Department of Neuroscience and Krieger Mind/Brain Institute, Johns Hopkins University, Baltimore, Maryland 21218
![]() |
ABSTRACT |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Vega-Bermudez, F. and K. O. Johnson. Surround suppression in the responses of primate SA1 and RA mechanoreceptive afferents mapped with a probe array. Twenty-four slowly adapting type 1 (SA1) and 26 rapidly adapting (RA) cutaneous mechanoreceptive afferents in the rhesus monkey were studied with an array of independently controlled, punctate probes that covered an entire fingerpad. Each afferent had a receptive field (RF) on a single fingerpad and was studied at 73 skin sites (50 mm2). The entire array was lowered to 1.6 to 3.0 mm below the point of initial skin contact (the background indentation) before delivering indentations with one to seven probes. Indentations were generally limited to 100 µm to minimize gross mechanical interactions. There were two major, new findings. 1) The discharge rates of both SA1 and RA afferents were strongly affected by the number of probes indenting the RF simultaneously. The effect was exponential. Each increase in probe number reduced the response by 24% in SA1 and 12% in RA afferents on average. When seven probes indented the skin simultaneously, the impulse rates in SA1 and RA afferents were reduced to 20 and 40% of the rates evoked by a single probe at the hot spot (all indentations were 100 µm). This shows that before any synaptic interaction in the CNS there is already a mechanism analogous to surround inhibition that suppresses an afferent's responses to uniform indentation and makes it especially sensitive to deviations from spatial uniformity. 2) The responses of both SA1 and RA afferents were independent of background array depth over the range from 1.6 to 3 mm below the point of initial skin contact. This shows that the neural responses to elements raised above a background are independent of the applied force over a wide range of forces. To relate the background depths to indentation force and to compare humans and monkeys, we studied the biomechanics of indentation with a uniform surface. A remarkable result is that the force-displacement relationships in humans and monkeys were the same; the skin is highly compliant for the first 2-3 mm of indentation and then becomes much stiffer. The results were the same in alert humans and monkeys and in monkeys anesthetized with pentobarbital. Ketamine anesthesia made the skin much stiffer and reduced the compliant range substantially.
![]() |
INTRODUCTION |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
This is the second of two papers
(Vega-Bermudez and Johnson 1999) describing the results
of a study of slowly adapting type 1 (SA1) and rapidly adapting (RA)
cutaneous mechanoreceptive afferents innervating the fingerpad
employing a stimulus array with probes spaced 1 mm apart. The first
paper reports an analysis of the responses evoked by single-probe
indentations at 73 skin sites in each afferent's receptive field (RF).
This provided a detailed characterization of the RFs of single
afferents, the effects of indentation amplitude, and estimates of the
population responses evoked by single-probe indentations. The present
paper reports an analysis of the responses evoked by multiple probes
and the effects of changes in background indentation.
This study was motivated by previous studies in human and nonhuman
primates that have shown that SA1 afferents respond much more
vigorously to surface discontinuities, gradients, and curvature than to
uniform skin indentation (Goodwin et al. 1995;
Johansson et al. 1982
; LaMotte and Srinivasan
1987b
; Phillips and Johnson 1981a
) and that they
do so whether a surface is stationary (Cohen and Vierck
1993
; Phillips and Johnson 1981a
;
Srinivasan and LaMotte 1987
) or scanned across the skin
(Blake et al. 1997
; Johnson and Lamb
1981
; LaMotte and Srinivasan 1987a
,b
). These SA1
response properties have been accounted for in quantitative detail by
the assumption that their receptors respond to the local maximum
compressive strain (Phillips and Johnson 1981b
) or
strain energy density (Grigg and Hoffman 1984
;
Khalsa et al. 1996
; Srinivasan and Dandekar 1996
), which are closely related strain components. In theory, sensitivity to these strain components confers response properties similar to those produced by surround inhibition in the CNS. In the
present study we explore the suppressive effects of surrounding stimuli directly.
Previous studies of the responses of RA afferents to the same complex
stimuli provide a less-consistent picture of their response properties.
Some studies suggest that RA afferents respond simply to local skin
indentation (Gardner and Palmer 1990; Goodwin et al. 1995
; Phillips and Johnson 1981b
) and that
their responses are the same whether that indentation is part of a
broad pattern of uniform indentation or is surrounded by regions of
varying indentation. Other studies suggest that RA afferents, like SA1 afferents, are sensitive to some component of the spatial pattern of
indentation (Goodwin et al. 1981
; Johansson et
al. 1982
). Data from the study reported here support the
conclusion that RAs are sensitive to spatial structure.
Both SA1 and RA afferents were studied with dual- and multiprobe stimuli whose indentation depths were generally limited to 10% of the probe spacing (i.e., to 100 µm) to minimize gross mechanical coupling between stimulus sites. Nonetheless, surrounding mechanical stimuli affected both SA1 and RA responses to a probe at the hot spot (HS, point of maximum sensitivity). Both afferent fiber types were also studied with a wide range of indentation patterns superimposed on varying degrees of background indentation, comparable to pressing a finger more or less firmly against a surface with raised surface features. The result was that background indentation had no effect on SA1 and RA RFs or their responses over a wide range of background indentations.
![]() |
METHODS |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
The neurophysiological and stimulus methods are described in
detail in Vega-Bermudez and Johnson (1999). Briefly, experiments were
performed on anesthetized monkeys (Macaca mulata) weighing between 3.0 and 5.0 kg. Single mechanoreceptive fibers were dissected from the median or ulnar nerves with methods described earlier (Mountcastle et al. 1972
). Peripheral afferent fibers
were classified as SA1, RA, or Pacinian according to their responses to
a single, vibrating punctate probe (Talbot et al. 1968
).
Only fibers with RFs on the distal pads of the digits were studied.
The tactile stimulator consisted of probes, 0.5 mm in diameter, arrayed
in a hexagonal pattern at 1.0-mm intervals (center to center). The
entire array was 13 mm in diameter. All 155 probes except the central
seven probes were stationary (see Fig. 1 in Vega-Bermudez and
Johnson 1999); the central seven probes were driven by
independent, servo-controlled linear motors (Schneider 1988
), capable of 1,000-µm indentation with a 2-ms rise time. The array was lowered until all skin within a 4-mm radius around the
central active probe (50 mm2) was in contact with the
array; this background indentation was typically 1.6-2.0 mm below the
point of first contact with the skin. The array was larger than any
fingerpad, and no array placement resulted in contact with the edge of
the array. Probes were indented for 200 ms followed by a 200-ms
interstimulus interval. The first stimulus sequences, whose results are
reported in a companion paper (Vega-Bermudez and Johnson
1999
), established the location of the HS, which became the
reference point for positioning the array in the studies reported here.
Three stimulus sequences were used: a dual-probe sequence, a
multiple-probe sequence, and a sequence aimed at studying the effects
of background indentation.
Dual-probe sequence
The dual-probe stimulus sequence consisted of indentations by each of the seven active probes followed by simultaneous indentation with all possible pairs of the seven active probes (21) at each array placement. Indentation depths of 100 µm were used to minimize mechanical interactions between probes. This was repeated 10 times for a total of 280 trials at each placement of the array. The dual-probe sequence was presented 1) with the central active probe over the HS (Fig. 1A), 2) at six placements with one of six surrounding active probes over the HS (Fig. 1B), and 3) at six hexagonal placements with the central probe displaced from the HS by 577 µm (Fig. 1C). These placements sampled an area of 10 mm2 with a resolution of 577 µm between adjacent points. All together there were 84 different paired stimulus sites separated by 1 mm, 42 by 1.7 mm, and 21 by 2 mm for a total of 147 different paired stimulus sites. In all of the analyses presented in this paper, Rdual represents the response evoked by two probes presented simultaneously, and Rmin and Rmax represent the minimum and maximum responses when the same two probes are presented singly.
|
Multiple-probe sequence
When the dual-probe sequence was completed, the array was recentered on the HS (Fig. 1A), and the multiple-probe sequence was initiated. The stimulus sequence comprised indentations by the probe over the HS together with all 64 possible combinations of the surrounding 6 probes. Stimuli were presented in randomized blocks of 5 trials per stimulus (320 trials total; 64 probe combinations × 5 trials each). All indentation depths were 100 µm. After this, the multiple-probe sequence was repeated at four sites with the central probe displaced 1, 2, 3, and 4 mm from the HS along a line that included as much of the RF as possible.
Background-indentation sequence
The array was positioned with the central probe over the HS and lowered to the fiber's initial background indentation as described previously. Stimuli were presented at this initial background indentation and again at background depths of 250, 500, 750, and 1,000 µm below the initial level. Three indentations (100, 200, and 300 µm) below the background depth were used.
The stimulus sequence at each background depth comprised 21 single-probe stimuli (7 probes × 3 indentation depths) and 81 dual-probe stimuli, each repeated 5 times for a total of 510 stimuli. The dual-probe stimuli comprised nine probe pairs (the central probe paired with each of the surrounding 6 probes and the 3 probe pairs straddling the central probe) presented at each of the nine possible pairings of 100-, 200-, and 300-µm indentation depths.
Indentation depth, force, and contact area
A large (20 × 30 mm), flat plate was driven into the skin of the distal pad of the index finger with a micrometer. Reaction force was measured with a digital force gauge (Omega Engineering DFG51-2, resolution 0.005 N). The difference between a flat plate and the array of densely spaced probes should be minimal insofar as the macroscopic biomechanics are concerned. Contact area at each indentation depth was measured by applying ink to the skin, sticking paper with adhesive on one side to the plate, and measuring the area of the resulting fingerprint. The plate was retracted after every indentation and ink was reapplied. The plate was tilted distally just enough to avoid contact with the middle phalanx at maximum indentation. At that tilt angle (15-20°) the plate first contacted the skin at the midpoint of the distal pad, and the edge of the skin contact region came within 2-3 mm of the crease between the distal and middle phalanges.
![]() |
RESULTS |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Data were obtained from 24 SA1 and 26 RA afferents with RFs on the distal fingerpads. All stimuli were 200 ms long, and all stimuli involving two or more probes indented the skin by 100 µm unless stated otherwise to minimize mechanical interactions between probes. The total protocol was long, and some stimulus sequences were not run on all afferents. The numbers are specified when that was so.
Responses to two probes
Two probes were presented at a total of 540 locations within the RFs of 19 SA1s and 590 locations within the RFs of 21 RAs. The response to two probes (measured as impulse rate during the 200-ms stimulus period) was greater than the response evoked by either probe presented singly at only 10% of those locations. Eighty percent of all responses to two probes (called Rdual) lay between the minimum (Rmin) and maximum (Rmax) responses to the same two probes presented singly. The remaining 10% of dual-probe responses were less than Rmin. These data are analyzed in greater detail subsequently.
DUAL PROBES WITH ONE PROBE AT THE HS. The effect of indentation with a second probe was studied with the array in 7 positions so that each of the seven active probes was over the HS (Fig. 1B). That yielded six different probe pairs where one was at the HS and the second probe was 1.0 mm from the HS, six where the second probe was 1.73 mm way, and six where the second probe was 2.0 mm away. All analyses are confined to probe pairs in which Rmin exceeded 5 impulses/s. Eighty-seven percent of all SA1 responses and 84% of all RA responses to two probes were suppressed relative to the response at the HS alone. Eleven percent of SA1 and 6% of RA responses to two probes were even less than Rmin. When the probe pairs were separated by 1.0 mm the response relative to a single probe at the HS was reduced 30% on average in SA1s and 23% in RAs (Fig. 2). The difference between SA1s and RAs was not large, but it was significant (P < 0.01, t-test). The distribution of Rdual/Rmax in single afferents is similar to the distribution for all afferents illustrated in Fig. 2.
|
|
|
NEITHER PROBE ON THE HS. During the dual-probe stimulus sequence the tactile array was also placed with the central probe at six locations surrounding the HS so that no probe was directly on the HS (Fig. 1C). The suppressive effect of dual-probe stimulation was smaller when neither was at the HS (Fig. 5). The mean effects, Rdual/Rmax, for all such probe placements were 0.890 and 0.885 for RAs and SA1s, respectively.
|
Responses to multiple probes
Next we studied how the response depended on the number of active probes. Twenty-two SA1 and 17 RA afferents were studied with the central probe positioned over the HS (Fig. 1A). Ten SA1s and 10 RAs were studied with the probe array positioned at varying distances from the HS (Fig. 1B). Probe indentation depth was 100 µm at all placements.
CENTRAL PROBE OVER THE HS. When the array was positioned with the central probe directly over the HS, all possible combinations of seven probes that included the central probe (64 combinations) were presented (i.e., the central probe alone, 6 dual-probe stimuli comprising the central probe and the surrounding 6 probes, 15 triple-probe stimuli comprising the central probe and 2 of the surrounding 6 probes, etc.). All SA1 and RA responses were suppressed progressively by increasing numbers of probes (Fig. 6, top row). The SA1 suppressive effect was described much better as a multiplicative than as a subtractive effect (i.e., the relationship between impulse rates and number of probes was linear in logarithmic but not in linear coordinates, cf. Figs. 6 and 8). The RA suppressive effect was described approximately equally well as multiplicative or subtractive (cf. Figs. 6 and 8). The mean reductions in response per additional probe (the slopes of the curves in Fig. 6, bottom row) were 24 and 12% for SA1 and RA afferents, respectively. The decrement in response per additional probe ranged from 13 to 52% for SA1s and from 1 to 22% for RAS.
|
CENTRAL PROBE AT VARYING DISTANCES FROM THE HS. The stimulus sequence used at the HS was repeated with the central probe displaced by 1.0, 2.0, 3.0, and 4.0 mm from the HS along a line through the HS and the most distant point on the RF boundary. To remain consistent with the analysis at the HS, the analysis was restricted to multiple-probe stimuli that included the probe at the most active site (64 combinations). This was usually the probe nearest to the HS. The results for 10 SA1s and 10 RAs are shown in Fig. 7. A monotonic decline in SA1 and RA responses with increasing numbers of active probes persists to distances where there is little if any response to the 100-µm indentations. The average responses at each distance are shown in Fig. 8. A model based on exponential decline with increasing numbers of probes continued to fit the SA1 data closely for distances up to 3 mm; the effect of increasing probe numbers was constant at 24% per probe. The RA responses were fit well by a 12% reduction per probe at all distances.
|
|
Effects of background indentation depth
Before presenting the effects of background indentation on the neural responses, we present the results of a study of the relationships between indentation, contact force, and contact area in the human and the monkey. We do so for two reasons. First, although we manipulated the background indentation, background force is the more relevant variable because force is so commonly dictated by the manual task at hand. Therefore we need to understand the relationship between the indentation depths that we have used and contact force. Second, the object is to understand tactile function in the human. Although many studies demonstrate the similarity in mechanoreceptive function between the two species, their fingerpad geometries are different.
The relationships between background indentation depth, force, and
total contact area in two humans and two monkeys are shown in Fig.
9. One of the monkeys was trained to let
its hand be restrained in a hand holder so these relationships could be
measured while it was relaxed and awake. Figure 9A shows
that the relationship between indentation depth and force was nearly
identical in the awake monkey and the same monkey anesthetized with
pentobarbital, as in the neurophysiological experiments reported here.
Ketamine anesthesia, in contrast, caused the skin to be much stiffer,
possibly because of the increased muscle tone, increased blood
pressure, and increased sympathetic activity related to ketamine
anesthesia (Goodman et al. 1990). The relationship
between reaction force and indentation depth was remarkably similar in
monkeys and humans; the skin reaction force rose slowly until ~2 mm
of indentation and then rose rapidly in both species. Put differently,
the compliant range in both species is about the same.
|
All the data reported up to this point were collected with the background indentation at 1,600-2,000 µm below the point of first contact with the skin. The effects of changes in background indentation depth were studied in 9 SA1 and 9 RA afferents by presenting 102 different stimuli at the array's initial depth and then at background depths 250, 500, and 750 µm below the initial background depth. Some were studied at 1 mm below the initial depth as well. On the basis of the biomechanical data displayed in Fig. 9, we estimate that as the background indentation increased from 1.6 to 3.0 mm the reaction force increased from 0.3 to 3.0 N. The most important result was that both SA1 and RA responses to one and two probe stimuli were unaffected by background depth (ANOVA, SA1, P = 0.76; RA, P = 0.27). RF maps, based on indentation with a single probe were, like these quantitative results, unaffected by the background array depth. The RFs of a typical SA1 and RA afferent, mapped at three different background array depths, are shown in Fig. 10.
|
![]() |
DISCUSSION |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
There were two main neurophysiological results. The first was that
both SA1 and RA afferents are maximally responsive to indentation by a
single point and that additional neighboring punctate stimuli have a
graded, suppressive effect. The surprising aspect of this finding was
the magnitude of the effect produced by very small indentations 1 mm
from the HS. The second result was that responses to single and
dual-probe indentations throughout the RFs of both SA1 and RA afferents
were unaffected by the background array depth within the range from 1.6 to 3.0 mm below the point of initial contact. Because the responses to
stimuli both on and off the HS were unaffected by background array
depth, we can infer that the population responses evoked by the stimuli
were unaffected by background indentation depth.
The significance of the first result is that SA1 and RA afferents are
much more sensitive to spatial variation in the stimulus profile than
to uniform indentation. A single probe indenting the skin produces
intense spatial stimulus gradients (spatial variation) in all
directions. Each probe that indents the skin in addition to the central
probe reduces the gradient (variation) in one direction. Uniform
indentation by seven probes in the RF (which covered most and sometimes
all of an SA1 RF) (see Fig. 2 in Vega-Bermudez and Johnson
1999) reduced the responses of SA1s and RAs on average to 20 and 40%, respectively, of the responses to a single probe at the HS.
It is evident from Figs. 6-8 that if we had indented the skin with
more probes so that all the skin in and around the RF was uniformly
depressed many responses would have been driven close to zero. In fact,
two SA1 afferents that responded with
20 impulses/s to a single probe
responded with <1 impulse/s when their RFs were indented with seven probes.
The significance of the second result is that the neural responses to
stimuli on a background surface are independent of the contact force
over a wide range (at least from 0.3 to 3.0 N). That fits the
observation that changes in contact force, at least between 0.2 and 1.0 N, do not affect the human ability to recognize complex, raised
patterns (Loomis 1985).
The most interesting biomechanical result was the similarity between the human and monkey force-displacement curves. Both had a highly compliant phase between 0 and 2-3 mm where indentation produced relatively slight reaction forces followed by a noncompliant phase where reaction forces rose rapidly. The similarity suggests that this architectural feature is important in tactile sensing. We discuss this subsequently.
Previous studies
No previous neurophysiological studies of which we are aware have
varied the number of probes or the background indentation. However,
many studies have used complex spatial stimuli (Blake et al.
1997; Connor et al. 1990
; Gardner and
Palmer 1989
; Goodwin et al. 1995
; Johnson
and Lamb 1981
; LaMotte and Srinivasan 1996
; Phillips and Johnson 1981a
; Phillips et al.
1992
; Sathian et al. 1989
). All of those studies
show that both SA1 and RA responses to a stimulus scanned across the HS
are strongly suppressed by surrounding stimuli; Blake et al. (1997)
showed that SA1 and RA responses to a single, raised scanned element
begin to be suppressed when neighboring raised elements are closer than
~6 mm.
Three previous studies have indented the skin with stimuli more complex
than a single point (Goodwin et al. 1995;
Phillips and Johnson 1981a
; Srinivasan and
LaMotte 1987
). The three studies show consistently that SA1 but
not RA afferents encode the shape of the object indenting the skin,
that SA1 afferents are very sensitive to spatial gradients close to the
HS, and that RA afferents are sensitive only to the velocity of
indentation over the HS. The study by Goodwin et al. (1995)
, in which
the curvature of a spherical stimulus indenting the skin at the HS was
varied, is perhaps most like the present study; gradually reducing
curvature, as they did, causes the skin surrounding the HS to be
stimulated progressively. They found that SA1 but not RA responses were
affected by stimulus curvature. A surface with zero curvature (a flat
surface) evoked an SA1 response that was, on average, one-sixth that
evoked by a 3-mm diam spherical probe. If they had used a 0.5-mm diam probe as in this study the fraction would be even smaller.
A major difference between our results and these three previous studies
is the RA surround suppression reported in this study. Goodwin et al.
(1995) found that the responses of RAs were independent of stimulus
curvature; the RAs in their study responded as vigorously to a flat
surface as to a 3-mm diam probe. Phillips and Johnson (1981a)
showed
that RAs respond as vigorously to a flat surface as a narrow bar. The
most likely explanation for the difference is that the indentation
amplitudes in the previous studies were outside the RA dynamic range
(the smallest indentation amplitude in the 3 previous studies was 500 µm). RA responses to rapid indentations >1-300 µm are strongly
saturated (Blake et al. 1997
; Vega-Bermudez and
Johnson 1999
). The surround suppression may have appeared in
this study but not in the others because of the small test amplitudes
(100 µm) used in this study.
Biomechanics
The relationships between indentation depth, reaction force, and
contact area when a flat surface is pressed into the skin of a
fingerpad have been studied previously in the human (Pawluk and
Howe 1999; Westling and Johansson 1987
) and the
monkey (Goodwin and Morley 1987
). The human data shown
in Fig. 9 are very similar to the previously published data. Goodwin
and Morley's data are restricted to indentations between 0.5 and 1.25 mm, but over that range their data and ours are similar.
The most interesting result in relation to tactile sensing is the
similarity in the force-displacement curves between humans and monkeys.
This curve has two phases, a highly compliant phase where the reaction
forces are small and a noncompliant phase where the reaction forces
rise very rapidly. The transition between these phases is 0.5 N. The
subcutaneous hard tissues produce an absolute indentation limit of ~5
mm (unpublished observations). The tendency toward stiffening begins at
small indentations, so factors other than compression against the
underlying hard tissues evidently play a prominent role (Fung
1993
). When subjects are asked to scan a surface the way they
would ordinarily do so the skin is pushed into the noncompliant range
(~1 N) (Johnson and Lamb 1981
; Lederman
1974
).
The significance of the highly nonlinear compliance function is, we
believe, the following. To sense the spatial pattern of a surface the
skin must conform to the pattern. If the skin were stiff, we would have
to press firmly to get the skin to conform to the pattern. Because the
skin is so compliant over the first 2-3 mm, we can hold an object
lightly and still sense surface form that varies by 2-3 mm. If a
manual task requires high forces the skin is still free to protrude by
2-3 mm or possibly a bit more to follow the contours of the object
held by the fingers. If monkeys were simply scaled-down humans the
compliant range in the monkey would be less than one-half that in a
human (the ratio of the volumes of the humans and monkeys in this study
was >10:1, thus the linear scaling factor is >2:1), and the monkey's ability to sense surface structure would be one-half that of a human.
However, nonhuman primates and humans deal with the same tactile
environment. The similarity of the force-displacement functions in the
two species suggests that sensing features defined by elevations of
2-3 mm is important. A conspicuous difference between the monkey and
human hand is the elevation of the distal pad. The exaggerated
elevation of the distal pads of some prosimians is even more
conspicuous (Jouffroy et al. 1993).
A significant outcome was the unexpected effect of ketamine. The
decreased compliance may account for some ketamine effects on
neurophysiological responses(Duncan et al. 1982). On
biomechanical grounds alone, ketamine should not be used in
neurophysiological experiments aimed at the normal response properties
of neurons in the somatosensory system.
Mechanisms
Two different mechanisms might explain the attenuation observed
when a second probe is placed in the RF. The attenuation could be
caused by interactions between the neural signals arising in the distal
branches of the afferent axon (Eagles and Purple 1974; Horch et al. 1974
; Lindblom and Tapper
1966
; Phillips and Johnson 1981b
; Proske
and Gregory 1976
). However, a strong argument against such a
mechanism is that the suppressive effect of additional probes was as
strong when the center of the array was 3 mm from the HS as when it was
directly over the HS. At that distance the nearest active probe was
within the RF of most SA1 afferents, but the rest were not.
The more likely mechanism is that both SA1 and RA afferents are
responsive to some component of skin deformation other than simple
indentation depth (Blake et al. 1997;
Johansson et al. 1982
; Johnson and Lamb
1981
; LaMotte and Srinivasan 1996
) and that
indentation with multiple probes distributes the stresses and strains
required for the deformation and thereby reduces the stresses and
strains at the transducer site(s) (Phillips and Johnson 1981b
). When the probes are all at the same depth, the
deformation is uniform, the shear strain is minimal, and the stress
beneath each probe is only that required to deform the skin directly
beneath the probe. When a single probe advances beyond the others it
unloads neighboring probes, transfers the deformation load to itself, and creates a shear field around itself. If the transducer site(s) is
within the strain field caused by the probe the result is a response to
the displacement. When additional probes indent the skin the stresses
and strains are redistributed. As the number of probes increases, the
whole strain field tends toward that which prevails in uniform
deformation. At first sight, it seems surprising that 100-µm
indentations by probes spaced at
1 mm should interact so profoundly.
On the other hand, it is clear that when one probe advances beyond the
others by any amount it will progressively transfer the deformation
load to itself, create an inhomogeneous strain field, and set up shear
stresses and strains in the skin. Although 100 µm is a small
displacement it is 10% of the probe spacing and therefore creates a
substantial change in the geometry and the mechanics of deformation.
![]() |
ACKNOWLEDGMENTS |
---|
D. Pawluk and T. Yoshioka collected the measurements of force and contact area during skin displacement. We also thank S. Hsiao, H. Dong, and W. Schneider for assistance.
This work was supported by National Institute of Neurological Disorders and Stroke Grant NS-18787 and by the W. M. Keck Foundation.
![]() |
FOOTNOTES |
---|
Address for reprint requests: K. Johnson, 338 Krieger Hall, Johns Hopkins University, 3400 N. Charles St., Baltimore, MD 21218.
The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
Received 25 June 1998; accepted in final form 22 February 1999.
![]() |
REFERENCES |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|