1 Introduction

Shoulder musculoskeletal (MSK) modelling and inverse dynamics (ID) are frequently used to estimate muscle and joint contact forces during motions [1, 2], as these forces are often difficult to measure in vivo [3–5]. Estimation of muscle forces through modelling provides critical knowledge of internal dynamics and enables answering several biomechanical questions; for instance, to understand physiological loadings during activities of daily living [6], to optimise sports performance [7] or to better design surgical and rehabilitation techniques [8, 9]. Predicting individual muscle forces is not trivial as most MSK systems, including the shoulder, have more muscles than degrees-of-freedom. Muscle redundancy provides flexibility and adaptability to motor control of musculoskeletal systems to produce a single targeted kinematics [10, 11].

While redundancy is beneficial for biological neuromusculoskeletal systems, it poses difficulties for biomechanical models. Emulating the complex neural control strategies underlying human movement, most state-of-the-art MSK models aim to solve the muscle redundancy problem by optimising an objective function. The main computational approaches can be grouped into static optimisation (SO), computed muscle control (CMC) and EMG-assisted optimisation. SO is an inverse dynamics optimisation. The objective function mostly adopted in the literature minimises the sum of muscle activation squared at each specific instant of a motion [12]. With CMC, the time-dependent properties of muscles are considered by using a controlled forward dynamics approach to target static optimisation solutions [13]. EMG-assisted methods, made popular by the development of the calibrated EMG-informed neuromusculoskeletal (CEINMS) toolbox [14] calibrates neural and musculotendon parameters of a model, then uses a forward-dynamics feedback loop that minimises muscle excitation differences with experimental EMG recordings. The advantages and drawbacks of these techniques may depend on the specific task, the experimental data that is available and the MSK system to be modelled, and they are not yet investigated in shoulder models.

Recently, a stochastic modelling method was proposed [15] to sample the solution space of muscle recruitments for a given task. This solution space is determined by the architecture of the selected MSK model (i.e. muscle lever arms) and the targeted kinetics (i.e. net joint moments) and comprises both optimised solutions defined above as well as all non-optimised solutions. Stochastic sampling has been used in lower limb models [16], but not yet in shoulder models. The technique can provide minimum and maximum boundaries for internal forces that are consistent with the observed kinetics and can explore the existence of targeted experimental solutions within the model.

For lack of a better solution, the accuracy of methods to solve the muscle redundancy problem is typically determined by comparing simulated glenohumeral joint reaction forces (GHJ-RF) to experimental measures [4, 17, 18]. A previous study found that SO generally underestimated GHJ-RF when the arm was elevated above shoulder level [19]. Another study found that CEINMS [20] better accounted for muscle co-contractions [21], but they did not quantitatively compare simulated and measured GHJ-RF. The use of CMC in shoulder modelling has been limited in the literature so far [22]. To the best of our knowledge, CMC has not yet been validated in shoulder MSK models.

The OrthoLoad shoulder database [4, 17, 19, 23] is a publicly accessible and comprehensive dataset of synchronised kinematics, EMG and GHJ contact forces, measured with an instrumented implant for six patients and various shoulder tasks. While GHJ contact force data were accessible previously, the complete dataset was only recently published [24].

The present study aimed to use experimental measurements of GHJ contact forces to compare and validate outcomes of the different muscle recruitment strategies for solving the shoulder muscle redundancy problem. First, a stochastic modelling approach was used to determine whether the experimental GHJ contact forces were part of the solution space of the shoulder model. Second, a benchmark and validation of the SO, CMC and CEINMS methods were undertaken. A selection guide was provided with advantages and drawbacks (e.g. accuracy and computational time) of each technique for shoulder modelling.

2 Methods

2.1 Experimental data

We used publicly available kinematic, surface electromyographic (EMG) and GHJ contact force data measured with an instrumented shoulder prosthesis implanted in the right shoulder of a 64-year-old male (163 cm, 85 kg, right arm) [4, 19, 24]. Data were synchronously captured during 1) shoulder abduction (up to 95° of GHJ elevation) and 2) shoulder flexion (up to 110° of GHJ elevation), both with no weight in hand, and 3) a shoulder abduction task while holding a 2.4 kg weight (up to 92° of GHJ elevation). Motions 1) and 2) will be used for model calibration (see Sect. 2.3.4.) and motion 3) will be used for validation of the different shoulder muscle recruitment strategies.

Clusters of three retroreflective markers were secured on the participant’s sternum, right scapula’s acromion; lateral aspects of the right upper arm and right forearm and their 3D trajectories were captured by four Optotrak camera-bars (Northern Digital Inc., Canada) at a sampling rate of 50 Hz [19, 24]. 14 bony landmarks (described in the supplementary materials) were digitised and rigidly linked to their respective segments using a 3D locator [25, 26]. The GHJ centre was previously determined using the instantaneous helical axes method [19, 27]. Marker trajectories were smoothed using locally weighted smoothing [28].

Surface EMG signals (Porti system, TMS International, Enschede, the Netherlands) were measured from eight superficial muscles (i.e. anterior, middle and posterior deltoid, upper and lower pectoralis major, biceps, triceps and infraspinatus) as described in detail in [23]. EMG signals were recorded at a frequency of 1000 Hz. EMG envelopes were extracted using 1) zero-lag, 8th order 40 – 400 Hz bandpass Butterworth filter, 2) full-wave rectification, 3) zero-lag, 8th order 5 Hz low-pass Butterworth filter [29, 30]. All envelopes were then normalised to the maximum values obtained from the available functional, force and maximum voluntary contraction tasks [23].

GHJ contact forces in three orthogonal directions between the instrumented shoulder hemiarthroplasty and the patient’s intact glenoid were recorded using a telemetric system at a sampling frequency of about 120 Hz [4, 17, 19, 23].

2.2 Shoulder modelling

A previously developed [2, 19] and adapted [31] upper limb MSK model was used. This OpenSim-adapted version of the Delft Shoulder and Elbow Model (DSEM) consists of 7 segments (thorax, clavicle, scapula, humerus, ulna, radius, hand), 11 degrees-of-freedom (3 for the sternoclavicular joint, 3 for the acromioclavicular joint, 3 for the GHJ, 1 for the elbow and 1 for the radioulnar joint) and is actuated by 18 muscle-tendon units divided into 67 elements [31]. The muscle-tendon model proposed by Millard et al. was used [32].

The clavicle, ulna, radius and hand segments of the generic OpenSim model were longitudinally scaled to match the participant’s anthropometry and landmark positions during the first 0.5 seconds of the abduction task when the participant was standing still. The thorax, scapula and humerus segments were scaled in three orthogonal directions to account for their more complex geometry [33]. For the abduction task with weight, the position of the hand’s centre of mass was shifted anteriorly by 3 cm and the hand’s weight was increased by 2.4 kg to mimic the changed dynamic properties of the hand-weight system. Optimal fibre and tendon slack lengths of all muscles were then optimised as in [22] (i.e. optimal fibre length incrementally increased by 2% and tendon slack length decreased by the same length) until their normalised fibre lengths during all tasks were within an expected physiological range of 0.5 to 1.5. Using the OpenSim 4.4 GUI, inverse kinematics, inverse dynamics and muscle analysis tools were performed for all tasks to compute upper-limb joint angles, moments and the related muscle lengths and moment arms.

2.3 Muscle recruitment modelling strategies

A stochastic modelling approach was used to map the solution space of muscle and GHJ reaction forces that were consistent with the motion, including the minimum, maximum and solutions closest to experimental GHJ contact force data. Additionally, three muscle recruitment methods were used to solve the muscle redundancy problem during a shoulder abduction task with a 2.4 kg weight in-hand: 1) static optimisation (SO) minimising the sum of muscle activation squared; 2) computed muscle control (CMC); and 3) EMG-informed methods 3a) without prior calibration; 3b) with a single prior calibration and 3c) with a double prior calibration (see Fig. 1).

Fig. 1
figure 1

Modelling workflow for computing muscle recruitment patterns using four different strategies. Static optimisation and stochastic sampling are inverse dynamics approaches that allow computations of muscle activations \(a_{m}\) and muscle forces, \(F_{m}\). CEINMS and computed muscle control approaches are hybrid approaches able to compute muscle excitations \(e_{m}\) and muscle forces \(F_{m}\). Glenohumeral joint reaction forces \(F^{GHJ}\) are all computed from \(F_{m} \) using a custom-made Matlab script. Solid black lines represent the use of a musculoskeletal model, dashed lines represent experimental inputs and dotted lines represent simulated outputs

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2.3.1 Stochastic sampling

Possible combinations of muscle forces \(\overline{F(i)}\) were sampled to determine the solution space of the joint equilibrium equation (1) for each frame \(i\) of the motion of interest. Muscle lever arms \(\overline{B(i)}\) and external joint moments \(\overline{\tau (i)}\) were obtained from the OpenSim muscle analysis and inverse dynamics toolboxes, respectively. Muscle forces \(\overline{F(i)}\) were constrained between 0 and their maximum isometric force.

$$ \overline{B(i)} \times \overline{F(i)} = \overline{\tau \left (i\right )} $$
(1)

The probability distribution of the spectrum of generated external joint moments \(\overline{\tau (i)}\) was selected to differ from the inverse dynamics values by 0 ± 0.1 N.m (mean ± standard deviation). 200,000 solutions per frame of the abduction motion were calculated using the Markov chain Monte Carlo method implemented in Metabolica [15, 16]. Note that the number of samples was determined sufficient to capture the minimum and maximum solutions of the model as part of a preliminary study. In this latter, the targeted error distribution (0 ± 0.1 N.m) was satisfied from 5,500 ± 2,300 samples onwards and the maximum GHJ-RF was reached around sample 110,200 ± 48,400 on average. Moreover, most muscle forces spanned the entire range from zero to tetanic, except for some of the largest muscles likely due to the weakness of the antagonist muscles. These observations provided confidence in the ensemble representativity of the intended probability distributions.

2.3.2 Static optimisation

A single set of muscle forces was determined using the SO tool in OpenSim 4.4 [34, 35]. This method minimises the sum of muscle activation \(a_{m}\) squared (equation (2)). Values for \(a_{m}\) were constrained between 0 and 1 and residual actuators were included with an optimal moment of 1 N.m.

$$ \min J = \sum _{m=1}^{n} a_{m}^{2} $$
(2)

2.3.3 Computed muscle control

CMC is an optimisation tool available within OpenSim that allows computation of muscle excitation levels of a MSK model towards a desired kinematic trajectory, by using a combination of proportional-derivative control and SO [13]. The acquired solution is consistent with the non-linear and time-dependent properties of muscles. The forces of muscles spanning the GHJ were determined using CMC in OpenSim 4.4 [13]. All predicted coordinates were tracked using the default OpenSim 4.4 settings (i.e. “fast target”), which minimise the sum of squared excitations that require the desired accelerations to be achieved within the tolerance set for the optimizer (i.e. 10−5) [13]. Muscle excitations were bound between 0.01 and 1 as per the OpenSim guidelines [13]. Residual actuators were included with an optimal moment of 1 N.m.

2.3.4 Calibrated EMG-informed neuromusculoskeletal modelling (CEINMS)

EMG-assisted solutions for muscle forces were calculated using the CEINMS toolbox [14]. The toolbox uses outputs from the OpenSim muscle analysis tool and the filtered and normalised EMG signals. The eight surface EMG signals were mapped to their respective muscle-tendon units (MTUs) in the DSEM as shown in the supplementary materials.

The CEINMS toolbox contains a model calibration step that modifies the non-linear relationships between EMG signals and MTU activations (C1, C2 and shape factor from [36] as well as muscle-tendon parameters (optimal fibre length, tendon slack length and maximal isometric force) such that the sum of external torque errors is minimised. CEINMS calibration parameters (Table 1) were selected to best fit shoulder task applications, which are different to values usually selected for lower-limb modelling [37]. The experimental data of the abduction and flexion tasks with no weight described in Sect. 2.1. are exclusively used to perform the CEINMS calibration(s), as suggested in [20].

Table 1 CEINMS calibration parameters for shoulder modelling
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EMG data were available for only eight superficial shoulder muscles, so we used two CEINMS calibration methods to account for the absence of EMG data for other muscles. First, the non-calibrated model used the muscle-tendon parameters of the scaled DSEM model with default values of −0.5, −0.5 and −0.1 for the C1, C2 and the shape factor parameters, respectively. Then, a “single-calibrated” model was developed using EMG signals of the eight recorded muscles. Note that MTUs with no EMG signal are considered inactive during the calibration procedure in CEINMS [14, 30]. Finally, based on a previously published study on neck muscles [38], a “double-calibrated” model was developed to calibrate all MTUs, even those without EMG signals. The procedure consisted of utilising the “single-calibrated” model to run an EMG-assisted optimisation on both the abduction and flexion tasks without weight to predict excitation controls for MTUs without experimental data. A second calibration step used either experimental EMG signals (for muscles with EMG recordings) or predicted excitations (for muscles without recordings), so that all muscles were considered for calibration.

Eventually, an EMG-assisted optimisation described in equation (3) [14] was performed using the three different models described above:

$$ \begin{aligned}\min J ={}& \sum _{\mathrm{d}}^{\mathrm{DOFs}} \alpha \boldsymbol{\cdot} \left ( \tau _{\mathrm{d}} - \tau _{\mathrm{d}}^{\exp} \right )^{2} + \sum _{\mathrm{j}}^{\mathrm{MTU}_{\mathrm{synth}}} \beta \boldsymbol{\cdot} \left ( \mathrm{e}_{\mathrm{j}} \right )^{2} \\ &{}+ \sum _{\mathrm{k}}^{\mathrm{MTU}_{\mathrm{adj}}} \gamma \boldsymbol{\cdot} \left ( \mathrm{e}_{\mathrm{k}} - \mathrm{e}_{\mathrm{k}}^{\exp} \right )^{2} +\beta \boldsymbol{\cdot} \left ( \mathrm{e}_{\mathrm{k}} \right )^{2}, \end{aligned}$$
(3)

where \(\tau _{\mathrm{d}}\) and \(\tau _{\mathrm{d}}^{\exp} \) are simulated and experimental net joint moments of degree-of-freedom \(d\), respectively. \(\mathrm{e}_{\mathrm{j}}\) corresponds to the muscle excitation of the synthesised muscle \(j\). \(\mathrm{e}_{\mathrm{k}}\) and \(\mathrm{e}_{\mathrm{k}}^{\exp} \) are the simulated and experimental excitations for the adjusted muscle \(k\). \(\alpha \), \(\beta \) and \(\gamma \) were selected based on [39]. For all optimised solutions, averaged GHJ moments tracking errors were below 0.1 N.m.

2.4 Analysis

A set of muscle forces was produced by the SO, CMC and the CEINMS methods to balance the external joint torque of the shoulder abduction task with the 2.4 kg weight in hand. GHJ torque residuals of the SO, CEINMS and CMC techniques can be found in the supplementary materials. 200,000 possible sets of muscle forces were sampled by the stochastic sampling method for the same task.

All computations were performed using the same computer (12th Gen Intel i7-12800H 2.4GHz, 32Gb RAM, Single CPU core used, Windows 10). Computational time was measured and compared for benchmarking and reported as total time divided by the number of frames of the motion.

Muscle forces from all methods were used to calculate the total GHJ-RF using a custom-made Matlab script for consistency between methods. The Matlab script was validated against the OpenSim joint reaction analysis toolbox.

Minimum and maximum GHJ-RF from stochastic sampling were calculated for all frames. The lower bound of the stochastic range was considered as an optimised solution minimising GHJ-RF for each static frame. This particular solution is noted as min(GHJ-RF) in the following. Furthermore, we obtained the solution that minimised the error between model prediction and experimental GHJ-RF. This solution is noted as min(GHJ-RF error) in the following.

Absolute error between the predicted GHJ-RF obtained from SO, CMC, CEINMS, min(GHJ-RF) and min(GHJ-RF error) and the experimental GHJ contact forces were calculated at each frame of the motion.

The overall accuracy of the optimisation methods was determined by calculating the RMSE between the predicted and experimentally measured joint force over all frames of the abduction task with weight. The RMSE between predicted and measured joint forces was then calculated for two different periods of time. First, RMSE was calculated exclusively when the experimental GHJ-RF was included in the stochastic range, noted as RMSE within stochastic range. Second, RMSE was calculated after the external GHJ elevation moment peaked (i.e. happening exactly when the arm was perpendicular to the ground, position reached at 75° of GHJ elevation) and until the end of the abduction task (with the arm weight progressively aligning with gravity but overhead). This latter period is noted as above shoulder level in the following.

Finally, experimental EMGs were compared qualitatively against predicted muscle forces. Computed muscle excitations from all methods can also be found in the supplementary materials.

3 Results

CEINMS and SO solutions were the fastest to compute with respectively 0.17 and 0.15 sec/frame. However, CEINMS calibration(s) took up to 3.5 hours. CMC and stochastic sampling (200,000 samples per frame) were computed at a speed of 13.2 and 11.2 sec/frame, respectively.

Total GHJ-RF are reported at the top of Fig. 2. The stochastic range spanned from a minimum of 21 to a maximum of 659%BW during abduction. At the start of the abduction movement, all joint forces were between 25 and 55%BW, increased up to 70 degrees of shoulder elevation before plateauing or decreasing. Only the GHJ-RF computed with the uncalibrated CEINMS model behaved unexpectedly with an unphysiological starting force of 109%BW. The experimental GHJ contact force was the lowest at the beginning of the motion, i.e. 4%BW, the highest at 70 degrees of shoulder elevation, i.e. 129%BW, and its values were within the stochastic range only from 40 degrees of shoulder elevation upwards. min(GHJ-RF error) followed the stochastic lower boundary until the experimental curve was included in the model. Then, min(GHJ-RF error) followed the experimental GHJ contact forces very closely.

Fig. 2
figure 2

Top: Total glenohumeral joint reaction force (GHJ-RF) as a function of shoulder elevation angle during a shoulder abduction task with a 2.4 kg weight in hand. Experimental force (in black) was measured by an instrumented shoulder hemiarthroplasty. Bottom: Total GHJ-RF error between the predicted and measured data as a function of shoulder elevation angle. Predicted forces were calculated through static optimisation (in red), EMG-assisted CEINMS technique (in blue), computed muscle control (in green). The grey band represents the available modelling solutions sampled by stochastic modelling and the orange curve represent the stochastic solution with the least error with the experimental joint contact force. Color figure online.

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Instantaneous absolute error in the predicted GHJ-RF reported at the bottom of Fig. 2 shows that SO was the closest to the measurements up to 46 degrees. CMC performed well with an error of less than 10%BW between 58 and 80 degrees and similarly with CEINMS between 79 and 91 degrees of humeral elevation. Both CMC and CEINMS reached at several occasions an error of less than 1%BW.

Validity of the different muscle recruitment strategies for the overall shoulder abduction task, as well as for when the arm was above shoulder level (i.e. from 75 degrees of shoulder elevation upwards) is reported in Fig. 3. For the overall abduction motion, joint force RMSE was between 21 (SO) and 24%BW (CEINMS – double calibration) for all methods, except CEINMS – no calibration, which had a RMSE of 61% BW. Then the experimental GHJ contact forces were comprised within the stochastic range, min(GHJ-RF error) had an error of 0.1% BW. Above shoulder level, where muscle co-contraction is most critical, CMC (11% BW), CEINMS – single calibration (14% BW) and CEINMS – double calibration (16%BW) performed better than SO (25%BW).

Fig. 3
figure 3

Top: Root mean square error in glenohumeral joint reaction force (GHJ-RF) over the total duration of the abduction task with a 2.4 kg weight in hand. Middle: Root mean square error in GHJ-RF from 40 degrees of shoulder elevation and upwards. Bottom: Root mean square error in GHJ-RF from 75 degrees of shoulder elevation and upwards

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A selection of the computed muscle forces can be found in Fig. 4. The complete set of muscle forces and excitations can be found in the supplementary materials. The stochastic range of all muscles commonly spanned between 0 and their respective maximum isometric force. The deltoid was always predicted to produce the largest force. The CEINMS – double calibration forces were generally the closest among all CEINMS computations to the normalised experimental EMG signals, with CEINMS – no calibration being the furthest. Above shoulder level, muscle forces were predicted to be larger with CMC than with SO, especially for subscapularis, teres major and latissimus dorsi.

Fig. 4
figure 4

Selection of muscle forces as a function of the shoulder elevation angle during a shoulder abduction task with a 2.4 kg weight in hand. Predicted forces were calculated through static optimisation (in red), EMG-assisted CEINMS technique (in blue), computed muscle control (in green). The grey band represents the available modelling solutions sampled by stochastic modelling. Normalised experimental EMG signals (yellow line – right axis) were reported alongside predicted muscle force for qualitative validation. The numbers in brackets correspond to the number of the muscle-tendon unit in the Delft Shoulder and Elbow Model. Color figure online.

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4 Discussion

This study served as a benchmark and validation of three of the most commonly used methods to solve the shoulder muscle redundancy problem in shoulder MSK modelling by using experimental patient-specific data including synchronised kinematics, EMG and GHJ contact forces measured by an instrumented shoulder implant. First, the admissible range of GHJ-RF solutions available in the selected shoulder model for the abduction task ranged between 21 and 659% BW. This force range included the experimental GHJ-RF only from 40 degrees of shoulder elevation upwards. However, the experimental recordings were not a solution of the model at low elevation angles between 20 and 40 degrees. Second, the solutions obtained via SO, CEINMS and CMC were validated against experimental GHJ contact forces from the instrumented implant.

The stochastic modelling approach [15] was used for the first time in the present paper for shoulder modelling. This technique samples the whole range of solutions within a model. On the one hand, the minimum stochastic bound (i.e. min(GHJ-RF)) is typically relatively close to the solutions obtained via the different optimisation techniques (SO, CEINMS and CMC) due to their propensity of minimising muscle activations and therefore, indirectly GHJ-RF. Note that the stochastic solution with minimal muscle activations is not necessarily the one with the lowest GHJ-RF, although they are likely to be closely related. On the other hand, the maximal bound reflects the muscle state for which the targeted motion is still achieved but the GHJ-RF is maximal, which might still be realistic and representing what happens under tetanic contractions but would likely lead to injuries [40]. Furthermore, the range of stochastic solutions provided information on the ability of the model to match experimental data, thus is complementary to the validation. Lastly, the stochastic modelling approach [15] used here for the first time in shoulder modelling provided comprehensive information about the overall synergistic muscular patterns embedded in shoulder musculoskeletal architectures. In the future, this method could likely deepen our understanding of shoulder co-contractions for overhead tasks by investigating probabilistic synergy patterns.

Specifically, the stochastic range allowed assessing whether the experimental GHJ contact forces could be reproduced in any physiological way by the model, i.e. it served to invalidate the model (cf. min(GHJ-RF error)). The experimental GHJ contact forces could not be modelled below 40 degrees of humeral elevation proving an inconsistency between the model and the experiment. This inconsistency could be explained by two factors. First, the low experimental GHJ-RF (4% BW/33 N at start frame) suggests a rather loose contact between the glenoid and the instrumented implant and can potentially be explained by a suspension of the humerus through tension of the deltoid muscle. The assumptions of rigid-body modelling, constraining the GHJ to be congruent with no translation, would not be accurate in this case. A shoulder model with humeral head translation [41–43] might better represent joint forces at low elevation angles in specific cases where clearance between the humeral head and glenoid is large (> 1.7 mm according to [43]). Another explanation for the lack of consistency between experimental data and model may be that the patient’s arm at rest may have been supported by the thorax, resulting in assisting external forces (see patient S2 in [19]), which were not modelled in the current study. More generally, a lack of model personalisation (i.e. bone geometry and muscle paths) [33] may be responsible for discrepancies in joint forces [44].

Despite being the most comprehensive experimental dataset in shoulder biomechanics, the data were often noisy and/or incomplete, which made processing challenging. This explains why we report results only for one participant and one task. The data from other participants with instrumented hemi-arthroplasties in this dataset were not of sufficient quality for the scope of this project. We assert that the OrthoLoad database [24] is an invaluable resource for many shoulder studies, but we also believe that the shoulder biomechanics community would benefit from an updated open-access set of experiments on instrumented patients that may take the shape of what has been done in the lower limbs with the “knee grand challenge” [45]. The new data collection could use recent technological advances in motion capture and scapula motion tracking [46, 47] as well as latest developments in electromyography, by using in-dwelling [21] or high-density electrodes, although the latest being utilised for isometric contractions only [48].

Based on data used in this study from one patient and one shoulder abduction task with a 2.4 kg weight in hand, the GHJ-RF was computed using SO, CMC and CEINMS and validated against experimental joint forces. A technical summary can be found in Table 2 and may serve as a selection guide for muscle recruitment strategies.

Table 2 Technical summary of the advantages and disadvantages of the different muscle recruitment strategies for solving the shoulder muscle redundancy problem based on data computed from one patient and one shoulder abduction task with a 2.4 kg weight in hand
Full size table

Although limited data was used, meaning that care should be taken in generalising our findings, technical interpretations in Table 2 are in accordance with the literature. First, SO underestimated GHJ-RF on average above shoulder level, as in [19], and does not account for passive muscle stiffness and fibre force–velocity relationships [12]. Interestingly, Fig. 2 (bottom) suggests that SO performed very well (i.e. instantaneous error < 4% BW) at some instants above shoulder level, in some cases even as well as/better than CEINMS and CMC. However, outcomes from SO largely deviated above 90 degrees of GHJ elevation, likely explaining the higher RMSE overall compared to CEINMS and CMC (Fig. 3). Second, EMG-assisted outcomes from CEINMS are more accurate than SO above shoulder level as reported by [20, 21] and were also faster to compute. However, the results presented in the current study suggest that the CEINMS model calibration, which takes a long time (up to 3.5 hours in our study), is critical to get accurate contact forces [20, 49] (see Fig. 3, non-calibrated vs calibrated models). This is due to the use of generic values for the neuromechanical parameters C1, C2 and \(\beta \) [36]. Third, compared to a single calibration, a double calibration procedure, as done in [38] for the neck region, did not improve the GHJ-RF predictions in this specific dataset, which suggests that surface EMG signals from a select number of superficial muscles are sufficient to calibrate a shoulder model for simple tasks [20]. Fourth, the present validation of the CMC method is novel in the field of shoulder MSK modelling. CMC seems to present great advantages (Table 2), especially since CMC is also capable of utilising experimental EMG signals to constrain computed muscle excitations. Further research needs to be undertaken in this direction.

CMC and CEINMS are partly using forward dynamics frameworks [13, 14] for which calibrating muscle-tendon parameters is critical. We used the calibration technique as in [22] to find the best optimal fibre and tendon slack lengths of the shoulder muscles. We have considered using the automatic calibration toolbox presented for the lower limb in [50], but the large range of motion of the shoulder and the large number of bi- or tri-articular muscle-tendon units made the calculation challenging. The field may benefit from an automated solution for calibrating muscle-tendon parameters in shoulder models.

The list of muscle recruitment strategies studied herein was not exhaustive, but we focused on the most commonly used and accessible optimisation techniques in OpenSim. For instance, other objective functions, as presented in [51, 52] (and considered as more sophisticated SO techniques), have been shown to perform better with movement above shoulder level [51]. Optimisation techniques like the “window moving inverse dynamics optimisation” [53] or the recent “muscle redundancy solver” presented in [54] seem promising to account for the time-dependent physiological properties of MTUs as well as GHJ-RF orthogonal directions and may be interesting to validate in the future. Another limitation of this study was that the model mimicking a “healthy” shoulder was validated against experimental data from a person who underwent shoulder arthroplasty who likely did not have intact rotator cuff muscles (i.e. patient S2R in [4]). Nonetheless, it is the most detailed validation of musculoskeletal models possible with current methods [6, 19, 20, 23].

5 Conclusion

Different muscle recruitment strategies have been benchmarked and validated against experimental GHJ contact forces during a shoulder abduction task. A guide has been proposed to best select muscle recruitment strategy techniques based on the application. At high elevation angles, CMC and CEINMS were the two most accurate methods in terms of predicted GHJ-RF, while SO performed best at low elevation angles. In addition, stochastic muscle sampling highlighted the lack of consistency between the model and experimental data at low elevation angles. Further shoulder model personalisation and better experimental data may be needed in the future to limit discrepancies.