Med. & biol. Engng. Vol. 7, pp. 321-324. P e r g a m o n Press, 1969. Printed in G r e a t Britain
SIX-ELECTRODE METHOD FOR THE M E A S U R E M E N T OF THE PASSIVE ELECTRICAL PROPERTIES OF BRAIN ENVELOPES* M. RAYPORT and B. SANDLER The Department of Neurological Surgery, Albert Einstein College of Medicine, Bronx, New York 10461, U.S.A. Abstract--In a previously-described four-terminal electrical model consisting of six branch impedances representing the passive electrical properties of the brain envelopes, alternating current signals were applied directly to two terminals of the tissue electrode system for determination of the lumped impedances of the model and for observation of transmission through the system. To obtain impedance values of the electrode-tissue system which would be representative of tissue impedance, electrode polarization impedance of the four electrodes of the model has been reduced by applying the signals to two additional electrodes inserted into the brain to form a dipole signal generator. An electronic half-bridge technique augments the sensitivity of the measurements. INTRODUCTION A FOUR-TERMINALelectrical model consisting of six branch impedances has been previously described to represent the passive electrical properties of the brain envelopes. Alternating current signals were applied directly to two terminals of the tissue-electrode system for the determination of the lumped impedances of the model and for observation of transmission through the system, (RAYPORT, SANDLER and KATZMAN, 1966). The silver-silver chloride electrodes employed were expected to show minimal polarization effects. However, with measurements made at low signal frequencies relevant to the frequency range of the clinical electroencephalogram, the contribution of electrode polarization to the impedance of the electrode-tissue system was likely to be significant. To obtain impedance values of the electrode-tissue system which would be more representative of tissue impedance, it appeared desirable to minimize electrode polarization impedance by reducing the current flow through the four electrodes of the model. Two additional
electrodes were therefore inserted into the brain to form a dipole signal generator. To increase the sensitivity of the measurements, an electronic half-bridge technique (FERRIS, 1963) was substituted for the previously described fullbridge and phase shift method. METHODS Adult cats were used, unselected as to age and sex. Under intravenous pentobarbital anaesthesia, the scalp was chemically epilated. After left hemicraniectomy, bilateral midcollicular decerebration was carried out and the left hemisphere removed. The soft tissues and skull of the right hemicranium were preserved intact. The arrangement of the six electrodes is portrayed in Fig. 1. A pair of calomel electrodes~ (O1 and 02) was placed on the right parietal scalp. The interelectrode distance O1-O2 was 1 cm. The calomel half-cells were linked to the scalp by an electrolyte column of 2-5 M KC1. A pair of chlorided silver ball electrodes (/1 a n d / 2 ) were placed against the inner surface of
*Received 12 April 1968; in revised form 18 November 1968. t Coming Scientific Instruments, Medfield, Massachusetts, Catalog No. 476017. 321
322
M. R A Y P O R T and B. S A N D L E R
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the transected corpus callosum. The holder of the plastic rod permitted rotation of the latter around its longitudinal axis for various orientations of the dipole within the brain. The signal electrodes St, $2 were connected into the upper arm of the half-bridge as shown in Fig. 2. The four-electrode array/1, 12, a t , 02, which defines the six-branch passive electrical model of the brain envelopes, was connected to amplifier A1 according to the shorting procedure previously described. Sine waves were applied from a signal generator (Hewlett-Packard, Model 200 CD) to an isolation transformer XF (General Radio, Model 578-A). The peak-topeak amplitude of the applied signal was 500 inV. Frequencies employed were 10, 100 and 1000 Hz. Ro and Co were decades of 5 per cent resistors and capacitors. Amplifiers At and A2 (Grass Instrument Company, Model P-5) were matched for signal amplification and phase shift. Their floating outputs were interconnected so as to subtract the amplified signals. The resultant signal was amplified in A3 (Tektronix, Type 122) and passed through a variable multipurpose filter (A.P. Circuit Corporation,* Model 250) in
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FIG. 1. Schema o f the six-electrode array.
the right parietal dura 1 cm apart, radially opposite the emplacement of a t and 02 respectively. In some experiments,/1 and 12 were calomel electrodes identical to a t and 02. Two bright platinum electrodes (St and $2) with ball tips 1 mm dia. 2.5 mm apart on centers and imbedded into the end of a plastic rod 3mm dia. were inserted into the centrum of the right hemisphere through a pial incision just above
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FIO. 2. Connection diagram for the half-bridge six-electrodemethodfor measurements of impedance of the brain. * 865 West E n d Avenue, New York, N e w York.
PASSIVE ELECTRICAL PROPERTIES OF BRAIN ENVELOPES the band pass mode. The filtered signal was displayed on an oscilloscope serving as a null detector. The bridge was balanced when the voltage across the decades was equal in magnitude and phase to the voltage across the four-electrode array. To achieve balance, the values of R o and CD were adjusted until a 'null' was obtained. The advantage of the six-electrode system is two-fold: (1) little current flows through the four-electrode network defined b y / 1 , 12, O1, 02 if the input impedance of At is high. Electrode polarization impedance is thus minimized and the measured impedance correspondingly more representative of the tissue impedance. (2) The value of tissue impedance can be read directly, from the decades, at all frequencies used. Signal attenuation was determined during transmission through the brain (St, $2 t o / 1 , / 2 ) and through the brain envelopes (It, /2 to O1, 02). F o r comparison, observations were also made at I~, /2 and at Or, O2 with the signals applied to S1, $2. RESULTS The impedance values of the electrode-tissue model were indeed smaller when measured with the signal applied to St, $2 by the six-electrode method than when the signal was applied directly t o / 1 a n d / 2 . This reduction in impedance values was similar whether electrodes/1, I2 consisted 350
323
of calomel half-cells or silver-silver chloride ball electrodes. The measured values of resistance were low with the six-electrode method, the effect of the shunting capacitances was not detectable. The original model of six resistances and parallel capacitances was thus reduced to a network of six resistances. It must be noted that the actual impedance values of the model remain in part dependent on the configuration and size of the four electrodes/1,/2, O1, 02. Examples of R and C of the model at 10, 100 and 1000 Hz are shown in Fig. 3 and Table 1. Table 1. R and C of the model with sine waves at 10, 100 and 1000 Hz
10 Hz
100 Hz
1000 Hz
R
C
R
C
R
C
(fl)
(#F)
(f~)
(/~F)
(f~)
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270
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250
0"6
250
0-03
350
--
330
0"7
340
0"05
625
--
580
1"1
600
0"12
385
--
375
0-8
375
0'06
395
--
340
0"8
355
0"03
380
--
390
0-9
400
0"03
The calculated signal attenuation between electrode p a i r s / 1 , 12 and O1, 02 is computed to be 1 : 6 4 , 1 "48 and 1 : 5 8 at 10, 100 and 1000 Hz respectively. The observed attenuations were of the same order of magnitude. by the United States Public Health Service Grant NB-06851-01 from the National Institute of Neurological Diseases and Blindness. Dr. RAYeORT Was recipient of a Career Scientist Award from the Health Research Council of the City of New York. Acknowledgements----Supported
625
270.
REFERENCES
Oz 385
FXG. 3. Four-terminal lumped parameter model. The values of resistance are in ohms. Sine waves 10 Hz.
FERmS, C. D. (1963) Four-electrode electronic bridge for electrolyte impedance determinations. Rev. scient. Instrum. 34, 109-111. RAY1,ORT, M., SANDLER,B. and KATZMAN,R. (1966) Observations in the passive electrical properties of the envelopes of cat brain. Eleetroenceph. clin. NeurophysioL 20, 513-519.
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M. RAYPORT and B. SANDLER M E S U R E D E S PROPRI]~TI~S ] ~ L E C T R I Q U E S P A S S I V E S D E S M I ~ N I N G E S L ' A I D E D E LA MI~THODE DES SIX ]~LECTRODES Sommaire--Un module 61ectriquequadripolaire d6crit pr6alablement se compose d'un r6seau de six imp6dances repr6sentant les propri6t6s 61ectriques passives des m6ninges. On applique des signaux p6riodiques directement sur deux des p61es du syst~me tissu-61ectrodes, de mani~re ~t mesurer l'imp6danee globale du modble et h observer les propri6t6s de transmission du syst~me. On cherche g obtenir des valeurs d'imp6dances du syst~me tissu-61ectrodes qui seraient repr6sentatives de l'imp6dance des tissus; pour cela, on applique les signaux ~t travers deux 61ectrodes suppl6mentaires ins6r6es dans le cerveau et formant un g6n6rateur de signaux dipolaire, de mani~re ~t r6duire l'imp6dance de polarisation des quatre 61ectrodes du module. La technique de demi-pont 61ectronique augmente la sensibilit6 des mesures. SECHS-ELEKTRODEN-METHODE ELEKTRISCHEN
ZUR MESSUNG
EIGENSCHAFTEN
DER PASSIVEN
DER HIRNHOLLEN
Zusammenfassung--In friiheren Mitteilungen wurde ein 4-terminales elektrisches Modell beschrieben. Es besteht aus sechs Zweigimpedanzen, welche die passiven elektrischen Eigenschaften der Hirnhiillen repr~isentieren. Wechselstromsignale wurden auf zwei Terminale des Gewebselektrodensystems direkt gegeben, um die Gesamtimpedanz des Modells zu bestimmen und um die Transmission durch das System zu beobachten. Um Impedanzwerte des Elektroden-Gewebe Systems zu erhalten, welche die Gewebsimpedanz repr/isentieren, wurde die Elektrodenpolarisationsimpedanz der vier Elektroden des Modells vermindert, indem die Signale auf zwei zusfitzliche, in das Gehirn gebrachte Elektroden gegeben werden, um einen Dipolsignalgenerator zu bilden. Ein elektronisches Halbbrtickenverfahren erh6ht die Empfindlichkeit der Messungen.