitude for each adjustment modality. Data regarding force were filtered using a digital filter with a 100-Hz low-pass cut-off frequency to produce a mean value for further analysis; this value was selected based on a previous report [16].

Time was calculated as follows (Fig. 3(a), (b)): the baseline force was calculated as the average force produced over a 300-ms period prior to the “go” signal; the average force development rate (N/s) was calculated over a 10-ms period following the “go” signal; subsequently, force onset was defined as the first time point during which the average RFD exceeded 50% of the baseline force during the force generation task or decreased below 50% of the threshold during the force relaxation task [16]. With respect to the keep adjustment modality, force offset was defined as the first time point during which the average RFD decreased below 40% of the threshold during both force generation and relaxation tasks.

Figure 3.

Definition of the force for peak (a) and keep (b) modalities during the force generation task.

Speed and accuracy were calculated as follows.

Reaction time

The reaction time was defined as the interval between the “go” signal and force onset.

Adjustment time

In the peak adjustment modality, the adjustment time was defined as the time between the force onset and maximum (generation task) or minimum force (relaxation task) occurrence, whereas in the keep adjustment modality, it was defined as the time between the force onset and offset.

Total adjustment time

The total adjustment time in the peak adjustment modality was defined as the time between the “go” signal and the maximum (generation task) or minimum force (relaxation task) occurrence, whereas in the keep adjustment modality, it was defined as the time between the “go” signal and force offset.

Peak RFD

The peak RFD was defined as the peak value of the RFD over the adjustment time and was calculated in the same manner. The time to reach peak RFD (time-to-peak RFD) was also calculated.

Force level

The force level (%MVF) was defined as the relative value of the maximum or minimum force of each participant’s MVF in the peak adjustment modality and as the relative value of the average force during the 1-s interval from the offset point in the keep adjustment modality [21].

Errors

The difference between the accuracy of the force level and each target force level was calculated to evaluate the following three errors: the constant error, which was defined as the difference between the signed values of the force level and each target force level; the absolute error, which was defined as the absolute value of the constant error; and the variable error, which measured force reproducibility in participants and was defined as the average of the difference between signed values of the force level and each participant’s average force level.

2.7 Statistical analysis

In this study, for the generation task in the peak adjustment modality, we conducted further analyses utilizing the same data from a previous study [18], while the rest of the data were all newly obtained from the present study.

To test the hypotheses, we compared magnitudes of force control and adjustment modalities in each task simultaneously using the following statistical analysis. The data set was tested for homoscedasticity prior to evaluating differences between magnitudes and adjustment modalities. A two-way repeated measure analysis of variance was conducted for error, time, and peak RFD parameters to test differences in mean values between each magnitude and adjustment modality. Intra-participant factors were magnitude (20%, 40%, and 60% magnitudes) and adjustment modality (peak and keep adjustment modalities). Pairwise comparisons were performed using Bonferroni post-hoc tests when significant effects were found. For repeated measures, we tested whether Mauchly’s sphericity assumption was violated. If the result of Mauchly’s test was significant and the assumption of sphericity was violated, Greenhouse-Geisser’s adjustment was used to correct sphericity by altering the degrees of freedom using the correction coefficient epsilon. Sphericity was maintained in all cases; thus, Greenhouse-Geisser’s correction was not used. Data were analyzed using SPSS software for Windows (IBM SPSS Statistics Version 25, SPSS Inc., NY, USA). A $p$ -value $<$ 0.05 was considered statistically significant.

Figure 4.

Mean values and standard deviations for the force level. Note: *: Significant difference between the magnitudes, ***: $p<$ 0.001. †: Significant difference between the adjustment modalities, †: $p<$ 0.05, ††: $p<$ 0.01.

3. Results

3.1 Accuracy

The mean and standard deviations of the force levels during the force generation and relaxation tasks of all participants are summarized in Fig. 4. During the force generation task, the force level was influenced by a significant interaction between the magnitude and adjustment modality ( $F\;2,14=$ 4.258, $p<$ 0.05) and by significant main effects of the magnitude ( $F\;2,14=$ 676.003, $p<$ 0.001) and adjustment modality ( $F\;1,7=$ 11.421, $p<$ 0.05). The force level increased when the magnitude increased from 20% to 60% (all: $p<$ 0.001), with the force level in the peak adjustment modality being significantly greater than that in the keep adjustment modality (20% vs. 40%; $p<$ 0.01 and $p<$ 0.05, respectively).

During the force relaxation task, the force level was influenced by significant main effects of the magnitude ( $F\;2,14=$ 379.752, $p<$ 0.001) and adjustment modality ( $F\;1,7=$ 20.748, $p<$ 0.01). The force level decreased when the magnitude increased from 20% to 60% (all: $p<$ 0.001), with the force level in the keep adjustment modality being significantly greater than that in the peak adjustment modality.

3.2 Error

The mean and standard deviations of the constant, absolute, and variable errors of all participants during both tasks are shown in Fig. 5(a)–(c).

Figure 5.

Mean values and standard deviations of the constant (a), absolute (b), and variable (c) errors. Note: *: Significant difference between the magnitudes, *: $p<$ 0.1, *: $p<$ 0.05, **: $p<$ 0.01, ***: $p<$ 0.001. †: Significant difference between the adjustment modalities, †: $p<$ 0.1, †: $p<$ 0.05, ††: $p<$ 0.01.

Regarding the constant error, a significant interaction between the magnitude and adjustment modality ( $F\;2,14=$ 4.258, $p<$ 0.05) and significant main effects of the aforementioned parameters ( $F\;2,14=$ 5.755, $p<$ 0.05 and $F\;1,7=$ 11.421, $p<$ 0.05, respectively) were identified during the force generation task. The constant error of peak adjustment was significantly greater at a 20% magnitude than at 60% and 40% magnitudes (60%: $p<$ 0.05, and 40%: $p<$ 0.1). Moreover, the constant error was significantly higher in the peak adjustment modality than in the keep adjustment modality at 20% and 40% magnitudes (20%: $p<$ 0.01, and 40%: $p<$ 0.05). During the force relaxation task, the constant error was influenced by significant main effects of the magnitude ( $F\;2,14=$ 34.697, $p<$ 0.05) and adjustment modality ( $F\;1,7=$ 20.744, $p<$ 0.01) and was greater from 20% to 60% magnitudes (20% and 40%: $p<$ 0.001 and 20%, 40% and 60%: $p<$ 0.01), implying that the constant error was worse in the peak adjustment modality than in the keep adjustment modality.

Regarding the absolute error, a significant interaction between the magnitude and adjustment modality ( $F\;2,14=$ 5.438, $p<$ 0.05) and main effects of the aforementioned parameters ( $F\;2,14=$ 21.261, $p<$ 0.001 and $F\;1,7=$ 6.285, $p<$ 0.05, respectively) were identified in the force relaxation task. In the peak adjustment modality, absolute error decreased when the magnitudes increased from 20% to 60% (20%, 60%, and 40%: $p<$ 0.05, 20% and 60%: $p<$ 0.01), and in the keep adjustment modality, the absolute error was greater at a 20% magnitude than at a 40% magnitude ( $p<$ 0.05). Moreover, the absolute error in the peak adjustment modality was greater than that in the keep adjustment modality at 20% and 40% magnitudes ( $p<$ 0.05 and $p<$ 0.1, respectively). There was no significant difference in force generation between the adjustment modalities.

Regarding the variable error, there were no significant differences in force generation and relaxation tasks between the adjustment modalities.

Overall, during the force generation task, no differences in the absolute and variable error values were observed across the three levels of force magnitude (20%, 40%, and 60%), with the constant error being higher at a 20% magnitude than at a 60% magnitude. During the force relaxation task, the constant error negatively decreased as the magnitude increased for both adjustment modalities; the absolute error decreased as the magnitude increased in the peak adjustment modality and decreased when the magnitude decreased from 40% to 20% magnitude in the keep adjustment modality. Moreover, when comparing adjustments modalities at the same magnitude, the constant error was greater in the peak adjustment modality than in the keep adjustment modality at the 20% and 40% magnitudes during the force generation task and lesser in the peak adjustment modality than in the keep adjustment modality in all magnitudes during the force relaxation task. The absolute error in the peak adjustment modality was greater than that in the keep adjustment at the 20% magnitude during the force relaxation task.

3.3 Speed

The mean and standard deviations of the reaction time, adjustment time, and total adjustment time of all participants during the two tasks are shown in Fig. 6(a)–(c). The reaction time was mainly influenced by the adjustment modality ( $F\;1,7=$ 19.850, $p<$ 0.01), with a significantly longer reaction time in the peak adjustment modality than in the keep adjustment modality during the force generation task. The force relaxation task was also influenced mainly by the adjustment modality ( $F\;1,7=$ 13.856, $p<$ 0.01), with a significantly longer reaction time in the peak adjustment modality than in the keep adjustment modality.

Figure 6.

Mean values and standard deviations of the reaction (a), adjustment (b), and total adjustment (c) times. Note: *: Significant difference between the magnitudes, *: $p<$ 0.1, *: $p<$ 0.05, **: $p<$ 0.01, ***: $p<$ 0.001. †: Significant difference between the adjustment modalities, †: $p<$ 0.05, ††: $p<$ 0.01.

Adjustment time was mainly influenced by the magnitude ( $F\;2,14=$ 40.859, $p<$ 0.001) and adjustment modality ( $F\;1,7=$ 20.777, $p<$ 0.01) and was significantly longer from 20% to 60% magnitudes (20% and 40%: $p<$ 0.01, 20%, 40%, and 60%: $p<$ 0.001). The adjustment time was significantly longer in the keep adjustment modality than in the peak adjustment modality during the force generation task. During the force relaxation task, the adjustment time was influenced mainly by the magnitudes ( $F\;2,14=$ 71.950, $p<$ 0.001) and was significantly longer from 20% to 60% magnitudes (20%, 40%, and 60%: $p<$ 0.001, 40% and 60%: $p<$ 0.05).

Figure 7.

Mean values and standard deviations of the peak rate of force development (a) and time-to-peak rate of force development (b). Note: *: Significant difference between the magnitudes, *: $p<$ 0.1, *: $p<$ 0.05, **: $p<$ 0.01. †: Significant difference between the adjustment modalities, †: $p<$ 0.05.

Regarding the total adjustment time, a significant interaction between the magnitude and adjustment modality ( $F$ 2, 14 $=$ 6.037, $p<$ 0.05) and significant main effects of the aforementioned parameters ( $F\;2,14=$ 36.696, $p<$ 0.001 and $F\;1,7=$ 13.627, $p<$ 0.01, respectively) were identified during the force generation task. Total adjustment times were longer at a magnitude of 20% than at the magnitudes of 40% and 60% in both the peak and keep adjustment modalities (40% and 20%, 60%: $p<$ 0.1; 20% and 60%: $p<$ 0.05; 20% and 40%: $p<$ 0.05; and 20%, 40%, and 60%: $p<$ 0.01, respectively). Total adjustment times were longer in the keep adjustment modality than in the peak adjustment modality at all magnitudes (all: $p<$ 0.05). The force relaxation task was mainly influenced by the magnitude ( $F\;2,14=$ 35.140, $p<$ 0.001) and was significantly longer at magnitudes of 40% and 60% than at a magnitude of 20% (all: $p<$ 0.001).

Overall, the adjustment time increased as the force magnitude increased during both force generation and relaxation tasks. Adjustment times for force generation tasks were consistently longer in the keep adjustment modality than in the peak adjustment modality at all magnitudes, while the reaction times for both force generation and relaxation tasks were consistently longer in the peak adjustment modality than in the keep adjustment modality at all magnitudes.

The mean and standard deviations of the peak RFD and the time-to-peak RFD of all participants during both tasks are shown in Fig. 7(a) and (b). The peak RFD was mainly influenced by the magnitude ( $F\;2,14=$ 47.724, $p<$ 0.001) and adjustment modality ( $F\;1,7=$ 10.970, $p<$ 0.05) and was significantly greater from 20% to 60% magnitudes (all: $p<$ 0.01). The peak RFD was also significantly greater in the keep adjustment modality than in the peak adjustment during the force generation task. The force relaxation task was mainly influenced by the magnitude ( $F\;2,14=$ 30.874, $p<$ 0.001) and adjustment modality ( $F\;1,7=$ 7.565, $p<$ 0.05) and was significantly greater from 20% to 60% magnitudes (20% and 40%: $p<$ 0.05, 20%, 40%, and 60%: $p<$ 0.01). The relaxation task was significantly greater in the keep adjustment modality than in the peak adjustment modality.

The time-to-peak RFD was mainly influenced by the magnitude ( $F\;2,14=$ 8.904, $p<$ 0.01) and was significantly longer from 20% to 60% magnitudes (20% and 40%: $p<$ 0.1, 20% and 60%: $p<$ 0.05) during the force generation task. During the force relaxation task, the main effect of the magnitude ( $F\;2,14=$ 13.049, $p<$ 0.01) was identified; the force relaxation task was longer at magnitudes of 60% and 40% than at a magnitude of 20% (60%: $p<$ 0.1, and 40%, $p<$ 0.01).

Overall, during both the force generation and relaxation tasks, the peak RFD increased as the magnitude increased, and this was associated with an increase in the time-to-peak RFD. The peak adjustment modality showed a greater peak RFD than the keep adjustment modality, while the time-to-peak RFD remained constant at all magnitudes.

4. Discussion

This study describes force generation and relaxation characteristics, with an emphasis on the difference between adjustment modalities during force relaxation.

4.1 Force control accuracy

First, three force levels could be graded in both adjustment modalities because force levels were positively related to the magnitude during both force generation and relaxation (Fig. 4). With respect to the characteristics of peak adjustment, our study reports results that were similar to those of several studies showing positive relationships between force levels and force control magnitudes for both force generation and relaxation in the upper [15] and lower limbs [16]. To the best of our knowledge, this study is the first to evaluate grading characteristics of keep adjustment modality by utilizing an experimental paradigm comparing peak adjustment modality.

Regarding the difference in accuracy between the peak and keep adjustment modalities for force generation at 20% and 40% magnitudes, the force levels of the peak adjustment modality were greater than those of the keep adjustment modality. Specifically, a greater constant error at the 20% magnitude was observed in the peak adjustment modality than in the keep adjustment modality (Fig. 5). These results indicate that accurately controlling force generation is more difficult by peak adjustment than by keep adjustment, especially when controlling small amounts of force. Our findings are consistent with the results of a previous study that reported the relationship between the intended force and the actual force during isometric plantar flexion [17].

Regarding force relaxation, force levels in the peak adjustment modality were greater than those in the keep adjustment modality at all magnitudes (Fig. 4). In addition, constant errors in the peak adjustment modality were lesser than those in the keep adjustment modality at all magnitudes, and absolute errors of the peak adjustment modality at 20% and 40% magnitudes were greater than those of the keep adjustment modality (Fig. 5). These results indicate that accurately controlling force relaxation is more difficult by peak adjustment than by keep adjustment. To the best of our knowledge, this study is the first to clarify that force relaxation by peak adjustment is more difficult to accurately control than by keep adjustment, irrespective of the magnitudes and force generation.

Regarding grading variability, no differences in variable error values were observed across the three magnitudes, both during force generation and relaxation (Fig. 5). Thus, the reproducibility of force control was constant, irrespective of the force adjustment modalities.

4.2 Force control speed

The reaction time in the peak adjustment modality was longer than that in the keep adjustment modality during both force generation and force relaxation (Fig. 6), suggesting that the keep adjustment modality enhances the speed to begin force control rather than the peak adjustment modality. Generally, the reaction time can assess the required time for nervous system processing [22]. Previous studies have reported the features of reaction time from various aspects as follows. Reaction time is negatively related to magnitudes of force control in various motor tasks in isometric finger movements [23] and in the lower limbs [16], and this relationship is similar during both force generation and relaxation [16].

The complexity of motor tasks is considered one of the reasons for this result. A previous study reported that the reaction time depends on the motor sequence length [24] and consecutive force control, including the switching of direction [25]. The length of the reaction time is affected by the time of searching for the motor program from the motor program buffer, so the difference in the motor control processing is one of the key elements of reaction time characteristics.

In this study, as for peak adjustment modality, it is necessary to prepare and conduct the motor program in a short period because of the short adjustment time. Besides, depending on the short adjustment time, the accuracy of the peak adjustment modality was lower and showed high complexity compared with the keep adjustment.

Furthermore, force conditions before adjustments begin are another key element. A study on motor planning perturbation showed that the reaction time is longer when the reaction stimulus occurs during the peak adjustment modality rather than during isometric sinusoidal tasks [26]. Another study showed that the reaction time is longer when preceded by a dynamic anticipatory strategy rather than a steady strategy and by a decreased phase rather than an increased phase [27].

Most importantly, our study shows the novel finding that the adjustment modality is one of the important factors affecting the reaction time. Specifically, the keep adjustment modality excels at initially controlling forces quickly compared with the peak adjustment modality during both force generation and relaxation.

Regarding the adjustment time, force generation in the keep adjustment modality was longer than that in the peak adjustment. Meanwhile, in terms of force relaxation, there was no difference between peak and keep adjustment modalities (Fig. 6). Moreover, regarding force generation, peak RFD and time-to-peak RFD results reinforced the characteristics of the adjustment time, which was lower in the peak adjustment modality than in the keep adjustment modality. The peak RFD in the peak adjustment modality was greater than that in the keep adjustment modality, although the time-to-peak RFD was constant between adjustment modalities at all magnitudes during force generation (Fig. 7). These results show that the peak adjustment modality could shorten the time to control forces compared with the keep adjustment modality.

One possible factor that increased the RFD was that MU synchronization occurred during rapid contraction [28]. Previous studies have reported that differences in contraction styles and speeds affect the MU activity because the magnitude of force production is controlled by the recruitment and firing rate of MUs [29, 30]. Moreover, the firing rate increases as the movement speed increases [31]. Since electromyography data were not analyzed in this study, such an interpretation is speculative. Based on the analysis of our results regarding the force control task, changes in the MU activity may affect the speed characteristics. Specifically, controlling forces with a great force development rate leads to a shortened adjustment time during rapid force generation.

In contrast, the adjustment time in force relaxation was constant regardless of the peak or keep adjustment modality (Fig. 6). Additionally, the peak RFD in the peak adjustment modality was greater than that in the keep adjustment at all magnitudes (Fig. 7). The length of the adjustment time was the same in both adjustment modalities. However, the peak RFD indicated that the peak adjustment modality steeply controlled forces compared with the keep adjustment modality. Hence, force relaxation was different between peak and keep adjustment modalities. It is speculated that the MU activity during force relaxation might markedly differ from that during force generation.

4.3 The underlying mechanism of the relationship between the accuracy and speed of force control

Our results showed that accuracy is low and control is rapid in the peak adjustment modality and vice versa in the keep adjustment modality. This relationship could be shown by the speed-accuracy trade-off function, which purports that speed is negatively correlated with accuracy [32, 33]. The effect of speed and accuracy has been investigated using “accurate” and “fast” grading tasks as rapidly as possible during isometric force control tasks with elbow flexion [34]. Consequently, both reaction and motor time became longer during the “accurate” task than during the “fast” task. Moreover, Buchanan, Park, and Shea reported a lower speed when the difficulty index increased during tasks conducted to evaluate upper limb motion [35]. The mechanism of this relationship may be influenced by afferent feedback. It has been reported that there is no sufficient time to use the available afferent feedback from peripheral sensory receptors to conduct motor commands with a feedback control system under ballistic conditions [36].

Considering our force generation results, which are certainly consistent with the speed-accuracy trade-off function, the accuracy of the peak adjustment modality was lower than that of the keep adjustment modality because the adjustment time is longer, and the peak RFD is greater. Similarly, for force relaxation, Choi et al. investigated motor responses to force relaxation by comparing the effects of durations and the magnitude of force control during isometric elbow flexion, focusing on force and electromyography responses [37]. Force relaxation guided by a longer ramp duration showed a lower force variability and overshoot ratio than that guided by a shorter ramp duration.

Nevertheless, force relaxation results do not completely and directly apply to the speed-accuracy trade-off. Although the adjustment time was constant during force relaxation in both modalities, peak RFD of the peak adjustment modality was greater than that of the keep adjustment modality. The greater peak RFD means that the magnitude adjusted per unit of time was greater, so the peak adjustment modality controlled a greater magnitude in a shorter time than the keep adjustment modality did. Thus, low force relaxation accuracy was considerably caused by a great peak RFD. A possible reason for these findings may be explained by Henneman’s size principle [6], which describes the relationship between the size and de-recruitment of MUs for force relaxation [7], as the early de-recruitment of large MUs in a short time does not induce accurate adjustments.

The practical implications of the results of this study are as follows. If possible, flexibility in the modality of adjustment should be made, depending on whether a quick or accurate adjustment is required, as this can result in a performance that made the desired objectives. The limitation of the present study is that we focused only on the force data, and it is necessary to analyze electromyography results in future studies to clarify the mechanism of the central nervous system in force control.

5. Conclusions

The findings of this study indicate that the differences in speed and accuracy in force control between the peak and keep adjustment modalities were significant. In particular, low accuracy and rapid control in the peak adjustment modality and vice versa in the keep adjustment modality were observed. The accuracy of the peak adjustment modality was lower than the keep adjustment modality during both force relaxation and generation. The reaction time was longer in the peak adjustment modality (and was, therefore, less quick) than in the keep adjustment modality during both force generation and relaxation. The adjustment time showed different tendencies between force generation and relaxation.

Author contributions

CONCEPTION: Chiaki Ohtaka, Motoko Fujiwara.

PERFORMANCE OF WORK: Chiaki Ohtaka.

INTERPRETATION OR ANALYSIS OF DATA: Chiaki Ohtaka.

PREPARATION OF THE MANUSCRIPT: Chiaki Ohtaka.

REVISION FOR IMPORTANT INTELLECTUAL CONTENT: Motoko Fujiwara.

SUPERVISION: Motoko Fujiwara.

Ethical considerations

All procedures were approved by the Academic Ethics Committee of Nara Women’s University, Japan (Approval Number: 17–27) and conformed with the tenets of the Declaration of Helsinki. Prior to enrollment, all participants were fully informed about the purpose of the study and its procedures, and written informed consent was obtained.

Funding

The authors report no funding.

Footnotes

Conflict of interest

The authors have no conflicts of interest to report.

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