156 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 38, NO. 2, FEBRUARY 1991

A Deconvolution Technique for Improved Estimation of Rapid Changes in Ion Concentration Recorded

with Ion-Selective Microelectrodes Jeffrey L. Tucker, Student Member, IEEE, Rong Wen, and Burks Oakley 11, Senior Member, IEEE

Abstract-In biological preparations, measurements of rapid, stim- ulus-evoked changes in ion concentration by ion-selective microelec- trodes can be distorted by the limited bandwidth of these sensors. Techniques were developed to reconstruct the actual change in ion con- centration using deconvolution of the electrode’s output signal and the electrode’s transfer function. In the vertebrate retina, a knowledge of the actual time course of a light-evoked increase in extracellular K’ concentration was used to provide a rigorous test of a hypothesis re- garding the electrical origin of a clinically important component of the electroretinogram.

I. INTRODUCTION ON-SELECTIVE microelectrodes (ISM’s) have been used to L easure stimulus-evoked changes in ionic concentration in a

variety of tissues. In these electrodes, a liquid sensor is con- fined within the open tip of a glass micropipette (tip diameter < 1 pm). The development of various ionic sensors now per- mits the measurement of many electrophysiologically-impor- tant ions, including K+, Cl-, Ca2+, and H + [ I ] .

In the vertebrate retina, the b-wave of the electroretinogram (ERG), which is a widely-used diagnostic measure of retinal function in humans [2]-[8], has been hypothesized to be gen- erated by a mechanism involving light-evoked changes in ex- tracellular K+ concentration, [ K+ ], [9]-[ 191. According to this “K f-hypothesis, ” light-evoked activity of ON-bipolar cells re- leases K + , which leads to an increase in [K+], in the outer plexiform layer (OPL). This increase in [ K + I, focally depolar- izes Muller (glial) cells, producing a current sink, which in turn leads to the flow of current from sources on other parts of the Muller cell membrane 191, [13], 1141. As the Muller cell cur- rents flow through the extracellular resistance, they produce the b-wave voltage.

A computer simulation of the K+-hypothesis of the b-wave has shown that the light-evoked increase in [ K + I,, must have essentially the same rapid time course as the b-wave, peaking -350-400 ms after light onset [14]. However, attempts to characterize the light-evoked increase in [ K+ 1 , with K+-ISM’s have found that the measured increase in [K’], has a longer latency than the b-wave, and that it peaks 150-400 ms after the

Manuscript received February 6, 1990; revised June 28, 1990. This work was supported by the National Institutes of Health Grant EY04364.

J. L. Tucker and B. Oakley 11 are with the Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Ur- bana, 1L 61801.

R. Wen was with the Department of Electrical and Computer Engineer- ing, University of Illinois at Urbana-Champaign, Urbana, IL 61801. He is now with the Department of Physiology. University of California, San Francisco, CA 94143.

IEEE Log Number 9041299.

b-wave [16], [17]. Assuming that this time course represents the actual change in [ K + I,, then this result is incompatible with the K+-hypothesis of the b-wave origin [17]. In a recent study, however, we suggested that the limited bandwidth of the Kt- ISM’s means that these sensors attenuate the high frequency information present in rapid, light-evoked changes in [ K+],, so that the K+-ISM signals are necessarily slower in time course than the actual changes in [K’],. After filtering the ERG b-wave with a single-pole low-pass filter that had a bandwidth (dc - 2.1 Hz) approximating that of the K+-ISM, the K+-ISM signal, and the filtered b-wave had nearly the same time course [19]. This experiment provided the first data consistent with the hypothesis that the light-evoked increase in [K+], is as rapid in time course as the b-wave.

Although our results supported the K+-hypothesis, a more rigorous test of this hypothesis must necessarily involve recon- struction of the actual time course of the light-evoked change in [K+], from the electrode signal. In the present study, we have used digital signal processing methods to implement this reconstruction.

METHODS AND THEORY Signal Acquisition

K+-ISM’S were fabricated and their responses to ramp-step changes in [ K’ 1, were measured as described in detail recently [18], 1191. To produce these changes in [K’],, the electrode tip was moved as rapidly as possible (10-16 pm in 16-25 ms) between two flowing streams that contained different [ K + 1, [ 181. The electrode position was assumed to be a linear measure of the change in [K’],. These electrodes also were used to measure light-evoked changes in [ K i l o in the isolated retina preparation of the toad Bufo marinus [19], 1201. The electrode tip was positioned in the OPL at the retinal depth where the light-evoked increase in [ K+ I, is hypothesized to produce the dominant current sink of the ERG b-wave [9], 1131, 1141. The transretinal ERG also was recorded from this preparation under identical stimulus conditions 1191. The light stimulus had a du- ration of 1.0 s in all experiments. All animal experimentation was conducted in accordance with NIH-approved guidelines for the care and use of animals. The analog signals were stored on an instrumentation tape recorder for subsequent analysis [20].

Ion-Selective Microelectrode Theory

The voltage signal from a K+-ISM is termed V K , and under dc conditions, its value (in millivolts) is related to [ K+ 1, by the following empirical equation:

0018-9294/91/0200-0156$01 .OO 0 1991 IEEE

TUCKER el al.: SIGNALS FROM ION-SELECTIVE MICROELECTRODES 157

(a) Ramp-Step Increase (b) Ramp-Step Decrease

Normalized A::/ krF 7

-0.2 I 0 1000 2000 0 1000 2000

Time (ms) Time (ms)

Fig. 1. K+-ISM responses to ramp-step changes in [K'],,. The A VK sig- nals were recorded as the electrode tip was moved between two flowing streams of differing [K'],. The electrode position, which was obtained from the microelectrode positioning system [23], was taken to be a linear measure of the change in [K+],, (termed A K ) . The two pairs of signals were recorded sequentially, as the electrode tip first was advanced ( 16 pm in 25 ms) into a stream having higher [ K+],, (a) and then was pulled back to its original position (b). In this figure, each type of response was nor- malized to its peak amplitude.

where CY is the logarithmic slope ( -58 mV/decade), p is the selectivity coefficient for K + over Na+ ( - 70), K is the [ K + 1, in mM, Nu is the extracellular Na+ concentration ( 110 mM), and V, is a constant [ l ] , [20]. The term N a / p was assumed to be constant ( 110/70 = 1.57), and the baseline level of retinal [ K f 1, in darkness was 2.50 mM [20]. Using these values and ( I ) , the light-evoked change in V,, is given by

where A K is the light-evoked change in [K'], in millimolar. In the OPL of the toad retina, the light-evoked increase in [ K + J, is < 0.4 mM [ 141, [ 161, and the electrode response in (2) can be approximated by a linear function over the range 0 5 A K 5 0.4 mM, given by the equation

A V , = 5.948 A K (3)

For these small values of A K , the linear approximation [see (3)] is an excellent fit (? = 1.000) to the actual logarithmic curve [see (2)], and the linear values deviate from the actual logarith- mic values by 5 2 . 7 % . Therefore, the Kf-ISM can be treated as a linear, time-invariant system for small A K input signals.

Data Analysis

Analog signals were sampled off-line at 1 .O kHz using a com- mercial hardware/software package (Axotape, Axon Instru- ments, Foster City, CA,) on an AST 286 computer. A 4000 point sample of the K+-ISM response to a ramp-step increase and decrease in [ K + 1, (2000 points as [ K + 1, was increased, 2000 points as [ K + I,, was decreased back to its original value; see below) was zero-padded to 4096 points. Light-evoked re- sponses ( A v, and ERG) were sampled for 2.0 s beginning at light onset. These digitized signals were zero-padded to 4096 points by the addition of 1000 points before and 1096 points after each response.

Digital signal processing was done using AT-Matlab (version 3.5 g, The Mathworks, South Natick, MA,). Certain signals

were filtered using a digital Butterworth filter (second-order low- pass, 25 Hz cutoff frequency). Due to the nearly-linear phase properties of the Butterworth filter, this filter delayed the sig- nals by -8 ms. All filtered signals were shifted back in time by 8 ms to account for this delay. Data were exported to a Macintosh I1 computer for plotting.

RESULTS We first characterized KC-ISM responses to both ramp-step

increases and ramp-step decreases in [ K+],. Sampled changes in VK and [ K + 1, (termed A V,(n) and A K ( n ) , respectively) rep- resenting typical electrode responses are shown in Fig. 1 . In this figure, the signals are displayed superimposed and normal- ized to their maximum value, to facilitate their comparison. As observed previously [ 181, the electrode response to the ramp- step change in ion concentration was rather slow, taking - 85 ms to reach 50% of its final value'. Since the K+-ISM is time- invariant, the signals of each type in Fig. 1 were joined to- gether, forming 4000 point sequences (zero-padded to 4096 points). The electrode transfer function H ( z ) then was calcu- lated using the equation

(4)

where A V K ( z ) is the FFT of A V,(n) and A K ( z ) is the FFT of A K ( n ) . Transfer functions for other electrodes with similar tip geometries also were calculated using this procedure.

We next analyzed light-evoked responses obtained from a bi- ological experiment. The digitized A V , and ERG signals [termed A V K ( n ) and ERG(n)] are shown in Fig. 2(a); the pos- itive component of the ERG is termed the b-wave. Each of these signals is the average of six similar responses. In Fig. 2(a), the onset of the 1.0-s flash was coincident with the start of the il- lustrated waveforms, and the entire flash duration is indicated

'The 50%-response times for the responses to ramp-step changes in [ K'],, reported herein are slightly longer than those we reported previously for similar electrodes [ 181, [ 191. In our previous studies, we used the value of A VK reached after -400 ms as the "final value," and we did not con- sider the very slow change in A V K that continues for > I s after the onset of the change in [ Kt I,, .

I

I58 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 38, NO. 2. FEBRUARY 1991

A. Original Signals B. Signals Filtered Without Filtering With Low-Pass

Butterworth Filter

Response :::b 0.6 ;b Amplitude o,4

'AV, (0.5~)

"VK \

(0 .5~) (mv) 0.2

0.0 0.0

-0.2 -0.2 0 loo0 2000 0 1000 2000

Time (ms) Time (ms)

Fig. 2. Time-domain signals from a biological experiment. (a) The A VK signal was recorded with the tip of the K+-selective microelectrode in the outer plexiform layer of the retina, and the ERG was recorded as the change in transretinal voltage [19]; the rapid, positive component of the ERG is termed the b-wave. The signals were sampled for 2.0 s, beginning at light onset (the stimulus duration of 1.0 s is indicated by the thick horizontal lines in this figure and in Fig. 3) . Each of these signals is the average of six similar biological responses that were recorded under identical condi- tions in a single experiment. Note that these digitized signals [ A V , and ERG] contained a significant amount of high-frequency noise. (b) Signals from (a) of this figure after filtering using a digital Butterworth filter (order 2) having a cutoff frequency of 25 Hz. This low-pass filtering procedure did not appear to affect significantly the signals of interest. The A VK signal peaked 147 ms after the ERG b-wave

by the thick horizontal line. Although these signals are similar to those recorded previously from the toad retina under similar conditions [19], the illustrated A V,(n) signal reached its peak amplitude at the earliest time of any response observed in over 25 individual experiments.

The A V, and ERG signals contained a significant amount of high-frequency noise that appeared to be unrelated to the change in [ K+ 1, and the b-wave, respectively. This noise was due pri- marily to the very large internal resistance of the K+-ISM ( 6 GQ for the ion-selective barrel of the electrode whose re- sponse is shown in Fig. 2; see also [ l ] ) . Even though the K+- ISM filtered out high frequency changes in [K+],, it actually served as a source of high frequency noise. In order to examine more closely the signals of interest, we filtered the sampled sig- nals shown in Fig. 2(a) using a low-pass Butterworth filter hav- ing a cutoff frequency of 25 Hz, and the filtered signals are shown in Fig. 2(b).

Examination of the filtered signals in Fig. 2(b) showed that the A V, signal peaked - 147 ms after the b-wave. As in earlier studies [16], [17], this result would be incompatible with the K+-hypothesis of the b-wave origin, if one assumed that the A V, signal was a valid indicator of the actual change in [ K+ 1,. However, we knew that the measured A V, signal was slowed by the electrode's transfer function, so we next used deconvo- lution to reconstruct the actual change in [ K+],. We calculated a 4096-point FFT of the zero-padded A V,(n) signal shown in Fig. 2(a). Deconvolution of A V,(z) and H ( z ) yielded a A K(z) sequence. The inverse FFT of this sequence yielded a signal that we termed A K,,,, ( n ) , which was a calculated reconstruc- tion of the actual change in retinal [K+],. Mathematically, this procedure may be expressed as

AKCal,(n) = FFT-' [AVAz) * H-'(z)] (5) where H-' (z) is the inverse of H ( z ) .

In implementing this deconvolution, values of H - I ( z ) rep- resenting high frequencies have very large magnitudes, which

can add a significant amount of high-frequency noise to the re- constructed signal [22]. We reasoned that the light-evoked in- crease in [K+] , would not have appreciably greater high- frequency content than the ERG b-wave. We computed the spectrum of the filtered ERG signal shown in Fig. 2(b), and we found that >99% of the signal's energy was in a dc - 4.0 Hz bandwidth. Thus, we only needed frequencies in this very lim- ited bandwidth to reconstruct a signal as rapid as the b-wave, and we eliminated the contributions of higher frequencies by setting to zero those values in the H- (z) sequence correspond- ing to frequencies >4.0 Hz. We assumed that these higher fre- quencies only would add noise to the reconstructed signal.

Since the transfer function of the electrode that recorded the A V, signal in the retina (Fig. 2) was not measured, we mea- sured the transfer function for seven electrodes having similar tip geometries and resistances, and we reconstructed the light- evoked change in retinal [ K+]], (A K,,,,) signal using each of the H - I (z) transfer functions and the deconvolution method de- scribed above. Each of the reconstucted signals had a shorter latency, a faster time-to-peak, and a larger amplitude than the original A V, signal. We averaged the seven reconstructed sig- nals, and the average A K,,,, signal and the original biological signal (A V,) are shown in Fig. 3(a) for comparison. While the original A VK signal corresponded to an increase in [ K+ 1, of 0.214 mM, the reconstructed A K,,,,signal was 27% larger, cor- responding to an increase in [K+], of 0.272 mM. To facilitate a comparison of the ERG b-wave and the reconstructed light- evoked increase [K+],, we normalized the ERG and the aver- age A K,,,, signals to their respective peak amplitudes, and the normalized signals are shown in Fig. 3(b). The average A Kcaic signal was as rapid in time course as the ERG b-wave, from the time of light onset until after the peak of the b-wave. The av- erage AK,,,, signal had a slightly shorter latency than the b-wave, and this average waveform actually peaked 10 ms be- fore the b-wave. There was, however, some variability in the reconstructed waveforms, due primarily to differences in the

TUCKER er U / . : SIGNALS FROM ION-SELECTIVE MICROELECTRODES I59

Normalized Amplitude

1.5

I .o

0.5

0.0 - I -0.5 ‘ I

0 1000 2000

Time (ms)

1 .o

0.8

0.6

0.4

0.2

0.0

-0.2 ‘ J

0 1000 2000

Time (ms)

Fig. 3 . Comparison of AK, , , , , A VK, and ERG signals. (a) The AK, , , , sig- nal shown here is the average of seven individual responses that were ob- tained using different electrode transfer functions. The scale representing A K was obtained from (3 ) . The average AK,, , , , signal was larger and more rapid than the original A V , signal. (b) The average A K , , , , , signal and the ERG signal were normalized to their respective peak amplitudes; the nor- malized signals were similar in latency and in time-to-peak. [The A V K and ERG signals were obtained from Fig. 2(a)].

speed of the ramp-step responses of the individual electrodes; the seven A K,,,, signals used to compute the average signal in Fig. 3 peaked in 369 f 23 ms (SEM), compared with 378 ms for the b-wave. Overall, the data illustrated in Fig. 3(b) are very strong support of the K+-hypothesis of the orgin of the ERG b-wave.

The use of a transfer function calculated from the ramp-step input ( A K ) will be valid only if this test signal contains higher frequencies than are present in the biological signal that is to be reconstructed with the technique [21]. Given our assumption that the light-evoked increase in [Y’], was not significantly faster than the ERG b-wave, we cqmpared the spectra of the ramp-step input signals ( A K ) used to compute each H ( z ) with the spectrum of the b-wave. We found that > 99% of the energy in these input signals was in a dc - 10 Hz bandwidth (compared to dc - 4.0 Hz for the ERG b-wave). We conclude that the transfer functions obtained from ramp-step changes in [ K + 1 , ( 16-25 ms ramp) contain sufficient high-frequency content to permit us to reconstruct light-evoked increases in [K+],, that are as fast as the b-wave.

DISCUSSION A N D CONCLUSIONS The limited bandwidth of ISM signals represents a serious

technical difficulty in the applications of ISM sensors to the measurement of rapid changes in ionic concentration in bio- logical preparations. The extremely high internal resistances (5-10 GQ) of these electrodes, coupled with the appreciable capacitance (3-5 pF) across the wall of the glass micropipette, causes these electrodes to behave as low-pass filters [ 11, [ 191.

Although recent improvements in electrode geometry have de- creased electrode resistance [ 181, the chemical response times of these sensors are still slow, compared to the time course of the stimulus-evoked changes in ion concentration that they must sense. In the case of the vertebrate retina, the limited bandwidth of K+-ISM’S has for many years prevented a rigorous test of the K+-hypothesis of the b-wave [ 161, [ 171. We now have used a deconvolution technique to improve our estimation of the ac- tual time course of the light-evoked increase in [ K+],,, and we have demonstrated that the ionic change is likely to be as rapid in time course (both latency and time-to-peak) as the b-wave. This result has rejected one of the strong challenges to the K+- hypothesis, namely, that the light-evoked increase in [ Kt],, was too slow to produce the b-wave [ 171. In combination with our other recent observations of the light-evoked increase [ K+ IC,, Muller cell responses, and the ERG b-wave [19], we now have provided strong support for this hypothesis. The use of the de- convolution technique is a significant improvement upon the much less rigorous method of comparing the time course of these signals that we used previously [19], in which the ERG was filtered by a low-pass filter having a bandwidth approximating that of the K+-ISM.

Our results were obtained using one of the most rapid A V, signals we observed in over 25 individual experiments; the speed of this signal presumably was due both to optimal place- ment of the electrode tip within the OPL and to minimal damage of cells by the electrode tip 1161 in this particular experiment. Since the seven AK,,,, signals we reconstructed peaked in 369

23 ms, compared with 378 ms for the b-wave, we believe that the actual time course of the light-evoked increase in [ Kf 1, in the outer plexiform layer is indistinguishable from that of the b-wave, as predicted by a previous computer simulation of the “K+-hypothesis” of the b-wave [ 141. Unfortunately, we did not characterize the frequency response of the actual electrode used in the biological experiment, but we do not feel that this is a problem, given the similarity of the transfer functions from the electrodes that we tested.

The technique that we have described in this paper should have widespread applications in many areas of physiology and neuroscience where it is critical to know the exact time course of stimulus-evoked changes in ion concentration. Since it does not appear likely that it will be possible to increase significantly the bandwidth of the ion-selective microelectrodes themselves, our digital signal processing technique will remain an effective way to increase the peformance of these sensors.

ACKNOWLEDGMENT We thank Dr. K. S. Arun, Dr. D. L. Jones, Dr. H. Lee, Dr.

D. C. Munson, Jr., and Dr. B. C . Wheeler for their invaluable suggestions regarding the implementation of the signal process- ing techniques used in this manuscript.

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[ 5 ] E. L. Berson, “Electrical phenomena in the retina,” in Adler’s Physiology of the Eye: Clinical Applications, 8th ed., R. A. Moses and W. M. Hart, Jr., Eds. St. Louis: C. V. Mosby, 1987,

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Jeffrey L. Tucker (S’89) received the B.S. de- gree in electrical engineering from the Univer- sity of Illinois at Urbana-Champaign in 1990.

He is currently pursuing the Ph.D. degree in the Department of Electrical Engineering, at Georgia Institute of Technology, Atlanta, where his research interests include digital sig- nal processing of speech and aids for the hear- ing impaired.

Mi-. Tucker received the E. C . Jordan Award from the Universitv of Illinois at Urbana-

Champaign for outstanding undergraduate research. He is a member of Eta Kappa Nu, Tau Beta Pi, and the Audio Engineering Society.

Rong Wen was born in Nanchang, Peoples Re- public of China, in 1952. He received the Bachelor of Medicine degree from Jiangxi Medical College, Nanchang, in 1983, gradu- ating first in his class Following a residency in ophthalmology at the Zhongshan Ophthalmic Center in Guangzhou (Canton), he went to the University of Illinois at Urbana-Champaign, where he received the Ph D degree in neuro- science in 1989

He currently is a postdoctoral fellow in the Department of Physiology at the University of California, San Fran- cisco His research interests include electrophysiology and ion move- ment in the vertebrate retina, and he currently is studying membrane currents of mammalian retinal pigment epithelial cells

Dr Wen is a member of the Association for Research in Vision and Ophthalmology

Burks Oakley I1 (M’SlLSM’89) received the B S. degree in chemical engineering from Northwestern University, Evanston, IL, in 1971, and the M S. and Ph D degrees in bioengineering from the University of Michi- gan, Ann Arbor, in 1973 and 1975, respec- tively.

Between 1976 and 1980. he worked as a postdoctoral fellow at the University of Cali- fornia, San Francisco, and Purdue University, West Lafayette, IN In 1981, he joined the fac-

ulty in the Department of Electrical and Computer Engineering at the University of Illinois at Urbana-Champaign, where he currently is an Associate Professor He also is a faculty member in the Bioengineering Program, the Neuroscience Program, and the Department of Biophys- ics. His research interests are centered around retinal electrophysiol- ogy.

Dr Oakley is a member of Tau Beta Pi, Eta Kappa Nu, the Society for Neuroscience, the Biophysical Society, the Association for Re- search in Vision and Ophthalmology, and the IEEE Engineering in Medicine and Biology Society