Extraocular muscle forces in normalhuman subjects

Carter C. Collins, Melvin R. Carlson, Alan B. Scott, and Arthur Jampolsky

Actively developed horizontal muscle forces and tissue stiffnesses were measured in 29 normalorthophoric volunteer subjects (18 to 33 years old) by means of noninvasive length-tensionforceps. Mean active fixation force developed at 50 deg extreme gaze was 26% greater for themedial rectus (74.8 gm) than for the lateral rectus (59.1 gm). The variation of maximum activeforce among individuals was 2:1 (48 to 103 gm). These muscles developed up to 25% of theirmaximum active force out of their field of action. Active (counter) hysteresis force differences ofover 10 gm were measured between nasal and temporal gaze directions. This study suggeststhat a muscle which develops a maximum active force of less than 45 gm ivould be suspect asparetic. Variations from the normal pattern of reciprocal innervation, reflected in the graded,active force of individual muscle contraction, may help in understanding some types ofoculomotor pathology. The mean tissue stiffness -restraining movement of the globe in thenasal direction (1.05 gm/deg) is 11 % greater than in the temporal direction (0.94 gm/deg). Thisis consistent with a stronger medial rectus balanced by a greater load. Variation of stiffness of2:1 was observed among individuals; 0.8 to 1.7 gm/deg pulling nasally and 0.77 to 1.2 gm/degtemporally. Passive hysteresis and viscous force differences of over 10 gm were observedbetween the passive forced pull and normal spring-return of the eye. Large stiffnesses may benormal if balanced by large active forces. Abrupt changes of the length-tension curve indicatethe magnitude and location of restrictions.

Key words: length-tension, active force, stiffness, hysteresis,reciprocal innervation, restrictions

AAccurate information is needed on the ac-tive and passive forces that are present at agiven positioning of the eyes. Strabismusdiagnosis and surgical planning benefit fromknowing the magnitude of the actively devel-oped forces of each muscle as well as the bal-ance of agonist and antagonist active forces.

From The Smith-Kettlewell Institute of Visual Sciences,San Francisco, Calif.

Supported by National Institutes of Health Researchgrants 5R01-EY 01719, 5P30 EY 01186, and 5S01RR 05566, and The Smith-Kettlewell Eye ResearchFoundation.

Submitted for publication Dec. 21, 1979.Reprint requests: Dr. Carter C. Collins, Smith-Ket-

tlewell Institute of Visual Sciences, 2232 Webster St.,San Francisco, Calif. 94115.

We also need to know the normal load (stiff-ness) that must be overcome to move the eyefrom a certain eye position. This informationcan be useful when making a differentialdiagnosis of the strabismus disorder andcan aid in decisions regarding surgical man-agement.

Most reported load (stiffness) values or ac-tive muscle forces are in one direction only1"3

or are unaccompanied by data on the relaxingantagonist muscle force acting against theagonist force.3"6 In addition, much of thisdata is from strabismic eyes, possibly non-representative of normal subjects.5' 6 There isan obvious need for such information from acomprehensive sample of normal individuals.

Using normal subjects, we have measuredthe magnitude of active (isometric) force de-

652 0146-0404/81/050652+13$01.30/0 © 1981 Assoc. for Res. in Vis. and Ophthal., Inc.

Volume 20Number 5 Extraocular muscle forces in human subjects 653

Fig. 1. Length-tension forceps as used with a subject. Electronic strain gauges in the forcepsshanks measure force. Note the forceps grasping the nasal limbus. A small loudspeaker (ultra-sonic pulse source) mounted on the frame of a pair of glasses can be seen. Time of flight ofsound from loudspeaker to a microphone mounted above the tip of the forceps is proportionalto the distance of the forceps from the source (fixed on the head).

veloped separately by the medial rectusmuscle and by the lateral rectus muscle dur-ing fixation in horizontal gaze. We have alsomeasured the magnitude of the load (stiff-ness) that these muscles must overcome tomove the eye in each direction.

These data provide a quantitative baselineof the active and passive forces acting on anormal eye. In a patient with strabismus, dif-ferences from these values aid in making adifferential diagnosis resulting in more accu-rate quantitative planning of strabismussurgery.

Methods and protocol

We have measured 29 normal volunteer sub-jects ranging in age from 18 to 33 years. Theyshowed no pathological conditions. All werewithin 2 A of being orthophoric.

A newly developed clinical technique previ-ously described7 was employed for assessing andrecording the individual medial and lateral rectusactive muscle force as a function of eye positionover a 100 deg range of horizontal gaze. The load(stiffness) of the orbital tissues was also deter-mined over a 60 to 100 deg range of eye position.The technique utilized a specially instrumentedforceps to obtain a measurement of force (up to

110 gm) and forceps-positioned eye displacement(up to 20 mm).

The forceps employed were the large Piersestraight fixation forceps (Storz Model E1942-13).The broad tip of the forceps permit a firm grip ofthe limbal conjunctiva. The shanks of the forcepstip were milled to a width of 0.7 mm for a distanceof 15 mm up the shank. Semiconductor straingauges were mounted on these narrow beams tomeasure any force applied at right angles to thelong axis of the forceps. The force required to ro-tate the globe or the force applied by muscles tothe globe as the forceps held the globe in a fixedposition could then be measured.7 Force readingswere linear within ±2% over a ±150 gm range.Hysteresis was less than ±0.50 gm after ±100 gmof load had been applied.7 A small microphonewith an opening near the tip of the forceps de-tected inaudible sound pulses from an ultrasonicsource attached to the head of the subject. Thisultrasonic device served as a sonar system andprovided a constant indication of the distance be-tween the ultrasonic source and the forceps tip.Because the ultrasonic source was fixed on thehead, a measure of eye position was obtained froma knowledge of the forceps tip location. Positionaccuracy was within ±3% over the range of ±50deg of eye position.

This noninvasive forceps and ultrasonic sound

654 Collins et al.Invest. Ophthalmol. Vis. Set.

May 1981

L-T FORCEPS PROTOCOL

Track

Temporal

Passive Load ^ 500 0 50°Eye Position

Nasal Temporal

LMR ActiveForces

Hold

•<V:-. % f \ NasalPassive Load

Pull

LLR ActiveForces

Track Hold

Fig. 2. Length-tension forceps protocol for left eye measurements. A, Subject maintains 30deg right fixation with right eye. The left eye is slowly (10 deg/sec) rotated temporalward andreturned several times. The resulting load (stiftness) record represents the resistance to tem-poral rotation of the eye. B, Forceps hold the left eye steadily at a 50 deg temporalwardrotation as subject tracks a slowly (10 deg/sec), smoothly moving target from 50 deg left to 50deg right and return with the right eye. A plot of actively developed force, FM, of the isolatedleft medial rectus muscle as a function of gaze effort can be determined. C, A mirror image ofA results in the load (stiffness) for nasal rotation. D, Mirror image of B results in the activeforce, FL, of the isolated left lateral rectus muscle as a function of gaze effort can be deter-mined.

source are shown in Fig. 1. The source of ul-trasound can be seen mounted on the frame of apair of glasses. The ultrasonic source may also bemounted on a headband, with a flexible piece ofheavy copper wire to permit adjustment forproper location (approximately 2 inches temporalto the outer can thus of the subject's eye). The ul-trasonic source provides a sound field immediatelyin front of the eye. This permits the position of theeye (forceps tip) to be monitored continuouslywith force measurements over a 100 deg range ofeye position.

The forceps are held perpendicular to the globeat all times in order to obtain proper readings offorce and position. An error in the recorded forcecan result from misalignment. If the forceps areheld within ±15 deg of the perpendicular to thesurface of the globe, the geometrical cosine erroris within 3% for force and position readings. Aseparate observer checked that the forceps wereheld within this angle at all times. During a typicalstiffness measurement, force and position errorstend to cancel each other, further ensuring reli-able measurements.

An X-Y oscilloscope was used to display force as

a function of eye position. This instantaneous dis-play of data enabled us to determine whether thedata were in the expected range, were reasonablylinear, and were free of artifacts. If not, the mea-surements were immediately repeated for confir-mation. These data were simultaneously recordedon a multitrack FM tape recorder for later play-back on an X-Y chart recorder to provide a perma-nent record.

From the family of innervated length-tensioncurves of oculorotary muscle it can be shown thatactive and elastic forces operate independently ofeach other and can be separately measured. In thisstudy we measured the stiffness associated withinnervated muscles, not passive muscles, perse. Ifthe muscle innervation remains constant, then theforce changes due to varying the length of themuscle are elastic in nature as seen from the con-stant slope of the length-tension curve.0' fi Con-versely, force changes made with a constant mus-cle length are active in nature (are due only tochanges of innervation). These separate active andelastic force components can be simply added toarrive at the total force acting on the eye.

It has been previously determined that the ac-

Volume 20Number 5 Extraocular muscle forces in human subjects 655

-3050 40 30 20 10 0 10 20 30 40 50

NASAL EYE POSITION, degrees TEMPORAL

Fig. 3. Load (stiffness) record for a temporal rotation of an intact, normal human left eyemeasured in Subject K. C. The left eye was abducted from 30 deg nasal to 45 deg temporal,returned to 30 deg nasal, and repeated with the length-tension forceps. The average loadstiffness, (KT), for this temporalward pull is 0.86 gm/deg. Although low, this stiffness is within9% of the mean value for all subjects in this study. On the return pull near the 30 deg nasalducted position, the subject attempted a saccade to the right.

tive force of an individual medial or lateral rectusmuscle can be effectively isolated and measuredby eliminating contributions of its antagonist overmost of its range of innervation.7 To do this, thesubject is requested to fixate a target at extremegaze. The eye is then pulled beyond this ex-treme-gaze position and held rigidly fixed with theforceps. The "excluded" muscle can thereby beshortened to the point that it is slack. Even whileinnervated, as long as the muscle is in a slack con-dition, by definition it exerts no tensile force.Therefore, as the subject is directed to track aknown target with the opposite eye, the force re-corded by the forceps is essentially due to theisometric-ally extended agonist muscle. The an-tagonist muscle may in some instances contributea small force change if not entirely slack near thezero force region of the measured muscle.

By Hering's Law, innervation of the right eyewill be accompanied by similar innervation of theyoke muscles of the left eye. Consequently, a plotoHeft eye active muscle force as a function of gaze

effort (attempted eye position) can be determinedby monitoring right eye position, as in Fig. 2, Band D. The right eye (target) position signal isused to deflect the horizontal axis, and the mea-sured force from the left eye is used to deflect thevertical axis of an X-Y oscilloscope or X-Y plotter.

The protocol followed in this investigation is nowdescribed. The tension developed by the left eye ismeasured in all subjects. Topical anesthesia drops{proparacaine hydrochloride, 0.5%) are instilled inthe subject's left eye. The force and displacementchannels of the length-tension forceps are zeroed.Fig. 2 illustrates the protocol employed.

1. For a measurement of the orbital load due toa temporal rotation, the subject is directed to fixthe gaze of his right eye on a 30 deg right target(Fig. 2, A). The nasal limbus of the left eye isgrasped with the forceps. The left eye is thenslowly rotated from its 30 deg right position tem-porally to 30 deg or more left and returned to itsstarting position. This slow (10 deg/sec) ductionmovement results in a graphic plot of the load

656 Collins et al.Invest. Ophthalmol. Vis. Sci.

May 1981

100*

90-

80?-

10-

-10*

-20-

-30-50 40 30 20 10 0 10 20 30 40 50

NASAL EYE POSITION, degrees TEMPORAL

Fig. 4. Record of the active force, FM, developed by the left medial rectus muscle of SubjectK. C. Upper curve, Agonist activity; lower curve, active antagonist graded relaxation force.Both are functions of gaze effort.

(stiffness) characteristics of the left eye, as shownin Fig. 3. The procedure is performed two or threetimes. The length-tension characteristics repre-sent the stiffness of the combined orbital tissuesconstituting the load the extraocular muscles mustmove, particularly in the temporal field of gaze.We chose the 30 deg position for fixation ratherthan the primary position in order to obtain anuninterrupted measurement of stiffness over alarge range of gaze extending through the primaryposition.

2. To measure active medial rectus force, theleft eye is held steadily in the extreme 50 degabducted position while the subject tracks asmoothly moving target with his free right eye(Fig. 2, B). The target is a small bright red spotprojected from a 0.3 mm helium-neon laser sourceand is moved electronically (by a triangle wave)from the 50 deg left gaze position at a constant rateof 10 deg/sec to the extreme 50 deg right gazeposition and is then returned. This procedure isperformed two or three times. The left eye is thenreleased, and the subject is permitted to rest.

Plotting force measured from the left eye vs.right eye position results in a graph of the activeforce pattern of the left medial rectus muscle as a

function of gaze effort, as shown in Fig. 4. Thisisometric, active force is directly proportional tomedial rectus muscle innervation.'

During the foregoing procedure, the left lateralrectus muscle is foreshortened to a slack length.As long as it is slack, it will not deliver force to themeasuring forceps. Thus the isometric, extendedmedial rectus muscle may be effectively isolatedover most of its range of innervation, and thereforeits actively developed force can be assessed.

3. The orbital load for a nasal rotation is ob-tained in a similar fashion to that of Fig. 2, A, butin mirror imagery (Fig. 2, C). The subject fixates atarget at 30 deg left with his right eye. The tem-poral limbus of the left eye is grasped with theforceps, and the left eye is slowly moved nasallyfrom 30 deg left to 30 cleg or more right and re-turned. This procedure is performed two or threetimes. The procedure measures the load (stiffness)of the left eye, particularly into the field of actionof the left medial rectus muscle. The resultinglength-tension characteristics represent the stiff-ness of the orbital tissues constituting the load themedial rectus muscle must move, as shown inFig. 5.

4. The active lateral rectus muscle force is

Volume 20Number 5 Extraocular muscle forces in human subjects 657

50 40 30 20 10 0 10 20 30 40 50

!, NASAL EYE POSITION, degrees TEMPORAL

Fig. 5. Measurement of the load (stiffness) of a nasal rotation of the intact left eye of SubjectK. C. The average load stiffness for this nasalward pull is 1.1 gm/deg.

obtained in a similar fashion to that of Fig. 2, B,but in mirror imagery (Fig. 2, D). As the left eye isfirmly held in the 50 deg adducted position, thesubject tracks the steadily moving target with hisright eye from 50 deg gaze right to 50 deg gaze leftand back again, repeating the constant velocity (10deg/sec) tracking movements through two or threecycles. At the end of a cycle when the right eye isonce again looking 50 deg right, the left eye isreleased, and the measurements are done. Thisprocedure measures the isolated left lateral rectusmuscle active force as a function of gaze effort,such as shown in Fig. 6.

Results

All the active force and load (stiffness) rec-ords shown in the figures of this report werepurposely chosen from a single typical sub-ject (K. C). This permitted a direct compari-son of the active force as well as the lengthtension characteristics of the medial and lat-eral rectus muscles within the same subject.

Tissue stiffness. Fig. 3 is a record of thedata resulting from a forced rotation with thelength-tension forceps. The "noise" on the

force channel was due primarily to tremor ofthe eye, plus some contributed by tremor ofthe forceps holder's hand. The measuredstiffness in the temporal field for SubjectK. C. could be seen to be 0.86 gm/deg (KT inTable I). Stiffness is defined here as the slopeof the length-tension curve as the eye ispulled away from the equilibrium or zero netforce position. Note that the stiffness mea-sured during the return phase was essentiallythe same as that measured during extension.Successive pulls resulted very closely in thesame measured forces, providing confidencein the method and credibility of the results oftissue load (stiffness) measurements (Fig. 3).

Fig. 3 shows two successive pulls (above)and one return phase (below). Note that themeasured force during the return phase wasconsiderably less than on the pulling phase.This force difference was due to viscosity andhysteresis caused by internal friction. Hys-teresis is defined as a retardation of dis-placement when the direction of force actingupon a body is changed. In this example the

658 Collins et al.Invest, Ophthahnol. Vis. Sci.

May 1981

50 40 30 20 10 0 10 20 30 40 50

NASAL EYE POSITION, degrees TEMPORAL

Fig. 6. Data comprising a record of the active force developed by the left lateral rectus muscle,FL, as a function of gaze effort (right eye position) in the intact eye of Subject K. C. Uppercurves, As the muscle acted as an agonist; lower curves, during graded relaxation of the muscleas tin antagonist; 1.5 cycles of activity are recorded.

effects of viscosity and hysteresis could beclearly seen as the nearly constant force dif-ference (of about 12 gm) between the exten-sion and return phase. A greater force differ-ence was seen with faster rates of pull andreturn due to viscosity. To reduce effects ofviscosity we pulled the eye at a low rate,about 10 deg/sec (2 mm/sec). Physiologicaldata indicate that the viscous force is about 3gm when oculorotary muscles are pulled at10 deg/sec.8 Thus in each direction the vis-cous and hysteresis forces were about equal,3 gm each, for 6 gm total in one direction and6 gm in the opposite direction.

Fig. 5 is a record of the load data obtainedby rotating the left eye nasally to about 40deg while the right eye maintained fixationon a 30 deg left target. Two successive nasalpulls could be seen to virtually coincide. Thestiffness of the tissue load was 1.1 gm/deg (KN

in Table I). There was also a force differencedue to hysteresis and viscosity of 10 to 15 gm

during the return phase, particularly in thenasal field, which is the field of action of themedial rectus muscle. Fig. 7 permits directcomparison of the separate loads (stiffnesses)associated with rotation of the eye, first tem-porally and then nasally.

Table I shows the results of stiffness mea-surements for temporal pulls (KT) and fornasal pulls (KN) for each of the 29 normal sub-jects in this study. A standard t test on indi-vidual pairs of stiffness values showed a sig-nificant difference (p = 0.01). It will benoted that the mean stiffness when the eyewas rotated in the nasal direction (1.049 gm/deg) was some 11% greater than the stiffnesswhen the eye was rotated in the temporaldirection (0.942 gm/deg). This indicates thata greater active force was required to rotatethe eye in the nasal direction than in thetemporal direction. This would suggest thatto maintain comitancy (both eyes pointing inthe same direction) during eye rotations, the

Volume 20Number 5 Extraocular muscle forces in human subjects 659

-50 40N

20 10 0 10 20 30 40 50

EYE POSITION, degrees T

Fig. 7. Load stiffness records of the left eye of a normal subject (K. C) . The record sloping upto the right on the graph represents the force required to pull the intact, covered left eyetemporal ward, The slope of this curve, KT = 0.86gm/deg, represents primarily the stiffness ofthe left medial rectus muscle and associated passive tissues restraining globe motion in thetemporal direction. The record sloping up to the left on the graph represents the forcerequired to pull the intact, covered left eye nasalward. The slope of this curve, KN = 1 . 1gin/deg, represents primarily the stiffness of the left lateral rectus muscle and associatedpassive tissues restraining movement of the globe in the nasal direction. The large asymmetryol stiffness in the two directions of gaze is clearly evident in these records, and KN was greaterthan KT in 24 of 29 normal subjects.

medial rectus muscle must be "stronger"than the lateral rectus muscle.

S.E.M.'s were less than 5% of the meanvalue for nasal rotations and less than 3% ofthe mean for temporal rotations. The indi-vidual variation of tissue stiffness was approx-imately two to one as found in this normalpopulation. The variation was 0.8 to 1.7gm/deg for nasal rotations and 0.77 to 1.2gm/deg for temporal rotations.

Active muscle forces. The active force dueto an effectively isolated, isometric left me-dial rectus muscle as a function of eye posi-tion is presented in Fig. 4. The upper curveshows the active force when the medial rec-tus muscle functioned as an agonist, and thelower curve shows the graded release of ac-tive force while the medial rectus muscle wasrelaxing as an antagonist. There was some10 gm greater force developed by this muscle

when it acted as an agonist than when it actedas an antagonist. This force difference wasnearly constant over the field of action of themuscle and up to 20 deg out of its field ofaction. (A muscle is said to be within its fieldof action when it is shorter than primarylength, i.e., the length when looking straightahead.) When functioning as an agonist, themaximum sustained fixational force devel-oped by the medial rectus muscle of this sub-ject was about 68 gm. The observed transientpeaks to 73 gm may be associated with sac-cadic refixation. Inadvertent small move-ments of the forceps were continuously moni-tored by means of the sonar length-detectingsystem, and representative active force rec-ords were selected only when forceps move-ment was less than 0.5 mm, e.g., Fig. 4.

The actively developed force data from theisometric left lateral rectus muscle of Subject

660 Collins et al.Invest. Ophthalmol. Vis. Set.

May 1981

0- 5 0

N

40 30 20 10 0 10 20 30 40 50

EYE POSITION, degrees T

Fig. 8. Single traces of the active force measured in Subject K. C. from the left lateral rectusmuscle (sloping up to the right) and the left medial rectus muscle (sloping up to the left). Bothof these records represent active force with the muscle acting as an agonist. Nasal gaze effort isleft on the graph, temporal to the right. The maximum medial rectus active muscle force isseen to be about 70 gm, whereas the maximum lateral rectus active muscle force is about 50gm. The nonlinear character of the active force as a function of gaze effort is clearly seen foreach muscle, with only 25% to 30% of the total active force being developed at the primaryposition and active force balance occurring at 12 to 15 deg temporally.

K. C. are shown in Fig. 6. The magnitudeand shape of the active force curves wereconsistent over a number of cycles of righteye movement from 50 deg nasal to 50 degtemporal rotation. When the lateral rectusmuscle was acting as an agonist, its maximumsustained active fixational force was 50 gm,with transient saccadic refixation peaks to 55gm. Again, there was some 10 gm greateractive force developed by the lateral rectusmuscle when acting as an agonist than whenacting as an antagonist over the entire 100deg range of muscle activity.

Fig. 8 plots on the same graph, for directcomparison, the active force data of the me-dial and lateral rectus muscles. It can beseen that an oculorotary muscle was able toexert a considerable amount of its active force(up to 25% of maximum) outside of its field ofaction. The active forces of the medial andlateral rectus muscles were not equally bal-

anced at primary gaze but instead at about 12to 15 deg of temporal gaze.

In general, for any gaze position, the me-dial rectus muscle acting as an agonist devel-ops more force than the lateral rectus muscleacting as an agonist. For Subject K. C. themaximum medial rectus active muscle forcewas about 70 gm vs. about 50 gm for thelateral rectus muscle (Fig. 8). This representsa 40% greater maximum active force for themedial rectus.

Fig. 9 graphically compares the maximumactive forces developed by the medial andlateral rectus muscles of each of the subjectsin this study, The mean of the maximum ac-tive force of the medial rectus muscle was74.83 gm (range of 48 to 103 gm) with anS.E.M. of 2.7 (Table I). The mean of the lat-eral rectus maximum active muscle force was59.14 gm (range of 45 to 92) with an S.E.M.of 2.3. The average value of the maximum

Volume 20Number 5 Extraocular muscle forces in human subjects 661

Table I. Extraocular muscle tension data(29 normal subjects)

Subject

Rank order of medial rectus muscle strength

M. C.J. L.F. H.C. S.D. D.B. G.C. B.A. D.K. L.N. P.F. C.B. C.M. W.J. S.R. 0.M. C.P. M.C. H.B. T.K. C.R. B.W. G.P. D.D. 0.V. S.B. C.B. B.B. K.E. M.XcrS.E.nRange

6669<J<JcJ6696669996669666699969

10398969690898988858080807372727271706868666562625858585348

74.82714.5432.70029

48-103

9278625250746157—8050506262585077704850484868525655484850

59.14312.0052.26928

48-92

1.000.901.001.200.951.100.83—0.910.861.200.800.891.00—0.800.921.200.850.860.901.200.94

1.000.800.800.800.770.9420.1420.02826

0.77-1.20

1.400.851.00—1.001.300.860.96—1.031.400.800.801.001.700.801.381.141.001.100.801.001.00

1.300.801.000.800.971.0490.2520.04926

0.80-1.70

active medial rectus muscle force was 25%greater than the maximum active lateral rec-tus muscle force. The maximum active forcedeveloped by the lateral rectus muscle wason average about 15 gm less than that of themedial rectus muscle. The active force de-veloped by the medial or lateral rectus mus-cle was greater than 45 gm for all the subjectsmeasured. A variation of maximum activeforce among individuals of two to one is seenin this study.

There was no clear correlation betweendeveloped tension and age within the narrowage range of these young adults.

Discussion

A detailed knowledge of normal activemuscle forces and passive forces restraining

10 15 20

SUBJECT NUMBER

25 30

Fig. 9. Plot of maximum active forces measured at50 deg extreme gaze effort for the medial and lat-eral rectus muscle pairs of the 29 normal subjectsin this study. The pairs are arranged in rank orderof descending medial rectus muscle force with theforce of one muscle directly below the other of thepair. The range of active force is 48 to 103 gm forthe medial rectus and 48 to 92 gm for the lateralrectus. Note, that the lateral rectus force in generaltends to be lower than that of the medial rectus.None of the normal active muscle forces in thisstudy were less than 48 gm.

rotation will permit quantitative verificationof existing theories of eye movement and maypermit further development of oculomotorcontrol theory and its attendant models thatwill lead to a clearer understanding of themechanisms of eye movements and the un-derlying causes of strabismus.

We have determined the normal range ofthe actively developed, individual, isometricforce for the medial and lateral rectus mus-cles and the magnitude of the load (stiffness)moved by these muscles by means of a newlydeveloped length-tension forceps. This tech-nique should permit differentiation betweenpassive mechanical restrictions and innerva-tional imbalances.

662 Collins et al.Invest. Ophthalmol. Vis. Sci.

May 1981

• • Active Force Difference (FL ag - F M antag)

A — - A Passive Temporal Load (KT x 0 )

60

40

~ 20

-60

Subj. K.C.

L.E.

Temporal Movement

40 20 0 20 40

Nasal Eye Position, © (Degrees) Temporal

Fig. 10. Net active force rotating the glohe tem-porally is the active force of the lateral rectusmuscle acting as an agonist, FL ag, minus the activeforce of the medial rectus muscle acting as an an-tagonist, FM antag. 'As taken from Figs. 6 and 4,respectively. This net active force is plotted asFL ag ~ FM antag and is responsible for moving thetemporal load of the intact eye, KT x 6, as takenfrom Fig. 3, all from Subject K. C. The two curvesmatch remarkably well and give credence tomodeling techniques utilizing clinically derivedforce measurements. The subject, as indicated bythis model result, was essentially orthophoric (seeFig. 11).

The results (Table I) are in good agreementwith previously reported values for strabis-mus patients.5"9 Our data will provide a use-ful baseline of the orbital mechanical forcesexisting in normal individuals. Differencesfrom these values in strabismus patients willaid in the differential diagnosis of their disor-der and in more accurate quantitative plan-ning of strabismus surgery. The maximumactive force of individual oculorotary musclesmay be useful in the diagnosis of paralyticstrabismus. In our investigations, the normalmaximum active muscle force of the medialand lateral rectus muscles was greater than45 gm. Therefore a maximum active force ofless than 45 gm would make one suspect that

20 0 20R Right Eye Position (Degrees) L

COMITANCE CHART

Fig. 11. Comitance chart for Subject K. C , withleft eye position calculated and plotted in relationto right eye position. If the active force differenceexactly coincides with the load curve, orthophoriaresults and is plotted here as the 45 deg dashedline. Significant shift from this 45 deg line indi-cates a deviation from orthophoria. In this case thevalues were calculated from the data in Fig. 10. InFig. 10 the difference between the net active forcedifference and the load force at each 10 deg eyeposition was divided by the load stiffness at thatpoint to calculate the deviation of the left eye fromorthophoria. This deviation is plotted here as thesolid curve illustrating the calculated phoria ateach position of gaze. These calculations agreewith the measured phoria for this subject.

the muscle was paretic. In a clinical sense, ahorizontal rectus muscle with a force greaterthan about 30% of normal maximum (orabove 20 gm) can make significant contribu-tions to eye rotation. A horizontal rectusmuscle force less than 25% of normal maxi-mum, or 15 gm, is functionally paralyzed andwould not exert sufficient force to contributesignificantly to eye rotation.

The shape of the actively developed forcevs. eye position curve leads us to an under-standing of otherwise hidden mechanisms ofstrabismus, for example, Duane's syndromewith paradoxical innervation. The pattern ofactive muscle force vs. gaze position for themedial and lateral rectus muscles (Fig. 8)

Volume 20Number 5 Extraocular muscle forces in human subjects 663

clearly shows the pattern of reciprocal inner-vation. As the force of one muscle increases,the force applied by its antagonist decreases.This nonlinear pattern resembles data de-rived from horizontal rectus muscles of awakepatients at surgery.5' 6 Such curves haveproved useful in rigorously defining the in-nervational input pattern of oculomotor sys-tem models.

Our results show the mean load stiffnessfor all 29 subjects to be 1 gm/deg. This valueis somewhat lower than that reported byRobinson1 (1.2 gm/deg) and by Childress andJones2 (1.25 gm/deg) for eye movements of 5deg or less. Their higher values of stiffnessmay be due in part to the additional force ofhysteresis. This would be particularly true ifthe measurements were made after returningto primary from abduction each time. Chil-dress and Jones2 reported a lower value, 0.65gm/deg, for forced traction of the eye withmovements in excess of 5 deg. Slight slippageof the contact lens at the higher forces mayhave contributed to their lower values.

Other studies have demonstrated that or-bital stiffness (the slope of the load curves) isindependent of the active force produced bytonic activity of the oculorotary muscles.2'3) 5

Thus the load curve determined at one fixedeye position appears to shift horizontally asthe fixed eye position is changed, so thatthe point on the stiffness curve at whichoculomotor forces balance corresponds to thepresent fixed eye position. This property isutilized in the following model calculations.

The active and passive forces measured inthis study were used as inputs for a me-chanical model of the oculomotor system.9

The net effective force rotating the globe wasthe active force-difference of the medial andlateral rectus muscles at each correspondingposition of gaze. For temporal gaze the activeforce of the medial rectus muscle acting as anantagonist (lower tracing in Fig. 4) was sub-tracted from the active force of the lateralrectus muscle acting as an agonist (middleand upper tracings in Fig. 6). This results in anet active force-difference which acts againstthe load (stiffness) restraining temporal rota-tion of the globe (Fig. 10). The active force-

difference curve matches remarkably wellthe measured load stiffness that the activeforce must overcome in temporal gaze. Ofcourse, this is the expected theoretical result,but it is remarkable that the agreement is sogood, considering the many exigencies ofclinical data collection procedures. In Fig. 10the left eye positions result in concomitancewith the right eye within 2.5 A over the en-tire 80 deg range of gaze over which stiffnessof the left eye was measured. (Concomitanceis defined as both eyes tracking together.)The calculated phoria of each eye position isdepicted on a comitance chart in Fig. 11.Comitance for this subject (K. C.) measuredto be within 2 A, lending credence to thecomputational methods and model approach.

Stiffness measurements made on the intacteye are probably a more valid indicator of theload presented to the muscles as they occurin real life than those made at surgery. Thereis a question whether changes in stiffnessmay be produced by the trauma of surgery.There are also unanswered questions aboutthe cross-coupling of globe-restraining tissuestiffness and muscle stiffness when attemptsare made to measure these values separatelyat surgery.

Our measurements of the stiffness of theintact eye provide the actual load that themuscles must move to rotate the eye. Thisload is the sum of the muscle and globe-restraining tissue stiffness. We cannot mea-sure noninvasively how much of this stiffnessis due to passive muscle components and howmuch is due to the other passive orbital tis-sues restraining globe motion. From ourprevious investigations at surgery, we canestimate that some two thirds of this stiffnessis due to muscle tissue.5' 6 In order to sepa-rate the contributions of stiffness due tomuscle and to the passive globe-restrainingtissues, it proves necessary to measure thepassive load at surgery before and after theoculorotary muscles are disinserted. We arecurrently obtaining such data.

In most of the normal subjects we havemeasured, the length-tension (stiffness) char-acteristics for abduction and adduction werenot symmetrical. Data from the subject K. C.

664 Collins et al.Invest. Ophthalmol. Vis. Sci.

May 1981

in Fig. 7 show a 30% greater stiffness mea-sured in the nasal direction (adduction). Theactive force data show the medial rectusmuscle to be 40% stronger than the lateralrectus. Thus a stronger active medial rectusforce is present to act against the greater loadstiffness which resists adduction. The obliquemuscles are also stretched in adduction andmay be partly responsible for this assymetri-cal load stiffness.

Although there is a difference in the nasaland temporal stiffness of the intact eye, allthe load stiffness curves have been found forthe most part to be linear (straight lines).Therefore discontinuities in the load curve(an abrupt change of stiffness) at some gazeposition would indicate a restriction, contrac-ture, or other pathological condition. Mea-surement of tissue stiffness over the entirerange of eye movement can contribute im-portant knowledge to the type, magnitude,and location of restrictions. It appears that alarge stiffness may be normal if associatedwith large active muscle forces.

The length-tension forceps can be a usefulinstrument for quickly and simply makingquantitative records of the passive and activeforces responsible for positioning the eyes.This forceps permits a detailed analysis of ac-tive muscle forces and tissue stiffness to beplotted in each direction of gaze. Mea-surements of imbalances in the active muscleforces and asymmetries of load stiffnesscharacteristics that resist eye movement offerthe surgeon a useful quantitative tool fordealing with the difficult task of balancingforces involved in strabismus.

We gratefully acknowledge the considerable efforts ofMr. Scott Bowman in setting up the equipment and inhelping to record and reduce the data. We thank Mr.Albert Alden for design contributions and continuedmaintenance of the length-tension forceps and Dr. JaneMash for statistical consultation. We thank Mr. DavidO'Meara for his efforts in obtaining and screening paidvolunteer subjects and in helping with taking data. Wethank Mr. Jack Shore and Mr. Philip Munkers for theirmechanical assistance and Mr. Gerald Dittbenner fortechnological contributions in applying strain gauges tothe length-tension forceps.

REFERENCES1. Robinson DA: The mechanics of human smooth pur-

suit eye movement. J Physiol (Lond) 180:569, 1965.2. Childress DS and Jones RW: Mechanics of horizontal

movemement of the human eye. J Physiol (Lond)188:273, 1967.

3. Robinson DA: The mechanics of human saccadic eyemovement. J Physiol (Lond) 174:245, 1964.

4. Robinson DA: The mechanics of human vergencemovement. J Pediatr Ophthalmol 31:377, 1966.

5. Collins CC, Scott AB, and O'Meara D: Elements ofthe peripheral oculomotor apparatus. Am J Optom46:510, 1969.

6. Robinson DA, et al. Mechanical components ofhuman eye movements. J Appl Physiol 26:548, 1969.

7. Collins CC: Length-tension recording strabismus for-ceps. In Smith-Kettlewell Symposium on Basic Sci-ences in Strabismus. Proceedings of the V Congress(Annex) of the Cons Elho Latino-Americano de Es-trabismo, Guaruja, Brazil, 1976, pp. 7-19.

8. Collins CC: Orbital mechanics. In The Control of EyeMovements, Bach-y-Rita P, Collins CC, and Hyde J,editors. New York, 1971, Academic Press, Inc., fig.11, p. 294.

9. Collins CC: The oculomotor control system. In BasicMechanisms of Ocular Motility and Their ClinicalImplications, Lennerstrand G and Bach-y-Rita P,editors. Oxford, 1975, Pergamon Press, Ltd., pp.170-179.