IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 38. NO. 4. APRIL 1991

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Communications A Beamformer for the Acquisition of Evoked Potentials C. A. McKinley and P. A. Parker Abstract-Evoked potentials (EP) contain information about various physiological parameters and the estimation and detection of these signals can aid in the diagnosis of many pathological conditions. However, the signal-to-noise ratio (SNR) for EP measurement is often very low, and thus signal processing techniques must he employed to enhance the SNR. A delay and sum heamformer acquisition system has the potential for significant SNR improvement in EP measurements. In this communication it is shown that an electrode array acquisition system implements a uniform coherent delay and sum heamformer. The performance of the heamformer is characterized in terms of the numher of electrodes, and cross-channel correlation. When compared to conventional ensemble averaging, the heamformer reduces the number of response repetitions required to achieve a given SNR by a factor which approaches the number of channels in the acquisition system.

I. INTRODUCTION Estimation and detection of evoked potentials (EP) provide valuable information about underlying physiological conditions, and thus these signals are used extensively in both research and clinical environments, [l]. A limiting factor in many of these measurements is the low signal-to-noise ratio (SNR), which requires the application of SNR-enhancement techniques. The noise sources are primarily amplifier thermal voltage noise, and electrode-tissue interface noise generated by amplifier current noise passing through the impedance of the electrode-tissue interface. The conventional approach to SNR enhancement involves ensemble averaging evoked response records acquired by an electrode pair and a single measurement channel. The SNR is increased by the number N of records averaged, but at the cost of increased measurement time. This communication presents an SNR-enhancement technique for EP measurements that has the potential to achieve improvement without the cost of increased measurement time. Applications in which this consideration is important include spinal cord monitoring during surgery [ 2 ] , single-trial EP signal estimation [3], and tracking of sensory nerve excitability changes [4]. The technique relies on the propagating nature of the response, and on signal acquisition with an electrode array. The array and appropriate signal processing constitute a beamformer or phased array, as often used in communication systems. While the phased array is an M-dimensional signal processor (time and one or more spatial dimensions), the conventional EP processor is one-dimensional (time). One-dimensional signal processing techniques that have been used include ensemble averaging, lowpass, bandpass, and matched filtering, and Wiener filtering, [ 5 ] . M-dimensional techniques exploit the propragating characteristic of the EP and the spatial characteristic of the multisensor array. Examples of M-dimensional power spectral density estimation applications for biological signals are given in [6], [7]. Manuscript received January 9, 1990. This work was supported by in by Grant MT-10166 from the Medical Research Council of Canada. The authors are with the Institute of Biomedical Engineering and Department of Electrical Engineering, University of New Brunswick, Fredericton, N.B., Canada E3B5A3. IEEE Log Number 9100027. part

The approach taken in this paper is to exploit the multielectrode array using a beamformer. An excellent introduction to this technique and its applications is given by Dudgeon [SI.In the following sections, the development and implementation of a “delay and sum” beamformer for median sensory nerve evoked potential, MSEP, measurement will be described, and its SNR enhancement performance evaluated. 11. BEAMFORMER

A delay and sum beamformer can be viewed as a finite impulse response (FIR) filter, and FIR signal processing theory as well as its associated analysis techniques can be used to characterize the array. The beamformer output g(t) is given by

1 N

g(t) = -

N-‘ k=O

w,s(t

-

k6

+ kA)

(1)

where s(t) is a signal propagating at velocity C, 6 = d sin ( O / C ) is the propagation delay per sensor, N is the number of sensors in the array, wk and k A are the weighting coefficient and inserted delay applied to the kth channel, and d is the interelectrode spacing. If S( f ) and G( f ) denote the Fourier transforms of s(t) and g ( t ) , respectively, then

G(f) = =

1

,zo

N-‘

s(f)[i

wk exp

[-$.lrfk(6

S( f)W( f)

- A)]

I (2)

where W( f ) may be interpreted as an FIR filter and the array as a discrete sampling system with an equivalent sampling period given by (6 - A ) . In the discrete sampling context, the problem of determining the sensor weights w, so that the array has some desired response characteristics is the same as designing an appropriate FIR filter. In this paper a “uniform” linear coherent delay and sum beamformer is used for discrimination between the EP and additive noise. The linear array axis is aligned with the nerve, and “coherent” refers to the fact that the inserted channel delay A is made equal to the propagation delay 6. The number of sensors of the system presented in this communication is eight, and the channel weightings are set to unity. The EP component of the beamformer output g ( t ) becomes 7

g(t)

=

G(f)

=

c s(t)

k=O

= s(t),

(3)

and S( f).

(4)

Thus, the output of the coherent “delay and sum” beamformer, in the absence of noise, is s(t). This result depends on two implicit assumptions: 1) that the EP waveforms detected at each sensor are identical, and 2 ) that the EP signal is uniformly delayed across channels. These two assumptions are expected to hold in most applications for small sensor spacing, and sensors placed along the nerve axis. For a sensor array placed perpendicular to the nerve axis, the EP waveforms must differ to some extent due to the varying distances form the sensors to the nerve. On the other hand, this is somewhat offset by the fact that in this arrangement, the delay 6 is known and equal to zero. If nk(t) denotes the nonpropagating additive input noise of the kth electrode channel, then the beamformer output noise n,(t) can

0018-9294/91/0400-0379$01.00 0 1991 IEEE

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IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 38, NO. 4. APRIL 1991

be written as 7

n,(f) =

k=O

n,(t

+ kA).

450 00

(5)

A

+

If the noise processes n k ( t k A ) , k = 0, I , . . ., 7, are zero mean with identical variances u 2 and with identical cross-correlation coefficients rj, j = 1, 2 , * * * , 7, for a given electrode pair spacing j . d , then the variance u 2 of n , ( t ) is easily shown to be ~

03

= E [ n ; ( f ) ]=

uL 8

-

7

uL '

-+-

64j=I

r,(16

-

2j)

Input and output signal-to-noise ratios, SNR; and SNR, respectively, will be defined by

SNR,

=

s:,

s:,

U

U"

7and SNR, = 7

Fig. 1. Beamformer electrode array acquisition system. The system includes active and reference electrode arrays, an arm support, and a hand support. All dimensions are millimeters.

(7)

where S,, is the magnitude of the MSEP signal peak. An SNR gain G can be defined by

M S E P (V)

0.2

I

-

4.-

In the case of uncorrelated noise sources, rj = 0 for all j and SNR gain G attains its maximum value of 8. In the case rj = 1 for all j (identical noise sources), G attains its minimum value of 1.

-

01

4,' 0

.

I I

4

(a)

111. SIGNALA N D NOISE CHARACTERISTICS In order to demonstrate the performance of a beamformer, EP measurements were carried out on the median sensory nerves. A Grass constant voltage stimulator and isolation unit provide 20 V amplitude and 0.2 ms duration stimuli. The stimulating electrodes consist of 2.5 x 10 cm conductive rubber strips, with the cathode and anode applied to the base and tip, respectively, of the middle finger in order to stimulate median sensory fibers. The MSEP signal amplification system consists of eight identical channels. Each channel contains a differential preamp of gain 100 and bandwidth 100 kHz followed by a variable gadbandwidth filter amplifier. The filter amplifier gain and bandwidth are set to typical MSEP measurement values of 500 and 50 to 5000 Hz, respectively. A DT2801 A/D board samples each channel at a sampling rate of 25 kHz, and the data are processed on a Zenith 80386 computer running ILS signal processing software. The electrode array and mounting hardware are shown in Fig. 1. The system consists of active and reference electrode arrays, both of which are attached to a supporting structure. The electrodes of the active array are made of I .2 X 30 mm stainless steel bars separated 3.2 mm on center. The supporting structure is mounted on a chair, and can be adjusted in height to each subject. The forearm rests in the support, and the structure fixes the active array on the subject's forearm, in a location proximal to the wrist and over the median nerve. The reference array is fixed on the opposite side of the subject's forearm, and provides a reference electrode for each active electrode. This ensures that noise sources associated with electrodes are uncorrelated from channel to channel. An experimental verification of the MSEP assumptions made in Section I1 was carried out with in vivo data collected from four subjects. The index finger was stimulated at a rate of two pulses per second, and for each channel 1600 MSEP records with 256 sample points per record were obtained. Ensemble averaging of the 1600 records was used to enhance the input SNR and reduce the noise to essentially zero compared to the MSEP amplitude. Fig. 2 presents the results and demonstrates that for each subject, the MSEP's have a high degree of similarity across the eight channels of the system. The figure also shows that the propagation delay characteristic across the array is approximately uniform. Stimulus artifact is not a problem in these mea-

5

Tlmr ( m i )

M S E P (V)

0 2

1

0

3

J

2

1

4

I

Tim- ( m i )

(b) M S E P (V)

0.2

-0.J

L

0

,

2

5

Tim- (mi)

0

.0.7

-O.=

-0 J

t

I 0

,

2

I 0

-

-

-

.

3

1

5

Tim- ( m i )

Fig. 2. MSEP signal characteristics from the beamformer electrode array for four subjects [(a)-(d)]. Solid thick lines display channel 0 MSEP's, solid lines display channel 2 MSEP's, dotted lines display channel 4 MSEP's, and dashed lines display channel 6 MSEP's.

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IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 38, NO. 4. APRIL 1991

TABLE I CHANNEL NOISECHARACTERISTICS FOR FOURSUBJECTS [(a)-(d)] . THE NOTATION “BASEBAND”REFERSTO A MEASUREMENT BANDWIDTH OF 50-5000 Hz, “BANDPASS”TO A MEASUREMENT BANDWIDTH OF 300-5000 Hz, i , TO THE ESTIMATE OF THE CORRELATION COEFFJCIENT BETWEENNOISE SOURCES O F ADJACENT CHANNELS, G TO THE ESTIMATE O F THE SNR G A I N , A N D G TO THE THEORETICAL SNR GAINFROM (8).

Subjects Measurements Baseband

Bandpass

(a)

(b)

(c)

(d)

AVG

i,

0.246

0.111

G

3.11

5.11

i,

0.008 6.98 7.46

0.006 7.85 7.79

0.160 3.33 0.030 6.80 6.84

0.444 1.95 0.043 6.09 6.18

0.24 3.40 0.02 6.93 7.04

G G

-

surements as it has disappeared before the MSEP arrives at the array. With the stimulator turned off, 100 noise records with 512 points per record were obtained for each channel. Estimates of the noise variance per channel and the covariance between each pair of channels were computed from the data. The estimation error, using the 100 records, will be less than 3 %. Estimates of the correlation coefficients, ?, j = 1, 2, * 7, for pairs of channels were computed from the variance and covariance estimates. The beamformer output variance of was computed and an estimate G of the beamformer SNR gain obtained from the ratio .’/of [see (S)]. Table I summarizes the results for the four subjects. The values F , are obtained by averaging over the correlation coefficients for all pairs of adjacent electrodes. “Baseband” refers to a measurement bandwidth of 50-5000 Hz. As even small amounts of 60 Hz interference will obscure the array performance in reducing wideband noise, a bandpass result is shown in which 60 Hz interference is eliminated by using a measurement bandwidth of 300-5000 Hz. The bandpass results best characterize the array performance. The theoretical noise gain G as found from (8) is also shown. The agreement between measured and theoretical gains is reasonably good. The maximum possible gain is of course limited by the number of electrodes to a value of 8. 3

IV. BEAMFORMER IMPLEMENTATIONA N D PERFORMANCE

=

(P4, - PO,)

+ (P.5,

-

Pl,)

MF

1 ,

Fig. 3 presents one possible implementation of the coherent delay and sum beamformer. Each channel consists of an antialiasing filter denoted by H( f),and A/D converter, a digital matched filter denoted by M( f),a peak detector and delay estimator, and a delay block. In order to implement the coherent delay and sum beamformer, MSEP propagation delay between sensors of the array must be estimated. Jasrotia et a l . , [9] have shown that the optimum EP delay estimator is a matched filter followed by a peak detector. The matched filters for the beamformer were designed from the MSEP waveform of channel 0 as shown in Fig. 2. The propagation delay 6, on the ith measurement is found from the equation

6,

AID

+ (P6, - P2,)+ (E’,

-

P3()

16

where i = 1, 2 , . . ., 50, and PO, through P7, denote the MSEP peak locations from channel 0 data through channel 7 data, respectively. Using the in yivo data obtained as described in Section 111, 50 consecutive delay estimates were made for a given signal-to-

delay estNnator delays

M(f) 1 ‘

M(f)

1 Peak\Delay

1

i

4

06

16

76

g(t)

Fig. 3 . Block diagram of the coherent delay and sum beamformer implementation with eight channels. Each channel consists of an electrode, an antialiasing filter H( f ) . and AID convertor, a matched filter M(f ) , a propagation delay estimator, and an insertion delay k 6 , k = 0, 1, . . ., 7. noise ratio, and the delay estimate mean and variance computed. The means and variances of the delay estimates, given in units of data samples, for various values of signal-to-noise ratio over four subjects are given in Table 11. The delay values can be converted to units of ms by multiplying sample units by 0.05. The signal-tonoise ratio was varied by ensemble averaging a number, #AVG, of MSEP records before measuring MSEP peak locations. The mean conduction velocity averaged across the four subject is approximately 63 m/s. For low values of #AVG, the delay estimate variance is large. As shown by Jasrotia et al. [ 9 ] , this large variance is due to anomalous peak position estimates which occur for low signal-to-noise ratios. In order to avoid this region of operation, the beamformer must ensemble average before the matched filter with #AVG set to at least a value of 8. The delay and sum beamformer with #AVG set equal to 32 was applied to the in vivo data of Section I11 in order to estimate the MSEP waveforms. The matched filter and peak detector estimate the propagation delays k6, k = 1, . . ., 7. These delays are then inserted by the beamformer in order to bring the MSEPs of the eight channels into time coherency. The subsequent averaging of the eight coherent signals provides the SNR enhancement expected of the beamformer. Fig. 4 shows the results for the four subjects. The SNR enhancement of a factor of 8 provided by the beamformer is evident.

IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 38, NO. 4, APRIL 1991

382

TABLE I1 PROPAGATION DELAY ESTIMATION DATAFOR FOURSUBJECTS [(a)-(d)]. THEDELAYESTIMATE MEANA N D VARIANCE ARE GIVENIN UNITS OF SAMPLES. #AVG DENOTES T H E NUMBER O F MSEP RECORDS ENSEMBLE AVERAGED BEFORE MEASURING MSEP PEAK LOCATIONS, A N D SNR, THE SIGNALTO-NOISE RATIO AT THE BEAMFORMER INPUT (a) SNR, = 1.89

(C) SNR, = 1.02

(b)

SNR, = 1.01

(4 SNR, = 0.492

#

0 2

Avg.

Mean 6

Var 6

Mean 6

Var 6

Mean 6

Var6

Mean 6

Var 6

1 2 4 8 16 32

-0.0400 0.838 0.869 0.885 0.864 0.875

12.80 1.71 0.037 0.017 0.007 0.006

0.880 0.839 1.36 1.26 1.25 1.27

9.25 4.79 0.270 0.042 0.035 0.020

0.560 1.15 1.25 1.31 1.24 1.28

7.83 0.888 0.254 0.076 0.039 0.021

0.171 1.05 0.793 0.678 1.18 1.13

15.70 16.30 4.53 1.30 0.346 0.045

MSEP (V) 0 2

0.4

0.7

0

0

*

-0.1

-0

a.2

.o 2 -0 J

Timr (mr)

Timr (mr)

(a)

(b)

0.2

0..

0

-0 1

.0.2

-0 ¶

Timr (mr)

Tim-

(C)

(mo)

(4 Fig. 4. Beamformer MSEP waveform estimation performance for four subjects [(a)-(d)]. The dotted line is the beamformer MSEP input after ensemble averaging 32 records. The solid line is the beamformer output MSEP estimate with #AVG = 32.

V. CONCLUSIONS An electrode array in a beamformer arrangement has the potential of providing significant signal-to-noise ratio enhancement. An eight-channel delay and sum beamformer was investigated in this communication. The cross-correlation between noise sources from pairs of channels was determined and found to be low for interelectrode spacings as small as 2 mm. This low correlation can be explained by the fact that the additive channel noise is primarily from the amplifier voltage noise source. The MSEP was found to be nearly identical over the eight channels, and the propagation delay close to uniform. Under these conditions, the delay and sum beamformer was implemented and shown to give an SNR improvement of close to the theoretical maximum of eight. Such a system would reduce, by a factor approaching the number of electrodes in the array, the total number of SEP records required in conventional ensemble averaging to achieve a given SNR.

REFERENCES [l] M. P. Smorto and J. V. Basmajian, Clinical Electromyography. Baltimore, MD: William and Wilkins, 1979. [2] R. Gopalan, P. A. Parker, and R. N. Scott, “Microprocessor based

[3]

[4]

[5] [6] [7]

[SI

[9]

system for monitoring spinal evoked potentials during surgery,” IEEE Trans. Biomed Eng., vol. BME-33, pp. 982-985, Oct. 1986. J. P. Arpaia, R. Isenhart, and C. A. Sandman, “A characterization of a single-trial adaptive filter and its implementation in the frequency domain,’’ Electroencephalogr. clin. Neurophys., vol. 73, pp. 362-368, 1989. P. Weigl, H . Bostock, P. Franz, P. Martins, W. Miller, and P. Grafe, “Threshold tracking provides a rapid indication of ischaemic resistance in motor axons of diabetic subjects,” Electroencephalogr. clin. Neurophys.. vol. 73, pp. 369-371, 1989. C. McGillem, J. Aunon, and C. Pomalaza, “Improved waveform estimation procedures for event-related potentials,” IEEE Trans. Biomed Eng., vol. BME-32, pp. 371-379, 1985. L. J. Pinson and D. G. Childers, “Frequency wavenumber spectrum analysis of EEG multielectrode array data,” IEEE Trans. Biomed. Eng., vol. BME-21, pp. 192-206, May 1974. C. L. Nikias, M. R. Raghuveer, J. H . Seigel, and M. Fabian, “The zero wavenumber spectrum estimation for analysis of array ECG signals: An alternative to isopotential mapping,” IEEE Trans. Biomed. Eng., vol. BME-33, pp. 435-451, Apr. 1986. D. E. Dudgeon, “Fundamentals of digital array processing,’‘ Proc. IEEE, vol. 65, no. 6, pp. 898-904, June 1977. V. Jasrotia and P. A. Parker, “Matched filters in nerve conduction velocity estimation,” IEEE Trans. Biomed. Eng., vol. BME-30, pp. 1-9, 1983.

A beamformer for the acquisition of evoked potentials.

Evoked potentials (EP) contain information about various physiological parameters and the estimation and detection of these signals can aid in the dia...
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