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Peripheral neural basis of tactile sensations in man: I. Effect of frequency and probe area on sensations elicited by single mechanical pulses on hairy and glabrous skin of the hand
Brain Research, 219 (1981) 1-12
I
Elsevier/North-Holland Biomedical Press
Research Reports P E R I P H E R A L N E U R A L BASIS OF TACTILE SENSATIONS IN M A N : I. E F F E C T OF F R E Q U E N C Y A N D PROBE AREA ON SENSATIONS ELICITED BY S I N G L E M E C H A N I C A L PULSES ON H A I R Y A N D G L A B R O U S SKIN OF THE HAND HEIKKI H/~M~L/~INEN and TIMO J/~RVILEHTO Department of Psychology, Experimental Laboratories, Ritarikatu 5, SF-O0170 Helsinki 17 (Finland)
(Accepted January 1st, 1981) Key words: single tactile pulses - - absolute thresholds - - touch thresholds - - magnitude estimation -
-
hairy skin - - glabrous skin - - man
SUM MARY Tactile thresholds and sensation magnitudes for single mechanical pulses of varying frequency and probe area were studied in order to provide psychophysical data for correlations of tactile sensations with functional properties of different types of human peripheral nerve fibers. Single mechanical pulses were delivered to the hairy or glabrous skin of the hand by means o f a perspex probe (area 0.07, 0.7, 3.1, or 12.5 sq.mm) fixed to the moving coil of an electromechanical vibrator. The frequency of the single pulse was 20, 60 or 150 Hz. Absolute and touch thresholds were measured with a method of production. Suprathreshold sensations were measured with the method of magnitude estimation (6 predetermined displacement amplitudes ranging from 50 to 950 am). Both absolute and touch thresholds were significantly higher on the hairy than on the glabrous skin. The absolute thresholds varied between 44 and 140 # m on the hairy and between 9 and 45/~m on the glabrous skin; the touch threshold varied between 75 and 300/~m and 24 and 153 #m, respectively. Lower threshold values were obtained on both skin areas with increasing frequency of the pulse and probe area, the latter effect being significant only for the hairy skin. Standardized magnitude estimation functions could be described with power functions on both skin areas, the exponents of the functions varying between 0.70 and 1.41 on the hairy and between 0.55 and 0.86 on the glabrous skin. The equi-sensation contours showed the difference of sensitivity between the skin areas. Larger sensation magnitudes were obtained with increasing frequency of the pulse and probe area on both skin areas. These psychophysical findings indicate that there is a functional difference at absolute sensation thresholds between hairy and glabrous skin. This difference, however, disappears at higher sensation levels. 0006-8993/81/0000-0000/$2.50© Elsevier/North-Holland Biomedical Press
INTRODUCTION The knowledge of peripheral neural coding of mechanical changes in the skin is based mainly on electrophysiological work in different animal species. These studies have shown that the transducing properties of cutaneous mechanoreceptors are so diverse that it is difficult to ascribe to them a functional role with respect to cutaneous sensations on this base. Therefore, in recent studies the electrophysiological analysis in animals was combined with psychophysical research in man using identical stimulation procedures 4-6. In some of these studies 14 psychophysical experiments were carried out also with the animal (monkey) who served in the electrophysiological experiments, in order to provide a better basis for comparisons. However, even in this case psychophysical observations and electrophysiological recording are carried out in different experiments, which prevents direct correlations between psychophysical performance and activity in peripheral neural units. During the last decade the method of percutaneous microelectrode recording from human peripheral nerves 17 has enabled a detailed study of the characteristics of human cutaneous neural units and it has also made it possible to perform simultaneous measurements of the sensations and activity in different receptor types. At present, several reports on physiological characteristics of different types of human receptors located in the hairy and glabrous skin are available (see refs. 9 and 18, for reviews), but simultaneous measurements of cutaneous sensations and unit activity in skin nerves are still few. In our approach to the neural basis of cutaneous sensations we proceeded on 3 lines. First, we determined in separate psychophysical experiments the dependence of sensations on some stimulus parameters. Second, with the method of percutaneous microelectrode measurements we collected data on the physiological properties of the peripheral units to screen possible candidates for the coding of sensations. Finally, we combined the psychophysical measurements of the sensations with simultaneous measurements of the unit activity from the nerves. In the first part of the present report we describe results from psychophysical measurements of tactile sensations elicited by short tactile pulses. As there are no systematic studies using this type of mechanical stimulation we have examined the dependence of sensation thresholds as well as magnitude of sensation upon the frequency of the single pulse and the area of the stimulus probe on both the hairy and glabrous skin of the hand. In the second part of the report properties of cutaneous mechanoreceptors in the human hairy skin are described and results of simultaneous recording of peripheral unit activity with measurements of sensation threshold and magnitude of sensation are presented. METHODS
Subjects and stimuli Eight healthy subjects (Ss; 3 females and 5 males; age 22-30 years) participated in sensation threshold measurements and two additional Ss (2 females) in the estimation of sensation magnitude. The S was sitting with his left hand resting on a table. The hand was supported by a vacuum cast.
The stimulation sites were the hairy skin of the back of the hand and the glabrous skin of the thenar eminence. In order to have comparable sites of stimulation in all Ss a spot on the skin with a sensation threshold below 0.05 g (determined with a von Frey hair) was marked. The skin around the spot was fixed at 3 points to prevent lateral movements of the skin in relation to the stimulation probe. White noise was delivered to the S with headphones to mask eventual noise caused by the equipment. The stimuli were applied to the skin by means of a perspex probe connected to the moving coil of an electromechanical vibrator (BriJel and Kjaer minishaker 4810). A preindentation of 1 mm was used to secure a good contact between the probe and the skin. The tip area of the probe was 0.07, 0.7, 3.1 or 12.5 sq.mm. The vibrator was driven by single cycle sine-waves delivered from a function generator and amplified by a power amplifier. The frequency of the single cycle was 20, 60 or 150 Hz. The movement of the probe was measured with an accelerometer (Br/Jel and Kjaer 4339) connected between the probe and the moving coil of the vibrator. The output of the accelerometer was amplified and fed to integrating circuits for displacement measurement (Briiel and Kjaer 2625; see Fig. 1 for the actual movement of the probe). The commercial calibration of the accelerometer and integrating circuits was checked under a binocular microscope. The amplitude of the displacement was determined by a multiplier which multiplied the constant amplitude sine-wave, delivered from the function generator, with a DC voltage. The DC level could be changed with a potentiometer either by the experimenter or by the S. When the S controlled the stimulus amplitude the experimenter could, with another potentiometer, change the stimulus amplitude to prevent possible positional cues in the use of the S's potentiometer.
150 Hz
6 0 Hz
20 Hz
t
50
ms
Fig. 1. Displacement of the stimulus probe when the vibrator is driven by single cycle sine-waves of 150, 60 and 20 Hz frequency. For each frequency the lower trace gives the sine-wave and the upper trace the displacement (towards the skin upwards). Displacement amplitude is measured from the shaded area from the base line to the peak.
Psychophysical methods The thresholds were measured with the method of production in which the S controlled the stimulus amplitude. A stimulus was presented every 5 sec preceded by a warning signal (interval 2 sec) given through the headphones. This interstimulus interval is long enough not to cause fatigue in cutaneous mechanoreceptors (cf. refs. 8 and 19; see also the following papedX). The task of the S was first to increase the stimulus amplitude so that the stimulus was just detectable (absolute threshold) and then so that a distinct tactile tap could be felt (touch threshold). The stimulus amplitude was then increased to a maximum and the measurements were carried out in reverse order. The threshold value was defined as a mean of the thresholds obtained with increasing and decreasing displacement amplitudes. Absolute and touch thresholds were determined with all frequency and probe area combinations which were presented in random order. One experiment lasted 1.5-2 h and in each experiment the measurements were carried out only on one skin area. Estimates of sensation magnitude were obtained by the method of magnitude estimation 16. During the experiment the S was presented with a randomized stimulus sequence (1 stim/5 sec) consisting of stimuli with 6 displacement amplitudes (50, 120, 250, 4130, 650 and 950/~m). The frequency of the pulse was 20, 60 or 150 Hz and each stimulus was presented 3 times (6 × 3 × 3 ~- 54 stimuli). After each stimulus the S gave an estimate of the sensation magnitude using a freely chosen numerical scale. No standard or anchor stimulus was used. The average estimate of the sensation magnitude was determined as a mean of the estimates to the 3 identical stimuli. The stimulus sequences were presented with each of the 4 stimulus areas in random order. One experiment lasted about 2 h and the measurements on hairy and glabrous skin areas were carried out during different days.
Statistical analysis The statistical significance of the effects of skin area (hairy and glabrous skin) and stimulus parameters (frequency of the pulse and probe area) on absolute and touch thresholds was determined with 3-way analysis of variance (variables: skin area, frequency of the single pulse and probe area). In order to determine the statistical significar, ce cf the effects of stimulus parameters on absolute and touch thresholds on the two skin areas separately, two-way analysis of variance (variables: frequency of the single pulse and probe area) was used. The magnitude estimates of each S were standardized by calculating them in per cent from the estimate given by the S to the stimulus with the largest area and displacement amplitude and with 150 Hz frequency of the pulse (100K). The average magnitude estimation functions were determined by calculating the means of standardized magnitude estimates over all Ss. RESULTS
Absolute thresholds The average thresholds varied between 44 and 140 # m on the hairy skin and
TABLE I Absolute thresholds: summary of 3-way analysis of variance
Variables: skin area, probe area, frequency of the single pulse. Source
Sum of squares
df
Mean squares
F-ratio
Significance
Skin area (A) Probe area (B) Frequency (C) AB AC BC
17494 2413 4272 1433 260 677
1 3 2 3 2 6
17494 804 2136 477 130 112
266.1 12.2 32.5 7.3 1.9 1.7
<0.01 <0.01 <0.01 <0.05 ---
394
6
65
Total
between 9 and 45 # m on the glabrous skin depending on the frequency of the single pulse and probe area. The absolute thresholds were significantly higher on the hairy than on the glabrous skin (Table I). The absolute thresholds decreased with increasing frequency of the single pulse (Fig. 2) and with larger probe areas (Fig. 3) on both skin areas. The effect of the increase of the frequency was more pronounced on the glabrous than on the hairy skin; however, two-way analysis of variance (variables: frequency of the single pulse and probe area) applied separately to absolute thresholds of the two skin areas showed that the decrease was significant for both skin areas. With 150 Hz frequency of the pulse the average threshold (Ss and probe areas pooled) was 69 ~ (P < 0.05; F(2,6) ---8.6) on the hairy and 28 ~ (P < 0.01 ; /'(2,6) = 71.4) on the glabrous skin of the average threshold obtained with 20 Hz frequency of the pulse. Hairy
O~
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i
i 100
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I
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T 40
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I 100
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I
[]
J
HZ
Frequency of the single pulse
Fig. 2. Absolute (continuous line) and touch (broken line) thresholds as a function of frequency of the single pulse for hairy and glabrous skin. Symbols for different probe areas indicated in the diagrams. Data of all Ss pooled.
[,q
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60
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o.,
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area
Fig. 3. Absolute (continuous line) and touch (broken line) thresholds as a function of area of the probe for hairy and glabrous skin. Symbols for different frequencies of the single pulse indicated in the diagram. Data of all Ss pooled.
The effect o f increasing the probe area was more pronounced on the hairy than on the glabrous skin. T w o - w a y analysis o f variance (variables: frequency o f the single pulse and probe area) revealed that the increase o f the probe area had significant effect only o n the hairy skin. The average threshold (Ss and frequencies pooled) obtained with 12.5 sq. m m probe area was 6 2 ~ (P < 0.05; F(3,6) = 7.5) on the hairy skin and 75 ~ (not significant) on the glabrous skin o f the average threshold obtained with 0.07 sq. mm. probe area.
TABLE I I Touch thresholds: summary of 3-way analysis of variance
Variables: skin area, probe area, frequency of the single pulse. Source
Sum of squares
df
Mean squares
F-ratio
Significance
Skin area (A) Probe area (B) Frequency (C) AB AC BC
42985 13626 48687 7201 2761 4828
1 3 2 3 2 6
42985 4542 24343 2400 1380 804
91.4 9.7 51.8 5.1 2.9 1.7
-:0.01 - :~0.05 <0.01 . _0.05 ---
2820
6
470
Total
Touch thresholds The average touch thresholds varied between 75 and 300 # m on the hairy skin and between 24 and 153/~m on the glabrous skin depending on the frequency of the single pulse and probe area. Also the touch thresholds were significantly (Table II) higher on the hairy than on the glabrous skin. As in the case of absolute thresholds the touch thresholds decreased on both skin areas with increasing frequency of the single pulse (Fig. 2) and probe area (Fig. 3). Two-way analysis of variance (variables: frequency of the single pulse and probe area) applied separately to the touch thresholds of the two skin areas showed that the effect of frequency was significant on both skin areas. The average threshold (Ss and probe areas pooled) obtained with 150 Hz pulse frequency was 4 7 ~ (P < 0.01;/7(2,6) = 17.9) on the hairy and 32% (P < 0.01; F(2,6) = 29.9) on the glabrous skirt of the average threshold obtained with 20 Hz pulse frequency. Thus the increase of the frequency of the single pulse had a larger effect on touch than on absolute thresholds on the hairy skin. The relative difference between the absolute and touch thresholds (Fig. 4) decreased with higher frequency of the pulse on the hairy, but not on the glabrous skin. Similarly to the case of absolute thresholds, two-way analysis of variance (variables: frequency of the single pulse and probe area) showed that the effect of probe area on the touch thresholds was significant only on the hairy skin, where the average threshold (Ss and frequencies pooled) obtained with 12.5 sq.mm probe area was 64 ~ (P < 0.05; F(3,6) = 6.2) of the average threshold obtained with 0.07 sq.mm probe area. On the glabrous skin the corresponding value was 77 ~ (not significant). Estimates of sensation magnitude The dependence of the subjective estimate of sensation magnitude on the displacement amplitude was generally well described by a power function (Fig. 5), Hairy
Glabrous
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Frequency
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I
I l J l 100
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Fig. 4. Relative difference between absolute and touch thresholds (in dB) as a function of the frequency of the single pulse for hairy and glabrous skin. Symbols for different probe areas indicated in the diagram. Data of all Ss pooled.
0.07 mm"
0.7 mrd
3.1 ram'
Hairy
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skin
¢.
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1oo
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[~.~]
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Fig. 5. Standardized magnitude estimates as a function of displacement amplitude for hairy (above) and glabrous (below) skin. Probe areas indicated above the diagrams. Open circles, 20 Hz; filled circles, 60 Hz; triangles, 150 Hz. Data of all Ss pooled.
although high correlation coefficients were occasionally obtained also with linear, logarithmic or hyperbolic functions. Power function was chosen as a general model of description in order to facilitate the comparisons with the results obtained in earlier studies. The exponents of the power functions obtained with different frequencies and probe areas varied between 0.70 and 1.41 on the hairy and between 0.55 and 0.86 on the glabrous skin (Table III). The exponents were the smaller the higher the frequency of the pulse on both skin areas. TABLE Ill The exponents o f standardized magnitude estimation functions
Skin area
Hairy Glabrous
Frequency o f the single pulse (Hz)
Probe area (sq. ram) 0.07 0.7
3.l
12.5
20 60 150 20 60 150
1.31 1.19 0.92 0.83 0.76 0.62
1.25 1.01 0.81 0.68 0.81 0.62
1.19 1.07 0.70 0.81 0.70 0.55
1.25 1.41 0.86 0.74 0.86 0.71
TABLE IV Equi-sensation contours: summary of 3-way analysis of variance
Variables: skin area, probe area, frequency of the single pulse. Source
Skin area (A) Probe area (B) Frequency (C) AB AC BC Total
Sum of squares
df
Mean squares
F-ratio
Significance
30317 29444 112576 5092 1720 3172
1 3 2 3 2 6
30317 9814 56288 1697 860 528
76.1 24.6 141.3 4.2 2.1 1.3
<0.01 <0.01 <0.01 ----
2389
6
398
In order to analyze in more detail the effects of the frequency of the pulse and the probe area on the sensation magnitude equi-sensation contours - - displacement amplitudes necessary to elicit the same magnitude of sensation with different frequencies and probe areas - - were graphically determined from power functions for both skin areas. The sensation level chosen for the analysis was 30 % (standardized estimate). Three-way analysis of variance (Table IV) applied to the equi-sensation contour data (Figs. 6 and 7) showed that significantly higher displacement amplitudes were needed on the hairy than on the glabrous skin to produce sensations of equal magnitude. Two-way analysis of variance (variables: frequency of the single pulse and probe area) applied separately to the data for the two skin areas showed that significantly lower displacement amplitudes were needed on both skin areas to produce sensations of equal magnitude with increasing the frequency of the pulse (P < 0.01 ;/'(2,6) : 64.3, hairy skin and F(2,6) = 57.7, glabrous skin) and probe area (P < 0.01 ; F(3,6) ---- 13.7, hairy skin and F(3,6) = 10.5, glabrous skin). Hairy
Glabrous
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i
i
i
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I
60
I,i
II
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I
i
l
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I
l
I
I
I
I
/
[.z ]
Frequency of the single pulse
Fig. 6. Equi-sensation contours for hairy and glabrous skin showing the amplitude necessary for equal sensation magnitude at different frequencies of the single pulse. Symbols as in Fig. 2.
10 Hairy
300i
• ix
~
Glabrous
e
~
300
Q
o. E
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~
A _
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10(]
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,
=,=,
3.0
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, i ||Hll
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*
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30
21
Em4
area
Fig. 7. Equi-sensation contours for hairy and glabrous skin showing the amplitude necessaryfor equal sensation magnitude with different probe areas. Symbols as in Fig. 3.
DISCUSSION Few earlier psychophysical studies have employed single mechanical pulses in assessing tactile sensibility. However, as pointed out by Horch and Burgess 7, sinusoidal stimuli are useful when studying neural coding of mechanical events on the skin, because displacement, velocity, and acceleration components of such stimuli vary differently with frequency. Thus, velocity dependence of the measurements is indicated by a downward sloping threshold curve. Consequently, the present results demonstrate a marked velocity dependence of absolute sensation thresholds both for the hairy and the glabrous skin. Recently, Lindblom 1~ reported a decrease of the sensation thresholds as a function of frequency of a single mechanical pulse applied to the finger tip. When compared with the present results considerably lower threshold values were reported and the main decrease of the threshold with increasing frequency of the pulse occurred from 0.1 to 1 Hz pulse frequency. Thereafter the decrease of the threshold was neglible, though systematic. Thus on the thenar eminence and on the hairy skin of the back of the hand the velocity component of the stimulus has effect on the threshold amplitude in a broader range than on the finger tip, indicating a difference in the coding mechanisms of the absolute thresholds in the different parts of the hand. This hypothesis is supported by the findings of Johansson and Vallbo 12 who showed that detection of a tactile stimulus on the finger tip well coincides with the thresholds of single low threshold rapidly adapting (RA) units, but in the proximal parts of the glabrous skin more units must be recruited. The increase of the probe area had a significant effect on absolute thresholds only on the hairy skin indicating that at threshold spatial summation may play a role only on this skin area. Thus more units should be recruited for the threshold sensation
11 than in the glabrous skin. The small insignificant decrease of the thresholds also on the thenar eminence supports the view that on this skin area the threshold sensation is not based on activity of a single unit. However, when using small probe areas as in the present study the decrease could, for both skin areas, also be due to higher probability of stimulating a low threshold receptor with the largest probe area. In this case the smaller effect on the glabrous skin could be due to higher density of low threshold receptors in the glabrous skin. As the quality of the sensation elicited by a mechanical pulse at absolute threshold is usually not a sensation of touch, but rather a recognition of a mechanical event on the skin, in the present study another threshold, the 'touch threshold' or the threshold for a distinct tap, was also determined, F o r these supraliminal measurements basically the same results were obtained as for the absolute thresholds, with the exception that the effect of increase in the frequency of the pulse was on the hairy skin of the same order of magnitude as on the glabrous skin. This finding, as well as the overlap of average threshold values, not found for the absolute thresholds, indicates that similar receptor populations are involved in both skin areas in the coding of this qualitative threshold. Supraliminal sensations were further studied by determining the magnitude estimation functions. The exponents of the average standardized functions corresponded to those obtained in earlier studiesl-3,~,l°, 13, but it should be pointed out that considerable variation exists both in the exponents of the present study as well as in those of the earlier studies. Equi-sensation contours constructed from magnitude estimation functions revealed that significantly smaller displacement amplitudes were needed on both skin areas in order to produce the same amount of sensation magnitude with increasing frequency of the pulse as well as with increasing probe area. Thus on both skin areas coding of supraliminal sensation magnitude seems to be based on a population of velocity sensitive receptors capable of some spatial summation over the size of the probe areas used in the present study. Consequently, although differences exist in the probable coding mechanisms of thresholds on the two skin areas, they disappear at higher sensation levels. However, the general sensitivity difference seen between the two skin areas at the threshold was present also at higher sensation levels. ACKNOWLEDGEMENTS This work was supported by The Finnish Academy.
REFERENCES 1 Franz~n, O., Somatosensory potentials from the exposed cortex in monkey and from the scalp in man related to the sensory magnitude of tactual stimulation. In Y. Zotterman (Ed.), Sensory Functions of the Skin in Primates, Pergamon Press, Oxford, 1976, pp. 119-126. 2 Franz6n, O. and Lindblom, U., Tactile intensity functions in patients with sutured peripheral nerve. In Y. Zotterman (Ed.), Sensory Functions of the Skin in Primates, Pergamon Press, Oxford, 1976, pp. 113-118. 3 Franz6n, O. and Offenloch, K., Evoked response correlates of psychophysical magnitude estimates for tactile stimulation in man, Exp. Brain Res., 8 (1969) 1-18.
12 4 Gardner, E. P. and Spencer, W. A., Sensory funneling. I. Psychophysicat observations of human subjects and responses of cutaneous mechanoreceptive afferents in the cat to patterned stimuli, J. NeurophysioL, 35 (1972) 925-953. 5 Gardner, E. P, and Spencer, W. A., Sensory funneling. 1I. Cortical neuronal representation of patterned cutaneous stimuli, J. NeurophysioL, 35 (1972) 954-977. 6 Harrington, T. and Merzenich, M. M., Neural coding in the sense of touch: human sensations of skin indentation compared with the responses of slowly adapting mechanoreceptive afferents innervating the hairy skin of monkeys, Exp. Brain Res., 10 (1970) 251-264. 7 Horch, K. W. and Burgess, P. R., Responses to threshold and suprathreshold stimuli by slowly adapting cutaneous mechanoreceptors in the cat, J. comp. PhysioL, 110 (1976) 307-315. 8 Horch, K. W., Whitehorn, D. and Burgess, P. R., Impulse generation in type 1 cutaneous mechanoreceptors, J, NeurophysioL, 37 (1974) 267-281. 9 J/irvilehto, T., Neural basis of cutaneous sensations analyzed by microelectrode measurements from human peripheral nerves - - a review, Scand. J. PsychoL, 18 (1977) 348-359. 10 J~rvilehto, T., H~m~il~inen, H. and Kekoni, J., Mechanoreceptive unit activity in human skin nerves correlated with touch and vibratory sensations. In Y. Zotterman (Ed.) Sensory Functions of the Skin in Primates, Pergamon Press, Oxford, 1976, pp. 215-230. 11 J/irvilehto, T., H~m/ilfiinen, H. and Soininen, K., Peripheral neural basis of tactile sensations in man: II. Characteristics of human mechanoreceptors in the hairy skin and correlations of their activity with tactile sensations, Brain Research, (1981). 12 Johansson, R. S. and Vallbo, /~. B., Detection of tactile stimuli. Thresholds of afferent units related to psychophysical thresholds in the human hand, J. Physiol. (Lond.), 297 (1979) 405-422. 13 KnibestSl, M. and Vallbo, ,~. B., Stimulus-response functions of primary afferents and psychophysical intensity estimation on mechanical skin stimulation in the human hand. In Y. Zotterman (Ed.) Sensory Functions of the Skin in Primates, Pergamon Press, Oxford, 1976, pp. 201-213. 14 LaMotte, R. H. and Mountcastle, V. B., Capacities of humans and monkeys to discriminate between vibratory stimuli of different frequency and amplitude: a correlation between neural events and psychophysical measurements, J. NeurophysioL, 38 (1975) 539-559. 15 Lindblom, U., Touch perception threshold in human glabrous skin in terms of displacement amplitude on stimulation with single mechanical pulses, Brain Research, 82 (1974) 205-210. 16 Stevens, S. S., Psychophysics. Introduction to Its Perceptual, Neural, and Social Prospects, J. Wiley, New York, 1975, 329 pp. 17 Vallbo,/~. B. and Hagbarth, K.-E., Activity from skin mechanoreceptors recorded percutaneously in awake human subjects, Exp. Neurol., 21 (1968) 270-289. 18 Vallbo, ~. B., Hagbarth, K.-E., TorebjSrk, H. E. and Wallin, B. G., Somatosensory, proprioceptive, and sympathetic activity in human peripheral nerve~, PhysioL Rev., 59 (1979) 919-957. 19 Werner, G. and Mountcastle, V. B., Neural activity in mechanoreceptive cutaneous afferents: stimulus-response relations, Weber functions, and information transmission, J. Neurophysiol. 28 (1965) 359-397.
I
Elsevier/North-Holland Biomedical Press
Research Reports P E R I P H E R A L N E U R A L BASIS OF TACTILE SENSATIONS IN M A N : I. E F F E C T OF F R E Q U E N C Y A N D PROBE AREA ON SENSATIONS ELICITED BY S I N G L E M E C H A N I C A L PULSES ON H A I R Y A N D G L A B R O U S SKIN OF THE HAND HEIKKI H/~M~L/~INEN and TIMO J/~RVILEHTO Department of Psychology, Experimental Laboratories, Ritarikatu 5, SF-O0170 Helsinki 17 (Finland)
(Accepted January 1st, 1981) Key words: single tactile pulses - - absolute thresholds - - touch thresholds - - magnitude estimation -
-
hairy skin - - glabrous skin - - man
SUM MARY Tactile thresholds and sensation magnitudes for single mechanical pulses of varying frequency and probe area were studied in order to provide psychophysical data for correlations of tactile sensations with functional properties of different types of human peripheral nerve fibers. Single mechanical pulses were delivered to the hairy or glabrous skin of the hand by means o f a perspex probe (area 0.07, 0.7, 3.1, or 12.5 sq.mm) fixed to the moving coil of an electromechanical vibrator. The frequency of the single pulse was 20, 60 or 150 Hz. Absolute and touch thresholds were measured with a method of production. Suprathreshold sensations were measured with the method of magnitude estimation (6 predetermined displacement amplitudes ranging from 50 to 950 am). Both absolute and touch thresholds were significantly higher on the hairy than on the glabrous skin. The absolute thresholds varied between 44 and 140 # m on the hairy and between 9 and 45/~m on the glabrous skin; the touch threshold varied between 75 and 300/~m and 24 and 153 #m, respectively. Lower threshold values were obtained on both skin areas with increasing frequency of the pulse and probe area, the latter effect being significant only for the hairy skin. Standardized magnitude estimation functions could be described with power functions on both skin areas, the exponents of the functions varying between 0.70 and 1.41 on the hairy and between 0.55 and 0.86 on the glabrous skin. The equi-sensation contours showed the difference of sensitivity between the skin areas. Larger sensation magnitudes were obtained with increasing frequency of the pulse and probe area on both skin areas. These psychophysical findings indicate that there is a functional difference at absolute sensation thresholds between hairy and glabrous skin. This difference, however, disappears at higher sensation levels. 0006-8993/81/0000-0000/$2.50© Elsevier/North-Holland Biomedical Press
INTRODUCTION The knowledge of peripheral neural coding of mechanical changes in the skin is based mainly on electrophysiological work in different animal species. These studies have shown that the transducing properties of cutaneous mechanoreceptors are so diverse that it is difficult to ascribe to them a functional role with respect to cutaneous sensations on this base. Therefore, in recent studies the electrophysiological analysis in animals was combined with psychophysical research in man using identical stimulation procedures 4-6. In some of these studies 14 psychophysical experiments were carried out also with the animal (monkey) who served in the electrophysiological experiments, in order to provide a better basis for comparisons. However, even in this case psychophysical observations and electrophysiological recording are carried out in different experiments, which prevents direct correlations between psychophysical performance and activity in peripheral neural units. During the last decade the method of percutaneous microelectrode recording from human peripheral nerves 17 has enabled a detailed study of the characteristics of human cutaneous neural units and it has also made it possible to perform simultaneous measurements of the sensations and activity in different receptor types. At present, several reports on physiological characteristics of different types of human receptors located in the hairy and glabrous skin are available (see refs. 9 and 18, for reviews), but simultaneous measurements of cutaneous sensations and unit activity in skin nerves are still few. In our approach to the neural basis of cutaneous sensations we proceeded on 3 lines. First, we determined in separate psychophysical experiments the dependence of sensations on some stimulus parameters. Second, with the method of percutaneous microelectrode measurements we collected data on the physiological properties of the peripheral units to screen possible candidates for the coding of sensations. Finally, we combined the psychophysical measurements of the sensations with simultaneous measurements of the unit activity from the nerves. In the first part of the present report we describe results from psychophysical measurements of tactile sensations elicited by short tactile pulses. As there are no systematic studies using this type of mechanical stimulation we have examined the dependence of sensation thresholds as well as magnitude of sensation upon the frequency of the single pulse and the area of the stimulus probe on both the hairy and glabrous skin of the hand. In the second part of the report properties of cutaneous mechanoreceptors in the human hairy skin are described and results of simultaneous recording of peripheral unit activity with measurements of sensation threshold and magnitude of sensation are presented. METHODS
Subjects and stimuli Eight healthy subjects (Ss; 3 females and 5 males; age 22-30 years) participated in sensation threshold measurements and two additional Ss (2 females) in the estimation of sensation magnitude. The S was sitting with his left hand resting on a table. The hand was supported by a vacuum cast.
The stimulation sites were the hairy skin of the back of the hand and the glabrous skin of the thenar eminence. In order to have comparable sites of stimulation in all Ss a spot on the skin with a sensation threshold below 0.05 g (determined with a von Frey hair) was marked. The skin around the spot was fixed at 3 points to prevent lateral movements of the skin in relation to the stimulation probe. White noise was delivered to the S with headphones to mask eventual noise caused by the equipment. The stimuli were applied to the skin by means of a perspex probe connected to the moving coil of an electromechanical vibrator (BriJel and Kjaer minishaker 4810). A preindentation of 1 mm was used to secure a good contact between the probe and the skin. The tip area of the probe was 0.07, 0.7, 3.1 or 12.5 sq.mm. The vibrator was driven by single cycle sine-waves delivered from a function generator and amplified by a power amplifier. The frequency of the single cycle was 20, 60 or 150 Hz. The movement of the probe was measured with an accelerometer (Br/Jel and Kjaer 4339) connected between the probe and the moving coil of the vibrator. The output of the accelerometer was amplified and fed to integrating circuits for displacement measurement (Briiel and Kjaer 2625; see Fig. 1 for the actual movement of the probe). The commercial calibration of the accelerometer and integrating circuits was checked under a binocular microscope. The amplitude of the displacement was determined by a multiplier which multiplied the constant amplitude sine-wave, delivered from the function generator, with a DC voltage. The DC level could be changed with a potentiometer either by the experimenter or by the S. When the S controlled the stimulus amplitude the experimenter could, with another potentiometer, change the stimulus amplitude to prevent possible positional cues in the use of the S's potentiometer.
150 Hz
6 0 Hz
20 Hz
t
50
ms
Fig. 1. Displacement of the stimulus probe when the vibrator is driven by single cycle sine-waves of 150, 60 and 20 Hz frequency. For each frequency the lower trace gives the sine-wave and the upper trace the displacement (towards the skin upwards). Displacement amplitude is measured from the shaded area from the base line to the peak.
Psychophysical methods The thresholds were measured with the method of production in which the S controlled the stimulus amplitude. A stimulus was presented every 5 sec preceded by a warning signal (interval 2 sec) given through the headphones. This interstimulus interval is long enough not to cause fatigue in cutaneous mechanoreceptors (cf. refs. 8 and 19; see also the following papedX). The task of the S was first to increase the stimulus amplitude so that the stimulus was just detectable (absolute threshold) and then so that a distinct tactile tap could be felt (touch threshold). The stimulus amplitude was then increased to a maximum and the measurements were carried out in reverse order. The threshold value was defined as a mean of the thresholds obtained with increasing and decreasing displacement amplitudes. Absolute and touch thresholds were determined with all frequency and probe area combinations which were presented in random order. One experiment lasted 1.5-2 h and in each experiment the measurements were carried out only on one skin area. Estimates of sensation magnitude were obtained by the method of magnitude estimation 16. During the experiment the S was presented with a randomized stimulus sequence (1 stim/5 sec) consisting of stimuli with 6 displacement amplitudes (50, 120, 250, 4130, 650 and 950/~m). The frequency of the pulse was 20, 60 or 150 Hz and each stimulus was presented 3 times (6 × 3 × 3 ~- 54 stimuli). After each stimulus the S gave an estimate of the sensation magnitude using a freely chosen numerical scale. No standard or anchor stimulus was used. The average estimate of the sensation magnitude was determined as a mean of the estimates to the 3 identical stimuli. The stimulus sequences were presented with each of the 4 stimulus areas in random order. One experiment lasted about 2 h and the measurements on hairy and glabrous skin areas were carried out during different days.
Statistical analysis The statistical significance of the effects of skin area (hairy and glabrous skin) and stimulus parameters (frequency of the pulse and probe area) on absolute and touch thresholds was determined with 3-way analysis of variance (variables: skin area, frequency of the single pulse and probe area). In order to determine the statistical significar, ce cf the effects of stimulus parameters on absolute and touch thresholds on the two skin areas separately, two-way analysis of variance (variables: frequency of the single pulse and probe area) was used. The magnitude estimates of each S were standardized by calculating them in per cent from the estimate given by the S to the stimulus with the largest area and displacement amplitude and with 150 Hz frequency of the pulse (100K). The average magnitude estimation functions were determined by calculating the means of standardized magnitude estimates over all Ss. RESULTS
Absolute thresholds The average thresholds varied between 44 and 140 # m on the hairy skin and
TABLE I Absolute thresholds: summary of 3-way analysis of variance
Variables: skin area, probe area, frequency of the single pulse. Source
Sum of squares
df
Mean squares
F-ratio
Significance
Skin area (A) Probe area (B) Frequency (C) AB AC BC
17494 2413 4272 1433 260 677
1 3 2 3 2 6
17494 804 2136 477 130 112
266.1 12.2 32.5 7.3 1.9 1.7
<0.01 <0.01 <0.01 <0.05 ---
394
6
65
Total
between 9 and 45 # m on the glabrous skin depending on the frequency of the single pulse and probe area. The absolute thresholds were significantly higher on the hairy than on the glabrous skin (Table I). The absolute thresholds decreased with increasing frequency of the single pulse (Fig. 2) and with larger probe areas (Fig. 3) on both skin areas. The effect of the increase of the frequency was more pronounced on the glabrous than on the hairy skin; however, two-way analysis of variance (variables: frequency of the single pulse and probe area) applied separately to absolute thresholds of the two skin areas showed that the decrease was significant for both skin areas. With 150 Hz frequency of the pulse the average threshold (Ss and probe areas pooled) was 69 ~ (P < 0.05; F(2,6) ---8.6) on the hairy and 28 ~ (P < 0.01 ; /'(2,6) = 71.4) on the glabrous skin of the average threshold obtained with 20 Hz frequency of the pulse. Hairy
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Frequency of the single pulse
Fig. 2. Absolute (continuous line) and touch (broken line) thresholds as a function of frequency of the single pulse for hairy and glabrous skin. Symbols for different probe areas indicated in the diagrams. Data of all Ss pooled.
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Fig. 3. Absolute (continuous line) and touch (broken line) thresholds as a function of area of the probe for hairy and glabrous skin. Symbols for different frequencies of the single pulse indicated in the diagram. Data of all Ss pooled.
The effect o f increasing the probe area was more pronounced on the hairy than on the glabrous skin. T w o - w a y analysis o f variance (variables: frequency o f the single pulse and probe area) revealed that the increase o f the probe area had significant effect only o n the hairy skin. The average threshold (Ss and frequencies pooled) obtained with 12.5 sq. m m probe area was 6 2 ~ (P < 0.05; F(3,6) = 7.5) on the hairy skin and 75 ~ (not significant) on the glabrous skin o f the average threshold obtained with 0.07 sq. mm. probe area.
TABLE I I Touch thresholds: summary of 3-way analysis of variance
Variables: skin area, probe area, frequency of the single pulse. Source
Sum of squares
df
Mean squares
F-ratio
Significance
Skin area (A) Probe area (B) Frequency (C) AB AC BC
42985 13626 48687 7201 2761 4828
1 3 2 3 2 6
42985 4542 24343 2400 1380 804
91.4 9.7 51.8 5.1 2.9 1.7
-:0.01 - :~0.05 <0.01 . _0.05 ---
2820
6
470
Total
Touch thresholds The average touch thresholds varied between 75 and 300 # m on the hairy skin and between 24 and 153/~m on the glabrous skin depending on the frequency of the single pulse and probe area. Also the touch thresholds were significantly (Table II) higher on the hairy than on the glabrous skin. As in the case of absolute thresholds the touch thresholds decreased on both skin areas with increasing frequency of the single pulse (Fig. 2) and probe area (Fig. 3). Two-way analysis of variance (variables: frequency of the single pulse and probe area) applied separately to the touch thresholds of the two skin areas showed that the effect of frequency was significant on both skin areas. The average threshold (Ss and probe areas pooled) obtained with 150 Hz pulse frequency was 4 7 ~ (P < 0.01;/7(2,6) = 17.9) on the hairy and 32% (P < 0.01; F(2,6) = 29.9) on the glabrous skirt of the average threshold obtained with 20 Hz pulse frequency. Thus the increase of the frequency of the single pulse had a larger effect on touch than on absolute thresholds on the hairy skin. The relative difference between the absolute and touch thresholds (Fig. 4) decreased with higher frequency of the pulse on the hairy, but not on the glabrous skin. Similarly to the case of absolute thresholds, two-way analysis of variance (variables: frequency of the single pulse and probe area) showed that the effect of probe area on the touch thresholds was significant only on the hairy skin, where the average threshold (Ss and frequencies pooled) obtained with 12.5 sq.mm probe area was 64 ~ (P < 0.05; F(3,6) = 6.2) of the average threshold obtained with 0.07 sq.mm probe area. On the glabrous skin the corresponding value was 77 ~ (not significant). Estimates of sensation magnitude The dependence of the subjective estimate of sensation magnitude on the displacement amplitude was generally well described by a power function (Fig. 5), Hairy
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Fig. 4. Relative difference between absolute and touch thresholds (in dB) as a function of the frequency of the single pulse for hairy and glabrous skin. Symbols for different probe areas indicated in the diagram. Data of all Ss pooled.
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Fig. 5. Standardized magnitude estimates as a function of displacement amplitude for hairy (above) and glabrous (below) skin. Probe areas indicated above the diagrams. Open circles, 20 Hz; filled circles, 60 Hz; triangles, 150 Hz. Data of all Ss pooled.
although high correlation coefficients were occasionally obtained also with linear, logarithmic or hyperbolic functions. Power function was chosen as a general model of description in order to facilitate the comparisons with the results obtained in earlier studies. The exponents of the power functions obtained with different frequencies and probe areas varied between 0.70 and 1.41 on the hairy and between 0.55 and 0.86 on the glabrous skin (Table III). The exponents were the smaller the higher the frequency of the pulse on both skin areas. TABLE Ill The exponents o f standardized magnitude estimation functions
Skin area
Hairy Glabrous
Frequency o f the single pulse (Hz)
Probe area (sq. ram) 0.07 0.7
3.l
12.5
20 60 150 20 60 150
1.31 1.19 0.92 0.83 0.76 0.62
1.25 1.01 0.81 0.68 0.81 0.62
1.19 1.07 0.70 0.81 0.70 0.55
1.25 1.41 0.86 0.74 0.86 0.71
TABLE IV Equi-sensation contours: summary of 3-way analysis of variance
Variables: skin area, probe area, frequency of the single pulse. Source
Skin area (A) Probe area (B) Frequency (C) AB AC BC Total
Sum of squares
df
Mean squares
F-ratio
Significance
30317 29444 112576 5092 1720 3172
1 3 2 3 2 6
30317 9814 56288 1697 860 528
76.1 24.6 141.3 4.2 2.1 1.3
<0.01 <0.01 <0.01 ----
2389
6
398
In order to analyze in more detail the effects of the frequency of the pulse and the probe area on the sensation magnitude equi-sensation contours - - displacement amplitudes necessary to elicit the same magnitude of sensation with different frequencies and probe areas - - were graphically determined from power functions for both skin areas. The sensation level chosen for the analysis was 30 % (standardized estimate). Three-way analysis of variance (Table IV) applied to the equi-sensation contour data (Figs. 6 and 7) showed that significantly higher displacement amplitudes were needed on the hairy than on the glabrous skin to produce sensations of equal magnitude. Two-way analysis of variance (variables: frequency of the single pulse and probe area) applied separately to the data for the two skin areas showed that significantly lower displacement amplitudes were needed on both skin areas to produce sensations of equal magnitude with increasing the frequency of the pulse (P < 0.01 ;/'(2,6) : 64.3, hairy skin and F(2,6) = 57.7, glabrous skin) and probe area (P < 0.01 ; F(3,6) ---- 13.7, hairy skin and F(3,6) = 10.5, glabrous skin). Hairy
Glabrous
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Fig. 6. Equi-sensation contours for hairy and glabrous skin showing the amplitude necessary for equal sensation magnitude at different frequencies of the single pulse. Symbols as in Fig. 2.
10 Hairy
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Fig. 7. Equi-sensation contours for hairy and glabrous skin showing the amplitude necessaryfor equal sensation magnitude with different probe areas. Symbols as in Fig. 3.
DISCUSSION Few earlier psychophysical studies have employed single mechanical pulses in assessing tactile sensibility. However, as pointed out by Horch and Burgess 7, sinusoidal stimuli are useful when studying neural coding of mechanical events on the skin, because displacement, velocity, and acceleration components of such stimuli vary differently with frequency. Thus, velocity dependence of the measurements is indicated by a downward sloping threshold curve. Consequently, the present results demonstrate a marked velocity dependence of absolute sensation thresholds both for the hairy and the glabrous skin. Recently, Lindblom 1~ reported a decrease of the sensation thresholds as a function of frequency of a single mechanical pulse applied to the finger tip. When compared with the present results considerably lower threshold values were reported and the main decrease of the threshold with increasing frequency of the pulse occurred from 0.1 to 1 Hz pulse frequency. Thereafter the decrease of the threshold was neglible, though systematic. Thus on the thenar eminence and on the hairy skin of the back of the hand the velocity component of the stimulus has effect on the threshold amplitude in a broader range than on the finger tip, indicating a difference in the coding mechanisms of the absolute thresholds in the different parts of the hand. This hypothesis is supported by the findings of Johansson and Vallbo 12 who showed that detection of a tactile stimulus on the finger tip well coincides with the thresholds of single low threshold rapidly adapting (RA) units, but in the proximal parts of the glabrous skin more units must be recruited. The increase of the probe area had a significant effect on absolute thresholds only on the hairy skin indicating that at threshold spatial summation may play a role only on this skin area. Thus more units should be recruited for the threshold sensation
11 than in the glabrous skin. The small insignificant decrease of the thresholds also on the thenar eminence supports the view that on this skin area the threshold sensation is not based on activity of a single unit. However, when using small probe areas as in the present study the decrease could, for both skin areas, also be due to higher probability of stimulating a low threshold receptor with the largest probe area. In this case the smaller effect on the glabrous skin could be due to higher density of low threshold receptors in the glabrous skin. As the quality of the sensation elicited by a mechanical pulse at absolute threshold is usually not a sensation of touch, but rather a recognition of a mechanical event on the skin, in the present study another threshold, the 'touch threshold' or the threshold for a distinct tap, was also determined, F o r these supraliminal measurements basically the same results were obtained as for the absolute thresholds, with the exception that the effect of increase in the frequency of the pulse was on the hairy skin of the same order of magnitude as on the glabrous skin. This finding, as well as the overlap of average threshold values, not found for the absolute thresholds, indicates that similar receptor populations are involved in both skin areas in the coding of this qualitative threshold. Supraliminal sensations were further studied by determining the magnitude estimation functions. The exponents of the average standardized functions corresponded to those obtained in earlier studiesl-3,~,l°, 13, but it should be pointed out that considerable variation exists both in the exponents of the present study as well as in those of the earlier studies. Equi-sensation contours constructed from magnitude estimation functions revealed that significantly smaller displacement amplitudes were needed on both skin areas in order to produce the same amount of sensation magnitude with increasing frequency of the pulse as well as with increasing probe area. Thus on both skin areas coding of supraliminal sensation magnitude seems to be based on a population of velocity sensitive receptors capable of some spatial summation over the size of the probe areas used in the present study. Consequently, although differences exist in the probable coding mechanisms of thresholds on the two skin areas, they disappear at higher sensation levels. However, the general sensitivity difference seen between the two skin areas at the threshold was present also at higher sensation levels. ACKNOWLEDGEMENTS This work was supported by The Finnish Academy.
REFERENCES 1 Franz~n, O., Somatosensory potentials from the exposed cortex in monkey and from the scalp in man related to the sensory magnitude of tactual stimulation. In Y. Zotterman (Ed.), Sensory Functions of the Skin in Primates, Pergamon Press, Oxford, 1976, pp. 119-126. 2 Franz6n, O. and Lindblom, U., Tactile intensity functions in patients with sutured peripheral nerve. In Y. Zotterman (Ed.), Sensory Functions of the Skin in Primates, Pergamon Press, Oxford, 1976, pp. 113-118. 3 Franz6n, O. and Offenloch, K., Evoked response correlates of psychophysical magnitude estimates for tactile stimulation in man, Exp. Brain Res., 8 (1969) 1-18.
12 4 Gardner, E. P. and Spencer, W. A., Sensory funneling. I. Psychophysicat observations of human subjects and responses of cutaneous mechanoreceptive afferents in the cat to patterned stimuli, J. NeurophysioL, 35 (1972) 925-953. 5 Gardner, E. P, and Spencer, W. A., Sensory funneling. 1I. Cortical neuronal representation of patterned cutaneous stimuli, J. NeurophysioL, 35 (1972) 954-977. 6 Harrington, T. and Merzenich, M. M., Neural coding in the sense of touch: human sensations of skin indentation compared with the responses of slowly adapting mechanoreceptive afferents innervating the hairy skin of monkeys, Exp. Brain Res., 10 (1970) 251-264. 7 Horch, K. W. and Burgess, P. R., Responses to threshold and suprathreshold stimuli by slowly adapting cutaneous mechanoreceptors in the cat, J. comp. PhysioL, 110 (1976) 307-315. 8 Horch, K. W., Whitehorn, D. and Burgess, P. R., Impulse generation in type 1 cutaneous mechanoreceptors, J, NeurophysioL, 37 (1974) 267-281. 9 J/irvilehto, T., Neural basis of cutaneous sensations analyzed by microelectrode measurements from human peripheral nerves - - a review, Scand. J. PsychoL, 18 (1977) 348-359. 10 J~rvilehto, T., H~m~il~inen, H. and Kekoni, J., Mechanoreceptive unit activity in human skin nerves correlated with touch and vibratory sensations. In Y. Zotterman (Ed.) Sensory Functions of the Skin in Primates, Pergamon Press, Oxford, 1976, pp. 215-230. 11 J/irvilehto, T., H~m/ilfiinen, H. and Soininen, K., Peripheral neural basis of tactile sensations in man: II. Characteristics of human mechanoreceptors in the hairy skin and correlations of their activity with tactile sensations, Brain Research, (1981). 12 Johansson, R. S. and Vallbo, /~. B., Detection of tactile stimuli. Thresholds of afferent units related to psychophysical thresholds in the human hand, J. Physiol. (Lond.), 297 (1979) 405-422. 13 KnibestSl, M. and Vallbo, ,~. B., Stimulus-response functions of primary afferents and psychophysical intensity estimation on mechanical skin stimulation in the human hand. In Y. Zotterman (Ed.) Sensory Functions of the Skin in Primates, Pergamon Press, Oxford, 1976, pp. 201-213. 14 LaMotte, R. H. and Mountcastle, V. B., Capacities of humans and monkeys to discriminate between vibratory stimuli of different frequency and amplitude: a correlation between neural events and psychophysical measurements, J. NeurophysioL, 38 (1975) 539-559. 15 Lindblom, U., Touch perception threshold in human glabrous skin in terms of displacement amplitude on stimulation with single mechanical pulses, Brain Research, 82 (1974) 205-210. 16 Stevens, S. S., Psychophysics. Introduction to Its Perceptual, Neural, and Social Prospects, J. Wiley, New York, 1975, 329 pp. 17 Vallbo,/~. B. and Hagbarth, K.-E., Activity from skin mechanoreceptors recorded percutaneously in awake human subjects, Exp. Neurol., 21 (1968) 270-289. 18 Vallbo, ~. B., Hagbarth, K.-E., TorebjSrk, H. E. and Wallin, B. G., Somatosensory, proprioceptive, and sympathetic activity in human peripheral nerve~, PhysioL Rev., 59 (1979) 919-957. 19 Werner, G. and Mountcastle, V. B., Neural activity in mechanoreceptive cutaneous afferents: stimulus-response relations, Weber functions, and information transmission, J. Neurophysiol. 28 (1965) 359-397.