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PSYCHOPHYSlOLffiY Copyri&hl 0 1989 by The Society for Psychophysiological Research, Inc I, Vol. 26. No. 6 Printed in USA. November, 1989 Smoothing to E, ner, Adler, & Freedman, 1984). The differences might be greater trial-to. neity in the evoked potentials of I than a fundamentally atypical respoi tain drugs increase CNS habituatic stimulation (Davis, Cedarbaum, P Gendelman, 1977), and this might t changes in the EP signal from trial 1 In this paper, we describe a meth ally suited for estimating EP signal slowly from trial-to-trial. By “slowly nals, we mean signals for which thc one trial to the next is small comparec over many trials. (A formal mathei tion is given in Raz, Turetsky, an< Gasser, Miicks, and Verleger (198 Emerson, and Pedley (1985) have I slow changes in the EP signal can bt smoothing the single-trial data in tw over trials and over time within triz (1985) have shown that simulatec changes In an EP signal can be success from the background EEG activity t sional smoothing. However, they di the issue of deciding how much to SII (Le., choosing the parameter that d amount of smoothing). If the da smoothed, trial-to-trial changes in the obscured, just as they are obscured i case of simple averaging (this is a pro Alternatively, if the data are undersn residual noise will be mistaken for tr erogeneity (this is a problem of vans For a known signal embedded in nl peting goals of minimizing the bias an the variance of a signal estimate car by selecting the smoothing paramet mizes the mean average square error ( smoothed data. The MASE is the exp difference between the smoothed data estimated signal, and the true signal can be expressed as the sum of the avl bias and the average variance. When t is not known, as is the case for all EP the MASE of the smoothed data can mined, but an estimate of the MASE puted (Rice, 1984; Hart & Wehrly, 19 1989). A smoothing parameter can thc to minimize the MASE estimate. Thi! choosing the smoothing parameter c mented with any type of one-dimens dimensional linear smoother. Below, we demonstrate the utilit Proach in the analysis of evoked pot< We apply the approach both to simula specific forms and amounts of signal I Estimation of Trial-to-Trial Variation in Evoked Potential Signals by Smoothing Across Trials BRUCE I. TURETSKY, JONATHAN RAZ, AND GEORGE FEIN University of California. San Francisco, and Veterans Administration Medical Center, San Francisco, CaliJornra ABSTRACT Averaging single trial evoked potential data to produce an estimate of the underlying signal obscures trial-to-trial variation in the response. We describe a method for estimating slow changes in the evoked potential signal by smoothing the data over trials. We discuss the crucial issue of deciding how much to smooth and suggest that an appropriate smoothing parameter is one that minimizes the estimated mean average square error of the smoothed data. Equations to estimate the mean average square error for a one-dimensional local linear regression smoother are presented. Performance of the method is assessed using simulated evoked potential data with several different models of a changing signal and different values of the signal-to-noise ratio. We find that the method rarely imputes trial-to-trial variation to data sets that have an unchanging signal, while it almost always produces less error than averaging when estimating a varying signal. The ability of the method to reveal signal heterogeneity is hampered by very low signal-to-noise ratios. When applied to real auditory evoked potential data from a sample of elderly subjects, the method indicated a changing signal in 35% of all subjects and in 56% of subjects with signal-to-noise ratios above 0.6. Consistent patterns of variation in the auditory evoked potential were present in this sample. DESCRIPTORS: Signal heterogeneity, Single-trial evoked potentials, Smoothing parameter, Signal estimation. In a typical evoked potential (EP) experiment, scalp electrical potentials, recorded in response to repeated exposures to a stimulus, are averaged to produce an estimate of the underlying EP signal. This technique is based on the assumption that the signal is homogeneous (i.e., that the same response occurs in every trial). Under the homogeneity as- sumption, averaging increases the signal-to-noise ratio (SNR) which is otherwise too low to permit reliable signal estimation. (See Turetsky, Raz, and Fein (1988) for a discussion of the relationship be- tween SNR and the reliability of the EP signal es- This work was supported by NIA Grant No. I-R01- AG03334, Veterans Administration General Medical Re- search Funds, and the Veterans Administration Psychia- try Research Training Program. Address requests for reprints to:. Dr. George Fein, De- velopmental NeuropsychologyLaboratory, Veterans Ad- ministration Medical Center (I 16R), 41 50 Clement Street, San Francisco, CA 94 I2 1. timate.) Sometimes, though, the EP signal may not be homogeneous throughout the course of an ex- periment, but instead may change from trial to trial. Using a statistical test that is sensitive primarily to smooth changes of the EP signal over trials, Mocks. Gasser, and Pham (1984) have shown that signal heterogeneity occurs in normal subjects with simple repetitive visual stimulation. Changes in the EP sig- nal during the course of an experiment may be of intrinsic interest in the study of: a) normal CNS function, b) CNS function in psychiatric subpop ulations, and c) the effects of drugs and other rna- nipulations on CNS function. As examples: a) the frontal P300 response to novel stimuli is known to habituate dramatically early in the course of an ex- periment (Courchesne, 1978); b) the average evoked potentials of schizophrenic patients differ from those of normal subjects in both peak ampli- tude and the morphology of several components (e.& Roth & Cannon, 1972; Roemer, Shagass, Straumanis, & Amadeo, 1979; Siegel, Waldo, Miz- 700
Transcript

PSYCHOPHYSlOLffiY Copyri&hl 0 1989 by The Society for Psychophysiological Research, Inc

I,

Vol. 26. No. 6 Printed in U S A .

November, 1989 Smoothing to E,

ner, Adler, & Freedman, 1984). The differences might be greater trial-to. neity in the evoked potentials of I than a fundamentally atypical respoi tain drugs increase CNS habituatic stimulation (Davis, Cedarbaum, P Gendelman, 1977), and this might t changes in the EP signal from trial 1

In this paper, we describe a meth ally suited for estimating EP signal slowly from trial-to-trial. By “slowly nals, we mean signals for which thc one trial to the next is small comparec over many trials. (A formal mathei tion is given in Raz, Turetsky, an< Gasser, Miicks, and Verleger (198 Emerson, and Pedley (1985) have I

slow changes in the EP signal can bt smoothing the single-trial data in tw over trials and over time within triz (1985) have shown that simulatec changes In an EP signal can be success from the background EEG activity t sional smoothing. However, they di the issue of deciding how much to SII (Le., choosing the parameter that d amount of smoothing). If the da smoothed, trial-to-trial changes in the obscured, just as they are obscured i case of simple averaging (this is a pro Alternatively, if the data are undersn residual noise will be mistaken for tr erogeneity (this is a problem of vans

For a known signal embedded in nl peting goals of minimizing the bias an the variance of a signal estimate car by selecting the smoothing paramet mizes the mean average square error ( smoothed data. The MASE is the exp difference between the smoothed data estimated signal, and the true signal can be expressed as the sum of the avl bias and the average variance. When t is not known, as is the case for all EP the MASE of the smoothed data can mined, but an estimate of the MASE puted (Rice, 1984; Hart & Wehrly, 19 1989). A smoothing parameter can thc to minimize the MASE estimate. Thi! choosing the smoothing parameter c mented with any type of one-dimens dimensional linear smoother.

Below, we demonstrate the utilit Proach in the analysis of evoked pot< We apply the approach both to simula specific forms and amounts of signal I

Estimation of Trial-to-Trial Variation in Evoked Potential Signals by Smoothing Across Trials

BRUCE I. TURETSKY, JONATHAN RAZ, AND GEORGE FEIN University of California. San Francisco, and Veterans Administration

Medical Center, San Francisco, CaliJornra

ABSTRACT Averaging single trial evoked potential data to produce an estimate of the underlying signal

obscures trial-to-trial variation in the response. We describe a method for estimating slow changes in the evoked potential signal by smoothing the data over trials. We discuss the crucial issue of deciding how much to smooth and suggest that an appropriate smoothing parameter is one that minimizes the estimated mean average square error of the smoothed data. Equations to estimate the mean average square error for a one-dimensional local linear regression smoother are presented. Performance of the method is assessed using simulated evoked potential data with several different models of a changing signal and different values of the signal-to-noise ratio. We find that the method rarely imputes trial-to-trial variation to data sets that have an unchanging signal, while it almost always produces less error than averaging when estimating a varying signal. The ability of the method to reveal signal heterogeneity is hampered by very low signal-to-noise ratios. When applied to real auditory evoked potential data from a sample of elderly subjects, the method indicated a changing signal in 35% of all subjects and in 56% of subjects with signal-to-noise ratios above 0.6. Consistent patterns of variation in the auditory evoked potential were present in this sample.

DESCRIPTORS: Signal heterogeneity, Single-trial evoked potentials, Smoothing parameter, Signal estimation.

In a typical evoked potential (EP) experiment, scalp electrical potentials, recorded in response to repeated exposures to a stimulus, are averaged to produce an estimate of the underlying EP signal. This technique is based on the assumption that the signal is homogeneous (i.e., that the same response occurs in every trial). Under the homogeneity as- sumption, averaging increases the signal-to-noise ratio (SNR) which is otherwise too low to permit reliable signal estimation. (See Turetsky, Raz, and Fein (1988) for a discussion of the relationship be- tween SNR and the reliability of the EP signal es-

This work was supported by NIA Grant No. I-R01- AG03334, Veterans Administration General Medical Re- search Funds, and the Veterans Administration Psychia- try Research Training Program.

Address requests for reprints to:. Dr. George Fein, De- velopmental Neuropsychology Laboratory, Veterans Ad- ministration Medical Center ( I 16R), 41 50 Clement Street, San Francisco, CA 94 I2 1.

timate.) Sometimes, though, the EP signal may not be homogeneous throughout the course of an ex- periment, but instead may change from trial to trial. Using a statistical test that is sensitive primarily to smooth changes of the EP signal over trials, Mocks. Gasser, and Pham (1984) have shown that signal heterogeneity occurs in normal subjects with simple repetitive visual stimulation. Changes in the EP sig- nal during the course of an experiment may be of intrinsic interest in the study of: a) normal CNS function, b) CNS function in psychiatric subpop ulations, and c) the effects of drugs and other rna- nipulations on CNS function. As examples: a) the frontal P300 response to novel stimuli is known to habituate dramatically early in the course of an ex- periment (Courchesne, 1978); b) the average evoked potentials of schizophrenic patients differ from those of normal subjects in both peak ampli- tude and the morphology of several components (e.& Roth & Cannon, 1972; Roemer, Shagass, Straumanis, & Amadeo, 1979; Siegel, Waldo, Miz-

700

1989 Smoothing to Estimate Variation in Evoked Potential Signals 70 1 Pnntcd in U,S,A

Gendelman, 1977), and this might be observed in changes in the EP signal from trial to trial.

In this paper, we describe a method that is ide- ally suited for estimating EP signals that change slowly from trial-to-trial. By “slowly changing” sig-

next that are small on the average, but which also contain points of abrupt transition. Smoothing is ideally suited to the estimation of signals that are truly “slowly-&anging”; we have pursued the ap- plication of the method to such cases in more detail

n in Evoked oss Trials

.I RAZ, AND GEORGE FEIN ;co. and 1 Pterans ,4dminisirarron -enter, Sun Francisco. California

h a t e of the underlying signal od for estimating slow changes %‘e discuss the crucial issue of ioothing parameter is one that data. Equations to estimate the wion smoother are presented. itial data with several different b ratio. We find that the method Banging signal, while it almost ;ing signal. The ability of the I-to-noise ratios. When applied bjects, the method indicated a ignal-to-noise ratios above 0.6. t present in this sample. mtials, Smoothing parameter,

?es, though. the EP signal may not i throughout the course of an ex- ,tead may change from trial to trial. 11 test that is sensitive primarily to 3f the EP signal over trials, Mocks, rn (1984) have shown that signal :urs in normal subjects with simple ;timulation. Changes in the EP sig- w s e of an experiment may be of in the study of a) normal CNS i function in psychiatric subpop- he effects of drugs and other ma- NS function. As examples: a) the m s e to novel stimuli is known to ically early in the course of an ex- :heme, 1978); b) the average 2 of schizophrenic patients differ mal subjects in both peak ampli- irphology of several components annon, 1972; Roemer, Shagass, nadeo, 1979; Siegel, Waldo, Miz-

702 Turetsky, Raz, and Fein Vol. 26. No. 6

statistical model and equations for the weighting function that we use are presented in the Appendix.

To determine the optimum amount of smooth- ing, we systematically vary the span from a small number up to the total number of single trials in the data set. For each value of A, we smooth the data and compute an esemate of the mean average square error (MASE), M(X). We also compute an estimated MASE for the average evoked potential, h(avg). This is an estimate of the error when the average evoked potential is taken as the estim?ted signal for each single trial. (The equations for M(A) and h(avg) are given in the Appendix.) We then select the span that minimizes M. In practice, the MASE estimator can take on negative values; this is not a practical problem, because we are interested only in finding the value of A that minimizes M(A) and we allow the minimum to be a negative num- ber. When the minimum MASE estimator is h(avg) , it suggests that the average evoked poten- tial provides the best signal estimate. This is the result that we would hope for when there are, in fact, no trial-to-trial changes in the signal. It also may occur when the signal-to-noise ratio is too low to allow adequate estimation of heterogeneous sig- nals.

-51 ~ ~~

1 TRIAL C 60

-5 - I ,,*L ” #

0 TIME

SIMULATION S N D Y

Method Simulated evoked potential (EP) data sets were

used to evaluate the performance of our approach to choosing the smoothing parameter for estimating EP signals. A changing signal was simulated by modifying the average auditory evoked potential recorded from a single subject to reflect trial-to-trial heterogeneity. This signal was then added to samples of spontaneous brain electrical activity (EEG), recorded from the same subject at rest with eyes open, to create a set of sim- ulated single-trial EP recordings. Each simulated EP data set was constructed by taking a random sample of 60 noise vectors from a population of 1500 vectors. multiplying each noise vector by an amplitude factor that determined the signal-to-noise ratio, and then adding the modified signal. The number of single trials in each data set was thus 60; the number oftime points was 112 (448 ms).

Simulated EP data sets were created for the same five models of a changing signal as were used by MGcks et ai. (1984): ( I ) The homogeneous signal model (HOM), in which the signal does not change at all. The same unmodified smoothed averaged evoked potential is used as the signal in each single trial. (2) The ha- bituation model (HAB), in which the signal amplitude decreases across trials. The signal is multiplied by a

1 0 TIME (msl 4 4 6 ‘

I r ‘ $’ -57 I I -’ ;lME L - _ ._ .. - L’ 1 TRIAL # 60

Figure 1. Simulated signals for the four models of a slowly changing signal. Orientation of each three-dimensional plot was selected to best show trial-to-trial changes. Top le8: Habituation model (HAB). Top right: Latency shift model (LAT). Bottom left: Absent signal model (ABS). Bottom right: Component switch model (COM).

November, 1989 Smoothing to

Table 1 Frequency distributions of:

smoothing paramete!

Percentages

SNR Smoothing Paran Lcrels 7 IS 21 29 37 43

HOM

High 0 0 0 0 0 0 Medium 0 0 0 0 0 10

o o o o o ( Y LOW

HAB

High 0 5 0 5 0 0 Medium 5 0 5 10 5 10

0 0 0 0 0 0 LOW

LAT

High, 0 5 5 1 0 1 0 5 Medium 0 0 10 5 I5 10 LOW 0 0 5 0 0 0

ABS

High 5 0 10 20 30 30 Medium 0 0 0 35 20 45 LOW 0 0 0 5 1 5 1 0

COM

High, 0 5 5 0 0 0 Medium 0 5 0 I5 10 0 LOW 0 5 1 0 0 5 0

scaling factor that decreases linearly across the 60 simulated trials. (3) I model (LAT). In the first 20 trials, the 5 points (20 ms) to the left, and s amount to the right in the last 20 tr 20 trials are left unchanged. (4) The ab el (ABS), in which the first 15 trials ci and the remaining trials contain a hc nal. ( 5 ) The component switch model ditional positive component is added homogeneous signal in the first 20 tri: ed from the signal in the last 20 trials. was constructed from the positive 1 curve, covering 31 data points (120 n around the 56th data point (220 ms this component was 25% of the how power. This produced an increase or amplitude of the P2 component of tb as a distortion of the waveform morp depicts the simulated signals from th signal models. The HAB model is a “s heterogeneous signal. The LAT, A models include abrupt changes but nl systematic trends across the entire se

The method for choosing the smoc was applied to 300 simulated data set! for each of the five signal models wi

VOl. 26. NO. 6

SIMULATION STUDY

Method voked potential (EP) data sets werp ! the performance of our approach to ioothing parameter for estimating Ep ing signal was simulated by modifying itory evoked potential recorded from to reflect trial-to-trial heterogeneitl.

[hen added to samples of spontaneous ctivity (EEG), recorded from the Same rith eyes open. to create a set of sim- 31 EP recordings. Each simulated EP istructed by taking a random sample )rs from a population of I500 vectors. I noise vector by an amplitude factor I the signal-to-noise ratio, and then fied signal. The number of single trials vas thus 60; the number oftime points 9. ’ data sets were created for the same :hanging signal as were used by Miicks 1) The homogeneous signal model I the signal does not change at all. The smoothed averaged evoked potential

gnal in each single trial. (2) The ha- (HAB), in which the signal amplitude trials. The signal is multiplied by a

TIME ( m s l 448 1

. # 60’ Orientation of each three-dimensional (HAB). Top right: Latency shift model tch model (COM).

L

Vovernber, 1989 Smoothing to Estimate Variation in Evoked Potential Signals 703

Table 1 Frequency distributions of selected

smoothing parameters - Percentases

SNR Smoothing Parameters Levels 7 15 21 29 37 43 51 60 Avg

HOM - High 0 0 0 0 0 0 0 0 1 0 0 Medium 0 0 0 0 0 10 0 0 90 LOW 0 0 0 0 0 0 0 5 9 5 -

HAB

0 5 0 5 0 0 1 5 7 0 0 5 0 5 10 5 10 10 55 0 0 0 0 0 0 0 1 0 8 0 10

LAT

4 High 0 5 5 1 0 1 0 5 5 6 0 0 3 Medium 0 0 10 5 I5 10 15 40 5

0 0 5 0 0 0 5 4 s 45

ABS

High 5 0 10 20 30 30 0 5 0 Medium 0 0 0 35 20 45 0 0 0 LAW 0 0 0 5 15 10 0 15 55

COM

0 5 5 0 0 0 1 0 8 0 0 0

0 5 10 0 5 0 1 0 7 0 0 I !&n 0 5 0 15 10 0 10 60

scaling factor that decreases linearly from 1.5 to 0.5 J across the 60 simulated trials. (3) The latency shift

model (LAT). In the first 20 trials, the signal is shifted 5 points (20 ms) to the left, and shifted the same amount to the right in the last 20 trials. The middle 20 trials are left unchanged. (4) The absent signal mod- el (ABS), in which the first 15 trials contain no signal, and the remaining trials contain a homogeneous sig- nal. (5) The component switch model (COM). An ad- ditional positive component is added to the otherwise homogeneous signal in the first 20 trials, and subtract- ed from the signal in the last 20 trials. The component 1 was constructed from the positive half of a cosine curve, covering 31 data points (I20 ms) and centered around the 56th data point (220 ms). The power of

, this component was 25% of the homogeneous signal power. This produced an increase or decrease in the amplitude of the P2 component of the signal, as well as a distortion of the waveform morphology. Figure 1 depicts the simulated signals from the four changing signal models. The HAB model is a “slowly changing” heterogeneous signal. The LAT, ABS, and COM models include abrupt changes but nevertheless have

f systematic trends across the entire set of trials. The method for choosing the smoothing parameter

was applied to 300 simulated data sets: 20 simulations

i

I i , for each of the five signal models with each of three

L

different values for the signal-to-noise ratio (SNR): 1 .O (high), 0.6 (medium), and 0.2 (low). SNRs in this range are commonly found in cortical evoked potential data. SNRs much less than 0.2 are also common, but our experience leads us to believe that signal heterogeneity in cortical evoked potentials would be very difficult to detect or estimate when the SNR is less than 0.2. The data were first smoothed in the time dimension using Blackman’s “lucky guess” window function (Black- man & Tukey. 1958), down 3dB at 15 Hz and down to zero at 50 Hz. This particular low-pass filter is im- plemented in the ASYST scientific software system (ASYST Software Technologies, 1987), and employs a frequency response function that yields negligible side lobes. Each data set was then smoothed eight times using a onedimensional local linear regression smoother with a span of: 7, 15.21,29, 37,43, 51, and 60 trials. The average of the 60 trials was also com- puted. For each value of the smoothing parameter and for the average, we computed the estimator M(X). We had a known signal, so we were also able to compute the average squared error or ASE. A@), the average square of the difference between the estimated signal and the-real signal (see Appendix).

Let h denote the value of the smoothing parameter that minimized M(X). (We _allowed the average to be a “value” that minimized M(X).) The value A, then, is the estimate of the optimum smoothing parameter. The ratio R = A(h)/A(avg) compares the residual error using the chosen value of the smoothing parameter to the residual error of the average evoked potential: this ratio is less than one when the chosen signal estimate performs better than the average, and is greater than one when the average is superior.

Results

Table 1 presents the frequency distribution of the selected smoothing parameter for each model and SNR level. The performance of the estimation procedure compared to standard averaging is sum- marized in Table 2, which presents the frequency distribution of the R ratio. The important question for any practical application of the method is whether the chosen smoothing parameter, A, pro- duces a better estimate of the true signal than the averaged evoked potential. Note that, for the HOM model, simple averaging always minimizes the av- erage squared error and provides the best signal estimate. Our estimation procedure was able to cor- rectly identify averaging as the preferred method in 95% of these cases. This suggests that the method only rarely produces a heterogeneous signal esti- mate when there are no trial-to-trial changes. Al- though the actual error ratios, for the 5% of cases in which the average was not correctly identified, were high (>2.00), this was sometimes the result of atypically small ASEs for the average, rather than atypically large ASEs for the chosen smoothing spans.

704 Turetsky, Raz, and Fein

Table 2 Comparison of single-trial estimation and averaging

Vol. 26, No. 6

Percentages of Error Ratios (R) in Each Category SNR

Levels R<.25 . 2 5 s R < 9 .50sR<1.00 R=1.00 1.00tRt2.00 R>2.00

HOM

High 0 0 0 100 0 0 Medium 0 0 0 90 0 10 Low 0 0 0 95 0 5

HAB

High 85 15 0 0 0 0 Medium 55 35 5 0 5 0 LOW 0 30 60 10 0 0

U T

High 0 70 25 0 5 0 Medium 0 35 60 5 0 0 Low 0 0 30 45 20 5

ABS

High 0 80 20 0 0 0 Medium 0 65 35 0 0 0 LOW 0 0 35 55 10 0

COM

80 15 5 0 0 0 20 70 10 0 0 0 Medium

L O W 0 45 40 0 15 0

H@,

When the signal was heterogeneous, smoothing performed better than averaging’(R< 1) or as well as averaging (R= 1) in at least 75% of the simula- tions, depending upon the particular model of het- erogeneity and the signal-to-noise ratio (SNR). For the medium and high SNR simulations, it produced less error when estimating a slowly changing signal in 98% of all cases, and the error ratios were gen- erally quite small. The relative superiority of the smoothing procedure was less marked when the SNR was low. In these cases, the optimum choice for the estimator was more apt to be either the smoother with the largest smoothing parameter or the averaged evoked potential. This suggests that, when the SNR is too low, the details of heteroge- neity cannot be well resolved by smoothing. Only occasionally did averaging actually perform better than the smoothing procedure (R> l) , and in only a single low SNR case did R exceed 2.00.

The ability of the smoothing procedure to pro- duce less error than averaging does not necessarily mean that the estimated single-trial evoked poten- tials accurately depict the morphology of the slow trial-to-trial changes of the underlying signal. Figure 2 presents the raw single-trial data and the smoothed signal estimate that minimized the mean

average square error (MASE) from one high SNR HAB simulation chosen at random. As can be seen from the raw single-trial data, discerning the un- derlying signal in the presence of noise is not a trivial task. Figure 3 presents the smoothed single- trial data from high SNR simulations for the LAT, ABS, and COM models of signal heterogeneity. Each example includes the value of the estimated MASE computed for each smoothing span. Visual inspection of the smoothed single trials suggests that the estimated signals are fair approximations of the underlying signals, and that they do allow US

to characterize the trial-to-trial changes in specific .cases. The estimated signal is most representative of the true signal for the HAB model, which is truly slowly changing. The change in the signal in this case was linear and continuous across the trials, and hence ideally suited for estimation by smoothing. Abrupt changes in the signal from one trial to the next, such as are seen in the ABS or COM signal models, cannot be accurately estimated by any sort of smoothing procedure which, by definition, at- tenuates the abrupt trial-to-trial changes. Never- theless, in these cases as well as in the LAT model. the trend in the data, from beginning to end of the trials, can be readily detected.

November, 1989 Smoothing to Est

SPAN

7 15 21 29 37 43 51 60

AVG

ESTIMATED M A E (UV2,

.so

.32

. l e

.09

.09

.07

.05

.03

.92

Figure 2. Raw and smootl with signal-to-noise ratio of of spontaneous EEG. Data wj span that minimized the est MASE for each smoothing sp a span of 60, which yields an consistent with the HAB mor

APPLICATION TO REAL EVOKED POTEI

Method

Subjects

Healthy elderly subjects, aged 63-71,’ from the community and studied in a included neuropsychological and electrc assessments. Candidates were screened to verify graduation from high school a English, and to gather medical and psycl data. They were rejected from the study diabetes, severe hypertension. drug abus diagnosis requiring hospitalization, he; coholism or heavy, prolonged alcohol I or epilepsy was reported. Of the appro candidates interviewed, 76 were select testing.

Subjects were screened using the Voca prehension, Block Design, Object Assem Span subtests of the Wechsler Aduli me-Revised (WAIS-R) (Wechsler, from these tests were used to approximat fomance, and Full Scale IQ. Eight subjc bel, Performance, or Full Scale scaled IC

eraging

b Category

.00tRt2.00 R s 2 . 0 0

Smoothing to Estimate Variation in Evoked Potential Signals 705

0 0 0 10 0 5

0 0 5 0 0 0

5 0 0 0

20 5

0 0 0 0

10 0

0 0 0 0

15 0

mor (MASE) from one high SNR I chosen at random. As can be seen ngle-trial data, discerning the un- in the presence of noise is not a re 3 presents the smoothed single- igh SNR simulations for the LAT, I models of signal heterogeneity. icludes the value of the estimated 1 for each smoothing span. Visual e smoothed single trials suggests :d signals are fair approximations ; signals, and that they do allow us l e trial-to-trial changes in specific ated signal is most representative for the HAB model, which is truly The change in the signal in this

td continuous across the trials, and ted for estimation by smoothing. n the signal from one trial to the seen in the ABS or COM signal

e accurately estimated by any sort xedure which, by definition, at- upt trial-to-trial changes. Never- ases as well as in the LAT model, hta, from beginning to end of the lily detected.

SPAN

b

7 15 21 29 37 43 51 60

AVG

ESTIMATED MASE (UV2)

.50

.32

.18

.09

.09

.07

.05

.03

.92

Figure 2. Raw and smoothed single-trial data from a randomly chosen HAB simulation with signal-to-noise ratio of I .O. Raw data consisted of a signal embedded in 60 samples of spontaneous EEG. Data were smoothed using local linear regression and the smoothing span that minimized the estimated mean average square error (MASE). The estimated MASE for each smoothing span is presented. Minimum estimated MASE was obtained for a span of 60, which yields an ordinary least squares linear fit to the data. This is perfectly consistent with the HAB model, in which the change in the signal across trials is linear.

#

APPLICATION TO REAL EVOKED POTENTIAL DATA

Method

Subjects

Healthy elderly subjects, aged 63-71, were recruited from the community and studied in a protocol that included neuropsychological and electrophysiological

90 were not included in the study. An additional 12 subjects who met the screening criteria withdrew from the study and ERP data were not collected for 2 ad- ditional subjects due to technician error or equipment malfunction. The data analyzed below were from a total of 54 subjects (25 females, 29 males) age 64-70 whose Verbal and Performance IQs ranged between 94- I50 and 9 1-1 37, respectively.

assessments. Candidates were screened by telephone to verify graduation from high school and fluency in English, and to gather medical and psychiatric history data. They were rejected from the study if a history of diabetes, severe hypertension, drug abuse, psychiatric diagnosis requiring hospitalization, head injury, al- coholism or heavy, prolonged alcohol consumption,

. or epilepsy was reported. Of the approximately 300 candidates interviewed, 76 were selected for initial testing.

Subjects were screened using the Vocabulary, Com- prehension, Block Design, Object Assembly, and Digit

? Span subtests of the Wechsler Adult Intelligence Scale-Revised (WAIS-R) (Wechsler, 198 I ). Scores from these tests were used to approximate Verbal, Per- formance, and Full Scale IQ. Eight subjects with Ver- bal, Performance, or Full Scale scaled IQ scores below

4

c

Event-Related Potential Procedures

In an oddball P300 paradigm, an auditory tone of 1000 Hz or 2000 Hz was presented on each trial. The intertrial interval randomly varied between 1.5 and 1.6 seconds. The tones were presented binaurally through earphones with a duration of 40 ms and an intensity of 50dB. The IO00 Hz standard tone was presented on 80 percent of the trials and the 2000 Hz infrequent target was presented on the other 20 percent of the trials. Subjects were instructed to count the infrequent targets.

Data were recorded from F,, Cz, Pz, and 0, ref- erenced to linked ears. EOG and EEG were monitored such that horizontal eye movement greater than 1.4" of visual angle, eye blinks, or A/D converter saturation ( 2 125pV) resulted in trial rejection. Each channel of

SPAN ESTIMATED USE (UV2)

7 1.32 15 .93 21 .67 29 .67 37 .62 43 .54 51 .49 60 .48

AV6 2.17 !

SPAN ESTIMATED MAS€ (UV2)

7 1.42 15 .43 21 .23 29 .ll 37 . 00 43 . O l 51 .04 60 .04 -5 - +

AVO 1.36 - ~. .. Y

0 TIME (ma) 440

7 1.50 uv

21 .75 +5, 15 .91

29 .40 37 .44 43 .33 O -1 51 .37 -5, 60 .31

AVO 3.00 _. 1 TAIAL- i 60 0

Figure 3. Smoothed signal estimates from randomly chosen simulations with signal-to- noise ratio of 1.0. Top: LAT model. Middle: ABS model. Botrom: COM model. The esti- mated mean average square error (MASE) for each smoothing span is presented alongside each smoothed signal estimate. Minimum estimated MASE was obtained using a span of 60 for the LAT and COM examples, and 37 for the ABS example.

EEG was sampled every 4 ms, from 40 ms prestimulus to 960 ms poststimulus on each trial. Stimuli were presented until 30 target and 80 standard trials without artifact were collected.

Smoothing Procedures The epoch from stimulus onset until 296 ms post-

stimulus (75 time points), which was expected to in- clude the principal NlWP200 response to the lo00 Hz standard tone, was analyzed using data from the vertex electrode. Due to current limitations in our mi- croprocessor memory and software capabilities, the data were restricted to the first 60 artifact-free standard tone trials. The single-trial data for each subject were prefiltered in the time dimension using the same low- pass filter that was applied to the simulation. data

above. The signal-to-noise ratio of each data set was estimated (see Appendix). The data were then smoothed eight times using the one-dimensional local linear smoother with spans of 7, 15,21,29, 37,43,51. and 60 trials, respectively. The estimated mean av- erage square error was computed for each value of the smoothing parameter, as well as for the averaged evoked potential.

Results The estimated mean average square error was

minimized by a smoothing span other than the av- erage in 19 of 54 cases (35%). Figure 4 presents the distribution of the signal-to-noise ratio (SNR) es- timates, separately for these 19 subjects and for the

November, 1989 Smoothing to EsD’

2.0

3 1.5

T- 2 ‘ 1.0 5 -. 1 z

2 0

s 0.5 0

0

“H.temgeneous“ “Hor Subject# : (n-19)

Figure 4. Distribution of the estimated ratio (SNR) of the auditory evoked potent]. IO00 Hz tone in an oddball paradigm am neous” and “homogeneous” elderly subjec whom the mean average square error (M. imized by a smoothing parameter other (“heterogeneous”) had significantly higher ratios than subjects for whom the estima minimized by the average evoked poten neous” subjects).

rest of the sample. When we limitec to the 27 subjects with “medium” ti mated SNR (i.e., r0.6), we found e% nal heterogeneity in 56% of the data timated SNR was significantly high “heterogeneous” subjects than for tl geneous” subjects (?(52)=2.94, p < Whitney rank test). The median estin the “heterogeneous” group was 0.84 0.49 for the “homogeneous” group. ’

in estimated SNR was consistent w ofour simulations, which suggested t heterogeneity was more apt to be s solved when the SNR was higher. resolve heterogeneity when the SP pends, of course, on the form and heterogeneity. Two subjects in the “t subgroup had extremely low SNR e! ever, the smoothed signal estimate subjects indicated rather extreme one had a large shift in the baseline

4 i

n simulations with signal-to- Porn: COM model. The esti- span is presented alongside

‘as obtained using a span of nple.

yovember, 1989 Smoothing to Estimate Variation in Evoked Potential Signals 707

2.O 1 ,$ 1.5

0 3

I

I

0

I “Heterogenaou8“ “HOmog~MOW”

(n-lS) ( n - W Subjocta Subject#

Figure 4. Distribution of the estimated signal-to-noise ratio (SNR) of the auditory evoked potential to a standard IO00 Hz tone in an oddball paradigm among “heteroge- neous” and “homogeneous” elderly subjects. Subjects for whom the mean average square error (MASE) was min- imized by a smoothing parameter other than averaging (“heterogeneous”) had significantly higher signal-to-noise ratios than subjects for whom the estimated MASE was minimized by the average evoked potential (“homoge- neous” subjects).

rest of the sample. When we limited our analysis to the 27 subjects with “medium” to “high” esti- mated SNR (Le., r0.6), we found evidence of sig- nal heterogeneity in 56% of the data sets. The es-

of the experiment, and the other had a marked mor- phological change in the P2 component. It is en- tirely possible that some of the data from the 35 “homogeneous” subjects were actually heteroge- neous, but that the changes in the signal were not as dramatic and therefore could not be detected due to lower SNR.

The smoothed single-trial data from the 19 “het- erogeneous” subjects had the same general N 1 -P2 component morphology that we typically see in the vertex-recorded average auditory evoked potential (e.g., Figure 5, which presents the smoothed data from 3 subjects selected at random). The minimum amplitude occumng between 50 and 150 ms on a single trial was selected as the N l trough. Similarly, the P2 peak was defined as the maximum value between 150 and 250 ms. N1 and P2 peak latencies, as well as the N1-P2 trough-to-peak amplitude, were computed for each of the 60 single trials. This permitted us to observe trends in both latency and amplitude over the course of an experiment. Figure 6, which depicts the Nl-P2 amplitude as it changes across trials for each of the 19 subjects, reveals a fairly characteristic pattern of signal heterogeneity. The trough-to-peak amplitude showed a progres- sive decline fiom its initial value for 15 of 19 sub- jects. In 12 of these cases, the amplitude either ta- pered off to a minimum or continued to decline steadily over the course of 60 trials. In the other 3 cases, though, the initial reduction in amplitude was followed by an amplitude increase, perhaps in- dicative of some change of state in these subjects. There were 3 subjects who exhibited an initial in- crease in amplitude, but this was then followed by a reduction over later trials. One of the 19 subjects’ data showed little change in amplitude from trial- t o-tri a1 .

The N1-P2 amplitude decrement was accom- panied, typically, by a decrease in the peak latencies of the two components. For each component, 13 subjects showed a pattern of decreasing latency across trials, 3 subjects showed a latency increase, and 3 were essentially unchanged. The magnitude of the latency shift was as large as 48 ms for one subject’s P2 component. The latencies of the two components appeared to shift in tandem for several subjects, but those who exhibited atypical patterns of latency change for N l were not necessarily the same ones who exhibited them for P2.

I

DISCUSSION

When an evoked potential signal changes slowly from trial to trial, the heterogeneous signal can be estimated by smoothing the recorded data across trials. Smoothing in the trial dimension can be done in conjunction with the more common technique

708

SPAN

7 15 21 29 37 43 51 60

AVG

ESTIMATED MASE (Uv2) 6.22 3.04 3.09 2.85 2.25 1.96 1.96 1.97 2.30

Turetsky, Raz, and Fein

SPAN ESTIMATED WISE (UV2)

7 2.39 15 .a 21 .49 29 .56 37 .43 43 .45 51 . 4 1 60 .24

AVG .86

SPAN ESTIMATED M A E (UV2)

7 3.74 15 1.85 21 i .54 29 .94 37 1.39 43 1.46 51 1.72 60 1.82

Figure 5. Smoothed single-trial data sets for 3 of the 19 “heterogeneous” subjects. Data were smoothed using local linear regression and the smoothing span that min- imized the estimated mean average square error (MASE). The chosen smoothing spans for the three data sets were 43, 60, and 29, respectively, from top to bottom. In each case, the typical NI-P2 component complex is readily apparent in the smoothed single-trial data.

of smoothing across time within the trial, either through the sequential application of a one-dimen- sional smoother in both the time and trial dimen- sions, or through the application of a two-dimen- sional smoother. We have presented a method for estimating slowly changing heterogeneous signals from single-trial evoked potential data, by smooth- ing across trials using a one-dimensional local linear regression smoother. Among the alternatives we could have used, though, are moving window av- eraging, quadratic regression smoothing across trials, or two-dimensional kernel smoothing across both trials and time (see Raz et al., 1989). We are

Vol. 26, No. 6

not suggesting that local linear regression is pref- I ! i

erable to other smoothing procedures. However. use of any smoother to resolve signal heterogeneity requires that the amount of smoothing (i.e., the smoothing parameter) be properly selected. In this paper, we present a general solution to the problem of choosing the smoothing parameter.

The mathematical form of the estimated mean average square error (MASE) depends upon the par- ticular type of smoother that is being used. E q a - tions for estimating the MASE using one-dimen- sional smoothing, tensor-product smoothing, and f two-dimensional smoothing can be found in Raz et

t

November. 1989 Smoothing to E

II

Figure 6. NI-P2 trough-to-peak amp1 erogeneous” subjects. Trial-to-trial chang finding is an amplitude reduction over tl

al. (1989). Whether certain types of consistently superior to others is a remains to be answered. We have r ined the performance of both local lii and two-dimensional kernel smoothi ferent set of simulations (Raz et : found little difference in their overa timate signals. Local linear regress provided a rather poor approximatio nal was exponentially decreasing across trials. It is not surprising that fits straight lines was less than ideal fc exponential changes in the data, and pect the performance of a smoother t ratic function to be superior in this ( that certain types of smoothers perf01 estimating certain types of trial-to- neity. Unfortunately, in real data s nature of the heterogeneity remains

Our investigation of the perfor method using simulated data suggest tions conservatively; when the unde not changing, the estimated mean i

Vol. 26. No. 6

rogeneous” subjects. !hing span that min- : chosen smoothing From top to bottom. ily apparent in the

it local linear regression is pref- noothing procedures. However, er to resolve signal heterogeneity amount of smoothing (i.e.. the :ter) be properly selected. In this a general solution to the problem noothing parameter. ical form of the estimated mean 3r (MASE) depends upon the par- oother that is being used. Equa- ng the MASE using onedimen- tensor-product smoothing, and

moothing can be found in Raz et

,Vovember, 1989 Smoothing to Estimate Variation in Evoked Potential Signals 709

Nl-P2 AMPLITUOE

b -------A

+10 uv

T \ I------- 30 60

- 1 I I 1 O1 TRIAL#

Figure 6. N1-P2 trough-to-peak amplitude measured from the 60 smoothed single trials for each of the 19 “het- erogeneous” subjects. Trial-to-trial changes in the amplitude can be observed for several subjects. The most common finding is an amplitude reduction over the course of an experiment.

al. (1989). Whether certain types of smoothers are consistently superior to others is a question that remains to be answered. We have recently exam- ined the performance of both local linear regression and twodimensional kernel smoothing using a dif- ferent set of simulations (Raz et al., 1989) and found little difference in their overall ability to es- timate signals. Local linear regression, however, provided a rather poor approximation when the sig- nal was exponentially decreasing in amplitude across trials. It is not surprising that a method that fits straight lines was less than ideal for representing exponential changes in the data, and we would ex- pect the performance of a smoother that fits a quad- ratic function to be superior in this case. It may be that certain types of smoothers perform better when estimating certain types of trial-to-trial heteroge- neity. Unfortunately, in real data sets, the precise nature of the heterogeneity remains unknown.

Our investigation of the performance of the method using simulated data suggested that it func- tions conservatively; when the underlying signal is not changing, the estimated mean average square

error is almost always minimized by simple aver- aging rather than smoothing the single trials. There is thus little chance of falsely attributing heteroge- neity to a data set that is actually homogeneous. When the underlying signal does change slowly, the method usually results in much less error than the average evoked potential. The ability of the smoothed data to accurately reflect underlying sig- nal heterogeneity depends upon both the degree and form of heterogeneity and the signal-to-noise ratio (SNR) of the recorded data. For the low SNR sim- ulations, the chosen smoothing parameter was close to the maximum amount of smoothing, indicating that resolving the details of signal heterogeneity was very difficult.

The application of the method to a real auditory evoked potential data set suggested the presence of slowlychanging N1 and P2 components in 35% of our elderly subjects. This “heterogeneous” sub- group had a higher estimated SNR than the rest of the sample, which raises the possibility that the prevalence of signal heterogeneity was even greater than 3596, but that it could not be detected in sub-

710 Turetsky, Raz, and Fein Vol. 26, No. 6

jects with lower SNR. If we look at the subsample of subjects with SNR estimates greater than 0.6, we see evidence of heterogeneity in 56% of the cases. These estimates of the prevalence of heterogeneity for the auditory evoked potential are comparable to those of Mocks et al. (1984) for the visual evoked potential (VEP). They estimated 29% and 41% het- erogeneous responders in two groups of normal children, using a flash VEP paradigm. The ability of their test to detect heterogeneity was, like our smoothing method, limited by the SNR of their data.

When the method selects a smoothing parameter other than averaging, visual inspection of the smoothed data permits a qualitative assessment of the particular form and extent of signal heteroge- neity. Quantitative measurements of typical com- ponent latencies and amplitudes can also be made on each single trial, and then reduced to such meas- ures as median latency and amplitude for a given subject. These are presumably more representative than measures derived from an average evoked po- tential that assumes an unchanging signa!. For our auditory evoked potential data, we observed a gen- eral pattern of heterogeneity that included both de- creasing amplitude and decreasing latency of the N1-P2 components over the course of an experi- ment. We cannot specify precisely what physiologic mechanisms or evolving state variables might have produced these changes in individual subjects. A recent review of the literature concerning the N1 auditory component(s) (NZWnen & Picton, 1987) noted that N1-P2 amplitude decrements could be seen: 1) over the course of a few trials, reflecting a prolonged refractory period in the neural circuits; 2) over more extended periods of repeated stimu- lation, presumably reflecting true habituation of the evoked response; 3) when subjects failed to attend adequately to the stimuli; 4) as subjects became more certain of the timing of stimulus presentation; and 5) as the certainty of the detection of near-

threshold signals diminished. Similarly, N 1 latency decreased both with the greater temporal certainty of stimuli and with the ease of signal detection. Which, if any, of these vaned processes, either alone or in combination, accounted for the changes that we observed is a question that requires further testing, with specific paradigms designed to test spe- cific models. Another question that remains to be explored is whether subjects with “heterogeneous” evoked potentials can be distinguished from sub- jects with “homogeneous” evoked potentials on variables other than transient state measures.

It is important to emphasize that the method we have described can only elucidate changes that oc- cur slowly over the course of an experiment. It is also limited by the inability of any smoother to completely resolve abrupt changes in the nature of the signal (e.& Figure 3). Estimating a signal when it is missing or corrupt in some trials, or when the underlying signal is modified by trial-specific am- plitude and/or latency parameters or by trial-spe- cific filters, must be addressed using different meth- ods (Woody, 1967; Brillinger, 1981; Gasser et al., 1983; Gevins, Morgan, Bressler, Doyle, & Cutillo, 1986; Pham, Mocks, Kbhler, & Gasser, 1987; Mo- lenaar & Roelofs, 1987). The performance of the method would, of course, be enhanced by any ex- perimental or data processing techniques that could increase the signal-to-noise ratio of the single-trial data. Possibilities include the use of more precise bandpass filters within each trial, as well as eye- movement or other artifact subtraction techniques (Jervis, Nichols, Allen, Hudson, & Johnson, 1985). to decrease the noise in single trials. Another option would be the use of statistical pattern classification methods to reject single trials that have only min- imal event-related signals (Gevins et a!., 1986). We are now considering a strategy that will examine multichannel recordings in an attempt to exploit differences in the spatial distribution of signal and noise to increase the signal-to-noise ratio.

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i (Manuscript received SI

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525-533.

I

Statistical Model The data are electrical potentials recordec

trode in each of J trials with T discrete time We assume the potential X ( i . r ) in trial j at til true deterministic signal p&rJ and a stationa

X0,t) = rO.1) + Nfj . t ) . j = 1, ..., J, r

4 ; process N0,t):

i 1

We further assume that the noise IS independe EO that

E[N(j.t)N(ku)] = 0.j + k. al The total nom power is

and the signal to noise ratio is of = E [ N ~ J ~ ~ ] ,

.VV” = Cl/JV P Opt)’ i I 1

we assume that the signal changes smoothl: b) and time (I) indices. The averge evoked potential (AEP) is f ( t ) = I

VOl. 26, No. 6

iinished. Similarly, N 1 latency the greater temporal certainty

I the ease of signal detection. these varied processes, either tion, accounted for the changes a question that requires further paradigms designed to test spe- ei question that remains to subjects with "heterogeneous"

'an be distinguished from sub- eneous" evoked potentials on 1 transient state measures. ) emphasize that the method we only elucidate changes that oc- ! course of an experiment. It is : inability of any smoother to abrupt changes in the nature of Jre 3). Estimating a signal when rupt in some trials, or when the s modified by trial-specific am- :ncy parameters or by trial-spe- : addressed using different meth- ; Brillinger, 198 1 ; Gasser et al.. rgan, Bressler, Doyle, & Cutillo. cs, Kohler, & Gasser, 1987; Mo- 1987). The performance of the course, be enhanced by any ex- processing techniques that could -to-noise ratio of the single-trial include the use of more precise ithin each trial, as well as eye- :r artifact subtraction techniques .Ilen, Hudson, & Johnson, 1985), se in single trials. Another option if statistical pattern classification single trials that have only min- signals (Gevins et al., 1986). We

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Appendix Statistical Model Smoothing Function

The data are electrical potentials recorded from a single elec- trode in each of J trials with T discrete time points in each trial. We assume the potential X 0,I) in trial j at time I is the Sum Of a true deterministic signal p0.f) and a stationary mean zero noise process Nfj,I);

X&rj = do.!) + N0.f). J = I . ...,J, f = I , ..., T.

Let A represent the smoothing parameter. For a one-dimen- sional linear smoother that smooths the data over the trials at each time point, the general form of the signal estimate is

jiu.~;A) = 2 gu.k;A)X(k.O.

where &.k;A) is a weight function. In the specific case of local linear regression, these weights have the form:

A

we further so that

that the noise is independent from trial lo trial,

E[N(jJ)N(k,u)] = 0, j f k. all t u .

The total noise power is u.i = EINo,f)z],

I

where the smoothing parameter A is the number of p ints in the smoothing window (which is taken to be odd), and j(A) denotes the mean of the values of j inside the smoothing window. We do not truncate the window at the boundaries of the data. Local linear regression in this form is the basis ofthe supersmooth algorithm of Friedman and Stuetzle ( 1982). Cleveland ( I 979) and Hastie and Tibshirani (1986) discuss related forms of local linear regression.

and the signal to noise ratio is SNR = (I/JlO 1 ~r U.02/a2,.

1 1

We assume that the signal changes smoothly over both the trial 0) and time ( 1 ) indices. The averge evoked potential (AEP) is x(1) = (1/J) 1 X u . f ) .

Turetsky, Raz, and Fein Vol. 26, NO. 6 712

Estimation of the Mean Average Spoue Error

is The mean average square error (MASE) of an estimated signal

M(M = ( I / J T ) 1 1 E[Xf0.l;M - &,t)lz.

The MASE is the mean over all possible data sets of the average squared error in the signal estimate. The actual deviation of a particular signal estimate from the true signal is measured by the average squared error (ASE):

I t

A(X) = ( l / J n c[LU.?;A) - ~ 0 ~ 0 1 ~ . I t

The general form of the esrrmated MASE is: Q(X) = (l/mRSS(X) - 6% + C(N,

where RSS is the residual sum of squares: RSS(X) = c [ X ( i . f ) - iro’.t;X)lz,

;: is the estimated total noise power, and C(X) depends on the particular type of smoother. For a one-dimensional linear smoother,

I f

C(M (2/W &LA). I

For the average evoked potential, C(M = (2 /Gf .

When the signal is homogeneous, a natural estimator of the total noise power is (Callaway & Halliday, 1973; Gasser et d., 1983; Raz, Turetsky & Fein, 1988):

X:CtX(i,t) - 401’ T ( I - 1) . ;;=

When the signal is heterogeneous, this estimator will have a large positive bias. Alternatives are estimators based on the plus-minus average (e.&, Wong & Bickford, 1980) or squared successive dif- ferences (M&ks et al. 1984). which are nearly unbiased when the signal is smoothly changing. We use the following successive dif- ference estimation of the noise power:

T I - I

Estimation of the Sipal-twNolso Ratio SNR can be estimated as the ratio of the estimated signal

power to the estimated noise power: ii: SBR = - 6’

This method assumes that the power of the average evoked PO tential is a reasonable estimate of the power of the signal.

Announcements Cognitive Psychophysiologist

The Cognitive Neuroscience Unit in the National Institute of Neurological and Communicative Disorders and Stroke has an opening for a cognitive psychophysiologist who is familiar with event- related potentials (ERPs) to study patients with a variety of neurological deficits. We are seeking a mature individual, with less than three years of postdoctoral experience, who is capable of independent research within an interdisciplinary team. Skills in recording and analyzing ERPs and programming in FORTRAN are essential. Salary ranges from $24,000-$27,000 depending upon qualifications. Please send CV, statement of research interests, explicit description of skills and work experience, the names and telephone numbers of three professionals you have worked with, and reprints/preprints of your work to: Ray Johnson, Jr., Ph.D., National Institutes of Health, NINCDS/Cognitive Neuro- science Unit, MNB, Building 10, Room 5C422, Bethesda, MD 10892. The NIH isan equal opportunity employer.

Postdoctoral Position at Southern Illinois University The Smoking Research Lab at Southern Illinois University, Carbondale, is seeking a research

associate (psychophysiology/statistics) to assist with grant-supported studies of electrocortical, hor- monal, and behavioral bases of cigarette smoking. The successful candidate will assist with grant- supported studies of electrocortical, hormonal, and behavioral bases of cigarette smoking. Salary is competitive. Research includes studies of smoking in relation to personality, affect, immune function, and stress. Expertise in electrophysiological recording, computer-based data acquisition, and standard statistical packages is required. Duties include coordinating day-to-day research activities, designing and conducting experiments, supervising graduate and undergraduate research assistants, and data analyses. Application deadline is December IS, or until the position is filled. Earliest starting date is January 2, 1990. Submit letter, resume, and three letters of reference to: Dr. David Gilbert, SIUC, Carbondale, IL 62901. Southern Illinois University is an Equal Opportunity/Affirmative Action Em- ployer.

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f’5YCHOPHVSIOLOGY Copyright 8 1989 by The Society for Bychopbysic

Historical No Born of Animal Psycho-Physiolo j

The historical beginnings 0:

first published English definitic DESCRIPTORS: Psychopl

The emergence of psychophysic tific discipline is traditionally date during the latter half of the 19th c Freienfels, 1935). Chester Darrow, tial address at the first meeting of Psychophysiological Research in both a year and a day to the birth iology:

We must remember that it was at tt century, only the day before yesterday, iology was born. In 1872 Darwin publi sion of Emotions in Man and Animals, lowing the Origin ofthe Species. (Dam

We would like to suggest, howevc of psychophysiology actually occ prior to Darwin’s seminal publicatic claim on what is possibly the first nition of psychophysiology. Accori ford English Dictionary (Simpson b!

This research was supported by Foundation Grant Nos. BNS-8414853 i to John T. Cacioppo. The authors wir lhrig for her insightful and helpful COI

Vious version of this manuscript. Address requests for reprints to: Lc

Department of Psychology, University c IA 52242.

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