Data Acquisition and Modeling in Clinical Electrooculography

DATA ACQUISITION AND MODELING IN CLINICAL ELECTROOCULOGRAPHY W. Poelzleitner*'**, A. U. Meyer* and G. M. Stephens*** 'Electrical Engineering Department, New J ersey Institute of Technology, 323 H igh Street, Newark, NJ 07 102 , USA "Now with Research Center for Digital Image Processing and Graphics, Wastiangasse 6, 8010 Graz, Austria "'Department of Ophthalmology, University of Medicine and Dentist,) and Eye I nstitute of New J ersey, 15 South 9 Street, Newark , NJ 07107 , USA

Abst~act. Elect~ooculog~aphy (EOG) is used in clinical measu~e the time ~esponse of the co~neo~etinal potential

ophthalmology to (CRP) to changes in light intensity. A system fo~ automatic data acquisition and model estimation has been developed. 'rhe data acquisition is pe~fo~med on a mic~op~ocesso~ based inst~ument, which supe~vises the EOG test, measu~es the potential and, afte~ completion of the test, t~ansfe~s the ~esults to a mainf~ame compute~ . Nonlinea~ cu~ve fitting is used fo~ the estimation of the model pa~amete~s. Seve~al models a~e conside~ed.

Biomedical; elect~ooculog~aphy; elect~ophysiology, identifica tion; medical data acquisition; medical data ~eduction and analysis; medical info~mation p~ocessing; physiological models. Kevwo~ds.

INTRODUCTION

decay toward its o~iginal base value, with a oscillato~y period and damping time constant each of the o~de~ of 3 0 minutes [see Figs. 3-6].

(EOG) is used in clini cal ophthalmology to detect physiological abno~malities in the human eye. Its utility is based on the co~neo~etinal potential (CRP), a d-c potential between the co~nea (positive) and the poste~io~ po~tion of the eye. The CRP dynamics appea~ to ~eflect metabolic changes in the pigment epithelium and contain info~mation ~elevant in the diagnosis of some ~etinal

Elect~ooculog~aphy

degene~ative

Duane, 1976;

diso~de~s (Adle~, Kolde~, 1974).

In

the most

commonly

EOG and associates in 1962 (A~den, Ba~~ada and Kelsey, 1962; K~ogh, 1979), the light adapted eyes are subjected to da~kness for (usually) 12 minutes afte~ which light is ~e-applied. The only info~mation usually ext~acted f~om that test is the t~ough of the EOG ~esponse due to da~k stimulation and its peak afte~ (app~oximately 12 minutes of) light ~e-stimulation. 'I'h ", info~mation is usually exp~essed in t e~ms of the (A~den-) ratio between " light peak " and " da~k t~ough " . Indeed, the incompleteness of info~mation ext~acted may well be a significant facto~ in the la~ge va~iability found in clinica l EOG data (K~ogh, 1979). p~ocedu~e,

1975;

Due to the CRP, the eye acts somewhat like a ~otating batte~y. Elect~ooculog~aphy (EOG) involves the measu~ement of a voltage obtained f~om skin elect~odes placed on opposite sides of an eye. This voltage ~eflects the CRP, modulated by the angula~ eye position. While elect~ooculo ­ g~aphy can be used as a simple method fo~ ~eco~ding eye motion, this wo~k deals with the co~neo~etinal potential itself, notably its ~esponse to changes in light level. Clinical elect~ooculog~aphy involves the ~eco~ding of the voltage between the two skin elect~odes, evoked by alte~nating ho~izontal eye movement ove~ some fixed angle, say 45 deg~ees. This is done during va~ious time inte~vals. The voltage changes due to each movement a~e sampled and ~eco~ded. The ~eco~d of these changes will be ~efe~~ed to as the EOG (voltage) ~esponse [see Figs. 3-8].

int~oduced

used clinical by A~den

Recognizing that the EOG ~esponse ~ep~e­ sents conside~ably mo~e info~mation. Homer, Kolde~ and associates in 1966 p~oposed step- ~esponse models and the identification of thei~ parameters (Home~ and Kolde~, 1966,1967; Home~, Kolde~ and Benson, 1967; Kolde~ and Hochgesand, 1973). F~equency ~eponse results (Benson, Kolde~ and Home~, 1967) and gain-phase plots (Taume~, Hennig and Pe~nice, 1 97 4; Taume~, Hennig and Be~ndt, 1975) have been f~om

0. 5

O~iginally, in clinical p~actice, the potential (diffe~ence ~ep~esenting movement between two fixation pOints) been obtained from cha~t ~ecordings of amplified voltage between the

EOG eye had the two

p~esented

fo~

to 4 cycles the eye adapted to a steady light level, the EOG voltage has a base value of the o~de~ of 0.5 millivolt. A step inc~ease (dec~ease) of light intensity causes a tempo~a~y ~ise (fall) of the EOG voltage, followed by a damped oscillato~y

f~equencies

pe~

~anging

hou~.

Fo~

IW'C6-o

3065

3066

W. Poelzleitner, A. U. Meye r and G. M. St ephens

electrodes. To eliminate the burden of that task, efforts have been made to automatize the data acquisition (Jones, 1976; Rohde, Taumer and Braas, 1976). The objective of this paper is the presentation of a combined data acquisition and modeling system which considerably automatizes the EOG test. The data acquisition process is performed by a microprocessor based instrument which supervises the test, measures the EOG potential and pre-processes the measured data by applying corrections necessary for imperfect eye movements and by averaging measuremens. After completion of the test, the averaged data are transferred from the instrument to a larger computer (e.g. a mainframe). Once the data are stored on the mainframe, filtering and modeling procedures, including parameter estimation, are applied . DATA ACQUISITION Measuring the EOG potential involves several problems. First, the d-c electrode and contact potential which is in the range 100 mV to 1 Volt, is superposed to the real EOG potential of the order of 0.5 mV; it is blocked by a-c coupling in the input amplification stage. Since the time constant of the RCcoupling circuit is known, a mathematical correction is applied to re-calculate the true value of the EOG potential response. Line frequency interference is suppressed by selection of a sampling frequency for

the A/D conversion of 240 Hertz (4 times the line frequency of 60 Hertz) and the use of a 4 th order moving average filter. A second problem pertains to the human individual taking the test. It is required that the patient performs left/right eye movements between two fixed points. Any deviation from these points will, of course, cause a measurement error. This error is being reduced by averaging out the EOG potentials obtained from a number of alternate eye movements (about 6 movements during 12 seconds). Third, hesitant or overshooting eye movements may cause steps in the measured potential which have to be distinguished. Measurement reliability is achieved by automatic detection of such a situation and computation of appropriate correction. The above considerations led to the design of a microprocessor based instrument which, as an additional feature, provides automatic timing of the experiment. The instrument is portable and, with the addition of a printing device (e.g. a terminal), provides a self-contained EOG computer. It is designed to automatically detect and identify acceptable transitions of the (EOG) potential due to eye movements between two fixation points. Such a trial (consisting of about 6 eye movements) may be repeated every 30 seconds. Other repetition intervals can also be selected but 30 seconds were used for the examples presented in this paper.

-1.0000 +1.0000 START TIME 00:07:18 MV FS -000.88 +00.855 +00.215 -00.826 +00.849 +00.847 -000.86 +00.839 -00.871 +00.862 AV START TIME 00:07:18 MV FS -1.0000 +1.0000 +00.851 -00.869 T +00.861 AM

-00.851 -00.887

Fig. 1. Instrument output at the end of a (12 second) measurement trial. After printing out the actual time and the (full-scale) value of the input range, the voltage changes are shown for all acceptable transitions due to eye motion from left to right and back. Then, after printing again the time and input voltage range, the averages are shown for both positive and negative voltage transitions, as well as the average of the two. Only time and the averages of the voltage transitions are retained in memory for data transfer and further analysis after completion of the test. DEPENDENT VARIABLE Y

NON-LINEAR LEAST SGUARES SUMMAR Y STATISTICS SOURCE

OF

SUM OF SGUARES

MEAN SGUARE

REGRESSION RESIDUAL UNCORRECTED TOTAL

9

58

3.30034863 0 .00017909

67

29 . 70313764 0.01038736 29 . 71352500

(CORRECTED TOTAL)

66

0.36573919

PARAMETER KI

K2 K3

Al A2 Wl W2

HI H2

ESTIMATE

ASYMPTOTIC STD. ERROR

0.64116603 0.08102559 0.20464834 0.14384540 0.04596538 0.60762629 0.25346441 1.31580667 -1.72332943

0.0019645 0 0.02032821 0.01105381 0.03506635 0.00340993 0.03797962 0. 00 460927 0.22 272557 0.07406941

ASYMPTOTIC 95 % CONFIDENCE INTERVAL LOWER UPPER 0.63723365 0.64509840 0 . 04033427 0 .1 2171691 0.18252174 0 .2Z677494 0.07365247 0.214 03£32 0.03913966 0 .05279110 0 .5 3160184 0.68365074 0 . 24423794 0.26269087 0 .86997306 1.76164028 -1.87159544 - 1.575 06343

Fig. 2. Result of Marquart fitting for Model (1) using Data model is shown by the dashed curve in Fig. 3.

Set 1.

The plot

for this

Dat a Acquisition and Mode li ng in Clini c al El ec tr oocu l ogr aphy

After each trial, the instrument provides a printout of the individual acceptable transitions (the first of which is ignored since the original fixation is not certain). This is shown in Fig. 1. The printout also shows the actual time and the input voltage range used. Finally, it shows the computed averages of the positive and negative voltage transitions, as well as the average of the two. Only the time and the average of the voltage transitions are retained in the memory for data transfer to another computer and/or cassette tape. Further data processing including parameter estimation is performed mainframe computer.

model on a

EOG RESPONSE MODELING Several models for the EOG response are considered and their parameters are estimated by use of Marquart ' s method (SAS User's Guide). The following basic candidate models for the EOG response to a step-change of light intensity are investigated first: yet) + K3 e

-A 2t

cos(w t + H ) 2 2

(l)

-AIt yet)

KI + K 2e + K3e

yet)

KI + K 2e

cos(wlt + HI) -A t 2

( 2)

-A It

( 3)

COS(WIt + HI)

Models (l) and ( 2) were introduced by Homer, Kolder and Benson (Homer and Kolder, 1966; Homer, Kolder and Benson, 1967) . Two data sets were taken from the same subject on two succeeding days. They are referred to as Data Set 1 and Data Set 2. Each measurement covers a period of 40 minutes. The Parameter estimates for Data Sets 1 and 2 are summarized in Table 1.

3067

trated by the graph in Fig. 3. The dashed curve represents the model response, the diamonds represent the measured data points. For Data Set 2, the corresponding graph is shown in Fig. 4. A comparison between the Model (1) parameters w2' H2 and A2 describing one of two oscillatory components are close to each other. For the other oscillatory component, the values of parameters_wI, HI and Al differ somewhat. However, their amplitude, K2, is quite small compared to amplitude K3 of the oscillatory component (w 2 ,H 2 ,A2)' This suggests a simplification of the model, namely to omit one cosine term to yield Model (3). Figs. 5 and 6 illustrate the curve fitting of Model (3) for Data Sets 1 and 2 respectively. The model parameter estimates for each data set are included in Table 1. Using Data Set 1, the curve fit for Model (3) appears to be poorer than that for Model (1). It should be noted, however, that the estimated values of the common parameters correspond for both models. As seen in Table 1, Model (2) shares the same common parameter estimates with Model (3). It should further be noted that the convergence of the Marquart routine for Model (3) is faster and less dependent on the initial values chosen for the parameter estimates than that for Model (1). So far, only the EOG response to a unit step input was considered. In common clinical practice, however, a different test is used where the light-adapted patient is subjected to a dark period, after which light is turned on aga~n (Duane, 1976; Arden, Barrada and Kelsey, 1962). In the present investigation a dark period of 10 minutes was used in a test whose response shall be referred to as Data Set 3. Under the assumption of of a linear system one may consider a superposition of two step responses, shifted by a time interval of 10 minutes. Using the simple Model (3), the assumed response becomes,

Fig. 2 shows the result of the fitting of Model (1) from Data Set 1; this is illusTABLE 1 Model (1) (Fiqs. 2 3)

DATA SET 1 Model ( 3) (Fiq. 5)

K I =0.6412

KI=0.6400

K =0.2046 3

K =0.1994 2 AI =0.0435 wI=0.2616 HI=-1.878

~=0.0460

2 =0.2535 H2 =-1. 723 K2=0.0810 AI =0.1438 W!=0.6076 HI =1.3158

_
Model

Summary of Parameter Estimates ( 2)

DATA SET 2 Model (l) Model ( 3) (Fiq. 4) (Fiq. 6)

KI =0.6413 K =0.1967 2 AI =0.0428 wI=0.2628 HI =-1.893

KI =0.6212 K =0.4979 3 A2 =0.0527 w2=0.2420 H2=-1. 757

K3 =0.1240 A2 =0.0380

K2=0.0843 AI=0.0886 wI=0.4530 HI=2.3399

KI =0.6195 K2 =0.5425 AI =0.0560 wI=0.2500 HI=-1.901

Mean-Square Residual = 0003634 I 0.00037812 I 0.00Q_2003 I 0.00036494 I

DATA SET 3 Model (4) Model ( 5) (Fiq. 8) (Fiq. 7) KI =0.8341 K2 =0.3679 AI=0.0404 wI=0.2379 HI=-2.128

KI =0.8354 K2 =0.2928 Al =0.0313 wI=0.2137

0.0037381 I 0.0085819

W. Poel z l e itner, A. U. Mey e r and G. M. St eph ens

306 8

where ul(t) is the unit-step function. Note especially that this model has a discontinuity of K2cos(Hl) at t = 10 minutes. This is illustrated by the dashed curve in Fig. 7 which compares the Model (4) response with measured data (Data Set 3). Table 1 shows the corresponding parameter estimates. Model (4), as well as Model (3) on which it is based,lacks physical reality because of its discontinuity. This discontinuity can be eliminated by removing Hl as a free parameter and setting it to -90 degrees. The model for the response then becomes, y(t)

= Kl - K2e

+ K2e

-Alt

-Al(t-lO)

sin[wltJu1(t) sin[wl(t-lO)Jul(t-lO)

(5)

The result is illustrated in Fig. 8 with the corresponding parameter estimates contained in Table 1. Though continuous, Model (5) does not fit the data as well as Model (4). Of course, the same kind of degradation would result if parameter Hl were frozen in the (stepresponse) Model (3). CONCLUSION

An

automated data acquisition and processing system for electrooculography has been developed which provides estimates for model parameters. The examples presented, based on three EOG tests with two subjects, can, of course, provide only an illustration of the system. The system will facilitate the acquisition and accumulation of the data base required to evaluate the models.

Duane, Thomas D. (1976). Clinical Ophthalmology. (ed.), Vol.3, New York. Homer, D. and H. Kolder (1966). Mathematical Model of Oscillations in the Human Corneo-Retinal Potential. Pfluger ' s Archiv 287, pp.197-202. Homer, D., H. Kolder, D.W. Benson, Jr. (1967). Parameter Variations of a Model of the Oscillation of the Human Corneoretinal Potential. Pfluger's Archiv 294, pp.l03-112. Homer, L.D. and H. Kolder (1967). The Oscillation of the Human Corneoretinal Potential at Different Light Intensities. Pfluger's Archiv ges. Physiol., vol.296, pp.133-142. Jones. R. (1976). Automated Oculography, Journal of the Optometric Association, no. 7, July 1976, p. 905.

ElectroAmerican Vol. 47,

Kolder, H. and P. Hochgesand (1973). Empirical Model of the Electrooculogram. Documenta Ophthalmologica (Den Haag) , vol.34, pp.229-241. Kolder, H. (1974). Electro-Oculography. 4th Congr. Europ. Soc. Ophthal. , Budapest 1972, Part I. Ophthalmologica 169, pp.127-140. Krogh, E. (1979). The Corneofundal Potential and the Electrooculogram: and Aspects of Normal Physiology Ophthalmologica, Variability. Acta Supplementum 140, 69 pp. Meyer, A.U., P. Chavis, G.M. Stephens (1980). Analysis of EOG Potential in Clinical Ophthalmalogy. Proceedings of the 1980 Internat. Conf. on Cybernetics and Society, Oct.8-10, 1980, Cambridge, Mass., pp.998-999.

ACKNOWLEDGEMENT The authors are indebted to Mr. Paul Bjorndahl who had designed the original instrument for EOG measurement and data processing.

Rohde, N. , R. Taumer and F. Braas (1976). An EOG Computer and Stimulator for the Investigation of the Slow Retinal Potential. Bibliotheca Ophtal., no. 85, p. 76. SAS

REFERENCES Adler, F.H. (1975). Physiology of the Eye. The C.V. Mosby Company, Saint Louis, pp.482-484. Arden, G.B., A. Barrada, H. Kelsey (1962). New Clinical Test of Retinal Function Based Upon the Standing Potential of the Eye. British J. Ophthal., vol.46,pp.449-467. Benson, D.W., H. Kolder and L.D. Homer (1967). Nonlinear Response of the Human Corneoretinal Potential to Sinusoidal Changes in Light Intensity. Pfluger ' s Archiv ges. Physiol., vol.295, pp.361-368.

User ' s Guide. Box 8000, Cary,

SAS Institute, Inc., North Carolina 27511.

Taumer, R., J. Hennig and D. Pernice (1974). The Ocular Dipole - a Damped Oscillator Stimulated by the Speed of Change of Illumination. Vision Research, vol.14, pp . 637-645. Taumer, R., J. Hennig and K. Berndt (1975). Zur Frage der Quantifizier barkeit des klinischen EOG Testes. Berichte der deutschen Ophthal. Ges., vol.73, pp.190-194.

Data Acquisition and Modeling in Clini cal Electroo culo graphy

EOG

Dol e' 3 / 24/83 Patient Nome : ~ . P . F; I enome , EOGDATA2

Model (1):

0.9

-Alt

y(t) = Kl + K2e

(fJ

30 69

cOS(Wl~

+ Hl ) + K3 e

-A 2 t

cOS(W2 t + H2 )

1-<

cl

0 .8

> H

j H

::;::

Z

0 .7

H

0 .6

LIGHT ON TIME IN MINUTES 0 . 5 .,.....~~..,., .~~r.~~~-rr' . ~.~.~,~""'T'~~~........~~...,....... ,.,.....,..,....

e

15

le

5

35

25

20

Fig. 3. EOG response of dark adapted eye to light turned-on at time t=O, from Data Set 1. For Model (1) parameter estimates, see Table 1 or Fig. 2.

EOG

y(t) = Kl + K2e

(fJ

1-<

0 .8

H H

0 .7

Name : ~.P .

Model (1):

0.9

cl

Patient

F; lenome,EOGDATA3

.0

> H

Dole , 3125/83

+ K3e

-A l t -A 2 t

COS (Wlt cOs(w 2 t

H

::;:: Z

0 .6

H

~

0 5

(fJ

~

p...

0.4

(fJ

~

0 .3 LIGHT ON

TIME IN MINUTES

0 .2

o

3

6

9

12

15

18

21

24

27

30

33

36

39

42

Fig. 4. EOG response of dark adapted eye to light turned-on at time Set 2. For Model (1) parameter estimates, see Table 1.

EOG

t=O, from Data

Dol. , 3124 / 81 PQllenl

No~e : ~ . P .

Fllenom. , EOGDATA2 0 .9

Model (3):

(fJ

1-<

cl

> H

0 .6

H H

H

::;:: Z

0.7

H

0 .6

o

5

10

15

21l

25

30

3S

Fig. 5. EOG response of dark adapted eye to light turned-on at time Set 1. For Model (3) parameter estimates, see Table 1.

t=O, from Data

W. Poelzleitner, A. U. Meyer and G. M. Stephens

3070

EOG

I .B

Dol. ' 3/25/83 Pollenl Nome'W.P . FII.nom. , EOGDATA3

Model (3): B. 9 VJ

F-<

5

B.8

:> H

t-l t-l

B. 7

H

~

Z

B. 6

W

B. 5

H

VJ

~ p..

VJ

B. J !

g2

"] B.2

LIGHT ON

TIME IN MINUTES

I

1•• ,'11';"'1"""""""""""""""""""'"1';"""""""""""

B

3

6

9

12

15

18

21

24

27

3B

33

36

39

42

Fig. 6. EOG response of dark adapted eye to light turned-on at time Set 2. For Model (3) parameter estimates see Table 1.

EOG

Dot • • 4/9/83

Poll.nl Nomo,E.G . Fllenom •• EOGDATA4

Model (4):

1.4

y(t)

t=O, from Data

-Alt Kl - K2e COs[wlt + H1JU1(t) -Al(t-10) + K2 e cos [Wl (t-10) + Hi] u (t-10) l

=

1.2

B. LIGHT ON e.4

TIME IN MINUTES

L1GHT OFf

e

5

10

15

20

25

30

35

40

45

50

55

60

65

70

Fig. 7. EOG response of light adapted eye with light turned-off at time t=o and turned-on again at t=lO minutes, from Data Set 3. For Model (4) parameter estimates, see Table 1.

EOG

Dale , 4/9 /83 Po~lenl

Model (5):

1. 4

FI

-A VJ

E-<

y( t) 1.2

5:> H

~

No~e:E.G.

lena~e,EOGDATA4

t

Kl - K e 1 sin[w l t]U (t) l 2 -A (t-10) + K e 1 sin[wl(t-10)]ul(t-10) 2

1. 0

H ~

Z

H

0 .8

TIME IN MINUTES

o

5

10

15

20

25

30

35

40

45

50

SS

60

65

70

Fig. 8. EOG response of light adapted eye with light turned-off at time t=O and turned-on again at t=lO minutes, from Data Set 3. For Model (5) parameter estimates see Table 1.