## Abstract

Regarding the prevention of injuries and rehabilitation of the human hand, musculoskeletal simulations using an inverse dynamics approach allow for insights of the muscle recruitment and thus acting forces on the hand. Currently, several hand models from various research groups are in use, which are mainly validated by the comparison of numerical and anatomical moment arms. In contrast to this validation and model-building technique by cadaver studies, the aim of this study is to further validate a recently published hand model [1] by analyzing numerically calculated muscle activities in comparison to experimentally measured electromyographical signals of the muscles. Therefore, the electromyographical signals of 10 hand muscles of five test subjects performing seven different hand movements were measured. The kinematics of these tasks were used as input for the hand model, and the numerical muscle activities were computed. To analyze the relationship between simulated and measured activities, the time difference of the muscle on- and off-set points was calculated, which resulted in a mean on- and off-set time difference of 0.58 s between the experimental data and the model. The largest differences were detected for movements that mainly addressed the wrist. One major issue comparing simulated and measured muscle activities of the hand is cross-talk. Nevertheless, the results show that the hand model fits the experiment quite accurately despite some limitations and is a further step toward patient-specific modeling of the upper extremity.

## Introduction

Musculoskeletal simulations offer enormous potential to provide insights into areas of biomechanics that are difficult to access; especially in areas where numerous mutually influencing structures come together—like in the hand. Over recent decades, numerous research groups have conducted simulations intending to depict this complexity of the human hand [2]. To address various functions and malfunctions because of disorders of the musculoskeletal system, the inverse dynamics modeling approach is an increasingly applied method.

With this approach, the complex dynamic force distribution in all structures of the hand can be analyzed during activities of daily life for both physiological and pathological evaluations. The major benefit of these models is the enablement of research questions regarding injury prevention and rehabilitation of the biomechanics of the hand without the need for in vivo or in vitro experiments. The AnyBodyTM modeling system (AMS) (Anybody, Aalborg, Denmark) is a widely utilized simulation software for musculoskeletal modeling using this inverse dynamics approach. The AMS contains body-scaling functions featuring a patient-specific scaling and algorithms to optimize complex motion capture data, like thumb and finger movements. In future releases of the anybody managed model repository (AMMR), a new comprehensive model of the hand from Engelhardt and Melzner et al. [1] will be available and for open access. To increase the validation depth of this model, the approach of comparing numerically calculated and experimentally gained moment arms [36] was used.

This comparison was adopted because studies of Maury et al. [7] and Raikovaa and Prilutsky [8] have indicated that the line of action and moment arms are critical parameters in predicting muscle and joint reaction forces. Therefore, when the moment arms of the proposed model fit experimental data, the resulting muscle activities and joint reaction forces of the hand should also correspond to reality. Furthermore, the above-mentioned models of Holzbaur et al. [2], Lee et al. [9], Mirakhorlo et al. [10], and Ma'touq et al. [11] were validated comparing muscle moment arms. However, as stated in the literature [12,13], there are many more ways to confirm the validity of a musculoskeletal model. A common type is an indirect validation using the comparison of measured electromyographic (EMG) signals of the muscles with predicted muscle activities of the simulation. Using the EMG signal, the evaluation of the different timings of on- and off-sets of muscle activities between the model and the experiment can result in the validation of a model [14,15].

This experimental validation approach is a decisive step that is necessary in determining whether the model predictions fit the measurements. This consistency between model and reality is crucial when the data obtained from the model (e.g., joint reaction forces) are to be used for answering musculoskeletal research questions. However, to the authors' knowledge, no experimental setup has to date been conducted in which experimentally captured motion data and simultaneously recorded muscle activities of hand motions are recorded, and the calculated muscle forces of an inverse dynamic approach are compared to the experimental outcomes. Because the moment arm studies of the hand model published by Engelhardt and Melzner et al. [1] revealed promising results and a good comparison of the experimental with simulated data, a further trend validation of the model could be realized using measured EMG signals of the muscles.

Therefore, the aim of this study is a further affirmation of the human hand model, based on insights through the EMG results and a more informative trend validation of the new detailed hand model by EMG experiments. This procedure is intended to answer the research question of whether the hand model produces reliable results and, therefore, could be used to address clinical and ergonomic questions in the future—like how the avoidance of certain malfunctions can be used to prevent long-term injuries.

## Materials and Methods

### Experiment Set-Up.

To provide a reference dataset for the validation of the musculoskeletal hand model, an experimental study was conducted including five subjects (three males, two females; age = 23.0 ± 2.4 years; weight = 69.2 ± 9.7 kg; height = 1.73 ± 0.11 m; hand length = 18.8 ± 1.4 cm). All persons were right-handed, performing the exercises with their dominant hand, which was not harmed or affected by any illness. Each test person was informed in advance about the procedure of the measurement, and a corresponding written consent was obtained concerning voluntary participation. All procedures performed involving human participation were in accordance with ethical standards and with the 1964 Helsinki Declaration and its later amendments or comparable ethical standards. The anthropometrics of the test persons were obtained to scale the musculoskeletal model afterward.

For the measurement of the muscle activities, four intrinsic and six extrinsic muscles were considered (see Table 1). The EMG activities of these muscles were captured via surface EMG (Delsys Trigno IM and Delsys Trigno Mini, Delsys® Inc., Natick, MA) using the recommended sensor placements according to Criswell and Cram [16] and Barbero et al. [17]. Prior to sensor placement, the skin was cleaned with an alcoholic solution to minimize the influences on the acquired signal resulting from dead skin cells, salt, or grease. For the intrinsic muscles, Extensor carpi ulnaris (ECU), and Flexor digitorum superficialis (FDS), the Trigno Mini sensors were applied, whereas the Trigno IM sensors were used for all others; but all sensor types had the same sampling frequency of 1.1 kHz and recorded only the raw signal without any filters.

Table 1

Measured EMG signal of intrinsic and extrinsic muscles

Extrinsic musclesSensorProtocol
Flexor carpi ulnaris (FCU)T-IM*
Extensor carpi ulnaris (ECU)T-Min*
Flexor digitorum superficialis (FDS)T-Min*
Extensor digitorum (ED)T-IM*
Intrinsic musclesSensorProtocol
Abductor pollicis brevis (APB)T-Min**
Flexor pollicis brevis (FPB)T-Min**
First dorsal interosseous (FDI)T-Min*
Extrinsic musclesSensorProtocol
Flexor carpi ulnaris (FCU)T-IM*
Extensor carpi ulnaris (ECU)T-Min*
Flexor digitorum superficialis (FDS)T-Min*
Extensor digitorum (ED)T-IM*
Intrinsic musclesSensorProtocol
Abductor pollicis brevis (APB)T-Min**
Flexor pollicis brevis (FPB)T-Min**
First dorsal interosseous (FDI)T-Min*

The placement of the sensors was performed according to Criswell and Cram [16]* and Barbero et al. [17]**. For the measurement, Trigno IM (T-IM) and Trigno Mini (T-Min) sensors from Delsys were applied.

For normalization of the EMG data, maximum voluntary contraction (MVC) measurements following Kendall [18] were performed. Each subject repeated the MVC measurement three times for each muscle group, and the maximum value was taken as the normalization factor.

The kinematics of each hand movement were recorded with a camera-based motion capture system (Vicon, Vicon Motion Systems Ltd., Oxford, UK) consisting of 12 cameras. A custom marker setup of 38 markers (22 on the hand) was designed, capturing the movement of the pelvis, thorax, humerus, forearm, and all segments of the hand. An overview of the marker and EMG sensor placement of the hand is given in Fig. 1 and in the Appendix (Fig. 6).

Fig. 1
Fig. 1
Close modal

The test subjects performed seven different muscle-specific activation movements for the fingers, thumb, and wrist (see Fig. 2). Additionally, the involved joints and expected active muscles according to Tillmann [19] are depicted in Table 2. Each task was repeated five times within one trial, and each subject repeated every trial three times. Every subject was instructed to use the full range of motion in each task and the EMG signals of all sensors were recorded. To guarantee the same initial time of the EMG signals and motion capture recordings, both measuring systems were synchronized.

Fig. 2
Fig. 2
Close modal
Table 2

Indication the joints moving in each task and the muscles involved in each motion according to Tillmann [19]

MovementInvolved jointInvolved muscles
Metacarpophalangeal joint extensionMetacarpophalangeal joint (finger), carpometacarpal (thumb)ED
Finger flexionMetacarpophalangeal joint (finger), carpometacarpal (thumb)FDS
Thumb flexionMetacarpophalangeal, carpometacarpal (thumb)FPB, APB
Wrist ab-/adductionWristFCU, FCR, ECU, ECR, ED
Wrist extension/flexionWristFCU, FCR, ECU, ECR, ED, FDS
MovementInvolved jointInvolved muscles
Metacarpophalangeal joint extensionMetacarpophalangeal joint (finger), carpometacarpal (thumb)ED
Finger flexionMetacarpophalangeal joint (finger), carpometacarpal (thumb)FDS
Thumb flexionMetacarpophalangeal, carpometacarpal (thumb)FPB, APB
Wrist ab-/adductionWristFCU, FCR, ECU, ECR, ED
Wrist extension/flexionWristFCU, FCR, ECU, ECR, ED, FDS

### Simulation.

The gained kinematic data were used for the musculoskeletal simulation with AnyBody (V. 7. 3 Beta)—see Fig. 3.

Fig. 3
Fig. 3
Close modal

For the hand model from Engelhardt and Melzner et al. [1], the configuration with only one muscle line of action for each muscle but with detailed wrapping pathing was chosen. Since only the EMG signal and motions of the dominant right hand were measured, the left arm segment and both legs of the entire AMMR human body model were omitted for this simulation to reduce the computational time.

Because a strong synergy of muscles within the hand for gross motor skills was assumed [20], a polynomial muscle recruitment criterion with a power of p =5 was chosen, and simple muscle models are applied. The polynomial describes the objective function G, which has to be minimized by the algorithm.
$G=∑i(fiNi)p$

where fi is the applied force and Ni is the strength of a muscle. The higher the polynomial coefficient p, the more the load is distributed between the individual muscles. All trials were calculated with 40 simulation steps per second. Prior to each motion simulation, a calibration of the skin resistance (see Fig. 3) according to the anthropometrics of the subject was performed.

Compared to the original detailed hand model [1], which was validated by moment arm studies and, therefore, simplified movements, smaller adjustments were made because of the complexity of the motions to assure a physiological pathing of the muscles. These adjustments mainly involved the initial wrapping vectors (like extensor pollicis brevis and extensor carpi radialis longus) and also the muscle path of the extensor carpi ulnaris muscle. Because the goal of this study was a real blind validation rather than just a calibration of the model [12], no further adjustments were made.

### Data Processing.

For each EMG signal, the baseline off-set was subtracted, the root-mean-square with an applied window size of 50 ms was calculated, and the signal was normalized according to the MVC measurements [21].

To be able to compare the numerical with the experimentally measured muscle activity, simulated muscles were compiled and only the maximum value at each time-step was taken into account. This compilation of muscles allows a numerical reproduction of the signal received by the EMG sensor. The exact list of enveloped muscles can be found in the appendix (Table 4).

Table 4

EMG sensor and envelope of corresponding AnyBody muscles

EMG signalAnybody muscles
Extensor digitorumExtensor_Digitorum_Finger2_1
Extensor_Digitorum_Finger3_1
Extensor_Digitorum_Finger4_1
Extensor_Digitorum_Finger5_1
Supinator_humerus_part_2
Supinator_ulna_part_1
Flexor carpi ulnarisFlexor_Carpi_Ulnaris_1
Flexor_Digitorum_Profundus_Finger5_1
Flexor_Digitorum_Superficialis_Finger5_1
First dorsal interosseusLumbricales_I
Interossei_Dorsales_I_Finger2_1
Interossei_Dorsales_I_Finger1_2
Interossei_Dorsales_I_Finger1_1
Interossei_Dorsales_I_Finger2_2
Interossei_Dorsales_I_Finger2_3
Abductor digit minimiAbductor_Digiti_Minimi_1
Flexor_Digiti_Minimi_Brevis
Opponens_Digiti_Minimi_1
Opponens_Digiti_Minimi_2
Abductor pollicis brevisAbductor_Pollicis_Brevis_1
Abductor_Pollicis_Brevis_2
Abductor_Pollicis_Brevis_3
Abductor_Pollicis_Brevis_4
Abductor_Pollicis_Brevis_5
Flexor_Pollicis_Brevis_Caput_Superficiale_1
Flexor_Pollicis_Brevis_Caput_Superficiale_2
Flexor_Pollicis_Brevis_Caput_Profundum
Opponens_Pollicis_1
Opponens_Pollicis_2
Opponens_Pollicis_3
Opponens_Pollicis_4
Flexor pollicis brevisFlexor_Pollicis_Brevis_Caput_Profundum
Opponens_Pollicis_1
Opponens_Pollicis_2
Opponens_Pollicis_3
Opponens_Pollicis_4
Flexor digitorum superficilialisFlexor_Digitorum_Superficialis_Finger2_1
Flexor_Digitorum_Superficialis_Finger3_1
Flexor_Digitorum_Superficialis_Finger4_1
Flexor_Digitorum_Superficialis_Finger5_1
Extensor carpi ulnariExtensor_Carpi_Ulnaris_1
EMG signalAnybody muscles
Extensor digitorumExtensor_Digitorum_Finger2_1
Extensor_Digitorum_Finger3_1
Extensor_Digitorum_Finger4_1
Extensor_Digitorum_Finger5_1
Supinator_humerus_part_2
Supinator_ulna_part_1
Flexor carpi ulnarisFlexor_Carpi_Ulnaris_1
Flexor_Digitorum_Profundus_Finger5_1
Flexor_Digitorum_Superficialis_Finger5_1
First dorsal interosseusLumbricales_I
Interossei_Dorsales_I_Finger2_1
Interossei_Dorsales_I_Finger1_2
Interossei_Dorsales_I_Finger1_1
Interossei_Dorsales_I_Finger2_2
Interossei_Dorsales_I_Finger2_3
Abductor digit minimiAbductor_Digiti_Minimi_1
Flexor_Digiti_Minimi_Brevis
Opponens_Digiti_Minimi_1
Opponens_Digiti_Minimi_2
Abductor pollicis brevisAbductor_Pollicis_Brevis_1
Abductor_Pollicis_Brevis_2
Abductor_Pollicis_Brevis_3
Abductor_Pollicis_Brevis_4
Abductor_Pollicis_Brevis_5
Flexor_Pollicis_Brevis_Caput_Superficiale_1
Flexor_Pollicis_Brevis_Caput_Superficiale_2
Flexor_Pollicis_Brevis_Caput_Profundum
Opponens_Pollicis_1
Opponens_Pollicis_2
Opponens_Pollicis_3
Opponens_Pollicis_4
Flexor pollicis brevisFlexor_Pollicis_Brevis_Caput_Profundum
Opponens_Pollicis_1
Opponens_Pollicis_2
Opponens_Pollicis_3
Opponens_Pollicis_4
Flexor digitorum superficilialisFlexor_Digitorum_Superficialis_Finger2_1
Flexor_Digitorum_Superficialis_Finger3_1
Flexor_Digitorum_Superficialis_Finger4_1
Flexor_Digitorum_Superficialis_Finger5_1
Extensor carpi ulnariExtensor_Carpi_Ulnaris_1

The validation was quantified by the comparison of the on- and off-set time points of the numerical and measured muscle activities, which implies the time difference in which a muscle was activated/deactivated in reality and the simulation, respectively. There are numerous methods using computer analysis for determining the on- and off-sets, but little agreement regarding the most appropriate [2224]. Therefore, a matlab (The MathWorks Inc., Natick, MA) tool was designed through which a total number of five trained biomechanical engineers were able to determine the various on and off times manually. Thereby, the graphs, as depicted in Fig. 4, were displayed and the on- and off-set time points were selected and saved in a database. This method is also taken as the “gold standard” when comparing different numerical on- and off-set approaches by Tenan et al. [25].

Fig. 4
Fig. 4
Close modal

For the respective comparison of the EMG signal and the simulated muscle activity of each task, only muscles with a measured maximum EMG activity >15% in at least 50% of all performed movements were considered.

### Statistical Analysis.

To determine to agreement between the model's prediction and measured EMG signal, the weighted kappa value for interrater agreement was calculated for all tasks and all muscles. Hence, the periods of time during which the muscles were active according to the experimental and numerical data were considered. The kappa value k ∈ [0,1] represents the agreement between the two raters: k ∈ [0, 0.2] slight, k ∈] 0.2, 0.4] fair, k ∈] 0.4, 0.6] moderate, k ∈] 0.6, 0.8] substantial, and k ∈] 0.8, 1.0] almost perfect agreement.

## Results

From the 105 potential trials, 100 motion data sets as input for the inverse dynamic simulation could be reconstructed, and 100 numerical simulations were performed. Because the aim of this study was a general comparison of measured and simulated muscle activities, Fig. 4 shows one example of the normalized EMG signal and the calculated muscle activity for the first dorsal interosseous (FDI) and abductor digiti minimi (ADM) muscles of a test subject for task 1 (ab-/adduction of the fingers). All other muscle activities of this trial can be found in the Appendix (Fig. 5).

Fig. 5
Fig. 5
Close modal
Fig. 6
Fig. 6
Close modal

The predicted progression of the muscle activity corresponded to the measured data, but a shift of the on- and off-set points could be observed. Additionally, for the ADM, the model appeared to overestimate the muscle activity, whereas the magnitude of the peak correlated with the abduction angle, which was not reflected in the experimental data.

Regarding the on- and off-sets of the muscle activities of all tasks as well as the weighted kappa values, these are summarized in Table 3. An overall difference of 0.58 s between the estimated and measured muscle activities was computed. The lowest variation (0.19 s) was detected for the flexor pollicis brevis (FPB) muscle in task 4 (ab-/adduction of the thumb), while the highest (1.5 s) was found in the same task for the ECU muscle. Concerning the weighted kappa value, the average kappa value for all trials (0.48) and all muscles (0.46) show a moderate agreement.

Table 3

Mean absolute difference of the measured and predicted muscle on- and off-set time points (±standard deviation) for all tasks and muscles

OnsetOff-setOnsetOff-setOnsetOff-setOnsetOff-setOnsetOff-setOnsetOff-setOnsetOff-set
ECU0.46 ± 0.410.89 ± 0.810.59 ± 0.620.58 ± 0.571.2 ± 1.11.2 ± 1.11.1 ± 0.961.5 ± 1.31.1 ± 1.01.2 ± 1.10.55 ± 0.780.58 ± 0.630.65 ± 0.610.54 ± 0.530.870.43
FCU0.28 ± 0.260.30 ± 0.330.50 ± 0.400.4 ± 0.330.56 ± 0.530.43 ± 0.420.410.42
ECR0.34 ± 0.30.30 ± 0.390.28 ± 0.350.39 ± 0.350.76 ± 0.720.59 ± 0.570.5 ± 0.540.75 ± 0.690.59 ± 0.580.71 ± 0.590.74 ± 0.670.72 ± 0.70.82 ± 0.680.48 ± 0.380.570.54
FCR1.0 ± 0.911.1 ± 0.951.0 ± 0.811.3 ± 1.21.10.44
ED0.20 ± 0.210.26 ± 0.240.34 ± 0.370.38 ± 0.360.45 ± 0.560.46 ± 0.480.41 ± 0.410.43 ± 0.460.72 ± 0.680.75 ± 0.710.440.48
FDS0.73 ± 0.740.63 ± 0.60.6 ± 0.540.49 ± 0.430.610.51
FDI0.62 ± 0.610.63 ± 0.580.630.27
ADM0.47 ± 0.420.91 ± 0.940.60 ± 0.580.42 ± 0.450.600.36
FPB0.23 ± 0.220.21 ± 0.260.51 ± 0.580.6 ± 0.590.19 ± 0.330.24 ± 0.320.32 ± 0.380.35 ± 0.320.53 ± 0.570.55 ± 0.550.370.54
APB0.21 ± 0.230.25 ± 0.290.66 ± 0.670.77 ± 0.760.24 ± 0.310.31 ± 0.30.38 ± 0.390.45 ± 0.430.6 ± 0.680.58 ± 0.620.450.56
Mean0.350.470.400.450.780.800.510.700.560.640.630.600.720.67
Kappa0.560.560.410.580.410.480.33
OnsetOff-setOnsetOff-setOnsetOff-setOnsetOff-setOnsetOff-setOnsetOff-setOnsetOff-set
ECU0.46 ± 0.410.89 ± 0.810.59 ± 0.620.58 ± 0.571.2 ± 1.11.2 ± 1.11.1 ± 0.961.5 ± 1.31.1 ± 1.01.2 ± 1.10.55 ± 0.780.58 ± 0.630.65 ± 0.610.54 ± 0.530.870.43
FCU0.28 ± 0.260.30 ± 0.330.50 ± 0.400.4 ± 0.330.56 ± 0.530.43 ± 0.420.410.42
ECR0.34 ± 0.30.30 ± 0.390.28 ± 0.350.39 ± 0.350.76 ± 0.720.59 ± 0.570.5 ± 0.540.75 ± 0.690.59 ± 0.580.71 ± 0.590.74 ± 0.670.72 ± 0.70.82 ± 0.680.48 ± 0.380.570.54
FCR1.0 ± 0.911.1 ± 0.951.0 ± 0.811.3 ± 1.21.10.44
ED0.20 ± 0.210.26 ± 0.240.34 ± 0.370.38 ± 0.360.45 ± 0.560.46 ± 0.480.41 ± 0.410.43 ± 0.460.72 ± 0.680.75 ± 0.710.440.48
FDS0.73 ± 0.740.63 ± 0.60.6 ± 0.540.49 ± 0.430.610.51
FDI0.62 ± 0.610.63 ± 0.580.630.27
ADM0.47 ± 0.420.91 ± 0.940.60 ± 0.580.42 ± 0.450.600.36
FPB0.23 ± 0.220.21 ± 0.260.51 ± 0.580.6 ± 0.590.19 ± 0.330.24 ± 0.320.32 ± 0.380.35 ± 0.320.53 ± 0.570.55 ± 0.550.370.54
APB0.21 ± 0.230.25 ± 0.290.66 ± 0.670.77 ± 0.760.24 ± 0.310.31 ± 0.30.38 ± 0.390.45 ± 0.430.6 ± 0.680.58 ± 0.620.450.56
Mean0.350.470.400.450.780.800.510.700.560.640.630.600.720.67
Kappa0.560.560.410.580.410.480.33

Only muscles with a measured maximum EMG activity >15% in at least 50% of all performed movements were considered. The weighted kappa values for the on- and off-set times. The on- and off-sets are given in seconds.

Table 3 depicts which muscle was mostly active during the corresponding movement in the experiment. It is noticeable, for example, that the FDS muscles were not active in task 3 (flexion of the fingers) such that it can be assumed that most of the test subjects simply used gravity to flex their fingers or did not use their full range of motions in the proximal and distal interphalangeal joint to fulfill the task. The time difference between model and experiment was best for task 1 (ab-/adduction of the fingers), where a force against the resistance of the skin during the abduction had to be applied. This is also reflected in the highest kappa values for tasks 1, 2, and 4, in which all a passively acting force had to be overcome

## Discussion

The aim of this study was an experimental validation of a recently developed detailed hand model [1] by an overall comparison between the computed muscle activities of the hand model and the experimentally derived EMG activities. Therefore, the on- and off-sets and the corresponding kappa values of the muscle activities were investigated. Because these two approaches bring their own advantages and limitations, first the model and then the validation process will be examined more closely.

### The Model.

For skilled movements, the AMS assumes the muscles to be recruited using more and fewer muscle synergies. Because hand movements are quite trained motions, our study used a strong criterion for the minimization of the muscles' efforts, which also previously showed good results for cycling, gait, and biting [26,27].

The current model has the limitation that the entire wrist is modeled as one rigid body, not including any ligaments within the wrist and hence lacking any passive forces, which might explain the divergence in the computed and experimentally derived activities of the ab-/adduction and the extension/flexion of the wrist (tasks 6 and 7). An implementation of such a detailed wrist model, like that of Eschweiler et al. [28], could provide a solution to address this issue.

Using a simple muscle model, additional passive forces from the muscle tendons are also omitted. The muscle model, which includes these forces, is the Hill-type model. Aurbach et al. [29] recently showed that using the Hill-type model could be one key modeling parameter for simulation of the joint reaction forces within the shoulder. Particularly for the extrinsic muscles with long tendons, using the Hill-type model could be an essential part, which, however, offers significant possibilities for additional uncertainties within the model.

### Validation.

Validating a musculoskeletal model is a necessary, albeit difficult step to take to determine when the model should be used for answering upcoming research questions.

Because there are no available datasets of instrumentalized prostheses and thus available joint reaction forces for the hand—compared to other joints [30]—only indirect validation remains, in which muscle activities and moment arms are compared. This validation method is based on the assumption that when the muscle activities match, the joint reaction forces are also acceptable.

The validation in this study should be accomplished through the comparison of the time difference of numerically determined and experimentally measured on- and off-set time points.

With regard to the EMG measurements, it can be stated that the wrist extensors were more active than the wrist flexors for most of the tasks (which is indicated by the fact that they more frequently overcome the 15% activity threshold), which correlates well with the findings of Forman et al. [31].

When considering Fig. 4, the EMG signal and the numerically calculated muscle activity displayed similar progressions. The on- and off-sets as well as magnitudes alternated in the same dimensions.

However, when considering and evaluating the results of Table 3, one must also always keep in mind which muscles should be primarily addressed in the respective task (see Table 2). For example, ab-/adduction and flexion of the thumb (tasks 4 and 5) mainly address the intrinsic muscles of the thumb, for which the on-/off-set time differences were much smaller than for the stabilizing muscles of the wrist, which are less affected by the movement.

Nevertheless, there are some uncertainties within the comparison which have to be born in mind. One major issue within EMG signals is cross-talk—neighboring muscles also produce an EMG signal, which is recorded by the sensor [21]. Particularly in the forearm/hand, which contains 39 muscles, cross-talk is a systematic bias of the EMG signals [32], but not in the simulation.

The lower the activity of the considered muscle is in comparison to the surrounding ones, the more pronounced the effects of the cross-talk become, which results in a lower signal-to-noise ratio [33]. Therefore, only muscles mainly targeted for the respective movement were compared to each other, and envelopes were introduced. Concerning at the individual tasks 1–7, it can be stated that cross-talk mainly influences tasks 2, 3, 6, and 7 since these task mainly involved extrinsic muscles which are bundled in the forearm. In contrast, the intrinsic muscles in the hand are in a more exposed position, which should reduce the influence of cross-talk in task 1, 4, and 5.

Additionally, the displacement of the innervation zones can produce some artifacts when considering dynamic movements [34]. An example in the collected data is the activity of the FDI during finger abduction. Only two of five subjects were able to abduct the index finger by more than 10 deg, but for all five subjects, EMG deflections during movement were detected. When only the two indicated test persons were included in the data evaluation, the on-/off-set was reduced to 0.39/0.42 s (in contrast to 0.62/0.63 s). This improvement clearly demonstrates the influence that interference signals can have in EMG.

Jungtäubl et al. [35] earlier introduced a method demonstrating how the numerical signal of a simulation can be contaminated with cross-talk and showed a positive effect on the corresponding Person correlation coefficient between measured and numerical obtained muscle activities. Contaminating the numerical outcome with synthetically generated cross-talk could help achieve a better comparison of experimental data and the model.

As the results of tasks 1, 2, and 4 (ad-/abduction of the fingers, extension of the fingers, abduction of the thumb) indicated, the EMG signal and simulated muscle activity became more distinctive when the movement was performed against a force (passive stiffness). All other tasks were performed with gravity as the only prevailing external force. For other scenarios, like measuring EMG in the lower limb, gravity as an additional force might be sufficient by using the bodyweight. However, for the movement of the hand weighing only a few hundred grams (0.575% body weight for the average hand [36]), the on- and off-sets of the muscle activities were not as distinctive, which makes it complicated to assume the correct on- and off-set timing. The results from task 1 also show that the model is much more consistent with the measured data in that loaded case. Due to the fact that the use of an artificially generated cross-talk algorithm brings its own potential sources of error, the authors believe that a further analysis of the model under external load, e.g., by a hand gripping tool, is the next consequential step.

Another limitation, which might explain the differences between reality and the model predictions, is that the models were scaled only to the anthropometric data and were not exact patient-specific models. The lengths of the single finger bones were gained by an optimization process of the adjustment to the defined markers. Because of the relative sliding of the skin and bones along the finger joints, a particular inaccuracy regarding the hand anthropometrics may have occurred.

In future studies, it would also be of interest to morph subject-based bone geometries (from CT data) into the model to make the outcome even more patient-specific. In this way, it would even be possible—also by scaling the strength of different muscle/muscle groups—to map any pathologies and accordingly obtaining even more realistic muscle activities in the numerical model.

A similar musculoskeletal validation study is the one by Wibawa et al. [37] for the lower limb. In this study, it was not the time difference between experimental and numerical data that was determined, but the number of on and off set points during lower limb movements. Here, the AnyBody model of the lower extremity [14], which has been validated in several studies, showed a slight agreement between the measured EMG and predicted muscle activity data (k was up to approximately 0.3). The average kappa for all muscles presented in this study was even slightly higher (0.46).

Apart from all this, the experimental setup restricted the comparison to only four intrinsic and six extrinsic muscles, which are not all, but the dominating hand muscles for most movements. Therefore, the question occurs whether the remaining muscle activity also fits quite well with reality. For this reason, this study attempted to perform a trend rather than an absolute validation. As a consequence, it should be expected that the underlying conceptual model is physically correct, although this is difficult to prove. One way could be the comparison of joint reaction forces to data obtained by an instrumentalized wrist or finger prosthesis in the future.

In general, a validation process based on the measurement of EMG is also restricted to the limitations of EMG. The major limitation of EMG signals in validation is that EMG is only able to reject models with a clearly wrong result [12], which according to the data of this study, is not the case for this hand model.

## Conclusion

The study presented the comparison of a musculoskeletal hand model recently developed within the AMS [1] with experimentally obtained data of muscle activities. The alignment of on- and off-set timings provides good initial agreement, also emphasized by kappa values between 0.27 and 0.56 for the muscles. Further studies might increase the accuracy of the validation by addressing external load cases. Nevertheless, the model provides a good basis to analyze future musculoskeletal research questions regarding the hand.

The presented generic model will become available in the AMMR and can be used for the biomechanical investigation of critical clinical problems affecting the human forearm.

## Disclaimers

Maximilian Melzner and Lucas Engelhardt contributed equally to this work and share the first authorship.

## Funding Data

• Bayerisches Staatsministerium für Wissenschaft, Forschung und Kunst (Grant No. BayWISS Verbundkolleg Gesundheit; Funder ID: 10.13039/501100005341).

• European Commission (Grant No. EFRE, Ziel ETZ BY-CZ 2014-2020 (Interreg V) (Pr. 182; Funder ID: 10.13039/501100000780).

• Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung (Grant No. 320030 L_170205; Funder ID: 10.13039/501100001711).

• Deutsche Forschungsgemeinschaft (Grant Nos. SI 2196/2-1 and IG 18/19-1; Funder ID: 10.13039/501100001659).

• Austrian Science Fund (Grant No. I 3258-B27; Funder ID: 10.13039/501100002428).

## Conflict of Interest

All authors of this paper have no conflict of interest.

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