BJORNTORP,P. (1982): 'Hypertension and exercise,' Hypertens., 1, Suppl. III, pp. 56-59 BLAIR, S. N., GOODYEAR,N. N., GIBaONS, L. W., and COOPER, K. H. (1984): 'Physical fitness and incidence of hypertension in healthy normotensive men and women,' J. Am. Med. Assoc., 252, pp. 487-490 BORG, G., and LINDERHOLM,H. (1967): 'Perceived exertion and pulse rate during graded exercise in various age groups,' Acta. Med. Scand., 472, Suppl., pp. 194-206 BRYDON,J. (1976): 'Automatic monitoring of cardiac arrhythmias' in HILL, D. W., and WATSON, B. W. (Eds.): IEE Medical Electronics Monographs Nos. 18-22. (Peter Peregrinus Ltd., Stevenage) pp. 27-41 BURKE, M. J. (1990): 'A microcontroller based athletic cardiotachometer'. PhD Thesis, Trinity College, Dublin BURKE, M. J., and WHELAN, M. V. (1987): 'The accuracy and reliability of commercial heart-rate monitors,' Br. J. Sports Med., 21, pp. 29-32 GOLDEN, D. P., WOLTHUIS,R. A., and HOFFLER,C. W. (1973): 'A spectral analysis of the normal resting electrocardiogram,' IEEE Trans., 20, pp. 366-372 Ko, W. H., and HYNECEK,J. (1974): 'Dry electrodes and electrode amplifiers' in MILLER, A. C., and HARRISON, D. C. (Eds.) 'Biomedical electrode technology' (Academic Press, London) pp. 169-181 MAXEIELD,M. E., and BROUHA,L. (1963): 'Validity of heart rate as an indicator of cardiac strain,' J. Appl. Physiol., 18, pp. 1099-1104 MCCLELLAN, A. D. (1981): 'Extracellular amplifier with bootstrapped input stage results in high common-mode rejection,' Med. Biol. Eng. Comput., 19, pp. 657-658 MOREHOUSE, L. E. (1972): 'Exercise heart rate' in 'Laboratory
manual for physiology of exercise' (C. V. Mosby Co., London) pp. 63-74 MORRIS,J. N., EVER1TT,M. G., POLLARD,R., CHAVE,S. P. W., and SEMMENCE. A. M. (1980): 'Vigorous exercise in leisure-time: protection against coronary heart disease,' Lancet, 2, pp. 1207-1210 PAFFENBARGER, R. S., and HYDE, R. T. (1980): 'Exercise as protection against heart attack,' New Eng. J. Med., 302, pp. 1026-1027 PALLAS-ARNEY,R. (1986): 'On the reduction of interference due to common mode voltage in two-electrode biopotential amplifiers,' IEEE Trans., BME-33, pp. 1043-1046 SHEPARD, R. J. (1978): 'The physical working capacity of the athlete' in 'Human physiological work capacity' (Cambridge University Press, Cambridge) pp. 136-178 SMITH, E. L., and GILLIGAN, C. (1983): 'Physical activity prescription for the older adult,' Physician Sportsmed., 11, (8), pp. 91-101 TAYLER, D., and VINCENT, R. (1983): 'Signal distortion in the electrocardiogram due to inadequate phase response,' IEEE Trans., BME-30, pp. 352-356 THAKOR, N. V., WEBSTER, J. G., and TOMPKINS, W. J. (1984): 'Estimation of QRS complex power spectra for design of a QRS filter,' IEEE Trans., BME-31, pp. 702-706 THIVIERGE, M., and LINER, L. (1986): 'Validite des cardiotachometres,' L 'Entraineur, April-June, pp. 28-29 WINTER, B. B., and WEBSTER, J. G. (1983): 'Reduction of interference due to common mode voltage in biopotential amplifiers,' IEEE Trans., BME-30, pp. 58-62 ZIpP, P., and AHRENS,H. (1979): 'A model of bioelectrode motion artefact and reduction of artefact by amplifier input stage design,' J. Biomed. Eng., 1, pp. 273-276
1 Introduction
2 Frequency r e q u i r e m e n t s
IN THE bioelectric field there is a requirement to stimulate tissue and measure its response. In bioimpedance, especially electrical impedance tomography, there is a requirement for the accurate application of current and measurement of voltage; the latter with an amplitude error equal to or less than 0"1% (BROWN and SEAGER, 1987). A wide-band approach has been adopted to allow the possibility of tissue characterisation and detecting pathology by impedance spectroscopy (SINGH et al., 1979; GRIFFITHS, 1988).
Tissue distinguishability depends on the probe current frequency; 100 kHz for intracellular/extracellular structures in muscle, 2 5 0 k H z for liver, 5 0 0 k H z - 1 M H z for fat and > 3 M H z for blood, (GRIFFITHS, 1988; RIU I COSTA, 1991). For bioelectric work, a bandwidth of 10 kHz is sufficient for the fast moving signals observed in electromyography (DE LUCA, 1988). Errors in impedance measurement result from errors in both voltage and current. In four-point impedance measurement, the current source must have at least 5 M ~ output impedance and very low capacitance for the required accuracy. This is difficult to achieve for the required bandwidth. This design proposes a novel voltage source
First received 18 March and in final form 9 August 1993
9 IFMBE: 1994 Medical & Biological Engineering & Computing
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683
The stability as determined by the phase margin is (CLAYTON, 1979) 4),,
Rc
= -.-5
-=-
I I i
Fig. I
Active electrode configuration--the circuit to the right of the dashed line; the circuit on the left models the electrode and object impedances; the impedance Z~ represents the electrode impedance; for the SPICE simulation, the switch was modelled by a pi network of 50 Q resistance and 2 pF either side to 9round for stray capacitance; the object Ro was modelled by a resistor of 100 Q
from which the resulting current is measured; this design is similar to the design published by Lidgey et al. (LIDGEY et al., 1992). 3 Electrode circuit c o n f i g u r a t i o n
The active electrode structure proposed is shown in Fig. 1. The device is intended to operate in differential mode, but only half is shown for convenience. It has two functions, a current-sensed voltage source and a voltage detector. With the switch S1 open, the structure operates as voltage buffer to voltages observed on the electrode, denoted by impedance Z~; when it is closed, it operates as a current-sensed voltage source (CSVS). This configuration has two advantages; the output node has low impedance and the current sense resistor is not a burden to the load circuit. 4 C u r r e n t sensed v o l t a g e source
Referring to Fig. 1 with $1 closed, the output voltage of amplifier A2 is V~Ao/(1 + [3Ao) where fl = (Z~w + Z~ + Ro)/(Z~ + Z,,, + Ro + R~), Z~, is the impedance of the switch network, Z, is the electrode impedance, R~ is the feedback resistance of A2, R o is the resistance of the object and A o is the open loop gain of the operational amplifiers. The current i in the load of Zsw+ Z ~ + R o
(f~2/f,)
tan_l
=
where f~ is the frequency at which the feedback network response intercepts the amplifier open loop response, and f~2 is the 3 dB break point frequency of the feedback network. In practice, the switch $1 is electronic, and is therefore finite on resistance and stray capacitance to earth. The dominant network on the inverting terminal is the switch modelled by an R - C pi network. The additional impedance of the electrode and object increases fez, thereby increasing the stability at frequencies > 1 MHz. The phase margin now becomes
\
4~,. = t a n - 1
R~I ( T I + "r2)Ao
where Rs~ is the analogue switch resistance, and rt and ~2 are the time constants of the switch network, r,o is the equivalent amplifier time constant of A2. It is therefore important to keep the switch time constants as small as possible. Typically for a phase margin > 30 ~ (results in gain peaking of ~ 6 dB), r t + ~2 = 240 x 10 -12 S, which translates to a total stray capacitance of < 5 pF for a 50D resistance of S 1. In the combined circuit, there are two other constraints to limit the error in the supplied current sensed across Rc. First, the capacitance of S1 and the capacitance of the electrode impedance form a divider. For example, for a 10 nF electrode capacitance, the error is increased by 0-1% for every additional 10 pF in the capacitance of S1. Secondly, the electrode resistance forms a potential divider with the input resistance of A3. Thus, for an error of <0"1%, the A3 input resistance should be more than 1000 times the largest electrode resistance. The other important factor is the common-mode rejection required to measure the current supplied by the source, A2. Referring to Fig. 1, the differential voltage Vd = iR~ and the common-mode voltage V~,,= i R J 2 + i ( Z , + Z , ~ + Ro). For the ratio Vd/V~,, to be large, R, must be large; however, in the limit for R , > > ( Z , + Z s ~ + Ro), this ratio will approach 2. R~ is further limited by the output voltage swing of the source amplifier. In magnitude alone for Z , = 2 0 0 f ~ and Z , ~ = 100Q, the common-mode rejection ratio of the differential amplifier (to measure Vd) Active Electrode 1, Active Electrode 1, Active Electrode 1, Date/-fime run: 07/28/93 16:42:34 Temperature: 27"0, 27.0, 27.0 .... 102
i = ( V _ -- Vo)/R ~
* ..................
10o~ .
.
.
* ..................
.
.
4- .................
-,---: . . . . . . . . . . . . . .
.
-+
t
V " -- Vo is measured and therefore 99 ; . . . . . . . . . . . . . . . . . . * . . . . . . . . . . . . . . . . . . +-. . . . . . . . . . . . . . . . . + . . . . . . . . . . . . . . . . . . t 0d *,=---'--. (_V(.5.:6)/!0_,.0s O_0_/!(.R..L1.).. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
i = (V'_(1 + 1/Ao) - Vo)/Rr If the response is taken to be first order, then the magnitude of the error e is =
x/((1 + (1/Ao)Z)/R~)
and the phase error ~~
- t d q d ~ . ~ ....... Y 6 ~ z .......... io67A~ ......... ~ - 5 ~ frequency, Hz
The phase error between the input voltage V~ and the applied current i is not significant as the resulting current magnitude and phase are now measured. 684
......... l O - ~ . z
VP(6,6) - VP(8)
~~ = tan-1 ( _ 1/Ao) Fig. 2
(a) Magnitude current error (%) of the CSVS: (h) phase error ('~) for three electrode impedances of 100 ( D ) , 500 ( 9 ) and 1000 (<) ) Q in series with 10 nF
Medical & Biological Engineering & Computing
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must be at least 60 dB (for 0.1% error) but, because of the small output impedances of At and A2, this is easily achieved. In electrical impedance tomography, measurement errors are minimised by driving the common mode voltage to zero at the measurement point. In the differential mode with two sources, this may easily be achieved by adjusting the relative amplitudes of the input voltage V~to each CSVS.
Active Electrode 1 volt detector and... Date/time run: 07/28/93 15:55:26 Temperature: 27.0, 27.0, 27.0 .... 1-000V t ................. § . . . . . . . . . . . . . . . . . ~ . . . . . . . . . . . . . . . . . +. . . . . . . . . . . . . . . . . .
0"999V t
0"998V [ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1 '000d
9 v(7)
- ~ ...............
a
..................
§ .................
~- . . . . . . . . . . . . . . . . .
+..................
0"000d
5 Voltage detector The measured voltage is buffered by the high input impedance of amplifier A3, whose error is determined by its open loop bandwidth. The stray capacitance of S1 was modelled by a 2 pF capacitor between the non-inverting input and ground. For bioelectric work, for a 2 KHz bandwidth, the calculated noise of an AD843 buffer with a 2 Kf2 source resistance was 5-8/xV peak to peak. This would be unacceptably high for myoelectric work. However, by replacing the buffer, A3, with an OPA627, this is reduced to 0-3 #V peak-to-peak and the bias current is reduced from 600 pA to 1 pA. Furthermore, as mentioned in Section 4, the higher input resistance of this amplifier decreases the error in the measured current. For accurate voltage measurement, at high frequency the input capacitance must be low; both the AD843 and OPA627 have an input capacitance of 8 pF. 6 S P I C E simulation The active electrode structure was simulated in PSPICE (PsPlCE, 1989), with expected electrode impedances given by Riu (RIu, 1991) and the analogue switch S1 modelled as a pi R-C network with 50 ~ resistance and a 2 pF capacitance to ground at each end modelling the strays. The isolation capacitance when the switch was open was set to 1 pF. Operational amplifier A2 was AD843 with a 32 MHz gain bandwidth, and the two buffers A1 and A3 were OPA627 with a 16 MHz gain bandwidth. All the amplifier outputs were loaded with 10K~, and input signals were 1V peak-to-peak. The upper trace in Fig. 2 displays the error in current as a percentage ratio of supplied current and current measured from CSVS, and the lower trace shows the phase error. The error was found to increase with electrode resistance, ranging from 0.1% and 1-2~ for an electrode resistance of 200 f2 to 1% and 5.6 ~ for 1000 ~ at 1 MHz. Fig. 3 shows the error in measured voltage and phase (0.25% and 4 ~ at 1 MHz) with frequency. 7 Discussion In four-point impedance measurement, the lowest common-mode voltage is achieved from a differential current source balanced about the measurement reference. If these were current sources with 5 M ~ output resistance, a 1 pA imbalance current would produce a 5 V commonmode voltage; in contrast, for voltage sources, this imbalance current would only produce 10 ~tV error from a 10 f2 source. The phase and amplitude adjustment of the drive for minimum common-mode voltages is therefore less critical for voltage sources than for current, sources. Impedance measurement using voltage sources forces the object to have a low impedance to ground (in contrast to a high impedance with current sources), thereby making the measurement less susceptible to electrically induced noise.
Medical & Biological Engineering & Computing
- - 5 90 0 0 d
~'- . . . . . . . . . . . . . . . . . . . . . . . . . . .~. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .-.-.-. -. -. .- - - - - - - - - - - - - , - - -
1
kHz
10 k H z
100 kHz
1 0 MHz
10 MHz
vp(7) - vp(8)
frequency, Hz b
Fig. 3 Bode plot of the voltage buffer circuit, (a) voltage error (input voltage = 1 V) ; (b) phase error (~ ; the three curves are for the same electrode impedances given in Fig. 2; the - 6 0 Q V error results Jrom the capacitor divider between the electrode capacitance and input capacitance
8 I m p l e m e n t a t i o n in silicon Within the Eurochip programme, there are available technologies which can provide the gain bandwidths required but only for a supply voltage of 5 V. For R c of 1 Kf2, this limits the applied current to 1 mA. We expect to integrate this structure in the near future. Flip chip or a surface amount assembly might also be considered as an intermediate solution. Acknowledgments--The authors would like to acknowledge the support of the SERC, UK, and the EC Concerted Action on Electrical Impedance Tomography for supporting this work.
References BROWN, B. H., and SEAGER, A. D. (1987): 'The Sheffield data collection system,' Clin. Phys. Physiol. Meas., 8, (suppl. A), pp. 91-97 CLAYTON, C. B. (t979): 'Operational amplifiers' (NewnesButterworth) DE LUCA, C. J. (1988): 'Encyclopedia of medical devices and instrumentation' in WEBSTER, J. G. (Ed.) 'Electromyography' (John Wiley), Vol. 2, pp. 1111-1122 GRIFFITHS, H. W. (1988): 'A phantom for electrical impedance tomography,' Clin. Phys. Physiol. Meas., 9, (suppl. A), pp. 15-20 LIDGEY, F. J., ZHU, Q. S., McLEOD, C. N., and BRECKON, W. R. (1992): 'Electrode current determination from programmable voltage sources,' Clin. Phys. Physiol. Meas., 13, (suppL A), pp. 43-46 PSPICE (1989): Microsim Corporation, 20 Fairbanks, Irvine, California 92718 RIU, P. J., LOZANO, A., FERNANDEZ, M., and PALLAS-ARENY,R. (1991): "Electrode requirements for electrical impedance tomography'. IV Int. Symp. on Biomed. Eng., Pefiiscota, Spain, pp. 141-142 Rxu I COSTA, J. (1991): 'Deteccio d'estructures estatiques en el cos huma usant metodes multifrequencia en tomografia d'impedancia electrical PhD Thesis, Universitat Politecnica Catalunya, Barcelona S~NGH, B., SMITH,C. W., and HUCHES, R. (1979): "In vivo dielectric spectrometer,' Med. Biol. Eng. Comput., 17, pp. 45-60
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