Optimal Motor Point Search Using Mm-Order Electrode Arrays

Human-machine integration has been widely implemented in various fields, such as entertainment, human movement assistance, and rehabilitation. This study focuses on electrically-induced muscle contractions. In this technology, it is important to stimulate the optimal position, called the motor point (MP), on the muscle belly to induce the contraction with the lowest current injection. Because the positional relationship between the skin surface and muscles varies according to muscle contraction and body posture, it is difficult to achieve constant and accurate stimulation. Therefore, targeted motor intervention is not possible in several instances. We propose an approach that automatically identifies and stimulates a single precise MP in response to individual differences and postural changes using mm-order electrode arrays in two dimensions (2D). In this study, we develop a system to search for MPs by arranging 2-mm diameter electrodes in a 2D array. Our experiments successfully visualized the MPs in a 2D skin surface, which shifts according to the elbow joint angle change and twisting movement. The results demonstrated the feasibility of 2D electrode arrays. These findings contribute to the design of future devices and an algorithm for electrical muscle stimulation that enables effective muscle contraction.


I. INTRODUCTION
Technological advancements in recent decades have helped humans develop tools that enhance their overall physical abilities. These advancements pivoted the development of motor intervention systems toward the capability of measuring and processing human motor skills that can be controlled with millisecond-order precision and provide appropriate motor interventions (e.g., power-assist suit [1], human-machine mutual actuation [2], interactive systems for controlling a user's motion [3], [4], and cognition [5], [6]). Because of The associate editor coordinating the review of this manuscript and approving it for publication was Alessandro Floris . their advantages, motor intervention systems are suitable for rehabilitation and human augmentation.
Electrical muscle stimulation (EMS) is a solution for motor intervention that induces muscle contraction through surface electrodes. It is used for rehabilitation as functional electrical stimulation (FES) [7], [8] and muscle training [9] because it externally drives muscle contraction.
The positioning of electrodes is critical when implementing EMS and the optimal positions are named motor points (MPs). Anatomical studies have defined an MP as the site where the motor branch, which is the efferent nerve, enters the muscle belly [10], [11]. When stimulation is performed from the skin surface, the MP is defined as a point on the skin that causes muscle contraction with the smallest current compared to the surrounding area because it can be stimulated via various tissues, such as the skin and muscles inside the arm. [12]. Previous studies searched for the MP on the skin surface [13], [14]. They reported that the stimulation of the MP helps to improve the intensity of the contractions and decreases the total current when compared to the stimulation of other areas in the same muscle. Because the high current stimulation is more likely to cause discomfort or pain, the stimulation of the MP is also expected to reduce discomfort and pain.
A simple approach to stimulate the MP is using large electrodes in contact with the skin over a wide area. It has been reported that decreasing the size of the electrodes reduces the pain threshold of applied current from the electrodes because the current density increases [15]. However, studies have shown that the amount of current required for muscle contraction also reduces [15], [16]. Consequently, the high current density of a mm-order electrode is expected to further decrease the current necessary to induce movement [17]. That is, locating MPs more precisely with smaller electrodes would not be a disadvantage in practical use.
One advantage of smaller electrodes is that they are less likely to stimulate other haptic receptors, which can reduce pain and tactile sensation. However, MPs are difficult to identify using small electrodes, and thus a larger current may be required because of possible stimulation outside the MPs. To address this issue, previous research focused on developing selective stimulation devices with multiple electrodes to stimulate the muscles necessary for the target motion in the forearms, which have many muscles [18], [19], [20], [21], [22], [23], [24]. Furthermore, during flexionextension movements, it becomes increasingly difficult to identify MPs because of positional changes in the muscles and skin ( Fig. 1a-b) [25], [26]. In addition, the positional relationship between the skin surface and muscles changes during twisting movements or wrist rotation ( Fig. 1c-d). If a large electrode was used, it could stimulate muscles other than the target particularly, in body regions with high muscle density, possibly causing unnecessary muscle contraction.
In previous studies [25], [26], the MP's positional change was observed only for the elbow-shoulder direction of the biceps brachii. The positional change of the MP caused by the twisting motion was not considered. To identify the MP for postural changes ensuing from natural movements involving rotation of the wrist, the electrodes' positions must be moved two-dimensionally.
One solution would be covering the 2D area with many electrodes and identifying the 2D distribution of the peak vibration intensity caused by the muscle contraction intensity with a fixed current. However, an exhaustive search method that identifies MPs with many electrodes, is time-consuming. If we successfully observe the gradient, which is the spatial distribution of the minimum current required for contraction, this search time is expected to be shortened with a gradient method. Therefore, in this research, we explored whether FIGURE 1. Concept of MP shift and electrode selector. Note that the degree of diffusion depends on the size and resistance distribution of the electrodes and the position of the electrodes. (a-b) The MP shifts with muscle contraction, and by selecting the appropriate electrodes simultaneously, the system can constantly stimulate the MP. The red curves represent the muscle. (c-d) The positional relationship between the skin surface and muscles changes during the twisting movement. If the electrode is not shifted, the device could stimulate other muscles.

FIGURE 2.
Electrode selector. One electrode is 2 mm in diameter, and is arranged vertically and horizontally in an 8 × 8 grid at a pitch of 2.5 mm. Overall size of the electrode array is 19.5 mm. The contact area between the electrode arrays and the human skin consists of a gel sheet (upper right). The distance of the extended states between the two grids was 26 cm. the peak of muscle contraction, measured by accelerometer intensity across the electrodes, has a 2D gradient.
To search for MPs, we developed a prototype system that uses mm-order-sized electrodes. Specifically, we developed 2-mm diameter electrode arrays at a pitch of 2.5 mm, expecting that this is sufficient resolution for a precise MP search, enabling accurate motor intervention.
To identify the optimal resolution and size of an electrode, the following examinations were conducted. First, we verified that the resolution of the electrode arrays is sufficient for the gradient descent algorithm. Next, we verified whether a The participant's forearm was placed on a platform with a dent. The palm is turned sideways. (b) Electrode placement for the right arm. y-axis was taken in the direction from the participant's shoulder to the elbow, and the x-axis in the direction from left to right for analysis. To ensure that the distance between the electrode pairs (one for each electrode array) was always constant, the electrode pairs were shifted simultaneously in the same direction at a pitch of 2.5 mm. The distance between the two grids was 2-6 cm. It varies depending on the participant's arm.
smaller electrode reduces the amount of EMS current, even for mm-order electrodes. Finally, we observed whether the position of the MP changed with posture changes. We also proposed a system that can search for the MP automatically in combination with mechanomyography (MMG).
This study contributes to the design of a future device and an electrical muscle stimulation algorithm that enables effective muscle contraction measurement by an accelerometer.

II. MATERIALS
We developed a device that contains two electrode arrays to identify MPs. The MP search is automated by combining electrode arrays with an accelerometer that measures muscle contraction.

A. ELECTRODE SELECTOR
We developed an electrode selector to change the electrode positions to capture the MP. One array consisted of 64 (8 × 8) electrodes, as shown in Fig. 2, with current flowing between two electrode arrays, as shown in Fig. 3. The diameter and pitch of the electrodes were 2 and 2.5 mm, respectively. An analog switch (HV-2803) and a microcontroller (ESP-32) were used to control the position of the electrodes. Some electrodes in one electrode array are connected to the anode and the others float. At that time, some electrodes in the other electrode array are connected to the cathode and the others become float. The two electrodes were either anode or cathode, and a current flowed between them. This configuration was constructed to correspond to the experiments in previous studies [25], [26].
The contact area between each electrode array and skin comprised a gel sheet ( Fig. 2 upper right). Note the gel sheet's high resistance (surface resistivity: 4.2×10 5 , volume resistivity: 4.2 × 10 4 /cm, thickness : 1mm). Although the position and size of the electrodes must be determined so that the current density at the MP inside the muscle is high, the actual current flow path depends on the skin's resistance distribution and the electrical properties of the volume through which the current flows. Note that the current diffuses even in the small electrodes, but changes in current density distribution affect contraction.
Four adjacent electrode pads were arranged in a 2 × 2 grid measuring 4.5 × 4.5 mm. These simultaneously activated pads were used as a single electrode. As shown in Fig. 3b, to ensure that the distance between the electrode pair (one for each electrode array) was always constant, electrode pairs were shifted simultaneously in the same direction at a pitch of 2.5 mm. Thus, in total, 49 (7 × 7) electrode-position patterns were used for the stimulation. The impedance at only one unit electrode pad-pair was high, and the current did not flow in the preliminary test. We set the smallest electrode size to 2 × 2 units.

B. EMS GENERATOR
A custom-made constant-current circuit was used in the EMS generator to ensure a constant output current. In this circuit, the computer and human body were insulated for safety at a maximum current of 10 mA. The current was adjusted in 0.01 mA increments (with a 200 Hz monophasic square wave, 200 µs pulse width, and a duration of 100 ms). Waveforms were determined with reference to previous studies [4]. The maximum voltage of this device is 84 V.

C. MECHANOMYOGRAM
An accelerometer (MPU9250) was used for the MMG to measure muscle contraction (2000 Hz sampling frequency, 5 Hz high-pass filter). The waveform of the MMG is the root mean square of the x-, y-, and z-axes, which are determined as shown in Fig. 3b, and the mean absolute value (MAV) of the 15-ms window was used as the index. It is widely used for MMG analyses, as shown in Fig. 4. The MAV corresponds to the intensity of the muscle contraction.

III. METHODS
Two experiments were conducted to validate the feasibility of the device in identifying the MP. Thirteen healthy male adults participated in this experiment (average age of 25.4, standard deviation (SD) = 2.3, one left-handed). All the participants provided written informed consent and the study design was approved by an ethics review board at the University of Tokyo.

A. PREPARATION 1) PARTICIPANTS' POSTURE
First, each participant thoroughly wiped the bicep area using an alcohol towel. Next, they sat on a chair and placed their right elbow on a trough-shaped platform (elbow joint at an angle of 30 • and the palm facing sideways, as seen in Fig. 3a). The elbow joint angle was adjusted by moving the platform upward and downward.

2) PRELIMINARY MP SEARCH
To place the electrode arrays approximately on the MP position in the reference posture, electrodes sized 19.5 × 19.5 mm were used (i.e., all electrodes were activated at the largest size) to search for the MP. Then, the electrode array device was manually moved over the biceps brachii from the elbow to the shoulder.
The electrode position was found through stimulation and by visually observing muscle contraction. Then, with the electrode size fixed at 2 × 2 pads (4.5 × 4.5 mm), we identified the approximate position of the MP by the following procedure.
1. The current value was determined to the extent that the muscle contracted, but the arm did not move at the center electrode position.
2. The stimulation was conducted at the center and four corners using the current values determined in step 1.
3. If the muscle contraction intensity observed at the center was the highest, the rough search was terminated. If the muscle contraction intensity at the center was not the highest, the electrode was reattached in the direction where the highest contraction intensity was observed, and we returned to step 1.

3) THRESHOLD
Next, the minimum current value (threshold) at which EMS-induced muscle contraction occurs was observed to determine the current value. Apart from using the four corner thresholds to determine the current value, we also created a heat map of the threshold values for the preliminary experiment to determine whether the MP can be identified with the 2D threshold distribution. We measured 49 electrode positions. The threshold values were measured using a staircase method as follows: 1. Start with the initial current. If muscle contraction occurs with the initial current, go directly to step 2. Otherwise, increase the current in 0.27 mA increments until muscle contraction occurs.
2. Decrease the current in 0.09 mA increments until muscle contraction stops.
3. Increase the current again in 0.03 mA increments until muscle contraction occurs.
4. Decrease the current again in 0.01 mA increments until muscle contraction stops. The current applied last is identified as the threshold at the electrode position.
In random order, 49 patterns of electrode positions were stimulated. Three stimulations were applied every 0.4 s, one for each electrode position and current value-pair. Muscle contraction was detected when the MAV exceeded 1.5 times that of the unstimulated, resting MAV in at least two of the three stimulation cycles. Electrical stimulation was performed with 588 stimuli for the participants with the largest number of stimuli. Preparation took 45-75 min.
The threshold values at the four corners were measured, and the average was used as the current value in Experiments 1 and 2. However, because muscle contraction was not observed at a corner at the maximum current for one participant, the other three corners were used to determine the current values. intensity was measured for nine posture combinations comprising three elbow joint angles (i.e., 15 • , 30 • , and 45 • ) and three palm orientations (i.e., top, side, and bottom). A heat map was created for each posture. A break of at least one minute was given between trials of each posture. Ultimately, a total of 1,323 trials were performed, three at each point X 49 points, and nine X postures. Note that the stimuli in this study were low enough that little movement was performed at all points except for the MP, which was virtually resting, and the effects of fatigue were minimal. The muscle contractions by stimulating outside of the MP also occasioned almost no movement. The experiments took 45 min. The maximum MAV was transformed into one for each participant (i.e., normalization).

C. EXPERIMENT 2: CHANGES IN CONTRACTION INTENSITY DUE TO THE SIZE OF ELECTRODES
Previous studies showed that the smaller the electrode size, the stronger the contraction intensity when a current remains constant [15], [16]. In these studies, cm-order electrodes were used, and the relationship in higher resolution (mm-order) was not investigated. Experiment 2 studied the relationship between the electrode size of the mm-order and the intensity of muscle contraction induced by EMS.
The experiment was conducted with the posture used in Experiment 1 (elbow joint angle: 30 • , palm orientation: side. We refer to this as the baseline posture). Four electrode sizes (i.e., 4, 6.5, 8, and 12.5 mm) were used for randomly ordered stimulation. The electrode size was varied to ensure that the MP entered the region. Similar to Experiment 1, three stimulations were applied every 0.4 s for each electrode position and current value-pair, and the average of the top two MAV values was used for analysis.
The experiments were conducted in the following order: Experiment 1 (baseline posture), Experiment 2, and Experiment 1 (other posture). MATLAB 2021b was used for statistical analysis.
It took approximately 45-75 min to prepare and approximately 45 min to complete experiments 1 and 2, for a total of 90-120 minutes.

IV. RESULTS
A. EXPERIMENT 1: MP POSITION AND ITS SHIFT WITH POSTURE Fig. 5 shows an MP heat map example. All data are summarized in Fig. 13 of the Appendix. The average value of the currents was 4.09 mA, and the maximum value was 8.44 mA (see Fig. 13 of the Appendix for the values of each participant). For all participants, the MP area with gradient was observed at specific postures.   baseline posture (30 • ). A Friedman test for the means of the three series (i.e., 15 • , 30 • , and 45 • ) showed significant differences (F = 9.12, p = 0.011). The multiple comparisons using the Wilcoxon signed-rank test (adjustment method: Bonferroni) also showed a significant difference between 15 • and 45 • (p = 0.049). It was observed that the MP tended to move toward the shoulder as the elbow joint angle increased.  orientation and the shift from baseline posture (side). A Friedman test for the means of the three series (i.e., top, side, and bottom) showed significant differences. (F = 6.58, p = 0.037). The multiple comparisons using the Wilcoxon signed-rank test (adjustment method: Bonferroni) revealed a significant difference between the bottom and side (p = 0.026) and bottom and top (p = 0.023). The position tended to move outward compared to when it was oriented downward.
The MP shift in these two directions is consistent with skinto-muscle positioning and previous studies [25], [26]. Fig. 7 shows the results of Experiment 2. The Friedman test for the means of the four series (i.e., 12.0, 9.5, 7.0, and 4.5 mm electrode sizes) revealed a significant difference (F = 11.12, p = 0.011). The multiple comparisons using the Wilcoxon signed-rank test revealed a significant difference between the 12.0 and 9.5 mm squares (p = 0.0366) and between 12.0 and 7.0 mm squares (p = 0.0073). These results indicate that the intensity of muscle contraction increases as the electrode size decreases. The most significant change was observed between the 12 mm and 9.5 mm squares, and the rate of increase in the contraction intensity reduced thereafter. The variance was higher at 4.5 mm squares, and there was no significant difference between the 12.0 and 4.5 mm squares.

A. IMPLICATIONS FOR THE DESIGN OF ELECTRODE ARRAYS USED IN CONDUCTING MP SEARCH 1) MP SEARCH METHOD
Experiment 1 revealed that the intensity of muscle contraction changes with a 2.5 mm shift in the electrode. We observed the maximum MAV point corresponding to the MP and the gradient toward the MP. This result indicates that, with the resolution of the electrode array, a full search over all electrodes could be avoided, and the optimal MP can be obtained by finding the direction of the gradient within a certain range and moving the electrode in that direction. Fig. 8 shows an example of such an instance. First, contraction intensity was observed when EMS was applied within a certain range. Next, the shift of the electrode in the direction where the contraction intensity was high enabled quick identification of the MP.
There are two MPs for the posture of a single participant (p5). To be robust to noise and not fall into a local optimal position, a stochastic gradient method is desirable. Note that we do not need to find the global minimum. The search can be terminated if the stimulation of the MP causes sufficient contraction for the objective, even if it is a local one.
In this experiment, three stimulations were conducted, and the average of the top two MAV values was used to create a heat map. However, one stimulation at each point would be sufficient.

2) MP SHIFT WITH POSTURE
Experiment 1 revealed that the position of the MP changes with posture. The shift in the MP in the direction of the y-axis is consistent with previous studies [25], [26]. In addition, the shift in the MP during the twisting movement demonstrated the effectiveness of a device that can shift the electrode in a 2D direction. Fig. 9 shows that there is a sudden change in the muscle contraction's intensity occasioned by postural changes that cannot be explained solely by a shift in the positional relationship between the muscle and skin. Postural changes may alter the surrounding musculoskeletal conditions as well as the ease of muscle contraction. This indicates that, for controlling the motion strength by EMS, the amount of current to the MP must be adjusted for each posture. We also expect that the accumulation of the MP database for each posture will contribute to the precise data-based modeling of the MP.

3) SIZE OF ELECTRODES
Experiment 2 revealed that the smaller the electrodes (corresponding to a greater current density), the greater the median of the contraction intensity induced by the same amount of current. This result also suggests that precise stimulation with small electrodes can reduce the amount of current needed to generate a fixed contraction intensity. Experiment 1 indicates that the mm-order resolution of the electrode array is effective because the intensity of the contraction changes due to the electrode's shift of 2.5 mm. However, note that the variance was high at the 4.5 mm squares, and there was no significant difference between the 12.0 and 4.5 mm squares (See Limitation 2).

4) RANGE OF ELECTRODE ARRAYS
In this study, a 2-cm square electrode array was used to capture the shift in the MP. However, from Experiment 1, for certain postures of several participants, the MP shift was sufficiently large that the MP shifted outside the range of the electrode array. Therefore, the range of the electrode array must be expanded. In addition, Crochetiere et al. [16] reported that the movement of the MP was 2.5 cm when bending increased from 15 • to 90 • , and an even larger electrode array size is needed because of the individual differences and room required to search for the MP.
However, if the size of the electrode array is increased without changing the electrode size, the number of electrodes will increase. Then, the number of elements also increases, the circuit becomes more complex, and the cost increases. Because of the trade-off between the number of electrode arrays and the array size, an appropriate design is required for each application. The priority of the extension orientation of the array is the y-axis (i.e., elbow-shoulder orientation) because Experiment 1 showed that the shift in the positional relationship between the skin surface and the muscles is larger for the flex-and-extract movement (y-axis) than when twisting (x-axis).

B. LIMITATIONS 1) CURRENT VALUE FOR THE MP SEARCH
In this study, the EMS current value for the MP search was set based on the average threshold, which is the minimum current value at which muscle contraction occurred at the four corners of the sheet. However, when the difference between the threshold at the MP and that at the four corners is large (i.e., the gradient is large), the stimulus near the MP results in movement of the arm, which is not necessary for the MP search. During the search, if an MAV that greatly exceeds the required contraction is detected, the current value should be lowered but not below the threshold, and the search should continue.

2) SIZE OF ELECTRODES
As indicated in Fig. 7, the variance was high with 4.5 mm squares, and there was no significant difference between the 12.0 and 4.5 mm squares. A possible reason is that the posture control in this experiment was not precise; we asked participants to maintain a fixed pose and not move. However, unintentional or uncontrollable slight posture changes during experiments were inevitable, and such changes caused failures in capturing the MP with 4.5 mm squares. As shown in the appendix Fig. 13, in several heat maps with the baseline posture, we cannot recognize clear and intense MPs. This issue of posture perturbation will be solved in a real-time MP search algorithm, which is discussed in the Future Work section.
In addition, current density is not the only factor that determines contraction intensity. The contraction is also influenced by individual physical differences, such as the resistance distribution on the skin, which contributes to the variance in the result of the experiment, variation of current diffusion with change in distance between electrode arrays; this will be explored further in future work.

3) HAPTICS DURING THE MP SEARCH
Ideally, the MP search would be unnoticeable, although the stimulation in the MAV-based search method in this experiment was somewhat noticeable by the participants.
To achieve a less perceivable MPs search, an alternative search method could be based on a distribution map of threshold values because, in principle, it requires a weaker current (Fig. 10). For that, we need to check whether both search methods successfully identify the MP at the same location or nearby because, depending on the search method, the MP position may differ [27]. Notably, using the staircase method to identify the threshold for each position requires more time than measuring the MAV at a fixed current. Furthermore, lengthy calibration leads to slight posture changes and a corresponding shift in the MP, resulting in inaccurate detection. The issue of detection time is revisited in Section C, Future work, point 1. In addition, to achieve a low current and an unnoticeable MP search, the MMG must be analyzed for smaller vibrations.

4) SENSORS FOR MUSCLE CONTRACTION (MMG)
In this study, muscle contractions were observed using accelerometers. However, for stimuli near the threshold, the motion was minute and could not be read because the accelerometer was insufficiently accurate. Minute muscle vibrations can be acquired by increasing the accuracy of the MMG using a sensor with a piezoelectric polymer [28], laser distance sensor [29], or microphone [30].

5) WAVEFORM
In this study, we used monophasic waves for electrical stimulation. However, biphasic waves are used to reverse the potentially damaging electrochemical processes and avoid electrode corrosion [31], [32]. Although the negative effect is minimal in the experiments due to low current stimuli, it should be noted that biphasic waves are suitable for applications that require high currents, such as inducing arm movement. In addition, stimulation at high frequency easily causes fatigue [33]. When applying torque, the frequency must also be adjusted.

C. FUTURE WORK 1) REAL-TIME MP SEARCH AND APPLICATIONS
The MP for each posture could be measured in advance (precalibration) and updated in real time (real-time calibration) by tracking the posture with accelerometers or a motion capture system. The procedure is: (1) Detect the posture by any posture-sensing device (such as orientation sensors or motion capture).
(2) If the MAV is not measured at the posture, continue the measurement. Go back to (1). Therefore, the database will be a set of posture data (e.g., palm orientation and joint angle in the case of arm posture) and an MAV. In the calibration process, the user tries various arm postures intentionally so that the minimally required basic postures will be covered. The process is similar to the calibration procedure of an optical motion tracking system with wands and can be done as pre-calibration. If it continues during any tasks or applications, more data with more posture types will be accumulated, increasing the quality of the MP identification. As the subject need not remain immobile during the calibration, alternative (less noticeable) search methods that require longer calibration steps, such as the threshold map-based method, could be applied.

2) APPLICATIONS
Much previous EMS research illustrates continuous and accurate stimulation during a series of movements, such as lifting items (i.e., a power assist system or during rehabilitation), as the future applications of EMS (Fig. 11a). However, such precise and continuous stimulation has not been implemented, simply because MPs tend to get lost during movement. It is expected that this research, which provides continuous electrical stimulation to the MP even during movement, enables such applications.

3) EMS OF MULTIPLE MUSCLES
The stimulation of multiple muscles will be part of future work. For example, flexor digitorum superficialis and profundus muscles are used for finger flexion and extension, and a single natural movement is achieved by using multiple muscles (Fig. 11b). VOLUME 11, 2023 For example, by using sensors to estimate the state of finger flexion and then precisely applying stimulation to multiple muscles with electrode arrays simultaneously while also considering the movement of the MPs according to that state, finger flexion and extension can be reproduced more naturally and smoothly. Previous research also focused on the dexterity of EMS, applying stimuli to multiple muscles simultaneously, although on a larger spatial scale than our method [4], [34]. Another research project integrated an exoskeleton into EMS to enhance dexterity [35]. Combined with such methods, in our future work, we believe that our method could achieve state-of-art dexterity.

4) TRANSPARENCY OF MOTOR INTERVENTION
In this study, we focused on reducing current using electrode arrays. Pain, discomfort, and haptic sensation can be reduced by low current. For motion augmentation in daily activities, both reducing the current and the user's intentions for motion must be considered otherwise, the induced movement competes with the intention [36]. The competition between the induced and intentional movement causes pain and discomfort and inhibits movement.
By creating circumstances where human intention and induced movement do not compete, an unaware intervention (i.e., transparency of the intervention [37]) can be realized. This approach is expected to contribute to the implementation of a transparent intervention.

VI. CONCLUSION
We proposed a system for high-resolution MP search by arranging electrodes 2 mm in diameter in a 2D array. The experimental results showed that finely pitched shifting of the electrodes can derive the MP distribution. The MP shift was observed in the elbow flexion and extension as well as during twisting, indicating the efficacy of the 2D electrode array. This study is expected to contribute to the design guidelines for devices needed to provide precise EMS to the MP.

A. IMPLICATIONS FOR PRACTICAL USE
To examine the device's effectiveness for producing torque, we used a force sensor (FFS055YA501U6, Leptrino.inc, sampling rate 1200Hz) for two participants (p14, p15) to see if the force changed. We used the same protocol as in Experiment 2, except for the current value (200 Hz, 0.8 s duration, 15 s interval), with instructions to push the force sensor, as shown in Fig. 12a. The current is determined at the value at which the muscle contraction is sufficiently visible and the force sensor is pressed more than 2 N from the offset during stimulation. The force shows the average of the top two peak sensor values. Note that the MAV in this torque experiment is not the same as the MAV in experiment 1 because the current values are high enough to produce torque. The force and MAV were measured simultaneously. Fig. 12b shows that both measuring methods have the MP on the upper right in p14 and the lower left in p15. The results indicate that there The results indicate that there is a correspondence between force and MAV. Note that p15 has an MP that causes muscle contraction only and produces little force.
is a correspondence between force and MAV. In addition, the mm-order shifts seem effective for producing the torque because the torque changes with one pitch (2.5 mm) electrode shift. Therefore, we believe that the MP search using this device is also effective in terms of motor performance, at least for low contraction levels.
Note that p14 has an MP on the left only in the force map where the stimulation produces torque with little muscle contraction. p15 has an MP on the upper right in only MAV where the stimulation causes only muscle contraction and produces little force. MP from MAV does not perfectly coincide with the MP from the force sensor. As discussed in Section B. 3), the position of the MP may vary depending on the condition [27]. Differently expressed, reducing the current flowing to MPs that are not directly related to movement may reduce fatigue. These results are preliminary because only two participants were involved. In the future, the correspondence between the MP position of the force sensor and MAV must be measured in detail.