Journal of Experimental Botany, Vol. 44, No. 265, pp. 1369-1375, August 1993

Electrical Impedance Analysis in Plant Tissues:Impedance Measurement in Leaves

M. I. N. ZHANG1 and J. H. M. WILLISON

Department of Biology, Dalhousie University, Halifax, N.S. Canada B3H 4J1

Received 7 October 1992; Accepted 13 May 1993

ABSTRACTElectrical impedance spectra (100 Hz-800 kHz) were measured in leaves of Peperomia obtusifolia L. (a succulent) and Brassicaoleracea L. (cabbage). By measuring impedances at three or more inter-electrode distances in a single leaf, electrode impedanceand specific tissue impedance were separated.

Analysis of impedance data from B. oleracea leaves in relation to an equivalent circuit model showed that leaf development wasaccompanied by increases in extracellular resistance, cytoplasmic resistance and vacuole interior resistance, together with decreasesin plasma membrane capacitance and tonoplast capacitance. After B. oleracea leaves were subjected to a — 6 °C freeze-thawstress, extracellular resistance, cytoplasmic resistance and vacuole interior resistance decreased, but plasma membrane capacitanceand tonoplast capacitance did not change. These results indicate that useful measurements of leaf parameters can be obtained bythis technique.

Examination of the electrode impedance spectrum showed that electrode insertion produced a damaged collar, 0-4-0-5 mmwide, around the electrode. This was confirmed by visual observation of the damage in P. obtusifolia leaf.

Key words: Peperomia obtusifolia L., Brassica oleracea L. (cabbage), electrical impedance, equivalent circuit, electrodepolarization.

INTRODUCTIONMeasurement of electrical impedances in plant tissues haslong been considered a technique with useful potential inplant physiology (for review, see Wilner and Brach, 1979;Ackmann and Seitz, 1984), but practical results havesometimes been disappointing. Nevertheless, the abilityto make measurements from living tissue with minimaldamage continues to make research into the methodologyattractive (Stout el al, 1987; Zhang and Willison, 1991a,b). In the past, most measurements have been made onbulk tissues (Hayden et al., 1969; Ackmann and Seitz,1984; Stout et al., 1987; Repo et al., 1990), although someattempts have also been made to make measurements inlaminar organs, notably leaves (Greenham et al., 1972,1978, 1980).

Like impedance measurement in bulk tissues, imped-ance measurement in leaves is complicated by the presenceof electrode impedance that results from electrode polar-ization if a two-terminal electrode arrangement is used(Schwan, 1963; Ferris, 1974; Ackmann and Seitz, 1984).In previous work on electrical impedance in leaves

(Greenham et al., 1972, 1978, 1980), electrode impedancewas not effectively eliminated. In this study, we usemultiple inter-electrode spacings, providing concentric(multi-circular) measurements, to eliminate electrodeimpedance. We present leaf tissue impedance in the formof specific impedance, which is more meaningful thanrelative values because the effects of leaf thickness andelectrode position are eliminated. We also examine tissuedamage due to insertion of electrodes and the effect ofimpedance measurement due to tissue damage.

MATERIALS AND METHODSMaterials and treatment

Peperomia obtusifolia and Brassica oleracea (cabbage) weregrown in soil in pots in a greenhouse at Dalhousie Universityunder natural light condition. In the case of P. obtusifolia, theleaves were taken from a 30 cm high plant. In the case ofB. oleracea, leaves were taken from plants grown for 8 weeks.

In compiling Table 1, leaves I, 2, 4, 7, 10, 14, and 15 fromthe bottom were selected from four plants. For freeze-thaw

1 To whom correspondence should be addressed.

© Oxford University Press 1993

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1370 Zhang and Willison—Electrical Impedance Analysis

stress experiments (Table 2) the 2nd leaves from the bottomwere selected from another four plants. Each leaf was halved;one half was left at room temperature for 6 h and the otherhalf was frozen at - 3 °C for 3 h and then cooled to - 6 °C ata rate of 4-8 °C h" 1 using a circulating bath (for full descriptionof the freezing facility, see Zhang and Willison, 1990). Thawingwas completed at room temperature for 2 h.

The impedance of a laminar tissue

In a relatively uniform plant tissue, specific impedance Zo

(ohm cm) is approximately the same everywhere. For a laminartissue with a thickness H (Fig. 1), if one electrode is insertedcentrally and another electrode, in the form of a surroundingring, is spaced some distance (r) from the centre, the totalimpedance between the 'central electrode' and the 'ring elec-trode' can be calculated as follows.

The laminar tissue between the central electrode and the ringelectrode can be regarded as the sum of many concentric thincylinders of height H (Fig. 1). For a cylinder with radius r andthickness dr (which is very small), the impedance between theinside surface and outside surface of the cylinder is proportionalto dr (along the direction of the electrical field), and inverselyproportional to the surface area of one side (outer surface orinner surface) of the cylinder, 2-nrH, i.e.

dZ,=Zpdr

2-nrH' (1)

As dZ, is inversely proportional to r, a cylinder closer to thecentral electrode will have a greater impedance than a cylinderof the same thickness further from the central electrode. Thetotal impedance of this laminar tissue between the centralelectrode and the ring electrode is the sum of all cylinderimpedance dZ^s in series, or the integration of Eq. (1):

or

Z| 2*7/1 r 2,r// lnU

(2)

in which A = Z0/(2nH), rl is the radius of the central electrodeand r2, the radius of the ring electrode (Fig. I).

Separation of tissue impedance from electrode impedance

If a two-terminal electrode arrangement is used, the imped-ance measurement contains electrode impedance (Stout et al.,

1987; Zhang and Willison, 1991a, b). With an electrode imped-ance Ze, the total measured impedance is

=Ze + A\n(r2/r1). (3)

In Eq (3), Zt and A can be determined from a series of Zvalues measured at different r2 values, based on linear leastsquares (regarding In(r2/r,) as a variable) (Stout et al., 1987;Zhang and Willison, 1991a, b). The specific tissue impedanceZ o is given by

Z0 = 2TTHA. (4)

Impedance measurement and analysis

I. Electrode arrangement: The electrode arrangement wasbased on that described by Greenham et al. (1972). Fourstainless steel entomological pins (radius 0-035 cm) were used:one pin as a 'central electrode' and the other three, which wereinterconnected with copper wire, as a 'ring electrode' (Fig. 2).Several concentric measurements were made in each leaf. Inlarge leaves, the radius r2 varied from 3 mm to 30—40 mm andup to 5 measurements at different inter-electrode spacings weremade. In smaller leaves, the radius varied from 3 mm to15-20 mm and only 3 inter-electrode spacings could bemeasured.

//. Impedance measurement: Electrical impedances were meas-ured with a microcomputer controlled HP Precision LCR meter(model 4284A) (Zhang and Willison, 19916). In the experimentto test 'Tissue damage by electrode insertion, Part II: Effect ofelectrode size on impedance', larger central electrodes werecreated. Figure 3 shows an electrode configuration in which theradius of the effective central electrode is relatively large (3 mm).In this case, the central electrode consists of three pins that areinterconnected (Fig. 3).

///. Impedance analysis: Impedance spectra measured atdifferent r2 's, in a single leaf, were analysed to determine thetissue impedance spectrum and the electrode impedance spec-trum. Analysis of the tissue impedance spectrum was made witha program 'MODEL3' (Zhang and Willison, 1992a) to determinethe various components of a double shell model (Fig. 4) whichcorrespond to extracellular resistance (R{), cytoplasmic resist-ance (Ri), vacuole interior resistance (/?4), plasma membranecapacitance (C3), and tonoplast capacitance (C5) (Zhang andWillison, 1991a).

FIG. 1. A disc of laminar tissue with thickness H. r= Radius of animaginary cylinder around the central electrode; dr = thickness of theimaginary cylinder; 2-nrH = radial surface area of the cylinder.

FIG. 2. Electrode configurations. One pin as the central electrode andthe other three as the ring electrode; r, is the radius of the centralelectrode and r2 is the radius of the ring electrode.

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Zhang and Willison—Electrical Impedance Analysis 1371

FIG. 3. A disc of leaf in impedance measurement with a relatively largeradius of the central electrode (3 mm). Three pins (each with radius of035 mm) were interconnected by copper wire to act as one centralelectrode.

Fio. 4. A double shell model. /?,= extracellular resistance; /?2 = cyto-plasmic resistance; fl4 = vacuole interior resistance; C3 = plasma mem-brane capacitance; C, = tonoplast capacitance.

Water content

The fresh weights of B. oleracea leaves were measured immedi-ately after impedance measurements. The dry weights weremeasured after leaving the leaves in an 80 °C oven for 24 h.

Tissue damage by electrode insertion

Part I: Calculating the damage effect in the impedance equa-tions (Hypothesis): When an electrode is inserted into planttissue, a collar of damaged tissue is created around the electrode(Fig. 5). In Fig. 5, r, and r2 are the same as in Eq. (3). Inaddition, the diagram shows / , which represents a hypotheticalrange of tissue damage due to insertion of the central electrode,the damaged tissue being that which lies between r, and r\(Fig. 5). Although tissue damage due to electrode insertionshould be the same when caused by either the central electrodeor any pin in the ring electrode, only damage produced by thecentral electrode is considered here. As seen in Eq. (3), damagearound the central electrode has a much greater effect on thecalculation than the same amount of damage around pins inthe ring electrode, when r, « r 2 .

Because damaged tissue has a much lower impedance thannormal living tissue (Hayden et al., 1969; Stout, 1988; Zhang

FIG. 5 A disc of leaf in impedance measurement. rx is the radius of thecentral electrode and r2 is the radius of the ring electrode. The areabetween r, and r\ represents tissue damage due to insertion of thecentral electrode.

and Willison, 1992a), the damaged region around the centralelectrode can be regarded as an extension of the central elec-trode. Accordingly, r\ should replace the r, in Eq. (3), i.e.

=Zc + A\n(r2/r'1). (5)

In Eq. (5), Ze is the electrode impedance. It includes the contri-bution made by the damaged tissue (let us call this 'actualelectrode impedance'). In reality, r\ is unknown and it mustbe guessed.

In Eq. (3), rx was effectively used as a guess for r\. Whenthere is tissue damage,

From Eq. (5)

Z=[ZC-A \n(b)] + A In(r2/r,) (6)

in which Z, is the actual electrode impedence calculated byEq. (5) and the component [Zc — A \n(b)\ is the estimated elec-trode impedance using Eq (3).Since b>\,ln(b)>0, then

Zt-A\n(b)<Zc. (7)

Equation (7) shows that the electrode impedance [Zc — A \n(b)]estimated by Eq. (3) is smaller than the actual electrode imped-ance Ze. When A\n{b)>Zt' [Zt-A\n(b)\ will be negative.However, the tissue impedance related parameter, A, remainsthe same in both Eq. (3) and Eq. (5). Therefore, the specifictissue impedance Zo is not affected by errors in guessing r\.

Tissue damage by electrode insertion

Part II: Effect of electrode size on impedance: The followingis a corollary of the hypothesis in Part I.

In Eq. (7), a decrease in the coefficient b will reduce thedifference between the electrode impedance [Ze — A In (b)] estim-ated by Eq. (3) and the actual electrode impedance Ze. If thewidth of tissue damage caused by insertion of the centralelectrode (indicated by r\ — r, in Fig. 5) is independent of theradius of that electrode, we should obtain the actual electrodeimpedance, Ze- by Eq. (3) at a radius of the central electrode(r,) at which b=\. In practice, as the radius of the centralelectrode (r,) increases, the electrode impedance [Zt-A ln(6)]estimated by Eq. (3) should approach the actual electrodeimpedance Ze. An experiment to test this corollary will, there-fore, further test the original hypothesis in 'Tissue damage byelectrode insertion'.

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1372 Zhang and Willison—Electrical Impedance Analysis

RESULTSTissue impedance propertiesA directly measured impedance spectrum (at any singler2 which included the electrode impedance spectrum), ineither P. obtusifolia leaf or B. oleracea leaf, had a charac-teristic pattern. In a Cole-Cole plot, it was an incompletesemicircle with a straight line pointing to the upper right(Fig. 6A, B). The greater the r2 the higher were both theresistance and reactance at any particular frequency (Fig.6A, B). When the spectra measured at several different r2

values were subjected to analysis with linear least squares,the tissue impedance spectra could be obtained (Fig.7A, B).

The tissue impedance spectra in P. obtusifolia leaf didnot vary much from sample to sample throughout therange of 100Hz-800 kHz and, therefore, the wholespectrum can be subjected to analysis in relation to thedouble shell model (Fig. 4). In B. oleracea leaves, sample-to-sample variations in tissue impedance in the range100 Hz-1 kHz were found. Because these variations couldnot be explained, only the data from 1 kHz to 800 kHzwere analysed. Similar inter-sample variations were alsofound in thin leaves of other species such as Pelargoniumsp. (Geranium) (data not shown).

The double shell model fitted well to impedance spectrameasured in leaves of both P. obtusifolia (Fig. 7A) andB. oleracea (Fig. 7B). The fit was better in P. obtusifoliathan in B. oleracea (cf. Fig. 7A and B).

When impedance data from B. oleracea leaves wereanalysed in relation to the double-shell model, it wasfound that (i) resistances were lower and capacitanceswere higher in younger leaves than in older leaves(Table 1); (ii) the correlation between percentage watercontent and any model parameter was poor (data not

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FIG. 6. Examples of impedance spectra, in Cole-Cole plot, measuredin a P. obtusifolia leaf (A) and a B. oleracea leaf (B). (A), r, =0-35 mm,/•j = 3, 6, 12, and 18 mm for curves 'a', 'b\ 'c' and 'd', respectively. Leafthickness 1-5 mm. (B). r, =0-35 mm, r2 = 3, 6, 12, and 24 mm for curves"a", "b\ 'c' and "d\ respectively. Leaf thickness 05 mm.

Origin: te.e.-l.ll)R: unlt= ZZ72 ohmX: unit= ZZ72 oh«ln(f): anit« Z.37

Best-fit parameters:

R,= 11348±44 (ohm)R,= 1842±242 (ohm)R4= 290.9±57.8 (ohm)C,= 2.945±0.046 (nF)C,"= 6.831 ±0.749 (nF)

Origin: (6,9.6.11)R: unit" 2925 ohaX: unit" 2925 oh>ln tD: unit- 1.88

Best-fit parameters:

R,= 13893±218 (ohm)R,= 6234±1104 (ohm)R4= 1029±321 (ohm)C,= 0.655±0.038 (nF)C,= 0.519±0.077 (nF)

FIG. 7. Tissue impedance spectrum from P. obtusifolia leaf (A) andB. oleracea leaf (B) and the corresponding curve-fit by double shellmodel to these spectra. In both (A) and (B), scattered data are fromexperiments and continuous lines are the best fit by the double shellmodel. ( • ) 3-D data in the space of R-X-ln(f); (V) projection of the3-D data on R-ln(f) plane; (|) projection of the 3-D data on X-ln(f)plane; (A) projection of the 3-D data on R-X plane (the Cole-Coleplot). The number following each parameter is the 95% confidenceinterval for that parameter.

shown); (iii) resistances were lower in leaves subjected toa — 6 °C stress than in non-stressed leaves (Table 2), eventhough there was no change in outward appearance ofthe leaves following - 6 °C stress.

Electrode impedance properties, Part IIt was consistently found that resistance values were

negative and reactance values were positive at manyfrequencies when the exact radius of the metal centralelectrode was used in Eq. (3) (Fig. 8).

In a computer simulation, electrode impedance spectrawere calculated by Eq. (5) with guessed values of r\(Fig. 9). The objective was to find an r\ which produceda hypothetical electrode impedance spectrum that wassimilar to a typical electrode impedance spectrum foundin previous measurements on appropriate materials such

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Zhang and Willison—Electrical Impedance Analysis 1373

TABLE 1. B. oleracea leaf development and per cent water contentin relation to the double shell model parametersAll resistances are in ohm cm and all capacitances are in nFcm"1.Standard errors are indicated in brackets. For both per cent watercontent and double shell model parameters, the averaged data andstandard error are calculated from four samples.

LeafID

1

2

4

7

10

14

15

Per centwatercontent

78-6(2-3)74-7(1-2)74-6(093)76-5(059)79-4(075)84-0(1-2)84-3(11)

6974(547)5842(326)4688(503)3421(215)3976(403)3632(436)3569(389)

Ri

5773(554)5184(147)4111(518)2832(248)3976(674)2255(374)2711(467)

R*

903(31)832(19)554(60)376(28)428(26)371(36)372(27)

0957(019)112(0076)1-77(030)2-38(033)1-93(O20)181(038)1-90(036)

0574(O062)0652(0-015)1-06(016)1-47(016)1-27(Oil)1-39(025)1-36(016)

TABLE 2. Double shell model parameter changes in relation tofreeze-thaw stress in B. oleracea leavesAll resistances are in ohm cm and all capacitances are in nFcm"1.Standard errors are shown in brackets. The averaged data and standarderror are calculated from four samples.

Treatment R* c,Control

- 6 ° C

6413(264)911

(124)

9141(1192)1822(737)

656(504)313

(07)

116(019)121

(040)

0622(O033)0624

(OOOO)

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FIG. 8. An electrode impedance spectrum in P. obtusifolia calculated byEq. (3). r, =035 mm. Many resistances are negative and many react-ances are positive.

as potato tubers (Zhang and Willison, 19926). The simula-tion (Fig. 9) shows that when r"x is 0-8 mm or more, thesimulated spectrum (Fig. 9, curves 'c'-'f') has a similarpattern to that of a typical electrode impedance spectrum

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FIG. 9. A simulation with guessed tissue damage (r\) resulting fromelectrode insertion into P. obtusifolia leaf. The actual radius of thecentral electrode is /̂ =035 mm. Curves 'a', 'b', 'c\ 'd', 'e\ and T areobtained with r\ equal to 035 mm, 0-6 mm, 08 mm, 1-0 mm, 1-2 mm,and 1-5 mm, respectively. At ^,=05 mm and greater, simulation pro-duces electrode impedance spectra with consistently positive resistanceand negative reactance.

in electrolytic solution (Bard and Faulkner, 1980) or inpotato tuber (Zhang and Willison, 1992A). The width ofthe surrounding collar which contributes to electrodepolarization is, therefore, probably at least 0-4-0-5 mm inP. obtusifolia leaves (in the case of Fig. 9, curve 'c', r"x =0-8 mm and rx = 0-35, the damaged zone is r\—rx =0-45 mm wide). It was later found that insertion of anelectrode in some P. obtusifolia leaves produced visibledamage (Fig. 10). The damaged zone surrounding the0-35 mm electrode shown in Fig. 10 is about 0-4 mm wide.

Electrode impedance properties, Part IIA typical example of an electrode impedance spectrum

in B. oleracea, using measurement with the large-radiuselectrode configuration in Fig. 3 and calculation byEq. (3), is shown in Fig. 11. As expected, the spectrum issimilar to a typical acceptable electrode impedance spec-trum (Bard and Faulkner, 1980; Zhang and Willison,1992*).

In 'Part I' of the 'tissue damage by electrode insertion',the hypothesis is supported by the simulation which showsthat the effective radius of the central electrode is under-estimated (Fig. 9). If this hypothesis is correct, we shouldalso be able to transform an acceptable electrode imped-ance spectrum into an erroneous spectrum, such as thatin Fig. 8, by setting the radius of the central electrode toa less-than-true value during calculation using Eq. (3).Figures 11 and 12 show the contrast between an accept-able electrode impedance spectrum obtained from a speci-men (Fig. 11) and the transformed spectra which areobtained when recalculated using various r, values inEq. (3) (Fig. 12).

The simulation (Fig. 12) shows that if rx values aresmaller than the true radius of the central electrode(3-0 mm), the erroneous electrode impedance spectrawhich arise are similar to those obtained when the pinradius (0-35 mm) was used in Eq. (3) (e.g. Fig. 8). Thisconfirms the prediction that an acceptable electrodeimpedance spectrum can be transformed into an errone-

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1374 Zhang and Willison—Electrical Impedance Analysis

FIG. 10. A photograph showing visible damage caused by electrodeinsertion into P. obtusifolia leaf. The radius of the electrode is 0-35 mmand the width of the zone of damage around the electrode is about04 mm, as indicated by the dotted line.

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FIG. 11. An electrode impedance spectrum in B. olcracea leaf measuredwith the electrode configuration in Fig. 3. and calculated by Eq. (3).r, = 3-0 mm.

ous spectrum just by setting the radius of the centralelectrode to a less-than-true value. This is further supportfor the hypothesis in 'Part I'.

Figure 12 also shows that when a larger rt value(3-5 mm, 40 mm or larger) was used, the electrode imped-ance spectrum calculated was similar in pattern to that

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FIG. 12. Simulated electrode impedance spectra with various r\ valuesin B. oleracea leaf. The actual radius of the central electrode is r, =3-0 mm. Curves V, 'b', 'c\ 'd', 'e', and T are obtained with r, equalto 1-5 mm, 2-0 mm, 2-5 mm, 3-0 mm, 3-5 mm, and 4-0 mm, respectively.When r1, is smaller than the real radius of central electrode (3-0 mm),simulation produces erroneous electrode impedance spectra (curves'a'-'c') that appear similar to those measured with a 035 mm radiuscentral electrode (see Fig. 8). At /, larger than the real radius of thecentral electrode, simulation produces similar electrode impedance spec-tral pattern (curves 'e'-'f') as that produced with the correct radius ofthe central electrode (30 mm).

with rx = 30 mm. This would suggest that it is possible toestimate a lower limit for the width of the collar ofdamaged tissue, but that an upper limit cannot be estim-ated. In the cases measured in this work, this collar wasat least 0-4-0-5 mm wide.

DISCUSSIONThe potential usefulness of the measurement of impedancein leaves and its analysis was demonstrated by Greenhamand co-workers in works concerned with taxonomy(Greenham et ai, 1972, 1980) and virus infections(Greenham et al., 1978). In the present work, the basictechnique has been improved by (i) using a broaderfrequency range (100 Hz to 800 kHz) than the 10 kHz to200 kHz used by Greenham and co-workers; (ii) usingmore frequency points (40) than the four used byGreenham and co-workers; (iii) measuring impedance at3-5 inter-electrode spacings (r2) and using this to elimin-ate electrode impedance. While the works of Greenhamand colleagues (1972, 1978, 1980) probably indicate realdifferences among the specimens tested, their use of afixed spacing between two electrodes made it impossiblefor them to eliminate electrode impedance. Given theinclusion of this unknown non-physiological variable intheir data, their conclusions must be considered tentative.

Tissue impedance propertiesThe impedance spectra obtained from leaves are similar

to those from other plant materials previously studied(Zhang and Willison, 1991a, b, 1992a, b), the Cole-Coleplot being almost a semicircle (Fig. 7A, B). A differencewhich may be important is that in B. oleracea leaves, aswell as similar thin leaves from other species such asPelargonium sp. (Geranium), there was unexplainable

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inter-sample variation in the low frequency range(100 Hz-1 kHz). Further experimentation may permit thesource of this variation to be identified and to be inter-preted usefully, if it is not artifactual.

As with organs like potato tuber and carrot root(Zhang and Willison, 1991a), the results described in thepresent paper indicate that plant leaf tissue can be repres-ented by the double shell model (Fig. 7A, B). Our measure-ments of impedance in relation to developmental stageand freezing injury in B. oleracea were planned as simpleand preliminary indications of the utility of this techniquein physiological studies. The data in Table 1 indicate thatresistances tended to be higher but capacitances tendedto be lower at later developmental stages of leaves (assum-ing that leaf age rather than time of initiation is mostsignificant). While these data have little physiologicalsignificance in the absence of correlative data other thanpercentage water content, they do show that the techniquehas the capacity to provide significant differences withina data-set of model parameters obtained from a develop-mental series. The observation that resistances droppedsignificantly following — 6 °C freeze-thaw stress inB. oleracea leaves (Table 2), despite the absence of damageby visual estimation, also indicates the utility of thetechnique in plant stress physiology. This finding accordswell with the findings of Zhang and Willison (1992a) onimpedance changes in carrot root tissue subjected to non-lethal freeze-thaw stress. The results indicate the presenceof sublethal injury which is not readily detectable byother means (for discussion, see Zhang and Willison,1992a).

Electrode impedance propertiesThere is enough evidence to support the hypothesis

that electrode insertion produces a 0-4-0-5 mm collar ofdamage in leaf tissue around a 0-35 mm radius electrode.The current hypothesis explains the unreasonable elec-trode impedance spectra obtained by using Eq. (3)(Fig. 8). On the other hand, the impedance technique iscapable of detecting the approximate degree of tissuedamage which is usually non-detectable by other tech-niques. In earlier works by Greenham and co-workers(1972, 1978, 1980), neither electrode impedance propertiesnor tissue damage around electrodes was studied. In theirwork, Greenham and colleagues (1972, 1978, 1980) useda 2 mm inter-electrode spacing. According to the presentresults, a significant proportion (50%) of their tissueunder measurement may have been damaged by electrodeinsertion.

Zhang and Willison—Electrical Impedance Analysis 1375

ACKNOWLEDGEMENTThis research was supported by NSERC (Canada).

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STOUT DG. 1988. Effect of cold acclimation on bulk tissueelectrical impedance. I. Measurements with birdsfoot trefoilat subfreezing temperatures. Plant Physiology 86, 275-82.

STOUT DG, HALL JW, MCLAUGHLIN NB. 1987. In vivo plantimpedance measurements and characterization of membraneelectrical properties: the influence of cold acclimation.Cryobiology 24, 148-62.

WILNER J, BRACH EJ. 1979. Utilization of bioelectric tests inbiological research. Engineering and Statistical ResearchInstitute, Canada.

ZHANG MIN, WILLISON JHM. 1990. Electrical conductance ofred onion scale tissue during freeze-thaw injury. ActaBotanica Neerlandica 39, 359-67.

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ZHANG MIN, WILLISON JHM. 19916. A microcomputer-basedprecision impedance analyser for measuring electrical imped-ance in plant tissues. Canadian Journal of Plant Science71, 1285-8.

ZHANG MIN, WILLISON JHM. 1992a. Electrical impedanceanalysis in plant tissues: The effect of freeze-thaw injury onthe electrical properties of potato tuber and carrot roottissues. Canadian Journal of Plant Science 72, 545-53.

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