650 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING. VOL. 37, NO. 6. JUNE 1990

[ I I ] W. 1. Grosky and R. Jain, “A pyramid-based approach to segmen- tation applied to region matching,” IEEE Trans. Part. Anal. Mach. Intell., vol. PAMI-8, no. 5, pp. 639-650, Sept. 1986.

( 5 ) 116:

w ( n . X , I ) = 1 , 6 ~ ,

f o r k = I , 2, . . . , c’

h = 311 fathers

where n is the node at level I , a n d h is its kth father. Then, using w , each node property g is recalculated: Real-Time Filtering for the Estimation of Steady-

w h e r e g [ i l , j j , 1 - 11 i s t h e k t h s o n o f g [ i , j , l ] a n d w h e r e w ( n L , f , 1 - 1 ) is the weight between the node g [ i, j , I 1, f, and its k t h son nk at level 1 - 1. As the process iterates in a bottom-to-top fashion the weight function w approaches either zero or one, with one being representative of a node most likely to be the father and zero being representative of a node least likely to be the father. In cases where 6, = 0 in (4), the kth node-father link gets the weight of one in ( 5 ) , and all the other c’ node-father links will get the weight of zero. It is possible that a node may not be picked as a father by any of the nodes on the lower level (when the denomi- nator of (6) is zero). In such an event, we let the node g [ i, j , I ] be the average of its eight brothers, and the iteration continues.

During the final phase, the tree generation phase, the segment values s are assigned top-down starting at a chosen level L 5 n - 1 to level 1 = 0. At level L

where [ i”, J ” , I 1 is the father of [ i , j , I ] chosen during node Iink- ing. At the end of this stage, s [ i , j , 01 will have the final segmen- tation of the image into 22“1-L’ homogeneous regions where the original image is 2“ X 2“; for L 5 3 there will be a maximum of 256 homogeneous regions.

ACKNOWLEDGMENT

The authors would like to thank Dr. E. M. B. Sorensen for pro- viding the microscope slides used in this research.

REFERENCES

[ I ] E. M. B. Sorensen and D. Acostd, “Erythromycin estolate-induced toxicity in cultured rat hepatocytes,” Toxicol. Lett., no. 27, pp. 73- 82, 1985.

[2] -, “Protective effects of calcium,” Alternative Methods in Toxi- cology, Vol . 3: In Vitro Toxicology. New York: Liebert, 1985, pp. IO I - 139.

131 M. A. Hayat, Principles and Techniques of Electron Microscopy: Bi- ological Application. New York: Van Nostrand Reinhold, 1970. ch. 6 , pp. 239-295.

141 T. H. Hong, K. A. Narayanan. S. Peleg, and A. Rosenfeld, “Image smoothing and segmentation by multiresolution pixel linking: Further experiments and extensions,” IEEE Trans. Sysr., Man , Cybern., vol. SMC-12, no. 5, pp. 611-622, Sept./Oct. 1982.

[SI P. J . Burt, T . H. Hong and A . Rosenfeld, “Segmentation and esti- mation of image region properties through cooperative hierarchial computation,” IEEE Trans. Syst., Man, Cybern., vol. SMC-I I , no. 12, pp. 802-809, Dec. 1981.

161 N. Ahuja and S. Swamy, “Multiprocessor pyramid architectures for bottom-up image analysis,” Multiresolution Image Procrssing and Analysis, A. Rosenfeld, Ed. New York: Springer-Verlag. 1984, ch.

[7] C. Lengauer, B. Sabata, and F. Arman, “A mechanically derived systolic implementation of pyramid initialization,” in Proc. Work- shop on Hardware Specification Verijcution, Synthesis: Mathemati- cal Aspects? Ithaca, NY. July 1989.

[8] C. R. Dyer, “A VLSI pyramid machine for hierarchial parallel image processing,” in Proc. PRIP ’81, Aug. 1981, pp. 381-386.

[9] A. Rosenfeld and A. Kak, Digital Picture Processing. New York: Academic, 1982.

1101 S . Kasif and A . Rosenfeld, “Pyramid Linking is a special case of ISODATA,” IEEE Trans. Syst., Man, Cybern., vol. SMC-13. vol. I , pp. 84-85, Jan./Feb. 1983.

3, pp. 38-58.

State Visual Evoked Brain Potentials

THOMAS F. COLLURA

Abstract-It is shown that EEG visual evoked potentials elicited by repetitive stimuli in the range of 2 to 20 per second can be readily estimated in real time using a simple filtering approach. This mea- surement takes advantage of the fact that a comb filter will pass the important Fourier harmonics of the signal to provide an estimate of the evoked activity, plus track time-variations in the signal. Results on human subjects demonstrate the effectiveness of the approach.

INTRODUCTION Repetitive visual stimuli such as flashing lights and reversing

checkerboards are commonly used in the production of brain- evoked responses for research and clinical studies. The brain re- sponse is buried in significant amounts of background EEG activ- ity, which necessitates the use of some type of averaging or filter- ing to increase the signal-to-noise ratio. Various methods have been studied, and there is increasing emphasis on adaptive techniques and techniques which can estimate single responses [1]-[4]. One reason for this emphasis is the realization that successive evoked potentials are not identical, and that short-term changes in brain responsivity create significant variation between them [ 5 ] .

A major problem in improving signal-to-noise ratio is the fact that there may be no “prototypical” evoked potential; the “aver- age” evoked potential is a fiction, much a s the “typical man” who is characterized by a certain average height and weight, but may never be represented by a particular individual. For this reason, there is value in techniques which do not make assumptions about the evoked potential other than the fact that it is time-locked to the stimulus. While averaging follows this assumption, amplitude and latency variations can reduce its accuracy in developing a valid estimate based upon many responses. Also, averaging of dozens of responses may be too slow to produce a good estimate before short- term changes degrade the measurement. Digital techniques which overcome these limitations may not be suited to low cost or real- time operation.

This technique is founded on the recognition that variation be- tween successive evoked potentials not only degrades the accuracy of averaging, but is itself a valuable part of the information in the signal. This work provides a method which allows the investigator to track short-term changes in evoked responses, and to make them available as part of the measurement paradigm.

METHOD The method is based on the strategy of increasing signal-to-noise

ratio before the system has time to change significantly. In practical terms, it is necessary to produce an estimate of the evoked re- sponses within 5 to I O s and to keep that estimate up to date, thus tracking changes in brain state.

Using stimulus rates between 2 and 20 per second, successive cortical evoked responses lead to a periodic wave. Simple overlap (linear superposition) is a dominant mechanism, particularly at the lower rates [6]. This is shown diagrammatically in Fig. 1. Above four responses per second, these are commonly referred to as “steady-state’’ evoked potentials. This periodic evoked wave can

Manuscript received April 20, 1989; revised September 5 , 1989. This

The author is with the Section of Epilepsy and Clinical Neurophyisol-

IEEE Log Number 9035447.

work was supported by NlH Training Grant GM-01090-14.

ogy, The Cleveland Clinic Foundation, Cleveland, OH 44195.

00 I8-9294/90/0600-0650$0 1 .OO 0 1990 IEEE

IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 37. NO. 6. J U N E 1990

cos cwot I

65 I

sintwot) 1

hlt) t

t Fig. 1. Time- and frequency-domain analysis of the generation of evoked

potential harmonics via repetitive stimulation, depicting the signals typ- ical of a four per second stimulus rate. Left: time-domain; right: fre- quency-domain. Top: single response; middle: stimulus train; bottom: repetitive response. Symbols are explained in the text.

be readily estimated in real time, using a set of filters which are locked to the fundamental and harmonics of the stimulus. Referring to Fig. I , if h ( t ) is taken to be the single response, a train of stimuli s ( t ) is applied, and the response is designated as r ( t ) , the following two relations apply:

r ( r ) = h ( r ) * s ( t )

R ( j w ) = H ( j w ) S ( j w )

where * denotes convolution, and R ( j w ) , H ( jo), and S( j w ) are the Fourier transforms of r ( t ), h ( t ), and s ( t ) , respectively. These relationships show that R ( j w ) will be a line spectrum that effec- tively samples the spectrum of h ( t ) a t the frequency of stimulation and its harmonics. The first 250 ms of a typical evoked response has two predominant energy bands from 5 to 12 Hz wide, one cen- tered at 7 to 10 Hz, the other at 15 to 20 Hz [ l ] , [4]. Thus, stim- ulation between 4 and 8 per second, with filtering of four o r more bands, will adequately sample these peaks and provide a good es- timate of the wavelet.

If H ( j w ) varies in time, the variation will result in spreading of the spectral lines of R( j w ) via amplitude modulation, so that a narrow-band filter with wide enough passbands will pass the changes and effectively track variations in h ( t ) . By selecting the bandwidth, hence time-constant, of the filters, adequate noise re- duction can be achieved while retaining the ability to track short- term changes.

As a verification of this technique, a comb filter was constructed by creating an analog Fourier analyzer whose output takes the form of a reconstruction of the periodic input (Fig. 2). This provides a single narrow passband at a desired frequency [ 7 ] . A four-channel system was constructed from commercially available integrated circuits (Fig. 3 ) . The analyzer passes the frequencies of interest, which are the fundamental and the first three harmonics of the stim- ulus rate.

The design is facilitated by the fact that the analyzer uses local oscillators which.are mutually locked in frequency and phase, and also produce the stimulus synchronization pulses.

RESULTS This system was tested on four individuals with closed eyes 30

cm from a Grass Model PS-2 strobelight flashed at the rate of 4 per second. A Grass silver chloride electrode was placed at Oz, refer- enced to the right ear, with a left ear ground. EEG was measured using standard differential amplification, with a passband of 0.5- 60 Hz. In each case, the output of the comb filter was superimposed on a computed average evoked potential taken from 64 successive responses. The filter output was taken from the instant of the last sweep of the averaging computer.

- Local Quadrature Oscillator ’

- + 4:Zzed L j Polend

Fig 3 Steady-state evoked potential measurement system Each box “W” represents one filter of the type in Fig 2 The local oscillator generates both sine and cosine waves at each frequency

Local I Quadrature I

Low-pass Filter

I I I

Low-pass Filter X(t1

Fig. 2 . Method for producing an accurately placed narrow-band filter. The filter bandwidth is equal to twice the cutoff frequency of each low-pass filter, and the passbands accurately replicate the shape of the low-pass filter characteristic.

The filter output is found to provide a good estimate of the major peaks and transitions of the response, when compared with this average (Fig. 4). A certain amount of detail is missing, which might be recovered by additional passbands at higher frequencies, if it were indeed present in the signal. It is possible, however, that some of the “faster” components in the average are in fact artifacts of latency and amplitude jitter, which introduce the deceptive illusion of detail in the averaged signal. Note that the filtered output was available within seconds and revealed slow changes, compared to the average which produced the single estimate after a 16-second wait.

This exercise thus compares two different evoked potential es- timates: an average which represents the entire 16-s stimulus in- terval, and a filtered signal which emphasizes the responses nearer the end of this interval. This highlights the difference between the two techniques; whereas averaging creates a single estimate from an extended period of time, real-time filtering reconstructs a se- quence of short-term estimates of the signal.

If the response is in fact stable and unchanging, the filter output will converge to that signal, without delay o r phase distortion. This results from the fact that the filters are centered at the energy max- imum of the desired signal, and have zero phase at this point; this is analytically true, and was verified using test input signals. When the signal is changing, the filtered output will provide an estimate which lags somewhat, depending on the rapidity of the changes, and the filter time-constants chosen. There is thus a tradeoff be- tween rapid filter response on the one hand, and superior noise removal on the other.

As a n illustration of this tracking ability, the output from one subject was recorded on a pen-chart recorder, as shown in Fig. 5 . Short-term changes in amplitude and harmonic content are clearly evident. In addition, latency shifts reveal that the time relationship between peaks is indeed undergoing changes. In the future, it would be of interest to compute averages of the filtered output, and com- pare them with conventional averaged VEP’s. One would expect that the short-term variations would thus be removed, and that the avkraged filtered evoked potential would show peaks and latencies that agree with the conventional average.

DISCUSSION This approach provides a simple, robust estimate of the ongoing

brain rcsponse to repetitive stimuli, while effectively removing the

652

I ”I

IEEE TKANSACrlONS ON BIOMEDICAL ENGINEERING, VOL 37. NO 6. JUNE 1990

SUBJECT R V SUBJECT C E

SUBJECT R F SUBJECT S V

I--- 200 m s e c 4

Fig. 4. Filtered visual evoked potentials superimposed on averages computed from 64 responses. S t ~ m u l u rate: four per second. three-pole Butterworth filter passbands at 4, 8, 12. and 16 Hz. bandwidth 0.062 H z . I n each casc. the smoother filtered VEP estitiiate IS superimposed o n the tiiore ”detailed“ averaged VEP.

SUBJECT S.V 4 flasheslsecond 5-second filter time-constant

32 seconds 36 ~

40 ~

44 48

Fig. 5 . Time-course of filtered output. illustrating the tracking of short-tertii changes in evoked activit). Top pair: onset 0 1 stimulation. Bottoni pair: beginning 32 s into the stimulation. Top trace of each pair: raw EEG. Bottoni trace: tiltered EEG. filters set as in Fig. 4.

background noise. In addition. at the slower stimulus rates (below about 5 per second), amplitude and latency of the early evoked potential components can be estimated. Many implementations are possible, including both digital and analog designs. An advantage of the analog method is low cost and the ability to process multiple channels without encountering processing speed limitations. The approach lends itself not only to real-time applications, but also to postprocessing, in which the time course of the evoked activity is desired after the fact.

This communication is intended to motivate and describe an al- ternative method for measuring evoked potentials in real time. Ad- ditional studies are required in order to rigorously develop the va- lidity, accuracy, and usefulness of this approach. If borne out, it should find utility in intraoperative monitoring, vigilance studies, biofeedback, psychophysiology, and other applications in which a rapid, accurate estimate of ongoing and changing evoked activity is required. While the approach is described and verified on visual evoked potentials, it may be applicable to auditory, somatosen- sory. and nerve cvoked potentials as well.

REFERENCES [ I ] C . D. McCillem and J . 1. Aunon. “Measurements of signal compo-

nents of single visually evoked brain potentials.” l E E E Trans. Biorned. Erig.. vol. BME-24. pp. 232-241. 1977.

121 N . V . Thakor. “Adaptive filtering of evoked potentials.” lEEE T r u m B i o m c f . E r ~ g . . vol. BME-34. pp. 6-12, 1987.

13) C. A. Vaz and N . V. Thakor. “Adaptive Fourier estimation of time- varying evoked potentials,” lEEE Trans. Bionied. Ertg. , vol. BME-36, pp. 448-455. 1989.

141 E. B. Moody. Jr.. E. Micheli-Tzanoakou. and S . Chokroverty, “An adaptive approach to spectral analysis of pattern-reversal visual evoked potentials,” IEEE Truris. Biorned. Eng . , vol. BME-36, pp. 439-447. 1989.

[5] R. E. Dustman and E. C. Beck, “Long-term stability of visually evoked potentials in man.“ Sciericc~. vol. 14. pp. 1480-1481. 1963.

161 M. W. van Hof, “The relation between the cortical responses to flash and to flicker in man,” Acta Physid. Phurmacol. Need. , vol. 9, pp. 210-224. 1960.

171 D. K. Weaver, “A third method of generation and detection of single- sideband signals.” in Proc. I r ist i t . Rudio Eng. , vol. 44, no. 12. pp. 1703-1705. Dec. 1956.