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Effects of rotator cuff tears on muscle moment arms: A computational study
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Journal of Biomechanics 40 (2007) 3373–3380 www.elsevier.com/locate/jbiomech www.JBiomech.com
Effects of rotator cuff tears on muscle moment arms: A computational study Corinne R. Adams, Mark A. Baldwin, Peter J. Laz, Paul J. Rullkoetter, Joseph E. Langenderfer Computational Biomechanics Laboratory, Department of Mechanical and Materials Engineering, University of Denver, Denver, CO, USA Accepted 8 May 2007
Abstract Rotator cuff tears cause morphologic changes to cuff tendons and muscles, which can alter muscle architecture and moment arm. The effects of these alterations on shoulder mechanical performance in terms of muscle force and joint strength are not well understood. The purpose of this study was to develop a three-dimensional explicit finite element model for investigating morphological changes to rotator cuff tendons following cuff tear. The subsequent objectives were to validate the model by comparing model-predicted moment arms to empirical data, and to use the model to investigate the hypothesis that rotator cuff muscle moment arms are reduced when tendons are divided along the force-bearing direction of the tendon. The model was constructed by extracting tendon, cartilage, and bone geometry from the male Visible Human data set. Infraspinatus and teres minor muscle and tendon paths were identified relative to the humerus and scapula. Kinetic and kinematic boundary conditions in the model replicated experimental protocols, which rotated the humerus from 451 internal to 451 external rotation with constant loads on the tendons. External rotation moment arms were calculated for two conditions of the cuff tendons: intact normal and divided tendon. Predicted moment arms were within the 1–99% confidence intervals of experimental data for nearly all joint angles and tendon sub-regions. In agreement with the experimental findings, when compared to the intact condition, predicted moment arms were reduced for the divided tendon condition. The results of this study provide evidence that one potential mechanism for the reduction in strength observed with cuff tear is reduction of muscle moment arms. The model provides a platform for future studies addressing mechanisms responsible for reduced muscle force and joint strength including changes to muscle length-tension operating range due to altered muscle and tendon excursions, and the effects of cuff tear size and location on moment arms and muscle forces. r 2007 Elsevier Ltd. All rights reserved. Keywords: Shoulder; Moment arm; Finite element analysis; Strength; Rotator cuff
1. Introduction Rotator cuff tendon tear causes morphologic changes to rotator cuff muscles and tendons, which can lead to functional degradation in shoulder strength, stability, and range of motion. Muscle architecture alterations associated with rotator cuff tear include: contracted muscle fascicle length and increased tendon length (Itoi et al., 1995), degeneration via fatty infiltration of the muscle fibers Corresponding author. Department of Mechanical and Materials Engineering, University of Denver, 2390 South York Street, Denver, CO 80208, USA. Tel.: +1 303 871 2700. E-mail address: [email protected] (J.E. Langenderfer).
0021-9290/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.jbiomech.2007.05.017
(Gerber et al., 2004; Goutallier et al., 1994; Nakagaki et al., 1996), muscle fiber pennation angle changes (Meyer et al., 2004), asymmetric muscle atrophy (Meyer et al., 2005; Shimizu et al., 2002), and altered muscle fiber-type composition (Barton et al., 2005). These alterations decrease the ability of muscles to generate force. Recently, division of the rotator cuff tendons in a manner similar to cuff tears has been shown to cause alterations in muscletendon excursions and reductions in muscle moment arms (Langenderfer et al., 2006a). Additionally, the alterations in muscle excursions, combined with changes in muscle fascicle length due to contracture and increased tendon lengths, may result in reduced rotator cuff muscle forces by altering the muscle length-tension operating range.
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However, the mechanisms by which these muscle architecture and moment arm changes affect clinically observed joint strength are not well understood. An improved understanding of how the morphological changes associated with cuff tear cause mechanical changes would aid in pre- and post-operative clinical decision making thereby increasing potential for restoration of normal joint strength following cuff repair. Shoulder strength following rotator cuff tear exhibits marked variability between patients: from extreme strength deficit to minimal reduction in strength (Ellman et al., 1986; Hawkins et al., 1985; Richards et al., 1994). Several factors have been associated with the strength reduction including the duration of symptoms (Ellman et al., 1986), cuff tear location (Shimizu et al., 2002), and cuff tear size (McCabe et al., 2005; Rokito et al., 1996). Previous investigations have documented a linear correlation between rotator cuff tear size and decreased shoulder strength either pre- (Gazielly et al., 1994) or post-operatively (Gore et al., 1986; Grana et al., 1994; Postacchini et al., 1992). Other studies have documented no relationship between tear size and strength (Essman et al., 1991). Reduced muscle force is correlated to atrophy, but the mechanisms by which tear size and location affect joint strength have not been well established, and no theory has been developed to standardize the effect. Two mechanisms are potentially responsible for the strength reduction with cuff tear: alterations in muscle forces and alterations in muscle moment arms. Cadaveric studies have examined how cuff tendon tear affects glenohumeral (GH) joint force (Halder et al., 2002) and abduction torque, and stability in terms of translation with simulated cuff tear (Mura et al., 2003). These studies considered the effect of the tear on muscles’ ability to generate and transmit force. The second mechanism relating moment arm alterations to reduced strength has not been previously evaluated. With this mechanism is an associated hypothesis that the differential response of shoulder strength to cuff tear is related to regional variations in muscle moment arm and muscle force generating capacity. Models for evaluating hypotheses such as this are virtually nonexistent since subjectspecific shoulder models have focused on healthy normal shoulders rather than pathological conditions such as cuff tear. Previous finite element (FE) modeling studies have analyzed joint contact pressure for normal and osteoarthritic shoulders (Buchler et al., 2002), scapular loading due to muscle forces (Gupta and Van der Helm, 2004; Lim et al., 2006), the performance of shoulder implants (Hopkins et al., 2006; Terrier et al., 2006), alterations to rotator cuff tendon stress with cuff tear (Luo et al., 1998; Sano et al., 2006; Wakabayashi et al., 2003), and capsular strain (Debski et al., 2005). Techniques for constructing models of cuff tear incorporating the mechanical changes outlined here have not been developed. Consequently, the effects of clinically observed changes in muscle and tendon morphology on mechanical factors such as muscle moment
arm and muscle force generating capacity have not been addressed with a computational model. Therefore, the goal of this study was to develop a FE model of the GH joint to investigate how rotator cuff tear results in mechanical changes to infraspinatus and teres minor tendon excursions and muscle moment arms, and to verify moment arm predictions through comparison with experimental data. In addition, the model was used to investigate the hypothesis that dividing the cuff tendon in a manner similar to cuff tear reduces cuff muscle moment arms. This is the first shoulder FE model used to analyze the effects of muscle and tendon morphologic changes similar to those encountered with cuff tear on shoulder mechanical performance in terms of muscle force and joint strength. In the future, with slight modifications, the current model can serve as a platform to investigate how cuff tear size and location affects muscle moment arms and forces. 2. Methods A three-dimensional model of the GH joint was developed in Abaqus/ Explicit 6.6–1 (Abaqus, Inc., Providence, RI). Boundary conditions were applied to replicate an experimental measurement of external rotation muscle moment arms for infraspinatus and teres minor (Langenderfer et al., 2006a) (Fig. 1). As in the experiment, moment arms were calculated with the model using the tendon excursion method for intact normal and divided tendon conditions (Fig. 2). Calculated moment arms were compared to empirically determined moment arms and used to investigate the reduction in moment arm following division of the cuff tendons. In this model, the tendon excursion method was used for determining muscle moment arms. This method uses the principle of virtual work, stating that the work performed by a muscle force over an infinitesimal tendon excursion is equal to the work done through an angle by a moment. Although this method was developed for long, fusiform, unipennate muscles, it has been applied widely to multipennate muscles by approximating muscle lines of action through one (Kuechle et al., 2000; Liu et al., 1998; Nakajima et al., 1999; Nyffeler et al., 2004) or multiple (Otis et al., 1994) muscle paths. The calculated tendon excursions and moment arms depend on the position of the tendon fibers relative to the instantaneous center of rotation. Altering either the instantaneous center of rotation, or the position of tendon fibers relative to the instantaneous center affects excursions and moment arms (Nyffeler et al., 2004). Rotator cuff tear is a potential mechanism that alters tendon position relative to the instantaneous center. Other studies have used the tendon excursion method to examine how shoulder moment arms change when the instantaneous center location is altered due to humeral head prosthesis malposition (Nyffeler et al., 2004), or when tendon transfer is performed to alter tendon insertion and position of tendon fibers relative to the instantaneous center (Liu et al., 1998; Nakajima et al., 1999). In contrast to these studies, the current study examines how alterations in tendon position in a manner similar to cuff tear affect moment arms.
2.1. Model development Model geometry was obtained from the right shoulder of the male visible human data-set (NLM, NIH, Bethesda, MD). Scapular and humeral geometry were extracted from computed tomography scans, while glenoid, humeral articular cartilage, and rotator cuff tendon geometry were extracted from cryosection photos. The scapula and humerus were modeled as rigid shell triangular elements. Glenoid and humeral cartilage was manually outlined in the cryosection photos and exported as three-dimensional surfaces using ScanIP (Simpleware Ltd.,
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Fig. 1. Experimental and finite element models of intact normal tendon for measuring infraspinatus and teres minor moment arms: (A) cadaver model and (B) finite element model.
Fig. 2. Finite element models for measuring infraspinatus and teres minor moment arms at 451 internal, neutral and 451 external rotation for intact normal tendon (A–C) and divided tendon (D–F).
Exeter, UK). The surfaces were meshed as hexahedral brick elements (80 elements for glenoid and 300 for the humeral cartilage) in HyperMesh (Altair Engineering, Troy, MI) to smooth discontinuities and minimize mesh skewness (Fig. 1B). Similar to cartilage, three-dimensional tendon volumes were originally extracted from cryosection photos and then remeshed as solid brick elements. The bursal tendon surface extracted from cryosection photos was outlined and described mathematically as a twodimensional spline, then offset by a total of 4 mm over two elements to create the three-dimensional anatomical representation of the cuff tendon using hexahedral brick elements. The 4 mm total tendon thickness was determined as an average thickness from experimental data (Langenderfer et al., 2006b) and from cryosection photo geometry. The infraspinatus tendon consisted of about 200 elements, and the teres minor tendon of about 25 elements each with an in plane element edge length of approximately 4 mm (Fig. 1B). A mesh convergence study revealed that a four-fold increase in the number of tendon elements yielded an average difference in calculated moment arms of less than 3.5%. Muscle origin and insertion sites were identified relative to scapular landmarks (Langenderfer et al., 2006a). The muscle insertions were defined by dividing the respective tendon into equal-width sub-regions and
attaching to the center of each sub-region. Muscle origins were defined along a plane at the spino-glenoid notch parallel to the glenoid and divided into corresponding equal sub-regions across the inferior–superior width of the infraspinatus fossa determined experimentally and from the cryosection photos. To attach tendons to the humerus, the lateral edge of the tendon was rigidly fixed to the humeral bone. Each tendon sub-region was attached to the scapula via a one-dimensional cylindrical connector to allow for physiologic wrapping around the humeral head and scapula. The humerus was modeled as a rigid body with assigned mass and rotary inertia (m ¼ 2467.4 g, I ¼ 394,789.8 g mm2) calculated from total body weight (Chaffin and Andersson, 1999). The glenoid and humeral cartilage surfaces were rigidly attached to the scapula and humerus, respectively, allowing for controlled movement of the cartilage with the bones. Penalty-based contact was used to define interaction between cartilage, bone, and tendons. Cartilage was modeled as a rigid body with a pressure–overclosure relationship to increase computational efficiency (Halloran et al., 2005). Cartilage-to-cartilage contact was defined by a linear pressure–overclosure relationship adapted from knee simulations (Blankevoort and Huiskes, 1996), while tendons were restricted from
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penetrating other tendons, bone, and cartilage surfaces. Tendons were represented with a linear elastic orthotropic material model (E1 ¼ 140 MPa, E2 ¼ 1 MPa, E3 ¼ 1 MPa, v ¼ 0.497). Tendon moduli were determined from literature values: E1 from the average reported value (Halder et al., 2000), and transverse moduli from the reported ratio relative to E1 (Luo et al., 1998). An average stable time increment of 6e05 s was selected automatically by Abaqus/Explicit to maintain material stability throughout the analysis. Manually selecting a 20% smaller time increment resulted in an average difference in calculated moment arms of only 2.4%. A sensitivity analysis was performed by perturbing E2 and E3 by 10%, resulting in less than 2% difference in model-predicted moment arms.
2.2. Experimentally derived boundary conditions The scapula was rigidly fixed in space and kinematic boundary conditions for internal–external rotation (I–E) (as in the experiment) were applied to the humerus to generate GH motion. Neutral I–E rotation was defined by aligning the epicondylar axis with the plane of the scapula, parallel to the experimental set-up. I–E rotation was applied at 101 of GH scapular plane abduction (Fig. 1) as shown previously to correspond to neutral humeral-thoracic abduction (Poppen and Walker, 1976). The humerus was rotated from 451 internal to 451 external rotation about an axis parallel to the humeral shaft with location defined by scapular landmarks (Veeger, 2000) (Fig. 2). Nonlinear tension-only spring elements were applied to constrain humeral inferior–superior and anterior–posterior translation, without affecting humeral orientation. These springs were added to represent the coupling constraint used experimentally, and to allow the minimal translation required for GH contact during external rotation.
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Two models were created: an intact normal tendon model (Fig. 2A–C) and a divided cuff tendon model (Fig. 2D–F). For the divided tendon, the tendons from the intact case were separated along sub-regions to the insertion on the humeral head. While applying the boundary conditions described earlier, the lengths of the connector elements were measured at increments of 2.251 rotation. Tendon excursions were calculated as the changes in lengths of the connector elements. Moment arms were calculated using the tendon excursion method by analytically differentiating second to sixth order polynomials fit to the tendon excursion-rotation angle relationship (An et al., 1984). The order of polynomial which minimized the root mean square error was selected. Moment arms were calculated for both conditions of the rotator cuff tendons. Moment arm reductions were calculated by subtracting divided tendon moment arms from intact normal moment arms. Calculated moment arms and reductions were compared to empirically determined results (Langenderfer et al., 2006a).
3. Results The FE model calculated moment arms for infraspinatus and teres minor were in agreement with moment arms determined empirically (Figs. 3 and 4). For the intact normal tendon case, calculated moment arms for all muscle sub-regions were within the 1–99% confidence interval (CI) of experimental data for the entire motion, with the exception of small differences in superior-middle (Fig. 3B)
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Fig. 3. Predicted external rotation muscle moment arms from 451 internal (45) to 451 external (45) rotation for intact normal tendon (blue dashed line) compared to experimental 1–99% confidence intervals (thick solid black lines) and 10 experimental specimens (thin solid black lines) for: (A) superior, (B) superior-middle, (C) inferior-middle, (D) inferior regions of infraspinatus, and (E) teres minor.
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and inferior infraspinatus (Fig. 3D), from 451 to 271, and from 451 to 181 rotation, respectively. Similarly, moment arm results for the divided tendon condition
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(Fig. 4) were also within the 1–99% CI of experimental data for all rotation angles, except for superior-middle infraspinatus from 451 to 221 rotation (Fig. 4B).
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Fig. 4. Predicted external rotation muscle moment arms from 451 internal (45) to 451 external (45) rotation for divided tendon (red dashed line) compared to experimental 1–99% confidence intervals (thick solid black lines) and 10 experimental specimens (thin solid black lines) for: (A) superior, (B) superior-middle, (C) inferior-middle, (D) inferior regions of infraspinatus, and (E) teres minor.
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Fig. 5. Model-predicted reduction in moment arms compared to experimental moment arm reduction (mean7S.D.) for: (A) superior, (B) superiormiddle, (C) inferior-middle, (D) inferior regions of infraspinatus, and (E) teres minor.
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Model calculated moment arms did not always match the mean experimentally measured moment arms, but agreed in magnitude and trend with moment arms measured for one or several of the experimental specimens. Average calculated moment arms with intact normal cuff tendons were 1.58, 2.03, 2.37, and 2.53 cm for superior, superior-middle, inferior-middle and inferior sub-regions of infraspinatus, respectively. Calculated teres minor moment arms were on average 2.21 cm for the intact normal tendon case. For the divided tendon case, average calculated moment arms were 1.24, 1.66, 2.04, and 2.48 cm for the superior, superior-middle, inferior-middle and inferior sub-regions of infraspinatus, respectively. For the teres minor with divided tendon condition, the average calculated moment arm was 2.07 cm. Compared to the intact condition, calculated moment arms were reduced for the divided tendon condition for nearly all tendon sub-regions and all rotation angles (Fig. 5). The model calculated moment arm reductions were within the experimentally determined 1–99% CI for all sub-regions of the infraspinatus (Fig. 5A–D). For teres minor the calculated moment arm reduction was less than 1 mm outside of the experimental bounds at 451 rotation (Fig. 5E). Average model calculated moment arm reductions across superior, superior-middle, inferior-middle and inferior sub-regions of infraspinatus were 0.32, 0.35, 0.32 and 0.08 cm, respectively. The average calculated moment arm reduction for teres minor was 0.21 cm. 4. Discussion The purpose of this study was to develop and verify an explicit three-dimensional FE model and to investigate the morphological changes and alterations in moment arms associated with rotator cuff tears, which also impact muscle force, joint strength and stability. Infraspinatus and teres minor moment arms were reduced for most joint angles and muscle sub-regions when the cuff tendons were divided to the insertion on the humeral head. Model calculated moment arms and reductions in moment arms following division of the rotator cuff tendons agreed reasonably well with experimental data. The results of this study, that moment arms are reduced when the rotator cuff is divided, have implications for understanding many complications that can arise with cuff tear. The model allows the quantification of the effects of conditions similar to cuff tears on muscle-tendon excursions and muscle moment arms. Moment arms are reduced with a divided tendon due to altered tendon morphology because the cuff tendons are less constrained and follow the most direct path between tendon origin and insertion. This path minimization results in reduced excursion for a given change in joint angle and therefore, a reduction in moment arm compared to normal tendon. The model results provide further evidence that a potential cause of the strength decrease observed following cuff tear is a reduction in muscle moment arms. An additional hypoth-
esis generated from this simulation is that changes in tendon excursion also impact muscle forces because of altered muscle length-tension operating range. However, this hypothesis has yet to be tested. Previous studies have measured rotator cuff muscle moment arms from cadaver specimens (Kuechle et al., 2000; Otis et al., 1994) and in vivo (Graichen et al., 2001; Juul-Kristensen et al., 2000). However, no studies have measured changes in muscle moment arms with rotator cuff tear. Other studies have examined the effects of pathologies similar to, or related to cuff tendon tear, on GH joint force (Halder et al., 2002) and GH abduction torque as well as GH stability in terms of translation with simulated cuff tear (Mura et al., 2003). Additionally, many prior FE shoulder models have been developed for analysis of various shoulder clinical issues (Buchler et al., 2002; Debski et al., 2005; Gupta and Van der Helm, 2004; Hopkins et al., 2006; Sano et al., 2006; Terrier et al., 2006). This is the first shoulder FE model used to analyze the effects of muscle and tendon morphologic changes similar to those encountered with cuff tear on shoulder mechanical performance in terms of muscle force and joint strength. Subject-specific shoulder models require techniques for modeling cuff tear, which will require utilizing techniques as developed here. In order to place this study in clinical context, it is important to note that cuff tears occur both along and transverse to tendon collagen fibrils with the more damaging tears frequently transverse to the tendon fibrils. A limitation of this study is that cuff tears were not simulated, but rather the tendons were divided along the force-bearing direction, in order to verify model predictions with available experimental data. The verified model could be used to simulate massive cuff tears involving tears transverse to the tendon collagen fibrils and confined to one region of the cuff. It is important to recognize that the model was developed from geometry of a single specimen and that the material properties are derived from a limited amount of data available in the literature. Therefore, because the specimen’s anatomy differed from the experimental specimens, the predicted moment arms differed slightly from measured data at some rotation angles and cuff conditions (Figs. 2 and 3). Model calculated moment arms were not always in strong agreement with the mean experimentally measured moment arms, but generally agreed in magnitude and trend with moment arms measured for one or several of the experimental specimens. Reductions in calculated infraspinatus moment arms closely matched the experimentally determined 1–99% confidence intervals (Fig. 4). Teres minor moment arm reductions were within experimental 1–99% confidence intervals, except at 451 rotation where predicted results were only slightly larger than experimental results (Fig. 4E). In the analysis of model results, moment arm reduction provides the most insightful measure as it reduces the effect of inter-specimen dependency and allows for a meaningful comparison of model
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and experimental results. In spite of some limitations, the model can be used in a heuristic fashion to evaluate certain specific clinical issues more efficiently than experimentation, such as impacts of isolated tears in different cuff regions, including bursal and articular tears, and the efficacy of partial and total cuff repairs, such as tendon transfers, in restoring normal function. From this initial study, hypotheses can be generated which can later be rigorously addressed with an empirical approach. In closing, the results of this study have important implications for understanding shoulder strength in rotator cuff tear patients and following surgery to correct cuff deficiency. Surgical procedures which restore normal moment arms are most likely to restore normal strength. An additional hypothesis enabled by the model is that alterations in tendon and muscle excursions associated with cuff tear can result in altered muscle length-tension dependency and are partly responsible for reduced force generating capacity. Subsequent modeling and experimentation can address this and related hypotheses. With slight alterations, this model can be used to parametrically investigate the effects of tear size and tear location on muscle moment arms and force generating capacity. Conflict of interest statement None of the authors have any conflicts of interest to disclose. Acknowledgment Financial support was provided by the University of Denver Partners in Scholarship (CRA). References An, K.N., Takahashi, K., Harrigan, T.P., Chao, E.Y., 1984. Determination of muscle orientations and moment arms. Journal of Biomechanical Engineering 106, 280–282. Barton, E.R., Gimbel, J.A., G.R., W., Soslowsky, L.J., 2005. Rat supraspinatus muscle atrophy after tendon detachment. Journal of Orthopaedic Research 23, 259–265. Blankevoort, L., Huiskes, R., 1996. Validation of a three-dimensional model of the knee. Journal of Biomechanics 29, 953–961. Buchler, P., Ramaniraka, N.A., Rakotomanana, L.R., Iannotti, J.P., 2002. A finite element model of the shoulder: application to the comparison of normal and osteoarthritic joints. Clinical Biomechanics 17, 630–639. Chaffin, D.B., Andersson, G.B.J., 1999. Anthropometry in occupational biomechanics. In: Occupational Biomechanics, third ed. Wiley, New York. Debski, R.E., Weiss, J.A., Newman, W.J., et al., 2005. Stress and strain in the anterior band of the inferior glenohumeral ligament during a simulated clinical examination. Journal of Shoulder and Elbow Surgery 14, 24S–31S. Ellman, H., Hanker, G., Bayer, M., 1986. Repair of the rotator cuff: endresult study of factors influencing reconstruction. The Journal of Bone and Joint Surgery 68-A, 1136–1144. Essman, J.A., Bell, R.H., Askew, M., 1991. Full-thickness rotator cuff tear. An analysis of results. Clinical Orthopaedics and Related Research 265, 170–177.
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Meyer, D.C., Hoppeler, H., von Rechenberg, B., Gerber, C., 2004. A pathomechanical concept explains muscle loss and fatty changes following surgical tendon release. Journal of Orthopaedic Research 22, 1004–1007. Meyer, D.C., Pirkl, C., Pfirrmann, M.Z., Gerber, C., 2005. Asymmetric atrophy of the supraspinatus muscle following tendon tear. Journal of Orthopaedic Research 23, 254–258. Mura, N., O’Driscoll, S.W., Zobitz, M.E., et al., 2003. The effect of infraspinatus disruption on glenohumeral torque and superior migration of the humeral head: a biomechanical study. Journal of Shoulder and Elbow Surgery 12, 179–184. Nakagaki, K., Ozaki, J., Tomita, Y., Tamai, S., 1996. Fatty degeneration in the supraspinatus muscle after rotator cuff tear. Journal of Shoulder and Elbow Surgery 5, 194–200. Nakajima, T., Liu, J., Hughes, R.E., et al., 1999. Abduction moment arm of transposed subscapularis tendon. Clinical Biomechanics 14, 265–270. Nyffeler, R.W., Sheikh, R., Jacob, H.A., Gerber, C., 2004. Influence of humeral prosthesis height on biomechanics of glenohumeral abduction. An in vitro study. Journal of Bone and Joint Surgery 86-A, 575–580. Otis, J.C., Jiang, C.-C., Wickiewicz, T.L., et al., 1994. Changes in the moment arms of the rotator cuff and deltoid muscles with abduction and rotation. The Journal of Bone and Joint Surgery 76-A, 667–676. Poppen, N.K., Walker, P.S., 1976. Normal and abnormal motion of the shoulder. The Journal of Bone and Joint Surgery 58-A, 195–201.
Postacchini, F., Perugia, D., Rampoldi, M., 1992. Rotator cuff tears. Results of surgical repair. Italian Journal of Orthopaedic Traumatology 18, 173–188. Richards, R.R., An, K.-N., Bigliani, L.U., et al., 1994. A standardized method for the assessment of shoulder function. Journal of Shoulder and Elbow Surgery 3, 347–352. Rokito, A.S., Zuckerman, J.D., Gallagher, M.A., Cuomo, F., 1996. Strength after surgical repair of the rotator cuff. Journal of Shoulder and Elbow Surgery 5, 12–17. Sano, H., Wakabayashi, I., Itoi, E., 2006. Stress distribution in the supraspinatus tendon with partial thickness tears: an analysis using two-dimensional finite element model. Journal of Shoulder and Elbow Surgery 15, 100–105. Shimizu, T., Itoi, E., Minagawa, H., et al., 2002. Atrophy of the rotator cuff muscles and site of cuff tears. Acta Orthopaedica Scandinavica 73, 40–43. Terrier, A., Bu¨chler, P., A., F., 2006. Influence of glenohumeral conformity on glenoid stresses after total shoulder arthroplasty. Journal of Shoulder and Elbow Surgery 15, 515–520. Veeger, H.E.J., 2000. The position of the rotation center of the glenohumeral joint. Journal of Biomechanics 33, 1711–1715. Wakabayashi, I., Itoi, E., Sano, H., et al., 2003. Mechanical environment of the supraspinatus tendon: a two-dimensional finite element model analysis. Journal of Shoulder and Elbow Surgery 12, 612–617.
Journal of Biomechanics 40 (2007) 3373–3380 www.elsevier.com/locate/jbiomech www.JBiomech.com
Effects of rotator cuff tears on muscle moment arms: A computational study Corinne R. Adams, Mark A. Baldwin, Peter J. Laz, Paul J. Rullkoetter, Joseph E. Langenderfer Computational Biomechanics Laboratory, Department of Mechanical and Materials Engineering, University of Denver, Denver, CO, USA Accepted 8 May 2007
Abstract Rotator cuff tears cause morphologic changes to cuff tendons and muscles, which can alter muscle architecture and moment arm. The effects of these alterations on shoulder mechanical performance in terms of muscle force and joint strength are not well understood. The purpose of this study was to develop a three-dimensional explicit finite element model for investigating morphological changes to rotator cuff tendons following cuff tear. The subsequent objectives were to validate the model by comparing model-predicted moment arms to empirical data, and to use the model to investigate the hypothesis that rotator cuff muscle moment arms are reduced when tendons are divided along the force-bearing direction of the tendon. The model was constructed by extracting tendon, cartilage, and bone geometry from the male Visible Human data set. Infraspinatus and teres minor muscle and tendon paths were identified relative to the humerus and scapula. Kinetic and kinematic boundary conditions in the model replicated experimental protocols, which rotated the humerus from 451 internal to 451 external rotation with constant loads on the tendons. External rotation moment arms were calculated for two conditions of the cuff tendons: intact normal and divided tendon. Predicted moment arms were within the 1–99% confidence intervals of experimental data for nearly all joint angles and tendon sub-regions. In agreement with the experimental findings, when compared to the intact condition, predicted moment arms were reduced for the divided tendon condition. The results of this study provide evidence that one potential mechanism for the reduction in strength observed with cuff tear is reduction of muscle moment arms. The model provides a platform for future studies addressing mechanisms responsible for reduced muscle force and joint strength including changes to muscle length-tension operating range due to altered muscle and tendon excursions, and the effects of cuff tear size and location on moment arms and muscle forces. r 2007 Elsevier Ltd. All rights reserved. Keywords: Shoulder; Moment arm; Finite element analysis; Strength; Rotator cuff
1. Introduction Rotator cuff tendon tear causes morphologic changes to rotator cuff muscles and tendons, which can lead to functional degradation in shoulder strength, stability, and range of motion. Muscle architecture alterations associated with rotator cuff tear include: contracted muscle fascicle length and increased tendon length (Itoi et al., 1995), degeneration via fatty infiltration of the muscle fibers Corresponding author. Department of Mechanical and Materials Engineering, University of Denver, 2390 South York Street, Denver, CO 80208, USA. Tel.: +1 303 871 2700. E-mail address: [email protected] (J.E. Langenderfer).
0021-9290/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.jbiomech.2007.05.017
(Gerber et al., 2004; Goutallier et al., 1994; Nakagaki et al., 1996), muscle fiber pennation angle changes (Meyer et al., 2004), asymmetric muscle atrophy (Meyer et al., 2005; Shimizu et al., 2002), and altered muscle fiber-type composition (Barton et al., 2005). These alterations decrease the ability of muscles to generate force. Recently, division of the rotator cuff tendons in a manner similar to cuff tears has been shown to cause alterations in muscletendon excursions and reductions in muscle moment arms (Langenderfer et al., 2006a). Additionally, the alterations in muscle excursions, combined with changes in muscle fascicle length due to contracture and increased tendon lengths, may result in reduced rotator cuff muscle forces by altering the muscle length-tension operating range.
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However, the mechanisms by which these muscle architecture and moment arm changes affect clinically observed joint strength are not well understood. An improved understanding of how the morphological changes associated with cuff tear cause mechanical changes would aid in pre- and post-operative clinical decision making thereby increasing potential for restoration of normal joint strength following cuff repair. Shoulder strength following rotator cuff tear exhibits marked variability between patients: from extreme strength deficit to minimal reduction in strength (Ellman et al., 1986; Hawkins et al., 1985; Richards et al., 1994). Several factors have been associated with the strength reduction including the duration of symptoms (Ellman et al., 1986), cuff tear location (Shimizu et al., 2002), and cuff tear size (McCabe et al., 2005; Rokito et al., 1996). Previous investigations have documented a linear correlation between rotator cuff tear size and decreased shoulder strength either pre- (Gazielly et al., 1994) or post-operatively (Gore et al., 1986; Grana et al., 1994; Postacchini et al., 1992). Other studies have documented no relationship between tear size and strength (Essman et al., 1991). Reduced muscle force is correlated to atrophy, but the mechanisms by which tear size and location affect joint strength have not been well established, and no theory has been developed to standardize the effect. Two mechanisms are potentially responsible for the strength reduction with cuff tear: alterations in muscle forces and alterations in muscle moment arms. Cadaveric studies have examined how cuff tendon tear affects glenohumeral (GH) joint force (Halder et al., 2002) and abduction torque, and stability in terms of translation with simulated cuff tear (Mura et al., 2003). These studies considered the effect of the tear on muscles’ ability to generate and transmit force. The second mechanism relating moment arm alterations to reduced strength has not been previously evaluated. With this mechanism is an associated hypothesis that the differential response of shoulder strength to cuff tear is related to regional variations in muscle moment arm and muscle force generating capacity. Models for evaluating hypotheses such as this are virtually nonexistent since subjectspecific shoulder models have focused on healthy normal shoulders rather than pathological conditions such as cuff tear. Previous finite element (FE) modeling studies have analyzed joint contact pressure for normal and osteoarthritic shoulders (Buchler et al., 2002), scapular loading due to muscle forces (Gupta and Van der Helm, 2004; Lim et al., 2006), the performance of shoulder implants (Hopkins et al., 2006; Terrier et al., 2006), alterations to rotator cuff tendon stress with cuff tear (Luo et al., 1998; Sano et al., 2006; Wakabayashi et al., 2003), and capsular strain (Debski et al., 2005). Techniques for constructing models of cuff tear incorporating the mechanical changes outlined here have not been developed. Consequently, the effects of clinically observed changes in muscle and tendon morphology on mechanical factors such as muscle moment
arm and muscle force generating capacity have not been addressed with a computational model. Therefore, the goal of this study was to develop a FE model of the GH joint to investigate how rotator cuff tear results in mechanical changes to infraspinatus and teres minor tendon excursions and muscle moment arms, and to verify moment arm predictions through comparison with experimental data. In addition, the model was used to investigate the hypothesis that dividing the cuff tendon in a manner similar to cuff tear reduces cuff muscle moment arms. This is the first shoulder FE model used to analyze the effects of muscle and tendon morphologic changes similar to those encountered with cuff tear on shoulder mechanical performance in terms of muscle force and joint strength. In the future, with slight modifications, the current model can serve as a platform to investigate how cuff tear size and location affects muscle moment arms and forces. 2. Methods A three-dimensional model of the GH joint was developed in Abaqus/ Explicit 6.6–1 (Abaqus, Inc., Providence, RI). Boundary conditions were applied to replicate an experimental measurement of external rotation muscle moment arms for infraspinatus and teres minor (Langenderfer et al., 2006a) (Fig. 1). As in the experiment, moment arms were calculated with the model using the tendon excursion method for intact normal and divided tendon conditions (Fig. 2). Calculated moment arms were compared to empirically determined moment arms and used to investigate the reduction in moment arm following division of the cuff tendons. In this model, the tendon excursion method was used for determining muscle moment arms. This method uses the principle of virtual work, stating that the work performed by a muscle force over an infinitesimal tendon excursion is equal to the work done through an angle by a moment. Although this method was developed for long, fusiform, unipennate muscles, it has been applied widely to multipennate muscles by approximating muscle lines of action through one (Kuechle et al., 2000; Liu et al., 1998; Nakajima et al., 1999; Nyffeler et al., 2004) or multiple (Otis et al., 1994) muscle paths. The calculated tendon excursions and moment arms depend on the position of the tendon fibers relative to the instantaneous center of rotation. Altering either the instantaneous center of rotation, or the position of tendon fibers relative to the instantaneous center affects excursions and moment arms (Nyffeler et al., 2004). Rotator cuff tear is a potential mechanism that alters tendon position relative to the instantaneous center. Other studies have used the tendon excursion method to examine how shoulder moment arms change when the instantaneous center location is altered due to humeral head prosthesis malposition (Nyffeler et al., 2004), or when tendon transfer is performed to alter tendon insertion and position of tendon fibers relative to the instantaneous center (Liu et al., 1998; Nakajima et al., 1999). In contrast to these studies, the current study examines how alterations in tendon position in a manner similar to cuff tear affect moment arms.
2.1. Model development Model geometry was obtained from the right shoulder of the male visible human data-set (NLM, NIH, Bethesda, MD). Scapular and humeral geometry were extracted from computed tomography scans, while glenoid, humeral articular cartilage, and rotator cuff tendon geometry were extracted from cryosection photos. The scapula and humerus were modeled as rigid shell triangular elements. Glenoid and humeral cartilage was manually outlined in the cryosection photos and exported as three-dimensional surfaces using ScanIP (Simpleware Ltd.,
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Fig. 1. Experimental and finite element models of intact normal tendon for measuring infraspinatus and teres minor moment arms: (A) cadaver model and (B) finite element model.
Fig. 2. Finite element models for measuring infraspinatus and teres minor moment arms at 451 internal, neutral and 451 external rotation for intact normal tendon (A–C) and divided tendon (D–F).
Exeter, UK). The surfaces were meshed as hexahedral brick elements (80 elements for glenoid and 300 for the humeral cartilage) in HyperMesh (Altair Engineering, Troy, MI) to smooth discontinuities and minimize mesh skewness (Fig. 1B). Similar to cartilage, three-dimensional tendon volumes were originally extracted from cryosection photos and then remeshed as solid brick elements. The bursal tendon surface extracted from cryosection photos was outlined and described mathematically as a twodimensional spline, then offset by a total of 4 mm over two elements to create the three-dimensional anatomical representation of the cuff tendon using hexahedral brick elements. The 4 mm total tendon thickness was determined as an average thickness from experimental data (Langenderfer et al., 2006b) and from cryosection photo geometry. The infraspinatus tendon consisted of about 200 elements, and the teres minor tendon of about 25 elements each with an in plane element edge length of approximately 4 mm (Fig. 1B). A mesh convergence study revealed that a four-fold increase in the number of tendon elements yielded an average difference in calculated moment arms of less than 3.5%. Muscle origin and insertion sites were identified relative to scapular landmarks (Langenderfer et al., 2006a). The muscle insertions were defined by dividing the respective tendon into equal-width sub-regions and
attaching to the center of each sub-region. Muscle origins were defined along a plane at the spino-glenoid notch parallel to the glenoid and divided into corresponding equal sub-regions across the inferior–superior width of the infraspinatus fossa determined experimentally and from the cryosection photos. To attach tendons to the humerus, the lateral edge of the tendon was rigidly fixed to the humeral bone. Each tendon sub-region was attached to the scapula via a one-dimensional cylindrical connector to allow for physiologic wrapping around the humeral head and scapula. The humerus was modeled as a rigid body with assigned mass and rotary inertia (m ¼ 2467.4 g, I ¼ 394,789.8 g mm2) calculated from total body weight (Chaffin and Andersson, 1999). The glenoid and humeral cartilage surfaces were rigidly attached to the scapula and humerus, respectively, allowing for controlled movement of the cartilage with the bones. Penalty-based contact was used to define interaction between cartilage, bone, and tendons. Cartilage was modeled as a rigid body with a pressure–overclosure relationship to increase computational efficiency (Halloran et al., 2005). Cartilage-to-cartilage contact was defined by a linear pressure–overclosure relationship adapted from knee simulations (Blankevoort and Huiskes, 1996), while tendons were restricted from
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penetrating other tendons, bone, and cartilage surfaces. Tendons were represented with a linear elastic orthotropic material model (E1 ¼ 140 MPa, E2 ¼ 1 MPa, E3 ¼ 1 MPa, v ¼ 0.497). Tendon moduli were determined from literature values: E1 from the average reported value (Halder et al., 2000), and transverse moduli from the reported ratio relative to E1 (Luo et al., 1998). An average stable time increment of 6e05 s was selected automatically by Abaqus/Explicit to maintain material stability throughout the analysis. Manually selecting a 20% smaller time increment resulted in an average difference in calculated moment arms of only 2.4%. A sensitivity analysis was performed by perturbing E2 and E3 by 10%, resulting in less than 2% difference in model-predicted moment arms.
2.2. Experimentally derived boundary conditions The scapula was rigidly fixed in space and kinematic boundary conditions for internal–external rotation (I–E) (as in the experiment) were applied to the humerus to generate GH motion. Neutral I–E rotation was defined by aligning the epicondylar axis with the plane of the scapula, parallel to the experimental set-up. I–E rotation was applied at 101 of GH scapular plane abduction (Fig. 1) as shown previously to correspond to neutral humeral-thoracic abduction (Poppen and Walker, 1976). The humerus was rotated from 451 internal to 451 external rotation about an axis parallel to the humeral shaft with location defined by scapular landmarks (Veeger, 2000) (Fig. 2). Nonlinear tension-only spring elements were applied to constrain humeral inferior–superior and anterior–posterior translation, without affecting humeral orientation. These springs were added to represent the coupling constraint used experimentally, and to allow the minimal translation required for GH contact during external rotation.
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Two models were created: an intact normal tendon model (Fig. 2A–C) and a divided cuff tendon model (Fig. 2D–F). For the divided tendon, the tendons from the intact case were separated along sub-regions to the insertion on the humeral head. While applying the boundary conditions described earlier, the lengths of the connector elements were measured at increments of 2.251 rotation. Tendon excursions were calculated as the changes in lengths of the connector elements. Moment arms were calculated using the tendon excursion method by analytically differentiating second to sixth order polynomials fit to the tendon excursion-rotation angle relationship (An et al., 1984). The order of polynomial which minimized the root mean square error was selected. Moment arms were calculated for both conditions of the rotator cuff tendons. Moment arm reductions were calculated by subtracting divided tendon moment arms from intact normal moment arms. Calculated moment arms and reductions were compared to empirically determined results (Langenderfer et al., 2006a).
3. Results The FE model calculated moment arms for infraspinatus and teres minor were in agreement with moment arms determined empirically (Figs. 3 and 4). For the intact normal tendon case, calculated moment arms for all muscle sub-regions were within the 1–99% confidence interval (CI) of experimental data for the entire motion, with the exception of small differences in superior-middle (Fig. 3B)
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Fig. 3. Predicted external rotation muscle moment arms from 451 internal (45) to 451 external (45) rotation for intact normal tendon (blue dashed line) compared to experimental 1–99% confidence intervals (thick solid black lines) and 10 experimental specimens (thin solid black lines) for: (A) superior, (B) superior-middle, (C) inferior-middle, (D) inferior regions of infraspinatus, and (E) teres minor.
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and inferior infraspinatus (Fig. 3D), from 451 to 271, and from 451 to 181 rotation, respectively. Similarly, moment arm results for the divided tendon condition
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(Fig. 4) were also within the 1–99% CI of experimental data for all rotation angles, except for superior-middle infraspinatus from 451 to 221 rotation (Fig. 4B).
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Fig. 4. Predicted external rotation muscle moment arms from 451 internal (45) to 451 external (45) rotation for divided tendon (red dashed line) compared to experimental 1–99% confidence intervals (thick solid black lines) and 10 experimental specimens (thin solid black lines) for: (A) superior, (B) superior-middle, (C) inferior-middle, (D) inferior regions of infraspinatus, and (E) teres minor.
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Fig. 5. Model-predicted reduction in moment arms compared to experimental moment arm reduction (mean7S.D.) for: (A) superior, (B) superiormiddle, (C) inferior-middle, (D) inferior regions of infraspinatus, and (E) teres minor.
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Model calculated moment arms did not always match the mean experimentally measured moment arms, but agreed in magnitude and trend with moment arms measured for one or several of the experimental specimens. Average calculated moment arms with intact normal cuff tendons were 1.58, 2.03, 2.37, and 2.53 cm for superior, superior-middle, inferior-middle and inferior sub-regions of infraspinatus, respectively. Calculated teres minor moment arms were on average 2.21 cm for the intact normal tendon case. For the divided tendon case, average calculated moment arms were 1.24, 1.66, 2.04, and 2.48 cm for the superior, superior-middle, inferior-middle and inferior sub-regions of infraspinatus, respectively. For the teres minor with divided tendon condition, the average calculated moment arm was 2.07 cm. Compared to the intact condition, calculated moment arms were reduced for the divided tendon condition for nearly all tendon sub-regions and all rotation angles (Fig. 5). The model calculated moment arm reductions were within the experimentally determined 1–99% CI for all sub-regions of the infraspinatus (Fig. 5A–D). For teres minor the calculated moment arm reduction was less than 1 mm outside of the experimental bounds at 451 rotation (Fig. 5E). Average model calculated moment arm reductions across superior, superior-middle, inferior-middle and inferior sub-regions of infraspinatus were 0.32, 0.35, 0.32 and 0.08 cm, respectively. The average calculated moment arm reduction for teres minor was 0.21 cm. 4. Discussion The purpose of this study was to develop and verify an explicit three-dimensional FE model and to investigate the morphological changes and alterations in moment arms associated with rotator cuff tears, which also impact muscle force, joint strength and stability. Infraspinatus and teres minor moment arms were reduced for most joint angles and muscle sub-regions when the cuff tendons were divided to the insertion on the humeral head. Model calculated moment arms and reductions in moment arms following division of the rotator cuff tendons agreed reasonably well with experimental data. The results of this study, that moment arms are reduced when the rotator cuff is divided, have implications for understanding many complications that can arise with cuff tear. The model allows the quantification of the effects of conditions similar to cuff tears on muscle-tendon excursions and muscle moment arms. Moment arms are reduced with a divided tendon due to altered tendon morphology because the cuff tendons are less constrained and follow the most direct path between tendon origin and insertion. This path minimization results in reduced excursion for a given change in joint angle and therefore, a reduction in moment arm compared to normal tendon. The model results provide further evidence that a potential cause of the strength decrease observed following cuff tear is a reduction in muscle moment arms. An additional hypoth-
esis generated from this simulation is that changes in tendon excursion also impact muscle forces because of altered muscle length-tension operating range. However, this hypothesis has yet to be tested. Previous studies have measured rotator cuff muscle moment arms from cadaver specimens (Kuechle et al., 2000; Otis et al., 1994) and in vivo (Graichen et al., 2001; Juul-Kristensen et al., 2000). However, no studies have measured changes in muscle moment arms with rotator cuff tear. Other studies have examined the effects of pathologies similar to, or related to cuff tendon tear, on GH joint force (Halder et al., 2002) and GH abduction torque as well as GH stability in terms of translation with simulated cuff tear (Mura et al., 2003). Additionally, many prior FE shoulder models have been developed for analysis of various shoulder clinical issues (Buchler et al., 2002; Debski et al., 2005; Gupta and Van der Helm, 2004; Hopkins et al., 2006; Sano et al., 2006; Terrier et al., 2006). This is the first shoulder FE model used to analyze the effects of muscle and tendon morphologic changes similar to those encountered with cuff tear on shoulder mechanical performance in terms of muscle force and joint strength. Subject-specific shoulder models require techniques for modeling cuff tear, which will require utilizing techniques as developed here. In order to place this study in clinical context, it is important to note that cuff tears occur both along and transverse to tendon collagen fibrils with the more damaging tears frequently transverse to the tendon fibrils. A limitation of this study is that cuff tears were not simulated, but rather the tendons were divided along the force-bearing direction, in order to verify model predictions with available experimental data. The verified model could be used to simulate massive cuff tears involving tears transverse to the tendon collagen fibrils and confined to one region of the cuff. It is important to recognize that the model was developed from geometry of a single specimen and that the material properties are derived from a limited amount of data available in the literature. Therefore, because the specimen’s anatomy differed from the experimental specimens, the predicted moment arms differed slightly from measured data at some rotation angles and cuff conditions (Figs. 2 and 3). Model calculated moment arms were not always in strong agreement with the mean experimentally measured moment arms, but generally agreed in magnitude and trend with moment arms measured for one or several of the experimental specimens. Reductions in calculated infraspinatus moment arms closely matched the experimentally determined 1–99% confidence intervals (Fig. 4). Teres minor moment arm reductions were within experimental 1–99% confidence intervals, except at 451 rotation where predicted results were only slightly larger than experimental results (Fig. 4E). In the analysis of model results, moment arm reduction provides the most insightful measure as it reduces the effect of inter-specimen dependency and allows for a meaningful comparison of model
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and experimental results. In spite of some limitations, the model can be used in a heuristic fashion to evaluate certain specific clinical issues more efficiently than experimentation, such as impacts of isolated tears in different cuff regions, including bursal and articular tears, and the efficacy of partial and total cuff repairs, such as tendon transfers, in restoring normal function. From this initial study, hypotheses can be generated which can later be rigorously addressed with an empirical approach. In closing, the results of this study have important implications for understanding shoulder strength in rotator cuff tear patients and following surgery to correct cuff deficiency. Surgical procedures which restore normal moment arms are most likely to restore normal strength. An additional hypothesis enabled by the model is that alterations in tendon and muscle excursions associated with cuff tear can result in altered muscle length-tension dependency and are partly responsible for reduced force generating capacity. Subsequent modeling and experimentation can address this and related hypotheses. With slight alterations, this model can be used to parametrically investigate the effects of tear size and tear location on muscle moment arms and force generating capacity. Conflict of interest statement None of the authors have any conflicts of interest to disclose. Acknowledgment Financial support was provided by the University of Denver Partners in Scholarship (CRA). References An, K.N., Takahashi, K., Harrigan, T.P., Chao, E.Y., 1984. Determination of muscle orientations and moment arms. Journal of Biomechanical Engineering 106, 280–282. Barton, E.R., Gimbel, J.A., G.R., W., Soslowsky, L.J., 2005. Rat supraspinatus muscle atrophy after tendon detachment. Journal of Orthopaedic Research 23, 259–265. Blankevoort, L., Huiskes, R., 1996. Validation of a three-dimensional model of the knee. Journal of Biomechanics 29, 953–961. Buchler, P., Ramaniraka, N.A., Rakotomanana, L.R., Iannotti, J.P., 2002. A finite element model of the shoulder: application to the comparison of normal and osteoarthritic joints. Clinical Biomechanics 17, 630–639. Chaffin, D.B., Andersson, G.B.J., 1999. Anthropometry in occupational biomechanics. In: Occupational Biomechanics, third ed. Wiley, New York. Debski, R.E., Weiss, J.A., Newman, W.J., et al., 2005. Stress and strain in the anterior band of the inferior glenohumeral ligament during a simulated clinical examination. Journal of Shoulder and Elbow Surgery 14, 24S–31S. Ellman, H., Hanker, G., Bayer, M., 1986. Repair of the rotator cuff: endresult study of factors influencing reconstruction. The Journal of Bone and Joint Surgery 68-A, 1136–1144. Essman, J.A., Bell, R.H., Askew, M., 1991. Full-thickness rotator cuff tear. An analysis of results. Clinical Orthopaedics and Related Research 265, 170–177.
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