Analysis on synergistic cocontraction of extrinsic finger flexors and extensors during flexion movements: A finite element digital human hand model.

Fine hand movements require the synergistic contraction of intrinsic and extrinsic muscles to achieve them. In this paper, a Finite Element Digital Human Hand Model (FE-DHHM) containing solid tendons and ligaments and driven by the Muscle-Tendon Junction (MTJ) displacements of FDS, FDP and ED measured by ultrasound imaging was developed. The synergistic contraction of these muscles during the finger flexion movements was analyzed by simulating five sets of finger flexion movements. The results showed that the FDS and FDP contracted together to provide power during the flexion movements, while the ED acted as an antagonist. The peak stresses of the FDS, FDP and ED were all at the joints. In the flexion without resistance, the FDS provided the main driving force, and the FDS and FDP alternated in a "plateau" of muscle force. In the flexion with resistance, the muscle forces of FDS, FDP, and ED were all positively correlated with fingertip forces. The FDS still provided the main driving force, but the stress maxima occurred in the FDP at the DIP joint.

Introduction

The human hand has the most sophisticated anatomy, including 27 bones, numerous muscles, tendons, ligaments, and other anatomical structures [1], which allows for a variety of complex and delicate movements. Many studies have long been conducted on the motor mechanisms of the hand [2,3], hand diseases [4,5], and bionic applications [6-8]. The main methods for studying the motor mechanism of the hand are muscle electrical signals (EMG) and numerical models of the hand. Among them, studies on EMG focus on the activation and inhibition of hand muscles [9-12], while numerical models of the human hand can explain the behavior of hand muscles in motion from a mechanical perspective [13-15].

The use of the Finite Element Digital Human Hand Model (FE-DHHM) to study hand motion mechanisms has a long history, starting from the earliest with Carrigan [16] and Anderson [17], to build 3D wrist models. These models were built from CT images and contained eight carpal bones and ligaments, usually focusing on the stress transfer in the normal or diseased carpal tunnel. Due to the structural incompleteness, such models had limitations for studying the synergistic contraction of the extrinsic finger flexors and extensors of the hand.

The models that can be used for muscle force analysis are FE-DHHMs containing at least fingers and tendons, and there are two main categories, local and global models. Local models mainly focus on the motion mechanisms of a single finger [18-21], such as the biomechanical model of the index finger developed by Brook et al. [18] and the index finger model containing ED network tendons by Hu et al. [21]. Such models contained structures such as three phalanges, joints, and tendons. The tendon was reduced to a one-dimensional linear unit or a network of multiple linear units. The joints were defined by constraint equations. This type of model can better reflect the control mechanism of tendon on a single finger, which is important for the exploration of finger movement mechanism and diagnosis of related diseases. However, due to the large degree of simplification of such models, it is difficult to reflect the real overall motion mechanism of the hand. Therefore, the establishment and use of a holistic model of the hand has become a hot issue for current research by scholars at home and abroad. Chamoret et al. [22] established an FE-DHHM including bone and skin to analyze the contact/impact of the human hand with a deformable rectangular block. Harih et al. [23] established an FE-DHHM including bone, joint and skin, and used the angular displacement of the joint measured by a motion capture system as the driving force, and analyzed the distribution of stress and contact pressure for gripping action. Their work focused on the ergonomic evaluation of handheld products. It is noteworthy that such FE-DHHMs usually reduced joints to simple hinge connections and did not model soft tissues such as muscles and tendons but used the angular displacement of joints as the driving force. This has led to the weak ability of the model to study the synergistic and antagonistic mechanisms of individual muscles during manual movement. Research in this area is important for clinical diagnosis and treatment of muscle and tendon injuries as well as for rehabilitation training.

In this paper, we have achieved accurate loading of Muscle-Tendon Junction (MTJ) displacements of different muscles under the same movement by combining FE-DHHM established by finite element technique and the MTJ displacements measured by ultrasound imaging, which was used to study the synergistic contraction of Flexor Digitorum Superficialis muscle (FDS), Flexor Digitorum Profundus muscle (FDP) and Extensor Digitorum muscle (ED) in flexion movements.

Materials and methods

To ensure uniformity of model and MTJ displacement data, all CT scans and ultrasound experiments were performed by the author as the volunteer. The volunteer was healthy a 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.

Geometric model

The geometric model of the human hand was built based on CT scan image files of the volunteer’s right hand by the 3D medical image modeling software MIMICS 19.0. The geometric model included 29 bones, such as 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; ligaments, such as the extensor retinaculum, flexor retinaculum, and annular ligaments that act as finger pulleys at the Interphalangeal (IP) joints and Metacarpophalangeal (MCP) joints (Fig 1).

Fig 1

FE-DHHM and human hand anatomy.

(A) FE-DHHM. (B) human hand anatomy.

Finite element model

The geometric model was smoothed, matched and 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 with interaction, material parameters, boundary conditions and loading conditions defined.

(1) Interaction

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) (Fig 2). 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, the following assumptions were made: each spring element at the IP joints had the same spring stiffness, and each spring element at the MCP joints had the same stiffness.

Fig 2

Loading conditions of flexion with resistance.

(A) The joints were connected by three spring elements. (B) The muscle connected to the tendon was defined as a rigid body.

(2) Material parameters

To simplify the calculations, the bones, tendons and ligaments were assumed to be linearly elastic isotropic materials (Table 1). In this case, the material parameters of the bones were determined. Due to the discrete nature of soft tissue elastic modulus and errors in model dimensions, the elastic modulus of tendons and ligaments, and the stiffness of spring elements need to be determined from the flexor finger experimental data described below. Therefore, 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.

Table 1

The preset values of the material parameters.

Material	Young’s modulus (MPa)	Poisson ratio	Density (Kg/m3)
Bone [24]	17000	0.3	2000
Tendon [20]	125.31	0.45	1000
Ligament [20]	114.03	0.45	1000

(3) Boundary conditions and loading conditions

The FDS, FDP and ED in FE-DHHM were split at the MTJ (the location where the cross section increases). The muscles in them were defined as rigid bodies and the MTJ displacement loads and extracted muscle forces were applied at the reference points of the rigid bodies (Fig 2).

The loading conditions were divided into flexion without resistance conditions and flexion with resistance conditions according to the flexion experiment described below. The flexion without resistance conditions were based on fixing the metacarpals, carpal bones, ulna and radius of FE-DHHM and loading displacement loads on the rigid reference points of FDS, FDP and ED. The flexion with resistance conditions were based on the flexion without resistance conditions with the proximal phalanges fixed and a fully fixed rigid plate added at the tip of the FE-DHHM to provide resistance (Fig 2). The model was calculated by the dynamic display algorithm.

Experimental measurement of MTJ displacements in flexion movements

Grouping of flexion movements

A force measurement platform was designed including a base plate, a movable steel plate, a fixed steel plate, guide rails and a pressure transducer (Fig 3). When the movable steel plate slid upward along the rail, the average value of the resistance was 0.7N, including the gravity of the movable steel plate and the frictional force between the movable steel plate and the rail. The pressure between the pressure transducer and the movable steel plate was displayed on the monitor when the hand was flat on the platform base plate and bent up to support the movable steel plate. The pressure between the finger and the movable steel plate was called the fingertip force in the text and was equal to the sum of the display and the resistance.

Fig 3

The force measurement platform.

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.

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 5N, 10N, 15N and 20N in sequence, which meant that the fingertip force was 5.7N, 10.7N, 15.7N and 20.7N.

Measurement of the MTJ displacements by ultrasound

The contraction deformation of the muscle is transmitted to the corresponding bone through the tendon, and the total deformation is reflected in the tendon as the displacement at the MTJ [25,26], which is referred to as the MTJ displacement in the text.The MTJ displacement is divided into two parts: one is the displacement of the tendon due to the change in position between the bones, and the other is the tensile deformation of the tendon during force transmission. When the muscle is actively contracted, the MTJ displacement is the sum of the two; when the muscle is passively stretched, the MTJ displacement is the difference between the two.

Experimental steps: 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.

We measured the MTJ displacements of the ED, FDS, and FDP in five groups of flexion movements using ultrasound imaging. Fig 4 demonstrates the localization of the FDS tendon and its MTJ. Fig 5 demonstrates the measurement process of the MTJ displacement of the FDS in action 1.

Fig 4

The positioning of the MTJ for FDS.

(A) Longitudinal section of FDS tendon. (B) Cross sectional section of the MTJ for FDS.

Fig 5

Measurement procedure of tendon displacement of FDS for action 1.

The MTJ displacement of ED in actions 2, 3, 4, and 5 was not significant and was approximated as zero displacement to simplify the calculation. We define the MTJ displacement that decreases the muscle length as positive and the MTJ displacement that increases the muscle length as negative.

Determination of material parameters and model validation

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 elastic modulus of the tendons directly determined the effect of MTJ displacement and was positively correlated with the fingertip force; the elastic modulus of the ligaments determined the effect of its restraint on the tendons and was also indirectly positively correlated with the fingertip force; the role of the joint spring elements were to maintain joint stability and provide joint stiffness and were negatively correlated with the fingertip force. 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 was made equal to the fingertip forces of the force measuring platform in the experiment, so that each parameter satisfying the accuracy was finally determined.

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. Table 1 shows the preset values of the material parameters.

Results

Table 2 demonstrates the MTJ displacements of each muscle for five sets of flexion movements, where the ED was elongated in action 1, so the MTJ displacement of the ED was negative. The MTJ displacements from action 2–5 were input to the corresponding FE-DHHM as displacement loads, and the elastic modulus of the tendons and ligaments as well as the spring stiffness were adjusted until the rigid plate reaction forces of the model were equal to the experimental fingertip forces (Table 3).

Table 2

MTJ displacements of each muscle during flexion movements (mm).

Flexion movements	FDS	FDP	ED
Action 1	18.22	22.22	-12.54
Action 2	4.33	6.60	0
Action 3	10.48	12.10	0
Action 4	15.88	16.30	0
Action 5	20.56	21.70	0

Table 3

Experimental fingertip forces and the rigid plate reaction forces (N).

Flexion movements	Fingertip forces	Reaction forces
Action 2	5.7	6.4
Action 3	10.7	12.6
Action 4	15.7	13.7
Action 5	20.7	20.6

As shown in Table 3, 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 Tables 4 and 5.

Table 4

The determined values of material parameters.

Material	Young’s modulus (MPa)	Poisson ratio	Density (Kg/m3)
Bone	17000	0.3	2000
Tendon	68	0.45	1000
Ligament	20	0.45	1000

Table 5

Stiffness of the spring unit at the joints.

Joints	DIP		PIP		MCP
	Left/Right	posterior	Left/Right	posterior	Left/Right	posterior
Stiffness (N/m)	1000	1000	1000	1000	2000	2000

DIP: Distal interphalangeal joints.

PIP: Proximal interphalangeal joints.

MCP: Metacarpophalangeal joints.

As can be seen in Table 4, the elastic modulus of both tendons and ligaments decreased substantially compared to the preset values. The FE-DHHM with parameters determined was validated with the loading conditions of action 1 (Fig 6).

Fig 6

The process of flexion without resistance.

The flexion process of the FE-DHHM under the loading conditions of action 1 after determining the parameters (Fig 6) is consistent with the experimental flexion without resistance (Fig 5). The model was validated.

Stress cloud of the tendons

The peak stresses of FDS, FDP, and ED were 23.1 Mpa, 15.6 Mpa, and 12.8 Mpa for the displacement load condition of action 1. The peak stresses of FDS, FDP, and ED were 23.2 Mpa, 32.5 Mpa, and 9.1 Mpa for the displacement load condition of action 5. And the peak stresses of FDS, FDP, and ED in the flexion movements were all at the joints (Fig 7).

Fig 7

Stress clouds of each tendon under load conditions of actions 1 and 5.

The variation of peak stresses with muscle forces for the three muscles is shown in Fig 8. In the flexion without resistance, FFDS>FFDP>FED, and SFDS,Max>SFDP,Max>SED,Max. In the flexion with resistance, FFDS>FFDP>FED, and SFDP,Max>SFDS,Max>SED,Max.

Fig 8

Variation of peak stresses of three muscles with muscle force during flexion movements.

Muscle force and fingertip force

Fig 9 shows that in the flexion movements, the FDS and FD contracted together to provide power; while the ED had a non-zero muscle force and acted as an antagonist. The FDS produced larger muscle forces with smaller MTJ displacements than the FDP. The muscle forces of FDS, FDP and ED were all positively correlated with fingertip forces during the flexion with resistance. The proportion of muscle force was greatest for FDS and gradually increased with increasing fingertip force, while the proportion of muscle force gradually decreased for FDP and ED. Combined with the MTJ displacements data in Table 2, it was found that both FDS and FDP produced larger muscle forces with smaller MTJ displacements during flexion with resistance compared to flexion without resistance.

Fig 9

Variation of muscle forces of the three muscles with fingertip forces during flexion movements.

According to Fig 10, it can be seen that in the flexion without resistance (action 1), the muscle forces of FDS and FDP both had a significant plateau period during the increase with time. In contrast, the muscle forces of FDS, FDP and ED were positively correlated with time in the flexion with resistance (actions 2–5), and the fingertip forces were also roughly positively correlated with time under small fluctuations.

Fig 10

Variation of muscle forces and fingertip forces over time in three muscles during flexion movements.

Discussion

The material parameters of the model were determined by the loading conditions of actions 2–5. The determined values of the elastic modulus of both tendons and ligaments were substantially lower than the preset values, but still within the reported range [27]. The reason for the error is that the tendon and ligament models have larger dimensions than the actual ones. Especially for the ligaments, they do not directly determine the joint angle displacements, and their role is to constrain the position of the tendon. Therefore errors in their material parameters have a limited negative impact on the calculation results. Furthermore, it has been shown [28] that: when the point of force application was at the distal phalanx, the extrinsic muscles are the main contributors to joint flexion of the DIP, PIP and MCP joints (accounting for more than 80% of the total force of all flexors); and that the effects of the extensor mechanism on the flexors were relatively small when the location of force application was distal to the PIP joint. The target task (fingertip force) addressed in this paper is consistent with it, so the simplification of the intrinsic muscles and extensor mechanisms in the model of this paper is justified.

Combining Figs 7 and 8, it can be seen that the muscle forces of FDP were smaller than those of FDS in the flexion with resistance, while the peak stresses were larger than those of FDS, and the peak stresses all appeared at the DIP joint of the index finger. In the working condition of resistance flexion in the model, the DIP joint was the interphalangeal joint with the largest angular displacement, and the FDP was the only flexor muscle that crossed the DIP joint. Although the muscle forces in the FDS were larger, the stress distribution was uniform and there was no stress concentration. This indicates that joint flexion has a significant effect on the stress distribution of the flexor tendons.

The torque produced by the muscle-tendon force on the joint is fundamentally influenced by the moment arm (MA), which is defined as the vertical distance between the center of rotation of the joint and the line of action of the muscle-tendon force [29]. One popular technique for estimating MA values is the tendon excursion method, which calculates the instantaneous MA based on the slope of tendon displacement versus joint angle [30,31]. In the present study of the flexion without resistance, the MCP, PIP, and DIP joints were angularly displaced by the combined muscle forces of FDS, FDP, and ED. In the current model’s loading conditions, the displacement loads were loaded uniformly. Initially, the MCP joint rotated at the largest angular velocity of the three joints due to the combined forces of the FDS and FDP. This was followed by the PIP joint rotating rapidly due to the rapidly increasing MA of the FDS and FDP on it. Finally, the DIP joint rotated rapidly due to the rapidly increasing MA of FDP on it. The difference in angular velocity of the three joints caused the FDS and FDP in turn to produce a structural MTJ displacement due to the change in the spatial position of the finger. With this displacement, the length of the tendon was constant and therefore the calculated muscle force did not increase. This resulted in a significant plateau in muscle force over time for both FDS and FDP in the flexion without resistance (Fig 10).

In the flexion with resistance, the muscle forces of FDS, FDP and ED were all positively correlated with time. During action 2, the muscle forces of FDS and FDP accounted for 48.9% and 51.1% of the total flexor force, respectively. This value was 62.6% and 37.4% during action 3 and remained stable during action 4 and action 5. Fluctuations in fingertip force over time were caused by changes in the angle of contact between the distal phalanx and the rigid plate in the model.

The ED acted as an antagonist muscle throughout the flexion movements with much smaller muscle forces than the FDS and FDP. The co-activation of the antagonist muscle can improve the precision of the movement and is also important for maintaining joint stability [32]. In a more popular research approach, the role of ED in flexion movements is elaborated as an extensor mechanism (EM) [33,34]. The so-called extensor mechanism is a complex network of tendons connecting the intrinsic and extrinsic muscles of the finger, which increases the maximum fingertip force over a wide range of postures and force directions, allowing for greater finger dexterity during grip. These studies provide new ideas for the refinement of FE-DHHM in this paper.

Schuind et al. [35] measured in vivo the tendon forces generated by the FDS and FDP during passive and active flexion of the index finger in five patients with carpal tunnel syndrome with force transducers. Among them, the active flexion without resistance of the index finger PIP was the result of FDS contraction with some involvement of FDP. The range of FDS tendon force was 3–13 N with a mean of 9 N. The active flexion without resistance of the index finger DIP was due to the contraction of the FDP, which had a muscle force range of 1–29 N with an average of 19 N. The muscle forces of the FDS and FDP in active flexion without resistance of the four fingers calculated in this paper were 14.42 N and 12.33 N, which were similar to the measurements in the literature.

Kursa et al. [36] measured in vivo the ratio of FDS and FDP tendon force to fingertip force in 15 subjects scheduled for open carpal tunnel surgery when the load cells were pressed with the index finger at different rates up to 15 N. The ratio of FDS tendon force to fingertip force for all tests averaged 1.5 ± 1.0, while the corresponding ratio for FDP averaged 2.4 ± 0.7. In our calculations, the corresponding values were 2.63 and 1.37, which were similar to the measurements in the literature.

The noteworthy difference is that in all the above-mentioned measurements in the literature, the muscle force of the FDS was smaller than that of the FDP, whereas our calculations yielded the opposite result: the FDS produced larger muscle forces with smaller MTJ displacements than the FDP in both the flexion movements with and without resistance. Possible factors contributing to the discrepancy: 1. Mode of movement; the movements studied in this paper were simultaneous flexion of all four fingers, whereas studies in the literatures have targeted the flexion of the index finger alone. This has been verified in the work of Allouch S et al. [37] on the muscle forces during a hand opening-closing paradigm: the muscle forces of the FDS were consistently greater than those of the FDP throughout the movements. 2, Finger posture; it has been noted that finger posture [38-40] and tendon loading conditions [41] could affect fingertip forces. The finger flexion movements in this paper took the palm extension state as the initial position, when both FDS and FDP were passively stretched. In contrast, the flexion movements in the literature all started with the resting position. 3. The intrinsic model of the tendon; to simplify the calculation, the intrinsic model of the tendon with linear elasticity was chosen for the FE-DHHM, which negatively affected the analysis of the tendon with large deformation. How to incorporate the active contraction intrinsic model of the muscle will be the content of our future work.

This study has focused on three extrinsic muscles among the many involved in finger flexion movements. Finger flexion is accomplished by the synergistic contraction of the FDP, FDS, and ED. In order to control 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 [42]. In addition, clinical practice requires data support in this area, such as the choice of traction force during claw hand traction orthodontics [43]. Therefore, future work requires a more refined FE-DHHM, including more precise construction and more rational material parameters, with the aim of playing a broader role in the field of clinical deformed hand correction or motor rehabilitation.

Conclusion

The FE-DHHM, which contains solid tendons and ligaments, is a prerequisite for the analysis of individual muscle collaboration and antagonism mechanisms using MTJ displacements as the driving forces. Five sets of MTJ displacements for flexion movements were used to complete the determination of material parameters and validation of validity for the FE-DHHM, and analysis of muscle forces for the external muscles. The model calculations have quantified the contribution of FDS, FDP and ED in flexion movements and elaborated the details of the behavior of each muscle in this process. These phenomena were reasonably explained by comparison with the literatures. The FE-DHHM established in this paper can analyze the synergistic contraction of FDS, FDP and ED, and also has a wide range of roles in medical and rehabilitation fields.

23 Oct 2021

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Reviewer #1: Overview

In this study, the authors created a finite element model of the musculoskeletal structure of the human fingers, which was used to estimate muscle forces during finger flexion. The proposed method incorporates some interesting approach (measuring musculotendon junction excursion), but there are many fundamental problems in the model structure and its validation, which makes it impossible to appreciate its validity or usability. The reviewer thinks that the authors may want to focus on utilizing the information obtained from ultrasound imaging and correlate this to the changes in the measured fingertip forces – FE model used in this study is too complex and contains too many unknown parameters to result in any meaningful estimation of muscle forces.

Major comments

1. Authors adopted an interesting approach, looking at the excursion of the musculotendon junction using ultrasound imaging. This could provide important information regarding the action of different muscles during movements. Unfortunately, there are numerous problems with the modeling approach, and the model validation was performed properly, which makes it very difficult to test the validity of the proposed model. For instance, intrinsic hand muscles are not considered (which are critical in force production), and many model parameters are not properly determined. Some important anatomical features, such as the extensor mechanism or finger pulleys, are not even included in the model.

2. More importantly, the model validation seems to be fundamentally flawed. The only measurements made in this study were musculotendon junction (MTJ) movements and fingertip forces (plate reaction forces). The methodology is not clearly described (which is a huge problem itself), but it appears that rest of the parameters (e.g., joint stiffness, material properties, muscle forces, etc.) were estimated during simulation to fit the data (plate force, I assume). Thus, it seems that all the important anatomical parameters were changed to fit the fingertip force (plate force) data – which means that the estimated muscle force values are not really “validated”. Since the model has numerous parameters that are “free” to change, the estimated muscle forces and other parameters (e.g., joint stiffness, tendon stiffness, etc.) are just one of possible combination of parameter values that result in the measured fingertip forces.

Minor comments

1. Joint stiffness – stiffness values used in this study were selected arbitrary, and are not based on literature. First of all, why the unit is N/m? Joint stiffness should be defined as N m/rad. Authors said this is a stiffness of springs at the joints – then how are these springs connected (e.g., moment arm - which would critically affect its function)?

Please refer to numerous previous studies on finger joint stiffness (e.g., Milner and Franklin, 1998; Kamper et al., 2002; Jindrich et al., 2004).

2. Page 11: “Validation of validity” – please revise. “Validation of model performance”?

3. MTJ measurement: Note that this represents a kinematic property, which in principle cannot measure any kinetic aspects. For instance, even if MTJ displacement of ED was zero (in Actions 2 – 5), it does NOT mean that ED was not activated. Previous studies show that the extensor muscles are always activated, albeit to a lower degree, during flexion movements.

4. Again, why no intrinsic muscles were considered at all? Intrinsic hand muscles were found to play an important role in force production.

5. Page 12 - Fig. 7: change “flexure” in the caption to “flexion”. Also it is not clear what data these graphs display – in the text (line 221 – 222), it is mentioned that “rigid plate reaction forces of the model were equal to the experimental fingertip forces (Fig 7)”. However, only one line is shown in each figure – what is shown here then? Does it mean that the experimental data and simulation results are in perfect match (which is highly unlikely)?

6. Page 14 - Fig. 9: This figure is not very informative – although the color bar shows a range of different colors, the picture only shows (or appears to show) one color – dark blue.

Also why did the authors show stress distribution throughout the tendons? It would be much more important to show stress at the FINGER PULLEYS (where most stress ruptures happen) – first of all, were the pulleys modeled at all? If so, how was it modeled?

7. The reviewer thinks that the authors may want to focus on utilizing the information obtained from ultrasound imaging (MTJ excursion) and see how that is correlated to the changes in the measured fingertip forces – FE model used in this study is too complex and contains too many unknown parameters to result in any meaningful estimation of muscle forces.

Reviewer #2: Review of PLOS One manuscript PONE-D-21-23164, “Analysis on synergistic cocontraction of extrinsic finger flexors and extensors during Flexion movements: a Finite Element Digital Human Hand Model”

General Comments:

The manuscript describes a model of the human hand performed using limited in vivo experimentation and finite element modeling. The study details are lacking. The results are may be interesting with potential implication. However, the reader is left to question some important details that are missing from manuscript and which are essential for determining if the model is indeed valid (as stated in manuscript) and how that model is any different from already existing human hand models.

Specific comments:

Abstract

Occasionally/many acronyms are defined only in abstract but should also be defined in body of manuscript, e.g. MTJ

Introduction

Line 83: The reader is confused, as the stated purpose is illogical and does not make sense in that the purpose of the paper can not be to develop anything. Rather the purpose of the paper is “to describe the development of an FE-DHHM….” Or the purpose of this paper is to “describe a study to develop an FE-DHHM…”

“The purpose of this paper is to develop a FE-DHHM including phalanges, metacarpals, solid unit tendons and ligaments by combining finite element techniques with ultrasound imaging to measure the MTJ displacements techniques to achieve accurate loading of the MTJ displacements of different muscles under the same movement.”

Lines 89-90: “….and also has a wide range of applications in clinical and rehabilitation fields”

Line 111: what is meant by “cells”? Do authors mean “element”, as this is a finite element model ?

Line 113: what were the “material parameters and boundary conditions defined” ? This specific information would be useful to readers to understand how model was implemented.

Lines 192-193 and 212-213: What exactly is meant by “validation of validity” ? Does not validity stem from validation and so without validation there is no validity ? So, again, specifically, what is meant here by “validation of validity”? How is validation of validity part of methods section but also part of results ? Reader is confused.

Lines 214-215: The table title is “Table 2 MTJ displacements of each muscle during flexion movements (mm)” But then immediately after table 2, sentence reads “Table 2 demonstrates the fingertip forces and MTJ displacements of each muscle…” But all the values in Table 2 have units of millimeters (as stated in title), so how are any of the values in Table 2 forces ? Reader is confused.

Lines 264-266: “FDS and FD contracted together to provide power; while the ED had a non-zero muscle force and acted as an antagonist.” How were forces apportioned between FDS, FD and ED ? This mathematics to determine apportionment is not described in methods section, except for lines 202 and 203 where says “after several fits and adjustments”, and so reader is left to wonder how the values in this Figure 11 were determined ? Was there any physics or mechanics behind the fits and adjustments? Or simply curve matching ?

Line 282-284 seems to say that material parameters are a result of the model. Yet, Table 1 indicates the material parameters were taken from references 26 and 20. So what is difference between table 1 and table 3, and how can material parameters be both input to the model and output from the model ?

Line 239 and Figure 8: this figure suggest the force at finger tip varies with time over 200 milliseconds of the simulation/experiment. What was the sample rate of the force measurement device shown in figure 3 so reader can understand if the variation in finger tip force is meaningful ?

Regarding results, specifically figures 9-12, reader is having difficult time understanding if any of the results are valid as no comparisons are made to in vivo data or even experimental/literature data.

The manuscript suggests some lack of rationality in the model material parameters (line 378). The manuscript suggests some utility of the model (lines 89-90 and 390-391). However, the reader is left to question utility of a model with lack of rationality and without explicitly stated or apparent utility.

**********

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Reviewer #1: No

Reviewer #2: No

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11 Jan 2022

Dear Editors and Reviewers:

Thank you for your letter and for the reviewers’ comments concerning our manuscript entitled “PONE-D-21-23164”. Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our researches. We have studied comments carefully and have made correction which we hope meet with approval. Revised portion were marked in red in the paper. The main corrections in the paper and the responds to the editors and reviewers’ comments were addressed point by point below.

Responds to the editors’ comments:

1. Response to comment: Please ensure that your manuscript meets PLOS ONE's style requirements, including those for file naming.

Response: The manuscript has been modified according to the PLOS ONE's style requirements.

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When you resubmit, please ensure that you provide the correct grant numbers for the awards you received for your study in the ‘Funding Information’ section.

Response: This study is a supported by the National Natural Science Foundation of China(No.11372208, No.31870934). The authors received no specific funding for this work.

3. Thank you for stating the following in the Acknowledgments Section of your manuscript:

“The support from the National Natural Science Foundation of China (No.11372208, No.31870934, No.11972243) was acknowledged.”

We note that you have provided additional information within the Acknowledgements Section that is not currently declared in your Funding Statement. Please note that funding information should not appear in the Acknowledgments section or other areas of your manuscript. We will only publish funding information present in the Funding Statement section of the online submission form.

Please remove any funding-related text from the manuscript and let us know how you would like to update your Funding Statement. Currently, your Funding Statement reads as follows:

“The author(s) received no specific funding for this work.”

Please include your amended statements within your cover letter; we will change the online submission form on your behalf.

Response: Funding information and other funding-related text have been removed from the manuscript. Funding Statement has been updated as “This study is a supported by the National Natural Science Foundation of China(No.11372208, No.31870934). The authors received no specific funding for this work” within cover letter.

4. In your Data Availability statement, you have not specified where the minimal data set underlying the results described in your manuscript can be found. PLOS defines a study's minimal data set as the underlying data used to reach the conclusions drawn in the manuscript and any additional data required to replicate the reported study findings in their entirety. All PLOS journals require that the minimal data set be made fully available. For more information about our data policy, please see http://journals.plos.org/plosone/s/data-availability.

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We will update your Data Availability statement to reflect the information you provide in your cover letter.

Response: The minimal data set is submitted as Supporting Information files.

5. Thank you for your submission to PLOS ONE. Before we can proceed, we kindly ask you to address the following concerns:

We understand that the author served as the volunteer in the study; however, we ask you to present this information in the Methods section of the manuscript. Please revise your Methods section to state all information about ethics committee approval in this section (including the name of the ethics committee), state that the volunteer was the author of the paper, and state any exclusion/inclusion criteria and any relevant demographic information (sex, age, etc.). We appreciate your attention to these queries and look forward to your response.

Response: Relevant information has been indicated in the manuscript:

To ensure uniformity of model and MTJ displacement data, all CT scans and ultrasound experiments were performed by the author as the volunteer. The volunteer was healthy a 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 (page 4, lines 91-96).

Responds to the reviewers’ comments:

Reviewer #1:

Major comments

1. Response to comment: Authors adopted an interesting approach, looking at the excursion of the musculotendon junction using ultrasound imaging. This could provide important information regarding the action of different muscles during movements. Unfortunately, there are numerous problems with the modeling approach, and the model validation was performed properly, which makes it very difficult to test the validity of the proposed model. For instance, intrinsic hand muscles are not considered (which are critical in force production), and many model parameters are not properly determined. Some important anatomical features, such as the extensor mechanism or finger pulleys, are not even included in the model.

Response: As Reviewer said, building a perfect model of the human hand is very complex and difficult. In our research work, the model of the hand has indeed been heavily and reasonably simplified. For example, the model does not take into account the intrinsic hand muscles and extensor mechanisms due to the overly complex structure of the hand. The intrinsic hand muscles are characterized by small size, short tendon length, and large numbers, which make modeling efforts difficult to be accurate and tendon displacements difficult to measure. Chang et al.(Chang J , Freivalds A , Sharkey N A , et al. Investigation of index finger triggering force using a cadaver experiment: Effects of trigger grip span, contact location, and internal tendon force[J]. Applied Ergonomics, 2017, 65:183-190.) also addressed only FDS and FDP, not intrinsic hand muscles and ED, in their study of tendon force and index finger triggering force using cadavers. Other studies on hand muscle forces using cadavers have faced the same problem (Schuind et al. ,1992; Valero-Cuevas et al., 1998; Schweizer and Hudek ,2011). This is because the intrinsic muscles of cadavers are difficult to be loaded, just like the intrinsic muscles of models in our work. However this simplification still makes the research work relevant in revealing the contraction mechanisms of the hand muscles. However, this simplification still makes these research efforts indispensable in revealing the contractile mechanisms of the hand muscles.

The extensor mechanism is a tendon network that connects the intrinsic muscles to the ED. In existing models of the human hand, the extensor mechanism is defined as a network of elastic lines or bands and is specific to one finger only. The ED tendon model established in this work is three-dimensional and the minimum cell size of MIMICS software is 1 mm. therefore, it is difficult to establish a three-dimensional extensor network for the whole hand under such conditions.

The main function of the finger pulley mechanisms is to keep the tendons close to the bones. The pulleys in existing models of the human hand are either defined as parametric equations or are ignored.The function of the pulleys in the model of this study is realized by the "joint capsules". The expression in the article is incorrect and has been corrected to "finger pulleys"(page 5, line 105).

The focus of this study is on the method of estimating muscle force using musculotendon junction excursion. The accuracy of the model does have a significant impact on the accuracy of the results. More accurate modeling of the anatomical structures will be our further work.

2. Response to comment: More importantly, the model validation seems to be fundamentally flawed. The only measurements made in this study were musculotendon junction (MTJ) movements and fingertip forces (plate reaction forces). The methodology is not clearly described (which is a huge problem itself), but it appears that rest of the parameters (e.g., joint stiffness, material properties, muscle forces, etc.) were estimated during simulation to fit the data (plate force, I assume). Thus, it seems that all the important anatomical parameters were changed to fit the fingertip force (plate force) data – which means that the estimated muscle force values are not really “validated”. Since the model has numerous parameters that are “free” to change, the estimated muscle forces and other parameters (e.g., joint stiffness, tendon stiffness, etc.) are just one of possible combination of parameter values that result in the measured fingertip forces.

Response: The description of the methodology for parameter determination and model validation in this paper is indeed unclear. It has been revised in the text (page6, lines 126-135). A brief description is as follows.

The parameters of the model, except for the elastic modulus of the bones, need to be determined, including the elastic modulus of the tendons (FDS, FDP, ED, etc.), the elastic modulus of the ligaments (finger joint rotation, extensor retinaculum, etc.), and the joint spring elements stiffness.The elastic modulus of the tendons determines the relationship between MTJ displacement and fingertip force. The elastic modulus of the ligaments determines their effectiveness in restraining the tendons and indirectly affects the relationship between MTJ displacement and fingertip force. There are three joint spring elements at each joint, whose function is to maintain joint stability and to provide joint stiffness (this section is described in detail in the first section of the following minor comments). The simplifying assumption for the spring elements is that each spring element at the IP joints has the same stiffness, and each spring element at the MCP joint has the same stiffness. This gives a total of four unknown quantities: the elastic modulus of the tendons, the elastic modulus of the ligaments, the spring unit stiffness at the IP joints, and the spring unit stiffness at the MCP joints. The experimentally measured known quantities are the MTJ displacement and the fingertip force (or flexion pattern), for a total of five sets. Four of these experimental data sets (MTJ displacement-fingertip force) were used to determine the four unknown quantities and one set of data (MTJ displacement-flexion pattern) was used to validate the model after determining the parameters. Thus the parameters of the model were able to be determined.The muscle force is not involved in the above process; it is the result of the calculation after both parameter determination and model validation have been completed.

Minor comments

1. Response to comment: Joint stiffness – stiffness values used in this study were selected arbitrary, and are not based on literature. First of all, why the unit is N/m? Joint stiffness should be defined as N m/rad. Authors said this is a stiffness of springs at the joints – then how are these springs connected (e.g., moment arm - which would critically affect its function)?

Please refer to numerous previous studies on finger joint stiffness (e.g., Milner and Franklin, 1998; Kamper et al., 2002; Jindrich et al., 2004).

Response: The spring unit connecting the joints in this paper is a different concept from the joint stiffness in the related literatures (Milner and Franklin, 1998; Kamper et al., 2002; Jindrich et al., 2004).

Specifically, the joint in this paper is connected by three spring elements simulating the left and right collateral ligaments and dorsal ligaments at the joint. The three spring elements were all one-dimensional linear elastic elements arranged along the lateral and dorsal midline of the phalanges (page 7, Fig 2A) . And its unit of stiffness is N/m. These three spring units serve two purposes: (1) stabilize the joint. The joint surfaces are held together during joint rotation without misalignment. (2) The combination of the axial forces of the three springs constitutes the stiffness of the joint during rotation. Therefore, this paper defines the spring element stiffness, not the joint stiffness.

The joint stiffness in the relevant literatures (Milner and Franklin, 1998, etc.) is a spring damper model defined as a combination of two-dimensional spring units at the joints. It measures the joint stiffness in Nm/rad by the net joint torque, the angular displacement of the joint and the angular velocity. This model can describe the joint stiffness directly, but it cannot stabilize the joint. Most of the joints in the literatures are defined by hinge constraints.

2. Response to comment: Page 11: “Validation of validity” – please revise. “Validation of model performance”?

Response: "Validation of validity" has been corrected to "model validation" (page 10, line 209).

3. Response to comment: MTJ measurement: Note that this represents a kinematic property, which in principle cannot measure any kinetic aspects. For instance, even if MTJ displacement of ED was zero (in Actions 2-5), it does NOT mean that ED was not activated. Previous studies show that the extensor muscles are always activated, albeit to a lower degree, during flexion movements.

Response: Indeed, the article elaborates that the displacements of the MTJ are divided into two parts: one part is the displacement of the tendon due to the change in position between the bones, and the other part is the tensile deformation that occurs when the tendon transmits force. Thus the MTJ displacement of the ED is approximately zero and the calculated muscle force of the ED is not zero. The co-activation of the ED during flexion movements is described in the Discussion section (lines 343-345).

4. Response to comment: 4. Again, why no intrinsic muscles were considered at all? Intrinsic hand muscles were found to play an important role in force production.

Response: As described in “response to minor comments 1”, intrinsic muscles have the characteristics of small size, short tendons, and large number, which make their modeling difficult to be accurate and tendon displacement difficult to measure. Moreover, previous cadaveric experiments have shown that studies on extrinsic muscles remain indispensable in revealing the contractile mechanisms of hand muscles without considering intrinsic muscles.

5. Response to comment: Page 12 - Fig. 7: change “flexure” in the caption to “flexion”. Also it is not clear what data these graphs display – in the text (line 221 – 222), it is mentioned that “rigid plate reaction forces of the model were equal to the experimental fingertip forces (Fig 7)”. However, only one line is shown in each figure – what is shown here then? Does it mean that the experimental data and simulation results are in perfect match (which is highly unlikely)?

Response: The purpose of Figure 7 is to show the variation of the rigid plate reaction force with time during the model simulation of Action 2-4, where the most important data is the final value of the reaction force. The representation in Figure 7 was inappropriate and has been removed and replaced with table 3 (page 12, line 244).

6. Response to comment: Page 14 - Fig. 9: This figure is not very informative – although the color bar shows a range of different colors, the picture only shows (or appears to show) one color – dark blue.

Also why did the authors show stress distribution throughout the tendons? It would be much more important to show stress at the FINGER PULLEYS (where most stress ruptures happen) – first of all, were the pulleys modeled at all? If so, how was it modeled?

Response: Indeed. Figure 9 shows the stress distribution of the whole tendon. Due to the size of the image, the color change (stress distribution) cannot be clearly shown. The peak stresses in the tendon are present at the joint area, while the stresses in the palm and wrist areas of the tendon are evenly distributed. Figure 9 has been modified to show the stress distribution of the tendon in the finger area (page 15, line 263, Fig 2A).

The pulley at the joint has been modeled as consisting of a ring ligament around the end of the phalanx at the joint. The right and left sides of the annular ligament are bound to the end of the phalanx. Holes are left on the palmar and dorsal sides of the annular ligament for the extensor and flexor muscles to pass through. An error was made in the article and has been corrected (page 7, Fig 2A).

7. Response to comment: The reviewer thinks that the authors may want to focus on utilizing the information obtained from ultrasound imaging (MTJ excursion) and see how that is correlated to the changes in the measured fingertip forces – FE model used in this study is too complex and contains too many unknown parameters to result in any meaningful estimation of muscle forces.

Response: The description of the methodology for parameter determination in this paper is indeed unclear. It has been revised in the text (page 6, lines 126-135).

The parameters of the model, except for the elastic modulus of the bones, need to be determined, including the elastic modulus of the tendons (FDS, FDP, ED, etc.), the elastic modulus of the ligaments (finger joint rotation, extensor retinaculum, etc.), and the joint spring elements stiffness. The spring elements are simplified as follows: each spring element at the IP joints has the same stiffness, and each spring element at the MCP joint has the same stiffness. This gives a total of four unknown quantities: the elastic modulus of the tendons, the elastic modulus of the ligaments, the spring unit stiffness at the IP joints, and the spring unit stiffness at the MCP joints. The experimentally measured known quantities are the MTJ displacement and the fingertip force (or flexion pattern), for a total of five sets. Four of these experimental data sets (MTJ displacement-fingertip force) were used to determine the four unknown quantities and one set of data (MTJ displacement-flexion pattern) was used to validate the model after determining the parameters. Thus the parameters of the model were able to be determined.The muscle force is not involved in the above process; it is the result of the calculation after both parameter determination and model validation have been completed.

Reviewer #2: Review of PLOS One manuscript PONE-D-21-23164, “Analysis on synergistic cocontraction of extrinsic finger flexors and extensors during Flexion movements: a Finite Element Digital Human Hand Model”

General Comments:

1. Response to comment: The manuscript describes a model of the human hand performed using limited in vivo experimentation and finite element modeling. The study details are lacking. The results are may be interesting with potential implication. However, the reader is left to question some important details that are missing from manuscript and which are essential for determining if the model is indeed valid (as stated in manuscript) and how that model is any different from already existing human hand models.

Response: The article is not clear about the details of the model description, and the following modifications have been made: (1) detailed description of the definition of interaction, material parameters, boundary conditions and loading conditions (pages 6-7, lines 116-152), especially the setting and simplification of the spring element at the joint; (2) detailed description of the method and process of parameter determination and model validation (pages 10-11, lines 209-232).

Specific comments:

1. Response to comment: Abstract

Occasionally/many acronyms are defined only in abstract but should also be defined in body of manuscript, e.g. MTJ

Response: Definitions of acronyms have been added to the text，such as FE-DHHM (page 3, line 51) and MTJ (page 4, line 84).

Introduction

2. Response to comment: Line 83: The reader is confused, as the stated purpose is illogical and does not make sense in that the purpose of the paper can not be to develop anything. Rather the purpose of the paper is “to describe the development of an FE-DHHM….” Or the purpose of this paper is to “describe a study to develop an FE-DHHM…”

“The purpose of this paper is to develop a FE-DHHM including phalanges, metacarpals, solid unit tendons and ligaments by combining finite element techniques with ultrasound imaging to measure the MTJ displacements techniques to achieve accurate loading of the MTJ displacements of different muscles under the same movement.”

Response: It has been modified to: In this paper, we have achieved accurate loading of Muscle-Tendon Junction (MTJ) displacements of different muscles under the same movement by combining FE-DHHM established by finite element technique and the MTJ displacements measured by ultrasound imaging, which was used to study the synergistic contraction of Flexor Digitorum Superficialis muscle (FDS), Flexor Digitorum Profundus muscle (FDP) and Extensor Digitorum muscle (ED) in flexion movements (page 4, lines 84-89).

3. Response to comment: Lines 89-90: “….and also has a wide range of applications in clinical and rehabilitation fields”

Response: Removed. The model developed in this paper will be used in the next step of work to study burnt deformities of the hand. This is addressed in the Discussion section, but not in detail. So this sentence is deleted.

4. Response to comment: Line 111: what is meant by “cells”? Do authors mean “element”, as this is a finite element model ?

Response: It does mean "element". Corrected (page 6, lines 112).

5. Response to comment: Line 113: what were the “material parameters and boundary conditions defined” ? This specific information would be useful to readers to understand how model was implemented.

Response: The following modifications were made to the above issues.

(1) Material parameters (page 6, lines 126-135)

The article covers a total of five material parameters, including the elastic modulus of bones, the elastic modulus of tendons, the elastic modulus of ligaments, the stiffness of spring elements at IP joints, and the stiffness of spring elements at MCP joints. Among them, the material parameters of the bones are known. The elastic modulus of tendons and ligaments need to be determined and have been given preset values (table 1). The stiffness of the spring elements at the IP and MCP joints also need to be determined. In total, four parameters need to be determined.

(2) Boundary conditions and loading conditions (page 6, lines 136-148)

The boundary and loading conditions were divided into flexion without resistance conditions and flexion with resistance conditions according to the flexion experiments. The flexion without resistance conditions were based on fixing the metacarpals, carpal bones, ulna and radius of FE-DHHM and loading displacement loads on the rigid reference points of FDS, FDP and ED. The flexion with resistance conditions were based on the flexion without resistance conditions with the proximal phalanges fixed and a fully fixed rigid plate added at the tip of the FE-DHHM to provide resistance (Fig 2).

6. Response to comment: Lines 192-193 and 212-213: What exactly is meant by “validation of validity” ? Does not validity stem from validation and so without validation there is no validity ? So, again, specifically, what is meant here by “validation of validity”? How is validation of validity part of methods section but also part of results ? Reader is confused.

Response: "Validation of validity" has been revised to "model validation". The parameters of the model, except for the elastic modulus of the bones, need to be determined, including the elastic modulus of the tendons (FDS, FDP, ED, etc.), the elastic modulus of the ligaments (finger joint rotation, extensor retinaculum, etc.), and the joint spring elements stiffness. The spring elements are simplified as follows: each spring element at the IP joints has the same stiffness, and each spring element at the MCP joint has the same stiffness. This gives a total of four unknown quantities: the elastic modulus of the tendons, the elastic modulus of the ligaments, the spring unit stiffness at the IP joints, and the spring unit stiffness at the MCP joints. The experimentally measured known quantities are the MTJ displacement and the fingertip force (or flexion pattern), for a total of five sets. Four of these experimental data sets (MTJ displacement-fingertip force) were used to determine the four unknown quantities and one set of data (MTJ displacement-flexion pattern) was used to validate the model after determining the parameters. Thus the parameters of the model were able to be determined.The muscle force is not involved in the above process; it is the result of the calculation after both parameter determination and model validation have been completed.

7. Response to comment: Lines 214-215: The table title is “Table 2 MTJ displacements of each muscle during flexion movements (mm)” But then immediately after table 2, sentence reads “Table 2 demonstrates the fingertip forces and MTJ displacements of each muscle…” But all the values in Table 2 have units of millimeters (as stated in title), so how are any of the values in Table 2 forces ? Reader is confused.

Response: The article was misrepresented. Fingertip forces were not present in Table 2. Correction has been made. The fingertip forces are listed in the revised Table 3 (page 12, line 244).

8. Response to comment: Lines 264-266: “FDS and FD contracted together to provide power; while the ED had a non-zero muscle force and acted as an antagonist.” How were forces apportioned between FDS, FD and ED ? This mathematics to determine apportionment is not described in methods section, except for lines 202 and 203 where says “after several fits and adjustments”, and so reader is left to wonder how the values in this Figure 11 were determined ? Was there any physics or mechanics behind the fits and adjustments? Or simply curve matching ?

Respons: The percentage of FDS muscle forces was the largest and gradually increased with increasing fingertip forces (54%-65%), while the percentage of FDP (45%-34%) and ED (0.7%-0.35%) muscle forces gradually decreased (page 17, lines 285-287).

The parameters were determined by comparing the fingertip forces with the rigid plate reaction forces calculated in the model under loads of MTJ displacements. For example, when the rigid plate reaction force was greater than the fingertip force, reducing the elastic modulus of tendon or ligament, or increasing the stiffness of the joint spring unit, the rigid plate reaction force was reduced. The four material parameters have different effects on the reaction force of the rigid plate: the elastic modulus of the tendon and the elastic modulus of the ligament are positively correlated with the rigid plate reaction force, and the effect of the tendon is more significant. The spring element stiffnesses of the IP and MCP joints were negatively correlated with the rigid plate reaction force, and the effect of the spring element was more significant for the MCP joint. Each adjustment of material parameters required fitting four sets of experimental data (MTJ displacement - fingertip force) simultaneously. After repeated calculations, the parameters that meet the accuracy requirements were obtained.

Figure 11 of the original article showed the variation of muscle force with fingertip force. Muscle force was not involved in the process of parameter determination and model validation, but was the result after all these processes had been completed.

9. Response to comment: Line 282-284 seems to say that material parameters are a result of the model. Yet, Table 1 indicates the material parameters were taken from references 26 and 20. So what is difference between table 1 and table 3, and how can material parameters be both input to the model and output from the model ?

Response: The model was finally built after the material parameters were determined and the model validation was completed. This process was calculated and adjusted several times. The material parameters were actually the result of the "last" calculation of the model.

Table 1 shows the elastic modulus of tendons and ligaments taken from the preset values of Refs. 26 and 20. In reality, the models of tendons and ligaments have larger dimensions than the real anatomy, for example the tendon model is thicker than the real tendon. This is a problem caused by the accuracy of the model. Therefore the determined values of the elastic modulus of tendons and ligaments in the model (Table 3) are smaller than the preset values (Table 1). And the preset values taken from Refs. 26 and 20 are the baseline for parameter adjustment.

10. Response to comment: Line 239 and Figure 8: this figure suggest the force at finger tip varies with time over 200 milliseconds of the simulation/experiment. What was the sample rate of the force measurement device shown in figure 3 so reader can understand if the variation in finger tip force is meaningful ?

Response: In the experiments, the fingertip forces displayed by the force measurement device were recorded only for the final values (5, 10, 15 and 20 N). In these processes, the change of fingertip forces with time were not concerned. At the same time, the displacements of the MTJs were recorded only for the corresponding final values, which were loaded uniformly as displacement loads in the model by Step time. Figure 8 was focused on showing the final values of the fingertip forces calculated by the model under MTJ displacement loading. Since Figure 8 was prone to ambiguity and misinterpretation, it has been removed and replaced with Table 3 (page 12, line 244).

11. Response to comment: Regarding results, specifically figures 9-12, reader is having difficult time understanding if any of the results are valid as no comparisons are made to in vivo data or even experimental/literature data.

Response: The data underlying the results shown in Figures 9-12 are the "muscle forces". Figure 9 shows the stress distribution of the tendon under muscle force, Figure 10 shows the relationship between maximum stress and muscle force, Figure 11 shows the relationship between muscle force and fingertip force (experimental value), and Figure 12 shows the variation of muscle force over time calculated by the model.

The results regarding the calculation of muscle force in this paper were described in the Discussion section. Firstly, the calculated results of muscle forces in this paper were compared with the in vivo experimental data of tendon forces in the literatures 34 and 35, and the results were similar with a maximum error of no more than 60%.

Secondly, the factors that affect the accuracy of muscle force calculation results were mainly the accuracy of the model and the ultrasound measurement of MTJ displacements. The simplification of the model in terms of both anatomical structure and material parameters affects the accuracy of the calculation results. However, this is unavoidable for digital methods, and the calculated results of the model are still in good agreement with the in vivo experimental data. This indicates that the model developed in this paper is reasonable and the calculation results are valuable.

12. Response to comment: The manuscript suggests some lack of rationality in the model material parameters (line 378). The manuscript suggests some utility of the model (lines 89-90 and 390-391). However, the reader is left to question utility of a model with lack of rationality and without explicitly stated or apparent utility.

Response: Admittedly, there are various models for material properties of soft tissues in the finite element software ABAQUS, such as viscoelastic model, hyperelastic model, and linear elastic model. Although the nonlinear material parameters (viscoelastic model, hyperelastic model, etc.) are closer to the real situation than the linear elastic model, they are complicated to calculate and difficult to amend and determine the parameters. In the research work on finite element methods for soft tissues, the simplification of linear elasticity is also very common and reasonable. This simplification not only makes the calculation easier to converge and reduces the computational time, but is also very beneficial for the amendment and determination of material parameters.

The practicality of the model was not described in detail in the manuscript. In subsequent work, skin and scar models have been developed and combined with FE-DHHM for the study of the formation and treatment of hand deformities after burn injury. Due to space limitations, only a brief description of the utility of FE-DHHM was provided in this manuscript.

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28 Feb 2022

11 Mar 2022

Dear Editors and Reviewers:

Thank you for your letter and for the reviewers’ comments concerning our manuscript entitled “PONE-D-21-23164”. Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our researches. We have studied comments carefully and have made correction which we hope meet with approval. Revised portion were marked in red in the paper. The main corrections in the paper and the responds to the editors and reviewers’ comments were addressed point by point below.

Responds to the reviewers’ comments:

Reviewer #1:

1. Response to comment: Model inaccuracy: missing muscles and anatomical structures.

Authors responded that the intrinsic hand muscles and extensor mechanism are ‘ignored’ in this model because they are basically ‘difficult to model’. They mentioned one study (Chang et al., 2017) from the applied ergonomics field to provide rationale for excluding intrinsic muscles. However, first, this study was looking at a specific “triggering” motion (concurrent flexion of the DIP and PIP joints without much MCP flexion), which does not require intrinsic action (this is close to intrinsic minus motion). Second, some studies they mentioned (e.g., Valero-Cuevas et al., 1998) did include intrinsic actions, so their answer to this question is basically inaccurate.

More importantly, in my opinion, the authors should focus on providing a proper rationale, i.e., why these muscles or mechanisms were not included in this study (e.g., if their force contribution is negligible) to respond to this reviewer's question. But instead, throughout their response the authors emphasized basically how “difficult” it is to include the intrinsic muscles or the extensor mechanism – the response should be, to properly justify their model selection, why the effects of the intrinsic muscles and/or the extensor mechanism on the model output is small enough (negligible) to exclude these structures. Note that, unfortunately, that will not be the case (i.e., the contribution of intrinsic muscles are quite significant indeed) – see Maier and Hepp-Reymond (1995) and/or Milner and Dhaliwal (2002), which emphasized the importance of intrinsic muscles during force production tasks (similar to what was done in this study).

Response:

Thank you for your comments on our article. The effect of the intrinsic muscles and/or the extensor mechanism on the model of this article was indeed insignificant. The literatures suggest that the contribution of the intrinsic muscles of the hand is relevant to the target task. For example, Li et al. (Li Z M , Zatsiorsky V M , Latash M L . Contribution of the extrinsic and intrinsic hand muscles to the moments in finger joints[J]. Clinical Biomechanics, 2000, 15( 3):203-211.) analyzed the contribution of intrinsic and extrinsic muscles to the knuckle moment using the experimental apparatus shown in Figure 1 in conjunction with a biomechanical model of the index finger and concluded: when the point of force application was on the distal phalanx, the force of the INT of the index finger accounted for only 22.5% of the combined FDP and FDS force. The moment contribution of the INT at the MCP joint of the index finger was only 12.4%. In further work, Li et al. (Li Z M , Zatsiorsky V M , Latash M L . The effect of finger extensor mechanism on the flexor force during isometric tasks[J]. Journal of Biomechanics, 2001, 34(8):1097-1102.) stated: when the point of force application was at the distal phalanx, the extrinsic flexor muscles flexor digitorum profundus (FDP) and flexor digitorum superficialis (FDS) accounted for over 80% of the summed force of all flexors, and therefore were the major contributors to the joint flexion at the distal interphalangeal (DIP), proximal interphalangeal (PIP), and metacarpophalangeal (MCP) joints. When the point of force application was at the DIP joint, the FDS accounted for more than 70% of the total force of all flexors, and was the major contributor to the PIP and MCP joint flexion. When the force of application was at the PIP joint, the intrinsic muscle group was the major contributor for MCP flexion, accounting for more than 70% of the combined force of all flexors. The results suggested that the effects of the extensor mechanism on the flexors were relatively small when the location of force application was distal to the PIP joint. When the external force was applied proximally to the PIP joint, the extensor mechanism had large influence on force production of all flexors.

Maier and Hepp-Reymond (M.A. Maier, M.C.Hepp-Reymond. EMG activation patterns during force production in precision grip[J]. Experimental Brain Research, 1995,103:108-122.) reported that the intrinsic muscles of the index finger and thumb were closely related to the low isometric forces generated between the thumb and index finger in the precision grasp experiment (Figure 2).

It can be seen that the contribution of the intrinsic muscles of the hand is related to the target task. The target task (fingertip force) addressed in this paper is very similar to the distal phalanx loading in the work of Li et al. Under this task, the extrinsic muscles are the main contributors to joint flexion of the DIP, PIP and MCP joints (accounting for more than 80% of the total force of all flexors). Therefore, the simplification of the intrinsic muscles and the extensor mechanism in the modeling of this paper is justified.

Admittedly, the intrinsic muscles are important components of the hand muscles, and a whole-hand model containing the intrinsic muscles has still not been created. The modeling and loading of intrinsic muscles in the whole hand model is worthy of consideration and is something we intend to carry out in further work (page 18, lines 308-315).

2 .Response to comment: Flawed model validation

The authors now provided details of the model parameter estimation process – which is basically estimating material properties of the tendons, ligaments, and joint stiffness. This is a problematic in itself since all these components are connected in series, which means that the effects of these parameters on measured data (fingertip force/MTJ motion) are intertwined (and cannot be told from each other). In other words, given the motion tested (concurrent flexion of all finger joints), there is no way for the model to distinguish the effects of joint stiffness from those of tendon stiffness. Thus, the outcome may appear to make sense, but there is no way to validate the results (or whether any of these estimated parameter values is reliable). Hypothetically, the solutions obtained by the authors may estimate the movement of MTJ correctly, but could lead to 5-fold overestimation of tendon stiffness in combination with 5-fold underestimation of joint stiffness. Therefore, it is possible that this model will work on the dataset collected in this experiment ('interpolation'), but won't be applicable to any other cases ('extrapolation').

Response:

The influence of the material parameters to be determined for the model on the measured data can be divided into two cases: the stiffness of tendons and ligaments was positively correlated (to different degrees) with the fingertip force, and the stiffness of the two groups of joints (IP and MCP joints) was negatively correlated (to different degrees) with the fingertip force. All parameters were approximated iteratively using experimental data on the basis of initial values (literature data). And four sets of data were sufficient to determine the four unknowns. The effect of each parameter on the measured data was not "proportional", so that the the solutions for parameter estimation would not lead to "5-fold overestimation of tendon stiffness in combination with 5-fold underestimation of joint stiffness ". Otherwise the determined material parameters would not satisfy the " MTJ-flexion pattern" data in the model validation, even if the four sets of "MTJ-fingertip force" data were satisfied simultaneously. In fact, the model validation process could be regarded as the "extrapolation" of the model after the parameters were determined.

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25 Apr 2022

Analysis on synergistic cocontraction of extrinsic finger flexors and extensors during Flexion movements: a Finite Element Digital Human Hand Model

PONE-D-21-23164R2

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2 May 2022

PONE-D-21-23164R2

Analysis on synergistic cocontraction of extrinsic finger flexors and extensors during Flexion movements: a Finite Element Digital Human Hand Model

Dear Dr. An:

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