Journal of Experimental Psychology:Human Perception and Performance1986, Vol. 12, No. 1,92-102

Copyright 1986 by the American Psychologic*] Association, Inc.0096-I523/86/S00.75

Integration of Noxious Stimulation Across Separate SomatosensoryCommunications Systems: A Functional Theory of Pain

Daniel Algom, Nehama Raphaeli, and Lior Cohen-RazBar-Han University, Ramat-Gan, Israel

Functional measurement analyses and psychophysical techniques were used to assess how separate,

cross-modal, aversive events are integrated in judgments of pain. Subjects made magnitude estimations

of noxious stimuli produced by a 6 X 6 factorial design of electric shocks and loud tones. Group data

and most of the individual results were consistent with a model of linear pain summation: The

estimates of pain approximated the linear sum of the pain estimates of the individual electrocutaneous

and auditory components. The relation between painful sensation and current intensity could be

described by a mildly expansive power function with an exponent of about 1.1. Auditorily produced

painful sensation related to sound pressure level by a mildly compressive power function with an

exponent of about 0.90 as a representative figure. Results are interpreted in terms of a functional

theory of pain. Noxious events are first transformed to psychological scale values via stimulus-specific

psychophysical transfer functions. The outputs of these functions are then combined with other pain-

related internal representations of either sensory or cognitive origin, according to simple algebraic

models.

Suppose you are suffering from an acute toothache. Then an-

other painful sensation appears, that one resulting from an upset

stomach. What is the overall level of pain you are feeling now?

Is it more severe than having either of the painful components

alone? And if it is, how much so? Of special interest is the question

whether pain summation—if it exists—is perfect: Is overall pain

equal to the simple sum of the component painful sensations?

To answer these questions requires that one have a means for

quantifying pain. Pain, however, is a complex phenomenon, de-

pending, among other things, on the mode and nature of the

noxious stimulation. Electrocutaneous pulses have become a

popular pain-inducing method in the experimental literature.

Uncomfortably loud tones, though less popular, seem to provide

an equally controllable experimental method. Both procedures

enable the experimenter to control carefully the spatiotemporal

characteristic of the aversive stimuli. These two types of noxious

stimulation were used in the present study to investigate the rules

by which painful information combines in perception and to

simultaneously evaluate the psychophysical relations involved.

Electrocutaneous Stimulation

Various investigators have reached different conclusions about

the form of the psychophysical function for the mostly painful

responses to electrocutaneous stimulation. Most of the studies

used direct procedures, notably magnitude estimation (Marks,

Discussions with Gary Rollman during the preliminary phases of de-signing this research and with Harvey Babkoffm matters of psychophysicaltheory and methods of data reduction improved the present work. MatWeisenberg was most helpful at various stages of the completion of thismanuscript, especially during the process of revision. We are also gratefulto Joel Walters for his comments on an earlier version of the manuscript.

Correspondence concerning this article should be addressed to DanielAlgom, Department of Psychology, Bar-Ilan University, Ramat-Gan52100, Israel.

1974a, 1974b; Stevens, 1975), for a response measure and various

versions of the power function as the main means of data re-

duction. Stevens, Carton, and Shickman (1958) found simple

power functions adequate to describe the growth of electrically

produced intensity, the stronger values of which were "very dis-

agreeable." However, even the weak shocks were found aversive

by the subjects. The authors reported exponents of about 3.5,

more than twice the value for the next steepest psychophysical

function examined until that time (Stevens, 1961; see Rollman,

1974).

Later researchers generally reported somewhat lower exponents

ranging from 1.3 to 2.7 (Babkoff, 1976,1977,1978; Cross, Tursky,

& Lodge, 1975; Ekman, Frankenhauser, Levander, & Mellis,

1964; Sternbach & Tursky, 1964), although Bujas, Szabo, Ko-

vacic, and Rohacek (1975) obtained exponents of 3.42 using

stimulation techniques very similar to those originally employed

by Stevens et al. (1958). Other researchers obtained values even

as low as 0.70 or 0.93 (Babkoff, 1978; Beck & Rosner, 1968) if

the data are corrected for threshold or if durations are para-

metrically varied. Linear psychophysical functions have also been

suggested as a viable alternative to the nonlinear descriptions

(Babkoff, 1976; Jones, 1980; Jones &Gwynn, 1984; McCallum

& Goldberg, 1975). As a result, the superiority of the power

equation over others in describing electrocutaneous input-output

functions has been questioned (Babkoff, 1976; Jones & Gwynn,

1984; McCallum & Goldberg, 1975; Rosner & Goff, 1967).

Some of this vast variability probably reflects rather large range

effects (e.g., Poulton, 1968; Teghtsoonian, 1971, 1973). An ad-

ditional portion is probably accounted for by the influence of

stimulus parameters that have yet to be systematically clarified.

Yet another source of variation, both within and across studies,

may stem from differences in the ways that subjects use numbers

to describe sensations (Algom & Marks, 1984). Hence, validity

is at issue, implying that at least some of the direct estimation

results may not faithfully reflect the underlying scale values. The

92

INTEGRATION OF NOXIOUS STIMULATION 93

validity of direct scaling techniques relies on the assumption that

putative numerical ratios represent actual ratios of painful sen-

sations, yet this fundamental assumption lacks empirical justi-

fication (Anderson, 1970, 1974, 1981; Curtis, Attneave, & Har-

rington, 1968; Garner, 1954; Garner & Creelman, 1967; Tor-

gerson, 1961).

The present study makes use of a substantive, multifactor

model of sensory and cognitive processes that contains pain scales

as its natural derivative. The validation of the model entails si-

multaneous validation of the scales, too. Thus, scaling becomes

an integral part of the psychophysics and cognition of sensory

processes (see Marks, 1978b). The present approach makes use

of the theory of scaling proposed by Anderson (1981, 1982),

designated "functional measurement," as the main analytic de-

vice for both data reduction and theoretical interpretation. The

main purpose of analysis in terms of functional measurement

methodology is to determine the integration function that com-

bines separate stimulus components into a unitary response. At

the same time, the theory also provides unique and validated

functional scales to each of the component stimulus dimensions.

As mentioned earlier, loud tone bursts were chosen as the

complementary aversive continuum to serve in the present fac-

torial design.1

Aversive Auditory Stimulation

The aversive, indeed harmful, properties of exposure to massive

auditory stimulation need no documentation here. Temporary

and permanent threshold shifts, hearing losses at particular bands

of frequency, and loudness recruitment constitute but a sample

of well-known pathologies within clinical acoustics that may re-

sult from powerful and prolonged auditory stimulation. However,

even short sounds may feel aversive and painful if presented at

sufficiently high levels. It is little wonder, then, that loud auditory

pulses serve as a convenient experimental substitute to (the more

ethically problematic?) electrical shock in many learning and

social psychology experiments (e.g., Feshbach, 1972; Hiroto,

1974; Hiroto & Seligman, 1975).

Overloading of the auditory mechanism gives rise to subjective

impressions of "feeling, tickle, touch and pricking" as well as

"discomfort" (Licklider, 1951, pp. 997-998). Thus, the painful

sensations induced have tactile as well as auditory characteristics.

These sensations arise fully at intensities of at around 110 dB

SPL and beyond, but as Licklider notes, complaints of discomfort

and tickle begin at levels 5 to 10 dB lower. Note, however, that

the above values were obtained for subjects who had become

used to intense acoustic stimulation for an extended period. Much

lower thresholds of discomfort are expected with inexperienced

subjects stimulated with abrupt sound bursts (the popular method

in the learning and social psychology literature). Recently, Cohen,

Naliboff, Schandler, and Heinrich (1983) obtained thresholds of

discomfort for a 4-s, 500-Hz tone burst with a group of chronic

low back pain patients as well as for healthy nonpatient controls.

The average uncomfortable threshold (dB) obtained for the group

of patients was 71.5 (SD = 8.5), whereas the normal controls

had an even lower value of 56.9 (SD = 6.2).

Although the aversive effects of intense auditory stimulation

are well recognized, no data regarding the functional relation

involved have been reported in the literature. An aim of the

present investigation was to functionally relate levels of induced

discomfort to levels of auditory physical magnitude to arrive at

a quantitative appraisal of the psychophysical contingency.

Integration of Painful Sensations

A significant feature of the present experiment is the com-

position of stimuli. It used a matrix of energy inputs in which

each of several electric shocks was combined simultaneously with

each of several loud auditory pulses to produce a factorial set of

noxious events. Assuming (a) a separate and independent trans-

duction process for each of the noxious dimensions and (b) some

equivalent internal representation for the two types of stimulation,

an additive model of integration seems a natural prediction. At

the least, linear addition of pain may serve as a useful working

hypothesis. Jones (1980) and Jones and Gwynn (1984) have in-

deed demonstrated that electrocutaneous data conform to linear

combination models (in particular weighted averaging). Note,

however, that their results relate to integration rules within a

sensory communication system, whereas the present study ex-

amines composition rules across completely separate systems.

Moreover, as Marks (1978b) has pointed out, superimposing

complex cognitive operations (such as judgments of averages of

stimulus sequences in Jones' studies) on sense perception may

actually add more nonlinear transformations onto the data and

thus complicate the solution. Gracely and Wolskee (1983) showed

an additive structure to operate on sensory signals (electrical

tooth pulp stimuli) and verbal symbols of pain. The present re-

search employed a most elementary judgmental task (subjects

were asked simply to report the degree of pain or discomfort

felt) relating to the intensity of concurrent, quantitatively con-

trollable, noxious stimuli to arrive at the specification of the

appropriate integration model.2

' The choice of an auditory noxious stimulus in the present study may

seem interesting in view of an earlier literature that dealt with intense

noise as an analgesic agent (e.g., Gardner & Licklider, 1959; Gardner,

Licklider & Weisz, I960). However, as later work has shown, "audio an-

algesia" largely depends on suggestion, expectation, and placebo effects

(e.g., Melzack, Weisz, & Sprague, 1969; see Melzack, 1973; Weisenberg,

1977). Even in their original report, Gardner et al. concede that "If the

subjects pay attention to the nociceptive stimulus and report upon the

magnitude of the resulting subjective pain, the effect of acoustic stimulation

is usually small" (p. 32). In contrast to these studies, the present exper-

iment called for an explicit (and to some extent exclusive) concentration

on the nociception of the stimuli presented.2 There are two analytical approaches that allow an investigator to test

composition rules of independent variables from unitary judgments based

on their compound presentations. The one chosen in this study was the

functional measurement approach (Anderson, 1981, 1982) because (a)

of the ease of obtaining direct magnitude estimations (rather than rank-

order responses), (b) utilizing more of the metric properties of the ex-

perimental data, and (c) the availability of relatively straightforward an-

alytic techniques for both model diagnosis and derivation of psycho-

physical functions. The other approach, conjoint measurement (Krantz,

Luce, Suppes, & Tversky, 1971), suffers from a major shortcoming,

namely, the lack of an error theory or an analytic way of handling response

variability in real data. The axiomatic model assumes error-free, rank-

order responses, thereby seriously limiting its applicability to empirical

research (e.g., Falmagne, 1976). Although several strategies have been

suggested to deal with random error (e.g., Coombs & Huang, 1970;

Coombs & Lehrer, 1981; Falmagne, 1979; Person & Barron, 1978), so-

94 D. ALGOM, N. RAPHAEL!, AND L. COHEN-RAZ

Besides its intrinsic interest—reflecting on important theo-

retical and practical issues—the specification of the integration

model makes other, perhaps equally intriguing, points. It entails

procedures allowing for validated estimations of the underlying

psychophysical functions. For electrical shock, the to-be-extracted

parameters bear heavily on the question of the form of electro-

cutaneous psychophysical input-output function. For loud tones,

we hoped to uncover the functional form of the dependency be-

tween degrees of discomfort and sound pressure level.

Method

Subjects

Ten young men and women (7 males and 3 females), all volunteers

from the Bar-Han University community, served as subjects. Their ages

ranged from 22 to 31 years, and four of them had previous experience

with the method of magnitude estimation, though not necessarily in

judging auditory or electrocutaneous stimuli. Each of the observers was

tested over two sessions separated by 1 day or more. All had been advised

that the experiment would comprise painful stimuli and were free to

withdraw participation at any time during the experiment.

Apparatus

A constant current stimulator (local design), powered by a Heathkit

Model IP-17 regulated H.V. power supply, delivered square-wave pulses

for a fixed duration of 3.2 ms through concentric electrodes. Pulse shape,

duration (controlled by locally designed timing and logic circuits), and

current were calibrated with a Tektronix P6042 current probe in series

with a Tektronix Type 454A oscilloscope. The pair of concentric platinum

electrodes was strapped over the underside of the wrist in the vicinity of

the ulnar nerve (the diameter of the inner electrode was 0.49 cm and was

separated from the outer electrode by a radius of 0.524 cm).

Tone stimuli were produced by a Coulbourn precision signal generator,

gated and timed by additional Coulbourn modules. The output was am-

plified (Shure mixer-amplifier unit) and then attenuated before being

fed to the AKG(Z50A) headphones. The binaural stimuli had abrupt

rise and decay times (i.e., 100 tis) and lasted 3.5 s.

A common trigger activated both electrical and auditory stimulus pro-

duction systems. The electrical shock appeared 450 ms after the onset

of the tone stimulus in each trial.

Shock durations of 3.2 ms, and tone durations of 3.5 s were determined

so as to be beyond the ranges of even partial temporal integration reported

for the respective stimulus dimensions (see Algom & BabkofT, 1978, 1984;

Algom, Babkoff, & Ben-Uriah, 1980; Babkoff, 1978; Babkoff, Brandeis,

& Bergman, 1975; Roll man, 1969a, 1969b). Of course, temporal inte-

gration of pain reactions may well exceed the values of critical duration

usually obtained for loudness or weak electric intensity. Nevertheless,

pilot data showed all stimuli to be uncomfortable or painful.

for judgment. Each stimulus was presented and judged three times in the

course of the first experimental session and three times at a second session,

making six judgments per stimulus in all. The initial part of the first

session, prior to data collection, comprised a preliminary practice phase

for all subjects to become familiar with both the stimulus setting and the

method of magnitude estimation. Order of presentation of stimuli was

irregular and different for each subject.

The experimental sessions took place in a booth removed from the

equipment. The subject was seated in an armchair, with the electrodes

strapped to the underside of his or her right wrist and the earphones on

the head.

The method was magnitude estimation. Subjects were instructed to

assign to the first stimulus whatever number seemed most appropriate

to represent the discomfort or pain it caused; then to succeeding stimuli

they were to assign numbers in proportion. If no pain was felt, subjects

were to assign the number zero. Subjects were told that they could use

whole numbers, decimals, and fractions as needed.3

Results and Discussion

Pooled Data

Group results are presented first. The magnitude estimates of

pain given to each stimulus were averaged geometrically, and

these means are plotted in Figure 1 as a function of current

intensity in milliamperes. The parameter is sound pressure level;

each contour represents a different constant level of sound de-

livered to the two ears.

Perhaps the most salient characteristic of this family of curves

is their roughly equal spacing in the vertical dimension, though

a slight trend toward divergence at the upper right is evident.

Because the pain estimates are plotted on a linear scale, the hy-

pothesis of linear pain summation may be assessed by visual

inspection. The parallel spacing implies linear additivity of the

overt numerical responses. Apparently, the aversiveness of an

electric shock and of a massive tone burst presented simulta-

neously at various intensities to the skin of the wrist and to the

ears, respectively, approximates the linear sum of the individual

painful components. This additive structure is evident in the

even spacing of the curves in Figure 1. The slight deviation from

additivity is probably attributable to the fact that the data sets

of at least some of the subjects did not follow a rule of exact

addition (see the section on individual analyses below).

Analysis of variance of the judgments of painful sensations

(performed on the geometric means of the various subjects) con-

firmed the linear addition rule drawn from the visual inspection

of the graphic display. Interaction variance is the critical term

to assess, because failure of additivity will appear as a significant

Procedure

Six different levels of electrical current (0, I, 2, 3, 4, and 5 mA) were

combined factorially with six levels of sound pressure (77, 81, 85, 89,93

dB. and a "zero," well below threshold stimulus), making 36 different

noxious stimuli in all. Stimuli were presented one at a time to the subject

lutions are still limited to only some classes of models, and the emerging

constraints make the derivation of psychophysical functions a difficult

issue. The interested reader should refer to Anderson's 1981 volume (pp.

347-356) for a thorough discussion of the issues involved or to a recent

joint application of conjoint and functional approaches (Weber, 1984).

3 The psychophysical functions derived in this study for sound and for

shock are related to different physical units; SPL in one case and mA in

the other. It would be, of course, elegant to use equivalent units (e.g.,

measures proportional to stimulus power, say Wans, in which case original

exponents are to be divided by 2). Nevertheless, we decided to report

psychophysical parameters re;SPL and re:mA in order to facilitate com-

parisons with studies extant in the literature. In addition, given the present

conditions of shock administration, the impedance of the human tissue

varies considerably as a function of current, so measures such as I1 (square

of current) do not yield accurate descriptions of stimulus power (see

Myers, 1982, for a thoughtful discussion of the effect of the choice of

stimulus measure on psychophysical scaling).

INTEGRATION OF NOXIOUS STIMULATION 95

100

— 80

Q 60

til

Lu

0 1 2 3 4 5

SHOCK INTENSITY (mA)

Figure 1. Average magnitude estimates of pain, plotted as a function of

current intensity delivered to the wrist. (Each curve represents a constant

SPL delivered to the two ears.)

interaction (Anderson, 1970, 1974, 1982). The data showed a

nonsignificant overall interaction at the 1% significance level,

but not at the 5% level, F(25,225) = 1.73, .01 < p < .05. However,

a major part of this rather small interaction variance resided in

the bilinear component (47%). The bilinear component was

highly significant, F(l, 25) = 20.34, p<. 01, whereas the residualwas not, F< 1.

Graphically, a significant bilinear interaction appears as a ten-

dency for the family of functions to converge or diverge at the

upper right. And divergence (or convergence) is the hallmark of

many nonlinear numerical response biases where the underlying

metric is additive (e.g., Algom & Marks, 1984; Marks, 1979b).

Nonlinearity of this type can be eliminated by reseating the nu-

merical values to obtain a theoretically prescribed criterion such

as complete elimination of the divergence (e.g., Marks, 1979a,

1979b) or removal of any significant interaction variance (see

Anderson, 1970). We used the class of power transformations

(in which the original estimates R were transformed by the equa-

tion K = Rm) and, by iteration, found the value of m that reduced

interaction variance beyond the 5% significance limit. This pro-

cedure entailed a mild, negatively accelerated transformation,

raising the magnitude estimates to the 0.90 power. (Complete

elimination of observed divergence involved raising estimates to

the 0.85 power.) Considering the transformed data, the additivity

of components is even more evident.

The data were subjected to analysis of variance by yet another

procedure because, as Anderson (1982) points out, the interaction

in a within-subject data matrix like this might be biased by in-

dividual differences. In order to eliminate any subject effect (and

to make the error term the Shock X Tone X Subject interaction),

each subject's numbers were multiplied by the constant needed

to make that subject's mean equal to all other means (i.e., to the

overall mean) (see Lane, Catania, & Stevens, 1961; Marks, 1980).

Results of this analysis showed a nonsignificant overall interac-

tion, F(25, 225) = 1.50, p > .05, substantiating once again the

results of the graphic test of parallelism: linear addition of painful

sensations across separate somatosensory systems.

As Anderson (1970, 1974) has pointed out, given a factorial

design of the type used in this investigation and results consistent

with additivity in the response domain, the marginal means pro-

vide estimates of the scale values. The lower portion of Figure

2 gives these calculated scale values for electrical shock, produced

by averaging across the rows of the data matrix (i.e., across the

different SPLs), and then setting to zero the scale value at zero

stimulus intensity.

However, the present design entails yet another indicant of the

underlying scale values. These derive from only a subset of the

results, namely, data for presentations that were electrocutaneous

only or auditory only (i.e., data from either the first column or

the first row of the factorial design). Because they derive from

the entire response matrix, the marginal means have, of course,

a fuller basis than do the unifactor pain judgments. Nevertheless,

both derivations are valuable in providing converging evidence

for a validated psychophysical function characterizing a specific

pain experience. The upper part of Figure 2 plots the unifactor

function for electrocutaneous pain, based on judgments of shock-

only presentations (i.e., derived from trials on which tones had

a value of "zero"—well below the threshold of audibility).

The electrocutaneous psychophysical functions—both the

magnitude estimates

1 3 4 5

SHOCK INTENSITY (mA)

Figure 2. Psychophysical functions for electrocutaneously induced pain.

(Top: average magnitude estimates of pain as a function of shock intensity.

Bottom: Same, but the estimates represent adjusted marginal means,

calculated from the entire 6 X 6 data matrix. Note that both the ordinate

and the abscissa are shown in logarithmic units.)

96 D. ALGOM, N. RAPHAEL!, AND L. COHEN-RAZ

magnitude estimates and the marginal means—approximate

power functions (with the proviso that the function includes a

substractive constant as a "threshold" correction). The functions

in both cases are mildly expansive, with exponents of 1.145 and

1.117 for the magnitude estimates and marginal means, respec-

tively. The fits to the power functions (straight lines in the double

logarithmic coordinates) are good (r1 equals .979 for the single

row function and .951 for the marginal function). Linear fits to

the same data were less satisfactory, yielding r2s of .972 and .903,

respectively.

Other assessments of the respective functions alter the absolute

values, but none of the slopes (exponents of the power functions),

described above, change appreciably. Thus, the reseated estimates

yielded exponents of 1.13 and 1.102, but with improved fits (r2

equals .981 and .960, respectively). When intersubject differences

in number magnitude are eliminated, the slopes have values of

1.102 (r2 = .990) and 1.157 (r1 = .986), respectively, for mag-

nitude estimates and for marginal means. The evidence for a

rather moderately expansive electrocutaneous psychophysical

power function characterized by an exponent in the vicinity of

1.1 seems quite strong.

The fact that felt unpleasantness is an expansive power function

of the physical intensity of the electrocutaneous pulse (current)

agrees with the conclusion of most previous investigations (see

introduction). Yet large portions of previous data are suspect

because they rest on the assumption that the overt response was

(at least) an interval scale of perceived aversiveness in each case.

However, as Anderson has repeatedly pointed out (e.g., 1981,

1982), this assumption may or may not be correct in special

cases, and, in general, it lacks needed empirical justification.

Nevertheless, the estimates of exponent obtained herein are

relatively small. Although they agree with some of the previous

results from this laboratory (Babkoff, 1976, 1977, 1978), they

are lower than those reported in the literature, with the exception

of the exponents calculated by Beck and Rosner (1968) after

correction for threshold. Note that the present estimates are also

threshold corrected, and yet they yield greater than unity ex-

ponents. Interestingly enough, a threshold correction applied in

conjunction with the stimulation technique originally used by

S. S. Stevens and his co-workers (Stevens et al., 1958)—resulting

usually in the highest estimates of exponent in the order of 3.5

(e.g., Bujas et al., 1975)—brought about a considerable reduction

in exponent magnitude (to 1.81, Ekman et al., 1964). The rel-

atively small exponent obtained in the present study may reflect

also the use of a shock duration (3.2 ms) that was considerably

shorter than that used in most other studies (but see Babkoff,

1978).

Jones (1980) and Jones and Gwynn (1984) have also employed

functional measurement methodology and derived validated

psychophysical scales. However, the various marginal means'

functions obtained by Jones are unique only up to a multipli-

cation by a constant and addition of a constant (i.e., they are

equal-interval scales) due to lack of threshold correction.

Figure 3 plots the psychophysical functions characterizing tone-

induced painful sensations. Again, the upper plot is based on

tone-burst judgments only, that is, on data that derive from the

first column of the response matrix. The lower part of Figure 3

depicts the function based on the SPL marginal means (i.e., on

data averaged across the different current levels).

2.1

1.9

Q. 1.3

Q

•er W

I/)Uj

1.9

1.7

1.3

magnitude estimates

marginal means

77 81 83 89 93

DECIBELS SPL

Figure 3. Psychophysical functions for auditorily induced pain. (Top:

average magnitude estimates of pain as a function of SPL. Bottom: same,

but the estimates represent adjusted marginal means, calculated from

the entire 6 x 6 data matrix.)

The corrected psychophysical functions for the sound-induced

aversive sensations—both the magnitude estimates and the mar-

ginal means—are well described by a power equation (straight

lines in the double logarithmic coordinates; r2 equals .986 for

the single column function and .998 for the marginal means

function). The respective exponents of 0.75 and 0.90 are notably

greater than 0.6, the value proposed by Stevens (1956) as gov-

erning the sone scale. Note that the subjects in the present study

were instructed to estimate the painfulness of stimuli, including

the tone-only presentations. Thus, the psychophysical functions

depicted in Figure 3 relate to degrees of discomfort caused by

the tones rather than to loudness. And the exponent governing

the pain-SPL function is clearly different from the well-docu-

mented values of 0.60-0.67 characterizing the loudness-SPL sone

scale.

The exponent values found here for the unpleasantness of

massive tone bursts remain stable across different determinations

of the underlying scale. Thus, the rescaled magnitude estimates

yield exponents in the order of 0.67 (r2 = .987) and 0.83 (r2 =

.998) for the magnitude estimates and marginal means, respec-

tively. Removal of individual differences in modulus—what

probably results in the best unbiased estimate of scale values—

yielded exponents of 0.74 and 0.86 (r2 = .989 and .997, respec-

tively). The results are, therefore, consistent with the notion of

a unique scale for painfulness of massive auditory stimuli. This

scale must be distinguished from the various loudness scales (e.g.,

Algom & Marks, 1984; Garner, 1954; Marks, 1974a, 1978a,

1978b, 1983; Stevens, 1956, 1975; see also Schneider, 1980, and

INTEGRATION OF NOXIOUS STIMULATION 97

Schneider, Parker, & Stein, 1974, for much lower loudness ex-

ponents derived by nonmetric scaling techniques) on the one

hand, and from other stimulus-specific representations of ex-

perimental pain on the other (e.g., Rollman, 1974,1983a, 1983b).

High-level auditory stimulation has for a long time been known

for its aversive properties (poor little Albert may be mentioned

here, Watson & Rayner, 1920; see Licklider, 1951) and has re-

cently become a popular pain-inducing device in both learning

and social psychology experiments (e.g., Hiroto, 1974). However,

this is the first time, to the best of our knowledge, that subjective

representations of auditory pain are functionally related to the

physical parameters of the stimulating tone signals.

Three main conclusions can be drawn from the group results:

First, rescaled or unrescaled magnitude estimates of pain evidence

additive structures. Taken as a whole, the results can, therefore,

be characterized by a simple rule: Overall pain equals the linear

sum of the component electrocutaneous and auditory pain when

pain is counted in stimulus-specific subjective units. Second, pain

as a function of electric shock and as a function of sound pressure

level can both be characterized by a simple two-parameter psy-

chophysical power function. Third, the parameters of the func-

tions differ. The electrocutaneous function is moderately expan-

sive, whereas the auditory function is moderately compressive

(though clearly differing from the rather extensively scrutinized

various loudness functions).

Individual Data

The type of analyses and kind of interpretation used with the

pooled results were applied to the data of each individual subject.

Thus, the group data serve as a common frame of reference to

evaluate individual cases.

Three aspects of each subject's results are of special interest:

(a) the rule of pain summation, (b) the psychophysical function

for pain induced by electric shocks, and (c) the psychophysical

function for pain induced by high-level tone bursts.

The question of integration rule may yield to an analysis of

the additivity evident within each subject's entire response matrix.

As Figure 1 shows, the pooled data conform well to a simple

additive mode. So, too, do most (but not all) of the individual

data. Graphic displays of each subject's pain contours show that

despite considerably greater noisiness, in most cases the curves

are about equally displaced in the vertical plane (see Figure 4

for two examples).

Analyses of variance confirmed that the data for 9 of the 10

subjects had nonsignificant (a = .01) interaction terms, implying

additivity of their numerical estimates: For the 9 subjects, F(25,

125) < 1.85, p > .01; for the remaining 1, the interaction term

was significant, F(25, 125) = 2.13, p < .01. Employing the 5%

significance level showed, however, that the data for only 6 of

the last 9 subjects had nonsignificant interactions: For the 6 sub-

jects, F(25, 125) < 1.55, p > .05; for the other 3 the interaction

terms were/{25, 125) - 1.77, 1.84, 1.85, 0.01 <p < .05.

As Anderson (1981, 1982) has pointed out, deviations from

a prescribed theoretical pattern must not automatically lead to

the rejection of that pattern as a valid representation. Possible

nonlinear response biases should always be considered. The

method of orthogonal polynomials can be diagnostic in this re-

spect, and so we applied it to the analysis of the interaction vari-

subject-.H

r-.

I..:::::LU

subject

SHOCK INTENSITY (mAJ

Figure 4. Magnitude estimates of pain: as in Figure 1, for 2 of the 10

subjects. (Note that the data of Subject H are approximately additive,

whereas those of Subject E are not.)

ances of the 4 subjects having significant terms at the 5% level

(using coefficients relative to the psychological values rather than

the standard ones). Results showed that interaction variance for

2 of the 4 subjects had sizable Linear X Linear components in

each case (60.3% and 40%). For these 2 subjects the bilinear

component was highly significant, F(l, 25) = 27.78 and 17.68,

p < .01, whereas the residual was not, F < 1, and F{24, 100) =

l . l l , p> .10, respectively. The data of these subjects were sub-

jected to the same type of rescaling (to additivity) used with the

pooled data. The procedure involved a strong negatively accel-

erated transformation (m - 0.45) in the first case, a mild posi-

tively accelerated transformation (m = 1.05) in the other.

Noteworthy is the fact that the above analyses failed with the

2 remaining subjects. Although both of them had some of the

interaction variance concentrated in the bilinear component

(15.8% and 19.7%), sizable (and significant) nonlinear compo-

nents appeared, too. For instance, the data for the second subject

(characterized originally by the most significant, p < 0.01, in-

teraction term) showed negligible Linear X Quadratic (Shock X

Tone; 0.3%) and Quadratic X Linear (0.8%) trends, but an im-

pressive 30.3% Quadratic X Quadratic component, F\l, 25) =

16.2, p < .01. We could find no monotonic (power-class) trans-

form to bring the two sets of data to parallelism. Most likely,

these 2 subjects used inherently nonadditive cognitive strategies

in coping with and integrating the sensations of pain coming

from the different bodily sources.

Besides their intrinsic interest, the present individual analyses

entail an important caveat with regard to the interpretation of

functionally derived factorial plots based on group data. Although

the possibility of artifact ual interpretation of pooled patterns is

at times acknowledged (e.g., Anderson & Cuneo, 1978), careful

individual analyses are needed to explore the exact nature of

individual differences. These should apply to both the integration

rule and the psychophysical function, and in special cases even

to possible trade-off relations between the two. The present out-

come suggests an additive integration rule for pain for 8 subjects,

but a more complex, distinctly nonadditive rule for 2 subjects.

On the assumption that additivity of pain exists at least as a

first-order approximation, we can derive scale values from each

subject's data matrix by calculating marginal means down col-

umns (i.e., across SPLs) and across rows (i.e., across current

levels), adjusting to zero the scale values for zero-intensity stimuli.

98 D. ALGOM, N. RAPHAELI, AND L. COHEN-RAZ

Single row (current only) and column (sound pressure only) scalescan also be calculated. Columns 2 and 4 in Table 1 show, re-spectively, for magnitude estimates and for marginal means, theexponents of power functions fitted to the electrocutaneous data.

The fits to the power functions are reasonably good. The spreadof exponent—somewhat more than 2:1—is typical (e.g., Ramsay,1979; Stevens &Guirao, 1964; see also Marks, 1974a). However,the variability is inflated by the extreme values of one of the(anomalous?) subjects (E), whose data agree with a complex bi-quadratic model rather than with a simple additive model. Theaverage exponents over subjects are much like the averages ob-tained from the pooled estimation. It is, perhaps, notable thatfor 9 of the 10 subjects at least one determination of exponentyielded a value greater than unity. The finding from the pooleddata of a moderately expansive electrocutaneous pain functionwith an exponent in the vicinity of 1.1 is, therefore, substantiatedby the individual results.

Table 2 gives the respective psychophysical functions and powerfits for the auditorily induced painful sensations.

Again, the fits to the power functions are excellent, especiallyfor the marginal means' functions. Variability of exponents issmaller though, inflated this time by an extreme value of thesecond deviant subject (B). Still, the most striking feature ofthese individual functions is the replication of the relatively highvalue for the auditory pain exponent (in the order of .90). No-table, too, is the fact that half of the individual exponents areequal to or greater than unity. Subjective representations of paininduced by tone-bursts rest on different scale values than dovalues of loudness aroused by the same sort of stimuli.

In sum, the results of the individual data suggest that the rulesunderlying the integration of separate painful somatosensory in-formation vary somewhat from person to person, but that thetypical underlying structure is an additive one. Sensory repre-sentations of pain are stimulus specific, the scales varying sys-tematically across different sources of induction. For electricalshock, pain is an expansive power function of the physical stim-ulus; for loud tones, it is a compressive power function of the

Table 1Parameters of the Psychophysical Power Functionfor Electrocutaneous StimulationIndividually for 10 Subjects

Subject b r1 b.

ABCDEFGH1J

MM'

0.7010.9100.9391.3512.4820.8340.8811.2251.0341.279

1.1641.013

.908

.923

.958

.838

.952

.986

.940

.952

.905

.917

0.7421.0751.0410.8022.5631.3721.4711.2990.8991.505

1.277

1.141

.933

.991

.846

.665

.937

.996

.969

.903

.771

.984

Table 2Parameters of the Psychophysical Power Functionfor Massive Auditory StimulationIndividually for 10 Subjects

Subject b r2 bn

ABCDEFGHI

J

MM'

0.520.400.620.72

0.820.600.740.860.760.92

0.700.72

.877

.767

.979

.963

.904

.989

.931

.989

.900

.989

0.520.60

0.821.080.881.061.041.000.82

1.08

0.890.93

.865

.996

.974

.996

.996

.991

.995

.990

.998

.994

Note, b = magnitude estimation exponent. bm = exponent derived frommarginal means. M' = mean based on 8 subjects; the two nonadditivedata sets (Subjects B and E) excluded.

Note, b = magnitude estimation exponent. bm - exponent derived frommarginal means. M' = mean based on 8 subjects; the two nonadditive

dat sets (Subjects B and E) excluded.

respective dimension. Here, too, there is some individual vari-ation; it is small enough, however, to warrant the above conclu-sions.

General Discussion

A Functional Theory of Experimental Pain

Perhaps the simplest way to interpret the present set of resultsis to treat pain as a multicomponent, multistage process involvingan amalgamation of sensory and cognitive transformations. Atthe initial sensory stage we assume that each noxious stimulus,S, undergoes a purely psychophysical transformation, F, into aninternal painful sensation, P. These sensory transformations are,as a rule, discriminably different from one type of noxious stim-ulation to another. Thus, assuming a valid linear response scale,we have

P=F(S). (1)

When task or natural requirements cause the painful componentsto be integrated, the cognitive operations act on values of sen-sation P rather than on the original stimuli S. Assuming thepainful context comprises two stimuli, integration presumablytakes the form

T=P,oPj, (2)

where T is the instantaneous level of pain and o is an arithmeticoperator such as addition. Again, we assume a valid linear re-sponse scale for T. The relation depicted in Equation 2 readilygeneralizes to any greater number of components.

The specific features characterizing each of the componentnoxious stimuli express themselves via their stimulus-specificsensory transformations. In the present study, for example, onesuch scale operates when subjects are called upon to make judg-ments of pain following powerful auditory stimulation. The sub-jective representations are best characterized by a mildly com-pressive power function governed by an exponent in the orderof 0.90. This auditory pain function does not approximate theprototypical scales for loudness (with exponents in the order of

INTEGRATION OF NOXIOUS STIMULATION 99

0.6) that come from magnitude estimation and magnitude pro-

duction studies (Marks, 1974a; Stevens, 1975). Sound-induced

painful sensations are rather transformed into values on what

may be termed the P* (auditorily induced pain) scale. These

scale values express themselves whenever auditory stimulation

is presented at sufficiently massive levels so as to cause discomfort

of one degree or another. Given a loud tone, there are simulta-

neously two sets of scale values. One set operates when judgments

of loudness are called for, but another nonlinearly related set of

values operates when subjects are instructed to report the degree

of pain or discomfort they feel. (Because loudness and pain are

both presumed to be power functions of sound pressure, with

different exponents for the different sensations, one scale must

be a power function of the other). Another more expansive psy-

chophysical transfer function PE (electrically induced pain)

characterizes the transduction of electrocutaneous stimulation.4

As mentioned earlier, these initial sensory transformations, F,

take place automatically like early transduction processes in other

sensory systems. Therefore, once a powerful enough noxious

stimulus is applied, it results in a painful central representation,

P. These transformed values are projected as equivalent points—

save for retaining their sensory identity—on a central cognitive

space (Aristotle's "common sense"?) to be integrated according

to simple algebraic rules. The simple fact that subjects can trace

their different painful sensations to discriminably different

sources of irritation argues against a (probably simpler) as-

sumption of a single common pain scale.5 In this sense, then,

pain seems to behave analytically: Although there exist an overall

feeling of pain or discomfort, the different noxious components

are, nevertheless, available to perception (see Marks, 1979a, 1980,

for analogous phenomena in loudness, especially in the perception

of complex tones whose frequency components are widely sep-

arated).6

Implications for Pain Theory and Research

The present theory spells out explicitly the assumptions of

functional measurement theory for pain domain. The recurrent

appearance of the additive structure both within a somatosensory

communications system (Jones, 1980; Jones & Gwynn, 1984)

and across separate systems (Gracely & Wolskee, 1983; the pres-

ent investigation) fits well with a functional theory of pain. Be-

cause what is summed in central integration processes is pain

rather than incoming electrocutaneous or acoustical energy, nei-

ther a priori dominance of one type of stimulus over the other

nor any masking effects are expected. The simple additive model

comes out, therefore, as a natural derivative of the information

integration strategies acting on transformed P values of pain.

Although the present study was not planned to test existing

theories of pain, its results pose difficult problems for the now

popular gate control theory (Melzack, 1973, Melzack & Wall,

1965, 1982).

Given (a) the ascending and descending projections assumed

to influence the gate control system and (b) the completely un-

related nature of shocks and tones as noxious stimuli to be mod-

ulated at the gate, the appearance of the present additive model

(as well as the ones demonstrated by Gracely & Wolskee, 1983;

and by Jones, 1980, and Jones & Gwynn, 1984), though possible,

is highly unlikely under the gate control theory. Some sort of a

nonlinear model is the natural prediction of the gate control

theory, given the complex and presumably different modulations

at the gate of electrical shocks originated at the surface of the

skin and auditory pulses coming from the ears. Indeed the notion

' It may be argued that the electrical stimuli used here might have

activated primarily low-threshold mechanoreceptivc afferent! unrelated

to nociception, so that the present study addresses mainly integration of

perceived discomfort. Several lines of reasoning argue against such an

interpretation. First, the same type of stimuli at much lower levels and

shorter durations (see Rollman's and Babkoff 's studies) have been shown

or convincingly interpreted as directly stimulating nerve endings (recall,

especially, the extremely steep psychometric functions obtained with such

stimuli). Second, tremors and/or thumb twitches characteristic of aversive

electrical intensity (Rosner & Goff, 1967) were occasionally observed

with all of the present subjects. Third, there is some evidence (e.g., Wol-

barsht, 1960) that mechanoreceptore respond overall in a negatively ac-

celerated fashion as a function of receptor potential. By contrast, positively

accelerated electrocutaneous functions were obtained throughout in the

present investigation. Fourth, and probably most important, our subjects

were instructed to report the degree of pain or discomfort they felt upon

the presentation of each compound stimulus. They completed this task

in the most natural and straightforward manner without virtually a single

"zero" judgment to nonzero stimulus intensities. Excessive pilot sessions

demonstrated that the stimulus values used (including tone-free presen-

tations) elicited aversive feelings that were reliably described as painful

or uncomfortable. With pain, being a psychological experience, the sub-

jective component should carry the most weight (Weisenberg, 1977). Taken

as a whole, the present results are compatible with Rollman's (1969a)

hypothesis that electrocutaneous stimuli bypass cutaneous receptors to

excite afferent nerves directly.

' If horizontal cuts are made at several values of the ordinate in Figure

1 , the results are sets of stimuli that produce equivalent pain judgments.

This analysis yields values of sound (dB) that are as noxious as appropriate

values of electric current (mA). We do not present these data — though

they are implicit — in order to avoid the impression of equivalent or in-

terchangable painful sensations. For even for identical ordinate values

there are salient and ineluctable differences between sound-induced and

electrically induced painful sensations. Of course, such an analysis can

be useful for practical purposes, and the interested reader may well want

to derive the respective values.6 An alternative model might be proposed to account for the present

data. The implicit combination rule may be of the form

where Ra is a response to combinations of tone and shock, the & are

scale values, and the Ws are weights. According to such a model, the

steeper rate of judgment for shock reflects the greater weighting of shocks

over tones. The hypothesis advanced in this article seems, however, a

more plausible explanation of our results. Given the peripheral and purely

sensory nature of the psychophysical trasductions process (Stevens, 1975),

the notion of weight (to be distinguished from purely mathematical coef-

ficients) does not, in our opinion, have much merit as an explanatory

device in present context. Different sensory input-output systems, the

operations of which are governed by different power function exponents,

are a more natural description. Most successful applications of weight

models in psychology have indeed been made in complex cognitive tasks

such as judgments of seriousness of offences (Leon, Oden, & Anderson,

1973). Besides substantive considerations, there are great difficulties in

separating weight and scale parameters, particularly when (a) an averaging

response is neither required nor assumed, and (b) row and column stimuli

are composed of different types of information (both conditions apply

to the present study). Because each weight parameter is confounded with

100 D. ALGOM, N. RAPHAEL!, AND L. COHEN-RAZ

that resulting pain depends on the relative level of the respective

noxious stimuli (i.e., there is an interaction) is at the very heart

of the gate concept (see Melzack & Wall, 1982, chapter 10).

Accordingly, one of the basic propositions of the theory states

that "The spinal gating mechanism is influenced by the relative

amount of activity in large-diameter (L) and small-diameter (S)

fibers.. . ." (Melzack & Wall, 1982, p. 226, emphasis supplied).

At other places it is argued that only when a stimulus is increased

to levels sufficient to trigger a specific class of fibers would a

"gate closing" effect exert (mostly inhibitory) influence on other

stimuli (Higgins, Tursky, & Schwartz, 1971; see also Weisenberg,

1977). The functional theory, by contrast, argues that a given

stimulus enters into the functional equation in the same way, no

matter what it is added to. The present results bear out this

prediction.

The gate control theory has been used to derive the interaction

(i.e., nonadditive) prediction in a couple of laboratory studies

that bear some resemblance to the present one. Thus Higgins,

Tursky, and Schwartz (1971) conclude that "the present results

are consistent with the postulated existence of a spinal gating

mechanism capable of selectively reducing the affective reaction

to a compound tactile-nociceptive stimulus" (p. 867, emphasis

supplied). Melzack, Wall, and Weisz (1963) found vibration to

reduce noxiousness of electric shock at low shock intensities but

to enhance the aversive properties of the shock at higher intensities

(see also, Halliday & Mingay, 1961; Melzack & Schecter, 1965;

Wall & Cronly-Dillon, 1960). However, as some of the cited au-

thors readily acknowledge, concurrency of nociception could not

always be assured with enough rigor, given the stimuli used. More

important, perhaps, is the fact that subjects in those studies were

instructed to assess pain resulting from only one of the noxious

dimensions. Considerations of adequate experimental control

have dictated the present choice of electrical shocks and loud

auditory pulses from an enormous available range of pain-in-

ducing stimuli (Rollman, 1983a, 1983b). Of course, the selection

of separate somatosensory communication systems was imper-

ative from a theoretical viewpoint.

The functional theory shares, therefore, the concern of the

gate control theory (Melzack, 1973; Melzack & Wall, 1965,1982)

and of other approaches (Weisenberg, 1977, 1980, 1983, 1984)

with motivational-affective and cognitive-evaluative components

of pain. Yet it displaces the unnecessarily narrow, relatively pe-

ripherally located7 on-off concept of a gate by a multidimensional

cognitive space where the different components interact (or fail

to interact) according to simple algebraic models. The proposed

integration processes, to be thought of as different organizations

somewhere in the higher centers of the nervous system, fit well

with the rich and multifaceted behavioral complexes character-izing pain phenomena.

Thus central representation of pain may interact with other

related representations so as to potentiate, attenuate, or even

eliminate a final painful reaction (such as in the following sub-

tractive structure: Perceived Pain = Sensory Pain — Shameful-ness of Overt Expression). Note that the associated integration

its stimulus scale unit, it is not, in general, identifiable (Anderson, 1981,

p. 20). The interested reader should refer to Anderson's 1981 volume

for a discussion of the methodological problems involved.

model may act consciously (as may welt be the case in the above

hypothetical example) or wholly automatically as is sometimes

found in the visual and the auditory systems (Algom & Cohen-

Raz, 1984; Algom & Marks, 1984; Marks, 1979a).

7 With respect to the present research, for example, the substantia

gelatinosa in the dorsal horn of the spinal cord seems an unlikely site

for the modulation of the auditory pulses, despite some available de-

scending pathways.

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Received November 9, 1984

Revision received May 3, 1985