integration of noxious stimulation across separate somatosensory communications systems
TRANSCRIPT
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