Bassett RW Glenohumeral Muscle Force

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406 R. W. BASSETT tr ui.

presented by this study. The orientation of eachspecimen required careful positioning with the as-sistance of radiography so as to place the brachium atapproximately 90 abduction, 90 of external rota-tion, and 0 Rexion and extension. All shoulder posi-tions were based on the thoracohumeral angle. Theforearm was placed in 90 of flexion and neutralpronation and supination. The elbow was incised andthe biceps and triceps tendons isolated. The tendonswere sutured to the distal end of the humerus throughdrill holes, thus maintaining their orientation andlength. The elbow was then disarticulated. The pre-pared specimens were placed in the freezer in such away as to avoid passive muscle sag.

Because of the significant clinical problem of shoul-der instability, two commonly performed surgicalprocedures involving the alteration of muscle ori-entation were done on three specimens. On two, aBristow-type procedure was performed, transplantingthe tip of the coracoid (just distal to the insertion of thepectoralis minor) with the conjoined tendon of theshort head of the biceps and the coracobrachialis ontothe anterior rim of the glenoid (Halley and Olix, 1975;Lombard0 et al.. 1976; May, 1970) and fixed with awooden peg. Glcnoid exposure was achieved by sub-scapularis split at the junction of the mid and lowerthird of the muscle and later m-approximated aroundthe transposed conjoined tendon with nylon sutures.A Magnuson -Stack (1943) proccdurc was pcrformcdon one shoulder specimen through an axillary skinincision. The subscapularis was sharply dissected fromthe lesser tubcrosity and transplanted 2 cm laterallyand I cm distally along the proximal humeral shaft.The tendon was anchored with nylon sutures throughdrill holes.

After freezing, each specimen was placed in a50 x 50 x 35 cm plexiglass container and embedded ina rapidly setting firm resin elastomer before the speci-

men had thawed. The abducted humeral shaft wasparallel to the long axis of the container. Once theelastomer had hardened, the specimen was placedback in the freezer until it was studied.

Biplanar radiographs were taken of the specimensatright angles to one another on a special radio-opaquegrid consisting of 2.5 x 2.5 cm squares (Fig. la). Thelocation of the humeral head within the glenoid fossacould be confirmed and accurately determined, thusavoiding possible subluxation resulting in a change insome moment arms. These radiographs allowed pre-cise three-dimensional location of bony landmarksfrom which a coordinate system could be defined(Morrey and Chao. 1976). The angular position of theshoulder waS calculated with respect to rotationsabout the X (axial rotation), Y(adduction, abduction),and Z (llexion and extension) axes at the positionstudied (Fig. I b).

Once the orientation had been determined. theembedded specimens were cut with a band saw toexpose serial cross-sections of the humeral shaft andshoulder musculature, proceeding proximally at I cmintervals from the humcral condyles (Fig. Ic). Thesection intervals were marked prior to cutting toprevent accumulative errors in section width, and thecuts were pcrpcndicular to the long (X) axis of thecube. After each cut, the surface was clcancd andmuscle boundaries emphasized prior to being photo-graphed from a fixed distance with a 35 mm camera.

The dcvclopcd 2 x 2 inch slides (Fig. 2) of eachcross-section were projected on a semi-opaque screen,positioned between two arms of a sonic digitizingsystem (Model 6P-3, Science AccessoriesCorporation,Southport. Connecticut). The circumference of eachmuscle was defined by digitizing the X and Y coord-inates of points on the periphery and stored in acomputer. From these data, the centroid and volumeof each muscle were calculated. The exact position of

(4 \ (b) (aFig. 1. (a) Radio-opaque grid. (b) Humcrd axis system. (c) Plane of cross-sections.


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(a) (h)Fig. 2. (a) A typid cross-section in the sagittd plane through the ccnkr of the humcrd head. (h) With

idcntilicdun of the muscles.

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Glenohumeral muscle brcc and moment mechanics

the humeral head relative to the glenoid fossa wasfurther confirmed on these serial gross muscle cross-section studies.

The muscle belly lengths were calculated by measur-ing the distance between the origin and insertion of themuscle-tendon junction based on the cross-sectionalslices. In most instances, the muscles were clearlydistinguishable (Fig. 2); however, since no distinctboundary could be made between the infraspinatusand teres minor on the photographic projections,these were treated as a single muscle. This assumptionwas felt to be reasonable, as these muscles were nearlyalways simultaneously active on EMG testing (Bas-majian. 1971). As it was impossible to identify theseparate heads of the deltoid distally, this muscle wasalso outlined as a single entity to the level of theacromion, where the anterior and posterior parts weremore clearly definable.

CALCtiLATION OF MOMENTSTo facilitate the calculation of the muscle moment

arm. a coordinate system was established. The centerof the coordinate system was placed in the center ofthe humernl head, as it had been shown IO coincidewith the center of rotation by Poppen and Walker(1976). The coordinate was d&cd as follows: the tipsof both humcral condylcs wcrc used to dcfinc the Yaxis: a lint from the ccntcr of the humeral head to apoint pcrpcndicular on the Y axis dcfincd the X axis;the % axis was then calculated as the cross-product ofthe unit vectors of X and Y. The Y axis thus deter-mined abduction and adduction of the shoulder inthe position studied. The X axis rcprcsented theinternal-external rotation axis of the shoulder.Finally, the 2 axis corresponded to flexion and exten-sion of this joint (Fig. I b). The moment of each muscleat the shoulder joint was calculated by first definingthe position of the centroid ofcach muscle with respectto the reference coordinate system using the techniquedescribed by Jensen and Davy (1975). The unit vectorof the muscle force was then detined based on thetangent to the line joining the centroid of each muscle.The moment arms were calculated based on the forcevector and position vectors at the section through thecenter of the humeral head.

RFStiLTSShouldrr orirntotion

The angular relationships were defined as the posi-tion of the arm with respect to the torso. The preciseEulerian angle calculations based on the coordinatesystem for the five specimens revealed a mean abduc-tion angle of 86 (range 78-89); Rexion of 4 (rangeO-8); and external rotation of 92 (range 89-101).Further, the glenohumeral contribution to abductionaveraged 64, while 22 occurred from scapulothor-acic rotation.


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410 R. W. BASSETT et al.

Muscle rolumc, fiber lm yt h, and physioloyicul cross-srctionul urea

The muscle volumes for the two specimens using theimmersion technique and the calculated muscle vol-umes for the remaining five specimens using the grossmuscle cross-section method are presented in Table I.Reasonable agreement was observed between the im-mersion method and the cross-section method ofcalculation. Extremely close agreement was notedbetween shoulders of the same cadavers (specimens 4and 5, and 6 and 7). thus establishing the reproducib-ility of the cross-section technique. To eliminate thelarge individual variation occurring from specimen tospecimen, the data were expressed as normalizedpercentages of the entire muscle volume. This pro-vided a relationship of the size of the muscle which wasalso observed to be reasonably consistent.

The muscle fiber length measured directly from theimmersion specimens and the muscle belly lengthscalculated from the specimens in the cross-sectionstudies are shown in Table 2. The physiological cross-sectional areas of each muscle calculated by dividingthe volume by the muscle fiber length in the immersionmethod and by the muscle belly length for the grossmuscle cross-section method are dcpictcd in Table 3.These values are also relatively consistent. particularlyin the normalized form. Some discrepancy may beattributed to varying dcgrbws of muscle utilization. theinfluence of the dominant extremity and the possibilityof hypertrophy.

The magnitude of the moment arm for the musclestudies in the five specimens are recorded in Table 4.The altered moments of the muscles for the threespecimens in which a surgical procedure was per-formed are excluded from the calculations for themean value. In some instances, an accurate orienta-

tion or delineation of one of the muscles could not bedefined with sufficient certainty to be included in thecalculations. For example, in specimens 3 and 4. thedeltoid was still present as a single muscle at the levelof the cross-section through the humeral head: there-fore, the anterior or posterior deltoid contributioncould not be accurately calculated.

By combining the data for magnitude of the mo-ment arm and the physiological cross-sectional area,the potential moments of each muscle for shoulderrotation were established (Table 5). To determine thepotential moment of each muscle, the magnitude ofthe moment arm was multiplied by the physiologicalcross-sectional area. This term was then multiplied bya constant of 3.5 kgcm-* (Ikai and Fukunaga. 1968)which related muscle force and physiological cross-sectional area, permitting the average potential mo-ment of each muscle for the shoulder to be calculated(Table 5).

The component of the moment arm of each muscleto rotate the shoulder joint with respect to a speciticaxis for a typical specimen are shown in Figs 3 and 4.In the position studied, rotation about the X axisrepresents the external axial rotation (-A. internalrotation). Rotation about the Yaxis represents adduc-tion (- Y, abduction). while rotation about the % axisrepresents forward flexion ( -Z, extension).

DISCUSSION

In the past, several problems have precluded thedefinition of the three-dimensional orientation andmagnitude of the moments and muscle distributionacross the shoulder. A definition of the plane oforientation is of some concern, since the plane of thescapula is not the same as the coronal plane of thebody. In addition, the orientation of the muscleschanges direction from longitudinal to transverse in

Table 2. Muscle Ii&r lengths (cm) and muscle belly lengths (cm)

SideMethodSpccimcn

n I IL R L R L R LFiber length Muscle belly lengthI 2 3 4 5 6 7Humerus (digitized length)Biceps (LH)Biceps (SH)CoracobrachailisDeltoid am.Deltoid mid.

- - 31 35 34 3412.9 16.3 31 36 34 34 ::14.6 19.6 I9 22 20 I9 I97.1 9.9 20 20 I9 I9 I79.6 II.97.8 10.8 I9 I9 20 23 I9

Deltoid post. 9.9 16.9 5 5 8 4 3Inka. + I. minor 8.5 9.3 12 10 :: 9 9Latissimus dorsi 21.7 34.6 I6 I8 I7 17Pee. major (sternal) 13.9 25.7Pet. major (clav.) 13.2 19.4 24 I6 I8 23 20Subscapularis 1.4 8.7 IO IO IS 8 IOSupraspinatus 7.0 6.9 II 8 I2 8 10Teres major 7.8 16.8 II 18 IITriceps (LH) 10.6 12.1 33 31 :: 29


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Glcnohumcral muscle force and moment mechwks JI Ithe abd ucted arm so that the cross-sectional area isdifficult to de termine with ce rtainty. The co rrelation ofwhich muscles may be ac tive for a given function, aswell as the relationship of the phy siolog ica l c ross-sectiona l area with its po tential force has. likewise,bee n the source of difficulty with respec t to definingthe force s whic h oc c ur at the shoulde r jo int. For thisreason, the previous works by Inma n et al. (19JJ),DeLuca and Forrest (1973). and Pop pen and Walke r(1976). while c ontributing valua ble information withrespec t to the problem . have not provided data whichallow an understanding of the three-d imensionalforce s oc c urring at this joint.

The present wo rk see ks to provid e a qua ntitativedescription of the muscles of the abd ucted and extern-ally rotate d shoulder in three dim ensions using thec ross-sec tion me thod. The c ross-sec tion m ethod forthe study of muscle force and mom ent arm m ec hanicshas ce rtain limitations. Due to its invasive nature. ea chspec imen c an only be studied for a given c onfigurationsimulating one particular loading condition. In ad-dition. using this method, a knowledg e of the loca tionof the ce nter of rotation of the glcnohumc ral joint isrequired for measurement of mom ent a rms. An altcr-native m ethod used for suc h studies and analysis isba sed on tend on joint exc ursion (An rt ~1.. 1983). Withthis technique. one may simulate multiple loadingc ond itions and pa tholog ica l states utilizing the sam espe cim en. Neverthele ss, the c ross-sec tion me thod hasprovided us with valuable information and allowedexam ination of the cha nge in mom ent a rm mag nitudeand direction for ce rtain proc cd urcs. The mom entarms for the live spe c imens were relatively c onsistentin their to tal le ngths, but due to mild d iffcrcnc es inpo sition, there wa s slightly grea ter variation in theindividual co mp one nts along the X. Y and Z axe s.

The mo me nt a rms for the latissimus do rsi, tc resmajor, a nd pectoralis ma jor ap pea red to be somew hatexc essive in som e of the spe cim ens. The extrem emo bility of these muscles and their d istant sites oforigin in relation to their hume ral insertions distingu-ish them from the rest of the shoulde r musculature.Their tendenc y to sag and the need to extend thec entroid line of the humerus p roximally pa st thehumeral head for ca lculations o f proximal musclesec tions undoubtedly co ntributed to some inacc uracyin the ca lculation of these mom ent arms.

The me thod used for the m usc le Fab er lengthme asurement and thus PCSA c alc ulation as de scribe dby Brand et ul. (1981) was ba sed on the rem arkab leinsight of the muscle ge om etry. They c onfirmed thatthe lengths of the libers arc co nstant throughout ea c hindividual muscle. We occ asionally observed a fewfibers at the proximal or distal end of the muscle thatwere long er tha n the others. As also observed b yBrand et ul.. the variation of fiber length w as c omm onfor those m uscles when the fiber wrapp ed around orc rossed the joint. The fbc rs that c rossed the jointc loser to the ce nter of rotatio n were shorter than thosefurther away.


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412 R. W. BASSEIT et 01.Table 4. Moment arm of shoulder muscles about the center of the humeral head (cm)

SideSpecimennumbern nL R L R L3 4 5 6 7 Mean

Biceps L H) 2 . 4 2 . 6 2 . 3 2 . 5 2 . 2 2 . 4Biceps (SH) 3.8 3.6 5.4 4.2 2.9 3.4Coracobrachialis 3.1 3.7 5.2. 3.8 3.5 3.6Deltoid 3.8 5.1 3.9 2.8 4.2Post. deltoid : t 5.0 5.4 5.6 5.3Infraspin. + I. minor 3.2 2.8 2.6 3.6 3.5 3.1Latissimus doni 8.7 17.5 6.0 ;:: 18.1 Il.7Pectoralis major 5.9 9.5 6.6 3.7 6.2Subscapularis 2.4 3.1 2.8 2.7 4.6: 2.8Supraspinatus 1.9 1.5 2.0 3.1 t 2.1Teres major 5.6 5.9 5.4 6.0 6.5 5.9Triceps (LH) 4.7 4.5 4.7 4.7 6.0 4.9

*Moment arm was altered by a surgical intervention to simulate a Bristow-type procedure andwas excluded from calculation of the mean.

tCalculation was omitted as delineation proved difficult.IMoment arm was altered by a surgical intervention to simulate a Magnuson-Stack-type

procedure and was excluded from calculation of the mean.

Table 5. Potential moment generated by shoulder muscles (Ncm-)

SideSpecimen numberr--l l---lL R L R L Mean SD.3 4 5 6 7

Biceps (LH) 1 3 . 5 1 5 . 7 I 3 . Y 2 1 . 5 1 9 . 4 1 6 . 8 3 . 5Biceps (SH) 32.1 20.8 35.0. 34.4 23.4 25.4 5.9Coracobrach. 14.8 16.8 25.19 26.1 27.7 19.1eltoidDeltoid post.

: 181.3 222.8 269.9 233. I 226.8 3zt 59.5 97.0 126.0 94.2 33:4

Infra. + I. min. 164.6 113.4 74.4 214.2 211.4 155.6 61.2Lat. dorsi 402.2 730.1 214.4 349.0 782.4 495.6 248.2Pet. major 290.3 427.6 254.3 253.9 201.9 285.6 85.4Subscapularis 94.Y 1 5 3 . 1 9 0 . 5 2 4 5 . 6 3 3 5 . 8 $ 1 4 6 . 0 7 2 . 3Supraspinatus 41.6 30.2 26.7 76.9 43.9 23.0Teres major 207.6 130.3 73.9 232. I 27:.0 183.4 80.3Triceps (LH) 69.6 43.8 48.4 75.8 109.8 69.5 26.3

*Potential moment altered by a surgical intervention to simulate a Bristow-type procedure and was excluded fromcalculation of the mean and standard deviation.

tCalculation was omitted as delineation proved ditlicult.:Potential moment was altered by a surgical intervention to simulate a Magnuson-Stack-type procedure and was excludedrrom calculation of the mean and standard deviation.

There were some differences between the musclefiber lengths in the two immersion specimens and themuscle belly lengths taken from the cross-sectionstudies, in particular the long head of biceps andcoracobrachialis. However, this appears to be com-pensated by the larger volumes as seen in Table 1.resulting in comparable physiological cross-sectionalareas as in Table 3. The apparent discrepancies be-tween these two methods for the latissimus dorsi andposterior deltoid may be explained by muscle sag.resulting in a shorter muscle belly observed with thecross-section technique.

Two other assumptions which may have affectedthe study were individual muscle structure and scapu-

lothoracic rhythm concurrent with glenohumeral ab-duction. The assumption that centroid lines are truerepresentations of force vectors is invalid for unipen-nate and asymmetrical muscles. This is not a largefactor in the shoulder, as the muscles are of a complexbipennate or multipennate nature. Finally, the scapu-lothoracic motion accompanying active shoulder ab-duction was possibly not exactly duplicated in thesecadavers in which the position was from passiverotations. Though Poppen and Walker (1976, 1978)found the glenohumeral rhythm of cadavers to bewithin the normal in viuo range, it is possible that moremotion occurred at the glenohumeral joint and less atthe scapulothoracic interface than would be seen in


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Glenohumeral muscle force and moment mechanics

rotation about - Y(abduction)

BKW!*. 4 Swrawh.aluus,

rotation about -2(extension)

rotation about l(adduction)

rotation about + 2(torward flexion)

PectoralIs Maior4 \ LsUsslmus Oorri

Fig. 3. Illustration of moment arm magnitude components and direction for a typical specimen in resistingload applied at the glenohumeral joint in llcxion, exlension. abduction. and adduction. For example, in the

position studied. the pectoralis major is a strong forward flexor and adductor.rotation about -Y(abduction)

IbCsm

rotation about +X(external rotation)

rotation about -X(Internal rotation)

Fig. 4. IllustraGon of moment arm magnitude components and direction for a typical specimen in resistingload applied at the glenohumeral joint in abduction, adduction. internal and external rotation. For example.

in the position studied. the latissimus dorsi is a strong internal rotator and adductor.


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-11-l R. W. BASEIT et al.

living subjects. Potential muscle atrophy or tears ofthe rotator cuff (i.e. supraspinatus and long head ofthe biceps) may alter the resultant moment of adjacentmuscles and should be a consideration with such astudy. However. no such tear was observed in theseparticular shoulder specimens. Consideration shouldbe given to the fact that due to the small number ofcadaveric specimens, the data presented here may notbe representative of the population as a whole.

The most effective flexors of the shoulder are thepectoral, the short head of the biceps. the coracobra-chialis. the anterior deltoid. and the subscapularis(Figs 3 and 4). These are also the structures whichappear to most effectively resist anterior dislocation ofthe humerus. In the position of 907 of external rota-tion, even the latissimus dorsi, teres major, and tricepshave weak tlexion moment arms. From this location,the abductors of the shoulder are the anterior deltoid.the short head of the biceps, the long head of thebiceps, and minimally supraspinatus. In this externallyrotated and abducted position, most of the rotator cuffmuscles and the posterior deltoid actually becameadductors.

There are few muscles acting as external rotators ofthe shoulder in the position studied, which is in nearmaximal external rotation (Fig. 4). The long head ofthe biceps, coracobrachialis. and posterior deltoid areorionted to increase external rotation from this po-sition. The short hcnd of the biceps acts as a minorexternal rotator, most of the other muscles havingpowerful internal rotation moment arms.The kinematics of the shoulder are c?mplica\ed bythe fact that a muscles function changes dependingupon its line of action referable to the center ofrotation, and this is dependent on the specific positionof the shoulder at any given time. Figures 3 and 4illustrate the fact that any vector lying on or close toan axis will have the potential to change its functionwith slight changes in joint position. Hence, in theabducted position, the supraspinatus, infraspinatus,and teres minor can act as either minor external orinternal rotators, depending on the exact rotationalposition of the humerus (Fig. 4).

Table 4 shows the mean magnitude of moment armfor each muscle. The values logically progress as oneconsiders the muscles going from deep to superficial.The only previous study to quote measurements formuscle moment arms was that of Poppen and Walker(1976). Their study of the shoulder in abductionexpressed the moment arm values in two-dimensionalterms of the plane of abduction, ignoring theanterior-posterior component. At 90 of shoulderabduction with neutral rotation. the supraspinatus isoriented to act as an abductor with little, if any,function as a flexor or extensor. The moment arm ofthe muscle described here is 21 mm which comparesfavorably with the 22 mm value described by Poppenand Walker (1976). However, in the position of abduc-tion and external rotation, we observed the majorcomponent of the moment arm of the supraspinatus to

be as an extensor and external rotator. Unfortunately,no other muscles are comparably oriented to allowcomparison in this fashion. All of the specimensdemonstrated moderate variation in moment armorientation. The major variation was the effect ofalignment that influenced abduction and externalrotation.

In the position studied. the effect of the modifiedBristow procedure was to change the short head of thebiceps and coracobrachialis from weak abductors andexternal rotators to poor adductors and internalrotators, while the flexion moment remainedunchanged.

The moment arm of the subcapularis appeared to beincreased by the Magnuson-Stack procedure in speci-men 7 and can be explained by the more distal transferof that muscle. With this procedure the subscapulariscan change from being an adductor to an abductor,depending on the exact placement. A more distaltransposition will retain, if not increase, adductionand increase both internal rotation and flexionmoments.

REFERENCES

An, K. N., Hui. F. C.. Morrcy. 8. F., Linsehcid. R. L. andChao, E. Y. (1981) Muscles across the elbow joint: abiomcchanieal analysis. J. Binmechunics 14, 659-669.

An. K. N.. Ueba. Y.. Chao. E. Y.. Cooncy, W. P. andLinscheid. R. L. (1983)Tcndon excursion and moment armof index linger muscles. J. Biomcchunics 16.419-425.

Basmajian. J. V. (1971) Musckes Alioe--Their Fun&m Re-ueded by Elecrromyography. Williams & Wilkins.Baltimore.Brand, P. W.. Beach. M. A. and Thompson, D. E. (1981)Relative tension and potential excursion of muscles in theforearm and hand. J. ffund Surg, 6. 209-219.DcLuca, C. J. and Forrest, W. J. (1973) Force analysis ofindividual muscles acting rimultancously on the shoulderjoint during isometric abduction. J. Biomechunics 6,385393.

Halley, D. K. and Olix. M. L. (1975) A review of the Bristowoperation for recurrent anterior shoulder dislocation inathletes. Clin. Orlhop. 106, 175-179.

Ikai. M. and Fukunaga. T. (1968) Calculation of musclestrength per unit of cross-sectional arca of human muscle.Z. Anyew. Physiol. Einschl. Argeilphysiof. 26, 26.

Inman, V. T., Sanders, M. and Abbott, L. C. (1944) Obscr-vations on the function of the shoulder joint. J. Bone JrSury. 26A. I-30.Jensen. R. H. and Davy, D. T. (1975) An investigation ofmuscle lines of action about the hip: a centroid lineapproach vs the straight line approach. J. Bbmerhunics 8,103-l IO.Jones, D. W. (1970) The role of shoulder muscles n control ofhumeral position (an electromyographic study). MastersThesis, Case Wcstcrn Rcscrve University.

Lombardo. S. J.. Kerlan, R. K.. Jobc. F. W.. Carter. V. S.,Blazina. M. E. and Shields, C. L. (1976) The modifiedBristow proecdure for recurrent dislocation of the shoul-der. J. Bone Jr Surg. SSA. 256-261.Magnuson. P. 8. and Stack, J. K. (1943) Recurrent disloca-tion of the shoulder. J. Am. med. Ass. 12X889-892.May. V. R. (1970) A modified Bristow operation for anteriorrecurrent dislocation of the shoulder. J. Bone Jr Sura. 52A.1010-1016.Morrcy. 8. F. and Chao, E. Y. S. (1976) Passive motion of theelbow joint. J. Bone Jr Surg. 58A, 501408.


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Glcnohumcral muscle force and moment mrchamcs 415

Poppcn, N. K. and Walker. P. S. (1976) Normal and ab Steno, N. (1667). Efemvntorum myokogiae specimen s. muscufinormal motion of the shoulder. J. Bone JI Surg. IA, descriprio geomerriccl. Inman. V. (Ed.) ( I9 IO) Opera Philoso-195-201. phico, Vol. 2. p. 108. Copenhagen. Quoted in Bastholm. E.

Poppcn. N. K. and Walker, P. S. (1978) Forces at the (195C) The History of ~%fuscle Physiology. Ejnar Munks-glenohumcral joint in abduction. Clin. Orthop. 135, gaard, Copenhagen.165-170.

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Bassett RW Glenohumeral Muscle Force