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IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 35, NO. 8, AUGUST 1988 649whereP;,j = ( l / T ) c [ X , ( t )- p ( t ) I 2 ( j = 1, . . , J ) , ( A . 2 )f-P = ( 1 / ~ ) G , j , (4.3)

( A . 4 )I

R = ( l / T ) c [ X ( t ) - &)I2.fUnder the assumptions given in Section 11, it can be shown thatthe variable J 1 / 2 [ J / ( J- l ) ] R tends in probability to zero as Jtends to inf in i ty . Therefore, the asymptot ic jo int d is tr ibut ion of

J / 2 ( 6 i- u i ) an d J / 2 ( 6 ;- u i ) (4.5)is the same as that of

J 1 / 2 [ 1 6 z- E ( F ; ) ] an d J / 2 [ 1 6 x- E ( F x ) ] ( A . 6 )where px s the average of the var iables Px , jdefined by (14).The var iables P;,j are independent and identically distributed(iid) unbiased estimators of u i . Similar ly , the var iables PX,,re iidunbiased estimators of u; . According to the mult ivar iate centrall imit theorem, the asy mptot ic jo int d is tr ibut ion of the var iablesgiven in (A.6) is normal if the variances of Px.j an d P;,j are finite.These var iances are complicated funct ions that can be expressed a sthe sum of terms involving the s ignal power , the noise power , thethird and fourth moments of the noise process, and cross productterms of degree less than four. They can be shown to be finite underthe assumptions given in Sect ion 11.In order to prove the asymptot ic normali ty of SNR, e write thisestimator in the form SNR = ( I ? $ / & ; ) - 1. Applying a theoremon differentiable functions of asymptotically normal variables [ 5 ,ch . 5 , theorem 1.91, we have that J 12 (SN R - SNR) is asymptot-ically normal with m ean ze ro and var iance given by J times (16).

A P P EN D I X 1: ESTIMATION F V ar (a$), V ar ( I ? ; ) A N Dc o v ( I ? $ , 6 ; )The unknown var iances and covar iances in (16) could be es t i -mated by writing dow n expressions for these parameters in termsof the properties of the signal and noise and replacing unknownquanti t ies by es t imates . H owever , these express ions are very com-plicated and require estimation of higher ord er moments of the noiseprocess. A simpler estimation procedure is suggested here.A natural es t imator of the var iance of Px,J s

[ 1 / ( ~ ( P x , j - Pxf. (4.7)[ 1 / ( J - 1 I -Gf. (4.8)

Equation (18) is obtained by noting that Var ( 6 ; ) = V ar ( P x , j ) / J .Similar ly , a n es t imator of the var iance of P& is-

Because the variables P;,J depend on the unknown s ignal , we sub-stitute P N , j or and obtain (19) by noting that

Va r ( 6 : ) = [ J / ( J - I ) ] Var (7 iN)= [ J / ( J - l ) ] V a r ( P N , , ) / J . ( A . 9 )

The term J / ( J - 1) can be neglected in the asymptot ic argumen t ,but is important in practical applications when J is small .Equation (20) is obtained in an analogous manne r .REF EREN CES

[ I ] N. J . Bershad and A. J . Rockmore, On estimating signal-to-noiseratio using the sample correlation coefficient, IEEE Trans. Inform.Theory, vol. IT-20, pp. 112-113, 1974.[ 2 ] E . Callaway and R. A. Halliday, Evoked potential variability: Ef-fects of age, amplitude and methods of measurement, Elecrroen-cephalogr. Clin.Neuro p hys io l . , vol. 34, pp. 125-133, 1973.[3 ] R. Coppola, R. Tabor, and M . S . Buchsbaum, Signal to noise ratio

and response variability measurements in single trial evoked poten-tials, Electroencephalogr. Clin.Neurophysiol . , vol. 44, pp. 214-222,1978.[4] C. Elberling and M. Don, Quality estimation of averaged auditorybrainstem responses, Scand. Audiol . , vol. 13 , pp. 187-197, 1984.[5] E. L. Lehmann, Theory ofpoin t Estimation. New York: Wiley, 1983.[6 ] J . Mocks, T. Gasser, and P. D. Tuan, Variability of single evokedpotentials evaluated by two new statistical tests, Elecrroencephalogr.Clin. Neuro p hys io l . , vol. 57, pp. 571-580, 1984.[7] B. I. Turetsky, J . Raz, and G. F ein, N oise and signal power and theireffects on evoked potential estimation, Electroencephalogr. Clin.Neuro p hys io l . , to be published.

Skin Impedance From 1 Hz to 1MHzJAVIER ROSELL, JOSEP COLOMINAS, PERE RIU,RAMON PALLAS-ARENY, AN D JOHN G . WEBSTER

Abstract-We measured the impedance of skin coated with gel, butotherwise unprepared from 1 Hz to 1MHz at ten sites on the thorax,leg, and forehead of ten subjects. For a 1 cm2 area, the 1Hz impedancevaried from 10kR to 1 MR, which suggests that biopotential amplifierinput impedance should be very high to avoid common mode to differ-ential mode voltage conversion. 1 MHz impedance was tightly clus-tered about 120 R . 100 kHz impedance was about 220 R,which sug-gests that the variation in skin impedance may cause errors in twoelectrode electrical impedance tomographs.

INTRODUCTIONThe m agnitude of skin impedance is of in teres t to des igners andusers of medical ins truments . Berson et a l . [l ] measured 10 Hzskin impedance at sev en locat ions on 24 subje cts and found valuesas high as 3.5 MS2.cm2 ( larger areas yield lower impedance) .Swanson and Webs ter [2] measured skin impedance on one subjectf rom 1 Hz to 1 MHz and found that for 1 cm2, the high impedanceat low frequencies decreased to a low value of about 200 !lt 1MHz. Abras ion of the skin produced a low impedance over theentire frequency range.We des ired to measure the skin impedance over a large f re-quency range at a var iety of locat ions on the body. T hus , the resul tsshould be applicable when m easur ing biopotent ials such as EC G,

EEG , E M G , EN G , EO G , EG G , and in b io impedance meas u re -ments such as electr ical impedanc e plethysmography, impedancecardiography, and electr ical impedanc e tomography.M ETH O D S

Fig. 1 shows the ten skin s i tes we tes ted on each of ten subjects .Others [3] have frequently tested the skin impedance on the ventralforearm because i t is a convenient s i te for a person to measure hisown skin impedance. In contras t , F ig . 1 shows that we selecteds i tes typical ly used when measur ing the ECG, impedance pleth-ysmography, impedance cardiography , and electr ical impedancetomograp hy. We selected s i tes that were f lat or convex because i tManuscript received October 9, 1987; revised March 2 5 , 1988. J . G .Webster was supported by the Fulbnght Professor/Specialist ExchangeProgram sponsored by la Caix a, the Fullbright Commission in Madrid, andthe United States Information Agency.J . Rosell, J . Colominas, P. Riu, and R. Pallas-Areny are with the De -

partamento de Ingenieria Electronica, D ivision de Instrumentacion y Bioin-genieria, U.P.C., 08080 Barcelona, Spain.J . G . Webster is with the Department of Electrical and Computer En-gineering, University of Wisconsin-Madison, Madison, WI 53706.IEEE Log Number 8821505.0018-9294/88/0800-0649$01OO 0 9 8 8 I E E E

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650 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 35, NO. 8 , AUGUST 1988

ELECTROOES POSITIONFig. 1 . Electrodes 1 , 2 , and 3 are at the level of the base of the sternum.Electrode 1 is on the anterior axillary line. Electrodes 2, 4, and 5 are onthe midclavicular line. Electrodes 3 and 6 are on the scapular line. Elec-trode R is in the reference electrode.

was difficult to maintain reliable contact with concave sites. Theten subjects were healthy males, aged 19-55 and weights 53-105kg. Te sts were run in Barcelona in July with typical temperaturesof 25C and relat ive humidity between 60 and 70 percent .Many electrodes are applied with gel, but without preparing theskin by cleaning o r abras ion. Thus to s imu late worst case condi-tions, we used no cleaning or abras ion. This is a critically impor-tant method because the slightest abrasion or nicking of the skinduring skin preparation will scratch though the ba rrier layer anddrastically lower the low-frequency impedance. This is in contrastwith Hary et al . [4] who prepared the skin by shaving and cleaningthe site with alcohol.Geddes and Valentinuzzi [5] applied metal electrodes to dry skin.In contrast, we used electrode gel sin ce it is almost universally usedwith surface electrodes. Like Grimnes 161, we controlled the areawetted by the electrode gel (Parker Spectra 360 Electrode Gel , Or-ange, NJ 0705 0) by constructing a plastic cylinde r 12.5 mm ID ,15 mm OD, 2.25 mm height with glued-on wings (See F ig . 2(a) . )After taping the wings to the skin, we carefully filled the cylinderwith gel and applied a Ag/AgC l electrode to the gel . This ar ran ement enabled us to achieve a cons tant known area of 0 .550 cm ateach location. This would have been im possib le by merely apply-ing disposable ECG electrodes because variations in applicationpressure would have spread the gel over various areas. We cor-rected all data to an area of 1 cm 2 by multiplying measured impe d-ances by ou r current-injecting electrode area of 0.550 cm'.Fig. 2(a) shows an arrangement that includes a special annularelectrode we designed to inject current and two different positionsfor the voltage-measuring elec trode ( V I , V 2 ) . The dashed l inesshow how the current disperses in the tissue after passing through

the skin. The current through the grounded test electr ode passesthrough Z,, Z,, Z,, an d Z, [F ig . 2(b)] that are the impedance of theelectrode, gel, skin and internal tissues, respectively. Voltage m ea-surements at I/, with respect to ground include the effect of allfour of these impedances. Measuring voltage at V , decreases theeffect of Z, because Vz measures the voltage of an isovoltage con-tour (show n by the solid lines) that is closer to the skin than the

F -

"1

I(a) (b)

Fig. 2 . (a) Current from a distant reference electrode R flows throughimpedances for the electrode Z, , ge l Z,, skin Z, , and tissue Z ,. Measure-ments at V , nclude all four impedances. Measurements at V , reduce Z, .(b) Numbers indicate impedances in ohms at 1 MHz. Dashed lines in-dicate current dispersion. Solid lines indicate isovoltage contours.I O O k Q

Oscilloscope,Tp;*QO-v peakReference Testelectrode electrode

Fig. 3. Current flows from the oscillator through the reference electrode,and then through the test electrode to ground. Impedance is calculatedfrom measurements made at the voltage electrode V,.isovoltage contour measured by V I . Then we m easured Z + Zpbyplacing two electrodes face to face. By varying the thickness ofgel, we determined separately Z , an d Z By subtracting Z , + Zwe obtained Z,.We performed ten measurements on each of ten subjects be-tween 1 0 and 300 s af ter gel applicat ion. The trend of the imped-ance measurement changed f rom s i te to s i te for a g iven person andalso depending on the subject . In some cases , repet it ive tes ts at thebeginning and ending of the tests at a single location showed nos ignif icant change in im pedance. How ever , in o ther cases we founda decrease of up to 20 percent , which Grimnes [6] at t r ibutes toelectrolyte penetration. We also found increases of up to 20 per-cent, which we attribute to closure of the sweat ducts after appli-cation of the cool gel. Where we encountered changes of more than10 percent, we repeated the tests until data were consistent within10 percent.F ig . 3 shows the measurement circui t , which is s imilar to thatof Swanson and Webster [2]. Current from a sinusoidal oscillatortravels through a large reference ECG plate el ectrod e, then throughthe test electrode to gr ound. Since it is difficult to m easure the volt-age under the skin , we placed the 2 by 5 mm voltage electrodeouts ide the cyl inder with a 2 mm spacing of skin to prevent anyposs ible br idging of the gel between electrodes . Th e 1 .6 pF capac-itor prevented any dc current from flowing through the skin. Toprevent current from affecting the impedance of the skin, currentswere 10PA fo r frequencies less than 10kHz, and 10 0 pA for h igherfrequencies. We measured voltage values by observing wiveformson an oscilloscope with an estimated error of 5 percent .

RESULTSFig. 4 shows the impedance for all data points. The tight clus-

tering of data between 100 kHz and 1 MH z suggests that the high-f requency impedance is near ly the same for al l e lectrode locat ionsand for all subjects. This suggests that the series resistance in theusual three-element model for skin impedance [2] can be fixed atapproximately 120 Q . Between 1 kHz and 100 kHz there is a widerdispers ion, which can be modeled by a 10-40 nF capacitor corre-sponding to the c apaci tance of the barr ier layer to the skin . T he

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IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 35 , NO . 8, AUGUST 1988 65 1

IM

lookQi Okp Ik

100

--

r- i iIIO 100 Ik IOk lOOk IM

Freqwncy. HzFig. 1. Impedance versus frequency for all data. High-frequency imped-ance is about 100 Q , whereas low-frequency impedance varies from

10 kR to 1 MQ.much wider var iat ion in the lower-f requency impedance can b emodeled by a resistor in parallel with the capacitor. This resistorcorresponds to the resistance of the ba rrier layer of the skin and iseasily reduced by any slight abrasion [2].Al l of the above results include the sum of the skin and the in-ternal tissue impedance. T he effect of Z, is only imp ortant at 1 M H z .By employing the methods described above we were able to esti-mate the impedance Z, for the ar rangement used as 2 5 0. he num-bers shown in Fig. 2(b) g ive the impedance in ohms of each ele-m e n t at 1 MHz. We note that for our choice of components , theimpedance of the gel is comparable to that of the skin . The imped-ance of the barrier layer is approximately 100 fl at 1 MHz andsuggests that the barrier layer acts as a pure ca pacita nce at highfrequencies.In al l subjects , the higher impedanc e was obtained at s i tes onthe leg , whereas the lower values were those at the forehead. Points3. 5 . an d 6 gave a value higher than points 7 an d 8, but lower thanpoints 1 , 2 , an d 4 .

CONCLUSIONSOthers have noted that the low-frequency impedance of the skinoccasionally reaches very high values [l]. This fact requires de-signers of biopotential amplifiers to achieve extremely high input

impedances o ver the frequency range of measureme nt in order toprevent the imbalance in skin impedance f rom conver t ing com monmode voltage to differential voltage.Our measurements a t h igh f requencies have implicat ions for de-s igners of electr ical imp edance tomographs . Des igners who use afour-electrode sys tem c an obtain skin impe dance values f rom Fig.4 that pennit them to determine requirements on current sourcesand voltage-measuring circuits. Designers who use two-electrodeinstruments should be particularly careful because measurementswith physical phantom s, which do not contain skin, may not yieldresults similar to measurements that do include skin . Kim and W oo[7] us e 100 kHz where the skin impedance is 100 fl higher than at1 MHz. Variations in this series impedance cannot be incorporatedinto the reconstruction algorithm and ma y produce large distortionsin the impedance image. Gisser et al. [8] use 12 kH z where theskin impedance is 900 fl higher than that at 1MH z, and their prob-lems should be worse.

REFERENCES111 A. S. Berson and H. V. Pipberger, Skin-electrode impedance prob-lems in electrocardiography, Amer. Heart J . , vol. 76, pp. 514-525.1968.[2] D.K. Swanson and J. G. Webster, A model for skin-electrodeimpedance, in Biomedical Electrode Technology, H. A. Miller andD. C. Harrison, Eds. New York: Academic, 1974, pp. 117-128.[3] Y. Yamamoto, T. Yamamoto, and T. Ozawa, Characteristics of skin

admittance for dry electrodes and the measurement of skin moisturis-ation, Med. Biol . Eng. Compur. , vol. 24, pp. 71-77, 1986.[4 ] D.Harry, G. A. Bekey, and D. . Antonelli, Circuit models andsimulation analysis of electromyographic signal sources-I: Theimpedance of EMG electrodes, IEEE Trans. Biomed. Eng . , vol .L. A. Geddes and M. . Valentinuzzi, Temporal changes in elec-trode impedance while recording the electrocardiogram with dry elec-trodes, Ann. Biomed. Eng. , vol. 1, pp. 356-367, 1973.S . Grimnes, Impedance measurement of individual skin surface elec-trodes, Med. Biol . Eng. Compur. , vol. 21, pp. 750-755, 1983.Y. Kim and H. W. Woo, A prototype system and reconstruction al-gorithms for electrical impedance technique in medical body imag-ing, Clin. Phys. Physiol . Meas. , vol. 8, suppl. A, pp. 63-70, 1987.D . G. Gisser, D . Isaacson, and J. C. Newell, Current topics inimpedance imaging, Clin. Phys. Physiol . Meas. , vol. 8, suppl. A,

BME-34, pp. 91-97, 1987.

pp. 39-46, 1987.

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65 2 IEEE TRANSACTIONS ON BIOMEDICAL ENGIN EERING, VOL. 35, NO . 8. AUGUST 1988

Call for Applications for EditorIEEE TRANSACTIONSN BIOMEDICALNGINEERING

LL those interested in apply ing for the Chief Editors position should send their applicationsA long with their resumes to the President of the IEEE Engineering in Medicine and BiologySociety:Dr. Willis J . TompkinsDept. of Electrical & Computer EngineeringUniversity of Wisconsin1415 Johnson DriveMadison, WI 53706-1691

Your application should give a brief statement of why you are interested in the position, a state-ment of your go als, and a description of your qualifications.The S ociety expects to fill the position by January 1989.

Call For PapersSpecial Issue on Laser-Tissue Interaction

REMENDOUS advances have recently been made in the understanding of the principles un-T erlying the interaction of laser light and tissue. These understandings are leading to the de-velopment of unique concepts for treatment and diagnostic devices. The IEEE TRA NSA CTIO NSNB I O M E D I C A LN G I N E E R I N Gnvites the submission o f papers reporting original research in the areasof laser applications in medicine and biology. Areas of interest include, but are not limited to,optics. spec troscop y, heat transfer, rate kenetics, photochemistry, and ablation of tissue. T he GuestEditor is Dr. A. J . Welch of the University of Texas at Austin. Papers should be about six trans-actions pages in length and conform to the format and other l imitations set for the TR AN SA CT ION S.Authors planning to make a contribution are asked to submit a preliminary title and a short abstr act.Manuscripts are due by October 1, 1988. Please submit all materials to the Guest Editor listedbelow:Dr. A. J . WelchDepartment of Electrical and Computer EngineeringUniversity of Texas at AustinAustin, TX 78712