J. Physiol. (1975), 245, pp. 351-369 With 1 plate and 8 text-figures Printed in Great Britain

351

MUSCLE TENSION DURING UNRESTRAINED HUMAN EYE MOVEMENTS

By CARTER C. COLLINS, DAVID O'MEARA AND ALAN B. SCOTT From the Smith-Kettlewell Institute and Department of Visual Sciences, University of the Pacific, San Francisco, California 94115, U.S.A.

(Received 18 April 1974) SUMMARY

1. Tensions in the horizontal rectus muscles have simultaneously and continuously been recorded during unrestricted eye movements in four strabismus patients, using force transducers small enough to be implanted in series between the tendons and their points of insertion on the globe. 2. Levels of tension required to maintain fixation at each position of gaze vary from a minimum of 8-12 g approximately 150 outside the muscle's field of action to a maximum of around 40 g at extreme gaze within the muscle's field of action. When tension is plotted as a function of eye position, the static locus of fixation tension levels exhibits a parabolic relationship. 3. Tensions recorded during smooth following movements parallel or slightly exceed those of fixation. 4. At the onset of a saccade, tension in the agonist rises isometrically, then, as the eye moves, tension levels parallel those of fixation but with an isotonic increment of 15-25 g. At the end of the saccadic movement, tension falls essentially isometrically to the new fixation level. 5. Tension in the antagonist reveals an unexpected peak at the onset of a saccade. 6. For saccadic movements tension increments of 15-25 g above the fixation levels suffice to move the eye rapidly to a new position of gaze, regardless of the duration of the saccade and the location of the new fixation point. 7. Maximum and minimum levels of tension during normal fixation, following and saccadic movements, plotted as a function of eye position, form an operational envelope which defines the limits of muscle forces during normal eye movements. The lowest level of this envelope is the parabolic static locus of fixation tensions. I3

P HY 245

C. C. COLLINS AND OTHERS 352 8. Normal tension levels in an agonist or an antagonist never fall below a minimal level of 8-12 g. 9. Tension characteristics observed in saccadic movements are consistent with minimal expenditure of energy, suggesting an innate mechanism to reduce eye muscle fatigue. INTRODUCTION

The means for direct observation of many of the mechanical factors determining human eye movements have not been available in the past. Only recently have there been measurements of tension in the human extraocular muscles themselves. The static, isometric properties of the horizontal recti have been analysed in studies on consenting patients during strabismus surgery (Robinson, O'Meara, Scott, Collins, 1969; Collins, Scott & O'Meara, 1969; Collins, 1971). The tension needed to maintain the eyes in any position of lateral gaze has been measured, together with quantitative assessment of the relative contributions of agonist, antagonist and orbital restraining tissues, as well as the innervation-tension relationship for human oculorotary muscles which should be of potential use in preparing models of strabismus surgery. Such mechanical models would conceivably be of great value in assessing the pathological factors underlying strabismus and other oculomotor defects. Direct evidence of dynamic changes during normal, unrestricted human eye movements has had to await the development of force transducers small enough to be implanted directly in series with the oculorotary muscles. The present paper describes such transducers, and their implantation in series with the muscle tendon and the globe. We shall present the results obtained simultaneously from both medial and lateral rectus muscles in four awake and cooperative strabismus patients during the course of required corrective surgery under topical anaesthesia. Continuous in vivo records have been obtained during voluntary, unrestrained, natural eye movements. This technique has provided a unique opportunity to record the pattern of muscle tension during fixation, following and saccadic eye movements. The results obtained are utilized to formulate a descriptive schema for the normal range of tensions employed by the horizontal rectus muscles. METHODS

The present investigations were performed on four selected adult strabismus patients who understood the research nature of the addition of tension measurements to their surgery. Patients were selected whose deviation remained essentially constant over a wide range of eye position. In each patient two miniature force transducers were implanted in series between the tendons of both the medial and lateral recti and their severed insertions on the globe.

HUMAN EXTRAOCULAR MUSCLE TENSIONS

353

The miniature force transducers consist of a ring of aluminium, split to form a C, with holes for sutures; a foil resistance strain gauge mounted on the ring; and flexible wire leads to the resistance bridge amplifier (P1. 1). The ring is 2 mm in diameter, 1 mm high and with a wall thickness of I mm. Holes of i mm diameter are drilled in each arm of the ring close to the slit. Sutures are threaded through these holes for making attachment to the muscle tendon and to its point of insertion on the globe. Tension applied to the sutures tends to open up the arms of the C, thus exerting a measurable strain on the walls of the ring, with the maximum strain opposite the slitted opening. At this point a small foil resistance strain gauge is attached to the ring with a thin layer of epoxy cement. The dimensions of the foil strain gauge are approximately 750 #esm square by 5 um thick; its resistance is 120 Q. The dimensions of the aluminium ring are chosen to produce a strain of approximately one half of yield value for a load of 120 g tension applied to the sutures. To protect the miniature force transducer from resistance changes due to moisture penetration, the strain gauge is coated with a layer of special moisture resistant varnish and baked,then finally dipped in a soft wax coating. The output of the strain gauge is sensed by a strain gauge bridge (Beckman type 9853) via no. 36 enamelled wires, forming one arm of a four-arm bridge. With 3 V of applied excitation to this bridge, the output sensitivity of the force transducer is 25 ,uV/g of applied tension. Temperature sensitivity of the miniature force transducer is approximately 100 1WV/0 C. Drift in the output of the transducer circuit is of the order of 1 flV/min. The over-all performance is satisfactory following a 30-min immersion in Zephiran 1:1000 and subsequent implantation for up to 3 hr. The procedures for implantation of the transducers during normal strabismus surgery are carried out following topical administration of Ophthaine. The tendons of the medial and lateral rectus muscles of the eye to be measured are located and prepared for section. Two 3-0 silk sutures are mattress laced and tied on either side of the intended point of section close to the globe. Following severance of the tendon between the sutures, the latter are threaded through the appropriate holes in the arms of the miniature force transducer. The transducer is first fastened securely to the muscle tendon with tight stitching, leaving minimal slack. The opposite arm of the transducer is then similarly fastened to the sclera, just ahead of the muscle stump in order that the muscle be as nearly at its original length as possible. In this way the working length of the muscle is essentially unchanged by insertion of the force transducer in series with the tendon and globe. The very flexible pair of twisted no. 36 enamelled wire leads from the transducer are then led out to the bridge amplifier. leaving approximately eight inches of loose slack in order not to place an unwanted load on either the eye or the force transducer. A zero calibration of each transducer is made by unloading all force from it. For this, the globe is grasped with forceps and rotated passively to shorten the muscle leaving it slack. At the same time the patient is asked to fix the fellow eye on a target completely out of the muscle's field of action so as to relax it completely. (A muscle is defined as being in its field of action when it is shorter than the length required to hold the eye in the straight-ahead position.) Calibration of force sensitivity in 8itu utilizes a suture attached between the globe and an external pre-calibrated strain gauge force transducer. The globe is pulled to stretch the measured muscle out of its field of action so it is tight and its antagonist slack. The patient is then instructed to fixate targets which increasingly innervate the measured muscle. This progressively loads both the miniature force transducer and the series external pre-calibrated force transducer with the same set of step function forces. Each of the miniature force transducers maintains this calibration throughout the 13-2

354

C. C. COLLINS AND OTHERS

duration of the experiment. The zero calibration, however, is checked periodically in order to compensate for any effects of zero drift. Recording of the output of the miniature force transducers is made with a 14-track Precision Instrument PS 214 one-inch tape recorder in the FM mode, and also with a Beckman RB six-channel ink writing strip chart recorder. Electro-oculogram (e.o.g.) electrodes, separately positioned for each eye, simultaneously monitor horizontal eye movements. The target position is recorded at the same time, and serves as a self-calibration for the e.o.g. When the external calibrating strain gauge force transducer is in use, its reading is also recorded.

Experimental procedures are of four types A. From a set of fixation data, isometric length-tension determinations are performed separately for each muscle, using both the external strain gauge and the implanted miniature force transducer. The muscle is fixed isometrically at its primary length and the patient is directed to fix the gaze of his unoperated eye on each of a series of targets spaced at 150 intervals between 450 left and 450 right of primary gaze. By this means the measured oculorotary muscle is innervated at each of a set of known levels. Each target is fixated for approximately 4 see and muscle force is measured at steady state near the end of the 4 see period. The series of seven target positions is then repeated. The same series is also repeated twice while the muscle is maintained at various lengths up to 9 mm shorter and 9 mm longer than its primary length. These measurements provide sufficient information to sketch a family of length-tension diagrams for the muscle at each of seven states of innervation (seven target positions). B. For the remainder of the experiments the restraining sutures are released so that the eye is unrestrained and completely free to rotate naturally. The tensions required to maintain the eye in positions of lateral gaze are determined as the subjects fixate targets spaced at 150 intervals with their measured eye. C. Force measurements during following movements are recorded with the miniature force transducer as the patient tracks a target moving at 100/sec between 450 right and 450 left. Recordings of tensions are made during two round trips between these extreme gaze positions. D. Force measurements are recorded during a series of saccadic refixations. This programme includes a repeated series of 15° saccades from 450 left to 450 right and return. Further, 30 and 450 saccades are made from primary position to left and to right and back, each saccade being repeated twice. Finally, two saccades each are made between 450 right and 15° right, 15, 30 and 45° left. From the recorded data, selected examples were reproduced from magnetic tape on to anX-Y recorder (Moseley Autograf Model 135C) with force as a function of eye position (muscle length) for following movements. Length-tension records of saccadic refixations were made on an X-Y storage oscilloscope (Tektronix Model 564). Target, force and eye position were recorded as a function of time for saccadic

refixations on an ink-writing chart recorder (Beckman Model RB). RESULTS

Each of the four subjects in the present study exhibited a pre-operative tropia or phoria in the operated eye as shown in Table 1. Within this admittedly small group, the minimal tension levels recorded ranged from 8 to 12 g; the maximum levels ranged from 28 to 44 g. In spite of variation between subjects, there was a high degree of consistency in the patterns of

HUMAN EXTRAOCULAR MUSCLE TENSIONS

355

TABLE 1. Details of subjects partaking in the experiment with individual forces required for horizontal gaze Max. Max. con-

Subject G. C.

Male

Age 43

D. G.

Male

36

L. M.

Male

24

L. C.

Male

60

Sex

1201r

Diagnosis at Muscle distance RMR 40A Alternating exotropia 30A Intermit- LLR tent exotropia LMR 14A Esophoria LLR 26A Exotropia

ex-

tracted force

Min. force

tended force

g

g

g

44

12

19

40

9

16

39

10

17

28

8

15

I 450

N

100 e 300 N

W C

15°N

0

o

C

s

u

W

XX,150

T

300 T

//1 450 T 00 150 150 Eye position

Text-fig. 1. A family of length-tension curves obtained by measuring the isometric tensions at seven fixed muscle lengths and seven levels of innervation established by directing the subject to look at the corresponding targets with the unhampered contralateral eye. Note that the length-tension curves are straight, parallel lines above about 10 g. Below the 10 g level the oculorotary muscles begin to go slack. This is evidenced by their curvilinear nature, finally slacking off into a dead limp or horizontal length-tension curve.

C. C. COLLINS AND OTHERS 356 recorded tension during fixation, following and saccadic movements for all subjects. A. Length-tension characteristics. From the data in Experimental procedures, A, a family of length-tension curves was constructed for each muscle tested. The mean data compiled from these results are presented in Text-fig. 1 and as the dashed lines comprising the background in Text-fig. 8. 50 RMR 40

430 0

4)

~20 10

0

450 N

300

150

00

150

300

450 T

Eye position

Text-fig. 2. Tensions recorded in a right medial rectus muscle tendon during unrestrained following movements by a patient with 30 prism diopters of intermittent exotropia. The eye followed a target moving from the primary position to 450 temporal, then to 450 nasal and back toward 15° nasal at 10° per second. The lower curve in each case closely approximates the static locus of fixation tensions in Text-fig. 8.

B. Fixation tensions. The tensions required to maintain the eye in each of seven positions of horizontal gaze (the circles in Text-fig. 8) were determined as described above under Experimental procedures, B. In the four subjects tested, as seen in Table 1, these levels ranged from a maximum of 28-44 g at the - 450 position (contracted 45° into the muscle's field of action) to a minimum of 8-12 g at the + 15° position (stretched 15° out of the muscle's field of action). In eye positions where the muscle was drawn further out of its field of action, there was an increased tension. Thus at the + 45° position, tensions were approximately 7 g greater than at the + 15° target. The shape of the curve connecting these static

357 HUMAN EXTRAOCULAR MUSCLE TENSIONS tensions at each position of gaze is parabolic, with an increase from the minimal tension (at + 150) both to the maximum observed with extreme gaze in the muscle's field of action (- 450) and to the lesser increase observed in extreme gaze out of the muscle's field of action (+ 45°). C. Following movements. Tension changes have been recorded in the horizontal recti during smooth following movements from 450 left to 450 right and back, with the target moving at 100 per second. Text-fig. 2 presents a typical example, in this instance, from a right medial rectus (RMR). It will be noted that there are two records in the left part of the Figure, as the eye looks left the RMR is acting as an agonist (into its field of action), and two in the right side of the figure, as the eye looks right in the temporal range of eye positions where the RMR becomes an antagonist. The lower right curve, in the temporal range, is actually continuous with the upper left curve. This curve was recorded while the eye moved from right to left. With the return movement from left to right, the muscle relaxed progressively to produce the lower tensions noted in the left part of the recording (there is a gap in the tracing from 15° nasal to primary). At or near the primary position, records from movements in the two directions cross over. The tensions recorded during progressive movement into the muscle's field of action (from primary position to - 450 nasal) are some 5 g greater than those in the opposite direction (from 450 nasal to primary position). The lower levels of tension recorded during slow following movements correspond quite closely with the static fixation levels recorded in part B. In each subject, tension recorded as a function of eye position during smooth following movements exhibited a parabolic relationship between extreme gaze positions, paralleling and in part duplicating the static locus of fixation tensions for that subject. D. Saccades. Tension changes have been recorded from horizontal recti during saccadic refixations of 5-600. Text-fig. 3 presents recordings of tension in left medial rectus (LMR) and left lateral rectus (LLR) muscle tendons during a series of 15° saccadic refixations. The movements of the target light, in 15° increments between 300 left and 300 right, are noted in the top tracing. The lower records show the appropriate reciprocal muscle forces, with a non-linearly increasing force in the agonist accompanied by a concomitant decrease in the antagonist. Each muscle, contracted - 300 into its field of action, exhibits a tension of 30-45 g compared with a tension of 10-15 g extended + 300 out of its field of action. A slight increase in tension can be noted in the relaxed antagonist as the eye approaches extreme gaze (i.e. LMR at 300 left; LLR at 300 right). At the onset of each refixation movement one can note the overshoot peak of force in the agonist, employed during the initial phase of the

358 C. C. COLLINS AND OTHERS saccade to overcome the viscosity of the muscle while producing a highvelocity movement of the eye. Additionally, there is an (unexpected) force peak in the relaxing antagonist at the onset of each saccadic refixation. 30L

bo

0 0.

0

50

s4o] 30 -j

C

50

10j-

4. 'S

j

0

10203 Time (sec)

Text-fig. 3. Tensions recorded in two horizontal rectus muscles during a series of unrestricted saccadic refixations on targets between 300 left and 300 right (upper tracing). Miniature force transducers were implanted at the tendons of the left medial rectus (middle tracing) and left lateral rectus (upper tracing) in a patient with 30 prism diopters of intermittent exotropia. The reciprocal tension changes can be noted as each muscle moved into and out of its field of action. Initial overshoots during the onset of refixation movements are evident in the antagonist as well as the agonist.

Text-fig. 4 presents recordings of tension in the LMR and LLR during a saccadic movement from zero to 300 right, with a faster recording speed. The agonist LMR (top trace) exhibits a nearly isometric tension rise of 18 g during the initial phase of the saccade, before any significant movement of the eye occurs (as seen in the lowest tracing). There is a distinct break in the rate of increase of tension to its peak (36 g) as the eye achieves significant velocity with shortening of the muscle. A lesser increase in tension is seen in the relaxing antagonist (LLR) prior to its assuming a steady-state fixation level. (Such initial force peaks were also noted in Text-fig. 3). It can also be seen that the steady-state tension in the antagonist LLR is actually greater when the eye is 300 right than at the primary position, even though the innervation to this muscle is much less for maintaining the 300 right position than for forward gaze. In Text-fig. 5 an isometric tension record is superimposed on a record

j

HUMAN EXTRAOCULAR MUSCLE TENSIONS 40 r

I-

00

30

F

20

F

1: _J

10 L

20

-

_j -J

-j

10 -L

C v .2 300 R

WU

jo

I

oJ

_____

V_____ M

a

a

I

a

200 300 400 Soo Time (msec) Text-fig. 4. Tensions recorded in a left medial rectus (upper channel) and a left lateral rectus (middle channel) during an unrestrained saccadic movement from primary position to 300 right (indicated on the lower channel). Note the initial isometric tension rise in the agonist left medial rectus before the eye moves appreciably, then a break in the curve as the eye achieves significant velocity. Note also that the tension in the relaxing antagonist left lateral rectus increases during the early stage of the saccade before it assumes the new steady-state fixation level, which is several grams greater than that for the primary position.

W

0 ._

ce

70 60 50 40 30 20 10 0-

0

100

IA

0

300 Time (msec)

600

Text-fig. 5. Two records of tension in an agonist right medial rectus during saccades from 150 left to 300 left. The upper curve is of an isometric response with eye movement prevented by means of sutures; tension rose from an initial 14 to 64 g before reaching a new fixation level of 40 g. The lower curve is of a freely moving response, and reveals a tension rise from 14 to 42 g during the movement, and a fixation level of 23 g at the 300 left position.

359

C. C. COLLINS AND OTHERS 360 of tension in a naturally contracting muscle. Both records are from the same RMR acting as agonist during identical 150 saccades from 15 to 300 left. Above the steady-state level of about 14 g the increased forces measured during the normal eye movement (lower trace) are about half those obtained isometrically (i.e. with the eye movement prevented by means of sutures). Thus, the freely moving eye shows a tension increment of about 28 g, while the isometric increase is 50 g. In the initial phase of the response the tension increases are nearly identical in the two tracings. Then, as the eye starts to move, the rate of increase of the contracting muscle force falls off sharply, as seen in the lower curve. As the muscle shortens its tension drops to the level required to maintain refixation at 300 left. 56 LC 48

40 0

32

24 _j

16 8

0 45 R

30

15 Degrees

0

15 L

Text-fig. 6. A length-tension recording during saccadic refixations of an agonist left medial rectus muscle made with an implanted miniature force transducer in a freely moving eye. Note the characteristic path described by the muscle force consists of three parts: (a) at initial isometric tension rise followed by (b) an essentially isotonic tension increment maintained about 15-25 g greater that the static locus of fixation force, and (c) a roughly isometric tension decay to the steady-state tension maintaining the eye at its new position of lateral gaze.

Text-fig. 6 presents a dynamic length-tension recording of a left medial rectus during 150 saccadic refixations starting from 15° left (on the right side of the record) to 450 right, progressively further into the muscle's field of action. With each change of fixation, there is an initial isometric rise of tension, then an approximately isotonic increment of tension about 15-25 g higher than the equivalent static fixation force for the corresponding eye position. This is followed by an approximately isometric

361 HUMAN EXTRAOCULAR MUSCLE TENSIONS decay of tension to the new steady-state tension needed to maintain the eye in its new position of lateral gaze.

Text-fig. 7 presents superimposed dynamic length-tension records of LMR tension during saccadic movements of 30 and 600. The upper portion of each trace was obtained while the eye moved to the right, into the maximal field of activity of the measured agonist LMR. The lower trace was made during the slow return movement from 450 right back to 15° right as the muscle relaxed. From the initial fixation point at 150 left (lower right), the tension of the LMR increased roughly isometrically by Id4- A .*Ad

LC

48

0

B°~~~~~~

1

12

0

45 R

0 15 Degrees

15 L

Text-fig. 7. Tension of a left medial rectus recorded during saccades of 30 and 600, both ending at 450 right gaze. During the longer saccade (indicated by arrow A), tension rose isometrically, then increased as the eye moved to the right, achieving a maximum level of 47 g at the 450 right position. Tension then fell isometrically to the new fixation level of 29 g. With the shorter saccade from 150 right to 450 right (indicated by arrow B), the tension rose isometrically then duplicated the tension path recorded during the same portion of the longer saccade (rising to 47 g and then falling to 29 g).

about 12 g, then continued to rise as the eye moved all the way to 450 right. This record of a 600 saccade (indicated by line A) essentially parallels the shape of the curves for both the fixation locus and following movements, but with an increment of about 20 g above the fixation locus throughout the 'isotonic' portion of the muscle activity. The 300 saccade (indicated by line B) started at 150 right with a similar isometric increase in tension; as the eye moved to 450 right the tension recording retraced

C. C. COLLINS AND OTHERS 362 the same dynamic course as was seen during the longer saccade. In each instance, when the eye reached the final fixation position of 450 right, the tension fell essentially isometrically to the new fixation level. DISCUSSION

Miniature implantable force transducers have now made it possible to observe some of the heretofore unknown and otherwise unobservable mechanisms of the unrestrained operation of the oculomotor system. The difference in tension between movement into and out of the muscle's field of action (5 g as seen in Text-fig. 2) is an example not only of viscous drag proportional to velocity of movement, but also of hysteresis, the quality of motion lagging its causative force, however slowly applied. The curve with higher tension represents the agonist contracting into its field of action; the lower curve represents the muscle progressively relaxing while being passively stretched. In the present study we have observed that the oculorotary muscles exhibit hysteresis at very low velocities. It is of interest that R. Eckmiller (personal communication) has also found evidence for hysteresis in recordings from the oculomotor nuclei in the monkey. In a series of saccadic refixations in the horizontal plane, the steadystate tension recorded during each fixation period of an unrestrained eye follows a parabolic curve similar to that recorded during normal following movements. The plateaus of higher tension in the agonist during the actual saccadic eye movement parallel this parabolic curve, but with an increment of 15-25 g throughout the duration of the saccade. This increment, illustrated in Text-figs. 6 and 7, is a confirmation by direct measurement of predictions which were calculated by Robinson in 1964. In the present study, an (unexpected) tension peak of several grams was recorded in the (relaxing) antagonist during saccadic movements, as seen in Text-figs. 3 and 4. This tension peak is presumably caused by the agonist stretching the passive antagonist at a rate faster than the antagonist can relax, due to its internal viscosity. This internal viscosity, or force-velocity relationship of the contractile element, is responsible for the relatively slow rise of tension measured at the muscle tendon. This viscosity results in an increase in tension in the tendon if a relaxing muscle is stretched at an initial rate exceeding about 50 mm/sec (250'/sec).

Operational envelope If we correlate all the data on tension levels recorded in the present study, it should be possible to formulate a length-tension schema to define the normal ranges of tensions for horizontal eye movements. Such

363 HUMAN EXTRAOCULAR MUSCLE TENSIONS a schema is presented in Text-fig. 8 in the form of an operational envelope for the ranges of extraocular muscle tension in normal fixation, following and saccadic movements. A family of length-tension curves such as presented in Text-fig. 1 is shown as the dashed lines in the background of Text-fig. 8. These are linear and parallel for tensions above about 10 g, as was noted in our

N

N

bO

C

C

0

0

C a,

co

*j

C C

T !0

To

450 N 300

150 0° Eye position

150

-''°450

300

T T

450 T

Text-fig. 8. An operational envelope of the normal ranges of extraocular muscle tension for a typical left medial rectus during fixation, following and saccadic movements. Dashed lines in the background represent a family of length-tension curves for each of the innervations shown. The lower curve represents the static locus or the tension required to maintain the eye in each position of horizontal gaze indicated on the abscissa. The upper curve represents the dynamic locus, or force increment producing a saccadic movement. The area between the static and dynamic loci represents the normal operational envelope. The counterclockwise loop between the zero and 15° nasal positions indicates tension changes in the muscle during a saccadic refixation into the muscles' field of action. The small clockwise loop from left to right indicates the passive tension changes occurring in the muscle as an antagonist during a saccade.

earlier studies (Collins et al. 1969). The lower heavy line, interrupted by open circles, depicts the static locus of fixation forces (i.e. the tension required to hold the eye in each position of gaze noted on the abscissa (Collins, 1971)). The upper heavy line represents the dynamic locus, or

C. C. COLLINS AND OTHERS 364 maximum total tension measured at the muscle tendon during saccadic movements. A typical dynamic length-tension loop for a saccadic movement by the agonist is shown (in Text-fig. 8) as a counter-clockwise curve (dashed curve with arrows) extending between the open circles on the static locus. This comprises a three-part dynamic loop (isometric increase, isotonic maintenance and isometric decrease) recorded in Text-figs. 6 and 7. During the high velocity portion of a saccadic eye movement, there is a transient tension peak which exceeds the final steady-state lengthtension curve. An example of this is the small area of the operational envelope in the upper left which lies above the highest length-tension curve. This area represents muscle tension momentarily achieving a transient peak before slowly decaying to the steady-state value. Comparable areas can be seen in any other counter-clockwise dynamic saccadic loop of the agonist muscle. A typical dynamic length-tension loop for the antagonist is shown as the smaller flattened clockwise path moving to the right between the open circles. This was obtained from recordings such as those of Textfigs. 6 and 7, and constituted the small initial rise of tension seen in the relaxing antagonist at the onset of each saccadic refixation plotted against eye position. The incremental forces producing a saccade are never more than about 20 % of the maximum potential muscle force capability, even in extreme saccades. It is evident from Text-fig. 8 that beyond a certain saccadic size (about 100) the incremental force delivered through the muscle tendon does not significantly increase with saccades of greater magnitude. Only the length of time that the force is applied is increased for a larger saccade. Thus, as Robinson (1964) indicated, the control of saccadic eye movements is effected by a pulse duration modulation system, larger saccades being effected by a longer duration of nearly constant applied force. Tensions recorded during smooth following movements lie on or above the lower curve of the operational envelope, the static locus (Text-fig. 2). Thus, as the muscle contracts within its field of action the tension achieves levels between the lower and upper curves; as it relaxes in movement from extreme gaze toward mid-position, the tension is essentially the same as with fixation at the corresponding eye position (i.e. it matches the lower curve). As the muscle is progressively stretched outside its field of action, the tension is slightly higher than that noted with fixation; as the stretched muscle shortens with movement from extreme gaze outside its field of action toward mid-position, the tension matches that of fixation. Following movements in the vicinity of mid-position exhibit tensions slightly greater than those recorded during fixation.

HUMAN EXTRAOCULAR MUSCLE TENSIONS

365 Under normal physiological conditions all agonist and antagonist muscle forces lie within the operational envelope. The maximal forces delivered at the muscle tendon never exceed the upper curve, nor do the minimum forces ever become less than the lower curve. This is true in spite of the fact that the innervation to an antagonist is completely shut off during a saccade greater than 10°. The reciprocally innervated and contracting agonist keeps the antagonist stretched to levels of tension associated with fixation. Indeed, the oculorotary muscles are perpetually kept under some degree of tension, even outside of their field of activity, so that muscle slack is avoided at all times. Recent evidence indicates that this is due to the actively antagonistic tonic activity of the small, outer fibres of the muscle (Collins & Scott, 1973). Abnormal conditions The operational envelope of eye movement tensions is determined by the programme of the central nervous system (C.N.s.) operating on the mechanical visco-elastic characteristics of the muscles and globe. The combination of these factors restricts normal activity to a mere 20 % of the area of the length-tension diagram. Thus, tension levels which lie outside the operational envelope are not recorded under normal physiological conditions. However under abnormal conditions, including diagnostic forced duction tests, muscle forces may be traced out over a length-tension line, exceeding the upper and falling below the lower limits of the evelope. Also, in pathological conditions involving contracture, adhesions, or other restrictions of eye movement, more nearly isometric muscle forces may be generated at some point. These can obviously leave the operational envelope of normal eye movements illustrated here (as seen for, example, in the comparison of isometric and freely moving responses in Text-fig. 5). Non-linearities The parabolic shapes of the static and dynamic locus curves (the lower and upper bounds of the operational envelope) are reflexions of the innervational strategy employed by the C.N.S. in the control of eye movements. This is manifest as a non-linear innervation-eye position relationship in which innervation increases as a power function of eye position (Collins & Scott, 1973). Although the observed (static locus) forces of each eye muscle vary as the square of eye position, the force difference between antagonistic muscle pairs (responsible for globe displacement) is a linear function of eye position. This occurs because each muscle is loaded by the opposing square law characteristic of its antagonist. The oculorotary muscles work together

C. C. COLLINS AND OTHERS 366 in reciprocally innervated push-pull opposition to cancel out the large second degree non-linearities in each. It can be seen that all points within the bounds of the operational envelope lie above the lower, curved portions of the (dashed) static lengthtension lines. Within the zero to 10-g region of small tensions the muscles go slack. Since the (relaxing) antagonist is always kept in a state of stretch beyond 10 g by tonic agonist fibres (Collins & Scott, 1973), the oculorotary muscles always work in the linear region of their length-tension characteristics. This greatly simplifies modelling of the oculomotor plant (Collins, 1971). Why are length-tension characteristics linear? The linear length-tension relationship, with constant slope and parallel curves, may be explained as a direct outcome of an intrinsic quality of the muscle itself, if we consider it in terms of Huxley's (1965) sliding filament hypothesis. According to this hypothesis a muscle generates maximum tension when the thin actin filaments touch at the centre of the A band of the muscle. As the muscle becomes shorter, the actin filaments overlap and the force-generating cross-bridges on the myosin molecules interact with improper (reversed) orientation in the region of actin molecule overlap. Thus, no force is developed in this region of overlap. Consequently, progressively less force is developed by the muscle as it shortens below its resting length where more overlap takes place. In this region force appears to be linearly proportional to the number of crossbridges effectively linking actin and myosin filaments. Inasmuch as extraocular muscle operates at less than its resting length over most of the range of normal eye movements, it operates within this linear range of force and length. Thus, there is no need to invoke a neural feed-back control mechanism as has been previously suggested (Granit, 1971; Collins, 1971); indeed, most evidence to date tends to rule out the contribution of stretch or tension receptors. Tendon forces are small An additional point for consideration is that the tensions delivered to the tendon are relatively small compared with the force developed by the contractile element itself. Thus, the tension measured isometrically in a stretched extraocular muscle may exceed 120 g (Robinson et al. 1969; Collins et al. 1969), whereas the tensions recorded in the present study, at the tendon, did not exceed 30 g in the stretched muscle. There are several factors contributing to this difference. First, the tension developed by the contractile element is still greater than 120 g, but the contractile element is paralleled by a large viscosity,

367 HUMAN EXTRAOCULAR MUSCLE TENSIONS which limits the rate at which it can change length. As a result, as previously mentioned, the force measured at the tendon can build up only slowly (with about a 20 msec time constant), taking some 100 msec to achieve its maximal value in the isometric case. Secondly, within the first few milliseconds the tendon force has built up sufficiently to move the eye a small amount thus reducing the length of the very stiff series elastic element. This shortening of such a stiff spring significantly reduces the larger developed muscle tension which would otherwise be observed in the isometric case. Consequently, at the tendon in an unrestrained eye, one does not observe the maximum tension which is developed by the contractile element. Energy considerations During a dynamic length-tension loop as in Text-figs. 6 and 7, the measured tendon force is initially isometric due to the large viscous load of the antagonist muscle and restraining tissues. The isotonic increment of tension recorded during the actual movement is a product of this viscosity and the equilibrium velocity of eye movement. At completion of the movement, tension drops with an isometric decay, related to the decrease of innervation and velocity drop. Now, certain conclusions relative to transmission of energy to the globe can be drawn from Text-fig. 8. Thus, in the dynamic length-tension loops for saccadic eye movement (as seen on the oscilloscope, Text-fig. 6 and in Text-fig. 8) changes in tension of the agonist move in a counter-clockwise direction. This is true because as the agonist delivers energy to the globe, its increasing developed force precedes the leftward muscle shortening, thereby following a counter-clockwise path in producing an eye movement. Passively stretching the muscle to its original length completes the counter-clockwise circuit. Counter-clockwise rotation on the lengthtension diagram indicates in a physical sense that energy is being delivered by the muscle to the globe. In contrast, when a muscle is acting as antagonist, its changes in tension follow a clockwise loop. This comes about as an external force (from the agonist) causes passive stretch of the antagonist; this upward force precedes the rightward extension movement, thus tracing a clockwise loop. The clockwise rotation indicates that energy is being extracted from the muscle, rather than being delivered by it; i.e. the force precedes relaxation. In this case the muscle acts as a brake rather than a motor. Some insight into the physical interpretation of these length-tension loops may be obtained from the engineering concept of the Carnot cycle of a heat engine. Indeed a muscle is a thermodynamic engine and consequently can be examined in terms of this well established principle. The Carnot cycle is a graphical display of energy delivered minus energy absorbed

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during a full cycle of motion of a thermodynamic engine. On a length-tension (or pressure-volume) graph, the area under the upper curve (and above the abscissa) represents the integrated product of force times distance and thus the energy delivered by the engine during a power stroke. The area under the lower curve (above the abscissa) represents the energy absorbed by the engine on the return stroke. The difference in area represents the net energy delivered to the load during a full cycle. The boundaries of the classical Carnot cycle comprise isothermal and adiabatic (isoenergetic) conditions which are analogous respectively to the muscle's isotonic and isometric modes of behaviour.

The counter-clockwise saccadic loops of Text-fig. 8 indicate the method of energy release from an oculorotatory muscle under central control. First, during the isometric tension increase the contractile element stores potential energy; since no external movement occurs during this phase, no external energy is dissipated. Only after the contractile element has completed its contraction does the eye move significantly, thus allowing the passive elastic muscle elements to shorten, delivering their stored potential energy in the form of kinetic energy of movement. Finally, after completion of the eye movement the contractile element is programmed to relax, but again isometrically with respect to the external world, thus minimizing energy dissipation. This strategy implies the least work demanded from the contractile element. It may be speculated that this process contributes to the eye muscle's not getting tired, even though continuously innervated during waking hours. This investigation was supported by NIH research grants No. PO1 EY-00299 from the National Eye Institute, No. NB-08582 from the National Institute of Neurological Diseases and Stroke, No. SO1 RR05566 from the Division of Research Resources, and the Smith-Kettlewell Eye Research Foundation. We wish to thank Mr Jerry Dittbenner, Mr Henry Freynick, Mr Jack Shore and Mr Elmer Johnson for their kind assistance. REFERENCES

COLLINS, C. C. (1971). Orbital mechanics. In The Control of Eye Movements, ed. BACH-Y-RITA, P. & COLLINS, C. C., pp. 283-325. New York: Academic Press. COLLINS, C. C. & SCOTT, A. B. (1973). The eye movement control signal. Proc. Second Bioengineering Conf. Ophthal. Sec., Milan, Italy. COLLINS, C. C., SCOTT, A. & O'MEARA, D. (1969). Elements of the peripheral oculomotor apparatus. Am. J. Optom. 46, 510-515. GRANIT, R. (1971). The probable role of muscle spindles and tendon organs in eye movement control. In The Control of Eye Movements, ed. BACH-Y-RITA, P. & COLLINS, C. C., pp. 3-5. New York: Academic Press. HUXLEY, H. E. (1965). The mechanism of muscular contraction. Scient. Am. 213, 18--27. ROBINSON, D. A. (1964). The mechanics of human saccadic eye movement. J. Physiol. 174, 245-264. ROBINSON, D. A., O'MEARA, D., SCOTT, A. B. & COLLINS, C. C. (1969). The mechanical components of human eye movements. J. apple. Physiol. 26, 548-553.

The Journal of Physiology, Vol. 245, No. 2

C. C. COLLINS AND OTHERS

Plate I

(Facing p. 369)

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EXPLANATION OF PLATE

A miniature 'C' gauge force transducer, with diameter of 2 mm, is shown in comparison with a dime (1 1 x 18 mm). A metal foil strain gauge element is cemented to an opened aluminium ring which can be sutured in series between the tendon of an extraocular muscle and its point of insertion on the globe. Muscle tensions have been measured during normal unrestricted voluntary eye movements.

Muscle tension during unrestrained human eye movements.

1. Tensions in the horizontal rectus muscles have simultaneously and continuously been recorded during unrestricted eye movements in four strabismus p...
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