1 Introduction. MEASUREMENT OF bioelectric events with skin surface elec- trodes is subject to unwanted noise components. This problem is noted particularly ...
1 Introduction MEASUREMENT OF bioelectric events with skin surface electrodes is subject to unwanted noise components. This problem is noted particularly in nerve and skeletal muscle measurements where signal levels are typically in the order of microvolts. In an effort to minimise electrode noise, it is necessary first to understand and model the noise generation process. This is of particular importance for applications in which an electrode array is used, as for example in spatial signal processing. In such cases, dry electrodes would normally be used to avoid the inevitable occurrence of electrode bridging associated with pasted electrodes. Electrode arrays are finding application in peripheral nerve evoked potential detection, and spinal cord monitoring during surgery (MCKINLEYand PARKER, 1991). It is also the case that dry stainless-steel electrodes are used in most clinical applications of myoelectric control for prostheses. These electrodes are used in preference to the pasted Ag/AgCl, owing to the skin reaction to paste in chronic use applications such as myoelectric control. Dry electrodes are, however, of relatively high impedance, raising questions with respect to noise characteristics. The object of this paper is to study and model the noise characteristics of electrodes, in particular dry stainless-steel electrodes for acquisition of myoelectric and neuroelectric signals, as a function of electrode area. Typically, a measurement system will be subject to Correspondence should be addressed to Philip A. Parker at the Electrical Engineering Department, University of New Brunswick.
several electrical noise sources of varying importance. The noise sources that can be associated with the electrode are thermal, electrochemical, and amplifier noise current. FLASTERSTEIN (1966a) suggested that electrochemical noise may be generated at the electrode/electrolyte interface presented by surface electrodes on skin. In short, chemical heterogeneities or surface defects become noise sources of electrochemical origin. Experiments conducted by Flasterstein involved placing silver disk electrodes in 0-9 per cent saline solution to isolate this noise source. In his experiments, increasing surface area by 20 : 1 resulted in approximately a 20 : 1 noise reduction. Amplifier noise sources can be modelled as shown in Fig. 1 (NETZER, 1981), where Z e is the magnitude of the effective impedance of the electrode/electrolyte interface, V, is a zero-mean white noise voltage source associated with the amplifier, and 1, is a zero-mean white current noise source associated with the amplifier. Finally, there will be a zero-mean white thermal noise source V,h generated as a result of the resistive component R e of the electrode impedance Z~. For the work which follows in this paper, the noise sources are assumed to be uncorrelated, and are described by their power spectral densities.
Vth Vn
Ze~In
~
First received 24th May 1990 and in final form 4th February 1991
9IFMBE:1991
Medical & Biological Engineering & Computing
0 output noiseless amplifier 0
Fig. 1 Amplifier noise source model N o v e m b e r 1991
585
2 A m p l i f i e r noise parameters A logical first step in evaluating noise is to isolate the amplifier noise components by determining values for V, and I, of Fig. 1, as referred to the output. A schematic of the instrumentation amplifier used in the experiments described in this paper is given in Fig. 2. The amplifier has a DC gain stage of 500 followed by an AC gain stage of 10 for a total gain of 5000. The 3 dB bandwidth of the amplifier is 8 Hz to 10 kHz and the differential input impedance is greater than 100 MfL V+ and V_ are isolated supplies.
obtained for the amplifier voltage noise source (referred to the output):
V~(f) = 3"5 x 10 -9 V2Hz -1
(3)
To determine a value for I,, resistors of values from 2 k ~ to 20 Mf~ were used for Z e at the amplifier input and total noise power and spectra were again observed. Spot value and spectral density due to the current noise source I, will be designated as I . ( f ) and I2(f), respectively. The thermal noise power spectral density V2,h(f) gener-
V-~
inverting input (electrode)
O
I
485 - I' ~ _ D2 485
R1 ]
lkO
V-
~
. 27
[-,
, R8
R9
1
r.lq
I1" U 68k~
O signal output I
LP~ LF441
R3 680k~
R,3 2.2M~
II
;2k~ ~ switch 1 reset V+
R4 680kf~ C2
V§
R2 , noninverting o input (electrode)
_485
I
68k~ R10 33k~
RII
R12 30kQ
D4
Ik~
j
~
trim
IRl5
22k~
22nF
H
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390k~
RI6 offset t_rJ10kQ trim
~85
R17 22kq~
V-
driven guord
o V-
to earth electrode
0
isolated eorth
$
Fig. 2 Low-noise instrumentation amplifier All the operational amplifiers are also supplied from these isolated sources: V§ pin 7; V_ pin 4. To determine parameters V. and I. for this amplifier, several measurements were made. All measurements were performed in a shielded room so as to minimise external interference. With the inputs of the amplifier shorted, Z e = 0, noise power spectral density and total noise power at the output were measured using a Bruel & Kjaer Type 2032 signal analyser. From the model of Fig. 1, this noise is a result of the voltage source II. and from the measurement its magnitude is determined. For simplicity, the spot frequency value due to the voltage source V~will be designated as V.(f) where VnRMS
V~(f) = - ~
V Hz-1/2
(1)
where B is the measurement bandwidth and V.RMs is the RMS value of the voltage source 1,I.. Power spectral density is defined as total power per unit bandwidth and the power spectral density due to I1. will be designated as V2.(f) where 2
V2.(f) = VnRMS V 2 Hz-1 n
(2)
From measurements of V2(f) the following result was 586
ated by Ze and referred to the output can be calculated using Nyquist's equation, i.e.
VZth(f) = 4 k T R e G 2 V z H z - I
(4)
where k = Boltzmann's constant = 1-38 • 10-z3 T = temperature in Kelvin = 300 K R e = electrode resistance in ohms G = voltage gain of system Assuming that the total noise measured at the output is, as modelled, the result of the three uncorrelated noise sources, the noise spectrum at the output Pro(f) can be expressed as
Pvo(f) = V2(f) + 4kTRe(f) G2 + l ,2( f ) Z e2( f ) V2Hz-1
(5)
where Ze(f) and Re(f) are the frequency-dependent electrode/skin impedance magnitude and resistance, respectively. P~o(f) can be measured, V~(f) is known from measurements, and Z e ( f ) = Re(f) because the source inputs are resistive. Hence values for l . ( f ) can be calculated. Values (referred to the output) obtained, as shown in Table 1,
Medical & Biological Engineering & Computing
November 1991
Table 1 Amplifier noise current Z~, kQ l.(50Hz), AHz -1/2
20 200 2000 20000
l.(lOOHz),A H z
2-8 X 10 -9 3"0 X 10 -9 2"5 x 10 -9 2.7 X 10 -9
0"01 m A c m -2. At this density, no current density impedance dependence is to be expected (GEDDES, 1972). As a cross-check, simultaneous impedance measurements were conducted at 400 Hz with a General Radio 1650-A imped-
-U2
2"8 • 10 -9 2,7 X 10 -9 2"5 X 10 -9 2.5 X 10 -9
IO~A
indicate that I . ( f ) for this amplifier may be modelled as a white current source with I.(J') = 2"7 x 10 .9 A H z -1/2
(6)
3 Electrode noise parameters As stainless-steel electrodes are of interest here, in all subsequent measurements the electrodes consist of five matched pairs of circular stainless-steel disks, diameters d = 2.5, 5, 10, 15 and 20mm, made from 2ram stainlesssteel plate. Electrode pairs were placed on the skin surface of the leg or arm with an interelectrode spacing of 30 cm, to ensure that interfaces at the two electrodes were independent. No skin preparation was used except for cleansing the skin with alcohol. To determine and understand the relative contributions of various sources to the total noise power, it is necessary to know electrode impedance as a function of area and and frequency. For the current levels necessary to ensure an electrode current density less than 0 . 1 m A c m -2, as specified by GEDD~ (1972), a measurement method is required which works well at low frequencies and minimal current. A technique outlined by BERGEV et al. (1971) was used for impedance magnitude measurement as it is a simple method which is claimed to work well at low frequencies. Referring to Fig. 3, high-impedance meters are
A
C
B
generator
o
P-
R 'F - - ' - ] ' ~
)b
oT o l T ea_b
)c
eb_c
Fig. 3 Impedance measurement setup. A, B and C designate electrodes, R designates the current-limiting resistor, and ea and et~ designate the electrical potential differences between a and b, and b and c, respectively used to measure potential drops ea-b and eb_ ~. The current ib can be calculated as ea - b
ib -- - ~ - A
(7)
Using high input impedance meters, it is assumed that current through b-c is negligible. Therefore, e ~ will be the drop due to current ib through electrode impedance Zb, i.e.
[ Zb I = eb~ Q ib
(8)
All impedance measurements were made at current levels which gave electrode current densities less than
Medical & Biological Engineering & Computing
g
o
Ac
10
A
I
I
I0
i
I
i ,.i
I
I
[
t
,
10 2
L
,
. .
iJ
10 3
frequency, Hz
Fig. 4 Impedance against frequency for circular electrode diameters of (a) 2"5ram; (b) 5ram; (c) lOmm; (d) 15ram and (e) 20 mm ance bridge. The results were in good agreement. Although the technique outlined by BERGEY et al. (1971) does not provide phase angle, based on work by HARY et al. (1987), the assumption is made that the electrode impedance maintained a constant phase angle, allowing us to define the resistive component R j f ) for any given electrode impedance. A phase angle of - 7 0 ~ is a reasonable average based on experimental findings for pasteless electrodes. Sets of impedance magnitude against frequency measurements were obtained for two subjects over the five pairs of electrodes. The data are plotted in Fig. 4. The impedance magnitude Z j f ) against frequency plots are in very good agreement with published values for pasteless electrodes (BERGEY et al. 1971; HARY et al., 1987). Because the plots for the various sized electrodes show nearly identical slopes, it is apparent that they can all be modelled by the same power function of frequency, i.e. Z e ( f ) = ~(d)f-~
(9)
where a(d) is a constant scale factor which depends on the electrode diameter d.
4 Relative magnitudes of noise components Having determined the amplifier parameters and electrode impedance as a function of frequency, the components of the total output noise power spectra Poo(f) can be compared. From eqn. 4 P~o(f) = V2,(f) + I,2Z e2( f ) + 4 k T R e ( f ) G 2
With the magnitudes of VE(f) and 1,(f) determined earlier and impedance phase angle of - 7 0 ~ plots of the three components of Pro(f) are shown in Fig. 5. It is evident that
November 1991
587
for Z e ( f ) greater than 40 kf~ the current noise term dominates. A further demonstration that, for this amplifier with dry electrodes, the current noise term dominates is to compare a measured Pro(f) with I ,2( f ) Z e 2( f ) for measured values of Ze(f). Fig. 6 shows a plot of Pvo(f) and, for the 5 m m 26 24 x "T N "1-
%
period, to check that conditions remained constant. Impedance magnitude values were normalised to the value at d = 2.5 m m and plotted as a function of electrode diameter. Results at 4 0 0 H z are given in Fig. 7. Values were averaged over the six subjects and the data fitted to a power function, as given in eqn. 10, to obtain electrode
o
22 20 18 16 ]4i 12 10
(IJ
._~
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8
b
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c
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+
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.
20
ii
i
,
40
I
80
impedonce, kQ
Fig. 5
:>
Magnitudes of noise components: ( a ) I 2 ( f ) Z Ze( f ) ; ( b ) V Z ( f ) ; (c) VZ.(f)
'il
+
10 .2
40
6o
i
i
8o loo 120 140 ~60 ~80 2oo
Comparison of measured Pro(f) with values I 2 ( f ) z E ( f ) at f = 20, 50 and lOO Hz (d = 5ram)
of
9 data points diameter electrode, values of 1 2, ( f ) Z e2( f ) at f = 20, 50 and 100Hz. The values of Z e ( f ) at these frequencies are 770, 460 and 250 kfl, respectively. The agreement is very good. The drop in power below 2 0 H z is due to the lowfrequency rolloff of the amplifier. 5 E f f e c t o f e l e c t r o d e area on i m p e d a n c e and noise It is of some interest to determine electrode impedance (strictly the impedance of the electrode/tissue interface) as a function of electrode surface area. Impedance measurements were performed on six subjects at 400 Hz using the General Radio Type 1650-A AC impedance bridge. A frequency of 4 0 0 H z was chosen because it is c o m m o n to both myoelectric signal, and spinal cord evoked potential signals. Fig. 4 presents similar data for a range of frequencies. The electrode current density was maintained at a value less tha 0.01 mA c m - 2 . The effect of area was investigated using the five pairs of stainless-steel circular electrodes. N o skin preparation was used except cleansing the skin with alcohol. Electrode paste was not used as it tends due to smearing to make definition of electrode area difficult. As electrode impedance may decrease with time due to perspiration buildup under the electrode, the first measurement with the smallest electrode was repeated, at the end of the measurement 588
,
,
,
,,,
,
10
,
.
,
. . . .
,
102
impedance as a function of diameter,
frequency, Hz
Fig. 6
,
electrode diameter,mm
Ze(f )
2o
,
Fig. 7 Electrode impedance (normalised) against electrode diameter (A designates mean value over six subjects, + designates +_ one standard deviation)
2 0
,
=
flf -o.7 d -
1.6
~'~
(10)
where fl is a constant scale factor. The correlation coefficient for this data regression is 0.95. While Fig. 7 and eqn. 10 are for data obtained at 400Hz, Fig. 4 indicates that this results holds over at least 10-1000 Hz. If the electrode/ tissue interface is modelled as an ideal circular parallelplate capacitor then
Z e ( f ) o c f - 1"0 d -2"~ which is consistent in form with eqn. 10. The difference in exponents is due, in part, to the fact that a capacitive model is not exact. Noise, as a function of electrode diameter, was determined experimentally for the stainless-steel surface electrodes on the skin over inactive muscle for eight subjects. Table 2 gives noise RMS values referred to amplifier input, against electrode diameter for the eight subjects. D a t a for
Table 2 RMS noise (input, ltV) Diameter mm Subject
2.5
5
10
15
20
A B C D E F G H
21 23 5-7 3-2 26 15 25 6.9
9.0 7.0 3-5 2.1 13 5.2 11 3.0
3-2 4.4 2.0 1.5 3.4 1-7 3.3 1.8
2.0 3.6 1.5 1.3 1.8 1.2 1-9 1.7
1.3 1.7 1.0 1.0 1.2 1.2 1.3 1.2
subject D was omitted from subsequent analysis, as excessive perspiration under the electrodes resulted in poorly defined electrode surface areas. The data from the remaining seven subjects were normalised and averaged to determine electrode noise as a function of diameter. Average normalised RMS noise voltage was plotted as a function of
Medical & Biological Engineering & Computing
November 1991
electrode diameter and is shown in Fig. 8. The slope of the log/log plot will determine the power relationship between noise and electrode diameter. For normalised RMS noise data a slope of - 1.26 with a correlation coefficient of 0.98 was calculated. This indicates that for the data noiseRsls = k d - 1.3 V
(11)
where k is a constant scale factor.
-o o
E O t--
x
10-~
O
x
x
tr) tz
]0-2
,
,
,
A
,
,
, , I
0
,
,
,
,
. . . .
10
10 2
electrode diameter, m m
Fig. 8 R M S noise voltage (normalised) against electrode diameter (A designates mean value over seven subjects, + designates -t- one standard deviation)
Because the dominant source of this noise was shown to be the current noise source associated with the amplifier, noiseRMS can be written in terms of 1 , ( f ) and Z e ( f ) as F/'~
-'11/2
noise.Ms- [ J _ o o I 2 . ( f ) Z ~ ( f ) d f l = AI,(f)d-
(12)
1"6
where
A
room to minimise external interference. For all sets o f electrodes, there was no evidence of an electrochemical noise above amplifier noise. The total noise at the output was identical to that found with the amplifier's inputs shorted, suggesting that the electrodes in saline appear as a short to the amplifier. Impedance measurements were performed at 400Hz on the electrodes immersed in saline. Impedances ranged from approximately 120 / - 2 5 ~ to 750 / - 4 0 ~ Amplifier noise with these source impedances is virtually the same as that for a short input, i.e., the amplifier current noise and electrode thermal noise effects are negligible. This indicates that, even for our smallest electrode, if interracial noise is present within the bandwidth of interest, it is well below amplifier noise. It is possible that significant interracial noise components, as seen by Flasterstein may exist below our bandwidth of interest. Unfortunately, the measurement bandwidth is not reported in the work of FLAST~RSTEIN (1966b). KRAM~R (1983), in work on electrodes in saline, reports finding significant noise components below 6 Hz. The only effect surface area appeared to have on noise was in the stabilisation of motion artefacts. Slight motion in or around the shielded room would cause a great deal of low-frequency noise which would eventually settle out. For larger electrodes this stabilisation would occur within seconds of the disturbance whereas with the smaller electrodes it would take upwards of a minute.
= J_o [flf-~
Equating eqns. 11 and 12 gives noiseRMS = k • d -= = A • l . ( f ) • d - " V
(13)
and therefore k = In(f) • A
and m=n
In experimental findings, m = - 1 - 3 , while n = - 1 . 6 . The slightly smaller slope for RMS noise from measured subjects can easily be accounted for in that it is not likely that most subjects were completely at rest. Any slight myoelectric activity recorded will be almost independent of electrode diameter and will therefore decrease the overall effect of electrode diameter on recorded activity. 6 Interfacial noise To investigate the possibility of electrochemical interracial noise as suggested by FLASTERSTEIN(1966b), measurements were conducted with electrodes suspended in a saline solution. The five sets of circular stainless-steel electrodes were tested. All measurements were performed in a shielded Medical & Biological Engineering & Computing
7 Discussion and conclusions From the results it becomes obvious that surface electrode generated noise will be very amplifier-dependent. Because amplifier designs vary, it will be necessary in a given application to look closely at the amplifiercontributed components of measurement noise and their relative importance. It is recognised that some details of the results are specific to the amplifier used; however, the more important results and conclusions are valid in general. Electrochemical interfacial noise was found to be not significant in the bandwidth 8 Hz-10 kHz. Fig. 5 is a plot of the relative magnitudes of the three noise components as functions of impedance for the amplifier used in this application. It can be seen that the l,(f)Ze(f) component will dominate for impedances greater than 4 0 k ~ . Typically, for dry electrodes of diameters used in the experiments, and over the frequency range of interest, impedances exceed this value. In principle, for a given source impedance, it is possible to miniraise amplifier-generated noise by matching the source to the amplifier through an appropriate transformer. However, at the source frequencies of interest here this is not very practical. Different amplifier designs will result in different specifications for V, and I,. The only noise component which will not be amplifier design dependent will be the thermal noise generated as a result of the resistive component of the electrode/electrolyte impedance. Assuming that it would be possible to reduce the current noise component without degrading the voltage noise generated by the amplifier, surface electrode noise will be limited to a theoretical minimum, i.e. the thermal noise component of the electrode resistance. The findings can be generalised to two situations. A worst-case situation can be defined where the noise is predominantly current source related and the RMS noise increases linearly with impedance. A best case or 'ideal' situation would occur where the amplifier contributes negligible noise and measurement noise is thereby limited to electrode thermal noise and increases as the root of imped-
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ance. The R M S noise values can then be defined in terms of electrode diameter d as noiseR~s oc d - ~.6
(14)
for the current noise source d o m i n a n t case, and noiseRMs oC d - ~
(15)
for an ideal amplifier. Acknowledoment--This work was supported in part by NSERC grant CRD 0039083. The authors wish to acknowledge the contribution of Dr D. F. Lovely to this work through the amplifier design of Fig. 2.
References BERGEY,G. E., SQUIRES,R. D. and SIPPLE,W. C. (1971) Electrocardiogram recording with pasteless electrodes. IEEE Trans., BME-18, 206-211. FLASTERSTEIN, A. H. (1966a) Voltage fluctuations of metalelectrolyte interfaces. Med. & Biol. Eng., 4, 583-588. FLASTERSTEIN,A. H. (1966b) A general analysis of voltage fluctuations of metal electrolyte interfaces. Ibid., 4,. 589-594. GEDDES, L. A. (1972) Electrodes and the measurement of bioelectric events. Wiley-Interscience, New York. HARY, D., BEKEY, G. and ANTOUELLI,D. (1987) Circuit models and simulation analysis of electromyographic signal sources-I: The impedance of EMG electrodes. IEEE Trans., BME-34, 91-97. KRAMER, G. S. (1983) Influence of electrode on bioelectric signal recording. J. Clin. Eng., g, (3), 243-247. MCKINLEY, C. A. and PARKER,P. A. (1991) A beamformer for the acquisition of evoked potentials. IEEE Trans., BME-38, 379382. NETZER, Y. (1981) The design of low-noise amplifiers. Proc. IEEE, 69, 728-740.
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Authors" biographies Donna T. Godin received the B.Sc.Eng. and M.Sc.Eng. degrees in Electrical Engineering from the University of New Brunswick, Fredericton, New Brunswick, Canada, in 1986 and 1988, respectively. She is currently working as a hardware design engineer with Bell Northern Research in Ottawa, Ontario. Philip A. Parker received the B.Sc. degree in Electrical Engineering from the University of New Brunswick, Fredericton, New Brunswick, Canada, in 1964, the M.Sc. degree from the University of St. Andrews, Scotland, in 1966 and the Ph.D. Degree from the University of New Brunswick in 1975. He is currently Professor of Electrical Engineering at the University of New Brunswick and a research consultant to the Bio-Engineering Institute there. His main research interests are in the areas of biological signal processing. Dr Parker is a member of the Canadian Medical & Biological Engineering Society. R. N. Scott has been director of the Bioengineering Institute at the University of New Brunswick (UNB) since its inception in 1965. Besides his administrative duties he is actively involved in the clinical application of technology, especially in the field of myoelectric control. He is also a Professor of Electrical Engineering at UNB, holding a B.Sc. in Electrical Engineering from UNB (1955) and D.Sc. from Acadia University (1981). He is a registered Professional Engineer, a Certified Clinical Engineer, a Fellow of the Canadian Medical & Biological Engineering Society, a Senior Member of the IEEE and a member of several other societies.
Medical & Biological Engineering & Computing
November 1991
