Automated estimation of implicit time and amplitudefrom the flicker electroretinogram

Matthew L. Severns, Mary A. Johnson, and Scott A. Merritt

The electroretinogram (ERG) has been shown to yield sensitive and specific information about the develop-ment of neovascularization in ischemic disorders such as diabetic retinopathy and central retinal veinocclusion. However, even though the test is quick, easy to perform, and carries few risks, the ERG is poorly

utilized in clinical situations because of the extended training period necessary for test interpretation. Wehave developed an algorithm that estimates the phase and amplitude of a 30-Hz flicker ERG and that isrelatively insensitive to many forms of interference in ERG recordings. These estimates can be directlycompared to established criteria for the risk of proliferative retinal disease. Key words: Flicker electroreti-nogram, implicit time, amplitude, automation.

1. Introduction

The two most common retinal vascular disorders inthe United States are diabetic retinopathy and retinalvein occlusion. Diabetic retinopathy is the leadingcause of vision loss among U.S. residents between theages of 14 and 65. Retinal ischemia produced by retinalvascular disorders can lead to neovascularization-thegrowth of new blood vessels in the eye. Retinal neo-vascularization may cause blindness from vitreoushemorrhage or fibrovascular scarring and subsequentretinal detachment. Iris neovascularization maycause blindness and chronic pain from acute angleclosure glaucoma. If detected in time, these complica-tions of retinal ischemia can be averted by panre-tinal laser photocoagulation (PRP), laser ablation oflarge segments of peripheral retina.1 2 Because PRPhas been shown to constrict visual fields3 and to reducenight vision,4 it is desirable to identify eyes at risk forneovascularization so that only eyes requiring PRPundergo treatment.

It has been repeatedly demonstrated that certainfeatures of the clinical electroretinogram (ERG) can be

Matthew Severns is with LKC Technologies, Inc., 2 ProfessionalDrive, Gaithersburg, Maryland 20879; Mary Johnson is with JohnsHopkins University School of Medicine, Wilmer Eye Institute, Bal-timore, Maryland 21205; and Scott Merritt is with University ofMaryland, Department of Electrical Engineering, College Park,Maryland 20740.

Received 11 August 1990.0003-6935/91/162106-07$05.00/0.© 1991 Optical Society of America.

used to predict progression to neovascularization indiabetic retinopathy (DR) and in central retinal veinocclusion (CRVO), presumably by detecting retinalischemia.5 -16 Clinical ERG measurements that havebeen used include b-wave implicit time, b-wave ampli-tude, ratio of b-wave to a-wave amplitude, intensity-response parameters, and implicit time of response to30-Hz flicker. Despite the efficiency of the ERG inpredicting eyes at risk, the clinical acceptance of elec-troretinography has been slow. Detailed analysis ofERG waveforms is time-consuming and requires a lev-el of sophistication in signal processing that is unrealis-tic to expect of the practicing ophthalmologist. In anattempt to remedy this problem, we have begun todevelop automated methods of analyzing features ofthe clinical ERG.

The use of the 30-Hz flicker ERG as a measure of theseverity of retinal vascular disorders is attractive.The subject needs only minimal dark adaptation, thetest is easier to perform than most ERG tests, and,because of the periodic nature of the stimulus, sophis-ticated automated analysis algorithms can be em-ployed. The 30-Hz flicker implicit time correlateswell with other ERG measures associated with thedevelopment of neovascularization in DR and CRVO.Bresnick and Palta17 have shown that the 30-Hz flickerimplicit time and oscillatory potential implicit timesboth correlate well with the development of high-riskcharacteristics in diabetic retinopathy. Direct com-parisons of 30-Hz implicit time with the ERG intensi-ty-response sensitivity parameter, log K, and with sco-topic b-wave implicit time in a population of ninety-twoCRVO patients15 indicate that all these parameters re-flect the underlying pathology that places the eye at

2106 APPLIED OPTICS / Vol. 30, No. 16 / 1 June 1991

0-C\:

5 msec/divFig. 1. Flicker ERG waveforms from the unaffected (upper trace)and affected (lower trace) eyes of a patient with unilateral CRVO.The vertical lines indicate when the xenon strobe was flashed. Inthe unaffected eye, the peak of the waveform occurs 2 ms before thepeak of the 30-Hz component. In the affected eye, the early peakhas disappeared and the peak of the waveform occurs at the peak ofthe 30-Hz component. This difference might spuriously affect the

estimation of the severity of the outcome.

risk. [Johnson and McPhee found that, for the correla-tion between 30-Hz flicker implicit time and log K, r2 =0.61 (p < 0.0001) and for the correlation between 30-Hzimplicit time and b-wave latency, r2 = 0.62 (p < 0.004).]We have thus concentrated on developing automatedmethods for determining the implicit time of 30-Hzflicker waveforms as well as their amplitude.

Flicker waveforms exhibit a variety of morphologies,and the shape of the waveform has been observed tochange in retinal disorders such as retinal ischemia.15The changes in waveform shape are caused by shifts inthe amplitude and phase of higher harmonics of thefundamental waveform. If the implicit time of thewaveform is measured from the flash to the highestpoint of the waveform (which is typically how implicittime is measured), shifts in the higher harmonics maycause apparent implicit time shifts that are unrelatedto shifts in the timing of the underlying process. Anexample of this behavior is shown in Fig. 1. Andersonand co-workers18 examined the response of the eye tosinusoidal light stimulation at a variety of frequencies.They found that the amplitude and implicit time of thefundamental component of the flicker ERG were use-ful in separating subjects with retinitis pigmentosafrom subjects with other retinal disorders and fromnormal subjects.

We have developed automated methods for measur-ing both the implicit time of the peak of the waveformand the implicit time of the underlying 30-Hz sinusoidalcomponent of the waveform. Additionally, we havedeveloped an automated method for assessing thequality of a recording based on an estimate of thesignal-to-noise ratio. Finally, we have developed amethod that is relatively insensitive to many forms ofinterference for estimating the amplitude of the flickerERG.

II. Methods

A. Electroretinogram Procedure

Excruciating details of the patient preparation andrecording procedures are documented elsewhere.'2,' 5The subjects' pupils were dilated with a mydriatic andthen adapted to the dark for at least 30 min. Prior tothe insertion of the ERG recording electrodes, thecornea was anesthetized; ERG's were recorded simul-taneously from both eyes with Burian-Allen bipolarelectrodes. A ground reference electrode was at-tached to the subject's wrist. Written informed con-sent was obtained from all subjects prior to the proce-dure. Data were recorded from patients using an LKCTechnologies UTAS-E 100019 or UTAS-E 2000 sys-tem. The ERG stimulus was a 20-As xenon strobeflash that uniformly illuminated the interior of a 50-cmdiam integrating sphere. The subject was positionedin the sphere so that a Ganzfeld view of the stimuluswas obtained. The data were filtered using analogfilters with a passband of 0.3-500 Hz.

The stimulus was repeated at a rate of 30.3 Hz (33.0-ms interflash interval) for the UTAS-E 2000 systemand 30.0 Hz (33.3-ms interflash interval) for theUTAS-E 1000 system. Both stimulus frequencies willbe referred to as 30 Hz, although analyses were per-formed separately using the correct frequency. Datawere collected at a rate of 2000 samples/s for 256 ms.Three to five seconds of preadaptation flicker werepresented to achieve a steady level of adaptation andto reduce the effects of muscular artifacts from squint-ing and blinking. The digitized ERG waveforms alongwith stimulus information and relevant patient datawere stored on disk for later analysis.

Two different sets of data were analyzed in thisstudy. In the first one, 210 recordings from the ERGlaboratory at the University of Wisconsin were ana-lyzed. The data were recorded from fifty-eight sub-jects, fourty-four of whom had DR of varying levels ofseverity, twelve had other miscellaneous retinopa-thies, and two were normal volunteers. Stimuli werepresented both with an adapting background light (30cd/M2 , n = 123) and without one (n = 86). These datawere collected using the UTAS-E 2000 system. Asecond set of data, consisting of eighty-seven subjectswith CRVO from a previous study of Johnson andMcPhee,15 had been collected using the UTAS-E 1000system. In these data, the stimuli were presentedwithout an adapting background light.

B. Estimation of Amplitude

The amplitude of the flicker ERG is conventionallymeasured as the peak-to-trough amplitude of thewaveform. Blink artifacts, muscle (EMG) noise, andother induced and intrinsic noise sources can compli-cate the estimation of ERG amplitude. Since theresponse to a periodic stimulus will be composed ofsinusoidal components that are multiples of the stimu-lus frequency, it is possible to reconstruct a less noisyversion of the waveform by determining the amplitudeand phase of each of the harmonics and summing

1 June 1991 / Vol. 30, No. 16 / APPLIED OPTICS 2107

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them. It has previously been shown'9 that almost allthe power in the 32-Hz flicker ERG was contained inthe first four harmonics. To improve waveform fideli-ty at some computational expense, the ERG responsesfrom our data were reconstructed from the first tenharmonics. The amplitude and phase of each har-monic were determined using the discrete Fouriertransform (DFT):

N-1A~i.(f) = - E X,, sin(27rfnT),

n=O

2 N-1Ac) = - >3 X,, cos(2fnTh

n=.O

where N is the total number of samples, T is the sam-pling interval, Xn is the amplitude of the ERG at timenT, and f is the frequency of interest (for our data, 30.0or 30.3 Hz or a multiple thereof).

The waveform was reconstructed by summing sineand cosine waves of the appropriate amplitude andfrequency. The amplitude of the waveform was takenas the difference between the maximum and minimumvalues in the reconstructed waveform. Note that theuse of the DFT at ten frequencies is computationallymore efficient than the use of the FFT (which wouldcalculate the amplitude and phase at 256 frequenciesin our data).

C. Estimation of Implicit Time

Two different types of implicit time estimator weredeveloped: one estimator determined the implicittime as the time to the highest feature in the waveform.Two other estimators determined the implicit time asthe time to the peak of the 30-Hz sinusoidal compo-nent of the waveform. The time to the highest fea-ture-in the waveform (called the time to peak) wasdetermined by finding the highest point in the recon-structed waveform used to estimate amplitude. If thetime from the previous flash to the peak of the wave-form was <15 ms, the interflash interval was added tothe implicit time estimate. Prior investigation of im-plicit time as a function of frequency has shown thatthe implicit time at 30 Hz is never <15 ms.15

One estimate of the implicit time of the underlying30-Hz component of the ERG response was deter-mined by cross correlation. An estimate of the cross-correlation between two signal sequences of length N isdefined by

N-k

Rxy(k) =N k E X>Y3 h (2)n=

where Ry(k) is the cross correlation between X and Ydelayed by k samples, X,, is the nth sample of the firstsignal (in our case the input), and Yn is the nth sampleof the second signal (in our case the ERG). It can beshown that adjusting k to maximize the cross correla-tion between two signals is equivalent to adjusting k tominimize the mean-square error between them. Sincewe wished to estimate the implicit time of the underly-ing sinusoidal component, the recorded ERG was crosscorrelated with an input consisting of a 30-Hz sinewave whose maximum value occurred at the time the

strobe fired. Since the input function is sinusoidaland the response is predominantly sinusoidal, thecross correlation is approximately a sine function.

The implicit time was determined by finding thefirst global maximum in the cross-correlation esti-mate. To minimize the number of computations, asearch algorithm was implemented to find the maxi-mum of the cross correlation. Two initial bracketingestimates of implicit time were made at 25 and 41 ms.(These starting points do not limit the latencies thatcan be estimated.) An interval bracketing algorithm20

was used to locate the cross correlation maximumwithin one sampling interval (0.5 ms in our data).

A second delay estimator was also developed. Thisalgorithm computes the delay from a measurement ofthe phase of the 30-Hz sinusoidal component of thesignal, an estimate that is inherently more precise thanthe interval between samples. Estimates of the sineand cosine components from the DFT were used toestimate the implicit time Ti of the response:

(3)Ti = 1 tan-'[ASn(fo)

where fo is the frequency of the stimulus (30.0 or 30.3Hz in our data).

A difficulty with both estimators is that they aresensitive to small changes in stimulus frequency. Acomputer simulation determined that the sensitivityof the estimator of Eq. (3) to changes of frequency near30 Hz is 4 ms/Hz. Thus, for this estimator to beaccurate to within the sampling time, the stimulusoscillator must have an accuracy of 0.4% in all foresee-able conditions. Since the UTAS systems utilize acrystal-controlled oscillator that is accurate to a fewparts per million, there is no difficulty in using thistechnique with our data. Other equipment, however,may not control the stimulus frequency preciselyenough. If this is the case, the stimulus should besampled simultaneously with the ERG. Cross corre-lating the stimulus and response will yield the implicittime.

D. Estimation of Signal Quality

Blinks can introduce significant low-frequencynoise into the data. The majority of the noise powerfrom these artifacts is below 2 Hz in the data record;the artifact appears as a straight line with a positive ornegative slope added to the ERG response. This arti-fact does not interfere with the estimation of implicittime because the low-frequency signal does not corre-late well with a 30-Hz sinusoid. These artifacts do,however, affect the estimation of the signal quality, asthey can contain substantial amounts of energy. Toremove low-frequency artifacts from the data, trendsin the data were estimated by linear regression andremoved by subtracting the best-fit line from eachpoint. After this filtering was performed, the signalquality was estimated.

The signal quality was estimated as the ratio of thesignal power, estimated as the power present at thefundamental frequency of 30 Hz, to the total power in

2108 APPLIED OPTICS / Vol. 30, No. 16 / 1 June 1991

I... I....|| ,, IT I ... T. .... Il ... I... I. .1|1| -Il

5 msec/divFig. 2. Flicker waveform that has been analyzed by the methodsdescribed. The vertical bars indicate when the stimulus flashesoccurred. The top trace is the original waveform. The middle traceis the estimate of the 30-Hz component of the waveform, estimatedfrom the DFT. The bottom trace is the reconstruction of the wave-

form from the first ten harmonics, as determined by the DFT.

the recording (signal plus noise). This quantity will bereferred to as S/(S + N). The power of the signal wascomputed from the components of the DFT at the'stimulus rate:

S = VAR (fO) + A~0 s(f0). (4)

The total power in the recording (signal plus noise) wascomputed using

(5)(S+ N) = _>X2.N=0

If the estimate of S/(S + N) was <0.1, the ERG record-ing was judged to be too poor for processing.

One deficiency of this estimator is that approxi-mately one third of the signal power occurs in thesecond through fifth harmonics of the fundamentalfrequency. The fraction of power in the higher har-monics varies among subjects: Two normal subjects(both males aged 35 and 39) were tested and found tohave 29 and 38% of the ERG power in higher harmon-ics. Nevertheless, this estimator of signal quality isconsiderably more sophisticated than the amplitudethreshold used by conventional systems.19

Figure 2 shows the results of the analysis of a 30-Hzflicker waveform using the algorithms describedabove. The figure shows the original waveform, theestimate of the 30-Hz sinusoidal component of thewaveform as determined by the DFT and the wave-form reconstructed from the first ten harmonics of thestimulus, as determined by the DFT. Note that all thewavelets in the reconstructed waveform are identical.This is because no frequency less than the stimulusfrequency was used to reconstruct the waveform,hence no variations slower than the stimulus frequen-cy are reproduced.

C0-50

o 45-U_

04

E 350

._ 4) 3

25

- 20 la 20 25 30 35 40 45 50

E Implicit TimeFrom DFT Phase

Fig. 3. Comparison of the cross correlation and phase estimates ofimplicit time of 383 flicker waveforms. The cross-correlation esti-mate is quantized at the sampling interval (0.5 ms), while the phaseestimate is not. The diagonal line represents equal implicit time

estimates.

3C

4)a_4-0

.`_

C)E

4 -

40-~ ~ ~ -ZX

3

25--"20 _ X I. I. _ M ...

201- ~ ~ / 1. i i

20 25 30 35 40 45

Implicit TimeFrom DFT Phase

Fig. 4. Comparison of automated phase and automated time-to-peak estimates of the implicit time of 295 waveforms. The time-to-peak estimate is quantized at the sampling interval (0.5 ms). Thediagonal line represents equal implicit time estimates. The time-to-

peak estimate is generally less than the phase estimate.

Ill. Results

A. Comparison of Methods of Implicit Time Estimation

Of the 210 flicker ERG's that were recorded at theUniversity of Wisconsin, 209 had an S/(S + N) > 0.1.Of the eighty-seven subjects (174 eyes) with centralretinal vein occlusion, 169 eyes had an S/(S + N) > 0.1.Figure 3 shows the implicit time of the flicker ERGobtained from the cross-correlation estimate plottedagainst the implicit time obtained from Eq. (3) (phaseestimate) for all the data available. (The affected eyesfor CRVO patients had latencies which, in general,

1 June 1991 / Vol. 30, No. 16 / APPLIED OPTICS 2109

CLX

C

E

I0LLa)E.4-

._

E

50

40- - . * /

4>

35

25- I __ i i25

I-L

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.-IL11-

E

30 35 40 4

Implicit TimeFrom DFT Phase

45 50

Fig. 5. Comparison of the automated phase estimate of implicittime with that of an expert human. The human estimate is quan-tized at the sampling interval (0.5 ms). The diagonal line representsequal implicit time estimates. The human estimate of implicit time

is generally longer than the automated phase estimate.

were longer than most of the other data.) The phaseestimate is on average 0.1 ms greater than the cross-correlation estimates (p = 0.001, paired t-test), and theslope of a linear regression is 0.999. The correlationbetween the two estimates is extremely high (r2 =

0.997), indicating that these two estimators are per-forming essentially identically. Because the phaseestimate gives a more precise value for the implicittime (the cross-correlation estimate is quantized to :1sample-0.5 ms in our data-while the phase estimateis not), it will be used for the remainder of the analysis.

Figure 4 shows the implicit time of the flicker ERGobtained by the phase estimate plotted against theimplicit time estimated by the time to the peak of thewaveform. Time to peak was automatically deter-mined by finding the implicit time of the maximumamplitude point in the DFT reconstructed waveform.The correlation between the two estimates is high (r2 =

0.88). The peak of the waveform occurs on average 1.7ms before the peak of the 30-Hz sinusoidal component(p < 0.00005, paired t-test).

B. Comparison of Automated Implicit Time Estimateswith Those of an Expert Human

Figure 5 shows the estimates of implicit time for thepopulation of CRVO patients (both affected and unaf-fected eyes) obtained using Eq. (3) and obtained froman expert human (MAJ) who placed cursors on thewaveforms using the technique described by Johnsonand McPhee.'5 This technique does not entail placingthe cursor at the peak of the waveform but ratherattempting to place it at the midpoint of the positive-going portion of the waveform. The two estimates arehighly correlated (r2 = 0.94), indicating that the hu-man expert and the computer program are performingsimilar functions. The mean implicit time estimated

.00

Amplitude From Human ExpertFig. 6. Comparison of the automated estimate of amplitude fromthe DFT reconstructed waveform with that of cursors placed by anexpert human. The diagonal line represents equal amplitude esti-mates. The human estimates of amplitude are generally greaterthan the automated estimates largely because of the presence of

noise in the data.

by the human expert is 0.8 ms greater than that of thecomputer program (p < 0.00005, paired t-test). Thecorrelation between the automated time-to-peak im-plicit time estimate and that of the human expert ismuch lower (r2 = 0.78) than the correlation with theimplicit time estimated using Eq. (3), indicating thatthe human expert is probably attempting to estimatethe implicit time of the 30-Hz sinusoidal component ofthe waveform rather than the time to the peak of thewaveform.

C. Comparison of Automated Amplitude Estimates withThose of an Expert Human

Figure 6 shows the comparison of automated andmanual estimates of 30-Hz flicker ERG amplitude forthe University of Wisconsin data set. The automatedestimates were obtained by finding the minimum andmaximum amplitudes in the DFT reconstruction ofthe waveform. The manual estimates were obtainedfrom an expert human (MLS), who placed cursors onthe waveform at the maximum and minimum ampli-tudes for a selected wavelet. The two estimates aremuch less correlated than the implicit time estimates(r2 = 0.65). In addition, the manual estimates of am-plitude, on average, exceed the automated estimatesby 8,uV (p < 0.0001, robust t-test). These effects arelargely caused by the presence of noise in the originalwaveform. Some of this noise is from external inter-ference (60- and 180-Hz interference from power linesand electromechanical devices), some is from EMGartifacts, and some is from blink artifacts. It appearsthat blink artifacts, which change the slope of thebaseline, cause most of the significant differences be-tween amplitude estimates.

To estimate the magnitude of the effect of the blinkartifact, cursors were placed on the waveform at theappropriate locations in the peak and trough of thewaveform, and the amplitude was determined. The

2110 APPLIED OPTICS / Vol. 30, No. 16 / 1 June 1991

..I;vII .ft .

Table 1. Relative Energy In the First Ten Harmonics of the 30-Hz FlickerERG

Relative energyFrequency (Hz) Photopic Scotopic

30 0.58 0.6360 0.11 0.1090 0.10 0.09

120 0.06 0.05150 0.04 0.03180 0.03 0.03210 0.02 0.02240 0.02 0.02270 0.02 0.02300 0.01 0.01

low-frequency blink artifact was then removed by lin-ear regression (as described in Section II D), and theamplitude was determined using the cursors that hadpreviously been placed. Most gross blink artifactsinduced changes in the 30-Hz ERG amplitude esti-mate of 10-20 AV, although changes as high as 61 ,Vwere observed. Because we did not attempt to sys-tematically detect blink artifacts, these estimates re-flect only the most obvious examples.

D. Relative Energy of Components of the 30-Hz FlickerERG

Table I shows the average values of relative energycontained in each of the harmonics of the University ofWisconsin data set. (It was not possible to analyze theCRVO data set in a similar manner, because in anunknown number of cases a 60-Hz notch filter hadbeen utilized to remove line frequency interference.)The relative energies are shown for both photopic(with adapting background light) and scotopic (noadapting background light) flicker waveforms. Forboth conditions, -86% of the total energy is containedin the first four harmonics (30, 60, 90, and 120 Hz) inaccordance with previous studies.18 Because thesedata are from a population consisting primarily ofpatients with diabetic retinopathy, these values maynot represent the relative amounts of energy in theharmonics of the normal flicker ERG. Additionally,because not all subjects were tested with both scotopicand photopic flicker, the apparent differences in rela-tive energy in the harmonics may be the result ofdifferences in the disease state rather than differencesin the stimulus conditions.

IV. Discussion

We have applied techniques from the signal process-ing literature to the determination of amplitude andimplicit time of the 30-Hz flicker ERG. The implicittime determinations made using this technique corre-late closely with those made by an expert human.Although the techniques work well for 30-Hz flicker,they have not been tested at other frequencies, and it islikely that their utility would be less at low stimulusfrequencies (i.e., <20 Hz) where the flicker ERG moreclosely resembles a train of single flash ERG's. Amajor advantage of this technique is its ability to workin conditions of low S/(S + N); implicit time informa-

tion can be extracted from an ERG with 9 times morenoise than signal [an S/(S + N) of 0.1] as long as theinterference is primarily at low frequencies.

Amplitude estimates from the waveform recon-structed from the DFT should be inherently moreaccurate than those derived from the placement ofcursors on the raw waveform. Since cursors for ampli-tude estimates are generally placed on the extrema ofthe waveform, they will be placed on or near a noisepeak at the peak of the wave (sometimes called the catear) and on or near a noise trough at the trough of thewave. Thus high frequency noise will almost alwaysadd to the estimate of the amplitude. Blink artifactscan in extreme cases add or subtract more than 50 Vfrom the amplitude of the waveform. It is possiblethat these sources of error in the determination offlicker ERG amplitude have decreased the apparentpredictive power of this measurement in disease states.

The techniques that we have used are easily imple-mented in software. Programs to perform the DFT(or the FFT) and cross-correlation analysis are in thepublished literature (see, for example, Ref. 21) or areavailable as part of commercially available signal pro-cessing program libraries from many sources. Theestimation algorithms described here take relativelysmall amounts of time to execute on a personal com-puter (<1 s on an IBM PC/AT compatible computerwith math coprocessor). They are thus well suited foruse in analyzing flicker ERG waveforms in a clinicalsetting.

We have tested these algorithms on populations ofpatients with retinal diseases, primarily DR andCRVO. This was done to ensure that the algorithmswork properly over a wide range of 30-Hz flicker ERGamplitudes, latencies, and signal-to-noise ratios. Thenext step will be to test them on a large population ofnormal subjects. Once normative data are available, itwill be possible to attempt to utilize these algorithmsin the diagnosis of retinal vascular disease.

This work was supported in part by NEI grants 2R44EY-07181 (M. L. Severns) and R01 EY-05118 (M. A.Johnson). We would like to thank Laura Gentry forpainstakingly preparing all the data from the Universi-ty of Wisconsin Department of Ophthalmology. Wewould like to thank Carolyn Perry and Stacy Cofieldfor performing a similar job on the CRVO data fromthe Wilmer Eye Institute. Finally, we would like tothank Julian Procope, who spent many boring hourstransferring data from UTAS-E 1000 diskettes into aformat compatible with our analysis programs.

Matthew Severns also works in the Johns HopkinsUniversity School of Medicine.

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