Comparison of model-predicted and measured moment arms for
the rotator cuff muscles
Christopher J. Gatti, BSE
a
, Clark Dickerson, PhD
c
, Edward K. Chadwick, PhD
d
, Amy G. Mell,
BSE
b
, and Richard E. Hughes, PhD
a,b
a Department of Biomedical Engineering, University of Michigan
b Department of Orthopaedic Surgery, University of Michigan
c Department of Kinesiology, University of Waterloo
d Department of Biomedical Engineering, Case Western Reserve University
Abstract
Background— The ability of mathematical models of the shoulder to accurately replicate
physiological muscle moment arms is unknown. The purpose of this study was to compare model-
predicted and experimentally measured moment arms for the rotator cuff muscles during arm
elevation.
Methods— Moment arms obtained from 6 mathematical models and 7 experimental studies were
compared for the supraspinatus, infraspinatus, teres minor, and subscapularis for elevation in the
scapular plane.
Results— All of the included models generated moment arms that generally fell within the range
of experimentally measured data.
Interpretation— The quantitative agreement between model-predicted and experimentally
measured moment arms supports the use of the included models for biomechanical shoulder analyses.
Keywords
shoulder; moment arms; computational model
INTRODUCTION
Mathematical models of shoulder and upper extremity muscles are useful for many
applications, including analysis of tendon transfers (Magermans et al., 2004), rehabilitation
(Labriola et al., 2005), finite element modeling of prosthesis components (Stone et al., 1999),
and ergonomics (Laursen et al., 2003). EMG-driven (Laursen et al., 1998) and optimization-
based models (Hogfors et al., 1987,1991,1995;van der Helm, 1994a,1994b) have been
developed for estimating muscle forces around the shoulder. A critical component of
optimization-based methods is the accurate determination of muscle moment arms as muscle
force predictions have been shown to be highly sensitive to these parameters (Raikova and
Prilutsky, 2001).
Contact information: Richard E. Hughes, PhD, MedSport, University of Michigan, 24 Frank Lloyd Wright Dr, POB 391, Ann Arbor,
MI 48106-0391, Phone 734-930-7388, FAX 734-930-7379, e-mail: rehughes@umich.edu
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Author Manuscript
Clin Biomech (Bristol, Avon). Author manuscript; available in PMC 2008 July 1.
Published in final edited form as:
Clin Biomech (Bristol, Avon). 2007 July ; 22(6): 639–644.
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There have been several experimental investigations of elevation moment arms for the rotator
cuff muscles (Graichen et al., 2001;Howell et al., 1986;Kuechle et al., 1997;Liu et al.,
1997;Nyffeler et al., 2004;Otis et al., 1994;Poppen and Walker, 1978), as these muscles are
critical for normal shoulder function. Although some models have used empirical
measurements of muscle moment arms (Hughes and An, 1996,1997,1999;Langenderfer et
al., 2006;Poppen and Walker, 1978), many modern shoulder models apply mathematical
representations of musculoskeletal geometry (Dickerson et al., 2005,2006;van der Helm,
1994a,1994b). One advantage of this approach is that the models can analyze arm positions
other than those for which moment arm data were experimentally collected. However, the
resulting accuracy of the models to predict muscle moment arms is unclear.
The objective of this paper was to compare model predicted moment arms of the rotator cuff
muscles to experimentally measured moment arms reported in the literature. Our comparison
was limited to elevation in the scapular plane because of the availability of experimental data.
METHODS
A structured literature review process, which is standard practice when conducting a meta-
analysis (Petitti, 2000), was followed to identify published experimental data on rotator cuff
muscle moment arms. Four inclusion criteria were defined: (1) experimental measurement of
moment arms of either the supraspinatus, infraspinatus, teres minor, or subscapularis, muscles
in vivo or in cadavera; (2) moment arm data presented for abduction in the plane of the scapula;
(3) data presented in text, tabular, or graphical format; and (4) clearly described experimental
method. A protocol was developed for selecting papers, which included searching Medline and
PubMed using keywords rotator cuff, shoulder, moment arm, lever arm, mechanical advantage,
and muscle line of action. Book chapters were also consulted for references to primary sources
of moment arm data. References in all documents were scrutinized for additional data sources.
Forty-two papers were identified and each full paper was checked for inclusion criteria by two
authors (AGM and CJG). Ten papers met the inclusion criteria; however, only seven were used
because some data sets from independent studies were published in multiple manuscripts.
The moment arms included in the comparison were for arm elevation in the scapular plane at
glenohumeral angles (GHAs) of 30° and 60° with 0° of humeral axial rotation for the
supraspinatus, infraspinatus, teres minor, and the subscapularis. Experimentally measured
moment arm data were obtained from studies by Graichen et al. (Graichen et al., 2001), Howell
et al. (Howell et al., 1986), Kuechle et al. (Kuechle et al., 1997), Liu et al. (Liu et al., 1997),
Nyffeler et al. (Nyffeler et al., 2004), Otis et al. (Otis et al., 1994), and Poppen and Walker
(Poppen and Walker, 1978). The methods used in these studies are presented in Table 1. Model-
predicted moment arm data were obtained from the use of the Dickerson model (Dickerson et
al, 2005,2006), Holzbaur model (Holzbaur et al., 2005), and Delft Shoulder and Elbow Model
(DSEM) (van der Helm, 1994a,1994b); these models are available to the biomechanics
community. It should be noted that the Dickerson model is an implementation of the model
developed by Hogfors and co-workers (Hogfors et al., 1987,1991,1995). For the other included
models, moment arm data were extracted from published or dissertation data from the Favre
model (Favre et al., 2005), Garner model (Garner and Pandy, 2001), and Newcastle model
(Charlton, 2003); the availability of these models is not known.
Moment arms were extracted from published figures for the studies performed by Graichen et
al., Kuechle et al., Liu et al., Nyffeler et al., Otis et al., and Poppen and Walker as well as for
the Garner and Newcastle models. For the study by Howell et al. and for the Favre model,
moment arms were taken from the published article text and tables, respectively.
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Graichen et al., Howell et al., and Poppen and Walker reported moment arms with respect to
arm elevation angle, whereas the current study compares moment arms with respect to GHA.
The arm positions of these studies were converted using a 2:1 ratio of arm elevation angle to
glenohumeral angle as reported by Inman et al. (Inman et al., 1944). Thus, GHAs of 30° and
60° correspond to arm elevation angles of 45° and 90°, respectively. The experimentally
measured moment arms are presented in Tables 2 and 3 for 30° and 60° GHA, respectively.
Two studies divided each rotator cuff muscle into multiple muscle elements and measured each
muscle element moment arm (Nyffeler et al. and Otis et al.). Thus, ranges of values were
obtained and are presented for each individual muscle element in the tables.
Moment arms from the Holzbaur and Dickerson models and the DSEM were computed directly
with the respective models. The Holzbaur model output moment arms with respect to arm
elevation angles that were converted to GHAs using the calculated scapulohumeral rhythm of
the model. A superior-inferior vector was aligned and attached to the medial border of the
scapula; the GHA was defined to be the angle between said vector and the long axis of the
humerus. The scapulohumeral rhythm was calculated and the moment arms at the GHAs of
interest were computed. For the Dickerson model, the position of the humerus was defined
with respect to the torso. Arm position was defined relative to a starting position extracted from
the geometric model of Hogfors et al. (Hogfors et al., 1987) (humerus abducted to 90°, with
epicondyles parallel to the gravity vector, the thumb pointed up and elbow range of motion in
the horizontal plane). Three sequential Euler rotations (3, −2, 1) defined humeral position
relative to the scapula in order to ensure consistency with the shoulder rhythm formulation
used (Hogfors et al., 1991). Glenohumeral angles were confirmed following humeral
positioning as matching those of the empirical data used. For the DSEM, the humerus was
positioned in 30° and 60° elevation with respect to the scapular vector in the scapular plane,
with zero degrees axial rotation. Moment arms were extracted in the local humeral system of
the model.
RESULTS
In general, all of the models evaluated generated moment arms that fell within the range of
experimentally measured data for the muscles reported by each. The moment arms predicted
by each model are shown together with the range of experimentally measured moment arms
in Figure 1 (a–h) for each rotator muscle at 30° and 60° GHA. The Favre, Dickerson, Holzbaur
models and the DSEM contained muscle elements for all four rotator cuff muscles. The Favre
model predicted both the infraspinatus and supraspinatus abduction moment arms within the
experimental range. However, for the subscapularis and teres minor, the predicted moment
arms tend towards a greater adduction function than that of the experimental data. The
Dickerson model produced moment arms in the experimental data range for all postures and
muscles except for supraspinatus at 60° GHA (over prediction by 0.05 mm) and the teres minor
at 30° GHA. Predictions from the Holzbaur model wholly agreed with the empirical data except
for underpredicting the teres minor adduction moment arm at 60° GHA. The DSEM has high
anatomical fidelity with multiple muscle elements for each muscle, and therefore produces a
range of predicted moment arms for each muscle. In several situations, some muscle elements
agree with experimental ranges, while others do not. For example, approximately half of the
muscle elements for the subscapularis are within the range. Moreover, substantial adduction
function was predicted for some muscle elements, while a substantial abduction function was
predicted for others. The Garner model predicted moment arms within the experimental range
for the supraspinatus and subscapularis, although data was unavailable for the infraspinatus
and teres minor. The Newcastle model accurately predicted subscapularis moments arms,
however, at 60° GHA it predicted higher abduction moment arms for both the supraspinatus
and infraspinatus. No data were available for the teres minor in the Newcastle model.
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DISCUSSION
This study compared rotator cuff moment arms obtained from multiple shoulder models to
those reported in several sets of experimental data. The moment arms from the models showed
overall agreement and were within the range defined by the empirically measured data. The
experimental data included represent the body of literature concerning moment arms for the
arm positions of interest, as these two arm positions are clinically relevant.
The Garner and Newcastle models did not publish moment arm data for all muscles at both
arm positions considered. Further, published data concerning experimentally measured
moment arms did not always include data on all muscles in both positions. Discrete positions
were selected due to the limited literature concerning experimental studies. The experimental
studies were performed independently; thus, variations in methodology and in the arm positions
at which moment arms were measured are possible. Some studies (Graichen et al., 2001;Howell
et al., 1986;Poppen and Walker, 1978) reported measured moment arms with respect to arm
elevation angle, whereas the current comparison uses glenohumeral angle. Conversion of these
angles is subject to variations in subject-specific scapulohumeral rhythm. The model moment
arms were either computed (Dickerson and Holzbaur models and DSEM) or extracted (Garner,
Favre, and Newcastle models) from published or dissertation data, and some variation in the
arm positions of the models is possible. The included studies did not report anthropometric
specimen data, and, with the exception of the Dickerson model, the models either did not report
or do not allow for subject scaling. Therefore, this comparison does not account for potential
anthropometric variation, which may alter the results. Finally, the method of subdivision of
muscles into functional mechanical elements differed across models and experiments and this
may have resulted in discontinuities between the data sets. These limitations should be
considered as they can influence experimental and model-predicted moment arms. It should
also be noted that variation in moment arm values would cause large variation in torque
calculations. Despite these limitations, however, the performance of the models in predicting
the empirical data confirms the robustness of the modeling approaches used and informs users
of the models as to their utility.
The quantitative agreement between model-predicted and experimentally measured moment
arms supports use of the included models for biomechanical analyses of the rotator cuff muscles
of the shoulder. The comparison between computational models and published empirical data
is important because moment arms are a critical factor in the outputs of muscle force prediction
models.
Acknowledgements
We thank the National Institute of Health for financial support via grant AR048540.
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Table 1
Moment arm measurement method used in each study
Study Method
Graichen et al., 2001 3-D measurement using reconstruction from MRI
Howell et al., 1986 Roentgenographic measurement
Kuechle et al., 1997 Tendon excursion/joint displacement method
Liu et al., 1997 Tendon excursion/joint displacement method
Nyffeler et al., 2004 Tendon excursion/joint displacement method
Otis et al., 1994 Tendon excursion/joint displacement method
Poppen and Walker, 1978 Radiographic measurement
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Table 2
Experimentally measured rotator cuff abduction moment arms at 30° glenohumeral abduction in the scapular
plane
Study Supraspinatus Infraspinatus Teres minor Subscapularis
Graichen et al.
Howell et al. 25.0 0.0
Kuechle et al. 16.0 4.0 −5.0 3.0
Liu et al. 29.0 11.0 6.0
Nyffeler et al. 27.5
8.5, 15.5, 21.5
†
−9.0
0.0, 10.0, 16.0
†
Otis et al.
Poppen and Walker
Range 16.0 to 29.0 0.0 to 21.5 −9.5 to −5.0 0.0 to 16.0
*
moment arms measurements in mm;
†
inferior, middle, superior muscle elements, respectively
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Table 3
Experimentally measured rotator cuff abduction moment arms at 60° glenohumeral abduction in the scapular
plane
Study Supraspinatus Infraspinatus Teres minor Subscapularis
Graichen et al. 21.0
Howell et al. 25.0 0.0
Kuechle et al. 7.0 2.0 −13.0 11.0
Liu et al. 23.0 10.0 1.0
Nyffeler et al. 22.5
13.0, 18.0, 22.0
†
−4.0
−1.0, 8.0, 11.0
†
Otis et al.
25.1, 27.0
‡
5.4, 8.4, 16.9
†
−2.2
4.3, 7.3, 13.6
†
Poppen and Walker 21.0 −1.0
Range 7.0 to 27.0 0.0 to 22.0 −13.0 to −2.2 −1.0 to 13.6
*
moment arms measurements in mm;
†
inferior, middle, superior muscle elements, respectively
‡
anterior, posterior muscle elements, respectively
Clin Biomech (Bristol, Avon). Author manuscript; available in PMC 2008 July 1.