Quantitative neural and psychophysical data for cutaneous mechanoreceptor function

Brain Research, 49 (1973) 1-24 © ElseMerScientificPublishing Company,Amsterdam- Printed in The Netherlands

Review Article QUANTITATIVE NEURAL AND PSYCHOPHYSICAL DATA FOR CUTANEOUS MECHANORECEPTOR FUNCTION

L A W R E N C E K R U G E R AND B E R N A R D KENTON*

Department of Anatomy and Brain Research Institute, UCLA Center for Health Sciences, Los Angeles, Calif. 90024 (U.S.A.} (Accepted May llth, 1972)

SUMMARY

First-order afferent fiber responses associated with two types of slowly adapting mechanoreceptors of hairy and glabrous skin have been analyzed quantitatively by several workers and psychophysical correlations have been inferred. The inputoutput relations for each fiber approximates a sigmoid curve, but other mathematical functions can be fit to these data if some widely accepted arbitrary decisions are made. However, power functions are heavily weighted by threshold measurement, are often not the best fit, and power function exponents vary widely for a given type of receptor. Our own observations as well as the results of previous workers fail to support an obligatory application of linear functions for glabrous skin and power functions for hairy skin. Psychophysical power functions based on subjective magnitude estimation are frequently discrepant with neural data power functions and fail to support the hypothesis of linear transformation of first-order afferent messages by the central nervous system. Information transmission below channel capacity is greater in a single fiber than has been measured in human category discrimination. Direct experimental observation of central neuronal processing is required for an understanding of the enormous difficulties in relating psychophysical and neural data at supraliminal levels.

INTRODUCTION

The form and range or spectrum of energy required to excite each of the known sense organs is known to correlate well with the threshold sensitivity range determined * Present address: Division of Clinical Neurology, City of Hope National Medical Center, Duarte, Calif. 91010, U.S.A.

2

L. KRUGER AND B. KENTON

behaviorally for a variety of organisms, a finding that had led sensory physiologists to hope that neural data concerning stimulus magnitude might be correlated in some quantitative fashion with sensory measurements. The preoccupation of modern psychophysics with determining the nature and validity of various scaling procedures has recently been influenced by attempts to quantify some attribute of sensation magnitude that might relate to stimulus intensity in a manner that could 'tally' with a measure of neural response 23,41,43. Complementary sensory (behavioral) and neurophysiologic (afferent impulse) data have been compared for some aspects of somesthetic discrimination and for single afferent fiber discharges recorded from populations of fibers appropriate to the modality under studyZZ,24,49. The most extensive findings deal with discrimination of the amplitude of skin displacement (studied in both hairy and glabrous skin) measured in terms of subjective magnitude scaling and the comparison of these data with stimulus-response functions and information transmission of slowly adapting low threshold cutaneous mechanoreceptor fibers8,23,26,'50,51. The results have been interpreted to indicate that (1) a relation exists between stimulus and response for a given attribute of sensation and for the appropriate afferent fibers; (2) both the neural and behavioral data display comparable attributes for a given region of skin, and (3) that neural and behavioral data both display linear functions for glabrous skin and power functions for hairy skin, suggesting (4) that the central nervous system operates upon each set of receptors in an essentially linear manner, and (5) that information transmission in single fibers can be correlated with the number of stimulus categories discriminable by human subjects 23. This discussion constitutes a survey and critical account of the available quantitative data including our own observations related to the amplitude of skin displacement in afferent channels and attempts to evaluate whether these findings display a concordance with or can be appropriately compared to behavioral discrimination capacities in supraliminal categories, and particularly those described by power functions.

Slowly adapting mechanoreceptors Evidence has been accumulated in several laboratories that there are at least two principal varieties of slowly adapting (SA) mechanoreceptor fibers innervating vertebrate skin and, although regional differences may prevail, it is apparent that both varieties are present in zones possessing or lacking hairs despite some difficulties in designation of each type in mammalian glabrous skin. The type I SA mechanoreceptor can easily be recognized as the Iggo-Pinkus dome receptors of hairy skin la where distinct epidermal protuberances or 'domes' demarcate the location of the underlying receptor. One or more receptor spots activate a given type 1 SA fiber which displays an irregular impulse discharge pattern, irregular spontaneous activity, sensitivity to cold and a relatively high dynamic sensitivity3,8,11,t2,17. Type II SA mechanoreceptor fibers innervating hairy skin exhibit a more regular impulse discharge pattern (also in its spontaneous discharge) are susceptible to lateral stretch, and therefore

SOMATOSENSORY NEURAL AND SENSORY RELATIONS

3

appear to possess larger receptive fields, and often have lower dynamic and static sensitivity than type I receptor fibers. Both types are undoubtedly present in glabrous skin12,17,18 but the same criteria are less easily applied here because (1) there are no distinct epidermal 'domes' demarcating type I receptors in glabrous skin, (2) there is a wide spectrum of sensitivity to lateral stretch and it is evident that the dermal attachment is less mobile than in hairy skin, (3) the grades of inter-spike interval histogram patterns impose some ambiguity because some irregular discharges are converted to fairly regular patterns at higher stimulus intensities and (4) the level of spontaneous activity or thermal sensitivity may be an unreliable criterion for identification due to variability among fibers and the effects of skin temperature. Despite these difficulties, both types have been identified in glabrous skin of reptiles, cat and primates3,12,17,TM and findings for the human hand indicate that the type I receptor is the most common of all receptor types in this regionla. It may also be argued however, that there is a wide spectrum and substantial overlap between the two principal varietiesa3. The tailure of many investigators to designate the receptor type for glabrous skin is presumably a consequence of this ambiguity. It has been argued by Mountcastle2a that it is the kind of skin rather than the receptor category that is the crucial determinant of sensory attributes. The implication of this view is that morphological and physiological specialization of receptors is less important than the mechanical properties of a given region of integument, i.e. hairy skin receptor fibers display power functions and those for glabrous skin, linear functions. It is our view that the underlying assumptions in constructing this hypothesis should be examined in some detail in order to demonstrate that the available experimental findings render untenable the major conclusions concerning the power law and its application to neural data and cutaneous sensation.

Application of the "power law' to neural data The problems inherent in fitting mathematical functions20 to input-output data are numerous and are influenced enormously by the variability in experimental findings and the means of transforming data for power function plotting. In principle, all data for SA mechanoreceptor fibers can be most readily visualized as a crude sigmoid curve with a fiat portion near threshold, a middle steep portion and an upper fiat portion at saturation. In the strictest sense, Poisson functions are more readily applied to sigmoid curves than power functions, but it is an acceptable practice to eliminate those portions of the curve below threshold and above saturation for fitting power functions. ThreshoM. If the function is substantially affected by the threshold value, the accuracy of this measurement is critical. Unfortunately, the determination of threshold is less precise than other portions of the function where the transducer measuring displacement is the limiting instrument. The small irregularities of epidermal ridges, difficulties in achieving complete depilitation and the errors inherent in placing the stimulus probe tip on the skin surface without displacement or an intervening air

4

L. KRUGER AND B. KENTON

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Fig. 1. The influence of threshold on power functions for 3 sets of hypothetical data. Sixteen points conforming to an ideal (correlation coefficient = 1.000) power function of the form R ~ kS n for each of 3 pre-selected exponents were displaced in 5 ffm steps, corresponding to successive 5 ffm errors of threshold measurement. Best-fitting power functions were calculated for each shift by least-squares analysis and the functions corresponding to thresholds of 5 ffm and 35 #m plotted for each set of points. Gross differences between functions at threshold extremes are a result of the unequal weighting of points by the logarithmic transformation, log R = n log S + log k, and the constraint that each curve must pass through the origin. R, response; S, stimulus intensity; r, correlation coefficient. A, Curve 1 represents an ideal power function with an exponent of 1.906 and a threshold of 35 #m. Curve 2 results from a 30 ffm shift of all points, corresponding to a threshold value of 5 ffm. B, A linear function (curve l, a power function with exponent 1.000) with threshold at 5 fire, and the power function fit resulting from a 30 ffm displacement of the data toward higher values of threshold (curve 2). The assignment of linearity based upon a power function fit is critically dependent upon threshold value. The fitting of linear functions of the form R = nS + k does not require a logarithmic transformation, and the resulting slopes and correlation coefficients are insensitive to threshold variations. C, A threshold variation of 30 #m in this example increases the power function exponent from < 1.000 to a value > 1.000. D, The variation of power function exponents as a function of threshold measurement for the hypothetical data presented in A, B and C. The number at each calculated point represents the correlation coefficient associated with the bestfitting power function.

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o n s t r a t e s t h a t s m a l l shifts in t h r e s h o l d s (in the r a n g e o f o b s e r v e d e x p e r i m e n t a l error), d i s p l a c e the entire c u r v e a n d m a r k e d l y alter the p o w e r f u n c t i o n e x p o n e n t . T h e c o r -

SOMATOSENSORY NEURAL AND SENSORY RELATIONS

5

relation coefficient for the assumed power regression (see below) is reduced as indicated by the values at each point. Slopes and correlation coefficients of the best-fitting linear relationships (Fig. 1D) are, of course, unaffected by such translations. For power functions, it is evident that difficulties in accurate measurement of threshold would impose substantial variability on the power function exponent because points approaching the origin of the curve are heavily weighted for fixing the value of the exponent.

'Normalization' of data Difficulties encountered in assigning accurate threshold values to mechanoreceptor data can be partially circumvented by some kind of 'normalization' in order to achieve meaningful comparison of the calculated stimulus-response relationships in the presence of wide variability. One normalization procedure50 involves the conversion of stimulus values from microns to percent of maximum skin indentation and the conversion of response values to percent of the response elicited by the maximum stimulus. Such a procedure permits the direct comparison of individual fiber parameters and the pooling of data from many fibers. This method, however, does not compensate for inaccuracies in threshold determinations. Applying this normalization procedure to stimulus-response data for a given fiber, the power function exponent will vary widely with translation of threshold values. It should be noted that if a power function is fit to data normalized, in the manner described 'from above', (i.e., assigning 100 ~o to the maximum stimulus value and its corresponding response) the resulting equation assumes the form 50 R

---- ( l O 0 ) t l - n ) . S n

(where S and R refer to the normalized stimulus and response respectively), only when the best-fitting power function passes through the point (100,100). A second normalization procedure entails setting all thresholds at some arbitrary value. For purposes of evaluation, normalization 'from below' was employed with thresholds set at 10/~m and the effect of this coordinate axis translation is shown in Fig. 2 for 3 typical fibers. Comparison of power function exponents before and after normalization reveals the diminution of exponent values upon translation toward the origin. This effect is a direct result of the constraint that a power function of the torm R = kS n must pass through a fixed intercept value. Thus, a receptor fiber yielding a threshold measurement of about 100 #m and a power function exponent greater than 2.0 before normalization, may display an exponent less than 1.0 upon translation. It should be noted that a power function with an exponent of 1.0 is not necessarily equivalent to the corresponding best-fitting linear function because of the logarithmic transformation of the power function equation required by the regression analysis and the constraint of passage through a fixed intercept value. Functional derivation. A critical test for a fiber stimulus-response function

6

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Fig. 2. Stimulus-responsedata for a one second rectangular displacement of the skin, before (A, C, E) and after (B, D, F) normalization, plotted as the best-fitting linear and power functions derived for each of 3 typical slowly adapting mechanoreceptor fibers in cat. Normalization was effected by arbitrarily shifting all measured response thresholds to a 10 #m skin displacement. Note the profound effect of these translations on the exponents and correlation coefficients (r) of the best-fitting power functions for all 3 fibers. Slopes and correlation coefficients for the linear fits are unaffected since the curve fitting procedure for linear functions does not require passage through a fixed intercept value. The best-fitting (least squares) linear function (1), power function (2) and the correlation coefficient (r) determined by regression analysis for each fiber is inserted with each pair of curves. See text for discussion of problems in use of correlation coefficients. would be to determine the validity o f the curve fitting procedure. To our surprise, a p p a r e n t l y high correlation coefficients for a linear regression could be d e m o n s t r a t e d for both hairy a n d glabrous skin of cat. However, these same data could also be fitted to a power function (Fig. 2). The crucial question is, 'which constitutes the better fit?' It has been suggested that the choice can be made objectively by choosing the higher correlation coefficient, b u t it is a p p a r e n t from the examples o f Fig. 2 that the data might appear compatible with either a linear or power function. F r o m the

SOMATOSENSORY NEURAL AND SENSORY RELATIONS

7

infinite set of mathematical functions, 4 families were chosen for analysis: linear, power, exponential and logarithmic. As indicated in Table I, the best-fitting curve selected on the basis of the highest correlation coefficient for a given regression T M is not an invariant function for any given region of skin, although examples of power functions were found for both glabrous and hairy skin. The use of correlation coefficients as a measure of 'goodness-of-fit' for nonlinear functions also might be questioned since the application of a linear regression to a non-linear metric may be misleading on theoretical grounds 9,15and the correlation coefficient does not account for the range of residual errors. The theoretical stochastic problem is beyond the scope of this review, but an analysis of variance in a number of examples readily revealed the practical limitation of identifying a best-fit by choosing the highest correlation coefficient. For example, fiber 10-5 in Fig. 2F shows that a normalized power function for which the correlation coefficient (r) is 0.989 appears to be a better fit than a linear fit where r -~ 0.979, but the standard errors in these two cases are 6.616 and 5.435 respectively, indicating that a linear function may be the best-fit in this case despite the slightly higher value of r for a power function. It should be emphasized that the common practice of choosing a best-fitting function on the basis of the highest correlation coefficient is not a legitimate procedure, and when employed, as in Table I, these values are presented for direct comparison with previous data and do not imply assent with its continued application. The wide variation of exponent values presents serious problems even if power functions are imposed, but this may be partially due to the somewhat arbitrary decisions involved in determining the threshold and saturation levels. In addition, there are several features of experimental design as well as analytic procedure that can potently influence a power function. Methodological discrepancies. Before attempting to compare experimental results in different laboratories it is important to recognize that there may be several variables capable of influencing the form of an input-output function aside from consideration of how to manipulate mathematically or to select data. These include: (a) Identification of the receptor. In many experiments the difference between type I and II SA mechanoreceptors was not or could not be adequately determined. The difference in range of dynamic sensitivity of these two types suggest that receptor category may be a more important variable than skin location. (b) Stimulus duration. Tabular data presented by Werner and Mountcastle 5° suggest that examination o f different fibers with varying stimulus duration might influence the value of the exponent. In order to test this, our own experiments were performed with stimuli of long duration (1 sec). This enabled us to determine the function for successive segments of the response train in 11 fibers (3 type I and 8 type II) of which two examples showing opposite trends are illustrated in Fig. 3. These typical results clearly indicate that stimulus duration significantly influences the power function exponent; especially for short durations. (c) Repetition rate. The slow compliance of the skin results in significant interactions between successive stimuli and, for large amplitude displacements, full recovery to the rest condition may exceed 10 sec 17 for reptilian skin type II SA receptors. Werner and Mountcastle 51 demonstrated that repetition

8

L. KRUGER AND B. KENTON

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rates o f 6 - 2 0 / m i n can p r o f o u n d l y alter the p o w e r function for m a m m a l i a n SA m e c h a n o r e c e p t o r s . S o m e o f the variation in experimental findings is almost certainly due to inter-stimulus intervals that are too short for full recovery. (d) Other variables. Several other variables are u n d o u b t e d l y significant in d e t e r m i n i n g the form o f the m a t h e m a t i c a l function but these require m o r e extensive systematic study for evaluation. They include: the size o f the p r o b e tip indenting the skin, its position in the receptive field, skin and p r o b e temperature, the velocity and acceleration o f i n d e n t a t i o n and regional variation o f cutaneous mechanical impedance. The experimental methods have been described in detail elsewhere 1~,17 but the features crucial to the data presented are the limitation of parameters. For type I fibers, the entire dome was displaced and for type I1 fibers the probe tip was placed approximately in the maximally sensitive point of the receptive field by adjusting lateral position with a micrometer. The probe tip was uniformly 0.25 mm diameter. The stimulus was applied by rectangular pulse activation of a Goodman V47 vibrator with a risetime of less than 2.5 msec at maximum amplitudes. Stimulus duration was uniformly 1 sec and only data for a repetition rate of 6/min are presented in the Tables. The output of a Microsystems strain gauge monitor for displacement measurement was recorded for each response. All functions were derived by at least two ascending and two descending intensity series and all points were included in the analysis. The computer programs used are given by Dixon ~ for the various

SOMATOSENSORY NEURAL AND SENSORY RELATIONS

9

analyses employed, but the basic data relate amplitude of displacement and the total number of impulses elicited in the same manner as previous workers in this field (Tables I and II) as described in detail elsewhere 17.

Coding. Numerous response parameters could be considered in determining input-output functions, but it has been a common, and presumably reasonable, practice simply to count the number of impulses elicited for the total duration of the stimulus. A 'frequency code' of this kind ignores variation in instantaneous frequency during adaptation because of its slow time course but it is obviously possible that the higher frequency initial portion of the discharge may be more important for central analysis. The problem is compounded by the fact that the initial portion of the discharge is critically dependent on the velocity of indentation, the 'phasic' component, whereas the later portion is clearly a function of the 'static' displacement amplitude 11, 47. In the discussion of experimental results to follow it has been assumed that a 'frequency code' provides a suitable response measure but it should be remembered that the central nervous system may process arriving information in a variety of ways and that the number of impulses or mean frequency may not constitute the only code for central analysis. Pooling. Summarizing data displaying significant variation presents numerous problems if differences in populations are to be identified. Averages, means and ranges are generally employed for such purposes, but in the initial studies of this subject the practice of pooling was introduced by Werner and Mountcastle~0. This method consisted of selecting the 10 presumably most typical of 18 fibers and normalizing the functions in the manner described above, in order to plot them together and find a best fitting function for all 10 fibers rather than treat them individually. This unorthodox procedure implicity assumes a central code dependent upon a 'pooled' input wherein the best and worst discriminative capacity of individual fibers may be ignored by the central nervous system in favor of a pooled power function more closely approximating an average value. The danger inherent in any approach of this kind is that the best experimental data may be submerged by the worst and there can be no assurance that the nervous system 'averages' its input or fails to utilize the extremes of any range of functions. This issue becomes particularly important, as we shall see later, in measuring maximum information transmission. Experimental resultsfor SA mechanoreceptorfibers (A) Hairy skin. The pioneer contribution of this subject was provided in an extensive analysis of 'Iggo-Pinkus dome receptor' (type I) fibers innervating hairy skin by Werner and Mountcastle50. Their findings, relating the number of impulses to the amplitude of skin displacement over a range of linearly spaced stimulus intensities, appeared to reveal a stimulus-response relationship for 18 fibers which was best fit by a power function, with exponents varying from 0.27 to 1.17. Some of the measurements were based on results obtained under different experimental conditions including short duration stimuli and high repetition rates; rarely slower than 12/min. The inherent complications in summarizing results in the presence of diverse

10

L. KRUGER

AND B. KENTON

experimental design a n d a wide variation o f exponents was to select the 10 most appropriate fibers a n d plot the normalized data together in order to obtain an exponent for the ' p o o l e d ' result. This procedure yielded a ' p o o l e d ' e x p o n e n t of 0.52 for 10 fibers, a n d the m e a n for all 18 fibers was 0.63 :k 0.24. Before c o m p a r i n g these results with those of other workers, it is i m p o r t a n t to recognize that there are some limitations in interpreting these experiments including: (1) most type I fibers are related to two or more punctate 'domes '3 each of which may exhibit a different d y n a m i c range a n d power function in our experience. (2) Regression analysis for fitting a power function yielded a range of correlation coefficients that would suggest other best-fitting mathematical functions and similar results could be obtained by analysis o f residual errors or variance. (3) It is likely that the analysis includes both type I a n d type II receptor fibers j u d g i n g by the one extensively illustrated series displaying the typical regular discharge pattern of type II receptor fibers. The latter p r o b l e m may be the least serious because subsequent experiments from the same laboratory by H a r r i n g t o n and Merzenich s provided data fitted to p o w e r functions from 7 type I ( ' d o m e ' receptor) fibers with exponents of 0.35-0.77

TABLE 1 QUANTITATIVE DATA ON SLOWLY ADAPTING MECHANORECEPTORS IN CAT ( C ) AND MONKEY

Animal

Type

Number o f units

Mean power function exponent

Range

C C

glabrous glabrous

l0 2

0.892 ± 0.321 0.266-1.256 0.756 ± 0.693 0.266-1.256

C C

II (hairy) II (hairy)

16 3

0.705 ± 0.302 0.161-1.150 0.729 ± 0.173 0.550-0.896

C C

I (hairy) 1 (hairy)

46 6

0.915 ± 0.235 0.480-1.310 0.972 4_ 0.130 0.733-1.310

18 16 7 7

0.634 3- 0.242 0.269-1.169 close to 1.0 0.35 -0.77 -0.39 -0.75

(M)

Mean correla- Source tion coefficient (r)

0.960-]- 0.028 All fibers* 0.988J- 0.001 Best fit by power function 0.939~ 0.049 Allfibers** 0.975J- 0.017 Bestfitby power function 0.951 J- 0.032 Allfibers*** 0.986 ~ 0.006 Bestfitby power function

Other sources

C M M M

1 (hairy) glabrous I (hairy) II (hairy)

0.982± 0.015 § 0.989 ,~§ -§§§ §§§

* 8 fibers best fit by linear function (r -- 0.982 ± 0.015). ** 10 fibers best fit by linear function (~ -- 0.982 3- 0.012), 3 by exponential function ({ -- 0.955 30.054). *** 38 fibers best fit by linear function (r = 0.974 ± 0.019), 2 by exponential function (r = 0.945 ± 0.018). § Werner and Mountcastle~0. §§ Mountcastle et al.Z6; Werner and Mountcastle~1. The value of r refers only to a linear function fit. §§§ Harrington and Merzenich 8. 53 type ! and 34 type II fibers were studied from which 7 of each were selected.

SOMATOSENSORY NEURAL AND SENSORY RELATIONS

11

and 7 type II fibers with exponents of 0.39--0.75; all in hairy skin. These data were selected (although by undefined criteria) from a large sample and suggest that there is no essential or significant difference between the range of power function exponents for type I and II receptor fibers of hairy skin; a conclusion consistent with our own experimental findings (Table I) although the range differs in the report from each group of workers. The summary of results in Table I might suggest that the application of power functions is supported by available findings because there is extensive overlap despite wide variation in the value of the exponent. However, it is important to recognize that some workers have failed or not attempted to apply power functions to similar data for hairy skin. For clearly identified type I 'dome' receptor fibers of hairy skin one might argue that linear functions might be more appropriate. Evidence for this view is found in the following observations: (1) Iggo and Muir 11 displayed a linear function for these receptors in cat hindlimb. (2) Our own findings for cat hairy hindlimb skin (Table I) indicate that 38 out of 52 fibers were best fit by a linear regression (correlation coefficient = 0.974 zk 0.019) and of the 6 fibers best fit (on the basis of highest correlation coefficient) to a power function the mean exponent was 0.972 zk 0.130 and therefore sufficiently close to unity to merit consideration for a rough linear fit although the range of exponent values might not support this conclusion. (3) Darian-Smith et al. 4 found that for 23 of 29 SA receptor fibers (type unspecified) innervating the hairy skin of the face, a linear function was the best-fit. The remarkable feature of these seemingly discrepant findings is that the experimental results do not appear to be strikingly inconsistent; only the interpretations differ. As noted above and illustrated in Fig. 2, power and linear functions can often be applied to the same data with reasonable success irrespective of whether the correlation coefficient or the residual error is employed as the criterion for goodness-of-fit. There is no compelling reason to choose between these alternatives and an agnostic view would not seem inappropriate. We shall return to this issue later when considering psychophysical data, for it is our thesis that preoccupation with the psychophysical 'power law' may have influenced attempts to impose power functions on neural data. (B) Glabrous skin. The arguments for applying linear functions to data from glabrous skin SA mechanoreceptor fibers are perhaps more persuasive than for hairy skin because there is less variation in experimental findings, but the same difficulties reappear. The conclusion of the Johns Hopkins workers 26,51 that linear functions can be applied to SA fibers in glabrous skin appear to be supported by our own findings (Table I). Power functions can also be applied to these same data with a degree of success comparable to that shown for hairy skin receptors, but the 'best-fit' (i.e. if the highest correlation coefficient is assumed to be an acceptable measure) for most fibers may be a linear function. Unfortunately, the available data fail to account for different receptor types. Other workers currently pursuing this problem (Pubols and Pubols, personal communication of unpublished data) have found examples of best-fitting linear functions for glabrous skin in squirrel monkey and raccoon, but have a larger sample that was best-fit by a logarithmic function. For the present, how-

12

L. K R U G E R A N D B. K E N T O N

ever, there is no serious contraindication for imposing linear functions; they prove adequate for description and possess the virtue of simplicity. (C) Conclusion. Imposing mathematical functions on input-output relations for SA mechanoreceptor fibers has not yet met with a firm consensus for a variety of reasons. Methodological differences emphasize that several identified variables affect the form of any function and the wide range of variation precludes a simple summary despite the application of procedures such as normalization and pooling of data. The available data surprisingly have failed to reveal the essential difference between two types of receptors of differing dynamic sensitivity. The suggestion that glabrous skin receptor fibers display linear functions might be supported by most findings, but compelling evidence is lacking for imposing power function rather than linear (or other functions) for hairy skin receptors 52. If power functions are nevertheless assumed to be appropriately applicable to hairy skin receptor fibers, (or specifically to type I 'dome' fibers as contended by Werher and Mountcastle 5°) for purposes of comparison with psychophysical data, some relevant physiological findings should be considered. It is now known that first-order fibers from several types of low threshold mechanoreceptor neurons, including SA type II fibers, enter the dorsal columns and that the type I SA fibers take another route 29. This does not preclude postsynaptic dorsal column representation of type I dome receptors 2 but a functional separation is suggestive. Of possible greater consequence are the observations noted by Harrington and Merzenich s concerning the sensory role of dome receptors. Their findings, as well as some early literature 6,a° that they have uncovered, indicate that excitation of domes in a manner suitable for eliciting fiber discharge fails to evoke a sensation of touch in man. However, even if type I SA mechanoreceptors lack a sensory role or fail to contribute to the lemniscal system, this does not preclude consideration of power functions for type II receptor fibers and thus brings us directly to a consideration ofpsychophysical power functions.

The psyehophysical 'power law' The merit of Stevens '4°,43 alternative formulation to Fechner's law is attested to by a large number of experiments which conform to the principle that equal stimulus ratios produce equal sensation ratios. This ratio rule implies that sensation magnitude grows as the stimulus magnitude raised to a power and that the power exponent may differ according to the estimated aspect of a given modality. Crossmodality matching, inverse scaling (e.g., dimness instead of brightness) and scaling at differing adaptation levels provide ample evidence that the psychophysical power law expresses a general formulation for sensory estimations in most modalities. Jones la showed that the application of Stevens' scaling method to subjective magnitude estimates for human hairy forearm skin revealed power functions with exponents of 0.74 (the value chosen by Mountcastle 2a to support exponents comparable to a 'pooled' exponent of 0.52 for neural data) and 1.3, using flat probes of 2.5 and 0.2 mm diameter respectively (Table II). A reinvestigation of the problem by Harrington and Merzenich 8 using a 2 mm diameter stimulus probe tip revealed a power

1.1 1.0 0.9 0.74 1.3 0.4

0.25 1 0.25 1 1 2 0.25 2

0.892 near 1.0 0.915 0.634 0.52** -0.705 --

0.266-1.256 -0.480-1.310 0.269-1.169 -0.35-0.77 0.161-1.150 0.39-0.75

(5) (6) (5) (7) (7) (3) (5) (3)

Source

* C, cat; M, monkey. ** Obtained by a power function fit to normalized, pooled data from 10 (of 18) fibers displaying power function exponents less than 1.0. (1), Stevens43; (2), Mountcastle2Z; (3), Harrington and Merzenich8; (4), Jones*S; (5), See Table I; (6), Mountcastle et al.2~; Werner and Mountcastle 51; (7), Werner and Mountcastle 5°.

-2 2 2.5 0.2 2

Region of skin Probe tip Mean exponent Range diameter (mm) Glabrous Glabrous Hairy (I) Hairy(I) Hairy(I) Hairy (I) Hairy (II) Hairy (II)

Glabrous Glabrous Glabrous Hairy Hairy Hairy

(1) (2) (3) (4) (4) (3)

C M C C C M C M

Animal*

Region of skin

Source

Probe tip Mean exponent diameter (mm)

Neural data

Subjective magnitude estimations

COMPARISON OF POWER FUNCTION EXPONENTS FOR SUBJECTIVE MAGNITUDE ESTIMATIONS AND NEURAL DATA

TABLE II

Z

> .]

r~

Z

>

0

>

~r

14

L. KRUGER AND B. KENTON

function exponent of 0.4 for mean normalized data (Table I1). The apparent discrepancy in these 3 values should not be construed to imply that the results were highly variable or that the experiments were in any way defective; the differences are presumably related only to the variables in experimental design. Published results for human glabrous skin are less extensive, but the power function exponents appear to differ from those reported for hairy skin. Subjective magnitude estimates appear to be approximately linear 23 or are best fit by a power function with a slope greater than 0.9 (ref. 8) and therefore approaching 1.0 (i.e., a linear function) as propounded earlier by S. S. Stevens 39 (Table II). Other measurements with larger probes and physical units measured in pounds rather than indentation 37 provided an exponent of 1.1, but the application of an alinear force-displacement conversion factor 13,50 would render this value discrepant (to an exponent of 1.83) with the above findings. The difficulty in obtaining an invariant power or linear function for a given region of skin may be a feature of this form of scaling. Several reviewers of this problemZ,~O,2S,32,35 have wrestled with the numerous variables that influence magnitude estimations and the difficulty in relating the results to liminal (differential) discrimination data. Experimental design and the history of the observers determine the exact form of magnitude scales and Poulton 32 has made explicit several factors that clearly influence the choice of magnitude values. These factors include: (1) the range of stimuli, (2) whether the range includes the threshold region, (3) the position of the standard (or reference stimulus) within the range, (4) the distance of the first variable from the standard, (5) whether the subject uses a finite set of numbers, and (6) the number given to the standard. After the first estimate, judgments have 3 distinct determinants: 'prior context, present context, and the observers' actual experience of sensory magnitude '32. The latter is what the experimenter generally wishes to study but the other factors listed above have been shown in numerous experiments to influence the exponents of the power function, and indeed the validity of a power function is not always secure 1. The generality of the exponent offered for a given sensory dimension is still to be established. The value of the exponent is perhaps more compatible with Poulton's 32 learned calibration theory than with the operation of a sense organ39, 43. It would be most surprising if central processes involving judgment could be described adequately in terms of the behavior of sense organs 41. Inevitably one must conclude that the power function for subjective magnitude estimation in a single sensory dimension or for a specific category of sense organs is not yet susceptible to precise specification. Context, learning, size of stimulus and the several crucial experimental design features discussed by Poulton 32, all dispute the choice of the single 'correct' exponent for magnitude estimation. Comparison of psychophysical and neural data. If an invariant magnitude or category scale estimate were obtainable, we might still ask 'what range of power function exponents would be acceptable as indicative of a correlation?" The findings are summarized in Table II and it is apparent that the wide range of exponents for neural input-output functions poses serious problems for valid comparison because small exponential changes may reflect wide variation in sensitivity (e.g., for a stimulus

SOMATOSENSORY NEURAL AND SENSORY RELATIONS

15

intensity of 500 #m, ST M represents an approximately 4-fold increase over S°.52). For hairy skin, human subjective magnitude estimation has been fitted with power functions displaying exponents ranging from 0.4 to 1.3 and for those neural data fitted to power functions (i.e., excluding several results fitted to linear functions discussed above), the exponents encompass at least as wide a range (Table II). The data for glabrous skin presents similar problems, but here an approximate linear fit for both neural and psychophysical data might be considered. However, this does not imply that the same linear functions are applicable to any given set of neural or psychophysical data and the significance of any such tally remains to be established. Mountcastle' s hypothesis

The assumption that linear functions are applicable to neural data for glabrous skin receptors (regardless of type) and to magnitude estimation for the human hand, and power functions to both neural and psychophysical data for hairy skin has led to a powerful generalization offered by MountcastleZ3: 'for one and the same afferent system, and dealing with the same attribute of the same sensory quality, quite different relations obtain between stimulus and response (both neural and behavioral), depending upon whether glabrous or hairy skin is stimulated, and that these differences are uniquely set by the transforming properties of the two sets of receptors concerned. The brain operates upon either in a linear manner'.

The latter statement is supported by an example of a thalamic ventrobasal neuron with a glabrous skin receptive field displaying an essentially linear function and an example of another thalamic neuron excited by a 'dome' receptor (type I) of hairy skin exhibiting a power function with an exponent of about 0.5. The 'different relations' for hairy and glabrous skin imply a fundamental difference between the power functions for hairy skin and linear functions for glabrous skin and not that different receptors are involved since none of the available data provide distinguishing functional relations for type I and II receptors. One might ask, 'is the functional difference between hairy and glabrous skin related to the mechanical properties of the surrounding tissue rather than the receptor?' and might further inquire into those neural data for hairy skin that conform to linear functions. At our present state of knowledge, the imposition of a simple dualism appears unwarranted. The suggestion of linearity in the central nervous system has been uniquely applied to the somatosensory system since data for at least the visual and auditory systems clearly document the complexity of processing at various neuronal levels. Taken at face value, Mountcastle's hypothesis implies that if a single first-order fiber displays a power function and the whole organism's behavior can be described by a power function, the intervening events must in net effect be linear. However, it should be intuitively evident that two power functions cannot be linearly related except in the special case of identity, and surely the range of exponents for neural data power functions eliminates the possibility of an exact tally. Thus the linear trans-

16

L. K R U G E R A N D B. K E N T O N

formation hypothesis is untenable for hairy skin unless fixed identical power exponents can be obtained. Glabrous skin receptor transformation may be susceptible to linear analysis, but this will require a detailed study of functional relations in medullary, thalamic and cortical neurons and it would be surprising if all input-output curves could be best fit by linear functions. In summary, neither the dichotomy in mathematical functions nor the linear transformation aspects of the hypothesis appear to be supported by available published data. It is our conclusion that the existence of close correlation between neurophysiological data and subjective magnitude estimation has not yet been demonstrated conclusively, and that any concordance of exponents in these two distinct measures might constitute nothing more than a gratuitous analogy. Other somatic receptors The failure to relate neurophysiological data to magnitude estimation does not imply that psychophysical correlates are unattainable. The smallest detectable position alteration of a joint by a human observer may approximate the smallest change in joint angle capable of altering the discharge rate of neurons subserving joint receptors 25, although here too the precision of the correlation might bear scrutiny. Rosner and Goffa4 have drawn attention to the observation that thalamic neurons sensitive to joint rotation display power functions with an exponent of approximately 0.7 (ref. 25), but the best comparable psychophysical studies, based on finger span 45, yielded an exponent of 1.3. Similarly, the threshold detection of vibration can be readily compared with two sets of rapidly adapting mechanoreceptor fibers or cortical neuron discharge patterns 21,27,46. Subjective magnitude estimates of vibratory sensation are approximately linear (with some deviations at different frequencies) 21,42,46; a relation that is not conferred by single first-order afferent mechanoreceptors (which also differ widely in their sensitivity). A nearly linear successive recruitment of many fibers sensitive to vibration has been invoked to explain the discrepancy with linear subjective magnitude estimation 27 and undoubtedly other models could be devised to relate the response of other neuronal populations to psychophysical data. However, until the inferences of such models can be tested experimentally, the relation of the stimulus-response function of single receptor fibers and human subjective magnitude estimation might reasonably remain an open issue. Discrimination and identification Discrimination of differences between two stimuli presented in pairs would provide another measure by which to evaluate the capacity of a sense organ discharge to distinguish stimuli of varying magnitude. It should be obvious that human discrimination might exceed the information capacity of a single afferent channel. Even untrained observers are capable of distinguishing the pitch of many thousands of tones, and this ability would certainly require a large array of neurons. However, individual identification of pitches is quite limited and perhaps related to the subject's concept of numbers because experimental findings for this 31 and a variety of other

17

SOMATOSENSORY NEURAL AND SENSORY RELATIONS 80-

U/V/7- 24AS = 5)j

4

R=0.270S+ 0.851 r =0.989 " ~

70-

60-,e~- 50o')

or" 4 0 -

N ~ z

30-

rc

20-

I0-

I T Analysis: No. of Levels : 24'3zzs : 17.54

4'o ~'o 8'o-,6o ,2~ ,40 ,~o ,@o 26o 2~o 24o s: DISPLACEMENT (#) Fig. 4. Determination of the number of discrete, identifiable levels for a type I slowly-adapting mechanoreceptor fiber using an intuitive graphical solution. The vertical and horizontal line segments which constitute each 'box' represent one standard deviation of stimulus intensity and fiber response, respectively. The initial stimulus categories were set at 5/~m increments and the standard deviations calculated for the responses within each 5/~m bin. The standard deviation for each stimulus category was then determined for each response category to complete the 'boxes'. Using an arbitrary criterion of less than a 50% overlap, 18 discrete levels of stimulus intensity could be distinguished for this fiber. The corresponding information theory analysis using a 5 #m stimulus bin width (see Fig. 5) yielded 17-18 discrete levels. This value for the number of levels is less than the channel capacity (i.e., the maximum possible information transmission). sensory continua reveal that the precise number of stimulus categories that can be identified by absolute judgment is relatively fixed at a 'magical number of 7 4- 2 '2~. For the analysis of afferent impulse data, categories of stimulus intensity can be distinguished by identification of response categories for different levels of stimulus intensity. This problem has been dealt with in recent years by applying the statistical concepts of information theory. But before pursuing this approach in detail, let us consider a simple intuitive graphic solution to category separation, assuming a code based on the number of impulses as in the earlier discussion. In this example (Fig. 4) a type I mechanoreceptor in cat hindlimb hairy skin displayed a stimulus-response relation that is here represented as a linear function. The statistical analysis was performed by dividing the stimulus continuum into 5 / t m 'bins' of stimulus intensity. For each bin, a mean response and its standard deviation was determined in order to define a range of responses to be subsumed within a single stimulus range. All other points which fell within this range were then determined in order to define a stimulus range for a given response range. The length and position of the horizontal bar for each 'box' indicates the standard deviation of all stimuli which elicited a response within one standard deviation of the response range, expressed as a vertical bar. The entire continuum was explored in this manner in 5 # m steps and a series

l 8

L . K R U G E R A N D B. K E N T O N

7-

UNIT 24-4 /

.... M~IM~MI ~ N N

~ ~ ~I ~ A ~

~

I ~~ i

~6~ ~~

~ ~ ............... l ~

/

........

/

25 Z O

~4Z a:2 Z (D

O ks~

_z

I.

~ 0

'

0 1 - -

I

I

2

----7

- - -

3

Ioo 200 300 DISPLACEMENI(,~)

I

$

I

I

4

5

6

7

STIMULUS UNCERTAINTY (bits)

Fig. 5. Information transmission functions for a type I hairy skin slowly-adapting mechanoreceptor fiber using two different values of response increment (AN = 1,2). Maximum measured information transmission for 6.74 bits of stimulus uncertainty (AN = 1) was 5.13 bits, corresponding to 35-36 distinguishable levels of stimulus intensity; channel capacity (i.e., saturated information transmission) must be above this value. The maximum discharge elicited by a rectangular-pulse mechanical displacement of 1 sec duration was 66 impulses, and the maximum possible channel capacity of 6.044 bits (corresponding to 66 discrete levels) is represented by the interrupted line. The best-fitting stimulus-response relationship, a linear function, is plotted in the inset. R, response; S, stimulus intensity; r, correlation coefficient. The arrow indicates the point calculated using a 5/zm stimulus bin width (I.T. = 4.13 bits corresponding to 17-18 discrete levels), the value employed for the calculations performed on the same stimulus-response data illustrated in Fig. 4.

o f ' b o x e s ' was constructed constituting g r a p h i c s t i m u l u s - r e s p o n s e categories, based on the a r b i t r a r y criteria stated above. Tests for independence o f categories m u s t also be chosen arbitrarily a n d in this example, we elected to define categories as any t w o ' b o x e s ' that showed less than 50 ~ overlap. These were then c o u n t e d as a m e a s u r e o f discrete categories. Obviously, other criteria or tests could be selected a n d s o m e w h a t different values would be derived. The cumulative exclusive categories a c c o r d i n g to the a b o v e criteria provides 18 discrete levels in this example. These same d a t a can be analyzed by a p p l i c a t i o n o f the m o r e sophisticated statistical m e t h o d s a p p r o p r i a t e to i n f o r m a t i o n theory, from which a similar value can be derived (Fig. 5, 17-18 levels in this example, for a stimulus uncertainty based on 5 / z m bin widths), a l t h o u g h there is no assurance that the m a x i m u m i n f o r m a t i o n transmission m e a s u r e d represents the true m a x i m u m o r channel capacity. However, before considering i n f o r m a t i o n theory analysis it would be useful to consider precisely what kind o f categories derived f r o m psychophysical d a t a might be meaningful a n d c o m p a t i b l e with s t i m u l u s - r e s p o n s e categories for afferent impulse data. Absolute j u d g m e n t s o f distinguishable stimuli obviously fall below the n u m b e r o f discriminable pairs a n d at present it is difficult to relate cumulative j u s t - n o t i c e a b l e

SOMATOSENSORY NEURAL AND SENSORY RELATIONS

19

differences (jnd's) to magnitude judgment scaling. The number of jnd's in a given sensory continuum is not a fixed value; it can be altered by a number of experimental factors such as stimulus size, interval between stimulus presentations, stimulus range, statistical criteria, sequence, etc. It is also clear that magnitude estimations, category judgments and jnd's provide different functions 3s,49. Although category and magnitude scales can be related in two classes of sensory continua 44 these relations are not yet secure and are seriously debated 1. Furthermore, it is not yet possible to derive jnd's from category or magnitude estimates. In principle, the graphic solution for afferent nerve discharge presented in Fig. 4, may be analogous to a discriminability scale based on counting jnd's, but the arbitrary factors introduced by experimental design, statistical assumptions, etc. might render any correlation rather fortuitous. In absolute judgments of magnitude for a variety of sensory continua, by contrast, an astonishing uniformity is revealed by information theory analysis, such that the mean maximum information transmission is approximately 2.6 bits, or 6-7 discrete levels within a given continuumT, 2~.

Information transmission in afferent channels The application of information theory to impulse data for afferent fibers can theoretically provide another means of determining the number of identifiable categories. The statistical method is simply to construct a joint uncertainty matrix wherein it is possible to determine whether response categories vary with stimulus categories over a given range. When finer subdivision of stimulus categories (i.e., increasing stimulus 'uncertainty') no longer yields different response categories, the curve of information transmission as a function of stimulus uncertainty reaches its maximum and is saturated, i.e., reaches zero slope, and 'channel capacity' is achieved. Channel capacity can be described as an exponent X where 2x equals the maximum number of discrete identifiable categories. This method has been applied with particular success to slowly adapting mechanoreceptors in which the number of impulses elicited by each stimulus can be studied systematically in great detail. The pioneer studies of Werner and Mountcastle 5°,51 suggested that information transmission in single afferent fibers provides the same number of identifiable categories as can be derived from human subjective magnitude estimations. This remarkable correlation requires careful examination of the method and its limitations as well as the nature of underlying assumptions and the security of conclusions drawn. Choice of variables. The experimental design in these studies is crucial to the range of stimulus uncertainty that can be measured. The simplest approach is to choose a given number of stimulus intensities (measured as amplitude of skin displacement) and apply iterative stimuli for each level in order to measure the range of response categories (or variance) for each intensity. The intervals between stimulus intensities may be spaced evenly50, but if the discriminable intensity increments (AS) are not constant, as might be expected, an alinear stimulus scale would provide a more intensive sampling of the continuum 16. This is intuitively obvious because a

20

L. K R U G E R A N D B. K E N T O N

difference of only a few microns can alter the response markedly near threshold but would have a negligible effect in the higher range. Since each value of stimulus uncertainty is based on the division of the stimulus range into bins of varying width, it is evident that small steps at the lower end of the scale are essential for determining the level at which stimulus intensity increments (AS) are no longer discriminable, i.e., the level of saturated intbrmation transmission or channel capacity. Choosing a small fixed number of stimulus categories sacrifices stimulus uncertainty for a large sample in each response category. Alternatively, a large number of stimulus categories would limit the sample in each response category, and might be warranted only in a system in which response variability for a given intensity is small. If the stimulus bins (AS) remain too wide, and each consists of stimuli capable of eliciting several response categories, saturated information transmission cannot be measured without introducing the dangerous procedure of extrapolating to channel capacity. The choice of response increments is less arbitrary because an increment in the number of impulses (A N) can only be expressed as integral values. Available experimental data do not permit us to decide whether second-order neurons detect differences of one, two, or more impulses in a train; thus, the choice here is an arbitrary one subject to future modification. Measurement of channel capacity. When an increase in stimulus uncertainty (i.e., an increase of the number of stimulus categories) fails to increase information transmission, this maximum is an estimate of the channel capacity. This has rarely been achieved 16 because exploration of more than 4-5 bits of stimulus uncertainty requires sampling a large number of different stimulus intensities and practical experimental circumstances necessarily often limit the size of the sample. The experimental results reported to date for slowly adapting mechanoreceptor fibers16, 5°,~1 preclude reaching a 'true' channel capacity within the range of stimulus uncertainty explored. The manner in which this difficulty might be circumvented is best considered by turning to the experimental findings. Experimental results. The first contribution to the subject by Werner and Mountcastle ~° established the basic methodology for application of information theory to this problem and provided extensive quantitative data for type I afferent fibers. For each of 14 fibers, a large number of responses was recorded for each of a fixed number of constant intensities spaced equally along the continuum and presented randomly. In the range of stimulus uncertainty explored (usually 4-5 bits maximum), information transmission varied in different fibers and apparently no single fiber yielded an information transmission function of zero slope. However, a negatively accelerating function was displayed for the last two points on the curve in some cases, suggesting that a maximum or asymptotic value might be extrapolated. Instead of extending the range of stimulus uncertainty until channel capacity (zero slope) was achieved, the tactic chosen was to pool the data points for the 14 fibers in the form of a scatter diagram. This procedure reveals a cluster of upper values for information transmission of approximately 2.5 bits, with only a single grossly discrepant high value. Before accepting this estimate at face value, it should be emphasized that 'pooling' may result in elimination of data reflecting higher discrimina-

SOMATOSENSORY NEURAL AND SENSORY RELATIONS

21

tive capacity. Furthermore, it cannot be claimed that the maximum information transmission measured is the maximum that can be reached, (i.e., channel capacity), unless the information transmission function for each fiber is extrapolated to zero slope. Such extrapolation may be unwarranted because channel capacity is often reached abruptly rather than asymptotically16. With these limitations in mind, reexamination of the data presented by Werner and Mountcastle suggests that the maximum information transmission measured for type I fibers of hairy skin was about 2.5-2.7 bits, and if it can be assumed that this value is not substantially below channel capacity, the 'pooled' system can approximate discrimination of 6-7 discrete intensity levels for the statistical criteria employed. In their analysis, response increments of 2 spikes (A N ---- 2) were chosen. If the system could measure one impulse differences, the estimate would be higher. An example of information transmission for receptor fibers of primate glabrous skin51 revealed a slightly higher value (3.3 bits) for a stimulus uncertainty of less than 4 bits, but since the curve displays a steep positive slope it is evident that the maximum transmission capability (channel capacity) was not determined and that glabrous receptors can distinguish at least 9-10 discrete levels. This brings us to the upper limit of the magical number of 7 ± 2 derived from psychophysics and with the upper limit of the afferent data still undetermined, it seems imperative to extend the information transmission function by exploring a wider range of stimulus uncertainty. A serious attempt to achieve this end proved disappointing because channel capacity was never reached for a single mammalian fiber, although one reptilian type II fiber displayed a channel capacity of 4.63 bits 16. Within the range of stimulus uncertainty we explored, the maximum information transmission measured for 19 fibers (including type I, and type II in both hairy and glabrous skin), ranged between 3.95 and 5.37 bits. In the lower range of stimulus uncertainty, the data were clearly compatible with those of the extensive earlier studies reported by Werner and Mountcastle5°,51 but higher values have been measured (Fig. 5). These maximum information transmission values must be interpreted cautiously because without extending the function, there can be no guarantee that they approach channel capacity. However, if the values did approximate channel capacity they would correspond to 15-42 discrete stimulus categories for a response increment of one impulse (A N = 1), and even if two impulse increments were required for discrimination, maximal transmission values would not be reduced by more than about 30~. These values are clearly discrepant with human subjective magnitude estimations. Conclusion. The assumption that the maximum information transmission capability of slowly adapting mechanoreceptor fibers has been determined adequately appears to be unwarranted at present and even the maximum values determined to date 16 are probably below channel capacity. Furthermore, most of the data have been collected at stimulus repetition rates that fail to exclude interactions between successive stimuli and it has been clearly shown that information transmission can be reduced dramatically at higher stimulus repetition ratesSL However, it is conceivable that channel capacities for single fibers might correlate with some measure of human discriminative ability; perhaps differential discriminations.

22

L. KRUGER AND B. KENTON

A fundamental difference in the mathematical functions describing receptors of glabrous v s . hairy skin and the accuracy in determining power function exponents or the legitimacy of applying power functions may not be established with sufficient certainty to warrant psychophysical comparisons and suggested correlations might be fortuitous. Perhaps the admonition of Rosner and Goffa4, 'beware of psychophysicists bearing gifts', is appropriate. In the absence of appropriate psychophysical and neurophysiological data, we can only conjecture that it would seem unlikely that a linear transformation of first-order afferent fiber information could define human discrimination of magnitudes without taking the interaction of patterns of input into account. If central neuronal processing of multiple fiber inputs is eclipsed by the limits imposed by first-order afferents, the use of statistical methods of information theory has not yet proven adequate to the task of establishing this principle. The psychophysical power law must be evaluated independently of neurophysiological data until the role of sense organs in magnitude estimations can be evaluated and related to a broader context of psychophysical data. The complexity of central processing in the visual system10and the variety of functions describing stimulus-response relations at several levels of the auditory systemx4 suggests that the differences between cortical neuron and first-order afferent functions still require unraveling before neurophysiologic data can be invoked for the quantitative description of sensory (behavioral) events. Cogent arguments on other grounds34, 4s have been offered by psychophysicists challenging the proposition that subjective power functions reflect the inherent properties of 'sensory transducers'. The challenge for the future of sensory neurophysiology lies in deciphering the mechanisms for processing the multiplicity of complex afferent channels to the central nervous system. ACKNOWLEDGEMENTS

We are indebted to numerous colleagues and friends who have contributed in various ways to the preparation of this review but must single out Albert W. Perga, Robert J. Sclabassi, Jos6 P. Segundo and Malcolm Brodwick for particularly invaluable discussions. This research was supported by U.S. Public Health Service grant NS-5685. Computing assistance was obtained from the Health Sciences Computing Facility, UCLA, sponsered by NIH grant RR-3 and from the Data Processing Laboratory, UCLA Brain Research Institute, sponsored by NIH grant NS-02501.

REFERENCES 1 ANDERSON, N . H . , Functional measurement and psychophysical judgment, Psychol. Rev., 77 (1970) 153-170. 2 BROWN, A. G., Cutaneous afferent collaterals in the dorsal columns of the cat, Exp. Brain Res., 5 (1968) 293-305. 3 BURGESS, P. R., PETIT, D., AND WARREN, R. M., Receptor types in cat hairy skin supplied by myelinated fibers, J. Neurophysiol., 31 (1968) 833-848. 4 DARIAN-SMITH, I., ROWE, M.J., AND SESSLE, B.J., 'Tactile' stimulus intensity: information transmission by relay neurons in different trigeminal nuclei, Science, 160 (1968) 791-794.

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