Experimental Study of Dielectric Properties of Human Lung Tissue in Vitro

Transcription

1 Journal of Medcal and Bologcal Engneerng, 34(6): Expermental Study of Delectrc Propertes of Human Lung Tssue n Vtro Je-Ran Wang 1 Ben-Yuan Sun 1 Hua-Xang Wang 1,* Shan Pang 1 Xao Xu Qng Sun 3 1 Insttute of Electrcal Engneerng and Automaton, Tanjn Unversty, Tanjn 37, P. R, Chna Department of Radotherapy, General Hosptal of Tanjn Medcal Unversty, Tanjn 35, P. R, Chna 3 Bradley Department of Electrcal and Computer Engneerng, Vrgna Polytechnc Insttute and State Unversty, VA 461, USA Receved 17 Dec 13; Accepted 4 Jun 14; do: 1.545/jmbe.1774 Abstract The present study nvestgates the dfferences n the delectrc propertes of normal and cancerous tssues of human lungs n vtro to extract the characterstc parameters from mpedance spectra and provde some reference data for the mpedance measurement of human lung cancer n vtro. Specmens were obtaned from operaton patents wth lung cancer. The mpedance spectra of the specmens were measured from 1 Hz to 1 MHz. The ar fllng factor F s defned for descrbng pulmonary ar content. The results show that the delectrc propertes of normal tssue decrease wth ncreasng F. The relatve permttvty of cancerous tssue s 1.-3 tmes larger than that of normal tssue wth F = The conductvty of cancerous tssue s 1.6- tmes larger than that of normal tssue and there s a sgnfcant dfference n ther mpedance spectra. The results show that the dfferences n the delectrc propertes and mpedance spectra of normal and cancerous tssues are sgnfcant, provdng basc data for the mpedance measurement of human lung cancer n vtro. Keywords: Impedance spectroscopy, Delectrc propertes, Human tssue, Lung cancer, In vtro measurement 1. Introducton Impedance spectroscopy, whch measures the complex mpedance of bologcal tssue over a range of frequences, s an mportant bophyscal property for estmatng the status of human lung tssue. Prevous study showed that lung cancer has the hghest morbdty and mortalty among all malgnant tumors [1]. The early detecton of lung cancer plays a leadng role n reducng the mortalty rate. Electrcal mpedance tomography (EIT) has receved research nterest for the clncal dagnoss of lung cancers due to ts safety, nonnvasveness, and low cost []. The delectrc property of bologcal tssue s a basc bophyscal parameter. Epsten et al. [3] studed the delectrc propertes of dog skeletal muscle n the frequency range of Hz to 1 MHz. Other study nvestgated the delectrc propertes of dog bran tssue [4]. Based on prevous studes, research [5-7] studed the delectrc propertes of goat tssue from 1 Hz to GHz. Based on anmal tssue research, Gabrel et al. measured the delectrc propertes of fresh human * Correspondng author: Hua-Xang Wang Tel: ; Fax: E-mal: hxwang@tju.edu.cn corpse tssue and establshed the correspondng parametrc models. The models were used to estmate the delectrc propertes of 55 knds of human tssues n the range of 1 Hz to 1 GHz by the Italan Insttute for Appled Physcs [8]. Studes on the delectrc propertes of dseased tssue have also been conducted ncludng normal and dseased dog spleen tssues, cancerous lver tssue and cancerous breast tssue [9-11]. However, the delectrc propertes of cancerous human lung tssue have not yet been measured. Establshng a mathematcal model of bologcal tssues s mportant for studyng the delectrc propertes of bologcal tssues. Bernsten et al. proposed cell membrane theory, whch states that the cell membrane s the man reason for tssue electrcal mpedance reducton wth ncreasng frequency. Phlppson proposed the resstance-capactance model for bologcal tssues to explan the above phenomena. Cole and Cole proposed the equvalent crcut model of bologcal tssue and Cole-Cole theory. Other study [1] proposed frequency dsperson theory, whch states that the delectrc propertes of bologcal tssue have three frequency domans of relaxaton. The Debye model, a smplfed Cole- Cole model, has been proposed [13]. The present study ams to provde some reference data for human lung tssue delectrc propertes research and EIT measurement by estmatng the dfference n the delectrc

2 599 J. Med. Bol. Eng., Vol. 34 o propertes of normal and cancerous tssues n vtro. The specmens n prevous studes on delectrc propertes were mostly anmals or fresh human corpses, wth very few studes usng human lung tssue. In order to get some basc data on the delectrc propertes of human lung tssue, the present study used a system for measurng human lung tssue n vtro, extracted the characterstc parameters from the mpedance spectra of the lung tssue, and nvestgated the dfferences n the delectrc propertes of normal and cancerous tssues. The mass and mpedance spectroscopy measurements of the specmens were completed wthn 3 mn after the removal of the tssue from the body.. Materals and methods.1 Materals In ths study, human lung tssue specmens from 19 patents (age: ± 9.96 years; 71 male, 38 female) n the General Hosptal of Tanjn Medcal Unversty who had surgery to remove a cancerous lung tumor were used. For each patent, specmens of the cancerous tumor and normal tssue around the tumor were pruned accordng to the shape of the test box. The specmen mass was measured. Both measurements the mass and the mpedance spectroscopy of the specmen were completed wthn 3 mnutes after the tssue removal from body. Hstologcal analyss of the specmens was carred out after the mpedance spectroscopy measurement n order to confrm cancerous tssue. Data from specmens from 91 cancer patents were used n ths study. The experment was approved by the ethcs commttee of General Hosptal of Tanjn Medcal Unversty. Fgure 1. Impedance spectroscopy measurement platform for human lung tssue. Measurement system and test box.. Expermental setup The mpedance measurement system, shown n Fg. 1, ncludes an mpedance analyzer (Aglent 494A, manufactured by Aglent Technologes of Amerca), an adaptor (Aglent 494A), a fxture (Aglent 169A), a test box (Fg. 1), and a personal computer. The mpedance analyzer was connected to the personal computer va the GPIB bus. The mpedances of the specmens were measured at 31 logarthmc ncreasng frequency ponts from 1 Hz to 1 MHz. The temperature was controlled at 37 C and the relatve humdty was controlled at above 9% durng the experment to mantan the actvty of measured tssues..3 Data processng In prncple, the delectrc propertes (relatve permttvty r and conductvty ) of human lung tssue can be calculated from the measured complex mpedance (seres resstance R and seres reactance X) usng: R G R X 1 X C f R X (3) r Cd / S dg / S (4) where G and C are the parallel conductance and capactance, respectvely, f s the frequency, d and S are the length and cross-sectonal area of the test box, respectvely, and s the delectrc constant of free space ( = F/m). In practce, the mpedance measurement of human lung tssue n the frequency range of 1 Hz to 1 MHz s affected by the electrode polarzaton and the dstrbuted capactance of the measurement system, whch become apparent at the lower and hgher ends of the frequency range under consderaton. Thus, the measured complex mpedance s gven by ZM Z ZE, where Z E s the electrode mpedance caused by the electrode polarzaton, whch decreases wth ncreasng f or S. Cell constant K was determned by measurements on normal salne soluton (.9% acl soluton, C). As the soluton s a pure resstve medum, ts resstance R was obtaned by extendng the measurement results between 1 Hz and 1 MHz to the real axs (Fg. ). K was then calculated from K 1 R. and r were calculated from Z. opp et al. [14] made delectrc measurements on the excsed lungs of slaughtered calves n the frequency range of 5 Hz to 1 Hz. They found that the conductvty and relatve permttvty r decreased wth ncreasng lung ar content. They defned a fllng factor F as the rato of ar volume V to lung tssue volume V : a F V V V V V g cm m V m V (5) 3 a c ( c) c (1 / ) / ( ) where m s the specmen mass and V s the volume of the test box. Equaton (5) assumes that the mass densty of lung tssue s close to that of water (1 g/cm 3 ) [15]. The decrease of c (1) ()

3 Delectrc Propertes of Human Lung Tssue 6 conductvty and relatve permttvty was explaned by the thnnng of the alveolar walls as well as the deformaton of the epthelal cells and blood vessels through the expanson of the alveol. tssue. The characterstc parameters were extracted usng the least-squares curve fttng method based on the Cole-Cole model [18]. The least-squares error functon between the measured mpedance ponts ( x, y) at varous frequences (where = 1,,, ; s the number of measurement frequency ponts) and the fttng crcle (center ( x, y ) and radus r) s: 1 Q( x, y, r) [ ( x x ) ( y y ) r] (8) Let a x, b y, c x y r. Then: (9) 1 Q( a, b, c) ( x y ax by c) Fgure. Estmaton of cell constant K from measurements of normal salne soluton (R: resstance of normal salne soluton; : conductvty of normal salne soluton)..4 Data statstcal analyss A nonparametrc test can be used to compare data whch s not Gaussan-dstrbuted or contans outlers [16]. Generally, the Wlcoxon rank sum test based on the Mann-Whtney statstc s used for a two-sample comparson, and the Kruskal- Walls test s used for a smultaneous comparson of three or more samples. Therefore, n order to test whether the 91 specmens mpedances orgnated from the same dstrbuton, the conductvtes were consdered as observatons and then the comparsons among the ndependent specmens were made at each samplng frequency pont usng the Kruskal-Walls test (sgnfcance level =.5). Comparsons between cancerous and normal lung tssues were evaluated usng the t-test. All statstcal analyses were performed usng SPSS 18. (Statstcal Product and Servce Solutons Verson 18., IBM of Amerca)..5 Extracton of mpedance characterstc parameter In bologcal meda, there are three typcal frequency domans of relaxaton, namely low ( < 1 3 Hz), medum ( Hz), and hgh ( > 1 9 Hz), referred to as,, and relaxaton, respectvely [1]. Cole and Cole proposed the Cole-Cole model to descrbe the frequency-dependent behavor of relatve permttvty r and conductvty. Each frequency doman of relaxaton can be descrbed by a smple frst-order approxmaton wth a tme constant : Z R 1- (6) 1 R R j where R and R are the resstance values at frequences of and, respectvely. s a constant value of between and 1, and s the angular frequency of the measurement sgnal [17]. The characterstc frequency ( f c ) can be calculated as: f =1 c (7) The plot of the magnary part of mpedance versus the real part s an arc of crcumference. Generally, R, R,, and f c are the characterstc parameters of mpedance spectra, representng the spectroscopc propertes of bologcal tssues. Fgure 4 shows the mpedance propertes of bologcal In order to obtan the optmal parameters (a, b, and c), let: Q (1) a ( x y ax by c) x 1 Q (11) b ( x y ax by c) y 1 Q (1) c ( x y ax by c) 1 Equatons (1-1) can be solved numercally by general teratve methods. Center ( x, y ) and radus r can be calculated from the optmal parameters (a, b, and c): x a/, y b/, r 1/ a b 4c (13) The characterstc parameters ( R, R,, and ) can be calculated analytcally from center ( x, y ), radus r, and the measured ponts ( x, y ) as: R x r y (14) R x r y (15) y arcsn r 1/(1 ) 1 1 R Z( ) 1 Z( ) R 3. Results (16) (17) The Kruskal-Walls test resulted n p >.5 at each samplng frequency pont, whch proves that the 91 lung tssue specmens mpedances orgnated from the same dstrbuton. 3.1 Relatonshp between delectrc propertes and fllng factor F of normal tssues In ths study, the mass m of a specmen was measured before the mpedance measurement and the correspondng fllng factors F were calculated usng Eq. (5). Table 1 shows typcal values of m and F. There s no complete alveolar structure n cancerous tssue, and therefore the effects of lung ar content on the delectrc propertes of cancerous tssues are gnored.

4 61 J. Med. Bol. Eng., Vol. 34. o Table 1. Mass and correspondng F values of normal tssue specmens. m/g F m/g F m/g F Typcal results of relatve permttvty r and conductvty for f = 1 khz are presented n Fgs. 3 and 3, respectvely, whch ndcate that and r decrease wth ncreasng F. In Fg. 3, each pont represents the mean value of relatve permttvty or conductvty for a gven fllng factor. 5 Roughly, vares wth 1 F and 4 r vares wth 1 F. The ft n Fg. 3 does not represent the expermental data well, whch s most probably due to fewer measurement data at hgh F values. Fgure 3 shows that relatve permttvty r and conductvty for f = 1 khz s not a constant, but a functon of fllng factor F. The sharp drop of relatve permttvty r and conductvty at low fllng factors (F <.5) s caused by the ncrease of lung ar content. However, at hgh fllng factors (F >.5), ths drop s less sgnfcant. Thus, t s reasonable to compare the delectrc propertes among dfferent specmens wth a gven fllng factor. Fgure 4. Cole-Cole plot of bologcal tssue reactance (-X = -Im(Z)) versus tssue resstance (R = Re(Z)) at all frequences (frequency ncreases from rght to left end of locus). One and two frequency domans of relaxaton. shows that bologcal tssue has one frequency doman of relaxaton. Fgure 4 shows that bologcal tssue has two frequency domans of relaxaton. There are seven ndependent parameters, namely R R 1 R, R1 R1 R 1, R R R, f c1, f c, 1, and. Another nterestng parameter s R R1 R. Fgure 5 shows typcal ftted curves from measured mpedance data of normal tssue wth F =.1781 (m =.8 g) and cancerous tssue for a gven patent n the frequency range of 1 Hz to 1 MHz. Accordng to the ftted curves n Fg. 5, normal tssue has two frequency domans of relaxaton and cancerous tssue has only one frequency doman of relaxaton. In Fg. 5, the complex mpedance loc of tssues are plotted on the yqust plane. R and X represent the real and magnary parts of the mpedance, respectvely. The fttng curves are n good agreement wth the measured data n the frequency range of 1 Hz to 1 MHz. Tables and 3 lst the characterstc parameters extracted from the mpedance spectra of normal and cancerous tssues, respectvely. Fgure 5. Cole-Cole plot of normal and cancerous lung tssues wth one frequency doman of relaxaton fttng). Fgure 3. Delectrc propertes versus fllng factor F. Relatve permttvty and conductvty. r 3. Parametrc models for mpedance spectroscopy of human lung tssues Fgure 4 depcts the Cole-Cole locus plot of bologcal tssue, reactance (-X = -Im(Z)) versus resstance (R = Re(Z)), n the frequency range of (from rght to left). Fgure 4 Table. Characterstc parameters of normal lung tssue. Dsperson 1 Dsperson R /Ω R 1 /Ω f 1 c1 /Hz R /Ω f c /Hz 1.7E E E7 Table 3. Fttng crcle parameters and characterstc parameters of cancerous lung tssue. center (x,y) radus r R /Ω R /Ω (1-7 ) f c /MHz (316.4,439.6)

5 Delectrc Propertes of Human Lung Tssue Comparsons of delectrc propertes of normal and cancerous tssues The mean and standard devaton of the relatve permttvty r and conductvty of cancerous and normal tssues adjacent to a tumor wth F =.1781 (m =.8 g) are presented n Fgs. 6 and 6, respectvely. relaxaton) were used for curve fttng, as shown n Fg. 7. The fttng curves are n good agreement wth the measured data n the frequency range of 1 Hz to 1 MHz and the mpedance spectra of cancerous lung tssue moves apparently to low mpedance drecton. Fgure 7. Cole-Cole plot of cancerous and normal lung tssues wth two frequency domans of relaxaton fttng. Fgure 6. Delectrc spectrum propertes of cancerous and normal tssues. Relatve permttvty and conductvty. As shown n Fg. 6, the mean values of relatve permttvty r of the two types of tssue decrease wth ncreasng f. The relatve permttvty r drops sharply at low frequences (f < 1 khz). In the frequency range of 1 khz to 1 MHz, relatve permttvty r shows a slow decrease and the dfference between normal and cancerous tssues dmnshes. However, the dfference becomes more pronounced at hgh frequences. The relatve permttvty r of cancerous tssue s 1.-3 tmes larger than that of normal tssue. Fgure 6 shows that, there s an overall ncrease n conductvty of the two types of tssue wth ncreasng f. The conductvty vares slghtly at low frequences. However, there s a sgnfcant ncrease for frequences hgher than 1 khz. The conductvty of cancerous lung tssue ( S/m) s hgher than that of normal lung tssue ( S/m). As stated above, cancerous tssue has only one frequency doman of relaxaton. In order to compare mpedance characterstc parameters of normal tssue wth those of cancerous tssue, the measured mpedance data n the frequency range of 1 Hz to 1 MHz (one frequency doman of Table 4 lsts the results of the fttng crcle parameters (center ( x, y) and radus r). Table 5 shows the characterstc parameters ( R, R,, and f c ) extracted from the mpedance spectra of normal lung tssues wth F >.5 and those of the correspondng cancerous lung tssues. In order to determne whether the dfferences n the fttng crcle parameters and characterstc parameters of the two types of tssue are statstcally sgnfcant, one-way analyss of varance (AOVA) was used. If homogenety of varance and a sgnfcant dfference were noted, the t-test was further appled to verfy the dfference between the two types of tssue. Table 4. Fttng crcle parameters of lung tssue. x y r ormal tssue ± ± ± Cancerous tssue ± ± ± 6.61 P Table 5. Characterstc parameters of lung tssue. R /Ω R /Ω α τ( 1-7 ) f c/mhz ormal 18 ± ± ± ± ±.4 tssue Cancerous 558 ± ± 8.64 ± ± ±.6 tssue P All tests were blateral, and the sgnfcance level was set at =.5. The one-way AOVA resulted n p >.5. The t-test results are shown n Tables 4 and 5. The dfferences n the fttng crcle parameters of normal and cancerous lung tssues are statstcally sgnfcant (p <.1). Although there are some structural dfferences, the two types of tssue have smlar characterstc components. Among the characterstc parameters ( R, R,, and f c ), the dfference n the low-frequency resstance ( R ) between the two types of tssue s statstcally sgnfcant (p <.5). 4. Dscusson In order to overcome the drawbacks of prevous studes on lung delectrc propertes, such as the use of fresh human corpse lung materals, the lack of temperature and relatve humdty control, the use of a sngle frequency or narrow

6 63 J. Med. Bol. Eng., Vol. 34 o frequency range, small numbers of lung samples, and gnorance of the effects of lung ar content, a measurement system and ts envronmental control platform were bult. A large number of cancerous and normal lung tssue specmens sampled from 19 operaton patents wth lung cancer were measured n the frequency range of 1 Hz to 1 MHz. The measurements were performed under carefully controlled condtons wth a stable temperature (37 C) and relatve humdty (above 9%), whch approach the envronment n the body. A quanttatve analyss of the relatonshp between the delectrc propertes and the lung ar content was conducted. The results show that many factors nfluence human lung delectrc propertes. 4.1 Influence of measurement errors The mpedance measurement of human lung tssue specmens n the frequency range of 1 Hz to 1 MHz s affected by electrode polarzaton and the dstrbuted capactance of the measurement system, whch becomes apparent at the lower and hgher ends of the frequency range under consderaton. o usng sheldng wre can reduce the effect of the dstrbuted capactance at hgh frequences. An adapter and a fxture were used to connect the test box to the mpedance analyzer n the measurement system. In addton, a platnum electrode wth hgh conductvty can reduce electrodetssue contact mpedance at low frequences. 4. Influence of lung ar content and comparson wth prevous studes The delectrc propertes change wth the amount of ar contaned n the lung. The ar content n a certan lung volume can be descrbed by the fllng factor F. The relatve permttvty and the conductvty decrease wth ncreasng F. Results for fresh human corpse lung nflated and deflated tssues were reported by the Italan Insttute for Appled Physcs [8]. The delectrc propertes of normal lung tssue wth the maxmum fllng factor F (m =.4g, F = 1.356) were compared wth those of fresh corpse lung nflated tssues and the delectrc propertes of normal lung tssues wth the mnmum F (m =.9g, F =.47) were compared wth those of fresh corpse lung deflated tssues. As shown n Fg. 8, the delectrc propertes of normal human lung tssues wth the maxmum (mnmum) fllng factor F are consstent wth fresh corpse lung nflated (deflated) tssues. 5. Concluson Under varous carcnogenc factors, local tssue cells may lose ther normal growth regulaton on the genetc level and abnormally prolferate (clonal expanson) to form a neoplasm, whch s known as a tumor. There are sgnfcant dfferences n the cell morphology, arrangement, and stromal cells between cancerous and normal lung tssues. Thus, ther delectrc propertes are dfferent. The mpedance spectra of cancerous lung tssue moves apparently to low mpedance drecton. Fgure 8. Delectrc propertes of human lung tssues wth maxmum fllng factor F (F = 1.356) and mnmum F (F =.47) and fresh corpse lung nflated and deflated tssues. Relatve permttvty and conductvty. In order to parameterze the mpedance spectra propertes and study the dfference between cancerous and normal lung tssues, the characterstc parameters ( R, R,, and f c ) were extracted usng the least-squares curve fttng method based on the Cole-Cole model. Among the characterstc parameters ( R, R,, and f c ), the dfference n the low-frequency resstance ( R ) between the two types of tssue s statstcally sgnfcant. The dfference s attrbuted to varyng degrees of dfference n the cell morphology and tssue structure between cancerous and normal lung tssue (referred to as atypa). Ths atypa manly manfests at low-frequency resstance ( R ) and the mpedance spectra moves to low mpedance drecton. Thus, low-frequency resstance ( R ) and the mpedance spectra movement to low mpedance drecton can be regarded as quanttatve ndces for parameterzng the delectrc propertes of normal and cancerous tssues of the human lung, and provde basc data for EIT measurements. The authors are plannng to study the dfferences n the delectrc propertes of varous lung cancer types n the future. Acknowledgments The authors gratefully acknowledge the fnancal support from the atonal atural Scence Foundaton of Chna (59375) and the atural Scence Foundaton of Tanjn Muncpal Scence and Technology Commsson (1JCYBJC 195 and 8JCYBJC35).

7 Delectrc Propertes of Human Lung Tssue 64 References [1] A. Jemal, F. Bray, M. M. Center, J. Ferlay, E. Ward and D. Forman, Global cancer statstcs, CA-Cancer J. Cln., 61: 69-9, 11. [] A. Adler, R. Amyot, R. Guardo, J. H. T. Bates and Y. Berthaume, Montorng changes n lung ar and lqud volumes wth electrcal mpedance tomography, J. Appl. Physol., 83: , [3] B. R. Epsten and K. R. Foster, Ansotropy n the delectrc propertes of skeletal muscle, Med. Bol. Eng. Comput., 1: 51-55, [4] E. C. Burdette, P. G. Frederch, R. L. Seaman and L. E. Larsen, In stu permttvty of canne bran: regonal varatons and postmortem changes, IEEE Transactons on mcrowave theory and technques, 34: 38-5, [5] C. Gabrel, S. Gabrel and E. Corthout, The delectrc propertes of bologcal tssues: I. Lterature survey, Phys. Med. Bol., 41: 31-49, [6] S. Gabrel, R. W. Lau and C. Gabrel, The delectrc propertes of bologcal tssues: II. Measurements n the frequency range 1 Hz to GHz, Phys. Med. Bol., 41: 51-69, [7] S. Gabrel, R. W. Lau and C. Gabrel, The delectrc propertes of bologcal tssues: III. Parametrc models for the delectrc spectrum of tssues, Phys. Med. Bol., 41: 71-93, [8] IFAC: An Internet resource for the calculaton of the delectrc propertes of body tssues n the frequency range 1 Hz-1 GHz, Avalable: [9] J. C. Astbury, M. H. Goldschmdt, S. M. Evans, G. W. ebauer and K. R. Foster, The delectrc propertes of canne and normal and neoplastc splenc tssues, Boengneerng Conference, 17-18, [1] A. P. O Rourke, M. Lazebnk, J. M. Bertram, M. C. Converse, S. C. Hagness, J. G. Webster and D. M. Mahv, Delectrc propertes of human normal, malgnant and crrhotc lver tssue: n vvo and ex vvo measurements from.5 to GHz usng a precson open-ended coaxal probe, Phys. Med. Bol., 5: , 7. [11] T. Km, J. Oh, B. Km, J. Lee and S. Jeon, A study of delectrc propertes of fatty, malgnant and fbro-glandular tssues n female human breast, Electromagnetc Compatblty and 19th Internatonal Zurch Symposum on Electromagnetc Compatblty, 16-19, 8. [1] H. P. Schwan, Electrcal propertes of tssues and cell suspensons, Adv. Bol. Med. Phys., 5: 147-9, 1957 [13] P. Q. Mantas, Delectrc response of materals: extenson to the Debye model, J. Eur. Ceram. Soc., 19: 79-86, [14] P. opp, E. Rapp, H. Pfutzner, H. akesch and C. H. Ruhsam, Delectrc propertes of lung tssue as a functon of ar content, Phys. Med. Bol., 38: , [15] R. Pethg and D. B. Kell, The passve electrc propertes of bologcal systems: ther sgnfcance n physology, bophyscs and botechnology, Phys. Med. Bol., 3: , [16] W. H. Kruskal and W. A. Walls, Use of ranks n one-crteron varance analyss, J. Am. Stat. Assoc., 47: , 195. [17] O. Casas, R. Bragos, P. J. Ru and J. Rosell, In vvo and n stu schemc tssue characterzaton usng electrcal mpedance spectroscopy, Ann. Y. Acad. Sc., 51-58, [18] S. Kun and R. A. Peura, Selecton of measurement frequences for optmal extracton of tssue mpedance model parameters, Med. Bol. Eng. Comput., 37: , 1999.