decomposing skin conductance into tonic and phasic components

Ž .International Journal of Psychophysiology 25 1997 97]109

Decomposing skin conductance into tonic and phasiccomponents

Chong L. LimaU , Chris Rennieb, Robert J. Barry c, Homayoun Bahramalib,Ilario Lazzarob, Barry Manorb, Evian Gordonb

aDepartment of Neurology, Westmead Hospital, Westmead, 2145 AustraliabCogniti®e Neuroscience Unit Psychological Medicine, Uni®ersity of Sydney and Westmead Hospital,

Westmead 2145 AustraliacDepartment of Psychology, Uni®ersity of Wollongong, Wollongong, 2522 Australia

Received 8 February 1996; revised 3 September 1996; accepted 11 September 1996

Abstract

Ž . Ž .Overlapping phasic skin conductance responses SCRs obtained using short interstimulus interval ISI paradigmssuch as those employed in cognitive research, confound measurement of each discrete phasic SCR as well as the

Ž .tonic skin conductance level SCL . We report a method of resolving this problem using a modelling technique thattakes advantage of the stereotyped nature of the within-subject SCR waveform. A four-parameter sigmoid-exponen-tial SCR model that describes the entire response, was developed and extended to five-, six- and eight-parameter skin

Ž .conductance SC models. These SC models were successfully curve-fitted to more than 60 SC segments, eachcontaining one SCR or two overlapping SCRs on a sloping baseline obtained from 20 normal subjects. The SCsegments were consequently decomposed into their components: the tail of the previous response, one or two SCRsand the SCL. The SCRs free of the complication of overlap were then quantified. The raw SCRs of the same data setwere also measured using a standard method. The standard measurement showed a significant reduction of 15% inamplitude and 140 ms in peak latency compared to our method. The basic four SCR model parameters}onset time,rise time, decay time constant and gain}showed increasing inter-subject variability in that order. These SCR modelparameters may be studied as variables in normal and patient groups and as indices of treatment response. Thisquantitative method also provides a means to assess the relationships between central and autonomic psychophysio-logic measures. Q 1997 Elsevier Science B.V.

Keywords: Skin conductance response; Skin conductance level; Electrodermal activity modelling measurementscoring; Sympathetic autonomic response; Orienting reflex

1. Introduction

Ž .The skin conductance response SCR is anŽ .important autonomic nervous system ANS mea-

U Tel.: q61 2 9845 6834; fax: q61 2 9633 3272; e-mail:[email protected]

sure in psychophysiological research, probablymore widely used than any other ANS measures.Its main attractions include its ease of recording,its simple waveform, its ability to indicate a re-sponse to single stimuli and its non-intrusive na-

Ž .ture. Venables stated in his overview 1991 that‘by appropriate processing of the signal or themeasurement of a critical portion of it, it may be

0167-8760r97r$17.00 Q 1997 Elsevier Science B.V. All rights reserved.Ž .P I I S 0 1 6 7 - 8 7 6 0 9 6 0 0 7 1 3 - 1

( )C.L. Lim et al. r International Journal of Psychophysiology 25 1997 97]10998

possible to provide a wanted index which wouldnot be evident in the gross recording’. Despite itswaveform simplicity, the SCR and skin conduc-

Ž .tance level SCL contain considerable informa-tion that may be associated with specific aspectsof brain state and information processing.

A limitation in the use of these indices incognitive research has partly been due to theresponse overlap in short inter-stimulus intervalŽ .ISI paradigms conventionally employed in cog-nitive studies. These overlapping responses havelimited efforts to study relationships between the

Ž .ANS and the central nervous system CNS activ-Ž .ity. Boucsein 1992 presented a good review of

various scoring methods and their different de-grees of success for use with long ISIs employedin traditional psychophysiological research. Forshort ISIs, SCR measurements have been madeusing a linear extension of the prestimulus base-

Žline in the post-stimulus period Barry et al.,.1993 , but this does not resolve the problem of

delineating overlapping SCRs. For more accuratemeasurement, there is a need to analyze the SCRmorphology and decompose skin conductanceŽ .SC activity into its components. We have previ-ously used exponential functions to characterisethe SCL obtained in an habituation paradigm inour study of the relationship of prestimulus EEG

Ž .and SCL Lim et al., 1996 . In this paper wereport a four-parameter model of ‘pure’ SCRŽ .excluding SCL based on a combination of anasymmetrical sigmoid and an exponential func-

Ž Ž . .tion Case 1: Eq. 1 , Appendix . This model andits extensions can characterise a wide variety ofresponse waveforms and sizes. Consequently, thecomposite SC activity is readily decomposed intoits components, namely, the residuals from the

Ž .previous SCR, the SCR s and the SCL. An accu-rate analytical estimate can be made of the peaklatency and peak amplitude of each SCR free ofthe complication of response overlap and fallingbaselines.

2. Methods

2.1. Subjects

Ž .Normal adults 13 m, 7 f aged between 20 and

Ž .49 years means29.9, SDs9.0 were studied.

2.2. Apparatus and data acquisition

The subjects were seated comfortably in a quiet,dimly lit laboratory with air-conditioned ambienttemperature set at 24"18C. Subjects sat facing amonitor screen and wearing a pair of head-phones. An auditory oddball paradigm with aconstant ISI of 1.32 s was used. Auditory stimula-tion consisted of tones at 80 dB SPL lasting 50 mshaving rise and fall times of 10 ms, with a fre-quency of 1000Hz for backgrounds and 1500 Hzfor targets. A total of 40 target tones was pre-sented pseudo-randomly with intertarget intervalsŽ .ITI varying between 2.64 s and 15.84 s. Subjectswere instructed to attend to the target tone andrespond with a button press as quickly as possible.They were asked to fixate on a coloured dot onthe screen. Skin conductance was recorded via apair of silver]silver chloride electrodes, approxi-mately 0.8 cm2 in contact area, filled with 0.05 Msodium chloride gel placed on the volar surface ofthe distal phalanges of digits II and III of thenon-dominant hand after the skin area was wipedwith an alcohol swab. The electrode pairs formingpart of the input circuit were excited by a con-

Žstant voltage of 0.5 V Lykken and Venables,.1971; Fowles et al., 1981 and the current change

representing conductance was recorded using aDC amplifier with low pass filter set at 50 Hz. SCand other signals were recorded continuously for6.5 min using a 32-channel PC-based system. Thesignals were digitised at 256 Hz and stored to ahard disk. The SC digital signal with a magnituderesolution of 0.0265 mS was compressed by afactor of 5 giving an effective time-base resolu-tion of 19.53 ms. This compression reduced thesize of the data set but still retained a generousover-sampling since SCR frequency is less than

Ž .0.5 Hz Fahrenberg et al., 1983 . Although fullhead EEG and EOG were recorded simultane-ously, only the SC data were studied for thisexercise.

A large number of SC segments of 10-s epochfollowing target onset were visually inspected andcategorised into three cases. They included sim-ple SC segments with an SCR on a flat baseline

( )C.L. Lim et al. r International Journal of Psychophysiology 25 1997 97]109 99

Ž .Case 2 . Case 3 inclusion criteria were that theepoch contained a discrete SCR response on a

Žsloping baseline mainly the tail of the previous.response and that the response time course oc-

curred within the epoch length. Case 4 consistedof complex SC segments containing two SCRs ona sloping baseline. Three SC models were devel-oped as an extension of a four-parameter sig-moid-exponential ‘pure’ SCR model that de-

Ž .scribes the entire SCR response see Appendix .Ž Ž ..A five-parameter SC model Appendix, Eq. 2

was adequate for Case 2, and this SC model wasŽ Ž ..extended to a six-parameter model Eq. 3 to

characterise signals of Case 3, and to an eight-Ž Ž ..parameter model Eq. 4 for Case 4 signals. In

Žall the models throughout this paper including. Ž .the Appendix the time unit is seconds s and the

amplitude unit for the SC components is micro-Ž .Siemens mS .

After a few preliminary tests of Case 2 usingŽ .Eq. 2 , this study used mainly the six-parameter

model in relation to the 60 SC segments of Case3. The signals were obtained largely from the first10 targets and the rest from the first 20 targetsand they were selected to represent a variety ofshapes and sizes containing one discrete SCRsuperimposed on a range of sloping baselines.The parameters were obtained by curve-fittingusing a standard non-linear least-squares method.They were then used to reconstruct three compo-

Ž .nents: f t describing the residual of the previous0Ž .SCR, f t describing the phasic SCR and c rep-s1

resenting the tonic SCL. A few double responseswere fitted using the eight-parameter model which

Ž .included an additional term, f t , for the seconds2SCR. The SCR peak latency and peak amplitude

Ž .were then analytically obtained using Eq. 5 andŽ . Ž .Eq. 1 Appendix . The SCR peak latency and

peak amplitude were also measured from theseraw SC signal using the standard traditional eval-

Ž .uation method B pp. 136]137, Bousein, 1992 .Paired t-tests were used to compare the SCRpeak latency and peak amplitude between the twoscoring methods.

Those readers who are interested in the mathe-matical description and discussion of signal mod-elling should refer to the Appendix. Based on themathematical concept and formulation outlined

in the Appendix, we have developed a softwarepackage known as Skin Conductance Response

Ž .Evaluation System SCORES . Those who wouldlike to use the software package, are invited tocontact the corresponding author.

3. Results

The six-parameter asymmetrical sigmoid-ex-ponential SC model successfully described all the60 selected SC signals obtained from 20 subjects.The diversity of the signals and their analyticallyfitted waveforms are shown in Fig. 1. The middletwo panels show two small SC signals at ex-tremely high display sensitivity. The jagged rawSC signal is a direct consequence of reaching

Ž .digitisation resolution 0.0265 mS of the system.Note that the peak-to-peak noise magnitude isabout 0.02 mS. Note also that the smooth fittedcurve going through the mid-course at variousregions of the raw signal. Figure 2 illustrates the

Ž .raw noiser signal, the fitted curves and the resid-uals. The residuals were well below 5% of thesignal amplitude. All the 60 SC signals were de-composed into three components: the tail of theprevious response, SCR and SCL. Two examplesof decomposition are shown in Fig. 3.

The four SCR parameter values and also thoseof two other parameters}initial SC amplitude atstimulus, a , and SCL, c}were obtained for ev-0ery SC segment studied. Their across-subject

Ž .means, SDs, coefficients of variation CVs andthe maxima were also obtained, and are shown inTable 1. The table also shows the data of SCRpeak latencies and the mean peak amplitudesobtained using our curve-fitted decomposedmethod and the standard method and the P-val-ues of a comparison between them. The standardscoring method returned a significant reductionof amplitude by 15% and latency by 140 msrelative to the curve-fitted decomposed SCRs.

The means and SDs of the four SCR parame-Ž .ters gain, T ,t and t are used to reconstruct ao s1 d r

family of curves, shown graphically in separatepanels in Fig. 4, which demonstrate the form andextent of observed variations. Deviations from themean by "1 SD of gain cause dramatic changesin appearance, from an absent to a large response


Ž .Fig. 4, gain . With a change in the time of onset,the whole waveform is shifted, as expected, alongthe time axis without any change in morphologyŽ .Fig. 4, T . A change in the decay time constanto s1produces a dramatic change in the wave shape,

Ž .especially the recovery limbs Fig. 4, t , and ad

change in the rise time affects mainly the risingŽ .slope Fig. 4, t .r

The variations of three of the four SCRparameters of the 20 subjects are shown in Fig. 5.Note the relatively stable response onset time,T and rise time, t , and the relatively variableo s1 r

Fig. 1. These are a few examples showing the diversity of the actual raw skin conductance traces and their fitted curvesŽsuperimposed. The six-parameter SCR model handles a wide range of response sizes and shapes including left to right, top to

.bottom a large signal with fast recovery, a broad signal with slow rise and fall, two small noisy ones on steep slopes and two typicalwaveforms.


Ž . Ž .Fig. 2. Left panels: two sets of actual SC signals nosier and their fitted curves smoother ; right panels: the residuals after the fit.The residuals were small and distributed about the zero line.

decay time constant, t . The parameter gain, g ,d 1which is most variable is not shown in the his-togram.

The eight-parameter double response modelŽ .yielded a good fit Fig. 6 in the three double-SCR

responses studied, and successfully decomposedeach signal into four components. The SCR pairswere of the same morphology and their onsettimes were separated by 3.99 s, 2.87 s and 2.79 s,or roughly simple multiples of the ISI. As this wasnot the main thrust of this communication, noattempt was made to study a larger number ofsuch cases.

4. Discussion

The six-parameter sigmoid-exponential SCmodel described adequately a wide variety of SC

signal shapes and sizes on a range of slopingŽ . Ž .baselines Fig. 1 with small residuals Fig. 2 . The

signals were effectively decomposed into theirŽ .components Fig. 3 . The significance of the four

SCR parameters is best appreciated by referenceto Fig. 4, which shows how each parameter modi-fies the SCR waveform and the extent of varia-tions.

Extending from successful application of thesix-parameter SC model, we also successfully ap-plied the eight-parameter model to a more com-plex signal of two SCRs on a sloping baselineŽ .Fig. 6 . The results were encouraging and suggestthat the basic methodological difficulty with theshort ISI paradigm used in cognitive studies hasbeen resolved, because all the complex overlap-ping SC signals can easily be classified into pat-terns corresponding to Case 2, 3 or 4, as de-


Ž .Fig. 3. Two sets of actual SC signals and the decomposed SCRs, the tails of the previous response and the SCLs top to bottom .The ‘pure’ SCRs are far easier to score consistently.

scribed in the method section, and we have aworking model for dealing with each of these SCpatterns.

Discrepancies in peak latency and peak ampli-tude scoring between our method and the tradi-

Ž .tional method Table 1 are no cause for concern,


because the traditional method operates on theapparent composite SC signal which is often amixture of an SCR or two on a decaying limb ofthe previous response. The direction of thesediscrepancies is expected because of the additiveeffect of the decaying tail of the previous re-sponse and the current SCR. Although the dis-crepancy seems modest in this series, in someconditions conventional methods are ineffectiveŽ .Barry et al., 1993 ; in the case of two closelyspaced responses the conventional scoring meth-ods would have resulted in even larger errors.This may have some impact on the nature of the

Žrecency effect on recovery phase Bundy and.Fitzgerald, 1975 .

It must be pointed out that this sigmoid-ex-ponential model is far from being a definitiveSCR model. There can be a multitude of mathe-matical representations of varying complexity for

Ž .the SCR Schneider, 1987 . Our method, whichrelies on the principle of superposition, is mathe-matically sound, and the principle allows us toconsider each SC component independently, lead-ing to signal decomposition. It is, however, notcertain if this principle is physiologically valid forthe autonomic electrodermal system in responseto repeated stimuli. A few clues, however, areencouraging. Recommending conductance to be

used to replace resistance on theoretical grounds,Ž .Lykken and Venables 1971 argued that SCR

size wasrelated to the number of parallel sweatgland conductance paths and hence was additive.This concept was confirmed by a recent report ofpositive correlation between the number of totaland open sweat glands and SCR amplitudeŽ .Freedman et al., 1994 . The system is far frombeing driven to saturation, which would have vio-lated this principle, since our maximum SCR andSCL across subjects were, respectively, less than 2mS and 13 mS}well within the expected maxi-

Žmum range Venables and Christie, 1980; Fowles.et al., 1981 for standard recording techniques.

All three electrical equivalent circuits proposed inthe past involving combinations of serial and par-allel resistors, with or without capacitors and po-

Ž .tential sources Boucsein, 1992 , are based onlumped electric-circuit theory, in which this prin-ciple is known to be valid. The fact that the fitteddecomposed SCRs summated almost exactly tothe recorded overlapping composite SC signalŽ .Figs. 1 and 2 suggests that the fitted decom-posed SCR reflects underlying physiological SCRactivity. The findings argue for the validity of theapplication of the superposition principle to elec-trodermal processes.

Apart from SCR, of equal importance in our

Table 1Ž .Skin conductance parameters and comparison of peak measurements ns60

Variables Mean SD CV Max

ParametersŽ .a mS 0.32 0.37 1.16 1.690

g 3.69 3.91 1.06 15.611Ž .t s 2.98 2.13 0.71 10.46dŽ .t s 1.59 0.68 0.43 4.36r

Ž .T s 1.51 0.37 0.24 2.78o s1Ž .c mS 8.87 2.19 0.25 12.90

Ž .SCR peak latency safitted 4.13 1.13 0.27 6.85astandard 3.99 0.10 0.25 6.68

Ž .SCR peak amplitude mSbfitted 0.46 0.38 0.83 1.73bstandard 0.39 0.32 0.83 1.39

a Paired t-test, P-0.0001b Paired t-test, P-0.00001


Ž .Fig. 4. Four panels of the normal waveforms solid lines generated using the four-parameter SCR model taking the parametermean values. Each panel shows the effect on the mean waveform caused by the parameter value deviating from the mean by "1 SDŽ .broken lines . Gain variation causes large amplitude changes including zero response. Changes in T , the SCR onset time, causeo s1shifts along the time axis without morphology changes. Variation of T , the decay time constant, causes changes in the recoverydlimb of SCR. Note that the amplitudes were normalised to depict the decay differences more clearly. T , the rise time, affectsrmainly the initial SCR incline.

method is its ability to measure SCL objectively.Previously, there has been no easy and consistentway of estimating the baseline, and hence SCL.

Our method, in another way, has an impactbecause of the advent of digital technology. Asimple and inexpensive 12-bit analog-to-digital

Ž .converter ADC offers a dynamic range of 4096levels corresponding to 40 mS, close to fulfillingthe needs for representing the large tonic SCLand also the fine-grain changes of phasicSCR}the requirements set by committee guide-lines for reporting electrodermal measurementsŽ .Fowles et al., 1981 . A 16-bit ADC would havefar exceeded the requirement without any needfor tonic level control at the time of recording}atechnique recommended by the committee mainly

for the paper recorder}although the reportingof both the tonic and phasic activity has long

Ž .been regarded as desirable Grings, 1974 . Digitalrecording is easier and the tonic information isnot lost. In this context our method exploits thefull advantages of digital recording by providingan effective method of accurately separating SCRfrom SCL, achieving greater efficiency and reli-ability.

In the absence of a physiological model of theSCR, it is difficult to interpret the model parame-ters with confidence. However, some plausibleinterpretationsmay be discussed here. As the gainparameter is able to modify the SCR from zero toany size, it may play a role in describing habitua-tion. In the second order sigmoid function, the


Ž . Ž .Fig. 5. The inter-subject variations of the three important model parameters. T black is most stable, followed by t grey and to s1 r dŽ .white .

rise time, t , is the time when the function reachesra quarter of its peak. This is equivalent to the halfamplitude rise time of the first order symmetricalsigmoid function. This parameter determines theincline in the initial phase of the SCR. It probablyreflects the cumulative effect of asynchronoussweat duct fillings mediated by responsiveness ofthe end-organs, i.e. the rate of recruiting increas-

Žing number of sweat glands into action Freed-.man et al., 1994 , and the effect of hydration of

the stratum corneum. T is the decay time con-dstant of the exponential decline typical of therecovery phase of the SCR, which has long been

Ž .recognised Darrow, 1937; Edelberg, 1970 . It ismost probably associated with terminal sweat duct

Ž .collapse Edelberg, 1993 and reabsorption ofŽ .sweat from the ducts Fowles, 1974 . T , theo s1

onset latency, has little effect on the waveformŽ .Fig. 4, Panel T and shows a remarkable levelo s1

Žof stability within and across subjects Table 1.and Fig. 5 . Our mean onset latency was 1.51 s

Ž . Ž .SDs0.37 giving a predicted upper limit 99%of 2.62 s. This is in keeping with the range of 1]3s recently advocated for the identification of sti-mulus-generated phasic electrodermal responsesŽ .Barry, 1990; Venables, 1991 . Wider responseonset latency criteria of 1]5 s and 1]4 s were

popular in the literature between 1977 and 1982Ž .Levinson and Edelberg, 1985 . The range hasnarrowed with time, perhaps reflecting advancesin both our understanding of the SCR and itsmeasurement.

The exact physiological processes leading to theSCR and SCL are yet to be determined, althoughthe effector action is now better understoodŽ .Edelberg, 1993 . It is hoped that more accuratemeasurement of SCR and SCL using a methodsuch as this may promote studies that elucidatethe psychophysiological processes involved, suchas central drive, sympathetic outflow and effectoraction. This may lead to a more comprehensivemodel, including perhaps, the central processes.

Our model may have some contribution in cog-Ž .nitive research. Boucsein 1992 presented the

view that two variables, the rate of habituation ofthe electrodermal response and its recovery time,were indicative of differential physiological in-volvement of the amygdala and the hippocampus,and these variables were given distinct psycholog-ical interpretations such as focussed versus dis-tributed attention, or closed versus open gating ofattention. As the gain parameter is capable ofdescribing habituation in a continuum, it mayimprove on measurement of raw SCRs in this


Ž .Fig. 6. The actual solid and fitted curves are on top. The flatline below them is the tonic SCL. At the bottom, the tail ofthe last response and the two discrete SCRs. The SCR peakamplitudes and latencies can now be measured accurately.

context. T , the decay time constant, is a conciseddescriptor of the recovery phase, regardless of

Ž .amplitude Edelberg, 1970 but was not easilyobtained previously. Our method makes this mea-surement more accessible and will hopefully pro-mote its use. The other parameter in our SCRmodel, t , may also be of some psychophysiologi-rcal research interest as this parameter dominatesthe initial incline, the region thought to warrant

Ž .more detailed study Venables et al., 1980 . TheseSCR model parameters may be studied as vari-ables in normal and patient groups and as indicesof treatment response. This quantitative method

also provides a means to assess the relationshipsbetween ANS and CNS in cognition.

Appendix A: Skin conductance signal modelling

A.1 Background

As a general strategy, we modelled incremen-Ž .tally the skin conductance SC signals in three

cases of increasing complexity. A simple SC signalconsists of a fixed baseline and skin conductance

Ž .response SCR which has an initial rapid risefrom the baseline to a peak and is followed by a

Žrecovery limb to the same baseline Venables,.1991; Boucsein, 1992 . When the baseline is fixed

at zero the SC signal is an idealised SCR, which ismost desirable for measurement. This ‘pure’ SCRwaveform may be described mathematically bycombining two distinct functions: a sigmoid func-

Ž Ž ..tion and an exponential decay function Eq. 1 .We are not aware of previously published reportsof the use of such a combination of the twofunctions to model the SCR. The exponentialdecay function is not new and is known to depict

Žthe recovery limb Darrow, 1937; Edelberg, 1970;.Venables, 1991 although there is no general con-

Ž .sensus Boucsein, 1992 .The use of an asymmetrical sigmoid function

for the initial phase of SCR needs to be dis-cussed. First let us assume that there is a fixedtotal number of sweat ducts that underlie therecording zone of the two surface electrodes.Following central drive, the sympathetic activa-tion of the sweat glands supplying the sweat ductsmust cause changes in conductance to follow adistribution curve of some sort because not allthe sweat ducts will be filled at the same time. Ifthe activation distribution function is known, onemay integrate the function to obtain the cumula-tive action of sweat duct fillings. This would de-scribe the rise of the SCR to a plateau when allthe activated sweat glands are exerting their fullinfluence. The sigmoid function is an approxima-tion of this integral, as the hypothetical activationfunction is not known. The second order sigmoidfunction that we use was found to work ade-quately, satisfying the requirements of an abrupt


onset and then a slower rise to a plateau. Itsbeauty lies in its simplicity, needing only onedescriptive parameter, the rise time, t .r

T reflects the sum of a number of actiono s1times including afferent signal transmission time,relay times, decision time, efferent signal tran-smission time, electro-chemical conversion times,endorgan action time and sweat release time.Naturally, before arrival of the activation signalthe effector endorgan will not respond, and hence

Ž .the f t does not come into action until T . Ass1 o s1Ž .the two opposing terms in f t have unit ampli-s1

tude, a combined gain factor, g , is used to scale1the resultant of these terms to match the actualresponse size. Physiologically, this parameter isrelated to the actual number of sweat glandsactivated, their sweat ducts, their physical dimen-sions and the degree of activation synchrony. Af-ter considering physiological realities and havingdecided on these parameters to simulate thephysiological dynamics, we use the mathematicalformulation to describe the SCR and then threecases of commonly encountered SC signals in thefollowing section. This is followed by some noteson how to use the models for SCR measurement.

A.2 SCR and SC models

Based on the preceding considerations, andsome trial and error, we propose a sigmoid-ex-

Žponential four-parameter ‘pure’ SCR model Case.1 as follows:

f s0; for tFTs1 o s1

w Ž . xf sg exp y tyT rts1 1 o s1 d

2y2ŽŽ . . Ž .r 1q tyT rt ; for t)T 1o s1 r o s1

where the four parameters are: g sgain; T1 o s1sresponse onset time; t srise time; and t sr ddecay time constant.

Ž .Following this ‘pure’ SCR case Case 1 , weconsidered three SC cases of increasing complex-ity: Case 2, a single SCR superimposed on a fixedSCL; Case 3, an SCR occurring on a decayinglimb of a previous response; and Case 4, twooverlapping SCRs on a decaying slope. Three SC

models were developed to handle them. Othermore complex signals can be considered as acombination of these three cases.

In applying the sigmoid-exponential four-Ž .parameter SCR model Case 1 to the SC pattern

of Case 2 we must add a term, c, representing theŽ .SCL to Eq. 1 . Thus we have a five-parameter SC

model:

Ž . Ž . Ž .f t s f t qc. 21 s1

For Case 3 we needed only one extra parameterŽ .to accommodate the initial value a of the sig-0

nal at stimulus onset by assuming the recoveryprocess of each response to be similar sharing thesame decay time constant t . This is a reasonabledassumption for the endorgan behaviour duringthe recovery process, including sweat duct collaps-

Ž .ing Edelberg, 1993 and emptying of the sweatŽ Ž .ducts see Fig. 1 A of Edelbert and Muller,¨

.1981 . The recovery phase is considered by thegroup to follow the exponential decay, which isexpected of many physical phenomena. There-

Ž .fore, we needed an additional term, f t s0Ž .a exp ytrt , leading to a six-parameter model,0 d

Ž . Ž . Ž . Ž .f t sa exp ytrt q f t qc. 32 0 d s1

It turns out that sharing of the same time con-stants for adjacent SCRs does not cause apprecia-

Ž .ble error see Fig. 2 . Had the approximation notbeen good enough because of the sharing of t ,dwe would see a systematic residual with a decaypattern.

For Case 4, we needed to accommodate a sec-ond SCR, which we assume to be similar to thefirst, but having its own gain g and onset time2T . We therefore have an eight-parametero s2model,

Ž . Ž . Ž . Ž . Ž .f t sa exp ytrt q f t q f t qc. 43 0 d s1 s2

A.3 Cur®e-fitting

As our models are nonlinear, an iterativecurve-fitting process is most appropriate. A stan-


dard non-linear least-squares routine known asŽthe Marquardt]Levenberg method Marquardt,

.1963; Press et al., 1992 was chosen. The object ofminimisation was the normalised chi-square andthe convergence criterion was that at least twosuccessive iterations did not alter the normalisedchi-square, by more than a tolerance limit of0.0001. This limit was chosen so that the algo-rithm does not ‘wander blindly’ in the minimumvalley with insignificant terrain variations, andalso to avoid problems due to floating point preci-sion limits.

Inherent in any curve fitting method is theneed for initial parameter values to be chosenappropriately to assure convergence to the globalminimum. Two processes are used to determinethe initial conditions. Firstly, the SCORES pro-gramme automatically scans the entire data file,

Žand detects stimulus events target or back-.ground and SC trough and peak latencies and

amplitudes to estimate roughly all the initialmodel parameter values. This is followed by vi-sual inspection of the waveform and the opportu-nity to accept or to modify these automaticallygenerated initial values before curve-fitting iscommitted. Convergence takes some ten to thirtyiterations and only a few seconds using a proces-sor running at 100 or 133 MHz in a standard IBMcompatible PC. The success or otherwise of the fitis immediately apparent, and if it is not at firstsatisfactory the initial values may be modifieduntil a satisfactory fit is achieved.

A.4 SCR peak latency and amplitude

The SCR peak latency and amplitude are notŽ Ž ..explicit in the SCR model Eq. 1 . However, the

SCR peak amplitude and latency may be obtainedŽ . Ž .by: i differentiating f t with respect to time, t,s1

Ž .to obtain the slope, d f t rd t, at any point ons1Ž .the curve; ii setting the slope to zero to define

Ž .the response peak; and then iii solving for theŽ .peak time. d f t rd ts0 can be shown to be as1

simple cubic function:

3 Ž . Ž .x qxy4 t rt s0; where xs tyT rt . 5d r o s1 r

A method for solving this function is readily avail-

Žable in many texts e.g. Press et al., 1992, pp..183]185 . There is a single unambiguous solution

for the peak time, which then enables calculationŽ .of the peak amplitude using Eq. 1 .

A.5 Application notes

We take the risk here of offending the experi-enced signal processing expert for the benefit ofother researchers and clinicians. The foregoingparagraphs should be sufficient for a competentscientific programmer to develop a working soft-ware package. Others can buy a commercial soft-ware package with curve-fitting facilities. They

Ž . Ž .then need to use any of Eqs. 2 ] 4 together withŽ .Eq. 1 for the appropriate SC signal patterns

Ž .Case 2, 3 or 4 respectively . One important con-straint in our model is that f s0 prior to T .s1 o s1The time steps and SC data may be ASCII for-matted and arranged column-wise in a spread-sheet. The time column starts with zero secondsŽ .row 1 corresponding to the stimulus onset and

Žending with the epoch length say 10 s in our.case, row 512 . The actual sample bin, i.e. the

difference between successive time samples mayvary from system to system. SCR is such a slowlyvarying signal that a sample bin between 30 and

Ž .10 ms a sampling rate from 33 to 100 Hz will besatisfactory. The accuracy of estimated peak la-tency will, of course, deteriorate with bin widthincrease. The epoch length need not be exactly 10s. However, too short an epoch may fail to repre-sent the entire SCR and too long an epoch maylead to extremely complex SC segments.

The parameter values are accepted when thecurve-fitting process converges to a minimum.The obtained values of the four parameters: T ,o s1

Ž .g , t and t and the time steps t can be substi-1 r dŽ .tuted in Eq. 1 to generate the decomposed SCR

curve. This fitted decomposed SCR is then avail-able for estimating the SCR peak latency andpeak amplitude using either the analytical evalua-tion outlined earlier, visual inspection or graphi-cal estimate. This ‘long-hand’ way of using ourmodels is labour-intensive and slow and we wouldnot recommend this approach for processing evenmoderate volumes of data.


References

Ž .Barry, R.J. 1990 Scoring criteria for response latency andhabituation in electrodermal research: a study in the con-text of the orienting reflex. Psychophysiology, 27:94]100.

Barry, R.J., Feldmann, S., Gordon, E., Cocker, K.I. and Ren-Ž .nie. C. 1993 Elicitation and habituation of the electroder-

mal orienting response in a short interstimulus intervalparadigm. Int. J. Psychophysiol., 15: 247]253.

Ž .Boucsein, W. 1992 Electrodermal Activity, Plenum Press,New York, pp. 442.

Ž .Bundy, R.S. and Fitzgerald, H.E. 1975 Stimulus specificity ofelectrodermal recovery time: an examination and reinter-pretation of the evidence. Psychophysiology, 12: 406]411.

Ž .Darrow, C.W. 1937 The equation of the galvanic skin reflexcurve: I. The dynamics of reaction in relation toexcitation-background. J. Gen. Psychol., 16: 285]309.

Ž .Edelberg, R. 1970 The information content of the recoverylimb of the electrodermal response. Psychophysiology, 6:527]539.

Ž .Edelberg, R. and Muller, M. 1981 Prior activity as a determi-¨nant of electrodermal recovery rate. Psychophysiology, 18:17]25.

Ž .Edelberg, R. 1993 . Electrodermal mechanisms: a critique ofthe two-effector hypothesis and a proposed replacement.In: J.-C. Roy, W. Boucsein, D. Fowles, and J. GruzelierŽ .Eds. , Progress in Electrodermal Research, Plenum Press,New York, pp. 7]29.

Fahrenberg, J., Walschburger, P., Foerster, F., Myrtek, M. andŽ .Muller, W. 1983 An evaluation of trait, state and reaction¨

aspects of activation processes. Psychophysiology, 20:188]195.

Ž .Fowles, D.C. 1974 Mechanism of electrodermal activity. In:Ž .R.F. Thompson and M.M. Patterson Eds. , Methods in

Physiological Psychology, Vol. 1, Bioelectric recording tech-niques, Academic Press, New York, pp. 231]271.

Freedman, L.W., Scerbo, A.S., Dawson, M.E., Raine, A., Mc-Ž .Clure, W.O. and Venables, P.H. 1994 The relationship of

sweat gland count to electrodermal activity. Psychophysi-ology, 31: 196]200.

Ž .Grings, W.W. 1974 Recording of electrodermal phenomena.Ž .In: R.F. Thompson and M.M. Patterson Eds. , Methods in

Physiological Psychology, Vol. 1, Bioelectric recording tech-niques, Academic Press, New York, pp. 273]296.

Ž .Levinson, D.F. and Edelberg, R. 1985 Scoring criteria forresponse latency and habituation in electrodermal re-search: a critique. Psychophysiology, 22: 417]426.

Lim, C.L., Barry, R.J., Gordon, E., Sawant, A., Rennie, C. andŽ .Yiannikas, C. 1996 The relationship between quantified

EEG and skin conductance level. Int. J. Psychophysiol., 21:151]162.

Ž .Lykken, D.T. and Venables, P.H. 1971 Direct measurementof skin conductance: a proposal for standardisation. Psy-chophysiology, 8: 656]672.

Ž .Marquardt, D.W. 1963 An algorithm for least-squares esti-mation of nonlinear parameters. J. Soc. Ind. App. Math.,11: 431]441.

Press, W.H., Flannery, B.P., Teukolsky, S.A. and Vetterling,Ž .W.T. 1992 Numerical Recipes in C: the art of scientific

computing, 2nd edn., Cambridge University Press, NewYork, pp. 183]185 and pp. 683]688.

Ž .Schneider, R.L. 1987 A mathematical model of human skinconductance. Psychophysiology, 24: 610.

Ž .Venables, P.H. and Christie, M.J. 1980 Electrodermal activ-Ž .ity. In I. Martin, and P.H. Venables Eds. , Techniques in

Psychophysiology, Wiley and Son, New York, pp. 3]67.Ž .Venables, P.H., Gartshore, S.A. and O’Riordan, P.W. 1980

The function of skin conductance response recovery andrise time. Biol. Psychol., 10: 1]6.

Ž .Venables, P.H. 1991 Autonomic activity. Ann. N.Y. Acad.Sci., 620: 191]207.

decomposing skin conductance into tonic and phasic components

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