Benchmark and Validation of State-of-the-art Muscle Recruitment Strategies in Shoulder Modelling

Benchmark and Validation of State-of-the-art Muscle Recruitment Strategies in Shoulder Modelling | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Benchmark and Validation of State-of-the-art Muscle Recruitment Strategies in Shoulder Modelling Maxence Lavaill, Claudio Pizzolato, Bart Bolsterlee, Saulo Martelli, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3890029/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 7 You are reading this latest preprint version Abstract Shoulder muscle forces estimated via modelling are typically indirectly validated against measurements of glenohumeral joint reaction forces (GHJ-RF). This validation study benchmarks the outcomes of several muscle recruitment strategies against public GHJ-RF measurements. Public kinematics, electromyography, and GHJ-RF data from a selected male participant executing a 2.4 kg weight shoulder abduction task up to 92° GHJ elevation were obtained. The Delft Shoulder and Elbow Model was scaled to the participant. Muscle recruitment was solved by 1) minimizing muscle activations squared (SO), 2) accounting for dynamic muscle properties (CMC) and 3) constraining muscle excitations to corresponding surface electromyography measurements (CEINMS). Moreover, the spectrum of admissible GHJ-RF in the model was determined via Markov Chain Monte-Carlo stochastic sampling. The experimental GHJ-RF was compared to the resultant GHJ-RF of the different muscle recruitment strategies as well as the admissible stochastic range. Admissible GHJ-RF spanned 21 to 659% of body weight (%BW), excluding the experimental GHJ-RF up to 40 degrees of humeral elevation. Joint force RMSE were between 23 (CMC) and 27%BW (CEINMS). At high elevation angles, CMC (11%BW) and CEINMS (14%BW) performed better than SO (25%BW). A guide has been proposed to best select muscle recruitment strategies. Overall, CMC and CEINMS were the two most accurate methods in terms of predicted GHJ-RF, especially at high elevation angles. SO performed best at low elevation angles. In addition, stochastic muscle sampling provided critical information on the shoulder model capabilities and the consistency between model and experimental data. Shoulder Modelling Muscle Recruitment Static Optimization EMG-informed Instrumented Shoulder Implant Joint Force Validation Figures Figure 1 Figure 2 Figure 3 Figure 4 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. This redundancy makes the shoulder highly adaptable with many different combinations of muscle actuations to produce the same kinematics. Neuromusculoskeletal systems can deal with muscle redundancy very well [ 10 , 11 ]. Emulating the complex neural control strategies underlying human movement, most state-of-the-art MSK models aims to solve the muscle redundancy problem by optimising an objective function. These 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 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 was 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 different muscle recruitment strategies to solve 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 (163cm, 85kg, 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 section 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 8 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 40–400Hz 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 120Hz [ 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 ] 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. Then, 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 ). 2.3.1. Stochastic sampling Possible combinations of muscle forces, \(\stackrel{-}{F\left(i\right)}\) , were sampled to determine the solution space of the joint equilibrium Eq. ( 1 ) for each frame \(i\) of the motion of interest. Muscle lever arms, \(\stackrel{-}{B\left(i\right)}\) , and external joint moments, \(\stackrel{-}{\tau \left(i\right)}\) , were obtained from the OpenSim muscle analysis and inverse dynamics toolboxes, respectively. 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. Muscle forces, \(\stackrel{-}{F\left(i\right)}\) , were constrained between 0 and their maximum isometric force and a mean ± standard deviation error of 0 ± 0.1 N.m was allowed for each external joint moment in \(\stackrel{-}{\tau \left(i\right)}\) . $$\stackrel{-}{B\left(i\right)}\times \stackrel{-}{F\left(i\right)}=\stackrel{-}{\tau \left(i\right)}$$ 1 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 (Eq. ( 2 )) Values for \({a}_{m}\) were constrained between 0 and 1 and residual actuators were included with an optimal moment of 1 N.m. $$\underset{}{\text{min}}J=\sum _{m=1}^{n}{{a}_{m}}^{2}$$ 2 2.3.3. Computed muscle control Forces of muscles spanning the GHJ were determined using CMC in OpenSim 4.4 [ 13 ]. All GHJ degrees-of-freedom were tracked using default “fast target” OpenSim values, 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 Lloyd and Besier, 2003) 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 section 2.1. are exclusively used to perform the CEINMS calibration(s), as suggested in [ 20 ]. Table 1 CEINMS calibration parameters for shoulder modelling Neuromuscular parameter Initial value Boundary C1 − 0.5 [− 0.95; − 0.05] C2 − 0.5 [− 0.95; − 0.05] Shape factor − 0.1 [− 3; 0] Tendon slack length Original OpenSim value ± 30% of initial value Optimal fibre length Original OpenSim value ± 30% of initial value Maximum isometric force Original OpenSim value [100% − 250%] of initial value Optimisation penalty Acceptable boundaries Weight Normalised fibre length [0.5; 1.4] 200 EMG data were available for only 8 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 8 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 Eq. ( 3 ) [ 14 ] was performed using the three different models described above. $$\text{m}\text{i}\text{n} J={\sum }_{\text{d}}^{\text{D}\text{O}\text{F}\text{s}}{\alpha }\bullet {\left({{\tau }}_{\text{d}}-{{\tau }}_{\text{d}}^{\text{e}\text{x}\text{p}}\right)}^{2}+{\sum }_{\text{j}}^{{\text{M}\text{T}\text{U}}_{\text{s}\text{y}\text{n}\text{t}\text{h}}}{\beta }\bullet {\left({\text{e}}_{\text{j}}\right)}^{2}+ {\sum }_{\text{k}}^{{\text{M}\text{T}\text{U}}_{\text{a}\text{d}\text{j}}}{\gamma }\bullet {\left({\text{e}}_{\text{k}}-{\text{e}}_{\text{k}}^{\text{e}\text{x}\text{p}}\right)}^{2}+{\beta }\bullet {\left({\text{e}}_{\text{k}}\right)}^{2}$$ 3 where \({{\tau }}_{\text{d}}\) and \({{\tau }}_{\text{d}}^{\text{e}\text{x}\text{p}}\) are simulated and experimental net joint moments of degree-of-freedom \(d\) , respectively. \({\text{e}}_{\text{j}}\) corresponds to the muscle excitation of the synthesised muscle \(j\) . \({\text{e}}_{\text{k}}\) and \({\text{e}}_{\text{k}}^{\text{e}\text{x}\text{p}}\) 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 SO, CMC and the CEINMS methods each produced a set of muscle forces that balanced 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 technique can be found in the supplementary materials. The stochastic sampling produced 200,000 possible sets of muscle forces for the same problem. 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, expressed in the scapula frame of reference, 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 over those frames where the experimental GHJ-RF was included in the stochastic range, noted as 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. 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 were between 23 (CMC) and 27%BW (CEINMS – double calibration) for all methods, except CEINMS – no calibration at a high 56%BW RMSE. When 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). 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. 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 range of GHJ-RF solutions available in the selected shoulder model and mimicking the studied participant and abduction task ranged between 21 and 659%BW and included the experimental GHJ contact force from 40 degrees 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 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 might reflect a loose contact between the glenoid and the instrumented implant. 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 , 42 ] might better represent joint forces at low elevation angles. Second, 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 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” [ 43 ]. The new data collection could use recent technological advances in motion capture and scapula motion tracking [ 44 , 45 ] 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 [ 46 ]. 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. Account for passive and non-linear properties of muscle-tendon units Use of experimental muscle excitations Validity of the joint reaction force Validity of the joint reaction force above shoulder level Computational time Static Optimisation (SO) - - + + + Computed Muscle Control (CMC) + + + ++ - Calibrated EMG-Informed Neuromusculoskeletal Modelling (CEINMS) + + + ++ +* Based on data computed from one patient and one shoulder abduction task with a 2.4 kg weight in hand. -, + refer to a method’s disadvantage and a method’s advantage, respectively. For the joint reaction force validity, + and + + represent a RMSE between 20 and 40% and a RMSE below 20% of the body weight, respectively.*: The EMG-assisted approach was computed relatively fast (50s for 6s of motion), however it is worth noting the model calibrations that preceded took approximately 3.5 hours. With an acquisition frequency of 50 Hz, 0.02 sec/frame means the technique could be utilised for real-time feedback. Although limited data was used, technical interpretations in Table 2 are in accordance with the literature. In particular, SO underestimated GHJ-RF above shoulder level (as in [ 19 ]and does not account for passive muscle stiffness and fibre force-velocity relationships [ 12 ]. 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 , 47 ]. 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. The validated outcomes of the CMC method reported in Table 2 are novel in the field of shoulder MSK modelling and seem promising. It is proposed that more shoulder modelling studies should utilise CMC instead of SO in the future, especially since CMC is also capable of utilising experimental EMG signals to constrain computed muscle excitations. 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 [ 48 ], 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. The recent “muscle redundancy solver” presented in [ 49 ] seems promising to account for the passive stiffness 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. 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. Overall, CMC and CEINMS were the two most accurate methods in terms of predicted GHJ-RF, especially at high elevation angles. SO performed best at low elevation angles. In addition, stochastic muscle sampling provided critical information on the shoulder model capabilities and should be used as part of future validation studies- to inform on the consistency between model and experimental data. Declarations Author Contributions Statement Maxence Lavaill: Writing – review & editing, Writing – original draft, Visualization, Validation, Software, Resources, Project administration, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. Claudio Pizzolatto: Writing – review & editing, Software, Methodology, Investigation, Conceptualization. Bart Bolsterlee: Writing – review & editing, Methodology, Investigation, Conceptualization. Saulo Martelli: Writing – review & editing, Supervision, Methodology, Investigation, Funding acquisition, Conceptualization. Peter Pivonka: Writing – review & editing, Supervision, Resources, Methodology, Investigation, Conceptualization. Acknowledgements The authors would like to deeply thank Dr Ali Asadi Nikooyan and Prof. DirkJan Veeger for giving us access to the shoulder-instrumented implant dataset and related materials. Funding ML, BB, SM and PP would like to gratefully acknowledge funding received through the Australian Research Council (ARC) Industrial Transformation Training Centre for Joint Biomechanics (IC190100020). SM would also like to acknowledge the support received through the following funding schemes of the Australian Research Council: DP180103146; FT180100338. Conflicts of Interest The authors declare that they have no conflict of interest. References van der Helm, F.C.T.: Analysis of the kinematic and dynamic behavior of the shoulder mechanism. J Biomech. 27, 527–550 (1994). https://doi.org/10.1016/0021-9290(94)90064-7 van der Helm, F.C.T.: A finite element musculoskeletal model of the shoulder mechanism. 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Version 1., https://data.4tu.nl/datasets/86db1d7d-13d9-4631-9c6b-1e3134a1ab38/1, (2023) Wu, G., Van Der Helm, F.C.T., Veeger, H.E.J., Makhsous, M., Van Roy, P., Anglin, C., Nagels, J., Karduna, A.R., McQuade, K., Wang, X., Werner, F.W., Buchholz, B.: ISB recommendation on definitions of joint coordinate systems of various joints for the reporting of human joint motion - Part II: Shoulder, elbow, wrist and hand. J Biomech. 38, 981–992 (2005). https://doi.org/10.1016/j.jbiomech.2004.05.042 Lavaill, M., Martelli, S., Kerr, G.K., Pivonka, P.: Statistical Quantification of the Effects of Marker Misplacement and Soft-Tissue Artifact on Shoulder Kinematics and Kinetics. Life. 12, 1–11 (2022). https://doi.org/https://doi.org/10.3390/life12060819 Veeger, H.E.J.: The position of the rotation center of the glenohumeral joint. J Biomech. 33, 1711–1715 (2000). https://doi.org/10.1016/S0021-9290(00)00141-X Cleveland, W.S., Devlin, S.J.: Locally weighted regression: An approach to regression analysis by local fitting. J Am Stat Assoc. 83, 596–610 (1988). https://doi.org/10.1080/01621459.1988.10478639 Quental, C., Azevedo, M., Ambrósio, J., S. B., G., Folgado, J.: Influence of the Musculotendon Dynamics on the Muscle Force-Sharing Problem of the Shoulder-A Fully Inverse Dynamics Approach. J Biomech Eng. 140, (2018). https://doi.org/10.1115/1.4039675 Assila, N., Pizzolato, C., Martinez, R., Lloyd, D.G., Begon, M.: EMG-Assisted Algorithm to Account for Shoulder Muscles Co-Contraction in Overhead Manual Handling. Applied Sciences (Switzerland). 10, (2020). https://doi.org/10.3390/app10103522 Lavaill, M., Martelli, S., Cutbush, K., Gupta, A., Kerr, G.K., Pivonka, P.: Latarjet’s muscular alterations increase glenohumeral joint stability : A theoretical study. J Biomech. 155, 111639 (2023). https://doi.org/10.1016/j.jbiomech.2023.111639 Millard, M., Uchida, T., Seth, A., Delp, S.L.: Flexing computational muscle: Modeling and simulation of musculotendon dynamics. J Biomech Eng. 135, (2013). https://doi.org/10.1115/1.4023390 Lavaill, M., Martelli, S., Gilliland, L., Gupta, A., Kerr, G., Pivonka, P.: The effects of anatomical errors on shoulder kinematics computed using multi-body models. Biomech Model Mechanobiol. 21, 1561–1572 (2022). https://doi.org/10.1007/s10237-022-01606-0 Delp, S.L., Anderson, F.C., Arnold, A.S., Loan, P., Habib, A., John, C.T., Guendelman, E., Thelen, D.G.: OpenSim: Open-source software to create and analyze dynamic simulations of movement. IEEE Trans Biomed Eng. 54, 1940–1950 (2007). https://doi.org/10.1109/TBME.2007.901024 Seth, A., Hicks, J.L., Uchida, T.K., Habib, A., Dembia, C.L., Dunne, J.J., Ong, C.F., DeMers, M.S., Rajagopal, A., Millard, M., Hamner, S.R., Arnold, E.M., Yong, J.R., Lakshmikanth, S.K., Sherman, M.A., Ku, J.P., Delp, S.L.: OpenSim: Simulating musculoskeletal dynamics and neuromuscular control to study human and animal movement. PLoS Comput Biol. 14, 1–21 (2018). https://doi.org/10.1371/journal.pcbi.1006223 Lloyd, D.G., Besier, T.F.: An EMG-driven musculoskeletal model to estimate muscle forces and knee joint moments in vivo. J Biomech. 36, 765–776 (2003). https://doi.org/10.1016/S0021-9290(03)00010-1 Hoang, H.X., Pizzolato, C., Diamond, L.E., Lloyd, D.G.: Subject-specific calibration of neuromuscular parameters enables neuromusculoskeletal models to estimate physiologically plausible hip joint contact forces in healthy adults. J Biomech. 80, 111–120 (2018). https://doi.org/10.1016/j.jbiomech.2018.08.023 Silvestros, P., Pizzolato, C., Lloyd, D.G., Preatoni, E., Gill, H.S., Cazzola, D.: Electromyography-Assisted Neuromusculoskeletal Models Can Estimate Physiological Muscle Activations and Joint Moments Across the Neck Before Impacts. J Biomech Eng. 144, 1–16 (2022). https://doi.org/10.1115/1.4052555 Sartori, M., Farina, D., Lloyd, D.G.: Hybrid neuromusculoskeletal modeling to best track joint moments using a balance between muscle excitations derived from electromyograms and optimization. J Biomech. 47, 3613–3621 (2014). https://doi.org/10.1016/j.jbiomech.2014.10.009 Kam, A.C.A., Kam, P.C.A.: Scapular and proximal humeral head fractures: An unusual complication of cardiopulmonary resuscitation. Anaesthesia. 49, 1055–1057 (1994). https://doi.org/10.1111/j.1365-2044.1994.tb04355.x Khandare, S., Vidt, M.E.: Development of a more biofidelic musculoskeletal model with glenohumeral ligaments and humeral head translations. Comput Methods Appl Mech Eng. (2022). https://doi.org/10.1080/10255842.2022.2127319 Sarshari, E., Farron, A., Terrier, A., Pioletti, D., Mullhaupt, P.: A simulation framework for humeral head translations. Med Eng Phys. 49, 140–147 (2017). https://doi.org/10.1016/j.medengphy.2017.08.013 Fregly, B.J., Besier, T.F., Lloyd, D.G., Delp, S.L., Banks, S.A., Pandy, M.G., D’Lima, D.D.: Grand challenge competition to predict in vivo knee loads, (2012) Lempereur, M., Brochard, S., Leboeuf, F., Rémy-Néris, O.: Validity and reliability of 3D marker based scapular motion analysis: A systematic review. J Biomech. 47, 2219–2230 (2014). https://doi.org/10.1016/j.jbiomech.2014.04.028 Aliaj, K., Henninger, H.B., Sulkar, H., Kolz, C.: Biplane fluoroscopy derived humerus and scapula kinematics during arm elevation and rotation. Version 6., https://zenodo.org/records/7542486, (2021) Lulic-Kuryllo, T., Negro, F., Jiang, N., Dickerson, C.R.: Standard bipolar surface EMG estimations mischaracterize pectoralis major activity in commonly performed tasks. Journal of Electromyography and Kinesiology. 56, (2021). https://doi.org/10.1016/j.jelekin.2020.102509 Hoang, H.X., Diamond, L.E., Lloyd, D.G., Pizzolato, C.: A calibrated EMG-informed neuromusculoskeletal model can appropriately account for muscle co-contraction in the estimation of hip joint contact forces in people with hip osteoarthritis. J Biomech. 83, 134–142 (2019). https://doi.org/10.1016/j.jbiomech.2018.11.042 Modenese, L., Ceseracciu, E., Reggiani, M., Lloyd, D.G.: Estimation of musculotendon parameters for scaled and subject specific musculoskeletal models using an optimization technique. J Biomech. 49, 141–148 (2016). https://doi.org/10.1016/j.jbiomech.2015.11.006 Belli, I., Joshi, S., Prendergast, J.M., Beck, I., Della Santina, C., Peternel, L., Seth, A.: Does enforcing glenohumeral joint stability matter? A new rapid muscle redundancy solver highlights the importance of non-superficial shoulder muscles. PLoS One. 18, e0295003 (2023). https://doi.org/10.1371/journal.pone.0295003 Additional Declarations No competing interests reported. Supplementary Files Supplementarymaterials.docx Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 14 Mar, 2024 Reviews received at journal 09 Feb, 2024 Reviewers agreed at journal 26 Jan, 2024 Reviewers invited by journal 25 Jan, 2024 Editor assigned by journal 24 Jan, 2024 Submission checks completed at journal 23 Jan, 2024 First submitted to journal 23 Jan, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-3890029","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":269020672,"identity":"d40ba5de-7dd8-43a0-994c-b2fa8ab541cf","order_by":0,"name":"Maxence Lavaill","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABDklEQVRIiWNgGAWjYDADPhCRUGAhB+GyEaEFrCbBQMKYgYGZFC0MBhKJDYS06LafMXxcUGPDwMZ+xvDDAwOJ9L4b+QcYPpQdZuCfkYBVi9mZtGTjGcfSGNh4cowlgA7LnXkjmYFxxrnDDBI3cGg5kHxMmrfhMNAlaQlgLRuAWph52w4zMODScv5h+2/ehv8MbPzPkn8AtaQbgLT8BWqRx6XlRvIxZt6GAwxsEsnHQLYkgLUwArUY4NTyLFma51gyD5vE42MWQC2GM888NjjYcy6dx/DMAxwOyzH8zFNjJ8fPn9h880eFjTzf8cSHD36UWcvJHcduCwzwIJgHwAhZhCA4QILaUTAKRsEoGBEAAFmUWa5jFR6ZAAAAAElFTkSuQmCC","orcid":"","institution":"Queensland University of Technology","correspondingAuthor":true,"prefix":"","firstName":"Maxence","middleName":"","lastName":"Lavaill","suffix":""},{"id":269020673,"identity":"b6f6e0f6-49e8-4e4e-b956-7fb0bbdcd9c9","order_by":1,"name":"Claudio Pizzolato","email":"","orcid":"","institution":"Griffith University","correspondingAuthor":false,"prefix":"","firstName":"Claudio","middleName":"","lastName":"Pizzolato","suffix":""},{"id":269020674,"identity":"61c0fd61-d726-4490-b8f0-aff474bfe3db","order_by":2,"name":"Bart Bolsterlee","email":"","orcid":"","institution":"Queensland University of Technology","correspondingAuthor":false,"prefix":"","firstName":"Bart","middleName":"","lastName":"Bolsterlee","suffix":""},{"id":269020675,"identity":"bd181854-33d1-4f56-a09e-d008a35ea1fb","order_by":3,"name":"Saulo Martelli","email":"","orcid":"","institution":"Queensland University of Technology","correspondingAuthor":false,"prefix":"","firstName":"Saulo","middleName":"","lastName":"Martelli","suffix":""},{"id":269020676,"identity":"3b68e2d3-fdfe-4d9c-ba36-7f0ba4033673","order_by":4,"name":"Peter Pivonka","email":"","orcid":"","institution":"Queensland University of Technology","correspondingAuthor":false,"prefix":"","firstName":"Peter","middleName":"","lastName":"Pivonka","suffix":""}],"badges":[],"createdAt":"2024-01-23 05:59:15","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3890029/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3890029/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":50170059,"identity":"0a502f1b-eee9-44ab-856d-91f14d228559","added_by":"auto","created_at":"2024-01-25 15:35:24","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":170716,"visible":true,"origin":"","legend":"\u003cp\u003eModelling 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\u003csub\u003em\u003c/sub\u003e and muscle forces, F\u003csub\u003em\u003c/sub\u003e. CEINMS and computed muscle control approaches are hybrid approaches able to compute muscle excitations e\u003csub\u003em\u003c/sub\u003e and muscle forces F\u003csub\u003em\u003c/sub\u003e. Glenohumeral joint reaction forces F\u003csup\u003eGHJ\u003c/sup\u003e are all computed from F\u003csub\u003em\u003c/sub\u003e \u0026nbsp;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.\u003c/p\u003e","description":"","filename":"Figure1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-3890029/v1/d1d17d2c83747fa4ed9f479d.jpg"},{"id":50168676,"identity":"a23b8d41-909b-4cc1-98fc-04ad890336de","added_by":"auto","created_at":"2024-01-25 15:27:24","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":384324,"visible":true,"origin":"","legend":"\u003cp\u003eTop: 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.\u003c/p\u003e","description":"","filename":"Figure2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-3890029/v1/0ce0a629280376eb055df328.jpg"},{"id":50168674,"identity":"d657fac3-80fa-40be-af29-fb0f8988ab0f","added_by":"auto","created_at":"2024-01-25 15:27:24","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":266751,"visible":true,"origin":"","legend":"\u003cp\u003eTop: 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.\u003c/p\u003e","description":"","filename":"Figure3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-3890029/v1/941a586bfe4093a6782c4cb3.jpg"},{"id":50168677,"identity":"e6678ebe-3bc8-41bd-b051-f6fdbcff3fb1","added_by":"auto","created_at":"2024-01-25 15:27:24","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":351663,"visible":true,"origin":"","legend":"\u003cp\u003eSelection 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 number in brackets correspond to the number of the muscle-tendon unit in the Delft Shoulder and Elbow Model.\u003c/p\u003e","description":"","filename":"Figure4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-3890029/v1/45ee0061a961201f116bb1e5.jpg"},{"id":50170966,"identity":"718fee8b-22b3-46d5-bb78-87e982cba62f","added_by":"auto","created_at":"2024-01-25 15:43:26","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":865834,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3890029/v1/29253202-6561-4f18-a458-649ac58f7804.pdf"},{"id":50168678,"identity":"4f14bb1f-907d-4027-a387-c86e1e9167d7","added_by":"auto","created_at":"2024-01-25 15:27:25","extension":"docx","order_by":6,"title":"","display":"","copyAsset":false,"role":"supplement","size":2692890,"visible":true,"origin":"","legend":"","description":"","filename":"Supplementarymaterials.docx","url":"https://assets-eu.researchsquare.com/files/rs-3890029/v1/77fe20af8ebd0af74d11071a.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"\u003cp\u003eBenchmark and Validation of State-of-the-art Muscle Recruitment Strategies in Shoulder Modelling\u003c/p\u003e","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eShoulder musculoskeletal (MSK) modelling and inverse dynamics (ID) are frequently used to estimate muscle and joint contact forces during motions [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e], as these forces are often difficult to measure \u003cem\u003ein vivo\u003c/em\u003e [\u003cspan additionalcitationids=\"CR4\" citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. 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 [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e], to optimise sports performance [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e] or to better design surgical and rehabilitation techniques [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e, \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. Predicting individual muscle forces is not trivial as most MSK systems, including the shoulder, have more muscles than degrees-of-freedom. This redundancy makes the shoulder highly adaptable with many different combinations of muscle actuations to produce the same kinematics.\u003c/p\u003e \u003cp\u003eNeuromusculoskeletal systems can deal with muscle redundancy very well [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. Emulating the complex neural control strategies underlying human movement, most state-of-the-art MSK models aims to solve the muscle redundancy problem by optimising an objective function. These 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 [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. With CMC, the time-dependent properties of muscles are considered by using a controlled forward dynamics approach to target static optimisation solutions [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. EMG-assisted methods, made popular by the development of the Calibrated EMG-Informed NeuroMusculoSkeletal (CEINMS) toolbox [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e] 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 are not yet investigated in shoulder models.\u003c/p\u003e \u003cp\u003eRecently, a stochastic modelling method was proposed [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e] 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 [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e], 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.\u003c/p\u003e \u003cp\u003eFor 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 [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. A previous study found that SO generally underestimated GHJ-RF when the arm was elevated above shoulder level [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. Another study found that CEINMS [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e] better accounted for muscle co-contractions [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e], 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 [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]. To the best of our knowledge, CMC has not yet been validated in shoulder MSK models.\u003c/p\u003e \u003cp\u003eThe Orthoload shoulder database[\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e] 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 was accessible previously, the complete dataset was only recently published [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe present study aimed to use experimental measurements of GHJ contact forces to compare and validate different muscle recruitment strategies to solve 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.\u003c/p\u003e"},{"header":"2. Methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1. Experimental data\u003c/h2\u003e \u003cp\u003e \u003cdiv class=\"BlockQuote\"\u003e \u003cp\u003eWe 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 (163cm, 85kg, right arm) [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e, \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]. Data were synchronously captured during 1) shoulder abduction (up to 95\u0026deg; of GHJ elevation) and 2) shoulder flexion (up to 110\u0026deg; 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\u0026deg; of GHJ elevation). Motions 1) and 2) will be used for model calibration (see section 2.3.4.) and motion 3) will be used for validation of the different shoulder muscle recruitment strategies.\u003c/p\u003e \u003c/div\u003e \u003c/p\u003e \u003cp\u003eClusters of three retroreflective markers were secured on the participant\u0026rsquo;s sternum, right scapula\u0026rsquo;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 [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e, \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]. 14 bony landmarks (described in the supplementary materials) were digitised and rigidly linked to their respective segments using a 3D locator [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e]. The GHJ centre was previously determined using the instantaneous helical axes method [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e, \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e]. Marker trajectories were smoothed using locally weighted smoothing [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eSurface EMG signals (Porti system, TMS International, Enschede, The Netherlands) were measured from 8 superficial muscles (i.e., anterior, middle and posterior deltoid, upper and lower pectoralis major, biceps, triceps and infraspinatus) as described in detail in [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]. EMG signals were recorded at a frequency of 1000 Hz. EMG envelopes were extracted using 1) zero-lag, 8th order 40\u0026ndash;400Hz bandpass Butterworth filter, 2) full-wave rectification, 3) zero-lag, 8th order 5 Hz low-pass Butterworth filter [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e, \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e]. All envelopes were then normalised to the maximum values obtained from the available functional, force and maximum voluntary contraction tasks [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eGHJ contact forces in three orthogonal directions between the instrumented shoulder hemiarthroplasty and the patient\u0026rsquo;s intact glenoid were recorded using a telemetric system at a sampling frequency of about 120Hz [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e].\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2. Shoulder modelling\u003c/h2\u003e \u003cp\u003eA previously developed [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e] and adapted [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e] 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 [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e]. The muscle-tendon model proposed by Millard et al. was used [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe clavicle, ulna, radius and hand segments of the generic OpenSim model were longitudinally scaled to match the participant\u0026rsquo;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 [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e]. For the abduction task with weight, the position of the hand\u0026rsquo;s centre of mass was shifted anteriorly by 3 cm and the hand\u0026rsquo;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 [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e] 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.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.3. Muscle recruitment modelling strategies\u003c/h2\u003e \u003cp\u003eA 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. Then, 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.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cdiv id=\"Sec6\" class=\"Section3\"\u003e \u003ch2\u003e2.3.1. Stochastic sampling\u003c/h2\u003e \u003cp\u003ePossible combinations of muscle forces, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\stackrel{-}{F\\left(i\\right)}\\)\u003c/span\u003e\u003c/span\u003e, were sampled to determine the solution space of the joint equilibrium Eq.\u0026nbsp;(\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e) for each frame \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(i\\)\u003c/span\u003e\u003c/span\u003e of the motion of interest. Muscle lever arms, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\stackrel{-}{B\\left(i\\right)}\\)\u003c/span\u003e\u003c/span\u003e, and external joint moments, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\stackrel{-}{\\tau \\left(i\\right)}\\)\u003c/span\u003e\u003c/span\u003e, were obtained from the OpenSim muscle analysis and inverse dynamics toolboxes, respectively. 200,000 solutions per frame of the abduction motion were calculated using the Markov-Chain Monte-Carlo method implemented in Metabolica [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. 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. Muscle forces, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\stackrel{-}{F\\left(i\\right)}\\)\u003c/span\u003e\u003c/span\u003e, were constrained between 0 and their maximum isometric force and a mean\u0026thinsp;\u0026plusmn;\u0026thinsp;standard deviation error of 0\u0026thinsp;\u0026plusmn;\u0026thinsp;0.1 N.m was allowed for each external joint moment in \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\stackrel{-}{\\tau \\left(i\\right)}\\)\u003c/span\u003e\u003c/span\u003e.\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\stackrel{-}{B\\left(i\\right)}\\times \\stackrel{-}{F\\left(i\\right)}=\\stackrel{-}{\\tau \\left(i\\right)}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section3\"\u003e \u003ch2\u003e2.3.2. Static optimisation\u003c/h2\u003e \u003cp\u003eA single set of muscle forces was determined using the SO tool in OpenSim 4.4 [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e, \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e]. This method minimises the sum of muscle activation, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({a}_{m}\\)\u003c/span\u003e\u003c/span\u003e, squared (Eq.\u0026nbsp;(\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e2\u003c/span\u003e)) Values for \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({a}_{m}\\)\u003c/span\u003e\u003c/span\u003e were constrained between 0 and 1 and residual actuators were included with an optimal moment of 1 N.m.\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\underset{}{\\text{min}}J=\\sum _{m=1}^{n}{{a}_{m}}^{2}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section3\"\u003e \u003ch2\u003e2.3.3. Computed muscle control\u003c/h2\u003e \u003cp\u003eForces of muscles spanning the GHJ were determined using CMC in OpenSim 4.4 [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. All GHJ degrees-of-freedom were tracked using default \u0026ldquo;fast target\u0026rdquo; OpenSim values, muscle excitations were bound between 0.01 and 1 as per the OpenSim guidelines [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. Residual actuators were included with an optimal moment of 1 N.m.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section3\"\u003e \u003ch2\u003e2.3.4. Calibrated EMG-Informed Neuromusculoskeletal Modelling (CEINMS)\u003c/h2\u003e \u003cp\u003eEMG-assisted solutions for muscle forces were calculated using the CEINMS toolbox [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. 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.\u003c/p\u003e \u003cp\u003eThe 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 Lloyd and Besier, 2003) 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\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e) were selected to best fit shoulder task applications, which are different to values usually selected for lower-limb modelling [\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e]. The experimental data of the abduction and flexion tasks with no weight described in section 2.1. are exclusively used to perform the CEINMS calibration(s), as suggested in [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eCEINMS calibration parameters for shoulder modelling\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNeuromuscular parameter\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eInitial value\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eBoundary\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eC1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026minus; 0.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e[\u0026minus;\u0026thinsp;0.95; \u0026minus; 0.05]\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eC2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026minus; 0.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e[\u0026minus;\u0026thinsp;0.95; \u0026minus; 0.05]\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eShape factor\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026minus; 0.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e[\u0026minus;\u0026thinsp;3; 0]\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTendon slack length\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eOriginal OpenSim value\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026plusmn;\u0026thinsp;30% of initial value\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eOptimal fibre length\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eOriginal OpenSim value\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026plusmn;\u0026thinsp;30% of initial value\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMaximum isometric force\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eOriginal OpenSim value\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e[100% \u0026minus;\u0026thinsp;250%] of initial value\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eOptimisation penalty\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAcceptable boundaries\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eWeight\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNormalised fibre length\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e[0.5; 1.4]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e200\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eEMG data were available for only 8 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 \u0026minus;\u0026thinsp;0.1 for the C1, C2 and the shape factor parameters, respectively. Then, a \u0026ldquo;single-calibrated\u0026rdquo; model was developed using EMG signals of the 8 recorded muscles. Note that MTUs with no EMG signal are considered inactive during the calibration procedure in CEINMS [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e, \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e]. Finally, based on a previously published study on neck muscles [\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e], a \u0026ldquo;double-calibrated\u0026rdquo; model was developed to calibrate all MTUs, even those without EMG signals. The procedure consisted of utilising the \u0026ldquo;single-calibrated\u0026rdquo; 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.\u003c/p\u003e \u003cp\u003eEventually, an EMG-assisted optimisation described in Eq.\u0026nbsp;(\u003cspan refid=\"Equ3\" class=\"InternalRef\"\u003e3\u003c/span\u003e) [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e] was performed using the three different models described above.\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\text{m}\\text{i}\\text{n} J={\\sum }_{\\text{d}}^{\\text{D}\\text{O}\\text{F}\\text{s}}{\\alpha }\\bullet {\\left({{\\tau }}_{\\text{d}}-{{\\tau }}_{\\text{d}}^{\\text{e}\\text{x}\\text{p}}\\right)}^{2}+{\\sum }_{\\text{j}}^{{\\text{M}\\text{T}\\text{U}}_{\\text{s}\\text{y}\\text{n}\\text{t}\\text{h}}}{\\beta }\\bullet {\\left({\\text{e}}_{\\text{j}}\\right)}^{2}+ {\\sum }_{\\text{k}}^{{\\text{M}\\text{T}\\text{U}}_{\\text{a}\\text{d}\\text{j}}}{\\gamma }\\bullet {\\left({\\text{e}}_{\\text{k}}-{\\text{e}}_{\\text{k}}^{\\text{e}\\text{x}\\text{p}}\\right)}^{2}+{\\beta }\\bullet {\\left({\\text{e}}_{\\text{k}}\\right)}^{2}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({{\\tau }}_{\\text{d}}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({{\\tau }}_{\\text{d}}^{\\text{e}\\text{x}\\text{p}}\\)\u003c/span\u003e\u003c/span\u003e are simulated and experimental net joint moments of degree-of-freedom \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(d\\)\u003c/span\u003e\u003c/span\u003e, respectively. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\text{e}}_{\\text{j}}\\)\u003c/span\u003e\u003c/span\u003e corresponds to the muscle excitation of the synthesised muscle \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(j\\)\u003c/span\u003e\u003c/span\u003e. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\text{e}}_{\\text{k}}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\text{e}}_{\\text{k}}^{\\text{e}\\text{x}\\text{p}}\\)\u003c/span\u003e\u003c/span\u003eare the simulated and experimental excitations for the adjusted muscle \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(k\\)\u003c/span\u003e\u003c/span\u003e. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\alpha }, {\\beta }\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\gamma }\\)\u003c/span\u003e\u003c/span\u003e were selected based on [\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e]. For all optimised solutions, averaged GHJ moments tracking errors were below 0.1 N.m.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e2.4. Analysis\u003c/h2\u003e \u003cp\u003eSO, CMC and the CEINMS methods each produced a set of muscle forces that balanced 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 technique can be found in the supplementary materials. The stochastic sampling produced 200,000 possible sets of muscle forces for the same problem.\u003c/p\u003e \u003cp\u003eAll 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.\u003c/p\u003e \u003cp\u003eMuscle forces from all methods were used to calculate the total GHJ-RF, expressed in the scapula frame of reference, using a custom-made Matlab script for consistency between methods. The Matlab script was validated against the OpenSim joint reaction analysis toolbox.\u003c/p\u003e \u003cp\u003eMinimum 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 \u003cem\u003emin(GHJ-RF)\u003c/em\u003e in the following. Furthermore, we obtained the solution that minimised the error between model prediction and experimental GHJ-RF. This solution is noted as \u003cem\u003emin(GHJ-RF error)\u003c/em\u003e in the following.\u003c/p\u003e \u003cp\u003eAbsolute error between the predicted GHJ-RF obtained from SO, CMC, CEINMS, \u003cem\u003emin(GHJ-RF)\u003c/em\u003e and \u003cem\u003emin(GHJ-RF error)\u003c/em\u003e and the experimental GHJ contact forces were calculated at each frame of the motion.\u003c/p\u003e \u003cp\u003eThe 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 over those frames where the experimental GHJ-RF was included in the stochastic range, noted as \u003cem\u003ewithin stochastic range\u003c/em\u003e. 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\u0026deg; 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 \u003cem\u003eabove shoulder level\u003c/em\u003e in the following.\u003c/p\u003e \u003cp\u003eFinally, experimental EMGs were compared qualitatively against predicted muscle forces. Computed muscle excitations from all methods can also be found in the supplementary materials.\u003c/p\u003e \u003c/div\u003e"},{"header":"3. Results","content":"\u003cp\u003eCEINMS 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.\u003c/p\u003e \u003cp\u003eTotal GHJ-RF are reported at the top of Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. 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. \u003cem\u003emin(GHJ-RF error)\u003c/em\u003e followed the stochastic lower boundary until the experimental curve was included in the model. Then, \u003cem\u003emin(GHJ-RF error)\u003c/em\u003e followed the experimental GHJ contact forces very closely.\u003c/p\u003e \u003cp\u003eInstantaneous absolute error in the predicted GHJ-RF reported at the bottom of Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e 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.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eValidity 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.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. For the overall abduction motion, joint force RMSE were between 23 (CMC) and 27%BW (CEINMS \u0026ndash; double calibration) for all methods, except CEINMS \u0026ndash; no calibration at a high 56%BW RMSE. When the experimental GHJ contact forces were comprised within the stochastic range, \u003cem\u003emin(GHJ-RF error)\u003c/em\u003e had an error of 0.1%BW. Above shoulder level, where muscle co-contraction is most critical, CMC (11%BW), CEINMS \u0026ndash; single calibration (14%BW) and CEINMS \u0026ndash; double calibration (16%BW) performed better than SO (25%BW).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eA selection of the computed muscle forces can be found in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e. 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 \u0026ndash; double calibration forces were generally the closest among all CEINMS computations to the normalised experimental EMG signals, with CEINMS \u0026ndash; 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.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"4. Discussion","content":"\u003cp\u003eThis 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 range of GHJ-RF solutions available in the selected shoulder model and mimicking the studied participant and abduction task ranged between 21 and 659%BW and included the experimental GHJ contact force from 40 degrees 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.\u003c/p\u003e \u003cp\u003eThe stochastic modelling approach [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e] 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., \u003cem\u003emin(GHJ-RF)\u003c/em\u003e) 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 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 [\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e]. 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 [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e] 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.\u003c/p\u003e \u003cp\u003eSpecifically, 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. \u003cem\u003emin(GHJ-RF error)\u003c/em\u003e). 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 might reflect a loose contact between the glenoid and the instrumented implant. 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 [\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e, \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e] might better represent joint forces at low elevation angles. Second, 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 [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e] is an invaluable resource for many shoulder studies, but 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 \u0026ldquo;knee grand challenge\u0026rdquo; [\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e]. The new data collection could use recent technological advances in motion capture and scapula motion tracking [\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e, \u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e] as well as latest developments in electromyography, by using in-dwelling [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e] or high-density electrodes, although the latest being utilised for isometric contractions only [\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eBased 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\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e and may serve as a selection guide for muscle recruitment strategies.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eTechnical summary of the advantages and disadvantages of the different muscle recruitment strategies for solving the shoulder muscle redundancy problem.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAccount for passive and non-linear properties of muscle-tendon units\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eUse of experimental muscle excitations\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eValidity of the joint reaction force\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eValidity of the joint reaction force above shoulder level\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eComputational time\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eStatic Optimisation (SO)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e+\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e+\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e+\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eComputed Muscle Control (CMC)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e+\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e+\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e+\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e++\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eCalibrated EMG-Informed Neuromusculoskeletal Modelling (CEINMS)\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e+\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e+\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e+\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e++\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e+*\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cem\u003eBased on data computed from one patient and one shoulder abduction task with a 2.4 kg weight in hand. -, + refer to a method\u0026rsquo;s disadvantage and a method\u0026rsquo;s advantage, respectively. For the joint reaction force validity, + and +\u0026thinsp;+\u0026thinsp;represent a RMSE between 20 and 40% and a RMSE below 20% of the body weight, respectively.*: The EMG-assisted approach was computed relatively fast (50s for 6s of motion), however it is worth noting the model calibrations that preceded took approximately 3.5 hours. With an acquisition frequency of 50 Hz, 0.02 sec/frame means the technique could be utilised for real-time feedback.\u003c/em\u003e \u003c/p\u003e \u003cp\u003eAlthough limited data was used, technical interpretations in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e are in accordance with the literature. In particular, SO underestimated GHJ-RF above shoulder level (as in [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]and does not account for passive muscle stiffness and fibre force-velocity relationships [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. EMG-assisted outcomes from CEINMS are more accurate than SO above shoulder level as reported by [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e, \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e] 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 [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e, \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e]. Compared to a single calibration, a double calibration procedure, as done in [\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e] for the neck region, did not improve the GHJ-RF predictions in this specific dataset. The validated outcomes of the CMC method reported in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e are novel in the field of shoulder MSK modelling and seem promising. It is proposed that more shoulder modelling studies should utilise CMC instead of SO in the future, especially since CMC is also capable of utilising experimental EMG signals to constrain computed muscle excitations.\u003c/p\u003e \u003cp\u003eCMC and CEINMS are partly using forward dynamics frameworks [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e] for which calibrating muscle-tendon parameters is critical. We used the calibration technique as in [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e] 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 [\u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e48\u003c/span\u003e], 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.\u003c/p\u003e \u003cp\u003eThe list of muscle recruitment strategies studied herein was not exhaustive, but we focused on the most commonly used and accessible optimisation techniques in OpenSim. The recent \u0026ldquo;muscle redundancy solver\u0026rdquo; presented in [\u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e49\u003c/span\u003e] seems promising to account for the passive stiffness 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 \u0026ldquo;healthy\u0026rdquo; shoulder was validated against experimental data from a person who underwent shoulder arthroplasty who likely did not have intact rotator cuff muscles. Nonetheless, it is the most detailed validation of musculoskeletal models possible with current methods [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e].\u003c/p\u003e"},{"header":"5. Conclusion","content":"\u003cp\u003eDifferent 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. Overall, CMC and CEINMS were the two most accurate methods in terms of predicted GHJ-RF, especially at high elevation angles. SO performed best at low elevation angles. In addition, stochastic muscle sampling provided critical information on the shoulder model capabilities and should be used as part of future validation studies- to inform on the consistency between model and experimental data.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAuthor Contributions Statement\u003c/h2\u003e\n\u003cp\u003e\u003cstrong\u003eMaxence Lavaill:\u0026nbsp;\u003c/strong\u003eWriting\u0026nbsp;\u0026ndash;\u0026nbsp;review\u0026nbsp;\u0026amp;\u0026nbsp;editing, Writing\u0026nbsp;\u0026ndash;\u0026nbsp;original draft, Visualization, Validation, Software, Resources, Project administration, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. \u003cstrong\u003eClaudio Pizzolatto:\u003c/strong\u003e Writing\u0026nbsp;\u0026ndash;\u0026nbsp;review\u0026nbsp;\u0026amp;\u0026nbsp;editing, Software, Methodology, Investigation, Conceptualization.\u003cstrong\u003e\u0026nbsp;Bart Bolsterlee:\u0026nbsp;\u003c/strong\u003eWriting\u0026nbsp;\u0026ndash;\u0026nbsp;review\u0026nbsp;\u0026amp;\u0026nbsp;editing, Methodology, Investigation, Conceptualization. \u003cstrong\u003eSaulo Martelli:\u0026nbsp;\u003c/strong\u003eWriting\u0026nbsp;\u0026ndash;\u0026nbsp;review\u0026nbsp;\u0026amp;\u0026nbsp;editing, Supervision, Methodology, Investigation, Funding acquisition, Conceptualization. \u003cstrong\u003ePeter Pivonka:\u0026nbsp;\u003c/strong\u003eWriting\u0026nbsp;\u0026ndash;\u0026nbsp;review\u0026nbsp;\u0026amp;\u0026nbsp;editing, Supervision, Resources, Methodology, Investigation, Conceptualization.\u003c/p\u003e\n\u003ch2\u003eAcknowledgements\u003c/h2\u003e\n\u003cp\u003eThe authors would like to deeply thank Dr Ali Asadi Nikooyan and Prof. DirkJan Veeger for giving us access to the shoulder-instrumented implant dataset and related materials.\u003c/p\u003e\n\u003ch2\u003eFunding\u003c/h2\u003e\n\u003cp\u003eML, BB, SM and PP would like to gratefully acknowledge funding received through the Australian Research Council (ARC) Industrial Transformation Training Centre for Joint Biomechanics (IC190100020). SM would also like to acknowledge the support received through the following funding schemes of the Australian Research Council:\u0026nbsp;DP180103146; FT180100338.\u003c/p\u003e\n\u003ch2\u003eConflicts of Interest\u003c/h2\u003e\n\u003cp\u003eThe authors declare that they have no conflict of interest.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003evan der Helm, F.C.T.: Analysis of the kinematic and dynamic behavior of the shoulder mechanism. J Biomech. 27, 527\u0026ndash;550 (1994). https://doi.org/10.1016/0021-9290(94)90064-7\u003c/li\u003e\n\u003cli\u003evan der Helm, F.C.T.: A finite element musculoskeletal model of the shoulder mechanism. J Biomech. 27, (1994). https://doi.org/10.1016/0021-9290(94)90065-5\u003c/li\u003e\n\u003cli\u003eMartin, J.A., Brandon, S.C.E., Keuler, E.M., Hermus, J.R., Ehlers, A.C., Segalman, D.J., Allen, M.S., Thelen, D.G.: Gauging force by tapping tendons. 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IEEE Trans Biomed Eng. 69, 2268\u0026ndash;2275 (2022). https://doi.org/10.1109/TBME.2022.3141067\u003c/li\u003e\n\u003cli\u003eWesterhoff, P., Graichen, F., Bender, A., Halder, A., Beier, A., Rohlmann, A., Bergmann, G.: In vivo measurement of shoulder joint loads during activities of daily living. J Biomech. 42, 1840\u0026ndash;1849 (2009). https://doi.org/10.1016/j.jbiomech.2009.05.035\u003c/li\u003e\n\u003cli\u003eLavaill, M.: Assessment of Musculoskeletal Modelling Procedures in Healthy Shoulders Towards Use for Clinical Applications, (2023)\u003c/li\u003e\n\u003cli\u003eNikooyan, A.A., Veeger, H.E.J., Westerhoff, P., Graichen, F., Bergmann, G., van der Helm, F.C.T.: Validation of the Delft Shoulder and Elbow Model using in-vivo glenohumeral joint contact forces. J Biomech. 43, 3007\u0026ndash;3014 (2010). https://doi.org/10.1016/j.jbiomech.2010.06.015\u003c/li\u003e\n\u003cli\u003eKian, A., Pizzolato, C., Halaki, M., Ginn, K., Lloyd, D., Reed, D., Ackland, D.: The effectiveness of EMG-driven neuromusculoskeletal model calibration is task dependent. J Biomech. 129, 110698 (2021). https://doi.org/10.1016/j.jbiomech.2021.110698\u003c/li\u003e\n\u003cli\u003eKian, A., Pizzolato, C., Halaki, M., Ginn, K., Lloyd, D., Reed, D., Ackland, D.: Static optimization underestimates antagonist muscle activity at the glenohumeral joint: A musculoskeletal modeling study. J Biomech. 97, 109348 (2019). https://doi.org/10.1016/j.jbiomech.2019.109348\u003c/li\u003e\n\u003cli\u003eSeth, A., Dong, M., Matias, R., Delp, S.: Muscle contributions to upper-extremity movement and work from a musculoskeletal model of the human shoulder. Front Neurorobot. 13, 1\u0026ndash;9 (2019). https://doi.org/10.3389/fnbot.2019.00090\u003c/li\u003e\n\u003cli\u003eNikooyan, A.A., Veeger, H.E.J., Bergmann, G., Westerhoff, P., Graichen, F., Bolsterlee, B., van der Helm, F.C.T.: An EMG-driven musculoskeletal model of the shoulder. Hum Mov Sci. 31, 429\u0026ndash;447 (2012). https://doi.org/10.1016/j.humov.2011.08.006\u003c/li\u003e\n\u003cli\u003eVeeger, D.H.E.J., van der Helm, F.C.T., Nikooyan, A.A.: Kinematic and kinetic data recorded with an instrumented shoulder prosthesis. Version 1., https://data.4tu.nl/datasets/86db1d7d-13d9-4631-9c6b-1e3134a1ab38/1, (2023)\u003c/li\u003e\n\u003cli\u003eWu, G., Van Der Helm, F.C.T., Veeger, H.E.J., Makhsous, M., Van Roy, P., Anglin, C., Nagels, J., Karduna, A.R., McQuade, K., Wang, X., Werner, F.W., Buchholz, B.: ISB recommendation on definitions of joint coordinate systems of various joints for the reporting of human joint motion - Part II: Shoulder, elbow, wrist and hand. J Biomech. 38, 981\u0026ndash;992 (2005). https://doi.org/10.1016/j.jbiomech.2004.05.042\u003c/li\u003e\n\u003cli\u003eLavaill, M., Martelli, S., Kerr, G.K., Pivonka, P.: Statistical Quantification of the Effects of Marker Misplacement and Soft-Tissue Artifact on Shoulder Kinematics and Kinetics. Life. 12, 1\u0026ndash;11 (2022). https://doi.org/https://doi.org/10.3390/life12060819\u003c/li\u003e\n\u003cli\u003eVeeger, H.E.J.: The position of the rotation center of the glenohumeral joint. J Biomech. 33, 1711\u0026ndash;1715 (2000). https://doi.org/10.1016/S0021-9290(00)00141-X\u003c/li\u003e\n\u003cli\u003eCleveland, W.S., Devlin, S.J.: Locally weighted regression: An approach to regression analysis by local fitting. J Am Stat Assoc. 83, 596\u0026ndash;610 (1988). https://doi.org/10.1080/01621459.1988.10478639\u003c/li\u003e\n\u003cli\u003eQuental, C., Azevedo, M., Ambr\u0026oacute;sio, J., S. B., G., Folgado, J.: Influence of the Musculotendon Dynamics on the Muscle Force-Sharing Problem of the Shoulder-A Fully Inverse Dynamics Approach. J Biomech Eng. 140, (2018). https://doi.org/10.1115/1.4039675\u003c/li\u003e\n\u003cli\u003eAssila, N., Pizzolato, C., Martinez, R., Lloyd, D.G., Begon, M.: EMG-Assisted Algorithm to Account for Shoulder Muscles Co-Contraction in Overhead Manual Handling. Applied Sciences (Switzerland). 10, (2020). https://doi.org/10.3390/app10103522\u003c/li\u003e\n\u003cli\u003eLavaill, M., Martelli, S., Cutbush, K., Gupta, A., Kerr, G.K., Pivonka, P.: Latarjet\u0026rsquo;s muscular alterations increase glenohumeral joint stability : A theoretical study. J Biomech. 155, 111639 (2023). https://doi.org/10.1016/j.jbiomech.2023.111639\u003c/li\u003e\n\u003cli\u003eMillard, M., Uchida, T., Seth, A., Delp, S.L.: Flexing computational muscle: Modeling and simulation of musculotendon dynamics. J Biomech Eng. 135, (2013). https://doi.org/10.1115/1.4023390\u003c/li\u003e\n\u003cli\u003eLavaill, M., Martelli, S., Gilliland, L., Gupta, A., Kerr, G., Pivonka, P.: The effects of anatomical errors on shoulder kinematics computed using multi-body models. Biomech Model Mechanobiol. 21, 1561\u0026ndash;1572 (2022). https://doi.org/10.1007/s10237-022-01606-0\u003c/li\u003e\n\u003cli\u003eDelp, S.L., Anderson, F.C., Arnold, A.S., Loan, P., Habib, A., John, C.T., Guendelman, E., Thelen, D.G.: OpenSim: Open-source software to create and analyze dynamic simulations of movement. 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J Biomech. 36, 765\u0026ndash;776 (2003). https://doi.org/10.1016/S0021-9290(03)00010-1\u003c/li\u003e\n\u003cli\u003eHoang, H.X., Pizzolato, C., Diamond, L.E., Lloyd, D.G.: Subject-specific calibration of neuromuscular parameters enables neuromusculoskeletal models to estimate physiologically plausible hip joint contact forces in healthy adults. J Biomech. 80, 111\u0026ndash;120 (2018). https://doi.org/10.1016/j.jbiomech.2018.08.023\u003c/li\u003e\n\u003cli\u003eSilvestros, P., Pizzolato, C., Lloyd, D.G., Preatoni, E., Gill, H.S., Cazzola, D.: Electromyography-Assisted Neuromusculoskeletal Models Can Estimate Physiological Muscle Activations and Joint Moments Across the Neck Before Impacts. J Biomech Eng. 144, 1\u0026ndash;16 (2022). https://doi.org/10.1115/1.4052555\u003c/li\u003e\n\u003cli\u003eSartori, M., Farina, D., Lloyd, D.G.: Hybrid neuromusculoskeletal modeling to best track joint moments using a balance between muscle excitations derived from electromyograms and optimization. J Biomech. 47, 3613\u0026ndash;3621 (2014). https://doi.org/10.1016/j.jbiomech.2014.10.009\u003c/li\u003e\n\u003cli\u003eKam, A.C.A., Kam, P.C.A.: Scapular and proximal humeral head fractures: An unusual complication of cardiopulmonary resuscitation. Anaesthesia. 49, 1055\u0026ndash;1057 (1994). https://doi.org/10.1111/j.1365-2044.1994.tb04355.x\u003c/li\u003e\n\u003cli\u003eKhandare, S., Vidt, M.E.: Development of a more biofidelic musculoskeletal model with glenohumeral ligaments and humeral head translations. Comput Methods Appl Mech Eng. (2022). https://doi.org/10.1080/10255842.2022.2127319\u003c/li\u003e\n\u003cli\u003eSarshari, E., Farron, A., Terrier, A., Pioletti, D., Mullhaupt, P.: A simulation framework for humeral head translations. Med Eng Phys. 49, 140\u0026ndash;147 (2017). https://doi.org/10.1016/j.medengphy.2017.08.013\u003c/li\u003e\n\u003cli\u003eFregly, B.J., Besier, T.F., Lloyd, D.G., Delp, S.L., Banks, S.A., Pandy, M.G., D\u0026rsquo;Lima, D.D.: Grand challenge competition to predict in vivo knee loads, (2012)\u003c/li\u003e\n\u003cli\u003eLempereur, M., Brochard, S., Leboeuf, F., R\u0026eacute;my-N\u0026eacute;ris, O.: Validity and reliability of 3D marker based scapular motion analysis: A systematic review. J Biomech. 47, 2219\u0026ndash;2230 (2014). https://doi.org/10.1016/j.jbiomech.2014.04.028\u003c/li\u003e\n\u003cli\u003eAliaj, K., Henninger, H.B., Sulkar, H., Kolz, C.: Biplane fluoroscopy derived humerus and scapula kinematics during arm elevation and rotation. Version 6., https://zenodo.org/records/7542486, (2021)\u003c/li\u003e\n\u003cli\u003eLulic-Kuryllo, T., Negro, F., Jiang, N., Dickerson, C.R.: Standard bipolar surface EMG estimations mischaracterize pectoralis major activity in commonly performed tasks. Journal of Electromyography and Kinesiology. 56, (2021). https://doi.org/10.1016/j.jelekin.2020.102509\u003c/li\u003e\n\u003cli\u003eHoang, H.X., Diamond, L.E., Lloyd, D.G., Pizzolato, C.: A calibrated EMG-informed neuromusculoskeletal model can appropriately account for muscle co-contraction in the estimation of hip joint contact forces in people with hip osteoarthritis. J Biomech. 83, 134\u0026ndash;142 (2019). https://doi.org/10.1016/j.jbiomech.2018.11.042\u003c/li\u003e\n\u003cli\u003eModenese, L., Ceseracciu, E., Reggiani, M., Lloyd, D.G.: Estimation of musculotendon parameters for scaled and subject specific musculoskeletal models using an optimization technique. J Biomech. 49, 141\u0026ndash;148 (2016). https://doi.org/10.1016/j.jbiomech.2015.11.006\u003c/li\u003e\n\u003cli\u003eBelli, I., Joshi, S., Prendergast, J.M., Beck, I., Della Santina, C., Peternel, L., Seth, A.: Does enforcing glenohumeral joint stability matter? A new rapid muscle redundancy solver highlights the importance of non-superficial shoulder muscles. PLoS One. 18, e0295003 (2023). https://doi.org/10.1371/journal.pone.0295003\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"multibody-system-dynamics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"mubo","sideBox":"Learn more about [Multibody System Dynamics](http://link.springer.com/journal/11044)","snPcode":"11044","submissionUrl":"https://submission.nature.com/new-submission/11044/3","title":"Multibody System Dynamics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Shoulder Modelling, Muscle Recruitment, Static Optimization, EMG-informed, Instrumented Shoulder Implant, Joint Force Validation","lastPublishedDoi":"10.21203/rs.3.rs-3890029/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3890029/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eShoulder muscle forces estimated via modelling are typically indirectly validated against measurements of glenohumeral joint reaction forces (GHJ-RF). This validation study benchmarks the outcomes of several muscle recruitment strategies against public GHJ-RF measurements.\u003c/p\u003e \u003cp\u003ePublic kinematics, electromyography, and GHJ-RF data from a selected male participant executing a 2.4 kg weight shoulder abduction task up to 92\u0026deg; GHJ elevation were obtained. The Delft Shoulder and Elbow Model was scaled to the participant. Muscle recruitment was solved by 1) minimizing muscle activations squared (SO), 2) accounting for dynamic muscle properties (CMC) and 3) constraining muscle excitations to corresponding surface electromyography measurements (CEINMS). Moreover, the spectrum of admissible GHJ-RF in the model was determined via Markov Chain Monte-Carlo stochastic sampling. The experimental GHJ-RF was compared to the resultant GHJ-RF of the different muscle recruitment strategies as well as the admissible stochastic range.\u003c/p\u003e \u003cp\u003eAdmissible GHJ-RF spanned 21 to 659% of body weight (%BW), excluding the experimental GHJ-RF up to 40 degrees of humeral elevation. Joint force RMSE were between 23 (CMC) and 27%BW (CEINMS). At high elevation angles, CMC (11%BW) and CEINMS (14%BW) performed better than SO (25%BW).\u003c/p\u003e \u003cp\u003eA guide has been proposed to best select muscle recruitment strategies. Overall, CMC and CEINMS were the two most accurate methods in terms of predicted GHJ-RF, especially at high elevation angles. SO performed best at low elevation angles. In addition, stochastic muscle sampling provided critical information on the shoulder model capabilities and the consistency between model and experimental data.\u003c/p\u003e","manuscriptTitle":"Benchmark and Validation of State-of-the-art Muscle Recruitment Strategies in Shoulder Modelling","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-01-25 15:27:20","doi":"10.21203/rs.3.rs-3890029/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2024-03-14T11:32:04+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-02-09T23:14:25+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"383edbb8-a5b1-4f33-8ce2-17c7509d3db5","date":"2024-01-26T13:27:56+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-01-25T10:34:25+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-01-24T12:57:43+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-01-23T14:56:12+00:00","index":"","fulltext":""},{"type":"submitted","content":"Multibody System Dynamics","date":"2024-01-23T05:56:36+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"multibody-system-dynamics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"mubo","sideBox":"Learn more about [Multibody System Dynamics](http://link.springer.com/journal/11044)","snPcode":"11044","submissionUrl":"https://submission.nature.com/new-submission/11044/3","title":"Multibody System Dynamics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"5ac309ff-c2b0-44b2-a357-2e3d2ddf6e28","owner":[],"postedDate":"January 25th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2024-05-13T10:06:27+00:00","versionOfRecord":[],"versionCreatedAt":"2024-01-25 15:27:20","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-3890029","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-3890029","identity":"rs-3890029","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}