# Analysis on Muscle Forces of Extrinsic Finger Flexors and Extensors in Flexor Movements with sEMG and Ultrasound

Authors: Ying Lv; Qingli Zheng; Xiubin Chen; Yi Jia; Chunsheng Hou; Meiwen An
Journal: Mathematical Problems in Engineering
 (2022)

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## Abstract

The coupling relationship between surface electromyography (sEMG) signals and muscle forces or joint moments is the basis for sEMG applications in medicine, rehabilitation, and sports. The solution of muscle forces is the key issue. sEMG and Muscle-Tendon Junction (MTJ) displacements of the flexor digitorum superficialis (FDS), flexor digitorum profundus (FDP), and extensor digitorum (ED) were measured during five sets of finger flexion movements. Meanwhile, the muscle forces of FDS, FDP, and ED were calculated by the Finite Element Digital Human Hand Model (FE-DHHM) driven by MTJ displacements. The results showed that, in the initial position of the flexion without resistance, the high-intensity contraction of the ED kept the palm straight and the FDS was involved. The sEMG-force relationship of FDS was linear during the flexion with resistance, while FDP showed a larger sEMG amplitude than FDS, with no obvious linearity with its muscle forces. sEMG-MTJ displacement relationships for FDS and FDP were consistent with the trend of their own sEMG-force relationships. sEMG of ED decreased and then increased during the flexion with resistance, with no obvious linear relationship with muscle forces. The analysis of the proportion of muscle force and integrated EMG (iEMG) reflected the different activation patterns of FDS and ED.


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## Body

## 1. Introduction

sEMG has been widely used in medical, rehabilitation, and sports applications due to the advantages of easy acquisition, noninvasive, and reproducibility [1–3]. sEMG contains rich information about human physiology, health, and movement, in which the coupling relationship between sEMG and muscle force or joint torque has been a fundamental and hot issue in this field. These research results are widely used in revealing muscle activation mechanisms [4, 5], disease diagnosis [6–8], motion recognition, and prosthesis control [9–11].The relationship between sEMG and force has been studied since Inman and Ralston [12] and Lippold [13]. Linear [14–16] and nonlinear relationships [17–19] have been reported. However, these studies did not address individual muscle forces, but rather the total force or moment output by a group of muscles contracting together at a joint. Since muscle forces cannot be measured directly and noninvasively, the primary issue in studies of the relationship between sEMG and individual muscle forces is the prediction of muscle forces.Different modeling approaches have been used to predict muscle forces, such as the parametric muscle models based on the Hill muscle model [20–22] and the biomechanical musculoskeletal models [23–26]. Among them, parametric muscle models relied on the optimization of at least one parameter. This free parameter reflected the maximum tension in the muscle that was in the optimal principal force-length relationship under isometric conditions [27]. The solution of biomechanical musculoskeletal models required the introduction of optimization equations, including static and dynamic optimization, due to the hyper-static characteristics of the human musculoskeletal system. The choice of either optimization method was somewhat subjective. Skeletal muscles are all random muscles and their contraction process is controlled by subjective consciousness [28, 29]. This can lead to poor applicability and reliability of the optimization principles chosen for the calculation.To address these issues, sEMG data of FDS, FDP, and ED during five groups of finger flexion movements were measured in this study. The FE-DHHM containing solid unit tendons and ligaments and driven by MTJ displacements of FDS, FDP, and ED measured with ultrasound was also established. This method allowed direct calculation of muscle forces of the FDS, FDP, and ED during flexor movements. The above data were combined to explore the sEMG-force relationships of the three muscles mentioned above.


## 2. Materials and Methods

To ensure the uniformity of the model and data, the hand CT scans, ultrasound experiments, and sEMG acquisition were performed by the author as a volunteer. The volunteer was a healthy 30-year-old male with no hand disease or associated neurological disorders. All experimental protocols and methods were performed in accordance with relevant guidelines and regulations, and were approved by the biological and medical ethics committee of Taiyuan University of technology. Moreover, informed consent was obtained from all subjects or their legal guardians.


### 2.1. Flexor Movements Grouping and sEMG Acquisition

The volunteer was seated with the right arm horizontally on the experimental table, palm up. The palm of the hand in the straightened position was the initial position; and the hand in the naturally relaxed position was the resting position. The finger flexion movements consisted of 5 sets of movements, including 1 set of flexion without resistance and 4 sets of flexion with resistance completed with the force measurement platform.Action 1 was flexion without resistance: the hand was flexed from the initial position to the resting position.Actions 2–5 were flexion with resistance: the hand was placed flat on the base plate of the force measurement platform. The movable steel plate was adjusted to a position just in contact with the finger belly and fixed to the rail with bolts. The hand was flexed up from the initial position to supporting the movable plate until the display showed 5 N, 10 N, 15 N, and 20 N in sequence.The average value of the resistance of the force measurement platform was measured to be 0.7 N, including the gravity of the movable steel plate and the frictional force between the movable steel plate and the rail. Therefore, the pressure between the finger bellies and the movable steel plate for movements 2–5 was 5.7 N, 10.7 N, 15.7 N, and 20.7 N in sequence, which was referred to as “fingertip force” in the text.The sEMG was acquired by a 16-channel wireless telemetry sEMG acquisition system manufactured by NORAXON, USA. The sampling frequency was 1500 Hz. The surface electrodes were bipolar electrodes, which were applied to the center of the muscle belly of the FDS, FDP, and ED of the volunteers in the same direction as the muscle fibers. The distance between the two electrodes was 1.8 cm, and the skin surface of the volunteers was scrubbed with alcohol and polished with fine sandpaper to remove the keratin.The sEMG was collected sequentially for actions 1–5. The measurements were repeated 4 times at 3 min intervals for each set of actions. In each measurement, each action lasted 2 s and was repeated 3 times at 2 s intervals. This meant that there were 12 sets of data for each action. The measurement procedure is shown in Figure1.Figure 1
Position of electrodes and acquisition of sEMG for action 3. (a) Electrodes for flexors; (b) electrodes for ED; (c) acquisition of sEMG.


### 2.2. Measurement of the MTJ Displacements by Ultrasound

Muscle and tendon are separated at the MTJ: on the muscle side, muscle force comes from the active contraction of the muscle and is measured by parameters such as the physiological cross section areas of the muscle and the length of the contraction, while on the tendon side, tendon force is determined by the elongation of the tendon and tendon stiffness. At the MTJ, muscle force and tendon force are equal. The focus of this study was to quantify the tendon force at the MTJ side of the tendon using the elongation of the tendon (part of the MTJ displacement) and the tendon stiffness, and the results would provide data to support the study of a constitutive model of the muscle force.The measurement instrument was a fully digital color Doppler ultrasound diagnostic instrument of the AixPlorer type from Supersonic Imagine (France), SL15-4 probe, frequency 4 to 15 MHz. Experimental steps are as follows: firstly, the ultrasound probe was swept along the forearm longitudinally to locate the target tendon; then, the ultrasound probe was swept along the target tendon transversely to locate the location where the cross section of the tendon becomes larger, which was the MTJ, and the location of the ultrasound probe was marked on the skin; finally, the location of the ultrasound probe before and after the target action was marked and the distance was measured, which was the MTJ displacement of the target action.The MTJ displacements of ED, FDS, and FDP of actions 1–5 were measured. Among them, the measurement procedure of the MTJ displacement of FDS for action 3 is shown in Figure2.Figure 2
Measurement process of MTJ displacement. (a) The initial position; (b) the rest position; (c) the fingertip force for action 3 was 10.7 N and the resistance was 0.7 N; (d) ultrasonic localization of MTJ for FDS and FDP.The measurement results are shown in Table1.Table 1
MTJ displacements of each muscle during finger flexion movements (mm).
Flexion movementsFDSFDPEDAction 118.2222.22−12.54Action 24.336.600Action 310.4812.100Action 415.8816.300Action 520.5621.700


### 2.3. Establishment of the FE-DHHM

The geometric model of the human hand was built based on CT scan image files of the normal human hand and completed using the 3D medical image modeling software MIMICS 19.0. The geometric model included 14 phalanges, 5 metacarpals, 8 carpal bones, and parts of the ulna and radius; 9 muscles and their tendons, such as the FDS, FDP, ED, flexor pollicis brevis, flexor pollicis longus, extensor pollicis longus, extensor pollicis brevis, extensor indicis, and extensor indicis minimi; and the extensor retinaculum, flexor retinaculum, as well as annular ligaments that act as finger pulleys at the Interphalangeal (IP) joints and metacarpophalangeal (MCP) joints (Figure3).Figure 3
The FE-DHHM.The geometric model was divided with a tetrahedral mesh C3D4 in 3-matic Medical, generating a total of 375514 elements. The inp files were imported into the finite element software ABAQUS2017 to generate the finite element model. The tendons and ligaments were constrained by “Tie” with their corresponding skeletal attachment points. A frictionless self-contact was set between each structure. Every joint was connected by three spring elements on the left, right, and dorsal sides (simulating the left and right collateral ligaments and dorsal ligaments at the joint) (Figure3). The three spring elements were all one-dimensional linear elastic elements arranged along the lateral and dorsal midline of the phalanges, which served to maintain joint stability and provide joint stiffness. To simplify the calculation, it was assumed that each spring unit at the IP joint had the same stiffness and each spring unit at the MCP joint had the same stiffness. Meanwhile, the bones, tendons, and ligaments were assumed to be linearly elastic isotropic materials. The model validation and material parameter determination were done based on the finger flexion movements experimental data.


### 2.4. Model Validation and Material Parameter Determination

The material parameters of the bones were according to literature data [23]. There were four parameters that need to be determined for the model: the elastic modulus of the tendons, the elastic modulus of the ligaments, the IP joint spring elements stiffness, and the MCP joint spring elements stiffness. The known quantities measured experimentally were MTJ displacement and fingertip force (or flexion pattern) in five actions. The four sets of experimental data (MTJ displacement-fingertip force) from actions 2–5 were used to determine the four parameters. The experimental data for action 1 (MTJ displacement-flexion pattern) were used to validate the model after the parameters were determined.Determination of material parameters: the MTJ displacements of actions 2–5 were input into the model as displacement loads, and after parameter adjustment and feedback calculations, the rigid plate reaction forces (fingertip forces calculated by the model) in FE-DHHM were made equal to the fingertip forces of the force measuring platform in the experiment, so that each parameter satisfying the accuracy was finally determined (Figure4(a)).Figure 4
Simulation of flexion movements working conditions. (a) Flexion with resistance, action 2–5; (b) flexion without resistance, action 1.
(a)(b)Model validation: the MTJ displacement of action 1 was input into FE-DHHM as displacement load after determining the parameters. The model was validated by comparing the flexion pattern of FE-DHHM with that of the hand in the experiment (Figure4(b)).The calculated rigid plate reaction forces are shown in Table2.Table 2
Experimental fingertip forces and the rigid plate reaction forces (N).
Flexion movementsFingertip forcesReaction forcesAction 25.76.4Action 310.712.6Action 415.713.7Action 520.720.6As shown in Table2, after adjusting the parameters, the error between the rigid plate reaction forces and the experimental fingertip forces is between 0.48% and 17.8%, which is within the tolerable range. The material parameters thus determined are shown in Table 3.Table 3
The determined material parameters and spring elements stiffness.
MaterialYoung’s modulus(MPa)PoissonratioDensity(kg/m³)Bone [23]170000.32000Tendon680.451000Ligament200.451000JointsIPMCPStiffness (N/m)10002000Figure4(b) shows the flexion pattern of the FE-DHHM after determining the parameters under the flexion without resistance working condition in agreement with the experimental action 1, and the model is validated.


## 2.1. Flexor Movements Grouping and sEMG Acquisition

The volunteer was seated with the right arm horizontally on the experimental table, palm up. The palm of the hand in the straightened position was the initial position; and the hand in the naturally relaxed position was the resting position. The finger flexion movements consisted of 5 sets of movements, including 1 set of flexion without resistance and 4 sets of flexion with resistance completed with the force measurement platform.Action 1 was flexion without resistance: the hand was flexed from the initial position to the resting position.Actions 2–5 were flexion with resistance: the hand was placed flat on the base plate of the force measurement platform. The movable steel plate was adjusted to a position just in contact with the finger belly and fixed to the rail with bolts. The hand was flexed up from the initial position to supporting the movable plate until the display showed 5 N, 10 N, 15 N, and 20 N in sequence.The average value of the resistance of the force measurement platform was measured to be 0.7 N, including the gravity of the movable steel plate and the frictional force between the movable steel plate and the rail. Therefore, the pressure between the finger bellies and the movable steel plate for movements 2–5 was 5.7 N, 10.7 N, 15.7 N, and 20.7 N in sequence, which was referred to as “fingertip force” in the text.The sEMG was acquired by a 16-channel wireless telemetry sEMG acquisition system manufactured by NORAXON, USA. The sampling frequency was 1500 Hz. The surface electrodes were bipolar electrodes, which were applied to the center of the muscle belly of the FDS, FDP, and ED of the volunteers in the same direction as the muscle fibers. The distance between the two electrodes was 1.8 cm, and the skin surface of the volunteers was scrubbed with alcohol and polished with fine sandpaper to remove the keratin.The sEMG was collected sequentially for actions 1–5. The measurements were repeated 4 times at 3 min intervals for each set of actions. In each measurement, each action lasted 2 s and was repeated 3 times at 2 s intervals. This meant that there were 12 sets of data for each action. The measurement procedure is shown in Figure1.Figure 1
Position of electrodes and acquisition of sEMG for action 3. (a) Electrodes for flexors; (b) electrodes for ED; (c) acquisition of sEMG.


## 2.2. Measurement of the MTJ Displacements by Ultrasound

Muscle and tendon are separated at the MTJ: on the muscle side, muscle force comes from the active contraction of the muscle and is measured by parameters such as the physiological cross section areas of the muscle and the length of the contraction, while on the tendon side, tendon force is determined by the elongation of the tendon and tendon stiffness. At the MTJ, muscle force and tendon force are equal. The focus of this study was to quantify the tendon force at the MTJ side of the tendon using the elongation of the tendon (part of the MTJ displacement) and the tendon stiffness, and the results would provide data to support the study of a constitutive model of the muscle force.The measurement instrument was a fully digital color Doppler ultrasound diagnostic instrument of the AixPlorer type from Supersonic Imagine (France), SL15-4 probe, frequency 4 to 15 MHz. Experimental steps are as follows: firstly, the ultrasound probe was swept along the forearm longitudinally to locate the target tendon; then, the ultrasound probe was swept along the target tendon transversely to locate the location where the cross section of the tendon becomes larger, which was the MTJ, and the location of the ultrasound probe was marked on the skin; finally, the location of the ultrasound probe before and after the target action was marked and the distance was measured, which was the MTJ displacement of the target action.The MTJ displacements of ED, FDS, and FDP of actions 1–5 were measured. Among them, the measurement procedure of the MTJ displacement of FDS for action 3 is shown in Figure2.Figure 2
Measurement process of MTJ displacement. (a) The initial position; (b) the rest position; (c) the fingertip force for action 3 was 10.7 N and the resistance was 0.7 N; (d) ultrasonic localization of MTJ for FDS and FDP.The measurement results are shown in Table1.Table 1
MTJ displacements of each muscle during finger flexion movements (mm).
Flexion movementsFDSFDPEDAction 118.2222.22−12.54Action 24.336.600Action 310.4812.100Action 415.8816.300Action 520.5621.700


## 2.3. Establishment of the FE-DHHM

The geometric model of the human hand was built based on CT scan image files of the normal human hand and completed using the 3D medical image modeling software MIMICS 19.0. The geometric model included 14 phalanges, 5 metacarpals, 8 carpal bones, and parts of the ulna and radius; 9 muscles and their tendons, such as the FDS, FDP, ED, flexor pollicis brevis, flexor pollicis longus, extensor pollicis longus, extensor pollicis brevis, extensor indicis, and extensor indicis minimi; and the extensor retinaculum, flexor retinaculum, as well as annular ligaments that act as finger pulleys at the Interphalangeal (IP) joints and metacarpophalangeal (MCP) joints (Figure3).Figure 3
The FE-DHHM.The geometric model was divided with a tetrahedral mesh C3D4 in 3-matic Medical, generating a total of 375514 elements. The inp files were imported into the finite element software ABAQUS2017 to generate the finite element model. The tendons and ligaments were constrained by “Tie” with their corresponding skeletal attachment points. A frictionless self-contact was set between each structure. Every joint was connected by three spring elements on the left, right, and dorsal sides (simulating the left and right collateral ligaments and dorsal ligaments at the joint) (Figure3). The three spring elements were all one-dimensional linear elastic elements arranged along the lateral and dorsal midline of the phalanges, which served to maintain joint stability and provide joint stiffness. To simplify the calculation, it was assumed that each spring unit at the IP joint had the same stiffness and each spring unit at the MCP joint had the same stiffness. Meanwhile, the bones, tendons, and ligaments were assumed to be linearly elastic isotropic materials. The model validation and material parameter determination were done based on the finger flexion movements experimental data.


## 2.4. Model Validation and Material Parameter Determination

The material parameters of the bones were according to literature data [23]. There were four parameters that need to be determined for the model: the elastic modulus of the tendons, the elastic modulus of the ligaments, the IP joint spring elements stiffness, and the MCP joint spring elements stiffness. The known quantities measured experimentally were MTJ displacement and fingertip force (or flexion pattern) in five actions. The four sets of experimental data (MTJ displacement-fingertip force) from actions 2–5 were used to determine the four parameters. The experimental data for action 1 (MTJ displacement-flexion pattern) were used to validate the model after the parameters were determined.Determination of material parameters: the MTJ displacements of actions 2–5 were input into the model as displacement loads, and after parameter adjustment and feedback calculations, the rigid plate reaction forces (fingertip forces calculated by the model) in FE-DHHM were made equal to the fingertip forces of the force measuring platform in the experiment, so that each parameter satisfying the accuracy was finally determined (Figure4(a)).Figure 4
Simulation of flexion movements working conditions. (a) Flexion with resistance, action 2–5; (b) flexion without resistance, action 1.
(a)(b)Model validation: the MTJ displacement of action 1 was input into FE-DHHM as displacement load after determining the parameters. The model was validated by comparing the flexion pattern of FE-DHHM with that of the hand in the experiment (Figure4(b)).The calculated rigid plate reaction forces are shown in Table2.Table 2
Experimental fingertip forces and the rigid plate reaction forces (N).
Flexion movementsFingertip forcesReaction forcesAction 25.76.4Action 310.712.6Action 415.713.7Action 520.720.6As shown in Table2, after adjusting the parameters, the error between the rigid plate reaction forces and the experimental fingertip forces is between 0.48% and 17.8%, which is within the tolerable range. The material parameters thus determined are shown in Table 3.Table 3
The determined material parameters and spring elements stiffness.
MaterialYoung’s modulus(MPa)PoissonratioDensity(kg/m³)Bone [23]170000.32000Tendon680.451000Ligament200.451000JointsIPMCPStiffness (N/m)10002000Figure4(b) shows the flexion pattern of the FE-DHHM after determining the parameters under the flexion without resistance working condition in agreement with the experimental action 1, and the model is validated.


## 3. Results

### 3.1. Features of sEMG

The raw sEMG signals were rectified and smoothed filtered (RMS, 50 ms) by Myoresearch3.16 software from NORAXON, using the calculation method proposed by Falconer and Winter [30]. Features such as peak absolute and integrated EMG (iEMG) were output by Myoresearch 3.16 software. Root mean square (RMS) feature was calculated by formulas written in the Excel worksheet where the sEMG data were recorded. The features of the sEMG were calculated as shown in Table 4.Table 4
Features of the sEMG of each muscle (μV).
Actions (duration = 2 s)FDSFDPEDPeak absoluteiEMGRMSPeak absoluteiEMGRMSPeak absoluteiEMGRMSInitial position5.78 ± 1.25392.66 ± 59.513.63 ± 0.388.65 ± 0.60768.45 ± 39.407.56 ± 0.3345.86 ± 5.043541.86 ± 394.1735.55 ± 4.54Resting position2.18 ± 0.09208.56 ± 5.732.09 ± 0.058.31 ± 0.12794.41 ± 6.677.94 ± 0.088.61 ± 1.16787.07 ± 121.097.71 ± 1.43Action 22.64 ± 0.68193.40 ± 30.431.95 ± 0.307.82 ± 1.80661.13 ± 133.956.64 ± 1.3529.45 ± 7.962011.46 ± 385.720.90 ± 3.77Action 33.74 ± 0.86226.07 ± 22.372.13 ± 0.2410.38 ± 0.50812.50 ± 52.108.19 ± 0.5426.41 ± 2.761756.06 ± 119.0817.55 ± 0.96Action 45.88 ± 0.60343.21 ± 34.073.58 ± 0.3211.64 ± 1.89740.64 ± 49.437.57 ± 0.5719.84 ± 4.531136.43 ± 128.2711.74 ± 1.47Action 57.38 ± 0.46478.93 ± 24.584.98 ± 0.2412.38 ± 0.25836.50 ± 56.968.50 ± 0.5919.28 ± 3.731188.94 ± 258.5112.19 ± 2.70From Table4, the sEMG of FDS decreased significantly in action 1, while the sEMG of FDP changed insignificantly and the sEMG of ED decreased dramatically. Action 1 was a relaxation movement, indicating that in the initial position of the action the high-intensity contraction of the ED kept the palm in extension and the FDS was involved.


### 3.2. The Calculation of Muscle Forces

The calculated results of the muscle forces were acquired at the MTJ of each muscle, as shown in Table5.Table 5
The calculation of muscle forces (N).
Flexion movementsFDSFDPEDAction 114.4212.331.48Action 28.036.710.11Action 325.1514.770.18Action 441.3621.480.22Action 553.7428.730.31


### 3.3. Relationships between sEMG, MTJ Displacement, and Muscle Force

The sEMG, MTJ displacement, and muscle force of the flexors were normalized based on the data of the FDS in action 5. The relationship between them is shown in Figure4. The sEMG of FDS was linearly related to muscle force during the flexion with resistance, and the peak absolute of sEMG was more suitable to describe this relationship. The peak absolute of FDP had a roughly linear relationship with its muscle force, but this linear relationship was not obvious for RMS and iEMG. Throughout the finger flexion movements, the FDP contributed less muscle forces than the FDS (Figure 5(a)). Meanwhile, the sEMG-MTJ displacement relationships of FDS and FDP were consistent with the trend of their respective sEMG-muscle force relationships (Figure 5(b)). The reason for this agreement was the linear relationship between muscle force and MTJ displacement (Figure 5(c)). The difference was that the FDP had greater sEMG and MTJ displacement compared to the FDS.Figure 5
Relationships between sEMG, MTJ displacement, and muscle force in the flexion with resistance. (a) sEMG-muscle force curves of FDS and FDP; (b) sEMG-MTJ displacement curves of FDS and FDP; (c) Muscle force-MTJ displacement curves of FDS and FDP; (d) sEMG-fingertip force curves of ED.
(a)(b)(c)(d)The ED, as an antagonist muscle, exhibited a more complex behavior throughout the finger flexion movements. The muscle force values of the ED calculated by the model were small and linearly correlated with its fingertip forces. sEMG of the ED was analyzed using its fingertip forces. For this purpose, we additionally measured the sEMG for fingertip force of 25.7 N and 30.7 N for finger flexion movements and normalized the data based on the value of sEMG of 30.7 N. The trend of the three sEMG features of the ED was consistent during the finger flexion movements: the maximum value appeared at the initial position and the minimum value was at the rest position. During the finger flexion with resistance, the sEMG of the ED first decreased and then increased (Figure5(d)).Figure6 shows the percentage of muscle force and iEMG of each muscle in the muscle combination during the finger flexion movements. As shown in the picture, as the fingertip forces increased, the proportion of FDS muscle force and iEMG increased and the proportion of ED decreased; the proportion of FDP muscle force decreased and its proportion of iEMG increased. This indicated that the FDS played a major driving role in the flexion with resistance. Furthermore, the FDS showed the largest proportion of muscle force and the smallest proportion of iEMG; the ED showed the opposite: the smallest proportion of muscle force and the largest proportion of iEMG. This indicated a different activation pattern of the two muscles.Figure 6
Percentage of muscle force and iEMG for each muscle in finger flexion movements. (a) The proportion of muscle force for FDS, FDP, and ED; (b) the proportion of iEMG for FDS, FDP, and ED.
(a)(b)


## 3.1. Features of sEMG

The raw sEMG signals were rectified and smoothed filtered (RMS, 50 ms) by Myoresearch3.16 software from NORAXON, using the calculation method proposed by Falconer and Winter [30]. Features such as peak absolute and integrated EMG (iEMG) were output by Myoresearch 3.16 software. Root mean square (RMS) feature was calculated by formulas written in the Excel worksheet where the sEMG data were recorded. The features of the sEMG were calculated as shown in Table 4.Table 4
Features of the sEMG of each muscle (μV).
Actions (duration = 2 s)FDSFDPEDPeak absoluteiEMGRMSPeak absoluteiEMGRMSPeak absoluteiEMGRMSInitial position5.78 ± 1.25392.66 ± 59.513.63 ± 0.388.65 ± 0.60768.45 ± 39.407.56 ± 0.3345.86 ± 5.043541.86 ± 394.1735.55 ± 4.54Resting position2.18 ± 0.09208.56 ± 5.732.09 ± 0.058.31 ± 0.12794.41 ± 6.677.94 ± 0.088.61 ± 1.16787.07 ± 121.097.71 ± 1.43Action 22.64 ± 0.68193.40 ± 30.431.95 ± 0.307.82 ± 1.80661.13 ± 133.956.64 ± 1.3529.45 ± 7.962011.46 ± 385.720.90 ± 3.77Action 33.74 ± 0.86226.07 ± 22.372.13 ± 0.2410.38 ± 0.50812.50 ± 52.108.19 ± 0.5426.41 ± 2.761756.06 ± 119.0817.55 ± 0.96Action 45.88 ± 0.60343.21 ± 34.073.58 ± 0.3211.64 ± 1.89740.64 ± 49.437.57 ± 0.5719.84 ± 4.531136.43 ± 128.2711.74 ± 1.47Action 57.38 ± 0.46478.93 ± 24.584.98 ± 0.2412.38 ± 0.25836.50 ± 56.968.50 ± 0.5919.28 ± 3.731188.94 ± 258.5112.19 ± 2.70From Table4, the sEMG of FDS decreased significantly in action 1, while the sEMG of FDP changed insignificantly and the sEMG of ED decreased dramatically. Action 1 was a relaxation movement, indicating that in the initial position of the action the high-intensity contraction of the ED kept the palm in extension and the FDS was involved.


## 3.2. The Calculation of Muscle Forces

The calculated results of the muscle forces were acquired at the MTJ of each muscle, as shown in Table5.Table 5
The calculation of muscle forces (N).
Flexion movementsFDSFDPEDAction 114.4212.331.48Action 28.036.710.11Action 325.1514.770.18Action 441.3621.480.22Action 553.7428.730.31


## 3.3. Relationships between sEMG, MTJ Displacement, and Muscle Force

The sEMG, MTJ displacement, and muscle force of the flexors were normalized based on the data of the FDS in action 5. The relationship between them is shown in Figure4. The sEMG of FDS was linearly related to muscle force during the flexion with resistance, and the peak absolute of sEMG was more suitable to describe this relationship. The peak absolute of FDP had a roughly linear relationship with its muscle force, but this linear relationship was not obvious for RMS and iEMG. Throughout the finger flexion movements, the FDP contributed less muscle forces than the FDS (Figure 5(a)). Meanwhile, the sEMG-MTJ displacement relationships of FDS and FDP were consistent with the trend of their respective sEMG-muscle force relationships (Figure 5(b)). The reason for this agreement was the linear relationship between muscle force and MTJ displacement (Figure 5(c)). The difference was that the FDP had greater sEMG and MTJ displacement compared to the FDS.Figure 5
Relationships between sEMG, MTJ displacement, and muscle force in the flexion with resistance. (a) sEMG-muscle force curves of FDS and FDP; (b) sEMG-MTJ displacement curves of FDS and FDP; (c) Muscle force-MTJ displacement curves of FDS and FDP; (d) sEMG-fingertip force curves of ED.
(a)(b)(c)(d)The ED, as an antagonist muscle, exhibited a more complex behavior throughout the finger flexion movements. The muscle force values of the ED calculated by the model were small and linearly correlated with its fingertip forces. sEMG of the ED was analyzed using its fingertip forces. For this purpose, we additionally measured the sEMG for fingertip force of 25.7 N and 30.7 N for finger flexion movements and normalized the data based on the value of sEMG of 30.7 N. The trend of the three sEMG features of the ED was consistent during the finger flexion movements: the maximum value appeared at the initial position and the minimum value was at the rest position. During the finger flexion with resistance, the sEMG of the ED first decreased and then increased (Figure5(d)).Figure6 shows the percentage of muscle force and iEMG of each muscle in the muscle combination during the finger flexion movements. As shown in the picture, as the fingertip forces increased, the proportion of FDS muscle force and iEMG increased and the proportion of ED decreased; the proportion of FDP muscle force decreased and its proportion of iEMG increased. This indicated that the FDS played a major driving role in the flexion with resistance. Furthermore, the FDS showed the largest proportion of muscle force and the smallest proportion of iEMG; the ED showed the opposite: the smallest proportion of muscle force and the largest proportion of iEMG. This indicated a different activation pattern of the two muscles.Figure 6
Percentage of muscle force and iEMG for each muscle in finger flexion movements. (a) The proportion of muscle force for FDS, FDP, and ED; (b) the proportion of iEMG for FDS, FDP, and ED.
(a)(b)


## 4. Discussion

Although research on the relationship between sEMG and muscle forces has been carried out extensively, it has mostly been limited to in vivo measured loads or joint moments. In this study, experimental data including fingertip forces and MTJ displacements of the muscles measured in vivo were combined by FE-DHHM to calculate the muscle forces and their trends of the three extrinsic muscles during finger flexion movements. The calculations were validated by relevant model calculations and in vivo measurement data [31–33]. And the linear relationship between muscle force and sEMG for FDS was corroborated with the study by Vigouroux L et al. [34].Due to the deep location, the sEMG-force relationship of FDP has been rarely mentioned. Firstly, the contribution of FDP in flexor movements is more difficult to be distinguished due to the synergistic contraction of FDS; secondly, FDP is a deep muscle, and its sEMG is subject to too much superposition and interference to be measured accurately. In this paper, the individual contributions of FDS and FDP in the co-contraction were well distinguished by the muscle forces calculated by the MTJ displacement work conditions of each muscle. The FDS provided more driving force in flexor movements, whereas the FDP showed more significant MTJ displacement and sEMG. It has been noted that the fingertip force was representative of the FDP as the FDP was the only flexor muscle that inserted into the distal phalanx [35]. This might be the reason why FDP was active in MTJ displacement and sEMG.The role of the ED as an antagonist muscle in flexor movements is important. Studies have shown that the contraction of the antagonist muscle contributed to maintaining joint stability [36] and improving the accuracy of the movements [37]. There are three main possible reasons for the complex sEMG changes of the ED during finger flexion movements. (1) Co-activation. The co-activation of antagonistic muscles is a physiological phenomenon in which muscles (or muscle groups) opposite to the expected action of the active muscle are recruited simultaneously during a given task [38]. Moreover, co-activation of antagonist muscles shows dependence on contraction intensity and contraction pattern [39]. (2) Reciprocal inhibition. That is, the nervous system controls the antagonist muscles in a relaxed state during the activation of the active muscle [40]. (3) Eccentric contraction. The forced lengthening of activated skeletal muscle is called eccentric contraction. A lower firing rate of the active motor unit is usually detected during eccentric contraction compared to concentric contraction [41]. In the initial position of the finger flexion movements, the ED is concentric contraction. During the movement of the fingers from the initial position to the flexion with resistance, the ED undergoes a concentric-eccentric contraction process. Under the combined effect of the above mechanisms, the sEMG of the ED exhibits a complex pattern of changes.In essence, sEMG is the sum of the motor unit action potential of the neuromuscular system when the motor unit [42] is activated, which is superimposed on the skin surface through the conduction of biological tissues [43]. Muscle force is mainly determined by the number, size (cross-sectional area), and firing rate of activated motor units [44]. Therefore, it has been pointed out that the relationship between contraction force and the motor unit action potential is an important determinant of the EMG-muscle force relationship [45]. For the sEMG-force relationship, there are additional influencing factors, such as the relative position of the electrode (electrode) to the muscle, the anatomical structure and size of the muscle, the contraction pattern of the muscle (isometric, concentric, eccentric), the intensity of the contraction, the contraction speed, subjective imagery and neuromodulation mechanisms (co-activation, reciprocal inhibition) and muscle fatigue, and even extrinsic environmental factors such as skin surface state and electronic device interference. Therefore, a linear relationship between sEMG and muscle force (both physiologically and biophysically) cannot be expected.There were three main challenges in this study. One was the accuracy of FE-DHHM. This study focused only on three muscles, FDP, FDS, and ED, which were involved in flexion movements. This was because FDP and FDS were the main contributors to DIP, PIP, and MCP joint flexion (more than 80% of the summed force of all flexors) during the distal phalanx loading according to Li et al. [46]. The target task addressed in this paper (fingertip forces) was consistent with this and therefore the model was suitably simplified. On the other hand, in order to control the external force output and finger position, other muscles must be activated to maintain postural stability and provide proper torque at all joints, including numerous intrinsic and extrinsic muscles. Their respective contributions and roles may vary depending on the force and finger posture. Work such as that of Valero-Cuevas [47], for example, described the effects of finger posture on hand muscle forces. The model developed in this paper therefore would require more precise anatomy if it is to explain the synergistic contraction of the hand muscles in other postures. In addition, there was space for further improvement in the geometric accuracy of soft tissues such as tendons and ligaments in the model due to the lack of soft tissue discrimination in CT images. The second was the accuracy of MTJ displacement measurement. FDS, FDP, and ED all had four tendons and the identification of their MTJ on ultrasound images was very dependent on the subjective judgment of the physician. Especially for the ED, which acted as an antagonist muscle, its MTJ displacement was not obvious. This may be an oversimplification in the calculation. The third was the design of the experimental movements. The fingertip force for this study was limited to 20.7 N. When the fingertip force exceeded this value, alterations in hand muscle activation were clearly experienced, including a dramatic increase in intrinsic muscle activation as well as the need for wrist strength. This could reduce the applicability of the FE-DHHM. In addition, to ensure the uniformity of the model and data, CT image data of the hand and ultrasound-measured MTJ displacement data as well as sEMG data were obtained from the investigators himself. After the feasibility of the method has been verified, the study would involve more volunteers. Therefore, future work would require a more complete FE-DHHM structure, a more accurate and validated MTJ displacement measurement method, a more rational experimental action design, and a larger sample size, with a view to more comprehensive and accurate findings and wider application in clinical diagnosis and rehabilitation.


## 5. Conclusion

In the present study, the following three works were linked to investigate the synergistic contraction of the FDS, FDP, and ED during flexion movements and their sEMG-force relationships: (1) sEMG data for FDS, FDP, and ED were measured in five sets of flexion movements; (2) MTJ displacements of FDS, FDP, and ED during flexion movements were measured by ultrasound; (3) The FE-DHHM containing solid unit tendons and ligaments models and driven by MTJ displacements of the muscles was established using CT data of the hand, where the MTJ displacements of the muscles were used as input values to the FE-DHHM, allowing the model to be validated and enabling muscle forces to be calculated. In conjunction with the muscle sEMG data, the sEMG-MTJ displacement and sEMG-force relationships for the FDS, FDP, and ED were analyzed, as well as the behaviour and contribution of each muscle in flexion movements were elaborated. The results showed that the method used in this study was feasible.



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