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Muscles across the elbow joint: A biomechanical analysis
0021 9290,‘81;100659 IO SO2.00/0 Pcrgmlnn Press L.,d
.I. Bwm-chmicr Vol. 14. No. 10. pp 659 -669, 1981 Printed m Great Britain.
MUSCLES ACROSS THE ELBOW JOINT: A BIOMECHANICAL ANALYSIS* K. N. AN, F. C. HuI~, B. F. MORREY,R. L. LINSCHEIDand E. Y. CHAO Biomechanics
Laboratory,
Orthopedic
Department, Mayo Clinic/Mayo MN 55901, U.S.A.
Foundation,
Rochester,
Abstract-In order to understand the mechanics of the human musculoslceIetal system, quantitative data on the functional anatomy of the muscles related to the joint are necessary. Several important biomechanical parameters of the muscles controlling the elbow joint were determined. Serial cross-sectional anatomy analysis was used to obtain the centroid and thus the moment arms of each of the muscles along the upper arm and at the elbow joint. Muscle volume and true fiber length at the resting position were also measured. From these data, the physiological cross-sectional areas were calculated. The volume provided the information on the work capacity of the muscles. The physiological cross-sectional area provided the potential tension which the muscle can generate.
INTRODUCTION
Though anatomy is an ancient medical science, until recently it has primarily been studied in a qualitative way. In order to understand the mechanics of the human musculoskeletal system, the quantitative data on the functional anatomy of the muscles related to the joint are necessary. Reliable information, of this nature, on the upper limbs, is scarce compared to that for the lower limbs. In the few previous force studies of the elbow joint, either a few major flexors and extensors were considered in the model or more muscles were included, but were grouped and arranged to be considered as a single unit (Groh, 1973 ; Simpson, 1975 ; Nicol, 1977). Furthermore, in these studies, a straight line joining the muscle origin and insertion was used to represent the direction of muscle action. Recently, Amis et al. (1979) examined the muscles across the elbow joint by direct dissection of cadaver specimens. The volumes and fiber lengths of all of the muscles crossing the elbow joint were measured. The moment arms of the muscles with respect to the elbow joint were estimated by the probe and grid method similar to that of Simpson (1975). This procedure allowed the moment arms to be directly measured at various elbow attitudes. Such a gross dissection procedure might disturb, however, the intact anatomical structure and the circumferential soft tissue envelope. In 1975, Jensen and Davy developed a method for obtaining musculoskeletal geometry by a serial crosssection technique. The orientation of each muscle was represented by joining the centroids of the series of cross-sections. However, the representation of the muscle line in this manner assumes that muscle fibers are uniformly distributed and contracted across the * Received 15 December 1980. t Toledo Clinic, 4235 Secor Road, Toledo, OH 43623, U.S.A.
entire cross-section. This assumption has not yet been verified. The same sectioning technique was later applied by other investigators to the study of muscles across the spine (Rab et 01.. 1977), the forearm (Gross et al., 1977), and the ankle (Ripperger et al., 1980). In addition to the calculation of the centroid used to represent the muscle action line, the cross-sectional areas as well as the total volumes of the associated muscles were calculated. Unfortunately, the physiological cross-sectional areas derived from these procedures were not exact in some instances. For muscles not oriented perpendicular to the plane of the cross-sectional cut, a portion of the muscle may not have been represented in the given section or the fibers may have been set obliquely. Both instances give rise to inaccuracies. Although correction factors can be employed if the muscle is cut obliquely, no such adjustment can be applied if a portion of the muscle is not included in the cross-section due to its orientation. The Renaissance genius, Nicholas Steno, derived a geometric analysis of the muscles in 1667 that clearly showed that fusiform as well as multipennate muscles, when rotated around the full extent of the tendon of origin and insertion, had the configuration of a parallelepipedon (Fig. 1). The individual muscle fibers were then parallel and of equal length. Brand et al. (1980) recently rediscovered this relationship and by measuring the resting length of the fibers in each muscle, were able to obtain a ratio of volume to length that appeared to provide a more accurate value for the work capacity of individual muscles than the physiologic cross-section of Fick (1911). The latter utilized the largest cross-sectional area of each individual muscle. We have adopted Brand’s technique to measure the volume, fiber lengths and physiologic cross-sectional areas of all the muscles across the elbow joint. The lines of action and associated moment arms of these muscles at different elbow angIes and forearm attitudes were obtained by the serial sectioning method. The moment
K. N.
AN er al.
The developed films were projected on a Vanguard Motion Analyzer. The coordinates of the envelope of both the muscles and bony cross-section were digitized with a sonic pen digitizer. The digitized data were then analyzed by using a PDP-1 l/34 computer. The crosssectional areas, centroids and volumes of the muscles were calculated. Gross dissection
Fig. 1 (a). Diagram by Steno showing the parallelepipedon of the muscle fibers. The individual muscle fibers were parallel and of uniform length. The tendons became progessively thicker as they accepted mote fibers.
potentials created by these muscles at the elbow joint
were thus derived. MATERIALS
AND METHODS
Series cross-section Six fresh unembalmed upper extremity specimens were obtained from cadavers as soon after death as possible and frozen at - 10°C. In order to preserve the muscles in as anatomical a position as possible, the extremity was disarticulated at the scapulothoracic articulation. Among the six specimens, the first three were prepared in elbow extension but with the forearm in supinated, neutral and pronated positions respectively. The fourth specimen was kept at 50” elbow flexion and in a neutral forearm rotational position. The fifth and sixth specimens were both maintained at 100” of flexion, with one in maximum supination and the other in the neutral position. The position of each specimen was maintained by force applied to the muscles and hand through strings and screws. The specimens were then frozen by hanging them vertically in a freezer. By hanging the specimens while freezing, the effects of localized pressure or gravity that would tend to distort the normal anatomy were minimized. The specimens were then embedded in wooden boxes and rigidly fixed using Pedilen foam. All the embedded specimens were then sectioned perpendicular to the long axis of the forearm with a Biro meat saw. For the three flexed specimens, the specimens were sectioned perpendicular to the long axis of the humerus after passing the elbow joint. Each section was cut at 1 cm intervals along the forearm and upper arm and cut at 0.5 cm intervals in the neighborhood of the elbow joint. The cross-sectional surface was cleaned, labeled and photographed using a Photo Sonic 61-1100 highspeed movie camera and 16 mm Ektachrome film.
Four upper extremity fresh, unembalmed cadaver specimens were used for this study. During the dissection, the skin and superficial fascia were carefully detached and the specimens were kept moist. The dissection technique developed by Brand et al. (1980) was employed. Origins and insertions of each muscle were identified and when possible, the insertion was freed and rotated such that the muscle fibers formed the parallelepipedon shape (Fig. 1). Only sufficient force to demonstrate the parallelepipedon shape was applied before careful measurement of the fiber lengths. If the muscle was not readily manipulated to the parallelepipedon configuration, the muscle fibers were measured in situ. With the elbow flexed about 70”, the lengths of the proximal and distal muscle fibers were measured from their origins to their tendmous insertions. Some muscles were primarily muscular rather than tendinous when crossing the joint and the fiber lengths became progressively longer as the muscles became more superficial. The averaged fiber lengths from three measurements were then obtained. When possible, the fiber length measurements were adjusted to the resting position of the elbow (70” flexion) to avoid errors from excessive fiber stretch (Pertuzon et al., 1973). The muscles were then dissected free and their volumes measured by a water displacement technique. The physiological cross:sectional areas were calculated by dividing the volume by its mean fiber length.
RESULTS
Descriptive anatomy results The muscles crossing the elbow joint were dissected according to the technique described above. Twentyfour muscles were studied (Table 1). Most muscles with rather discrete origins and tendinous insertions could be demonstrated to assume the parallelepipedon configuration. The fiber lengths varied little when this configuration could be demonstrated. Those muscles with broad or extensive origins such as the brachialis, medial and lateral heads of the triceps and the supinator could not be as readiiy manipulated into the parallelepipedon shape and their fibet lengths varied. Some muscles remained more muscular then tendinous as they crossed the joint; for example, the brachialis. Muscle fiber variation occurred in these muscles with longer fibers situated farther from the axis of rotation as the muscle crossed the joint.
Fig.
I (b). The Pnrallelepipedon of the muscle fibers were demonstrated in the muscles across the elbow joint.
Muscles across the elbow joint
663
Table 1. Muscles which cross the elbow joint Abbreviation
Muscle 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24.
Long head of biceps Short head of biceps Brachialis Medial head of triceps Lateral head of triceps Long head of triceps Brachioradialis Anconeus Pronator teres Flexor carpi radiahs Extensor carpi radiahs longus Extensor carpi radialis brevis Flexor carpi ulnaris Extensor carpi ulnaris Supinator Extensor digitorum communis, Extensor digitorum communis, Extensor digitorum communis, Extensor digitorum communis, Palmaris longus
LHB (BIC) SHB (BIC) BRA MHT (TRI) LHT (TRI) LNGT (TRI) BRD ANC PRO FCR ECRL ECRB FCU ECU SU EDC, 2 EDC. 3 EDC; 4 EDC, 5 PL FDS, 2 FDS, 3 FDS, 4 FDS, 5
index long ring little
Flexor digotorum superficialis, index Flexor digotorum superficialis, long Flexor digotorum superfkialis, ring Flexor digitorum supertkialis, little
Centroid line Serialcross-sectioning of the upper arm and forearm specimens provided the cross-sections of the bones and all muscles that cross the elbow joint. The centroid of each muscle cross-sectional area was calculated. The lines of action of all the muscles crossing the elbow joint at six different elbow positions were represented by joining the centroids ofeach muscle. These centroid lines can be graphically presented in either the AP or lateral view (Fig. 2). By using the information obtained in this manner, the components of moment and force generated by each muscle to the bone or joint can be estimated. A Cartesian coordinate system was defined for the study. The origin of the system was located at the center of the
23
trochlea and the flexionextension axis was along the center of the trochlea. The coordinate representing the supination-pronation component of the forearm was defined to be perpendicular to the flexion-extension axis and lies in a plane that passes through the center of the distal ulna. The axis for medial-lateral deviation rotation was defined by the right-hand orthogonal rule based on the above two axes. The three-dimensional data of the centroid lines of muscles were used to calculate the direction of force application by a line tangent to thecentroid line curves at the particular level of interest. The moment arms at the center of the trochlea in the plane of the crosssection and perpendicular to the forearm axis were calculated. The components of the moment arms of all
27 DISTANCE
FROU
NURRAL
31 MAD
(CM )
l o l
T01
33
BRA BIG
Fig. 2 Graphical representation of the centroid tines of a few muscles across elbow joint in extended/neutral position.
664
K. N. AN et al. Table 2. Flexion-extension moment arm (cm)
Group
Muscle
I
BIC BRA BRD PRO ECR
II
III
Elbow and forearm configuration E/P E/N
E/S -
1.964 0.869 2.565 1.186 1.162
-
1.468 0.592 2.467 1.481 1.205
- 1.271 - 1.098 - 2.502 -0.483 - 1.531
FW/N
FlW/S
FlW/N
-
2.674 1.292 3.697 1.585 1.982
- 3.203 - 1.977 -5.188 - 2.005 - 3.378
-3.431 - 2.052 -4.164 - 1.646 -2.871
FCR FDS
0.434 0.861
0.363 0.210
0.561 0.961
- 0.205 0.665
-0.751 - 0.235
- 0.923 - 0.027
TRI ANC FCU ECU
2.564 1.331 1.854 0.907
2.809 0.622 1.735 0.488
2.256 0.691 1.888 1.513
EDC
-0.321
-0.019
-0.133
2.474 1.738 1.877 1.202 1.134
1.867 0.715 0.769 0.632 - 0.748
2.039 1.126 1.326 0.659 -0.443
* Negative = Flexion
-
; Positive = Extension. Table 3. Varus-valgus moment arms (cm) Elbow and forearm configuration
Group
I
‘I
III
E/N
E/P
F50”/N
FlW/S
1.339 0.697 1.996 2.008 2.672
- 2.614 - 1.386 - 3.449 - 3.464 -4.015
- 1.322 - 1.084 - 2.751 - 3.064 -3.521
-0.758 -2.168 - 1.641 - 3.293 - 2.992
-
PRO FCR FCU FDS
2035 2.800 2.170 2.770
0.824 1.757 1.419 2.095
1.927 2.316 1.622 1.976
BIC BRA TRI
0.179 0.521 -0.398
0.978 -0.143 -0.260
- 0.378 0.321 -0.818
Muscle BRD ANC ECR ECU EDC
E/S -
FlW/N
1.314 1.754 1.841 2.852 3.243
-0.182 - 1.762 -0.462 - 2.873 -2.045
1.683 1.890 1.237 1.631
2.002 2.213 1.614 1.880
1.528 2.294 1.611 1.887
0.041 0.182 - 1.175
1.388 -0.146 -0.175
1.133 0.129 - 0.027
* Positive = Varus; Negative = Valgus.
the muscles across the elbow joint obtained from the six specimens at various elbow and forearm configurations are summarized in Tables 2,3 and 4. Since the data of the moment arms were obtained from six cadaver specimens, a normalization procedure was performed to compare the results. The data are adjusted such that the arm sizes are equivalent to that of the first specimen (i.e. extended-supinated specimen). The normalization length for each specimen is based on the ratio of the square root of the area of cross-section (excluding fat and skin) at the junction of the middle and proximal thirds of the forearm of the specimen with respect to the first specimen. Based on the variation of the flexion-extension moment arms through the range of elbow motion at the extended (OO),semi-flexed (So”), and flexed (100”) positions, the muscles across the elbow can be divided into three groups (Table 2). In Group I, which consists of BIC, BRA, BRD, ECR and PRO, the flexion+extension moment arms tended to increase with progressive flexion of the elbow joint in the flexed position. The moment arms of the major elbow flexors
in the flexed position were almost twice as great as those in the extended position. In Group II, which consists of the FCR and FDS, the muscles created an extension moment arm when the elbow was in the extended position but changed to a flexion moment as the elbow was flexed. In the third group, which consists of the rest of the muscles, the moment arms either did not change significantly in magnitude or direction, or their pattern of alteration was not well defined. The muscle grouping as described above is generally true whether the forearm was in the neutral or supinated position. However, the forearm rotation does have a slight effect on the flexion-extension moment arms for some muscles. In terms of the varus-valgus moment arms, the muscles could again be divided into three groups (Table 3). In Group I, all muscles arose from the lateral aspect of the distal humerus and consisted of the ANC, BRD, ECR, EDC and ECU. These muscles created valgus moments with respect to the joint center at the trochlea. In Group II, all muscles arose from the medial aspect of the distal humerus which consisted of
Muscles across the elbow joint Table 4. Rotational moment arm
665
about ulna axis (cm) __-
Muscle BIC BRA PRO BRD TRI ANC ECR FCR FDS FCU EDC ECU
Elbow and forearm configuration F50”/N E/P E/N
E/S -0.12 - 0.98 1.23 -0.22 - 0.40 0.83 -0.80 1.92 0.96 1.05 0.22 0.45
0.49 -0.32 0.75 - 1.29 0.28 2.23 - I.31 1.08 -0.54 0.29 -0.23 1.57
0.64 0.19 1.51 0.53 0.61 1.85 -0.94 1.52 0.68 -0.14 -0.75 0.40
FlW/S
1.29 -0.01 0.83 0.06 0.65 1.87 2.09 0.89 0.26 -0.20 0.36 0.79
0.91 -0.29 0.64 0.32 0.67 1.11 1.54 0.89 0.31 0.16 0.11 0.74
FlOO”/N 1.33 0.44 -0.01 -0.22 1.27 2.29 2.41 -0.29 -0.28 -0.19 -0.32 1.35
* Negative = Medial rotation.
Table 5. Volume, fiber length and physiological cross-sectional area Muscle
Volume km3)
Length (cm)
PCSA (cm’)
PCSA (%)
LHB SHB BRD BRA MHT LHT LNGT ANC PRO FCR ECRL ECRB
33.4 (8.6) 30.8 (9.1) 21.9 (8.5) 59.3 (16.2) 38.7 (17.1) 47.3 (11.8) 66.6 (19.5) 6.7 (3.4) 18.7 (9.5) 12.4 (4.9) 18.3 (7.5) 15.8 (8.1)
13.6 (2.4) 15.0 (3.4) 16.4 (2.9) 9.0 (2.9) 6.3 (1.4) 8.4 (1.0) 10.2 (1.9) 2.7 (0.3) 5.6 (1.7) 5.8 (0.9) 7.8 (0.5) 5.3 (0.6)
2.5 (0.5) 2.1 (0.5) 1.5 (0.5) 7.0 (1.9) 6.1 (2.3) 6.0 (1.2) 6.7 (2.0) 2.5 (1.2) 3.4 (1.5) 2.0 (0.6) 2.4 (1.0) 2.9 (1.4)
FCU
4.0 (0.6 j 3.4 (0.8) 2.4 (0.8) 11.8 (4.7) 9.8 (3.1) 10.0 (2.3) 11.1 (3.6) 3.9 (1.1) 5.3 (1.4) 3.3 (0.6) 3.7 (0.9) 4.5 (1.4)
15.2 (0.0)
4.8 (0.0)
14.9 10.9 4.9 5.9 8.0 4.7 11.1 13.7 7.8 3.3 5.1
3.2 (0.0)
4.5 (0.5) 3.3 (0.6) 6.7 (1.3) 6.9 (1.3) 6.1 (2.1) 5.9 (1.4) 4.5 (0.3) 7.7 (0.8) 6.4 (1.1) 4.5 (0.4) 5.7 (1.0)
4.7 (0.0)
3.4 (1.3) 3.4 (1.0) 0.7 (0.3) 0.9 (0.4) 1.4 (0.7) 0.8 (0.2) 2.5 (1.6) 1.7 (0.6) 1.2 (0.7) 0.7 (0.4) 0.9 (0.6)
4.8 (1.4) 5.6 (1.7) 1.2 (0.2) 1.3 (0.3) 2.2 (0.8) 1.3 (0.4) 3.8 (1.7) 2.7 (0.4) 1.8 (0.8) 1.1 (0.5) 1.2 (0.6)
ECU su EDC, EDC, EDC, EDC, FDS, FDS, FDS, FDS, PL
2 3 4 5 2 3 4 5
(5.7) (2.1) (1.5) (2.8) (3.9) (1.9) (6.7) (6.1) (5.5) (2.1) (3.9)
* Mean (S.D.); n = 4. PRO, FCR, FDS and FCU. These muscles generated varus moments. The major flexor and extensor muscles of the elbow, BIC, BRA and TRI, were centrally located with respect to the varus-valgus axis of rotation and tended to have a small varus-valgus moment arm to the elbow joint center. Individual variations were often noticed for these muscles. The configuration of forearm rotation seemed to have only a slight effect on the varus-valgus moment of any muscle. In general, with the forearm in a neutral position, the moment arms were relatively larger in Group I (lateral muscle), and smaller. for Group II (medial muscle). This difference was less noticeable in the supinated and pronated positions. Rotation of the elbow joint (flexion-extension) did not affect varus-valgus moment arms significantly.
The moment arms of muscles relating to the rotation along the forearm ulnar axis is recorded in Table 4. Both forearm and elbow joint configurations seem to have influence on this moment arm. Volume, jiber length and physiological cross-section area The results (Table 5) described in this section were obtained based on the dissection of four cadaver specimens following Brand’s technique. Volumes of all the muscles were measured by the water displacement method. The muscle fiber lengths obtained by this technique were considered to be a representation of the true fiber length, thus the corrections of the crosssectional areas for pennation angle described by Alexander (1975) were not required. The physiological
K. N. AN et
666
cross-sectional area was calculated by dividing muscle volume by its fiber length. Since the four specimens used for the study were comparable in size, normalization of the raw data was not necessary, although the physiological cross-sectional areas were normalized based on the total cross-sectional areas of the individual specimens. Each of the three components of the triceps mechanism had a larger volume but a shorter fiber length as compared to those of the biceps muscles. The long head of the biceps had the largest volume. In contrast, the brachioradialis had a smaller volume and a longer fiber. In general, the three components of the triceps and brachialis muscles had comparable values of physiological cross-sectional areas. Because‘of the long fiber length, the biceps and brachioradialis had relatively small physiological cross-sectional areas. On the other hand, all the wrist and finger muscles in the forearm had intermediate values of physiological cross-sectional area. Comparison of both raw and normalized data of physiological cross-sectional area indicated that normalization by expressing the data in percentages did not reduce the scattering of the data significantly. Finally, due to the difficulty in separating the composite proximal portions of the EDC and FDS during dissection, larger variations of the volume measurements of the components were noticed. DI!XXJSSION
When dealing with a force analysis of the musculoskeletal systems, the necessary biomechanical parameters must be derived through anatomical experiments. Several parameters were obtained in this study. By serially cross-sectioning the upper extremity, the centroids of all the muscles along the arm which cross the elbow joint were obtained. Jensen and Davy (1975) proposed using the centroid of a muscle’s cross-section as its point of action. The line of action of the muscle can be obtained by joining these centroids. This approach assumes that the muscle fibers, are distributed and contract uniformly across the cross-section and that the lines of action are perpendicular to these cross-sections. These assumptions may not be true under some conditions. For instance, when the crosssection is made oblique to the fiber length, the centroid line of that oblique cross-sectional area will not be an exact representation of the line of action of the muscle force. However, the majority of the muscles become tendinous near a joint and the cross-section of a tendon is usually normal to its fibers, thus accurate representation of the lines of action are generally possible. In certain instances, the muscle fiber might not contract uniformly at the cross-section except perhaps at maximum contraction. Nevertheless, the centroid line still provides the best estimation of the line of action and is more accurate than a straight line approximation. One disadvantage associated with the method of the
al.
serial sectioning technique for obtaining the centroid lines of the muscles is that only one elbow and forearm configuration is possible for each specimen. The error introduced by the anthropometric variation among additional specimens to obtain data for other positions is significant. In this study, the coordinates of the centroid lines or moment arms were normalized to the equivalent size based on the ratio of the square root of the forearm cross-sectional area, including those of bones and muscles. The selection of this normalization factor is based on the observation that the muscles and tendons are stacked up around the bones. Larger cross-sectional areas imply a farther distance from the joint center of the muscles and tendons. However, this normalization procedure has not yet been substantiated. Nevertheless, we believe the value of these moment arms, varying with the elbow and forearm configurations, are accurate. Another inherent error of using the results from in vitro cadaveric study for the in uiuo analysis should be kept in mind: when certain muscles contract, the position and orientation of their tendons may be different from those at the passive resting position. If reasonable resolution can be provided by the non-invasive computerized scanning technique, the errors from specimen variation as well as the lack of muscle tone could be resolved in future investigations. The results of the variation of muscle flexion moment arms at the elbow joint during flexion are similar to those. reported by Braune et al. (1890), Wilkie (1949) and Amis et al. (1979). In view of the limited‘joint positions and forearm configurations in the present study, the exact nature of either the linear or parabolic relationship cannot be assessed. However, the results suggest that the determination of the major components of moment arms based on both the crosssectional method (Jensen et al., 1975) and direct dissection method (Simpson, 1975) are relatively comparable. The results of the moment arm measurement indicate that the majority of the muscles create moments about all three axes but usually have one principal axis which is most dominant. The muscles with the greatest moment arm in flexion are BRD, BIC, BRA and ECR. Those with major moment arms contributing to extension are the TRI, FCU and ANC. The moment arm of a muscle merely indicates the efficiency of the muscle for rotation about that particular axis. The strength of each muscle is proportional to the physiological cross-sectional area. The work capacity is related to the muscle volume. The physiological cross-sectional area (PCSA) is obtained by dividing the muscle volume by its true fiber length. This calculation is used as an indicator of the possible tensile strength that can be developed by the individual muscle during maximum contraction. The rationale of this assumption is simply that the cross-sectional areas of muscles are:proportional to the number of muscle fibers, and the muscle fibers are the basic elements which generate tension. The relationship of a muscle’s
Muscles across the elbow joint force generation to its cross-sectional area is expressed as a proportional constant. The proportional eonst&t of the force, generated by a unit of cross-sectional area of a muscle, has been attempted in the past by many investigators (Ikai, 1968). However, widely divergent results have been reported. The discrepancies of these reports might simply be due to the variations among the types and functions of various muscle studies. However, we believe the variation reported in the literature is due to the fact that the exact physiological cross-sectional areas were not accurately measured during those experiments. Although the constants for the force generation per unit area are not consistent, the relative contribution based on the accurate measurement of physiological cross-sectional area can still be estimated. The potential moment contribution of each muscle at the elbow joint can be estimated by multiplying the moment arm of the muscle by its physiological crosssectional area. The contributions to flexion-extension and varus-valgus rotation for all of the muscles across the elbow joint have been calculated and are illustrated in Fig. 3. From these diagrams, it is obvious that the triceps muscle generates the largest moment about the elbow joint in all of the six elbow and forearm configurations studied. Although it is difficult to clearly and concisely express these data, the diagrams (Fig. 3) are very useful in understanding the moments generated by the muscles at the elbow joint. During maximum contraction, the overall moment in any direction could easily be obtained graphically or numerically. Of note, the potential moment in varus appears balanced by the valgus moment under all the six conditions. However, for flexion and extension, the flexion potential moments seem to be balanced by the extension moments when the elbow is flexed, while the extension moments exceed the flexion moments when the elbow is extended. It should be realized that the construction of Fig. 3 and the above discussion of the balance of the moments are based on the assumption that all of the muscles are simultaneously contracted maximally and at optimum length. To apply the data in Fig. 3 to more general conditions, a proportional adjustment for the potential moments should be made, based on the muscle force-length relationship (Inman and Ralston, 1968). In addition, for the purpose of calculating joint moments contributed by the muscles under non-isometric conditions, the muscle forces must be adjusted according to the muscle force-velocity relationship (Stem, 1974). And finally, when submaximum isometric contractions are encountered, the data shown in Fig. 3 can be scaled in proportion to the level of individual muscle activation as determined by electromyography (Dempster, 1947 ; Fidelus, 1973 ; Messier et al., 1971). During the gross dissection experiment, the tendon excursion through a fuIl range of joint rotation was measured by Brand in his study. A unique concept had thus been observed. The resting muscle fiber lengths, a middle position
within the full excursion, are thought
667
to be equal to the entire excursion length of that ptiticular muscle. If this concept is correct, then the muscle volume can be treated as the index of possible work capacity of that particular muscle. This is because the physiological cross-sectional area times fiber length (or excursion) is proportional to the work developed during maximum contraction through the entire excursion. In general, the triceps muscles and the brachialis muscle have relatively large strength potentials (large PCSA) and also work capacities (large volume). On the other hand, the wrist and finger muscles in the forearm have relatively small work capacities (small volume) but moderate strength potentials (large PCSA). Finally, an interesting and potentially useful observation has been noticed during this study. The physiological cross-section of a muscle was found to be closely correlated to its tendon cross-sectional area. This finding suggests that the tendon fibers may be related in some way to the sarcomere sheath in the muscle bundle. This relationship may also be useful in assisting the separation of muscle volume for the EDC and FDS muscles into appropriate subgroups.
SUMMARY
Several important biomechanical parameters of the muscles controlling the elbow joint have been determined. Serial cross-sectional anatomy analysis was used to obtain the centroid and thus the moment arms of each of the muscles along the upper arm and at the elbow joint. A special dissection technique developed by Brand was utilized to measure the muscle volume and true fiber length at the resting position. From these data, the physiological cross-sectional areas of the muscle were also obtained. The volume provided the information on the work capacity of the muscles. The physiological cross-sectional area provided the potential tension a muscle can generate. Based on the moment arm measurements, the BRD, BIC, BRA and ECR were demonstrated to be the major flexors for the elbow joint ; the TRI, FCU and ANC were the major extensors. Similarly, the ECU, EDC, ECR and BRD were the major muscles producing valgus forces and the FCR, FDS, PRO and FCU were the major muscles producing varus forces for the elbow. Based on the volume and physiological crosssectional area measurements, the triceps and brachialis had the largest work capacity (volume), as well as potential contractile strength (physiological crosssectional area).
Acknowk&emenr-This study was supported in part by NIH Grant Ah4 26287.The authors also acknowledge the help of Dr. P. W. Brand in demonstrating the special technique of muscle dissection and his interpretation.
K. N.
AN et al. ANTERIOR
ANTERIOR
-
cmxcm2 cmxcm2 ECR 11.978
MEDIAL
LATERAL
MEDIAL
LATERAL
TRI 48.520
I
POSTERIOR POsTERiOR
(b)
(a)
ANTERIOR
ANTERIOR
cmxcm2
cmxcm*
MEDIAL
LATERAL
LATER
MEDIAL
POSTERIOR POSTERIOR
(4
(4
ANTERIOR
LATERAL
LATERAL
POSTERIOR POSTERIOR
(4
Fig. 3. The potential moment contribution of each muscle at the elbow joint was estimated by multiplying the moment arm (cm) of the muscle by its physiological cross-sectional area (cm’). These diagrams show the contributions to flexion+xtension and varus-va lgus rotation about the joint center at six elbow and forearm configurations. (a) Extended/supinated; (b) extended/neutral; (c) extended/pronated; (d) semiflexed/neut4; (e) flexed/supinated; (f) flexed/neutral.
Muscles across the elbow joint
669
REFERENCES Alexander, R. McN. and Vernon, A. (1975) The dimensions of knee and ankle muscles and the foras they exert. J. Human Movement Studies 1, 115-123. Amis, A. A., Dowson, D. and Wright, V. (1979) Muscle strengths and musculoskeletal geometry of the upper limb. Engng Med. 8(l), 41-48. Brand, P. W., Beach, R. B. and Thompson, D. E. (1980) Relative tension and potential excursion of muscles in the forearm and hand. 1. Hand Surg. 6,209-219. Braune, W. and Fischer, 0. (1890) Die Rotationsmomente der Beugemuskeln am Ellenbogengelenk des Menschen, Abh. d. KiiniglsBchs. Ges. Wiss.. Mathem-plrys. KI.15, cited by Groh, 1973. Dempster, W. T. and Finerty, J. C. (1947) Relative activity of wrist moving muscles in static support of the wrist joint: an elactromyographic study. Am. J. Physiol. 150, 596-606. Fick, R. (I91 1) SpezieUe Gelenk und Muskefmechanik. Vol. I. Gustav Fischer, Jena. Fidelus, K. (1973) The significance of the stabilizing function in the process of controlling the muscle groups of upper extremities. Medicine and Sport. Vol. 8, Biomechanics III pp. 129-133. Groh, H. (1973) Proceedings I : elbow fractures in the adult. General: anatomy, biomechanics. Biomechanics of the elbow joint. Hfi. Unfaliheilk. 114, 13-20. Gross, R. M., Chao, E. Y., An, K. N. and Linscheid, R. L. (1977) Quantitative analysis of the forearm and wrist muscles. Trans. 23rd Annual Meeting of the Orthopaedic Research Society, p. 215. Ikai, M. and Fukanaga, T. (1968) Calculation of muscle strength per unit of cross-sectional area of human muscle by means of ultrasonic measurement. Int. Z. angew. Physiol. 26, 26-32.
Inman, V. T. and Ralston, H. J. (1968) The mechanics of
voluntary muscle. Chapter II, pp. 296-317. Human Limbs Their Substitures. Hafner. New York. Jensen, R. H. and Davy, D. T.. (1975) An investigation of muscle lines of action about the hip; a centroid line approach vs. the straight line approach. J. Biomechunics 8, 103-110. Messier, R. H., Duffy, J., Litchman, H. M., Pasley, P. R., Soechting, J. F. and Stewart, P. A. (1971) The electromyogram as a measure of tension in the human biceps and triceps muscles. Int. J. mech. Sci. 13. 585-598. Nicol, A. c. (1977) Elbow joint prosthesis design: biomechanical aspects. Ph.D. Thesis. Universitv of Strathclyde. _ Pertuzon, E. and Lestienne, F. (1973) atermination dynamique de la position d’tiuilibre dline articulation. Int. Z. an&w. Physiol. 31,315-j25. Rab, G. T., Chao, E. Y. S. and Stauffer, R. N. (1977) Muscle force analysis of the lumbar spine. Orth. Clin. N. Amer. 8(l), 193-199. Ripperger, R. R., Chao, E. Y. and Stauffer, R. N. (1980) A quantitative analysis of leg musculature. Trans. 26th Annual Meeting of the Orthopaedic Research Society, p. 52. Simpson, D. (1975) An examination of the design of an endoprosthesis for the elbow. M. SC. Thesis. University of Strathclyde. Steno, N. (1667) Elementorum myologiae specimen s. muscuti descriptio geometrica, p. 108 in Opera Philosophico, Vol. II (Edited by Vilhelm Maar) Copenhagen (1910) Quoted in Bastholm E. The History of Muscle Physiology, Copenhagen, Ejner Munksgaard (1950). Stem, J. T. (1974) Computer modelling of gross muscle dynamics. J. Biomechanics 7,41 l-428. W&e, D. R. (1949) The relation between force and velocity in human muscle. J. Physiol.. Land. 110, 249-280. and
.I. Bwm-chmicr Vol. 14. No. 10. pp 659 -669, 1981 Printed m Great Britain.
MUSCLES ACROSS THE ELBOW JOINT: A BIOMECHANICAL ANALYSIS* K. N. AN, F. C. HuI~, B. F. MORREY,R. L. LINSCHEIDand E. Y. CHAO Biomechanics
Laboratory,
Orthopedic
Department, Mayo Clinic/Mayo MN 55901, U.S.A.
Foundation,
Rochester,
Abstract-In order to understand the mechanics of the human musculoslceIetal system, quantitative data on the functional anatomy of the muscles related to the joint are necessary. Several important biomechanical parameters of the muscles controlling the elbow joint were determined. Serial cross-sectional anatomy analysis was used to obtain the centroid and thus the moment arms of each of the muscles along the upper arm and at the elbow joint. Muscle volume and true fiber length at the resting position were also measured. From these data, the physiological cross-sectional areas were calculated. The volume provided the information on the work capacity of the muscles. The physiological cross-sectional area provided the potential tension which the muscle can generate.
INTRODUCTION
Though anatomy is an ancient medical science, until recently it has primarily been studied in a qualitative way. In order to understand the mechanics of the human musculoskeletal system, the quantitative data on the functional anatomy of the muscles related to the joint are necessary. Reliable information, of this nature, on the upper limbs, is scarce compared to that for the lower limbs. In the few previous force studies of the elbow joint, either a few major flexors and extensors were considered in the model or more muscles were included, but were grouped and arranged to be considered as a single unit (Groh, 1973 ; Simpson, 1975 ; Nicol, 1977). Furthermore, in these studies, a straight line joining the muscle origin and insertion was used to represent the direction of muscle action. Recently, Amis et al. (1979) examined the muscles across the elbow joint by direct dissection of cadaver specimens. The volumes and fiber lengths of all of the muscles crossing the elbow joint were measured. The moment arms of the muscles with respect to the elbow joint were estimated by the probe and grid method similar to that of Simpson (1975). This procedure allowed the moment arms to be directly measured at various elbow attitudes. Such a gross dissection procedure might disturb, however, the intact anatomical structure and the circumferential soft tissue envelope. In 1975, Jensen and Davy developed a method for obtaining musculoskeletal geometry by a serial crosssection technique. The orientation of each muscle was represented by joining the centroids of the series of cross-sections. However, the representation of the muscle line in this manner assumes that muscle fibers are uniformly distributed and contracted across the * Received 15 December 1980. t Toledo Clinic, 4235 Secor Road, Toledo, OH 43623, U.S.A.
entire cross-section. This assumption has not yet been verified. The same sectioning technique was later applied by other investigators to the study of muscles across the spine (Rab et 01.. 1977), the forearm (Gross et al., 1977), and the ankle (Ripperger et al., 1980). In addition to the calculation of the centroid used to represent the muscle action line, the cross-sectional areas as well as the total volumes of the associated muscles were calculated. Unfortunately, the physiological cross-sectional areas derived from these procedures were not exact in some instances. For muscles not oriented perpendicular to the plane of the cross-sectional cut, a portion of the muscle may not have been represented in the given section or the fibers may have been set obliquely. Both instances give rise to inaccuracies. Although correction factors can be employed if the muscle is cut obliquely, no such adjustment can be applied if a portion of the muscle is not included in the cross-section due to its orientation. The Renaissance genius, Nicholas Steno, derived a geometric analysis of the muscles in 1667 that clearly showed that fusiform as well as multipennate muscles, when rotated around the full extent of the tendon of origin and insertion, had the configuration of a parallelepipedon (Fig. 1). The individual muscle fibers were then parallel and of equal length. Brand et al. (1980) recently rediscovered this relationship and by measuring the resting length of the fibers in each muscle, were able to obtain a ratio of volume to length that appeared to provide a more accurate value for the work capacity of individual muscles than the physiologic cross-section of Fick (1911). The latter utilized the largest cross-sectional area of each individual muscle. We have adopted Brand’s technique to measure the volume, fiber lengths and physiologic cross-sectional areas of all the muscles across the elbow joint. The lines of action and associated moment arms of these muscles at different elbow angIes and forearm attitudes were obtained by the serial sectioning method. The moment
K. N.
AN er al.
The developed films were projected on a Vanguard Motion Analyzer. The coordinates of the envelope of both the muscles and bony cross-section were digitized with a sonic pen digitizer. The digitized data were then analyzed by using a PDP-1 l/34 computer. The crosssectional areas, centroids and volumes of the muscles were calculated. Gross dissection
Fig. 1 (a). Diagram by Steno showing the parallelepipedon of the muscle fibers. The individual muscle fibers were parallel and of uniform length. The tendons became progessively thicker as they accepted mote fibers.
potentials created by these muscles at the elbow joint
were thus derived. MATERIALS
AND METHODS
Series cross-section Six fresh unembalmed upper extremity specimens were obtained from cadavers as soon after death as possible and frozen at - 10°C. In order to preserve the muscles in as anatomical a position as possible, the extremity was disarticulated at the scapulothoracic articulation. Among the six specimens, the first three were prepared in elbow extension but with the forearm in supinated, neutral and pronated positions respectively. The fourth specimen was kept at 50” elbow flexion and in a neutral forearm rotational position. The fifth and sixth specimens were both maintained at 100” of flexion, with one in maximum supination and the other in the neutral position. The position of each specimen was maintained by force applied to the muscles and hand through strings and screws. The specimens were then frozen by hanging them vertically in a freezer. By hanging the specimens while freezing, the effects of localized pressure or gravity that would tend to distort the normal anatomy were minimized. The specimens were then embedded in wooden boxes and rigidly fixed using Pedilen foam. All the embedded specimens were then sectioned perpendicular to the long axis of the forearm with a Biro meat saw. For the three flexed specimens, the specimens were sectioned perpendicular to the long axis of the humerus after passing the elbow joint. Each section was cut at 1 cm intervals along the forearm and upper arm and cut at 0.5 cm intervals in the neighborhood of the elbow joint. The cross-sectional surface was cleaned, labeled and photographed using a Photo Sonic 61-1100 highspeed movie camera and 16 mm Ektachrome film.
Four upper extremity fresh, unembalmed cadaver specimens were used for this study. During the dissection, the skin and superficial fascia were carefully detached and the specimens were kept moist. The dissection technique developed by Brand et al. (1980) was employed. Origins and insertions of each muscle were identified and when possible, the insertion was freed and rotated such that the muscle fibers formed the parallelepipedon shape (Fig. 1). Only sufficient force to demonstrate the parallelepipedon shape was applied before careful measurement of the fiber lengths. If the muscle was not readily manipulated to the parallelepipedon configuration, the muscle fibers were measured in situ. With the elbow flexed about 70”, the lengths of the proximal and distal muscle fibers were measured from their origins to their tendmous insertions. Some muscles were primarily muscular rather than tendinous when crossing the joint and the fiber lengths became progressively longer as the muscles became more superficial. The averaged fiber lengths from three measurements were then obtained. When possible, the fiber length measurements were adjusted to the resting position of the elbow (70” flexion) to avoid errors from excessive fiber stretch (Pertuzon et al., 1973). The muscles were then dissected free and their volumes measured by a water displacement technique. The physiological cross:sectional areas were calculated by dividing the volume by its mean fiber length.
RESULTS
Descriptive anatomy results The muscles crossing the elbow joint were dissected according to the technique described above. Twentyfour muscles were studied (Table 1). Most muscles with rather discrete origins and tendinous insertions could be demonstrated to assume the parallelepipedon configuration. The fiber lengths varied little when this configuration could be demonstrated. Those muscles with broad or extensive origins such as the brachialis, medial and lateral heads of the triceps and the supinator could not be as readiiy manipulated into the parallelepipedon shape and their fibet lengths varied. Some muscles remained more muscular then tendinous as they crossed the joint; for example, the brachialis. Muscle fiber variation occurred in these muscles with longer fibers situated farther from the axis of rotation as the muscle crossed the joint.
Fig.
I (b). The Pnrallelepipedon of the muscle fibers were demonstrated in the muscles across the elbow joint.
Muscles across the elbow joint
663
Table 1. Muscles which cross the elbow joint Abbreviation
Muscle 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24.
Long head of biceps Short head of biceps Brachialis Medial head of triceps Lateral head of triceps Long head of triceps Brachioradialis Anconeus Pronator teres Flexor carpi radiahs Extensor carpi radiahs longus Extensor carpi radialis brevis Flexor carpi ulnaris Extensor carpi ulnaris Supinator Extensor digitorum communis, Extensor digitorum communis, Extensor digitorum communis, Extensor digitorum communis, Palmaris longus
LHB (BIC) SHB (BIC) BRA MHT (TRI) LHT (TRI) LNGT (TRI) BRD ANC PRO FCR ECRL ECRB FCU ECU SU EDC, 2 EDC. 3 EDC; 4 EDC, 5 PL FDS, 2 FDS, 3 FDS, 4 FDS, 5
index long ring little
Flexor digotorum superficialis, index Flexor digotorum superficialis, long Flexor digotorum superfkialis, ring Flexor digitorum supertkialis, little
Centroid line Serialcross-sectioning of the upper arm and forearm specimens provided the cross-sections of the bones and all muscles that cross the elbow joint. The centroid of each muscle cross-sectional area was calculated. The lines of action of all the muscles crossing the elbow joint at six different elbow positions were represented by joining the centroids ofeach muscle. These centroid lines can be graphically presented in either the AP or lateral view (Fig. 2). By using the information obtained in this manner, the components of moment and force generated by each muscle to the bone or joint can be estimated. A Cartesian coordinate system was defined for the study. The origin of the system was located at the center of the
23
trochlea and the flexionextension axis was along the center of the trochlea. The coordinate representing the supination-pronation component of the forearm was defined to be perpendicular to the flexion-extension axis and lies in a plane that passes through the center of the distal ulna. The axis for medial-lateral deviation rotation was defined by the right-hand orthogonal rule based on the above two axes. The three-dimensional data of the centroid lines of muscles were used to calculate the direction of force application by a line tangent to thecentroid line curves at the particular level of interest. The moment arms at the center of the trochlea in the plane of the crosssection and perpendicular to the forearm axis were calculated. The components of the moment arms of all
27 DISTANCE
FROU
NURRAL
31 MAD
(CM )
l o l
T01
33
BRA BIG
Fig. 2 Graphical representation of the centroid tines of a few muscles across elbow joint in extended/neutral position.
664
K. N. AN et al. Table 2. Flexion-extension moment arm (cm)
Group
Muscle
I
BIC BRA BRD PRO ECR
II
III
Elbow and forearm configuration E/P E/N
E/S -
1.964 0.869 2.565 1.186 1.162
-
1.468 0.592 2.467 1.481 1.205
- 1.271 - 1.098 - 2.502 -0.483 - 1.531
FW/N
FlW/S
FlW/N
-
2.674 1.292 3.697 1.585 1.982
- 3.203 - 1.977 -5.188 - 2.005 - 3.378
-3.431 - 2.052 -4.164 - 1.646 -2.871
FCR FDS
0.434 0.861
0.363 0.210
0.561 0.961
- 0.205 0.665
-0.751 - 0.235
- 0.923 - 0.027
TRI ANC FCU ECU
2.564 1.331 1.854 0.907
2.809 0.622 1.735 0.488
2.256 0.691 1.888 1.513
EDC
-0.321
-0.019
-0.133
2.474 1.738 1.877 1.202 1.134
1.867 0.715 0.769 0.632 - 0.748
2.039 1.126 1.326 0.659 -0.443
* Negative = Flexion
-
; Positive = Extension. Table 3. Varus-valgus moment arms (cm) Elbow and forearm configuration
Group
I
‘I
III
E/N
E/P
F50”/N
FlW/S
1.339 0.697 1.996 2.008 2.672
- 2.614 - 1.386 - 3.449 - 3.464 -4.015
- 1.322 - 1.084 - 2.751 - 3.064 -3.521
-0.758 -2.168 - 1.641 - 3.293 - 2.992
-
PRO FCR FCU FDS
2035 2.800 2.170 2.770
0.824 1.757 1.419 2.095
1.927 2.316 1.622 1.976
BIC BRA TRI
0.179 0.521 -0.398
0.978 -0.143 -0.260
- 0.378 0.321 -0.818
Muscle BRD ANC ECR ECU EDC
E/S -
FlW/N
1.314 1.754 1.841 2.852 3.243
-0.182 - 1.762 -0.462 - 2.873 -2.045
1.683 1.890 1.237 1.631
2.002 2.213 1.614 1.880
1.528 2.294 1.611 1.887
0.041 0.182 - 1.175
1.388 -0.146 -0.175
1.133 0.129 - 0.027
* Positive = Varus; Negative = Valgus.
the muscles across the elbow joint obtained from the six specimens at various elbow and forearm configurations are summarized in Tables 2,3 and 4. Since the data of the moment arms were obtained from six cadaver specimens, a normalization procedure was performed to compare the results. The data are adjusted such that the arm sizes are equivalent to that of the first specimen (i.e. extended-supinated specimen). The normalization length for each specimen is based on the ratio of the square root of the area of cross-section (excluding fat and skin) at the junction of the middle and proximal thirds of the forearm of the specimen with respect to the first specimen. Based on the variation of the flexion-extension moment arms through the range of elbow motion at the extended (OO),semi-flexed (So”), and flexed (100”) positions, the muscles across the elbow can be divided into three groups (Table 2). In Group I, which consists of BIC, BRA, BRD, ECR and PRO, the flexion+extension moment arms tended to increase with progressive flexion of the elbow joint in the flexed position. The moment arms of the major elbow flexors
in the flexed position were almost twice as great as those in the extended position. In Group II, which consists of the FCR and FDS, the muscles created an extension moment arm when the elbow was in the extended position but changed to a flexion moment as the elbow was flexed. In the third group, which consists of the rest of the muscles, the moment arms either did not change significantly in magnitude or direction, or their pattern of alteration was not well defined. The muscle grouping as described above is generally true whether the forearm was in the neutral or supinated position. However, the forearm rotation does have a slight effect on the flexion-extension moment arms for some muscles. In terms of the varus-valgus moment arms, the muscles could again be divided into three groups (Table 3). In Group I, all muscles arose from the lateral aspect of the distal humerus and consisted of the ANC, BRD, ECR, EDC and ECU. These muscles created valgus moments with respect to the joint center at the trochlea. In Group II, all muscles arose from the medial aspect of the distal humerus which consisted of
Muscles across the elbow joint Table 4. Rotational moment arm
665
about ulna axis (cm) __-
Muscle BIC BRA PRO BRD TRI ANC ECR FCR FDS FCU EDC ECU
Elbow and forearm configuration F50”/N E/P E/N
E/S -0.12 - 0.98 1.23 -0.22 - 0.40 0.83 -0.80 1.92 0.96 1.05 0.22 0.45
0.49 -0.32 0.75 - 1.29 0.28 2.23 - I.31 1.08 -0.54 0.29 -0.23 1.57
0.64 0.19 1.51 0.53 0.61 1.85 -0.94 1.52 0.68 -0.14 -0.75 0.40
FlW/S
1.29 -0.01 0.83 0.06 0.65 1.87 2.09 0.89 0.26 -0.20 0.36 0.79
0.91 -0.29 0.64 0.32 0.67 1.11 1.54 0.89 0.31 0.16 0.11 0.74
FlOO”/N 1.33 0.44 -0.01 -0.22 1.27 2.29 2.41 -0.29 -0.28 -0.19 -0.32 1.35
* Negative = Medial rotation.
Table 5. Volume, fiber length and physiological cross-sectional area Muscle
Volume km3)
Length (cm)
PCSA (cm’)
PCSA (%)
LHB SHB BRD BRA MHT LHT LNGT ANC PRO FCR ECRL ECRB
33.4 (8.6) 30.8 (9.1) 21.9 (8.5) 59.3 (16.2) 38.7 (17.1) 47.3 (11.8) 66.6 (19.5) 6.7 (3.4) 18.7 (9.5) 12.4 (4.9) 18.3 (7.5) 15.8 (8.1)
13.6 (2.4) 15.0 (3.4) 16.4 (2.9) 9.0 (2.9) 6.3 (1.4) 8.4 (1.0) 10.2 (1.9) 2.7 (0.3) 5.6 (1.7) 5.8 (0.9) 7.8 (0.5) 5.3 (0.6)
2.5 (0.5) 2.1 (0.5) 1.5 (0.5) 7.0 (1.9) 6.1 (2.3) 6.0 (1.2) 6.7 (2.0) 2.5 (1.2) 3.4 (1.5) 2.0 (0.6) 2.4 (1.0) 2.9 (1.4)
FCU
4.0 (0.6 j 3.4 (0.8) 2.4 (0.8) 11.8 (4.7) 9.8 (3.1) 10.0 (2.3) 11.1 (3.6) 3.9 (1.1) 5.3 (1.4) 3.3 (0.6) 3.7 (0.9) 4.5 (1.4)
15.2 (0.0)
4.8 (0.0)
14.9 10.9 4.9 5.9 8.0 4.7 11.1 13.7 7.8 3.3 5.1
3.2 (0.0)
4.5 (0.5) 3.3 (0.6) 6.7 (1.3) 6.9 (1.3) 6.1 (2.1) 5.9 (1.4) 4.5 (0.3) 7.7 (0.8) 6.4 (1.1) 4.5 (0.4) 5.7 (1.0)
4.7 (0.0)
3.4 (1.3) 3.4 (1.0) 0.7 (0.3) 0.9 (0.4) 1.4 (0.7) 0.8 (0.2) 2.5 (1.6) 1.7 (0.6) 1.2 (0.7) 0.7 (0.4) 0.9 (0.6)
4.8 (1.4) 5.6 (1.7) 1.2 (0.2) 1.3 (0.3) 2.2 (0.8) 1.3 (0.4) 3.8 (1.7) 2.7 (0.4) 1.8 (0.8) 1.1 (0.5) 1.2 (0.6)
ECU su EDC, EDC, EDC, EDC, FDS, FDS, FDS, FDS, PL
2 3 4 5 2 3 4 5
(5.7) (2.1) (1.5) (2.8) (3.9) (1.9) (6.7) (6.1) (5.5) (2.1) (3.9)
* Mean (S.D.); n = 4. PRO, FCR, FDS and FCU. These muscles generated varus moments. The major flexor and extensor muscles of the elbow, BIC, BRA and TRI, were centrally located with respect to the varus-valgus axis of rotation and tended to have a small varus-valgus moment arm to the elbow joint center. Individual variations were often noticed for these muscles. The configuration of forearm rotation seemed to have only a slight effect on the varus-valgus moment of any muscle. In general, with the forearm in a neutral position, the moment arms were relatively larger in Group I (lateral muscle), and smaller. for Group II (medial muscle). This difference was less noticeable in the supinated and pronated positions. Rotation of the elbow joint (flexion-extension) did not affect varus-valgus moment arms significantly.
The moment arms of muscles relating to the rotation along the forearm ulnar axis is recorded in Table 4. Both forearm and elbow joint configurations seem to have influence on this moment arm. Volume, jiber length and physiological cross-section area The results (Table 5) described in this section were obtained based on the dissection of four cadaver specimens following Brand’s technique. Volumes of all the muscles were measured by the water displacement method. The muscle fiber lengths obtained by this technique were considered to be a representation of the true fiber length, thus the corrections of the crosssectional areas for pennation angle described by Alexander (1975) were not required. The physiological
K. N. AN et
666
cross-sectional area was calculated by dividing muscle volume by its fiber length. Since the four specimens used for the study were comparable in size, normalization of the raw data was not necessary, although the physiological cross-sectional areas were normalized based on the total cross-sectional areas of the individual specimens. Each of the three components of the triceps mechanism had a larger volume but a shorter fiber length as compared to those of the biceps muscles. The long head of the biceps had the largest volume. In contrast, the brachioradialis had a smaller volume and a longer fiber. In general, the three components of the triceps and brachialis muscles had comparable values of physiological cross-sectional areas. Because‘of the long fiber length, the biceps and brachioradialis had relatively small physiological cross-sectional areas. On the other hand, all the wrist and finger muscles in the forearm had intermediate values of physiological cross-sectional area. Comparison of both raw and normalized data of physiological cross-sectional area indicated that normalization by expressing the data in percentages did not reduce the scattering of the data significantly. Finally, due to the difficulty in separating the composite proximal portions of the EDC and FDS during dissection, larger variations of the volume measurements of the components were noticed. DI!XXJSSION
When dealing with a force analysis of the musculoskeletal systems, the necessary biomechanical parameters must be derived through anatomical experiments. Several parameters were obtained in this study. By serially cross-sectioning the upper extremity, the centroids of all the muscles along the arm which cross the elbow joint were obtained. Jensen and Davy (1975) proposed using the centroid of a muscle’s cross-section as its point of action. The line of action of the muscle can be obtained by joining these centroids. This approach assumes that the muscle fibers, are distributed and contract uniformly across the cross-section and that the lines of action are perpendicular to these cross-sections. These assumptions may not be true under some conditions. For instance, when the crosssection is made oblique to the fiber length, the centroid line of that oblique cross-sectional area will not be an exact representation of the line of action of the muscle force. However, the majority of the muscles become tendinous near a joint and the cross-section of a tendon is usually normal to its fibers, thus accurate representation of the lines of action are generally possible. In certain instances, the muscle fiber might not contract uniformly at the cross-section except perhaps at maximum contraction. Nevertheless, the centroid line still provides the best estimation of the line of action and is more accurate than a straight line approximation. One disadvantage associated with the method of the
al.
serial sectioning technique for obtaining the centroid lines of the muscles is that only one elbow and forearm configuration is possible for each specimen. The error introduced by the anthropometric variation among additional specimens to obtain data for other positions is significant. In this study, the coordinates of the centroid lines or moment arms were normalized to the equivalent size based on the ratio of the square root of the forearm cross-sectional area, including those of bones and muscles. The selection of this normalization factor is based on the observation that the muscles and tendons are stacked up around the bones. Larger cross-sectional areas imply a farther distance from the joint center of the muscles and tendons. However, this normalization procedure has not yet been substantiated. Nevertheless, we believe the value of these moment arms, varying with the elbow and forearm configurations, are accurate. Another inherent error of using the results from in vitro cadaveric study for the in uiuo analysis should be kept in mind: when certain muscles contract, the position and orientation of their tendons may be different from those at the passive resting position. If reasonable resolution can be provided by the non-invasive computerized scanning technique, the errors from specimen variation as well as the lack of muscle tone could be resolved in future investigations. The results of the variation of muscle flexion moment arms at the elbow joint during flexion are similar to those. reported by Braune et al. (1890), Wilkie (1949) and Amis et al. (1979). In view of the limited‘joint positions and forearm configurations in the present study, the exact nature of either the linear or parabolic relationship cannot be assessed. However, the results suggest that the determination of the major components of moment arms based on both the crosssectional method (Jensen et al., 1975) and direct dissection method (Simpson, 1975) are relatively comparable. The results of the moment arm measurement indicate that the majority of the muscles create moments about all three axes but usually have one principal axis which is most dominant. The muscles with the greatest moment arm in flexion are BRD, BIC, BRA and ECR. Those with major moment arms contributing to extension are the TRI, FCU and ANC. The moment arm of a muscle merely indicates the efficiency of the muscle for rotation about that particular axis. The strength of each muscle is proportional to the physiological cross-sectional area. The work capacity is related to the muscle volume. The physiological cross-sectional area (PCSA) is obtained by dividing the muscle volume by its true fiber length. This calculation is used as an indicator of the possible tensile strength that can be developed by the individual muscle during maximum contraction. The rationale of this assumption is simply that the cross-sectional areas of muscles are:proportional to the number of muscle fibers, and the muscle fibers are the basic elements which generate tension. The relationship of a muscle’s
Muscles across the elbow joint force generation to its cross-sectional area is expressed as a proportional constant. The proportional eonst&t of the force, generated by a unit of cross-sectional area of a muscle, has been attempted in the past by many investigators (Ikai, 1968). However, widely divergent results have been reported. The discrepancies of these reports might simply be due to the variations among the types and functions of various muscle studies. However, we believe the variation reported in the literature is due to the fact that the exact physiological cross-sectional areas were not accurately measured during those experiments. Although the constants for the force generation per unit area are not consistent, the relative contribution based on the accurate measurement of physiological cross-sectional area can still be estimated. The potential moment contribution of each muscle at the elbow joint can be estimated by multiplying the moment arm of the muscle by its physiological crosssectional area. The contributions to flexion-extension and varus-valgus rotation for all of the muscles across the elbow joint have been calculated and are illustrated in Fig. 3. From these diagrams, it is obvious that the triceps muscle generates the largest moment about the elbow joint in all of the six elbow and forearm configurations studied. Although it is difficult to clearly and concisely express these data, the diagrams (Fig. 3) are very useful in understanding the moments generated by the muscles at the elbow joint. During maximum contraction, the overall moment in any direction could easily be obtained graphically or numerically. Of note, the potential moment in varus appears balanced by the valgus moment under all the six conditions. However, for flexion and extension, the flexion potential moments seem to be balanced by the extension moments when the elbow is flexed, while the extension moments exceed the flexion moments when the elbow is extended. It should be realized that the construction of Fig. 3 and the above discussion of the balance of the moments are based on the assumption that all of the muscles are simultaneously contracted maximally and at optimum length. To apply the data in Fig. 3 to more general conditions, a proportional adjustment for the potential moments should be made, based on the muscle force-length relationship (Inman and Ralston, 1968). In addition, for the purpose of calculating joint moments contributed by the muscles under non-isometric conditions, the muscle forces must be adjusted according to the muscle force-velocity relationship (Stem, 1974). And finally, when submaximum isometric contractions are encountered, the data shown in Fig. 3 can be scaled in proportion to the level of individual muscle activation as determined by electromyography (Dempster, 1947 ; Fidelus, 1973 ; Messier et al., 1971). During the gross dissection experiment, the tendon excursion through a fuIl range of joint rotation was measured by Brand in his study. A unique concept had thus been observed. The resting muscle fiber lengths, a middle position
within the full excursion, are thought
667
to be equal to the entire excursion length of that ptiticular muscle. If this concept is correct, then the muscle volume can be treated as the index of possible work capacity of that particular muscle. This is because the physiological cross-sectional area times fiber length (or excursion) is proportional to the work developed during maximum contraction through the entire excursion. In general, the triceps muscles and the brachialis muscle have relatively large strength potentials (large PCSA) and also work capacities (large volume). On the other hand, the wrist and finger muscles in the forearm have relatively small work capacities (small volume) but moderate strength potentials (large PCSA). Finally, an interesting and potentially useful observation has been noticed during this study. The physiological cross-section of a muscle was found to be closely correlated to its tendon cross-sectional area. This finding suggests that the tendon fibers may be related in some way to the sarcomere sheath in the muscle bundle. This relationship may also be useful in assisting the separation of muscle volume for the EDC and FDS muscles into appropriate subgroups.
SUMMARY
Several important biomechanical parameters of the muscles controlling the elbow joint have been determined. Serial cross-sectional anatomy analysis was used to obtain the centroid and thus the moment arms of each of the muscles along the upper arm and at the elbow joint. A special dissection technique developed by Brand was utilized to measure the muscle volume and true fiber length at the resting position. From these data, the physiological cross-sectional areas of the muscle were also obtained. The volume provided the information on the work capacity of the muscles. The physiological cross-sectional area provided the potential tension a muscle can generate. Based on the moment arm measurements, the BRD, BIC, BRA and ECR were demonstrated to be the major flexors for the elbow joint ; the TRI, FCU and ANC were the major extensors. Similarly, the ECU, EDC, ECR and BRD were the major muscles producing valgus forces and the FCR, FDS, PRO and FCU were the major muscles producing varus forces for the elbow. Based on the volume and physiological crosssectional area measurements, the triceps and brachialis had the largest work capacity (volume), as well as potential contractile strength (physiological crosssectional area).
Acknowk&emenr-This study was supported in part by NIH Grant Ah4 26287.The authors also acknowledge the help of Dr. P. W. Brand in demonstrating the special technique of muscle dissection and his interpretation.
K. N.
AN et al. ANTERIOR
ANTERIOR
-
cmxcm2 cmxcm2 ECR 11.978
MEDIAL
LATERAL
MEDIAL
LATERAL
TRI 48.520
I
POSTERIOR POsTERiOR
(b)
(a)
ANTERIOR
ANTERIOR
cmxcm2
cmxcm*
MEDIAL
LATERAL
LATER
MEDIAL
POSTERIOR POSTERIOR
(4
(4
ANTERIOR
LATERAL
LATERAL
POSTERIOR POSTERIOR
(4
Fig. 3. The potential moment contribution of each muscle at the elbow joint was estimated by multiplying the moment arm (cm) of the muscle by its physiological cross-sectional area (cm’). These diagrams show the contributions to flexion+xtension and varus-va lgus rotation about the joint center at six elbow and forearm configurations. (a) Extended/supinated; (b) extended/neutral; (c) extended/pronated; (d) semiflexed/neut4; (e) flexed/supinated; (f) flexed/neutral.
Muscles across the elbow joint
669
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