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Length-Tension Recording System for Strabismus Surgery Carter C. Collins, Member, IEEE, Arthur Jampolsky, Albert B.Alden, Maureen B. Clarke, Steven T. Chung, Member, IEEE, and Sarah V. Clarke

Abstract-To meet the need for both scientific information and a clinical means for measurement of the mechanical parameters of the most difficult individual strabismus cases we present a technique for directly measuring and plotting the length-tension characteristics of the tissues supporting the eye. Semiconductor strain gauges mounted on the shanks of a custom machined eye forceps and an ultrasonic method of making continuous duction measurements of the eye have proved feasible. When the forceps are interfaced with a dedicated microcomputer, the system provides a permanent, quantitative, length-tension record displayed in real-time. The instrumented length-tension forceps system has provided a noninvasive means for quickly and simply assessing the mechanical underlying determinants of strabismus pathology in the ofice, the laboratory or in the operating room, and can aid in the planning and immediate intraoperative alteration of strabismus surgery. Under operator coordination, measurements can be made which precisely define the mechanical load which the eye muscles must move. The resulting objectively determined tissue stiffness asymmetries and muscle restrictions limiting ocular motion indicate the purely mechanical contributions to a patient’s strabismus. Measurements of active force indicate the magnitudes and patterns of innervation over the entire range of gaze. By comparison of these active force and passive stiffness records, nerve signal imbalances may be quantitatively distinguished from @echanical imbalances in strabismus. It is the detailed interaction of these nonlinear muscle forces and mechanical elements which determines the position of each eye in strabismus and therefore the proper surgical treatment. A brief description of actual use and a few examples of clinical results are included from over 200 human records.

INTRODUCTION

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HOUSANDS of strabismus operations are performed yearly and up to half of the average clinician’s patients must return for another corrective operation [I]. This alone indicates a need for better understanding and more quantitative mechanical data about the human oculomotor system. Early laboratory studies on animal muscle physiology were long the primary source of information on which to model the oculomotor system [2], [3]. Forced-duction measurements provided early clinically applicable information [4] and human physiological studies have supplied the rationale and required basic data, both for modeling of the eye 151, [6] and for implementing an objective strabismus surgical plan 171, [8]. However, a need remains for a noninvasive, clinically feasible means for safely, accurately, and conveniently measuring the mechanical characteristics of the more involved strabismus cases in order to help provide a guide for the planning and management of corrective surgery. We previously introduced a Manuscript received May 8, 1989; revised April 10, 1990. This work was supported by NE1 grant 5 R01 EY05947 (CCC), NE1 grant P30EY06886, and the Smith-Kettlewell Eye Research Institute. The authors are with the Smith-Kettlewell Eye Research Institute. San Francisco, CA 94115. IEEE Log Number 9043732.

strain gauge instrumented forceps and measured displacement with a ruler 191; but our technique of replacing the ruler with an automatic ultrasonic method of measuring length has proved more accurate, faster, and convenient [ 101. Other approaches for clinically measuring the mechanics of the eye have subsequently been described in the literature [ 111-[ 141. Described here is a technique for quickly assessing and graphically displaying the mechanical length-tension (L-7) characteristics of the passive tissues restraining eye movement as well as for measuring the patterns and magnitudes of active forces developed by the individual oculorotary muscles. When implemented in a microcomputer-controlled system, this method provides both immediate and permanent records of the static and dynamic forces required to produce any given angular displacement of the eye or extension of a muscle. METHODS Force Measurement

In keeping with long standing physiological tradition, well understood by biologists and physicians as well as engineers, we will refer to force in terms of grams (g) as well as newtons (N). Shown in Fig. I , as a base for the hand-held instrument we currently employ a modified Dumont number 2 stainless steel jeweler’s forceps 1151, 10 cm long, having a tapered shank thickness averaging about 1 mm which supports the necessarily large tissue holding forces. The shanks are modified by milling down their width to 0.80 mm for a length of 17 mm in order that they may bend very slightly with muscle or globe (eyeball) tissue forces acting in a direction perpendicular to the plane of the surgeon’s grasping force. The shank dimensions of these work hardened 316 stainless steel cantilever beams result in a calibrated compliance of the system of 1 pm/g at the tip, i.e., a stiffness of 1000 g/mm (9.8 N/mm). To ensure that the system is rugged, repeatable, and accurate the cantilever beams are stress tested with a five times overload safety factor. 500 g of force (4.9 N) can be applied at the forceps tips on the normal load axis with less than 1 pm permanent offset in strain. Force is measured tangentially to the long axis of the forceps and is independent of longitudinally applied forces. This is important since only the muscle forces tangent to the globe contribute to eye rotation, and the forceps can thus isolate these forces when held radially to the globe. Safety has been enhanced by incorporating a nonlocking finger stop which permits the surgeon to release the eye from his grip and retract the forceps instantly at any time. Otherwise, if the forceps grip should slip under the high forces required to hold the eye to one side the cornea might be scratched as the eye sprang back to its rest position. To provide a secure grip,

0018-9294/91/0300-0230$01.OO 0 1991 IEEE

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our forceps tip design incorporates a very small tissue grasping area in order to raise the tissue holding pressure. Due to the nonlocking mechanical stop under the finger pressure area, the surgeon’s normal grasping force of 300-400 g (2.9-3.9 N) results in a constant 150 g of force (4.9 N) at the forceps tips. Under these conditions we have found that tip dimensions measuring 150 pm X 600 pm result in the required pressure. From the tissue holding tip area of 0.09 mm2, the pressure applied to the tissue is calculated to be some 1.7 kg/mm2. This pressure is sufficient to hold the globe while measuring tissue forces of over 100 g (0.98 N), but in our experience is not sufficient to unduly damage the limbus, a tough, thick ring of tissue surrounding the comea, which the surgeon usually grasps. The tissue contact surface is raised to a height of 150 pm above the shank surface of the forceps allowing the shanks to clear the tissue and leaving the tips alone to bear on the tissue. A special tread or surface-roughening treatment is required to prevent the tissue from slipping. As seen in Fig. 1, our design calls for 10 lands, 40 pm wide, perpendicular to the applied force, and 10 grooves, 20 pm wide and 20 pm deep. This is approximated by drawing a number 2 diamond file between the closed tips, parallel to the long axis of the forceps. To permit the surgeon free movement, the 2.7 m long, six conductor-shielded cable connecting the forceps to its electronics must be quite limp; 10 g normal force (0.098 N) produces a 15 mm radius bend.

waterproof and able to withstand repeated exposures to ethylene oxide gas during sterilization. For accuracy, attachment of the gauges must result in a high degree of linearity and adhesion, along with low hysteresis and creep. Linearity of the force channel is within 0 . 5 % , one digital count, over the range of _+ 100 g (0.98 N). The force hysteresis, due to strain gauge cement and organic coating, is 0.5 g (0.0049 N) after a 100 g load (0.98 N), and settles to 0.1 g (.00098 N) within 5 s. As shown in Fig. 1, the gauges are mounted on opposite edges of each shank at the root of the milled-down portion approximately 16 mm from the tip. They are placed such that the tension to be measured is applied to the tips perpendicular to the surgeon’s grasping force. Although the clamping force is applied perpendicular to the direction of the measured tension and is held constant by means of mechanical stops on the forceps, it is relatively large, 150 g (1.477 N), compared with the measured tension, 1-100 g (0.0098-0.98 N); consequently care must be taken to align the strain gauges precisely on the mechanical neutral axis of the shanks to minimize cross-coupling of the unwanted clamping force into the measurement. The small residual second-order clamping force reading is nullified by a simple zero-tension calibration procedure which is performed by activating a sample-and-hold circuit (described later) when the forceps are closed but with no tissue clamped between the tips, i.e., with zero tension on the measuring axis. Force Measurement Electronics

Force Transducers

To measure either muscle tension or force applied to the globe by the forceps, we have utilized a matched pair of bare, unbacked, microminiature silicon semiconductor strain gauges [16]. These gauges measure 12 x 350 x 1250 p n and have 50 pm diameter gold wire leads 20 mm long. The gauges are nominally 500 Q in resistance and pairs are matched to 0.5% for effective temperature compensation. The gauges are insulated from the forceps by a thin sheet of glass and are bonded to the forceps shanks by means of a thin layer of especially low hysteresis thermosetting phenolic cement [ 171. They are subsequently coated with multiple layers of low adsorption epoxy polymer and microcrystalline wax so that the assembly will be

We have designed and built an analog circuit card installed in a personal computer which controls the operation of the length and force transducers. In the lower part of the diagram, Fig. 2 , the signal from the junction of the pair of microminiature active silicon strain gauges is input to an operational amplifier with a gain of approximately IO. Electrically, the strain gauges are connected in a simple half-bridge configuration so that the desired slight bending of the forceps shanks due to applied tissue forces produces opposite resistance changes but additive voltages at the bridge output. The common mode voltages due to temperature variations are cancelled out in this circuit configuration. Although the dynamic response from the forceps is over 1000 Hz their output is fed to a 20 Hz low-pass second-order

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R C integrator, hum and noise filter. This signal, a voltage proportional to applied force, then passes to a sample-and-hold “zero force” biasing circuit, and is in turn sent to the A / D converter. In operation, the “zero force” calibration is set by pressing a switch in a control pendant while no force is applied to the forceps. The switch closes a relay contact which impresses the desired “zero force” bias voltage across a low leakage capacitor. The very low input current of the following JFET operational amplifier, typically 30 PA, assures stability of the zero voltage for a relatively long period of time. The gain of this amplifier is set to give a scale factor of 20 mV/g. The shunt diodes limit the output so as not to saturate the input circuitry of the following 8-channel multiplexed A /D converter. The output resistance of both the length and force channels is 500 a; however, the load resistance is generally kept greater than 10 K Q . The 20 Hz response of the output filters has proved entirely adequate to the task. In fact, the hand-held forceps should be moved at a traction velocity less than 2 mm/s, or 10°/s in order to avoid introducing the spurious forces of tissue viscosity. Since the output filters in each channel are closely matched to each other in amplitude and phase, both the static and dynamic L-Trelationships are correctly preserved in all records.

Patient safety from electrical shock is provided by a medically approved isolation transformer in the power supply.

Force Calibration The forceps are calibrated by using precise laboratory balance weights to measure and plot the linearity of the force channel response. More conveniently, both the length and force output of the forceps may be simultaneously calibrated with a high-quality steel piano wire coil spring with linear L-T characteristics, i.e., with a constant stiffness, and exhibiting essentially no viscosity or hysteresis. The force span is f 125 g (1.23 N) full scale, 150 g (1.47 N) maximum overload. Using a five point running average in software the force resolution is better than 0.5 g (0.0049 N) with a 40 mg (0.00039 N) noise level. The zero drift rate is approximately 30 mg (0.00029 N) per minute. The temperature coefficient of sensitivity change is -0.2%/”C, and the temperature coefficient of dc offset is + 0 . 5 % , resulting in approximately 0.6 g / ” C zero shift.

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LENGTHMEASUREMENT The stretching of a muscle or rotation of the eye is measured as a movement of the forceps by means of an ultrasonic time of flight technique [lo]. A small 2 X 4 X 5 mm microphone [18]

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with a 24 mm long, 1.2 mm ID, thin-wall hypodermic needle tubing extension having an opening 1 mm from the tip of the forceps receives ultrasonic pulses produced by a 35 mm diameter extended source, 10-100 kHz wide-band electrostatic acoustic transducer [ 191 held fixed with respect to the head and eye by two parallel guide rods. Since the velocity of sound in air is essentially constant, 330 m / s , the time of flight of these sound pulses is proportional to the distance between the sound source and the receiver and amounts to 3 ps/mm. The demodulated time of flight signal is a voltage proportional to the distance of the forceps tip from the ultrasonic transducer. As with the force channel, zero relative length is set into a sample-andhold circuit by pressing a switch in a control pendant when appropriate. To measure the detailed L-T characteristics of a detached muscle, the ultrasonic source is oriented vertically with the ends of the guide posts held against the zygomatic bone and the temporal aspect of the supraorbital ridge of the supine patient. The muscle is then pulled straight up and the resulting length measurements are strictly linear. To measure the normal range of horizontal eye positions, 50" nasal to 50" temporal, the ultrasonic source is fixed at an optimal angle with respect to the skull, by being held against the bones of the malar process and the temple, with the guide posts resting on the bones of the supraorbital ridge and the ridge of the nose. In this preferred orientation the axis of the ultrasonic beam assumes about a 115" temporal relationship with respect to the patient's line of sight at primary (see Fig. 3 ) . Under these conditions, indication of the forceps tip position is strictly linear in the entire nasal quadrant and up to 25" of temporal gaze position because the ultrasonic beam diffracts around the eye to fill the "sound shadow" in the nasal quadrant, and thus the sound path traverses an essentially circular arc following the contour of the globe. Over an arc of 75" of equivalent eye rotation, from 50" nasal to 25" temporal, the accuracy of the system is within 0.05 mm, equivalent to an accuracy of 0.25" of eye position. From 25" to 50" temporal rotation, the 25" region beyond tangency of the ultrasonic beam with the globe, the straight line ultrasonic path approximates the circular arc of movement of the forceps and eye to within 3% trigonometric accuracy. In the worst case, holding the temporal limbus at the extreme temporal position, this amounts to kO.1 mm or 0.5" of eye rotation. In practice, the surgeon grasps the limbus, the 12 mm diameter ring of tissue encircling the cornea which subtends a 60" arc over the center of the globe. This results in two surmountable constraints: limiting the extreme gaze position in one direction and offsetting the forceps tip 30" from the patient's line of sight, depending on which side of the limbus is grasped. With the forceps holding the nasal limbus, accurate eye position measurements can be made over the entire temporal quadrant and up to 20" of nasal gaze position at which point forceps movement is limited by the nasal canthus. Grasping the temporal limbus permits accurate measurements over the entire nasal quadrant and up to 20" of temporal gaze position, limited by the temporal canthus. Continuous 100" ( 5 5 0 " )eye position records may be produced by electronically joining the computer records of these two measurements. Length Measuring Electronics

In the upper section of the circuit diagram, Fig. 2 , a 48 V, 8 ps pulse drives the electrostatic acoustic source transducer [ 191

Fig. 3. Illustration of the proper use of the length-tension forceps and ultrasonic source during strabismus surgery showing their radial orientation to the globe at incremental locations during a smooth pull. The forceps are grasping the nasal limbus to perform a temporalward forced traction.

at a repetition rate of 1000 Hz. The transducer in turn emits pulses of ultrasonic energy with a 2 ps rise time which travel to the tip of the forceps. As shown in the left center of the diagram, the miniature ultrasonic transducer [ 181 detects these pulses through the tube opening near the forceps tip, and converts them into an electrical signal which is amplified by a two-stage integrated circuit amplifier with a gain of approximately 12 000. The 1 mm tube set back from the tip of the forceps is compensated in software. The outgoing ultrasonic signal sets, or turns on, a multivibrator which stays on until the leading edge of the received pulse resets it, or turns it off. The output of the multivibrator is a rectangular wave with a duty cycle, and thus dc component, proportional to time of travel of the sound pulse and thus to the distance between the transducer and microphone tube tip. A second-order low-pass R C filter with a -3 dB cutoff of 20 Hz is used to extract the dc signal from the output of the multivibrator, which in turn is fed into a sample-and-hold "zero position" circuit identical to that of the force channel. The gain of the output amplifier is set to produce a length channel scale factor of 100 mV/mm. As with the force channel, shunt diodes limit the output so as not to saturate the input circuitry of the A / D converter. Length Calibration

The sensitivity and linearity of the forceps length channel may be calibrated by using a micromanipulator or a detented scale. As previously mentioned, a more expedient method of calibration employs a continuous plot of the linearity of the combined length and tension systems using a precalibrated steel spring. Grams of force are recorded vertically and millimeters of displacement (or equivalent degrees of eye rotation) horizontally in such L-Tcalibration records. The length span is 5 10 mm in practice, i.e., f50", with a 500 mm maximum range. The length linearity is 0.5% or 0.1 mm nasally, or 0.5", and 0.2 mm at extreme temporal gaze. The resolution is 0.05 mm or 0.25" over the normal range of eye positions of 550".The zero drift rate is under 50 p m per minute. The sensitivity stability has been better than 1.5 % /year in both length and force. There is no length hysteresis observable. Length measurements de-

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pend on the fundamentally constant speed of sound. The small variation with temperature and humidity amounts to less than 0.04% with a 5°C temperature change and 0.015% for a 5 % relative humidity change. In general, both length and force transducer performances exceed A / D resolution, which is better than 0.5%. In a recent, representative six month period, both the length and force channels of typical forceps exhibited a stability of response within 0.25 % per month. To further increase accuracy we routinely recalibrate before each surgery.

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“Passive” indicates that the patient is under general anesthesia and the eye muscles are not innervated. Pancuronium@is administered to completely relax the muscles. Passive measurements may be made in the horizontal or vertical directions on the: a) intact eye, b) detached muscles, and c) isolated globe. The forceps are designed to be held similarly to the manner in which surgeons use noninstrumented forceps in measuring both passive and active forces. While measuring duction movements of the intact eye or the isolated globe, the forceps should be held radially with respect to the eye, that is such that an extension of their long axis would pass through the center of rotation of the globe at all times during measurements. Fig. 3 illustrates the proper use of the forceps for passive horizontal measurements of the eyes. For vertical and other nonhorizontal measurements, other placements of the ultrasonic source are required. Prior to use, the surgeon grasps the forceps in the fully closed position with no load applied. The operator then “zeroes” the force channel by pressing the zero force button. Next, the surgeon places the open end of the two parallel spacing rods of the ultrasonic source on the brow and ridge of the nose and braces the transducer against the bone of the cheek, thus fixing the source with respect to the head at about 115” inclination to the line of sight of the eye in the primary position. The surgeon grasps the limbus with the forceps and rotates the eye to the primary position. The operator then presses the zero length button, and the system is ready for use. Force is immediately displayed as a function of length on the computer monitor screen and the resulting L-T plots indicate the successive forces required to pull the eye through any given distance. The immediate on-line display facility proves useful in the operating room by providing qualitative and quantitative data from which the surgeon can more accurately implement or change his surgical plan. Typical L-T records are shown in Fig. 4. For a detached muscle it is easy to determine zero force from the slack muscle, however the “zero” or primary length is more difficult, requiring that the muscle be brought to its point of insertion while the globe is held at the primary position, or else primary length must be estimated. Active

In this context “active” means the patient is awake, alert, and the eye muscles are innervated. In the intact eye under these circumstances the active force of an individual medial or lateral rectus muscle can be effectively isolated and measured by eliminating contributions of its antagonist over most of its range of innervation [lo], [20]. In brief, the patient is requested to fixate a target at extreme gaze. The eye is then grasped and held fixed in supraextreme gaze position, say laterally, with the forceps. The lateral rectus muscle is thus shortened to a point such that

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it cannot now deliver force to its tendon. Consequently, as the patient is directed to track a known target, or to fixate a series of known targets, with his other eye, the force exerted on the forceps will be due essentially to the measured agonist medial rectus muscle alone. By this means, a graph of active, individual muscle force as a function of eye position can be plotted. Similarly, the active lateral rectus muscle force may be measured holding the eye in the supra extreme nasal position. These procedures also provide a measure of innervation since we have found that the isometric force developed by a muscle is directly proportional to its innervation [ 5 ] .

COMPUTER CONTROLSYSTEM We have designed a separate digital interface card for a microcomputer which supports digital input and output ports, a hardware timer and an 8-channel multiplex A / D converter. To control the data collection procedures from the vicinity of the operating table, a hand-held control pendant comprising a switch box with six control buttons and two indicator LED’s on a 3.5 m cable is used. The momentary-contact pushbutton switches control: 1) the length zero setting, 2 ) the force zero setting, 3) the start and 4) stopping of data recording, 5) clearing of the previous L-Tdisplay from the monitor screen, and 6 ) the placing of a digital event mark in the record to label an occurrence of special interest. The indicator lights show when the system is a) ready to take data and b) writing patient data to disk. We have written our own disk operating system to improve storage speed and control programs to handle forceps calibration, data collection, data reduction and data analysis. The resulting speed and ease of operation enhances both patient safety and convenience for the surgeon. To keep track of the continuous stream of collected data containing patterns of variation of active muscle forces and the in-

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trinsic stiffnesses of the passive tissues, and also to accurately differentiate among them over the required range of eye positions is a difficult task. But it is the reciprocal influence of these basically nonlinear mechanical elements which determines the individual eye positions and therefore comitance, the pointing of the eyes in the same direction. To bring order to this data, we use a microcomputer to: 1) control and interface with the forceps, 2) collect and A / D convert the resulting, on line, realtime length and force measurements, 3) display the data graphically in real time on a monitor in the operating room as L-T plots, 4) store the data in RAM, 5 ) permanently archive the data from each patient on a separate floppy disk, and 6) reduce, analyze. and plot the data as hard copy to yield publishable L-T diagrams. Other information may optionally be keyed into the patient’s disk record. Postsurgical data reduction, analysis, and plotting routines automatically screen out unwanted portions of the record. In this program, one algorithm extracts meaningful data regions from the background by searching for L-T curves with reasonably long, continuous, elevated, coherent, and varying length and force signals. Another algorithm discards wild, inconsistent, saturated or “out of bounds” length points. A third algorithm makes offset length and force corrections from the zeroset and calibration button presses which are recorded with the data at surgery. In this program, two data plotting options are available. The first routine, using the above selection criteria, plots the L-T curves for the entire series of data records from a surgical case, and the second plots the length and force records as a function of time.

RESULTS Over the past ten years of operation more than 200 patients and paid normal subjects have been measured using the system. The forceps have made it possible to determine the mechanical L-T characteristics of both normal and abnormal muscles and passive globe restraining tissue stiffnesses that the muscle forces must overcome to move the eyes [51, [71, [lo], [20]. As an example of the clinical and scientific utility of the L-T forceps system, Fig. 4 shows a complete series of L-T records for a 50 prism diopter exotropic strabismus patient anesthetized at surgery; the records at each stage of surgery are filtered for clarity. In each, the surgeon moves the tissue in each direction with the forceps, slowly to minimize the effects of viscosity, and returns it to the initial position. Record A shows the characteristics of the intact eye which rests at 25” temporally, appropriate for a 50 prism exotrope. One can see the effects of mechanical hysteresis of the eye tissues which separates the higher force “pull” phase from the lower force “return” phase. The stiffness K is normal at about 2.5 g / m m (0.025 N/mm), and was measured as the slope of the central part of the L-Tcurve. Record B represents the isolated globe which can be seen to have a smaller stiffness, as it should with the muscles detached; K is about 1 .O g/mm (0.0098 N/mm). In record C the detached medial rectus muscle appears normal with a tension of 20 g (0.196 N) at 50” of extension. Note the force becomes very great just beyond the extreme gaze position of 50”. The continuously varying slope of an isolated passive muscle L-Tcurve makes it necessary to specify the muscle length at which its stiffness is measured. This problem does not exist in the active state. In record C the lateral rectus muscle is seen to require 40 g (0.39 N) to stretch it to only 35“ nasally. Since this is as much force as the normally contracting medial

rectus muscle can exert to pull the eye nasally, this eye cannot be voluntarily moved beyond this position. Such a graphical representation describes a muscle restriction clinically referred to as a contractured or “tight” lateral rectus. This objectively determined restricted length can more accurately establish the amount and type of surgery to be employed. D is a surgeon’s sketch describing this limitation of voluntary eye rotation as “ - 1 1/2 in adduction.” The shaded area, associated with forces greater than 40 g (0.39 N), is unattainable by this eye until proper surgical alteration is performed. DISCUSSION Surgeons are quite familiar with eye forceps so for them, the L-Ttechnique is easy to learn and use. Since most of the system is coordinated by the operator, the surgeon needs only to utilize a few extra moments of time to uncover and record potentially crucial clinical data. The noninvasive method allows the L-T forceps to be used also outside of surgery, which broadens its usefulness as both a clinical and investigative tool. We will herewith briefly review some of the studies made possible by application of the L-T forceps.

Basic Studies Our human investigations have attempted to discover the fundamental mechanisms responsible for eye movements and their disorders using the L-T forceps system. The basic quantification of human oculomotor parameters originated in this laboratory [21], [22], and our team has been able to determine many of the major mechanical characteristics of the extraocular muscles and orbital tissues [5], [20], [23]-[26]. We initially investigated the passive mechanical characteristics of muscles and globe restraining tissues. The slopes of such resulting L-Tcurves indicate the stiffness of the tissues measured, i.e., the load the muscles must overcome to move the eyes [5], [lo], [201, [211, [22], [27]. In general, passive tissue stiffness is not constant, but varies with the degree of extension of a tissue or the position of the eye [ 5 ] .A passive, i.e., anesthetized, muscle exerts little force and exhibits quite nonlinear L-T characteristics [5], [25], [281. However, when the patient is awake and a muscle is innervated, as opposed to the passive state, the muscle develops up to 100 g (0.98 N) of force [SI and the L-Tcharacteristics become linear and parallel above 10 g (0.098 N), that is, the stiffness assumes a constant value of about 4.0 g/mm or 0.8 g per degree of eye movement (0.039 N / m m or 0.0079 N / ” ) [7], [211, W l . We have also investigated the innervational code used by the brain to communicate with the eye muscles and the changes of muscle force, length and stiffness due to these signals [SI, [20], [29], [30]. We have found that the brain selects different control strategies for the various types of eye movements [SI, [29], [3 11. The L-T forceps have permitted the determination of the levels of innervation and the resultant active forces required to hold the eyes at any position of gaze in some 30 volunteer subjects [20]. Surprisingly, the innervation and active forces developed by the eye muscles are quite nonlinear with respect to linearly spaced eye positions, and in fact can be described by a square law 151, [27l, POI. Such objective physical data have permitted a more precise understanding of the many interrelated mechanical factors involved in oculomotion, especially through the use of modeling

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techniques which we have pursued and have been used by others [SI, [611 (221, [231, L311, 1321.

and limits, at each stage of his surgery rather than using fixed, purely experiential or judgmental factors.

ACKNOWLEDGMENT

Clinical Applications The major causes of strabismus are either mechanical or innervational imbalances. The forceps provide a means for quickly and simply making quantitative records of these innervational and mechanical underlying determinants of strabismus pathology in the operating room, clinic or in the office [23], [25]. The system can provide a quantitative assessment of restraining tissue stiffness, locations and severity of restrictions or muscle contractures, asymmetries of stiffness contributing to tropia, or misalignment of the eyes, and in general objective quantitative measurements of clinical pathological conditions. In addition, the forceps permit the determination of the magnitude of active muscle forces, the degree of paresis or paralysis of a muscle, the balance of innervation between antagonist muscles, and the pattern of innervation of individual muscles over the entire range of gaze 171, [lo]. [201, [231, 1251, [ X I . The forceps assist the physician in diagnosing clinical entities [25], [26]. Gross imbalances in innervation patterns of agonistantagonist muscle pairs are one of the major causes of ocular misalignment and may suggest that the surgeon use an altemative treatment plan. For example, the forceps permit the measurement of the maximum active force of individual oculorotary muscles which can be useful in the differential diagnosis of strabismus caused by a paresis, i.e., weak innervation, as opposed to a mechanical restriction. We have found that a maximum active force of less than 45 g (0.44N) would make one suspect that the muscle was paretic [20]. The forceps can help the clinician to plan surgery from objective measurements [7], [8]. For example, an unusual stiffness may produce a restriction of movement, and objective measurement of the L-T characteristics can precisely locate and quantitatively describe the severity of such a restriction or tether which may aid or alter the plan of surgery. These research findings have introduced new clinical concepts and have found application in the diagnosis and management of strabismus [7],

We wish to thank Dr. P. Howe for a critical reading of the manuscript and contributing many helpful suggestions in the preparation of this paper.

REFERENCES [ l ] E. M. Helveston, “Reoperations in strabismus,” (Abstract), Ophthalmol., vol. 85, pp. 66-67, 1978. [2] A. Fick, “Uber die anderung der elasticitat des muskels wahrend der zukung,” Arch. fur die Ges Physiologie, vol. 4 , pp. 301315, 1871. [3] H. S. Gasser and A. V. Hill, “The dynamics of muscular contraction,’’ Proc. Roy. Soc. B . , vol. 96, pp. 398-437, 1924. [4] K . F. Stephens and R. D. Reinecke, “Quantitative forced duction.” Trans.. Amer. Acad. Ophthal., vol. 71, p. 324, 1967. [5] C. C. Collins, “The human oculomotor control system,” in Basic Mechanisms of Ocular Motility and Their Implications, G. Len-

nerstrand and P. Bach-y-Rita, Eds. Oxford, England: Pergamon, 1975, pp. 145-180. [6] J. M. Miller and D. A. Robinson, “A model of the mechanics of binocular alignment,” Comput. Biomed. Res., vol. 17, pp. 436440, 1984. [7] C. C. Collins and A. Jampolsky, “Objective calculation of strabismus surgery,” in Functional Basis of Ocular Motility Disorders, G. Lennerstrand, E. Keller, and A. Scott, Eds. Oxford, England: Pergamon, 1981, pp. 185-194. [8] C. C. Collins, J. M. Miller, and A . Jampolsky, “The roles of

expert systems and biomechanical models in eye muscle surgery,” IEEE Eng. Med. Biol. Mag., vol. 4 . no. 4 , pp. 17-25 Dec. 1985. [9] A. B. Scott, C. C. Collins, and D. M. O’Meara, “A forceps to measure strabismus forces,” Arch. Ophthal., vol. 88, pp. 330333, 1972. [lo] C. C. Collins, “Length-tension recording strabismus forceps,” in Smith-Kettlewell Symp. Basic Sciences in Strabismus: Mechan. and Tonic Factors on Strabismus Diagnosis and Surg. Annex to the V Cong. Conselho Latino-Americano de Estrabismo (C.L.A.D.E.),Oct. 16-17, 1976, Guaruja-Brazil, C. Souza-Dias Ed. Sao Paolo: Oficinas das Edicoes Loyola, 1978, pp. 7-19. [ 1 I ] I. M. Strachan et a l . , “An apparatus for measuring forces in strabismus,” in Orthoptics-Past. Present and Future. S. Moore, J.

[201, [231-[261. The forceps have aided in the design of new surgical approaches [8], [24], [26]. We have explored a number of promising surgical uses for these L-Tfindings and their contributions suggesting new techniques for strabismus management [23][26]. In one study we have attempted to apply this basic technique and the information which we and others have obtained to determine whether one can more accurately quantify and thus improve the results of strabismus surgery [6]-[SI, [28]. From our L-T forceps measurements a computer model of the eye movement control system has been made which successfully duplicates both healthy and pathological eye movement performance [ 5 ] , [32]. Such models tailored individually by means of L-T measurements at surgery, may eventually be able to qualitatively and quantitatively aid the ophthalmologist in his diagnosis and choice of surgical treatment plans. Simulated operation on the model would permit the surgeon to compare various amounts and types of strabismus surgery and to choose an optimum approach from many model responses before performing the actual surgery in the operating room [ 5 ] , [SI. The primary significance of the length-tension recording system will be to provide a rational approach utilizing physical measurements, capable of easy performance by the average clinician, which will allow him to derive the necessary surgery,

A

[I21 [I31 [I41

[I51

Mein and L. Stockbridge, Eds. New York: Stratton Intercontinental Med., 1976, pp. 123-128. A. L. Rosenbaum and J. H. Meyer, “New instrument for the quantitative determination of passive forced traction,” Ophthalmol., vol. 87, pp. 158-163, 1980. H. S. Metz and G. Cohen, “Quantitative force traction measurement in strabismus,” in Strabismus 11, Proc. Fourth Meet. I.S.A., R. D. Reinecke, Ed. Grune and Stratton, 1984, pp. 755-764. H. A . Garcia, J. R. Lavin, N . Lavin, and A. 0. Ciancia, “A new and practical model transducer forceps for measurement of active and passive forces in eye movements,” Binocular Vis., vol. 2 , no. 2, pp. 69-76, 1987. Stainless steel forceps, Model #4 Inox Tweezer. Manufactured by A. DuMont Fils & Co. Succ., Switzerland. Available from Bore1 & Frei, 420 W. Seventh St., Los Angeles, CA 90014. Tel.

(800) 654-9591. [I61 Semiconductor strain gauge, Model POI-05-500, available in minimum quantities of 50 four-unit packages, manufactured by Celesco Transducer Products, Inc., 7800 Deering Ave., Canoga Park, CA 91304. [17] G. R . Dittbenner, Strain Gauge Engineering, 4353 Findlay Way, Livermore, CA 94550. [ 18) Subminiature electret condenser microphone with self-contained FET amplifier, 3500 Q output impedance at 1 kHz. Part number EA 1843, manufactured by Knowles Electronics, Inc., 1151 Maplewood Drive, Itasca, IL 60143. [I91 Instrument grade electrostatic transducer, 4 0 mm diameter, 9 mm thick, 500 pf capacitance; broad-band acoustic output, 20 to 100

kHz. Manufactured by Polaroid Corporation, Ultrasonic Ranging Division, Cambridge, MA 02139.

COLLINS et

U / .:

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LENGTH-TENSION RECORDING SYSTEM

C. C. Collins, M. R. Carlson, A. B. Scott, and A. Jampolsky, “Extraocular muscle forces in normal human subjects,” Invest. Ophthalmol. Visual Sri., vol. 20, no. 5 , pp. 652-664, 1981. C. C. Collins, A. Scott, and D. O’Meara, ”Elements of the peripheral oculomotor apparatus,” Amer. J. Oprom., vol. 46, pp. 510-515, 1969. D. A. Robinson, D. O’Meara, A. B. Scott, and C. C. Collins, “The mechanical components of human eye movements,” J. Appl. Phy~iol.,vol. 26, pp. 548-553, 1969. C. C. Collins, and A. Jampolsky, “The mechanism of the observed weakness of the inferior oblique muscle in elevating the eye,” in Proc. Japan. Neuro-ophthalmol. Soc., July 1984, pp. 132- 168. C. C. Collins, ”Design of artificial muscles for extraocular implantation,” in Proc. First Symp. Advances in Strabismus Surg., Barcelona, Instituto Castanera, Barcelona, Spain, 1985, pp. 234270. C. C. Collins and A. Jampolsky, “Mechanical correlates of extraocular muscle contracture,” in Adaptive Processes in Visual and Oculomotor Systems, E. L. Keller and D. S. Zee, Eds. Oxford, England: Pergamon, 1986, pp. 27-35. C. C. Collins and A. Jampolsky, “The medial rectus muscle in Duane’s Syndrome,” in preparation. C. C. Collins. “Orbital mechanics,” in The Control of Eye Movements. P. Bach-y-Rita and C. C. Collins, Eds. New York: Academic, 1971, pp. 283-325. A. B. Scott, C. C. Collins, and D. O’Meara, “Extraocular muscle forces in strabismus,” in First Congr. Internat. Strabismolog. Assoc., Peter Fells, Ed. London: Henry Kimpton, 1571, pp. 125-136. C. C. Collins and A. B. Scott, “The eye movement control signal,” in Proc. Second Bioeng. Conf. Ophrhalmol., Milan, Italy, Italian Soc. Ophthalmol., 1973, article 4, pp. 1-18. C. C. Collins, D. O’Meara, and A. B. Scott, “Muscle tension during unrestrained human eye movements,” J . Physiol., vol. 245, pp. 351-369, 1975. A . B. Scott and C. C. Collins, “Division of labor in human extraocular muscle,” Arch. Ophthal.. vol. YO, pp. 319-322, 1973. C . C. Collins, “Human oculomotor control,” in Proc. 1975 Winter Comput. Simulation Conf.,Sacramento, CA, Soc. for Comput. Simulation, La Jolla, CA, 1976. pp, 69-76. Carter C. Collins (M’56) received the B S. degree in engineering physics in 1949, the M S.

degree in electrical engineering i n 1953, and the Ph.D degree in biophysics in 1966, all from the University of California, Berkeley. He is Senior Scientist at the Smith-Kettlewell Eye Research Institute Dr Collins received the American Medical Association Hektoen Silver Medal in 1972, the Bronze Medal in 1976, and the Kettlewell Research Chair in Ophthalmology in 1980. He has held memberships on the National Academy of Sciences Committee on Vision and the NINCDS Scientific Programs Advisory Committee. He is also a member of the IEEEIEMBS, Sigma Xi, AAAS, NYAS, and the Association of Research in Vision and Ophthalmology. Arthur Jampolsky received the B.A. degree in optometry in 1940 from the University of California, Berkeley, and the M.D. degree in 1543 from Stanford University School of Medicine, Stanford CA. He is Executive Director of the Smith-Kettle-well Eye Research Institute. Dr. Jampolsky holds memberships on the National Academy of Sciences, National Research Council Committee on Vision; National Institutes of Health, National Advisorv Eve Council; and the Visual Sciences Study Section, Division of Research Grants, NIH (Consultant to the Surgeon General).

Albert B. Alden received the B.A. degree in

physics in 1959 from the University of California, Berkeley. He is Senior Electronics Engineer at the Smith-Kettlewell Eye Research Institute. He spent I O years in private industry before joining the staff at Smith-Kettlewell in 1971. He has contributed to the design of numerous research projects and has been Senior Engineer in the Rehabilitation Engineering Center at Smith-Kettlewell since 1975.

Maureen B. Clarke received the B.S. degree

mathematics from Fontbonne College of St. Louis University, St. Louis, MO, in 1553. She is Senior ProgrammeriAnalyst at the Smith-Kettlewell Eye Research Institute She has been Senior Programmer at the Heart Research Institute of the Institute of Medical Sciences and has also done engineering/ programming at the Martin Company, Jet Propulsion Laboratory and the Aerospace Corporation. in

Steven T. Chung (S’72-M’75) was born in China. He received the B . S . degree in electri-

cal engineering from the California State University, Sacramento, in 1973 and the M.S. degree in electrical engineering from the University of California, Berkeley. in 1974. He is Senior Electronics Engineer at the Smith-Kettlewell Eye Research Institute. He has performed digital circuit analysis and design and computer interfacing at Smith-Kettlewell since 1975.

Sarah V. Clarke received the B.S. degree in computer science from San Francisco State University, San Francisco, CA, in 1984 (major emphasis in numerical analysis) with high honors (summa cum laude). She is Data Coordinator at the Smith-Kettlewell Eye Research Institute and has been engaged in computer programming, statistical analysis, database administration, and clinical data coordination since 1982.