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An entropy-assisted musculoskeletal shoulder model
Accepted Manuscript An entropy-assisted musculoskeletal shoulder model Xu Xu, Jia-hua Lin, Raymond W. McGorry PII: DOI: Reference:
S1050-6411(16)30192-4 http://dx.doi.org/10.1016/j.jelekin.2017.01.010 JJEK 2052
To appear in:
Journal of Electromyography and Kinesiology
Received Date: Revised Date: Accepted Date:
16 September 2016 19 January 2017 26 January 2017
Please cite this article as: X. Xu, J-h. Lin, R.W. McGorry, An entropy-assisted musculoskeletal shoulder model, Journal of Electromyography and Kinesiology (2017), doi: http://dx.doi.org/10.1016/j.jelekin.2017.01.010
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An entropy-assisted musculoskeletal shoulder model Xu Xua*, Jia-hua Linb, Raymond W. McGorryc a
Edward P. Fitts Department of Industrial and Systems Engineering, North Carolina State University, Raleigh, NC 27695, U.S.A
b
Safety and Health Assessment and Research for Prevention (SHARP) Program, Washington State Department of Labor and Industries, Olympia, WA 98504, U.S.A. c
Liberty Mutual Research Institute for Safety, 71 Frankland Road, Hopkinton, MA 01748, U.S.A.
*Corresponding Author Tel: +1 919 513 7205 Email: [email protected] Abstract Optimization combined with a musculoskeletal shoulder model has been used to estimate mechanical loading of musculoskeletal elements around the shoulder. Traditionally, the objective function is to minimize the summation of the total activities of the muscles with forces, moments, and stability constraints. Such an objective function, however, tends to neglect the antagonist muscle co-contraction. In this study, an objective function including an entropy term is proposed to address muscle co-contractions. A musculoskeletal shoulder model is developed to apply the proposed objective function. To find the optimal weight for the entropy term, an experiment was conducted. In the experiment, participants generated various 3-D shoulder moments in six shoulder postures. The surface EMG of 8 shoulder muscles was measured and compared with the predicted muscle activities based on the proposed objective function using Bhattacharyya distance and concordance ratio under different weight of the entropy term. The results show that
a small weight of the entropy term can improve the predictability of the model in terms of muscle activities. Such a result suggests that the concept of entropy could be helpful for further understanding the mechanism of muscle co-contractions as well as developing a shoulder biomechanical model with greater validity.
1. Introduction A biomechanical model can be helpful to understand the mechanical loading of musculoskeletal elements for clinical applications and injury prevention. In the past decades, a few shoulder biomechanical models have been developed (Charlton and Johnson, 2001; Dickerson et al., 2007; Holzbaur et al., 2005; Karlsson and Peterson, 1992; van der Helm, 1994) to investigate the shoulder tissue loading. When applying these biomechanical models to estimate shoulder muscle activities, optimization can be achieved by minimizing an efficiency criterion in the objective function, which is usually the summation of the square or cubic term of activities of all the muscles around the shoulder, with constraints that joints forces and forces generated by the muscles equal to those generate by the external forces and moments. Shoulder muscle co-contraction has been well observed (Brookham and Dickerson, 2013), and is believed to play an important role for improving glenohumeral joint stability (Steenbrink et al., 2009). However, one common issue in optimization-based inverse dynamics biomechanical model is that antagonist muscle co-contraction is generally neglected (Dickerson et al., 2008; Nikooyan et al., 2012; van Dieen and Kingma, 2005). Since the antagonistic muscles do not
directly contribute to the joint moments satisfying the constraints, the efficiency criterion in the objective function minimizes the activities of the antagonistic muscles (Hughes et al., 1995).Therefore, other studies have developed different methods, such as introducing stability measurement in the constraints (Brown and Potvin, 2005), using antagonist muscle activities to satisfy the minor components in moments constraints (Favre et al., 2005), or deriving regression model from the empirical data (Xu et al., 2014a), to address the issue of antagonist muscle activities prediction in a biomechanical model. In addition, electromyography (EMG) signals have been used to address the muscle co-contraction in an EMG-driven model (Lloyd and Besier, 2003; Sartori et al., 2012). The EMG-driven model can further be calibrated by the optimization method to reach a greater bio-fidelity level (Pizzolato et al., 2015; Sartori et al., 2014). While these methods provide insights into muscle co-contraction mechanism, some of them are not dedicated to the shoulder joint or can be difficult to apply while only human kinematics and external force data are available. In a recent study (Jiang, 2007), a novel entropy-assisted biomechanical model was proposed to address the muscle co-contraction for the elbow joint. Entropy is a measure of the level of disorder, and has been used in thermodynamics and information theory. In information theory, the Shannon’s entropy has the form of
, where pi is the probability (a value between
0 and 1) of a discrete random variable in the i-th state.The entropy reaches the maximum value when the possibility of each state is equally likely. When applying the concept of entropy in biomechanical modeling, the probability can be replaced by muscle activity level (also between 0 and 1). Maximizing the entropy will then result in promoting muscle activities for all the involved muscles in the model. In Jiang (2007), the objective function to be minimized for the optimization included two components: one is the efficiency criterion, which is the summation of
the cubic term of all muscle activities, and the other one is the entropy (without the negative mark) of all the muscle activities. The efficiency criterion with a greater weight induces the muscle activities for major agonist, while the entropy term with lighter weight results in the cocontraction of antagonist. The results in that study indicated that the predicted muscle activity from such an entropy-assisted objective function was closer to the muscle activity measured by the EMG for both the agonist and antagonist muscles around the elbow joint, compared with only using efficiency criterion as the objective function. However, since a simplified planar elbow model was adopted in that study, it remains unclear whether an entropy-assisted model will still hold a better validity in a more complex joint, such as the shoulder and hip joint. In the current study, the objective is to further investigate whether applying the concept of entropy can improve the validity of a shoulder biomechanical model in muscle activity prediction. Specifically, the two main goals are: 1) to build a computational shoulder biomechanical model that can be used to evaluate the effect of different optimization criterion on predicted muscle activity; and 2) to evaluate the performance of incorporating the entropy in the objective function for muscle activity prediction.
2. Methods 2.1 Shoulder model In general, the proposed computational model (Figure 1) of shoulder joint in this study is similar to those in Karlsson and Peterson (1992) and Dickerson (2007). The shoulder model includes the following bone segments: thoracic cage, clavicle, scapula, upper arm, and a radiusand ulna combined forearm (Dickerson et al., 2007). Each of the bone segments has a local coordinate system which conceptually aligned with ISB recommended standard (Wu et al., 2005). The segment is connected to each other through sternoclavicular, acromioclavicular, glenohumeral, and elbow joints with only rotational degree of freedom (DoF). The center of glenohumeral joint is estimated using location of bony landmarks on scapula (Veeger, 2000). The characteristic length of each segment is consistent with previous study (Hogfors et al., 1987)except the scapula for which the characteristic length is the distance from angulus acromialis and angulus inferior (Xu et al., 2012). There are 38 muscle slips (Hogfors et al., 1987) in the model. The coordinates of the muscles and ligaments attachment sites are with respect to the local coordinate systems of each bone, and proportional to the character length of each bone. The coordinates on each segments other than the scapula are based on Hogfors et al. (1987), and the coordinates on the scapula are from Xu et al. (2012). The muscles are modeled as strings between their corresponding attachment sites. Specifically, to improve biomechanical validity, wrapping techniques in previous shoulder models (Dickerson et al., 2007; Makhsous, 1999; van der Helm, 1994)are adopted. The deltoid muscles wrap around the spherical shoulder joint with a radius of 11% of the humerus length (Meskers et al., 1998). The rotator cuff muscle slips are wrapped around the spherical shoulder
joint with a radius of 7% of the humerus length (Makhsous, 1999). The serratus anterior muscles slips wrap around the rib cage which is modeled as a cylinder (Makhsous, 1999). In addition, two scapulothoracic contact force are included in the model (Makhsous, 1999). During shoulder movement, the orientations of the clavicle, scapula, and humerus are not completely independent. Such movement pattern of the bones is referred as the shoulder rhythm. Similar to previous shoulder modeling studies (Dickerson 2007; Karlsson and Peterson 1992), a regression-based shoulder rhythm (Xu et al., 2014b) has been adopted to estimate the clavicle and scapula orientation based on the orientation of the humerus. As an optimization-based biomechanical model, the model includes a few constraints. The major constraints include 3-D force and moment equilibrium equations for humerus, scapula, and clavicle. For each bone, the muscle-generated force and moment equal to those calculated through inverse dynamics with measured upper extremity kinematics and external force and moments. The ith muscle force Fi is calculated as activities of the ith muscles ( muscle adjusted by bodyweight, and
,where xi is the muscle
), PCSAi is the physiological cross sectional area of ith is the muscle tension parameter which is assumed to be
88N/cm2 (Wood et al., 1989) in this model. In addition, as discussed in Dickerson et al., (2007), an additional set of constraints is applied to ensure the shear / compression force ratio of the glenohumeral joint is within a certain range that matches the empirical data (Lippitt and Matsen, 1993). All the constraints are parameterized in a linear form to enhance computational efficiency (Dickerson et al., 2007). The objective function is in the form of the following equation, which is similar to that in Jiang (2007), in which the first term is the efficiency criterion, and the second term is the entropy:
Minimize: where w is the weight factor for the entropy term. The boundary for muscle activities of each muscle is between 0 and 1. The optimal weight factor w will be derived from empirical data from an experiment described below. 2.2 Experiment for weight factor Twelve participants were recruited from local communities (6 males and 6 females, age: 30.9 (10.5), height: 1.72 (0.09) m, weight: 71.8 (15.8) kg, all right-handed). The experiment protocol and the written informed consent were approved by the local Institutional Review Board. The experiments protocol was similar to that in a previous study (Xu et al., 2014a), where the detailed experiment setup can be found. An external frame (Xu et al., 2014c) was used to standardized the thoracohumeral joint. The external frame provided 3 DoFs: planes of elevation (γTH1), elevation angles (βTH), and humerus axial rotation angles (γTH2), which is consistent with the description of thoracohumeral joint in ISB recommendation (Wu et al., 2005). Six arm postures, including γTH1= 0 º, 30º, or 60º, and βTH = 30 º or60º was adopted in the experiment. γTH2 remained at 0 º for all the postures. Activities of the following 8 muscles were monitored by surface EMG: Anterior Deltoid, Middle Deltoid, Posterior Deltoid, Supraspinatus, Infraspinatus, Serratus anterior, Teres minor, and Teres major. Bipolar surface electrodes (Ag-AgCl, Noraxon Inc., Scottsdale, AZ, USA,) were place on each muscle with an inter electrode distance of 20 mm (Basmajian and Blumenstein, 1980). Medical tapes and patches were wrapped over the electrodes to secure their position. The ground electrode was placed on the middle part of the right clavicle. The raw EMG signals were
pre-amplified with a gain of 2000. A force and moment transducer (MC3A-1000, Advanced Mechanical Technology, Inc., Watertown, MA, USA) was placed underneath the forearm support and is used to measure the external force and moment on the right arm. Both the EMG and the transducer signal were collected with an A/D converter at 1024 Hz. Orientations of the right upper arm, right forearm, thorax, and transducer were measured by a motion tracking system (Optotrak Certus System, Northern Digital, Canada) at 100 Hz. Anatomical landmarks for creating the ISB recommended anatomical coordinate systems (Wu et al. 2005), except for glenohumeral (GH) joint, were digitized with the participants in a standing reference posture. Since GH joint center could not be directly digitized, acromion process (ACR) was adopted instead under the assumption that GH joint was on the line between the elbow joint and ACR (de Leva, 1996). The motion tracking system was synchronized with the EMG signal. The real-time GH joint 3-D net moment with respect to the humerus coordinate system was then calculated by inverse dynamics by a customized software (LabView 8.5, National Instruments, Austin, TX, USA) using the data from the transducer and upper arm length (Xu et al., 2014a) All six static arm postures were randomly ordered before the experiment. Basic anthropometry data, such as the arm length and circumference, were measured for estimating the inertial properties of body segments. The participants performed two maximum voluntary contraction (MVC) in each of 8 postures, which can greatly activate one or multiple muscles of the 8 measured ones (Xu et al., 2014a).During the experiment, the participants needed to generate 3-D shoulder moment in different magnitudes and directions for 20 seconds in each arm postures. While there was no target moment for participants to generate, they were instructed to generate submaximal shoulder moment in all 8 quadrants in the 3-D moment space. To facilitate the
participants, the real-time shoulder net moment in 3-D moment space was displayed on a monitor placed in front of the participants. There was a 90-second break between the force exertions for each arm posture. 2.3 Data Processing The raw EMG signals were first band-pass filtered with a 10-400 Hz 4th order Butterworth zerolag filter (van Dieen and Kingma, 2005).The filtered EMG signal of each muscle was then normalized by the maximum filtered EMG signal of the same muscle collected during the MVC trials. The normalized EMG (nEMG) was then shifted by 40ms to compensate electromechanical delay (Gatti et al., 2008; Lloyd and Besier, 2003).The transducer data was low-pass filtered at 8 Hz by a 4th order zero-lag Butterworth filter (Gatti et al., 2008). For each arm posture, the anatomical coordinate systems of thorax and humerus were generated from the measured bony landmarks (Wu et al., 2005). The character lengths of the bones were also extracted from the measured bony landmarks. GH joint was assumed to locate at 10.8% from the ACR on the line between the elbow joint and ACR during the reference posture (de Leva, 1996).The center of mass (CoM) location of the upper arm and the forearm (including hand) was estimated from body inertial property data (Dempster, 1955). The mass of the upper arm, forearm, and hand was estimated based on the measured anthropometry data (Zatsiorsky, 2002).The shoulder joint net moment as well as the net moment on sternoclavicular and acromioclavicular were then calculated by inverse dynamics method using the measured external moment and force, as well as the position and mass of the upper extremity segments. The mass of clavicle and scapula was ignored in the calculation. 2.4 Model evaluation
As the weight factor for the entropy term (w) remains unknown, various magnitudes of w were examined. Given w is a number between 0 and 1 in this study, and the weight on entropy term is much smaller than the weight for efficiency criterion term, the following w was investigated in the model: 0, 0.00005, 0.0001, 0.0003, 0.0005, 0.0007, 0.001, 0.002, 0.003, 0.004, 0.005, 0.006, 0.007, 0.008, 0.009, 0.01, 0.02, 0.04, 0.06, 0.08, 0.1, 0.2, 0.5, and 1. As describe in section 2.1, the major constraints in this shoulder biomechanical model is that the muscle-generated force and moment need to equal to those calculated through inverse dynamics. At each time frame in an experiment trial, the upper extremity posture and the joint net moments were used as the input for the model. The output of the model is the predicted muscle activitylevel of 38 muscles around the shoulder area by solving the objective function incorporating different level of w (Eq. 1) (fmincon function, Matlab R2014a, Mathworks, Natick MA, U.S.A). To evaluate the performance of the model, Bhattacharyya distance and concordance ratio between the measured EMG level and the predicted muscle activity level for each muscle and each trial were calculated. In statistics, Bhattacharyya distance is used to measure the similarity of two probability distributions (Theodoridis and Koutroumbas, 2006). If two distributions are identical, this distance would be zero. When the shapes of the two distributions are deviated from each other to a greater extend, the distance value would increase. In the current study, this concept was used to measure to what extent the distribution of the predicted muscle activity in a trial is similar to their measured EMG counterpart. The concept of concordance ratio has been used in a previous study (Dickerson et al., 2008) to evaluate the predicted muscle activities. In this study, the concordance ratio was calculated as follow: at each time instant during an experiment trial, the optimization model-based predicted muscle activity as well as the measured
EMG level are categorized as ‘on’ or ‘off’, based on whether they exceed 0.05 (viz. 5% of maximum contraction capacity) (Dickerson et al., 2008). Concordance ratio is the proportion that the predicted muscle activity is in correct category over the proportion that the predicted muscle activity is in wrong category. Bhattacharyya distance and concordance ratio are adopted in this study over the correlation coefficient as they are less sensitive to the large variance of the measured EMG signals (Dickerson et al., 2008). --------------------Figure 1 ---------------------
3. Results Across all the participants and arm postures, the recorded range of 3-D shoulder net moments were -23 Nm < Mhx<16 Nm, -31 Nm < Mhy<27 Nm, and -28 Nm < Mhz<16 Nm. The average nEMG across all the participants, all the trials and all the muscles was 0.12. Using 0.05 as the criterion for a muscle categorized as ‘on’, 64.4% of the recorded muscle activities across all the participants and all the arm posture was ‘on’. Within each muscle, anterior deltoid had the least average activity of 0.08 across all the participants and all the arm postures, and 45.2% of the recorded muscle activities was ‘on’, while infraspinatus had the greatest average activity of 0.15, and 83.0% of the recorded muscle activities was ‘on’ (Figure 2). Across all the participants and all the trials, there is a prominent trend that the Bhattacharyya distance between the predicted muscle activity and the measured EMG for shoulder muscles decreased as the entropy weight slightly increases from 0. As the entropy weight further increases, the Bhattacharyya distance drastically increase (Figure 3 and 4). The entropy weight that minimized the Bhattacharyya distance is affected by the muscles as well as the tested postures and ranges from 0 to 0.2. An entropy weight of 0.005 minimizes the lump sum of the Bhattacharyya distance across all muscles and all tested postures. The concordance ratio also increases as the entropy term slightly increase from 0 (Figure 5 and 6). However, as the entropy term keeps increasing towards 1, the concordance ratio eventually diminished to 0. The weight that maximized the concordance ratio ranges between 0 and 0.02 across all muscles and all tested postures. An entropy weight of 0.001 maximized the lump sum of the concordance ratio across all muscles and all tested postures.
-------------------Figure 2, 3, 4, 5, and 6 --------------------
4. Discussion In this study, an entropy term was introduced to the objective function to account for the shoulder muscle co-contractions. By modifying the objective function in the optimization criterion, the muscle co-contraction around the shoulder area can be better predicted with the measured human kinematics and external force and moment data. Although some previous studies (Forster et al., 2004; Raikova, 1999) have shown that adequately modifying the objective function can be helpful to promote the predicted muscle activities of antagonist muscles, directly applying the objective functions in those studies for shoulder joint could be challenging. In Raikova (1999), a negative sign needs to be assigned to the antagonist muscles in order to increase their activities in the optimization solution. Unlike a planar joint, the shoulder joint has 3 DoF which makes a shoulder muscle not strictly agonist or antagonist muscle. In such a case, the efficiency criterion can predict the antagonist muscle activities to some extent (Jinha et al., 2006), but the level of the magnitude could be quite different from the true muscle activities (Dickerson et al., 2008). In Forster et al. (2004), a shift parameter is introduced to the objective function which works as a penalty factor to force all the predicted muscle activities, including agonist and antagonist muscle, to be deviate from zero, and in turn to promote antagonist muscle activities. However, this study only theoretically demonstrates the effect of the shift parameter, but the magnitude of the shift parameter and whether it depends on the muscles were not discussed. As mentioned in Jiang (2007), the adapting the concept of entropy is based on the neurophysiological principle that antagonist muscle activity is a weighted summation of reciprocal inhibition and muscle co-contraction (Feldman, 1993). In the proposed objective function, the efficiency criterion term addresses the reciprocal inhibition and the entropy term
addresses the co-contraction. Such an objective function is physiologically meaningful and can be applied to body joints without restriction of the DoF of the joints. The weight of the entropy term in this study is assumed to be a fixed value regardless the shoulder posture or shoulder net moment. Such assumption is inconsistent with the findings in Jiang (2007) in which the optimal weight of the entropy term could be affected by the external load level as well as the joint angular velocity. In that study, the elbow joint moment and the elbow joint angular velocity were well controlled by a dynamometer, and the results showed that a greater joint moment or a greater angular flexion angular velocity tended to lead to a greater optimal weight of the entropy term, though the optimal weights across different conditions are all in a small range. Allowing various weight of entropy term for different shoulder posture or shoulder net moment is likely to increase the model fitness as an additional flexibility is introduced into the biomechanical model. However, the physiological reason that how elbow moment and elbow angular velocity affect the weight of the entropy term remains unclear. In addition, the shoulder joint has 3 rotational DoF and the muscle wrapping mechanism of shoulder joint is different from that of elbow joint. Therefore, given the lack of knowledge regarding how the shoulder moments and posture affect the weight factor, the weight factor is assumed to be constant for all shoulder moments and shoulder posture in this study. Mathematically, introducing the entropy term into the objective function increases the predicted muscle activity level for all muscles. When the weight of entropy term is zero, the objective function degenerates to a traditional efficiency criterion. As the weight of entropy gradually increases, the entropy term results in greater predicted muscle activities. In the extreme case that the weight of entropy term is one, the solution would maximize the predicted muscle activities under the concept of information entropy. In this case, the objective function would violate the
assumption that central nervous system (CNS) attempts to minimize muscle activities to satisfy the constraints. Thus, the difference between the predicted muscle activities and the measured ones rapidly increases once the weight of the entropy term exceeds the optimal weight. In this study, both Bhattacharyya distance and concordance ratio showed that the optimal weight of entropy term is a relatively small value compared the weight of efficiency criterion term in the objective function. Therefore, the results suggest that the efficiency criterion still account for the majority for predicting muscle activities, while the entropy term contributes to address muscle co-contraction. In addition, the optimal weight of the entropy term is affected by what measurement is used to measure the predictability of the model. In this study, the optimal weight based on Bhattacharyya distances for various muscles tend to be greater than that based on concordance ratio. Specifically, compared with Bhattacharyya distances in Figure 3 and 4, concordance ratios in Figure 5 and 6 looks less smooth and have a sudden drop once the weight of the entropy terms exceed the optimal value. This is because of a specific value, namely 0.05 in this study, is used as the criterion to categorize ‘on’ and ‘off’ of a muscle. As the weight of the entropy term increases, the predicted muscle activity of all the muscles at each time instant will eventually exceed this criterion and be categorized as “on”. Considering that for each muscle in a trial the time for “on” is less than the time for “off”, the concordance ratio drops sharply once the entropy term results in the predicted muscle activities greater than 0.05. Since both 5% (Dickerson et al., 2008) and 20% (Pedersen et al., 1987) have been used in literature as the criterion for the on-off threshold of muscle activity, a sensitivity analysis was performed to understand the effect of the selection of the criterion for muscle “on” and “off” on the optimal weights of the entropy terms. Other than the 5%, three other levels (2.5%, 10%, and 20%) of maximum contraction capacity were applied. The corresponding optimal weights of the entropy
term were 0.00005, 0.009, and 0.04, respectively. The results clearly indicated that the choose of the on-off threshold will affect the optimal weights of the entropy. This is because a greater onoff threshold would require a greater weight of entropy to increase the predicted muscle activity. One of the major limitations of the proposed shoulder biomechanical model is that it is assumed that the muscle force is linearly related to the muscle activation level without considering other muscle physiology properties, such as the force-length relation. In the early stage of the model development, the force-length and force-velocity relations proposed in Lloyd and Besier (2003) and van Dieen and Kingma (2005) were included in the model. However, it was then observed that the optimization method cannot find a feasible solution for rotator cuff muscles under many external load conditions. This is probably due to that the current model does not include the additional muscle attachment points other than the origins and insertions, which artificially enlarged the effect of the force-length relation on predicted muscle forces. The other possible reason is that the optimal length used for force-length relation is from Garner and Pandy (2000), which is based on the CT-scan of a cadaver. For each participant in this study, the optimal length of muscles can be affected by between-participant variability. Therefore, the predicted deviation from the optimal length could be overestimated which results in a lowered maximum force capacity. In addition, a previous shoulder model (Dickerson et al., 2007) made the same assumption and has been validated with empirical dataset (Dickerson et al., 2008) for static and less extreme shoulder postures. Therefore, the same assumption was made in this study. However, a shoulder biomechanical model with valid muscle physiological properties would be necessary for better understanding the effect of the entropy term in the objective function, especially for the tasks with extreme shoulder postures and dynamic shoulder movement.
There are also other limitations need to be addressed. First, the anatomical validity of the model need to be further improved. Although muscle origin and insertion have been scaled by the character length of bones in the model (Hogfors et al., 1987), it remains unclear if the original coordinates for the origin and insertion is representative in general population. The movement of scapula and clavicle in the model is estimated by regression-based shoulder rhythm equations. Such estimation does not reflect the inter-participant variability of shoulder rhythm. Second, the computational efficiency need to be enhanced. Currently it takes approximately 7 seconds to reach the optimal solution for the constraints in each time frame (CPU: Intel Xeon E5-1650 3.2GHz, Memory: 16 GB, OS: Windows 8 64-bit). Such computational speed obstructs applying the model to predict the muscle activities in real-time, as well as testing the validity of the model in more shoulder postures. Third, the objective function in the current study is extended from efficiency criterion. Recent study (Nikooyan et al., 2013) has shown a novel energy-based criterion (Praagman et al., 2006)can provide a good estimate on glenohumeral joint reaction force. Whether the entropy term could contribute to energy-based criterion need to be further investigated. Fourth, previous studies (Pizzolato et al., 2015; Sartori et al., 2014)have shown that including the measured muscle activity in an EMG-informed model could provide adequate predictability on joint moment and muscle forces. Within such framework, the current objective function could be further fine-tuned by measuring the shoulder muscle activity under a wider range of shoulder motion.
Conflict of Interest Statement All authors declare that there is no proprietary, financial, professional or other personal interest of any nature or kind in any product, service or company that could be construed as influencing the position presented in the manuscript entitled, “An entropy-assisted musculoskeletal shoulder model”.
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J., Karduna, A.R., McQuade, K., Wang, X.G., Werner, F.W., Buchholz, B., 2005. 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. doi:10.1016/j.jbiomech.2004.05.042 Xu, X., Lin, J.-H., Li, K., Tan, V., 2012. Transformation between different local coordinate systems of the scapula. J. Biomech. 45, 2724–2727. doi:10.1016/j.jbiomech.2012.08.021 Xu, X., McGorry, R.W., Lin, J.H., 2014a. A regression model predicting isometric shoulder muscle activities from arm postures and shoulder joint moments. J Electromyogr Kinesiol 24, 419–429. doi:10.1016/j.jelekin.2014.02.004 Xu, X., Lin, J., McGorry, R.W., 2014b. A regression-based 3-D shoulder rhythm. J. Biomech. 47, 1206–1210. doi:10.1016/j.jbiomech.2014.01.043 Xu, X., McGorry, R.W., Lin, J.H., 2014c. The accuracy of an external frame using ISB recommended rotation sequence to define shoulder joint angle. Gait Posture 39, 662–668. doi:10.1016/j.gaitpost.2013.08.032 Zatsiorsky, V.M., 2002. Kinetics of Human Motion. Human Kinetics, Champaign, IL, U.S.A.
Figure 1. A simple visualization of the proposed musculoskeletal shoulder model. The thick solid lines represent for bone elements, the thin solid lines represent muscles around the shoulder, and the dashed line is the net moment on glenohumeral joint calculated by inverse dynamics for each time instant. T8: the 8th thoracic vertebrae, C7: the 7th cervical vertebrae, IJ: incisura jugularis, SCJ: sternoclavicular joint, ACJ: acromioclavicular joint, GHJ: glenohumeral joint, TS: trigonum scapulae, AI: angulus acromialis, EJC: elbow joint center, WJC: wrist joint center. It should be noted that due to the 3-D perspectives, the 2-D distance on this figure is not to scale. The shoulder posture showed in this figure is γTH1 = 30º, βTH = -30º, and γTH2 = 0º.
Figure 2. An example demonstrating the effect of the entropy term. The solid line is the measured EMG signals of infraspinatus, the dot line is the predicted muscle activity purely based on the efficient criterion, the dash line is the predicted muscle activity purely based on the entropy criterion, and the dash-dot line is the predicted muscle activity with the weight of entropy term as 0.005. This figure shows that from time 0 to 2 second, the measured muscle activity and the predicted muscle activity with the weight of entropy term as 0.005 and 1 are all greater than the muscle “on” and “off” criterion (5% of MVC), while the efficiency criterionbased predicted muscle activity is less than the criterion. However, the predicted muscle activity with the weight of entropy term as 1 greatly overestimated the muscle activities.
Figure 3. The average Bhattacharyya distance across all tested shoulder posture and all participants when shoulder elevation is 30º. X-axis for each subplot is in logarithmic scale. Note that the x-axes from Figure 3 to Figure 6 are not in linear scale. The bar groups from left to right represent the investigated weight of the entropy term from least to most.
Figure 4. The average Bhattacharyya distance across all tested shoulder posture and all participants when shoulder elevation is 60º. X-axis for each subplot is in logarithmic scale.
Figure 5. The average concordance ratio across all tested shoulder posture and all participants when shoulder elevation is 30º. X-axis for each subplot is in logarithmic scale.
Figure 6. The average concordance ratio across all tested shoulder posture and all participants when shoulder elevation is 60º. X-axis for each subplot is in logarithmic scale.
Author short bio Xu Xu is an assistant professor in Edward P. Fitts Department of Industrial and Systems Engineering at North Carolina State University. His research interests are mainly on human factors and ergonomics engineering, occupational biomechanics, optimization-based biomechanical modelling, data mining on human motion data, and musculoskeletal injury prevention. He earned a B.S. in industrial engineering from Tsinghua University in 2004, and an M.S and Ph.D. in industrial engineering from North Carolina State University in 2006 and 2008. He also completed a postdoctoral fellowship in Department of Environmental Health at Harvard School of Public Health in 2010.
Jia-Hua Lin received Ph.D. and M.S. degrees in industrial engineering from the University of Wisconsin-Madison in 2001. Currently, he is a senior ergonomist in the Safety and Health Assessment and Research for Prevention (SHARP) Program at Washington State Department of Labor and Industries. His research includes general physical ergonomics and occupational biomechanics, particularly in the area of upper extremity physical capacities and human-machine and tool interfaces.
Raymond W. McGorry, a senior research scientist, has been with the Liberty Mutual Research Institute for Safety since 1993. He conducts laboratory and field investigations of work-related injury and illness and is a regular collaborator on ergonomic studies with other investigators. His research interests include developing work measurement instrumentation, biomechanics, exposure assessment, force measurement during hand tool use, and investigating approaches to musculoskeletal rehabilitation. Prior to joining the Research Institute, Mr. McGorry worked as a physical therapist and as a biomedical engineer. Mr. McGorry holds a B.S. in biology from Villanova University, a graduate certificate in physical therapy from Emory University, and an M.S. in
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bioengineering from Clemson University. He also completed a post-graduate fellowship in rehabilitation engineering at the Massachusetts Institute of Technology.
S1050-6411(16)30192-4 http://dx.doi.org/10.1016/j.jelekin.2017.01.010 JJEK 2052
To appear in:
Journal of Electromyography and Kinesiology
Received Date: Revised Date: Accepted Date:
16 September 2016 19 January 2017 26 January 2017
Please cite this article as: X. Xu, J-h. Lin, R.W. McGorry, An entropy-assisted musculoskeletal shoulder model, Journal of Electromyography and Kinesiology (2017), doi: http://dx.doi.org/10.1016/j.jelekin.2017.01.010
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An entropy-assisted musculoskeletal shoulder model Xu Xua*, Jia-hua Linb, Raymond W. McGorryc a
Edward P. Fitts Department of Industrial and Systems Engineering, North Carolina State University, Raleigh, NC 27695, U.S.A
b
Safety and Health Assessment and Research for Prevention (SHARP) Program, Washington State Department of Labor and Industries, Olympia, WA 98504, U.S.A. c
Liberty Mutual Research Institute for Safety, 71 Frankland Road, Hopkinton, MA 01748, U.S.A.
*Corresponding Author Tel: +1 919 513 7205 Email: [email protected] Abstract Optimization combined with a musculoskeletal shoulder model has been used to estimate mechanical loading of musculoskeletal elements around the shoulder. Traditionally, the objective function is to minimize the summation of the total activities of the muscles with forces, moments, and stability constraints. Such an objective function, however, tends to neglect the antagonist muscle co-contraction. In this study, an objective function including an entropy term is proposed to address muscle co-contractions. A musculoskeletal shoulder model is developed to apply the proposed objective function. To find the optimal weight for the entropy term, an experiment was conducted. In the experiment, participants generated various 3-D shoulder moments in six shoulder postures. The surface EMG of 8 shoulder muscles was measured and compared with the predicted muscle activities based on the proposed objective function using Bhattacharyya distance and concordance ratio under different weight of the entropy term. The results show that
a small weight of the entropy term can improve the predictability of the model in terms of muscle activities. Such a result suggests that the concept of entropy could be helpful for further understanding the mechanism of muscle co-contractions as well as developing a shoulder biomechanical model with greater validity.
1. Introduction A biomechanical model can be helpful to understand the mechanical loading of musculoskeletal elements for clinical applications and injury prevention. In the past decades, a few shoulder biomechanical models have been developed (Charlton and Johnson, 2001; Dickerson et al., 2007; Holzbaur et al., 2005; Karlsson and Peterson, 1992; van der Helm, 1994) to investigate the shoulder tissue loading. When applying these biomechanical models to estimate shoulder muscle activities, optimization can be achieved by minimizing an efficiency criterion in the objective function, which is usually the summation of the square or cubic term of activities of all the muscles around the shoulder, with constraints that joints forces and forces generated by the muscles equal to those generate by the external forces and moments. Shoulder muscle co-contraction has been well observed (Brookham and Dickerson, 2013), and is believed to play an important role for improving glenohumeral joint stability (Steenbrink et al., 2009). However, one common issue in optimization-based inverse dynamics biomechanical model is that antagonist muscle co-contraction is generally neglected (Dickerson et al., 2008; Nikooyan et al., 2012; van Dieen and Kingma, 2005). Since the antagonistic muscles do not
directly contribute to the joint moments satisfying the constraints, the efficiency criterion in the objective function minimizes the activities of the antagonistic muscles (Hughes et al., 1995).Therefore, other studies have developed different methods, such as introducing stability measurement in the constraints (Brown and Potvin, 2005), using antagonist muscle activities to satisfy the minor components in moments constraints (Favre et al., 2005), or deriving regression model from the empirical data (Xu et al., 2014a), to address the issue of antagonist muscle activities prediction in a biomechanical model. In addition, electromyography (EMG) signals have been used to address the muscle co-contraction in an EMG-driven model (Lloyd and Besier, 2003; Sartori et al., 2012). The EMG-driven model can further be calibrated by the optimization method to reach a greater bio-fidelity level (Pizzolato et al., 2015; Sartori et al., 2014). While these methods provide insights into muscle co-contraction mechanism, some of them are not dedicated to the shoulder joint or can be difficult to apply while only human kinematics and external force data are available. In a recent study (Jiang, 2007), a novel entropy-assisted biomechanical model was proposed to address the muscle co-contraction for the elbow joint. Entropy is a measure of the level of disorder, and has been used in thermodynamics and information theory. In information theory, the Shannon’s entropy has the form of
, where pi is the probability (a value between
0 and 1) of a discrete random variable in the i-th state.The entropy reaches the maximum value when the possibility of each state is equally likely. When applying the concept of entropy in biomechanical modeling, the probability can be replaced by muscle activity level (also between 0 and 1). Maximizing the entropy will then result in promoting muscle activities for all the involved muscles in the model. In Jiang (2007), the objective function to be minimized for the optimization included two components: one is the efficiency criterion, which is the summation of
the cubic term of all muscle activities, and the other one is the entropy (without the negative mark) of all the muscle activities. The efficiency criterion with a greater weight induces the muscle activities for major agonist, while the entropy term with lighter weight results in the cocontraction of antagonist. The results in that study indicated that the predicted muscle activity from such an entropy-assisted objective function was closer to the muscle activity measured by the EMG for both the agonist and antagonist muscles around the elbow joint, compared with only using efficiency criterion as the objective function. However, since a simplified planar elbow model was adopted in that study, it remains unclear whether an entropy-assisted model will still hold a better validity in a more complex joint, such as the shoulder and hip joint. In the current study, the objective is to further investigate whether applying the concept of entropy can improve the validity of a shoulder biomechanical model in muscle activity prediction. Specifically, the two main goals are: 1) to build a computational shoulder biomechanical model that can be used to evaluate the effect of different optimization criterion on predicted muscle activity; and 2) to evaluate the performance of incorporating the entropy in the objective function for muscle activity prediction.
2. Methods 2.1 Shoulder model In general, the proposed computational model (Figure 1) of shoulder joint in this study is similar to those in Karlsson and Peterson (1992) and Dickerson (2007). The shoulder model includes the following bone segments: thoracic cage, clavicle, scapula, upper arm, and a radiusand ulna combined forearm (Dickerson et al., 2007). Each of the bone segments has a local coordinate system which conceptually aligned with ISB recommended standard (Wu et al., 2005). The segment is connected to each other through sternoclavicular, acromioclavicular, glenohumeral, and elbow joints with only rotational degree of freedom (DoF). The center of glenohumeral joint is estimated using location of bony landmarks on scapula (Veeger, 2000). The characteristic length of each segment is consistent with previous study (Hogfors et al., 1987)except the scapula for which the characteristic length is the distance from angulus acromialis and angulus inferior (Xu et al., 2012). There are 38 muscle slips (Hogfors et al., 1987) in the model. The coordinates of the muscles and ligaments attachment sites are with respect to the local coordinate systems of each bone, and proportional to the character length of each bone. The coordinates on each segments other than the scapula are based on Hogfors et al. (1987), and the coordinates on the scapula are from Xu et al. (2012). The muscles are modeled as strings between their corresponding attachment sites. Specifically, to improve biomechanical validity, wrapping techniques in previous shoulder models (Dickerson et al., 2007; Makhsous, 1999; van der Helm, 1994)are adopted. The deltoid muscles wrap around the spherical shoulder joint with a radius of 11% of the humerus length (Meskers et al., 1998). The rotator cuff muscle slips are wrapped around the spherical shoulder
joint with a radius of 7% of the humerus length (Makhsous, 1999). The serratus anterior muscles slips wrap around the rib cage which is modeled as a cylinder (Makhsous, 1999). In addition, two scapulothoracic contact force are included in the model (Makhsous, 1999). During shoulder movement, the orientations of the clavicle, scapula, and humerus are not completely independent. Such movement pattern of the bones is referred as the shoulder rhythm. Similar to previous shoulder modeling studies (Dickerson 2007; Karlsson and Peterson 1992), a regression-based shoulder rhythm (Xu et al., 2014b) has been adopted to estimate the clavicle and scapula orientation based on the orientation of the humerus. As an optimization-based biomechanical model, the model includes a few constraints. The major constraints include 3-D force and moment equilibrium equations for humerus, scapula, and clavicle. For each bone, the muscle-generated force and moment equal to those calculated through inverse dynamics with measured upper extremity kinematics and external force and moments. The ith muscle force Fi is calculated as activities of the ith muscles ( muscle adjusted by bodyweight, and
,where xi is the muscle
), PCSAi is the physiological cross sectional area of ith is the muscle tension parameter which is assumed to be
88N/cm2 (Wood et al., 1989) in this model. In addition, as discussed in Dickerson et al., (2007), an additional set of constraints is applied to ensure the shear / compression force ratio of the glenohumeral joint is within a certain range that matches the empirical data (Lippitt and Matsen, 1993). All the constraints are parameterized in a linear form to enhance computational efficiency (Dickerson et al., 2007). The objective function is in the form of the following equation, which is similar to that in Jiang (2007), in which the first term is the efficiency criterion, and the second term is the entropy:
Minimize: where w is the weight factor for the entropy term. The boundary for muscle activities of each muscle is between 0 and 1. The optimal weight factor w will be derived from empirical data from an experiment described below. 2.2 Experiment for weight factor Twelve participants were recruited from local communities (6 males and 6 females, age: 30.9 (10.5), height: 1.72 (0.09) m, weight: 71.8 (15.8) kg, all right-handed). The experiment protocol and the written informed consent were approved by the local Institutional Review Board. The experiments protocol was similar to that in a previous study (Xu et al., 2014a), where the detailed experiment setup can be found. An external frame (Xu et al., 2014c) was used to standardized the thoracohumeral joint. The external frame provided 3 DoFs: planes of elevation (γTH1), elevation angles (βTH), and humerus axial rotation angles (γTH2), which is consistent with the description of thoracohumeral joint in ISB recommendation (Wu et al., 2005). Six arm postures, including γTH1= 0 º, 30º, or 60º, and βTH = 30 º or60º was adopted in the experiment. γTH2 remained at 0 º for all the postures. Activities of the following 8 muscles were monitored by surface EMG: Anterior Deltoid, Middle Deltoid, Posterior Deltoid, Supraspinatus, Infraspinatus, Serratus anterior, Teres minor, and Teres major. Bipolar surface electrodes (Ag-AgCl, Noraxon Inc., Scottsdale, AZ, USA,) were place on each muscle with an inter electrode distance of 20 mm (Basmajian and Blumenstein, 1980). Medical tapes and patches were wrapped over the electrodes to secure their position. The ground electrode was placed on the middle part of the right clavicle. The raw EMG signals were
pre-amplified with a gain of 2000. A force and moment transducer (MC3A-1000, Advanced Mechanical Technology, Inc., Watertown, MA, USA) was placed underneath the forearm support and is used to measure the external force and moment on the right arm. Both the EMG and the transducer signal were collected with an A/D converter at 1024 Hz. Orientations of the right upper arm, right forearm, thorax, and transducer were measured by a motion tracking system (Optotrak Certus System, Northern Digital, Canada) at 100 Hz. Anatomical landmarks for creating the ISB recommended anatomical coordinate systems (Wu et al. 2005), except for glenohumeral (GH) joint, were digitized with the participants in a standing reference posture. Since GH joint center could not be directly digitized, acromion process (ACR) was adopted instead under the assumption that GH joint was on the line between the elbow joint and ACR (de Leva, 1996). The motion tracking system was synchronized with the EMG signal. The real-time GH joint 3-D net moment with respect to the humerus coordinate system was then calculated by inverse dynamics by a customized software (LabView 8.5, National Instruments, Austin, TX, USA) using the data from the transducer and upper arm length (Xu et al., 2014a) All six static arm postures were randomly ordered before the experiment. Basic anthropometry data, such as the arm length and circumference, were measured for estimating the inertial properties of body segments. The participants performed two maximum voluntary contraction (MVC) in each of 8 postures, which can greatly activate one or multiple muscles of the 8 measured ones (Xu et al., 2014a).During the experiment, the participants needed to generate 3-D shoulder moment in different magnitudes and directions for 20 seconds in each arm postures. While there was no target moment for participants to generate, they were instructed to generate submaximal shoulder moment in all 8 quadrants in the 3-D moment space. To facilitate the
participants, the real-time shoulder net moment in 3-D moment space was displayed on a monitor placed in front of the participants. There was a 90-second break between the force exertions for each arm posture. 2.3 Data Processing The raw EMG signals were first band-pass filtered with a 10-400 Hz 4th order Butterworth zerolag filter (van Dieen and Kingma, 2005).The filtered EMG signal of each muscle was then normalized by the maximum filtered EMG signal of the same muscle collected during the MVC trials. The normalized EMG (nEMG) was then shifted by 40ms to compensate electromechanical delay (Gatti et al., 2008; Lloyd and Besier, 2003).The transducer data was low-pass filtered at 8 Hz by a 4th order zero-lag Butterworth filter (Gatti et al., 2008). For each arm posture, the anatomical coordinate systems of thorax and humerus were generated from the measured bony landmarks (Wu et al., 2005). The character lengths of the bones were also extracted from the measured bony landmarks. GH joint was assumed to locate at 10.8% from the ACR on the line between the elbow joint and ACR during the reference posture (de Leva, 1996).The center of mass (CoM) location of the upper arm and the forearm (including hand) was estimated from body inertial property data (Dempster, 1955). The mass of the upper arm, forearm, and hand was estimated based on the measured anthropometry data (Zatsiorsky, 2002).The shoulder joint net moment as well as the net moment on sternoclavicular and acromioclavicular were then calculated by inverse dynamics method using the measured external moment and force, as well as the position and mass of the upper extremity segments. The mass of clavicle and scapula was ignored in the calculation. 2.4 Model evaluation
As the weight factor for the entropy term (w) remains unknown, various magnitudes of w were examined. Given w is a number between 0 and 1 in this study, and the weight on entropy term is much smaller than the weight for efficiency criterion term, the following w was investigated in the model: 0, 0.00005, 0.0001, 0.0003, 0.0005, 0.0007, 0.001, 0.002, 0.003, 0.004, 0.005, 0.006, 0.007, 0.008, 0.009, 0.01, 0.02, 0.04, 0.06, 0.08, 0.1, 0.2, 0.5, and 1. As describe in section 2.1, the major constraints in this shoulder biomechanical model is that the muscle-generated force and moment need to equal to those calculated through inverse dynamics. At each time frame in an experiment trial, the upper extremity posture and the joint net moments were used as the input for the model. The output of the model is the predicted muscle activitylevel of 38 muscles around the shoulder area by solving the objective function incorporating different level of w (Eq. 1) (fmincon function, Matlab R2014a, Mathworks, Natick MA, U.S.A). To evaluate the performance of the model, Bhattacharyya distance and concordance ratio between the measured EMG level and the predicted muscle activity level for each muscle and each trial were calculated. In statistics, Bhattacharyya distance is used to measure the similarity of two probability distributions (Theodoridis and Koutroumbas, 2006). If two distributions are identical, this distance would be zero. When the shapes of the two distributions are deviated from each other to a greater extend, the distance value would increase. In the current study, this concept was used to measure to what extent the distribution of the predicted muscle activity in a trial is similar to their measured EMG counterpart. The concept of concordance ratio has been used in a previous study (Dickerson et al., 2008) to evaluate the predicted muscle activities. In this study, the concordance ratio was calculated as follow: at each time instant during an experiment trial, the optimization model-based predicted muscle activity as well as the measured
EMG level are categorized as ‘on’ or ‘off’, based on whether they exceed 0.05 (viz. 5% of maximum contraction capacity) (Dickerson et al., 2008). Concordance ratio is the proportion that the predicted muscle activity is in correct category over the proportion that the predicted muscle activity is in wrong category. Bhattacharyya distance and concordance ratio are adopted in this study over the correlation coefficient as they are less sensitive to the large variance of the measured EMG signals (Dickerson et al., 2008). --------------------Figure 1 ---------------------
3. Results Across all the participants and arm postures, the recorded range of 3-D shoulder net moments were -23 Nm < Mhx<16 Nm, -31 Nm < Mhy<27 Nm, and -28 Nm < Mhz<16 Nm. The average nEMG across all the participants, all the trials and all the muscles was 0.12. Using 0.05 as the criterion for a muscle categorized as ‘on’, 64.4% of the recorded muscle activities across all the participants and all the arm posture was ‘on’. Within each muscle, anterior deltoid had the least average activity of 0.08 across all the participants and all the arm postures, and 45.2% of the recorded muscle activities was ‘on’, while infraspinatus had the greatest average activity of 0.15, and 83.0% of the recorded muscle activities was ‘on’ (Figure 2). Across all the participants and all the trials, there is a prominent trend that the Bhattacharyya distance between the predicted muscle activity and the measured EMG for shoulder muscles decreased as the entropy weight slightly increases from 0. As the entropy weight further increases, the Bhattacharyya distance drastically increase (Figure 3 and 4). The entropy weight that minimized the Bhattacharyya distance is affected by the muscles as well as the tested postures and ranges from 0 to 0.2. An entropy weight of 0.005 minimizes the lump sum of the Bhattacharyya distance across all muscles and all tested postures. The concordance ratio also increases as the entropy term slightly increase from 0 (Figure 5 and 6). However, as the entropy term keeps increasing towards 1, the concordance ratio eventually diminished to 0. The weight that maximized the concordance ratio ranges between 0 and 0.02 across all muscles and all tested postures. An entropy weight of 0.001 maximized the lump sum of the concordance ratio across all muscles and all tested postures.
-------------------Figure 2, 3, 4, 5, and 6 --------------------
4. Discussion In this study, an entropy term was introduced to the objective function to account for the shoulder muscle co-contractions. By modifying the objective function in the optimization criterion, the muscle co-contraction around the shoulder area can be better predicted with the measured human kinematics and external force and moment data. Although some previous studies (Forster et al., 2004; Raikova, 1999) have shown that adequately modifying the objective function can be helpful to promote the predicted muscle activities of antagonist muscles, directly applying the objective functions in those studies for shoulder joint could be challenging. In Raikova (1999), a negative sign needs to be assigned to the antagonist muscles in order to increase their activities in the optimization solution. Unlike a planar joint, the shoulder joint has 3 DoF which makes a shoulder muscle not strictly agonist or antagonist muscle. In such a case, the efficiency criterion can predict the antagonist muscle activities to some extent (Jinha et al., 2006), but the level of the magnitude could be quite different from the true muscle activities (Dickerson et al., 2008). In Forster et al. (2004), a shift parameter is introduced to the objective function which works as a penalty factor to force all the predicted muscle activities, including agonist and antagonist muscle, to be deviate from zero, and in turn to promote antagonist muscle activities. However, this study only theoretically demonstrates the effect of the shift parameter, but the magnitude of the shift parameter and whether it depends on the muscles were not discussed. As mentioned in Jiang (2007), the adapting the concept of entropy is based on the neurophysiological principle that antagonist muscle activity is a weighted summation of reciprocal inhibition and muscle co-contraction (Feldman, 1993). In the proposed objective function, the efficiency criterion term addresses the reciprocal inhibition and the entropy term
addresses the co-contraction. Such an objective function is physiologically meaningful and can be applied to body joints without restriction of the DoF of the joints. The weight of the entropy term in this study is assumed to be a fixed value regardless the shoulder posture or shoulder net moment. Such assumption is inconsistent with the findings in Jiang (2007) in which the optimal weight of the entropy term could be affected by the external load level as well as the joint angular velocity. In that study, the elbow joint moment and the elbow joint angular velocity were well controlled by a dynamometer, and the results showed that a greater joint moment or a greater angular flexion angular velocity tended to lead to a greater optimal weight of the entropy term, though the optimal weights across different conditions are all in a small range. Allowing various weight of entropy term for different shoulder posture or shoulder net moment is likely to increase the model fitness as an additional flexibility is introduced into the biomechanical model. However, the physiological reason that how elbow moment and elbow angular velocity affect the weight of the entropy term remains unclear. In addition, the shoulder joint has 3 rotational DoF and the muscle wrapping mechanism of shoulder joint is different from that of elbow joint. Therefore, given the lack of knowledge regarding how the shoulder moments and posture affect the weight factor, the weight factor is assumed to be constant for all shoulder moments and shoulder posture in this study. Mathematically, introducing the entropy term into the objective function increases the predicted muscle activity level for all muscles. When the weight of entropy term is zero, the objective function degenerates to a traditional efficiency criterion. As the weight of entropy gradually increases, the entropy term results in greater predicted muscle activities. In the extreme case that the weight of entropy term is one, the solution would maximize the predicted muscle activities under the concept of information entropy. In this case, the objective function would violate the
assumption that central nervous system (CNS) attempts to minimize muscle activities to satisfy the constraints. Thus, the difference between the predicted muscle activities and the measured ones rapidly increases once the weight of the entropy term exceeds the optimal weight. In this study, both Bhattacharyya distance and concordance ratio showed that the optimal weight of entropy term is a relatively small value compared the weight of efficiency criterion term in the objective function. Therefore, the results suggest that the efficiency criterion still account for the majority for predicting muscle activities, while the entropy term contributes to address muscle co-contraction. In addition, the optimal weight of the entropy term is affected by what measurement is used to measure the predictability of the model. In this study, the optimal weight based on Bhattacharyya distances for various muscles tend to be greater than that based on concordance ratio. Specifically, compared with Bhattacharyya distances in Figure 3 and 4, concordance ratios in Figure 5 and 6 looks less smooth and have a sudden drop once the weight of the entropy terms exceed the optimal value. This is because of a specific value, namely 0.05 in this study, is used as the criterion to categorize ‘on’ and ‘off’ of a muscle. As the weight of the entropy term increases, the predicted muscle activity of all the muscles at each time instant will eventually exceed this criterion and be categorized as “on”. Considering that for each muscle in a trial the time for “on” is less than the time for “off”, the concordance ratio drops sharply once the entropy term results in the predicted muscle activities greater than 0.05. Since both 5% (Dickerson et al., 2008) and 20% (Pedersen et al., 1987) have been used in literature as the criterion for the on-off threshold of muscle activity, a sensitivity analysis was performed to understand the effect of the selection of the criterion for muscle “on” and “off” on the optimal weights of the entropy terms. Other than the 5%, three other levels (2.5%, 10%, and 20%) of maximum contraction capacity were applied. The corresponding optimal weights of the entropy
term were 0.00005, 0.009, and 0.04, respectively. The results clearly indicated that the choose of the on-off threshold will affect the optimal weights of the entropy. This is because a greater onoff threshold would require a greater weight of entropy to increase the predicted muscle activity. One of the major limitations of the proposed shoulder biomechanical model is that it is assumed that the muscle force is linearly related to the muscle activation level without considering other muscle physiology properties, such as the force-length relation. In the early stage of the model development, the force-length and force-velocity relations proposed in Lloyd and Besier (2003) and van Dieen and Kingma (2005) were included in the model. However, it was then observed that the optimization method cannot find a feasible solution for rotator cuff muscles under many external load conditions. This is probably due to that the current model does not include the additional muscle attachment points other than the origins and insertions, which artificially enlarged the effect of the force-length relation on predicted muscle forces. The other possible reason is that the optimal length used for force-length relation is from Garner and Pandy (2000), which is based on the CT-scan of a cadaver. For each participant in this study, the optimal length of muscles can be affected by between-participant variability. Therefore, the predicted deviation from the optimal length could be overestimated which results in a lowered maximum force capacity. In addition, a previous shoulder model (Dickerson et al., 2007) made the same assumption and has been validated with empirical dataset (Dickerson et al., 2008) for static and less extreme shoulder postures. Therefore, the same assumption was made in this study. However, a shoulder biomechanical model with valid muscle physiological properties would be necessary for better understanding the effect of the entropy term in the objective function, especially for the tasks with extreme shoulder postures and dynamic shoulder movement.
There are also other limitations need to be addressed. First, the anatomical validity of the model need to be further improved. Although muscle origin and insertion have been scaled by the character length of bones in the model (Hogfors et al., 1987), it remains unclear if the original coordinates for the origin and insertion is representative in general population. The movement of scapula and clavicle in the model is estimated by regression-based shoulder rhythm equations. Such estimation does not reflect the inter-participant variability of shoulder rhythm. Second, the computational efficiency need to be enhanced. Currently it takes approximately 7 seconds to reach the optimal solution for the constraints in each time frame (CPU: Intel Xeon E5-1650 3.2GHz, Memory: 16 GB, OS: Windows 8 64-bit). Such computational speed obstructs applying the model to predict the muscle activities in real-time, as well as testing the validity of the model in more shoulder postures. Third, the objective function in the current study is extended from efficiency criterion. Recent study (Nikooyan et al., 2013) has shown a novel energy-based criterion (Praagman et al., 2006)can provide a good estimate on glenohumeral joint reaction force. Whether the entropy term could contribute to energy-based criterion need to be further investigated. Fourth, previous studies (Pizzolato et al., 2015; Sartori et al., 2014)have shown that including the measured muscle activity in an EMG-informed model could provide adequate predictability on joint moment and muscle forces. Within such framework, the current objective function could be further fine-tuned by measuring the shoulder muscle activity under a wider range of shoulder motion.
Conflict of Interest Statement All authors declare that there is no proprietary, financial, professional or other personal interest of any nature or kind in any product, service or company that could be construed as influencing the position presented in the manuscript entitled, “An entropy-assisted musculoskeletal shoulder model”.
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Figure 1. A simple visualization of the proposed musculoskeletal shoulder model. The thick solid lines represent for bone elements, the thin solid lines represent muscles around the shoulder, and the dashed line is the net moment on glenohumeral joint calculated by inverse dynamics for each time instant. T8: the 8th thoracic vertebrae, C7: the 7th cervical vertebrae, IJ: incisura jugularis, SCJ: sternoclavicular joint, ACJ: acromioclavicular joint, GHJ: glenohumeral joint, TS: trigonum scapulae, AI: angulus acromialis, EJC: elbow joint center, WJC: wrist joint center. It should be noted that due to the 3-D perspectives, the 2-D distance on this figure is not to scale. The shoulder posture showed in this figure is γTH1 = 30º, βTH = -30º, and γTH2 = 0º.
Figure 2. An example demonstrating the effect of the entropy term. The solid line is the measured EMG signals of infraspinatus, the dot line is the predicted muscle activity purely based on the efficient criterion, the dash line is the predicted muscle activity purely based on the entropy criterion, and the dash-dot line is the predicted muscle activity with the weight of entropy term as 0.005. This figure shows that from time 0 to 2 second, the measured muscle activity and the predicted muscle activity with the weight of entropy term as 0.005 and 1 are all greater than the muscle “on” and “off” criterion (5% of MVC), while the efficiency criterionbased predicted muscle activity is less than the criterion. However, the predicted muscle activity with the weight of entropy term as 1 greatly overestimated the muscle activities.
Figure 3. The average Bhattacharyya distance across all tested shoulder posture and all participants when shoulder elevation is 30º. X-axis for each subplot is in logarithmic scale. Note that the x-axes from Figure 3 to Figure 6 are not in linear scale. The bar groups from left to right represent the investigated weight of the entropy term from least to most.
Figure 4. The average Bhattacharyya distance across all tested shoulder posture and all participants when shoulder elevation is 60º. X-axis for each subplot is in logarithmic scale.
Figure 5. The average concordance ratio across all tested shoulder posture and all participants when shoulder elevation is 30º. X-axis for each subplot is in logarithmic scale.
Figure 6. The average concordance ratio across all tested shoulder posture and all participants when shoulder elevation is 60º. X-axis for each subplot is in logarithmic scale.
Author short bio Xu Xu is an assistant professor in Edward P. Fitts Department of Industrial and Systems Engineering at North Carolina State University. His research interests are mainly on human factors and ergonomics engineering, occupational biomechanics, optimization-based biomechanical modelling, data mining on human motion data, and musculoskeletal injury prevention. He earned a B.S. in industrial engineering from Tsinghua University in 2004, and an M.S and Ph.D. in industrial engineering from North Carolina State University in 2006 and 2008. He also completed a postdoctoral fellowship in Department of Environmental Health at Harvard School of Public Health in 2010.
Jia-Hua Lin received Ph.D. and M.S. degrees in industrial engineering from the University of Wisconsin-Madison in 2001. Currently, he is a senior ergonomist in the Safety and Health Assessment and Research for Prevention (SHARP) Program at Washington State Department of Labor and Industries. His research includes general physical ergonomics and occupational biomechanics, particularly in the area of upper extremity physical capacities and human-machine and tool interfaces.
Raymond W. McGorry, a senior research scientist, has been with the Liberty Mutual Research Institute for Safety since 1993. He conducts laboratory and field investigations of work-related injury and illness and is a regular collaborator on ergonomic studies with other investigators. His research interests include developing work measurement instrumentation, biomechanics, exposure assessment, force measurement during hand tool use, and investigating approaches to musculoskeletal rehabilitation. Prior to joining the Research Institute, Mr. McGorry worked as a physical therapist and as a biomedical engineer. Mr. McGorry holds a B.S. in biology from Villanova University, a graduate certificate in physical therapy from Emory University, and an M.S. in
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bioengineering from Clemson University. He also completed a post-graduate fellowship in rehabilitation engineering at the Massachusetts Institute of Technology.