 |
INTRODUCTION |
Noxious indentation of skin is transduced by
cutaneous mechano-nociceptors that can lead to the percept of pain.
Pain, because of acute mechanical stimuli, is not perceived until
mechano-nociceptors respond at firing rates substantially greater than
threshold (Garell et al. 1996
; Greenspan and
McGillis 1991
). It is questionable whether suprathreshold
firing of single mechano-nociceptors is sufficient to be perceived as
painful (Greenspan 1997
; Greenspan and McGillis
1991
;Heppelmann et al. 1991
). This implies that
it requires a population of nociceptors to accurately encode the location and intensity of noxious mechanical stimuli.
Neuron population studies have been used widely to examine encoding of
tactile stimuli. It has been demonstrated that single, low-threshold,
slowly adapting mechanoreceptors cannot unambiguously encode even
simple features of mechanical stimuli (Ray and Doetsch 1990a
,b
) because they can be confounded by force and velocity of the applied stimulus (Burgess et al. 1983
; Mei
et al. 1983
; Poulos et al. 1984
). In the monkey
fingerpad, population studies have been used to examine encoding of
spheres (Goodwin et al. 1995
), toroidally smooth objects
(Khalsa et al. 1998
), cylindrical probes (Cohen
and Vierck 1993
), and probe arrays (Vega-Bermudez and
Johnson 1999
). Population studies thus have demonstrated coding mechanisms of shape, location, and intensity for low-threshold mechanoreceptors and suggest possible analogous roles for
mechano-nociceptors.
Mechano-nociceptors comprise a heterogeneous population consisting of
neurons with different ranges of conduction velocities (A
: 2-20
m/s, and C: < 2 m/s) because of their axon diameters and relative
myelination and with different responsiveness to other stimuli (i.e.,
heat, cold, and chemicals). Their sensitivities to mechanical stimuli
also vary widely, though A fibers generally respond at higher rates of
firing than do C fibers (Garell et al. 1996
).
Mechano-nociceptors cannot only respond to compression but also to
tension (Grigg 1996
; Khalsa et al. 1997
)
and shear loads produced with sharp edges (Greenspan and
McGillis 1991
).
Indentation of skin overlying a hard substrate (e.g., bone) produces
primarily compressive stress and strain. However, the same indentation
of skin overlying a soft substrate (e.g., muscle or fat) also will
create tensile and shear stress and strain that is greatest at or near
the indenter and decreases distally. This suggests that for an adequate
indentation of skin overlying a soft substrate, a population of
nociceptors surrounding the site of indentation should be activated. A
first-order model of such a response has been described previously
(Khalsa et al. 1997
).
Determining a cutaneous, mechano-nociceptor population response
to noxious indentation in vivo can be problematic. First, it is not
currently feasible to record simultaneously and unambiguously all the
neural responses of an actual nociceptor population (and identify their
receptor fields) to a noxious mechanical stimulus. An approach to
estimating a population response has been to record the neural
responses of single neurons to mechanical stimuli at discrete intervals
from the most sensitive spot of their receptive fields (Goodwin
et al. 1995
). The responses then can be normalized and averaged
to estimate the spatial population response. Second, the nonlinear
geometry of skin can complicate interpretation of the neural response
to mechanical stimuli. For example, indentation of a spherical object
into the monkey fingerpad produced an asymmetrical spatial population
response (from low-threshold mechanoreceptors) biased along the long
axis of the finger (Khalsa et al. 1998
). Indentation
with a symmetrical object (e.g., a flat tipped cylinder) would produce
different mechanical states distal to the contact site. Third, the bulk
compressive compliance of a large enough region would not be spatially
homogeneous because of the different tissues involved, their
dimensions, and their potential interactions with hard tissues like
bone. Hence the same magnitude stimulus at different spatial locations
could produce different mechanical states in the skin. Fourth, the
receptive endings of single nociceptors are often multiple
(particularly for A
fibers) and can extend over many square
millimeters of skin (Lynn and Carpenter 1982
). Hence
different terminal endings of a single parent axon presumably could be
subjected to different mechanical states even with a single stimulus.
To overcome these difficulties, an isolated skin-nerve preparation,
suspended directly on the surface of a compliant platform, was
developed. The platform was constructed to emulate the nonlinear, bulk
compressive compliance of the substrate underlying the skin in the
intact animal. However, its compliance was spatially homogenous and its
surface was linear (i.e., flat). Hence indentations of in vitro skin
overlying the compliant platform produced consistent mechanical stimuli
to the nociceptors regardless of their location within the skin. Thus a
spatial population response could be constructed from the neural
responses of single mechano-nociceptors and used to examine the ability
of a nociceptor population to encode location and intensity of noxious indentation.
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METHODS |
Preparation
Experiments were conducted using an isolated skin-nerve
preparation similar to that previously reported in detail
(Khalsa et al. 1997
). Briefly, hair was removed from the
medial thigh of an anesthetized rat (Sprague-Dawley, 250 g, either
sex), and small markers (0.5-mm diam) were glued to the skin and their
locations measured relative to one another (Fig.
1A). The markers served to
identify the in vivo reference state of the skin. The patch of skin and
its intact innervation then was harvested and placed in a dish
containing circulated and gassed (100% O2)
rodent, synthetic interstitial fluid (Koltzenburg et al.
1997
). Tabs (7 mm wide × 14 mm long) were cut into the
margins of the skin (3 tabs per side, total of 12) and coupled to force
transducers mounted on the ends of linear actuators (3 actuators per
side, total of 12; Fig. 1B). The skin then was stretched
until the markers closely approximated their in vivo locations.

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Fig. 1.
A: skin was obtained from the medial aspect of the right
thigh of the rat along the line drawn. Dots were spheroids (0.5 mm
diameter) glued to the depilated skin. B: skin was
suspended, corium side down, in a dish containing synthetic
interstitial fluid. Each skin tab was coupled by a length of suture to
a force transducer
(L1-L12) mounted on a
linear actuator. Rotary actuator (C) applied compression to the skin by
actuating a lever arm. The nerve (N) was threaded into an abutting
chamber, filled with mineral oil, for recording.
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Pure compressive and pure tensile loads were applied as previously
reported (Khalsa et al. 1997
). Briefly, tensile loads
were applied to the skin by actuating the tabs until predetermined loads were achieved. Compressive loads were applied by indenting the
skin with a flat tipped cylinder (3-mm diam) between a compliant or a
hard platform. The cylinder was actuated with a force controlled DC
motor (model 305B, Aurora Scientific, Aurora, Canada) mounted on a
three axis positioning stage (resolution 0.1 mm and range 40 mm on each
axis). Actuator control and data acquisition was accomplished via a
laboratory computer, A/D and D/A converter, and custom software. Loads
(12 tensile and 1 compressive) were sampled at 500 Hz.
Compliant platform
To emulate the in vivo response of indenting the skin overlying
a compliant substrate, a platform was constructed with nonlinear compliance similar to the in vivo, bulk-compressive compliance of the
rat medial thigh. The approach we adopted was to develop a platform
composed of multiple layers of silicone rubber varying the compliance
and thickness of each layer appropriately. Thus while the material
properties of each layer were intrinsically linear, the bulk compliance
of the multilayered platform to indentation was nonlinear for large
deformations. Four sequential steps were required to construct the
platform that have been reported previously in abstract form
(Qin and Khalsa 1999
).
First, the in vivo, compressive compliance of the skin/muscle of the
medial thigh region was measured by indenting the region in intact
Spraque-Dawley rats. A rat was anesthetized with an intraperoneal
injection of pentobarbital sodium (25 mg/kg), laid on its back, and its
right hindlimb was externally rotated (so that the medial thigh was
"up") and clamped to a hard platform. Anesthesia was maintained by
periodic supplemental injections of pentobarbital sodium (5 mg/kg) to
keep the animal areflexic to noxious stimuli. The skin of the medial
thigh, overlying muscle and not the bone, was indented using the same
indenter system as employed in the neurophysiological experiments.
Compressive "creep" tests were performed as follows. Under force
feedback control, the indenter was lowered to the skin until a minimal force was registered and held at this position for 0.5 s. Then a
step indentation was performed to the desired force, the force maintained for 10 s, and then unloaded. Intertrial intervals were 3 min to allow the skin and underlying substrate (principally muscle)
to fully recover. Force and displacement were recorded at 100 Hz with
the same equipment used for the neurophysiological experiments and were
reported as the means of the last 0.5 s of the indentation. Each
indentation was performed three times, and the results were averaged.
Subsequently the compliance of just the underlying substrate was tested
by excising the patch of skin being indented and repeating the same
series of tests. No significant differences (P > 0.05)
were found between the two sets of data, indicating that the
bulk-compressive compliance of the hindlimb was determined by the
underlying substrate and not the skin. By visual inspection, it was
observed that the compliance curve could be represented by three linear
regions. This suggested that the deformable platform could be
constructed of three layers of silicone rubber with different
thicknesses and different linear compliances, and thus reproduce the
empirically determined nonlinear bulk compliance.
Second, the thicknesses of three layers of different linear
compliances necessary to produce a nonlinear bulk compliance were calculated using finite element analysis with commercially available software (ABAQUS version 5.6, HKS, RI) (see APPENDIX for a
description of finite-element analysis). Because the compliant platform
was designed to be axially symmetric, it was sufficient to model it in
two rather than three dimensions (Fig.
2). The compliant material was
represented by 300 four-noded quadrilaterals (336 nodes), with
dimensions of 35 (wide) × 17 (thick) mm. The model used a large
strain, elastic formulation (hyperelastic) under plane stress. The
constitutive behavior of the material was defined by the strain energy
density. The elasticity was based on the Ogden (n = 2) form of total strain and total stress relationship. In the model, the
material was compressed by a rigid indenter (3-mm diam) using the
ABAQUS nonlinear geometry parameter. The geometry and the mesh
refinement were biased toward the center of the specimen where the
largest deformation occurred (Fig. 2). Bottom and side boundaries were
constrained. A contact pair was defined between the surfaces of the
indenter and the silicone in the contact region. Loading was applied
through downward displacement of the indenter by a distance of 10 mm.
Different combinations of the thicknesses of three layers were used in
the model. Material properties for each silicone layer were defined
from the linear regions of measured in vivo compliance curve and for
rat skin came from those previously reported (Khalsa et al.
1997
).

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Fig. 2.
Deformed mesh of the finite element model (FEM) of skin overlying a
compliant substrate with an applied load of 0.6 N.
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The nonlinear, compressive compliance of the intact skin-muscle was
well fit with a power function (Fig. 3,
solid line overlying crosses: y = 1.544*x0.3836,
R2 = 0.997). The finite element model
(FEM) produced a close fit to the in vivo data using three layers of
silicone rubber with different thicknesses and compliances (from the
bottom to the top layer: 2, 3, and 12 mm; and 0.036, 0.092, and 0.389 mm/g, respectively). The compliance was largest for the most
superficial layer because the rat thigh became stiffer with greater
indentation.

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Fig. 3.
Compliance of rat medial thigh, prediction of FEM, and multilayer
silicone platform. Error bars (SE) for skin/muscle and silicone
platform are smaller than symbols.
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Third, pure silicone rubber (rubber compound, RVT615A; curing agent,
RTV615B; courtesy of GE Silicones, Waterford, NY) was made with
different compliances by varying the ratio of the compound with the
curing agent. After curing for 24 h, the compressive compliance of
the silicone rubber was measured in the same manner as described for
the skin/muscle. Once the correct ratios of compound to curing agent
were determined, the layers could be formed inside a rigid cylinder
(35-mm diam and 17-mm height). To assure continuity between the three
layers in the multilayer silicone platform, the bottom layer was poured
first and allowed to cure for 24 h, followed in similar fashion by
the middle and top layers. The bulk-compressive compliance of the
platform then was measured as described previously to verify that it
adequately emulated the in vivo nonlinear compliance (Fig. 3). It was
not required that it match it exactly, only that it produced a similar
form, as undoubtedly, the actual bulk compliance would vary by location of indentation in the hindlimb and in different animals.
Finally, validation that indentation of the in vitro preparation was
similar to in vivo indentation was performed as follows. A rat was
anesthetized and his hindlimb clamped as described previously. Hair was
removed from the medial hindlimb with a chemical depilatory (Nair).
Small flat reflective markers (1-mm diam) were glued on the skin,
forming two lines orthogonal to one another with the ends of the lines
meeting in the center of the patch of skin covering the medial thigh.
The thigh was indented as described previously while optically tracking
in three dimensions the positions of the markers with a kinematic
analysis system (model 50, Qualisys, Glastonbury, CT). Subsequently,
the same skin patch was excised from the rat, placed in the saline
dish, coupled to the actuators, and suspended above the compliant
platform. The in vitro skin then was indented as described previously
while again optically tracking the displacements of the markers.
Displacements of the in vivo and in vitro preparation were compared and
found to be similar (Fig. 4).

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Fig. 4.
Kinematic comparison of in vivo indentation of skin from the medial
thigh of the rat with same area of skin indented in vitro over the
compliant platform. Skin was indented with a cylinder (3-mm diam) under
servo-force control. See METHODS for indentation protocol.
The system was axi-symmetric, and hence the results for markers 7-11
were virtually the same as for markers 1-5. For clarity, results for
only markers 1-6 are shown. A: in vivo indentation of
50 g-f. Because of their visco-elastic nature, the skin and its
underlying substrate (i.e., principally muscle) continue to displace
during the indentation. This is called "creep" in biomechanics.
B: in vitro indentation of 50 g-f showing a similar rate
and magnitude of indentation and creep. C: differences
(residual displacements) between the in vivo and in vitro displacements
for indentations ranging from 10 to 80 g-f. Values were compared at a
reasonable, though arbitrary, choice of 10 s during each
indentation.
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Neuron recording, classification, and receptive field mapping
Neural recording and classification has been reported previously
in detail (Khalsa et al. 1997
). Briefly, the nerve was
threaded from the saline compartment through a hole into an adjacent
oil-filled chamber. Bundles of nerve filaments were teased apart until
the neural response of single neurons could be discriminated. Neural responses were monitored on a digital oscilloscope, over an audio speaker, and by a template matching system (Spike2, Cambridge Electronic Design, UK). Only neurons responsive to mechanical stimuli
and with conduction velocities (corrected for the room temperature
saline bath) in the A
- and C-fiber range were included in this
study. Neurons also were categorized by their response to noxious heat
(35 and 55°C for 5 s.) and cold (ice chips on the skin for
10 s). The response of a neuron to the mechanical stimulus (10 s)
was reported simply as the total number of action potentials that
occurred (Khalsa et al. 1997
).
The "compressive receptive field" (RFC) of
some afferents were mapped using calibrated monofilaments (Stoelting,
Chicago, IL) with the skin overlying a hard platform. A video camera
imaged the skin onto a monitor over which was placed a clear acetate sheet. A dot was marked onto the acetate sheet at each location where
indentation with the monofilament produced a neural response. The
threshold response was defined as the minimal force that consistently produced at least one spike. The suprathreshold response was defined as
the minimum force necessary to produce the largest area of response
(i.e., by increasing the stiffness of the monofilament, no increase in
area of the RFC was observed). The most sensitive spot (MSS) within the RFC was used for the center
of the location of indentation. The RFC differs
from more traditional receptive fields because, using the hard
platform, the monofilaments essentially produced only local
compression, without tension as would typically occur in vivo (except
over bone). An advantage of the RFC is that it
more clearly discriminates the actual areal extent of the receptive ending(s) for single units. Only neurons whose MSS was within the
demarked region (196 mm2) of the skin specimen
were included in this study.
Experimental procedure
Once a suitable afferent was identified, its neural response
first was calibrated to pure compression (i.e., compression of the skin
overlying a hard platform) and, for some afferents, pure tension.
Compressive loads were applied at the MSS by first lowering the
indenter to the surface of the skin until a minimal force (3 g-f) was
detected, maintaining this position for 0.5 s, step indenting to a
predetermined force, maintaining this load for 10 s, and then
unloading (Fig. 5). Intertrial intervals
were 3 min to allow the skin to recover its prestimulus state and to allow the mechano-nociceptors to have stable responses for repeated stimulations (Garell et al. 1996
; Grigg
1996
). Ranges of loads were applied to encompass the threshold
to saturation level for compression for each neuron. Compressive
sensitivity was defined as the slope of a linear regression of the
compression response curve. Uniform tensile loads (with no compression)
were applied by actuating the skin tabs until the predetermined load
was achieved on each tab, maintaining this position for 10 s, and
then unloading. Tensile loads were applied in increments of 5 g up
to a maximum of 50 g with intertrial intervals again of 3 min.

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Fig. 5.
Top: compressive force (axis on left) and
displacement (axis on right) curves for a single
indentation trial with the skin overlying the compliant platform. All
indentations were under load control (in this example, 70 g-force), and
because the platform was designed to be viscoelastic, the displacement
"creeps" during the constant load. Bottom: raster
plot is the times of occurrences of action potentials for this trial
for an AM nociceptor. The neural response for this trial was reported
as the total number of action potentials that occurred during the
constant 10-s load.
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The hard platform then was replaced with the compliant platform
centered under the MSS of the neuron. Indentation was performed in the
same manner as described previously; however, because of the
substantial compliance of the platform, the indenter would displace
more than with the hard platform and because of the platform's viscoelasticity, the indenter would "creep" during the 10-s
stimulus (Fig. 5). The compressive force of the indentation was
selected by choosing the value at or just below the saturation level
determined from the sensitivity trials using the hard platform.
Indentation first was performed at the MSS and then at consecutive 1-mm
intervals, circling the MSS in an expanding clockwise fashion until an
outer boundary was reached where there was no neural response. The
intertrial interval was maintained at 3 min. Neurons the MSS of which
was located at the periphery of the demarked central 14 mm square were
stimulated only up to the margin of the square. The total number of
trials for each neuron varied depending on the spatial extent of its
response and whether it was possible to indent completely around the
MSS. Hence for a neuron centrally located in the skin and with a large
response area, to fully explore its response could require in excess of
150 trials to be performed. With a 3-min intertrial interval, this
resulted in recording times that could, and did, exceed 7 h for
some neurons. To verify that a neuron was not changing its sensitivity
during these long recording periods, indentations at the MSS were
repeated periodically (~1-h intervals) and the neural responses
compared. Any neurons the sensitivity of which did change were no
longer stimulated, and only the data from the earlier verified periods
were used.
Spatial population response
An interpretation of the data collected as described in the
preceding text was that it estimated, using the responses of a single
neuron to stimulation at spatially discrete locations, how a uniformly
distributed population of neurons with the same thresholds and
sensitivities would respond to a single stimulus (Goodwin et al.
1995
). Such a uniform spatial population response (SPRu) was represented by plotting, for each
nociceptor, the neural response (No. of action potentials/10-s
stimulation) versus the x, y location of each indentation.
The SPRu was depicted as two-dimensional contour
and/or three-dimensional (3D) surface plots; each method used a Kriging
algorithm (Surfer, Version 6.02, Golden Software, Golden, CO), which is
a "best-estimate method" of interpolating unknown data points of a
surface while not altering the known data (Davis 1973
).
A few of the neurons had MSS near the edge of the allowable stimulation
area of the skin and hence were not able to be stimulated completely
around the MSS. The SPRu for these neurons were
estimated by reflecting only the zero-responses of the stimulated
region to the nonstimulated region and allowing the Kriging algorithm
to interpolate the unknown data from the recorded responses.
A spatial population response at a given stimulus intensity
(SPRi) was developed from the
SPRu as follows. The sensitivity and threshold
(compressive load above which the neuron began to respond) data for
each neuron were used to linearly scale the neural responses of its
respective SPRu in 10-g-f increments (forming SPRu,i's for each neuron) from the actual
recorded values down to a minimum of 40 g or its threshold,
whichever came first. For example, for a C fiber that was stimulated at
80 g-f (i.e., this value was at, or just below its saturation level)
and had a threshold of 30 g-f, SPRu,i's could be
estimated at 70, 60, 50, and 40 g-f as well as the
SPRu that was recorded at 80 g-f. Each
SPRu,i was regressed nonlinearly (SigmaPlot 5.04, SPSS), using an equation for a Gaussian surface (Khalsa et al.
1998
) of the form
where x and y were the spatial
coordinates, z was the neural response, and the rest were
parameters to be fit to the surface (i.e., a was the peak
magnitude; x0 and
y0 were the offsets from 0 for the
x and y axes, respectively, and, b and
c were the widths of the surface at 60.7% of the peak
magnitude along the x and y axes, respectively).
At each stimulus intensity for A
- and C-mechano-nociceptor
subpopulations, the means and standard errors of the fit parameters
were reported.
The population responses at each stimulus intensity (i.e., 40-90 g-f)
were displayed by the following procedure. First, for a given stimulus
intensity and A
or C subpopulation, the neural responses were
averaged at each spatial location. Second, the averaged spatial
population response (SPRa,i) was nonlinearly regressed in the same manner as described for the
SPRu,i. Third, the SPRa,i
was displayed as a surface plot. The horizontal extent (i.e., the
widths and areas) of the "base" of the SPRa,i
was calculated at a reasonable, though arbitrary, value chosen at 10 spikes/10 s. The area of a slice was calculated by integrating over one of the horizontal parameters (e.g.,
xmin to
xmax) the equation for a Gaussian
surface solved for the remaining horizontal parameter (e.g.,
y) (Khalsa et al. 1998
).
Statistics
Significance of the surface fit parameters was evaluated by
one-way ANOVAs with repeated measures or Friedman's one-way ANOVAs (if
the data failed a normality test). Student's t-tests were used to assess differences between individual groups. All statistical tests were done with a probability criterion for significance of
= 0.05.
 |
RESULTS |
Seventy-eight afferents, either A
or C fibers, were isolated
during 33 successful experiments. Afferents that did not display mechanical sensitivity were inappropriate for this investigation (i.e.,
they were either sympathetic efferents, chemo-nociceptors, or so-called
"silent nociceptors" requiring chemical sensitization before they
exhibit any mechanical sensitivity). Some afferents had mechanical
thresholds too low to be considered nociceptors; and, some afferents
had high mechanical thresholds but stopped responding prematurely to
the stimulation protocol. Hence the results are based on recordings
from 23 mechanically sensitive nociceptors (13 A
and 10 C) (Fig.
6). Corrected conduction velocities averaged 4.6 and 1.4 m/s for the A
and C afferents, respectively, and within each group, were not significantly different based on their
ability to respond to noxious heat and cold (Fig.
7).

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Fig. 6.
Location on skin and classification of all mechano-nociceptors
reported in this study. The outline of the skin and the grid (14 × 14 mm) are drawn to scale, but the tabs have been shortened in the
drawing for conciseness.
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Fig. 7.
Conduction velocities (CVs) of nociceptor subpopulations
(n = 23: 8 CM, C mechano-nociceptor; 2 CMH, CM + responsive to noxious heat; 7 AM, A mechano-nociceptor; 6 AMC, AM + responsive to noxious cold).
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Nociceptor receptive fields
Compressive receptive fields (RFc), mapped
using Semmes-Weinstein monofilaments, for A
and C
mechano-nociceptors (n = 9) averaged 4.51 mm2 for suprathreshold stimuli and 1.60 mm2 at threshold (Fig.
8), slightly smaller than those reported
in the monkey hairy skin (Treede et al. 1990
) and much
smaller than those in human hairy, leg skin (Schmidt et al.
1997
). The mean threshold and suprathreshold
RFc were larger for the A
(1.80 and 5.05 mm2, respectively) than the C population (1.20 and 3.43 mm2, respectively), but these
differences were not significant (ANOVA, P > 0.05).
For both A
and C nociceptors, receptive fields typically were
composed of spot-like areas of response rather than a contiguous area
to which the neuron responded. Hence the margins of the
RFc were composed of the outer-most spots that
responded to the monofilaments (either at threshold: median 36 mN,
range 15-116 mN; or supra-threshold: median 150 mN, range 54-751 mN).
Using monofilaments with larger compressive forces (i.e., greater than
suprathreshold) did not increase the area of the supra-threshold
RFc. Although threshold and suprathreshold
RFc occasionally shared a boundary, the threshold RFc always were enclosed by the suprathreshold
RFc. The mean compressive stress at threshold
produced by the monofilaments was 34 kPa (range: 21-59; SE: 6.3), but
given the small cross-sectional area of the filament, substantial, and
immeasurable, out-of-plane shear stresses undoubtedly also were
present.

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Fig. 8.
Widths and areas (means ± SE) of compressive receptive field
(RFc) maps for A and C nociceptors (n = 5 and 4, respectively). Min were the threshold RFc, and Max were the
suprathreshold RFc. Widths were the largest extent of the RFc along the
x and y axes. All the areas and widths of
the suprathreshold RFc were significantly larger than the threshold RFc
(ANOVA, P < 0.05), except for the y
width of the C nociceptors.
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Nociceptor threshold and sensitivity to compression
Nociceptor compressive thresholds (mean: 45 kPa) were the same
whether indenting the skin over the hard or the compliant platforms and
were not significantly different for the A
or C mechano-nociceptor populations (Fig. 9). This mean was only
slightly larger than the compressive threshold calculated using the
monofilaments. Compressive sensitivity, however, was substantially and
significantly greater using the compliant versus the hard platform
(Fig. 10). The increased sensitivity
was undoubtedly related to the more complex stimulus (combined
compression, tension, and shear) that developed during indentation
using the compliant platform (Fig. 11).

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Fig. 9.
Compressive thresholds for A and C nociceptors
(n = 9 and 8, respectively) using the hard and
compliant platforms. There was no significant difference between any of
the means (ANOVA, P > 0.05).
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Fig. 10.
Increase in compressive sensitivity (means and SE) during indentation
for the same compressive load using the compliant and hard platforms.
The maximum compressive load was just below the saturation level for
each nociceptor (range: 40-160, mean 74 g). Horizontal labels are
the same as in Fig. 7. Mean sensitivities were significantly larger
between groups (ANOVA, P < 0.001) and for the AM
and CM subpopulations (ANOVA, P < 0.02) but not
for either of the AMC or CMH subpopulations (ANOVA,
P > 0.10).
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Fig. 11.
Estimated stress distribution in the skin (midthickness) calculated
using finite element analysis (FEA) during compression (0.6 N applied
to 3-mm-diam indenter) of skin overlying the compliant platform. The
center of the indenter was located at Distance 0.0. By convention,
magnitudes of compression and tension are negative and positive,
respectively. The FEA used an axi-symmetric model to calculate the
stresses with the z axis perpendicular to the plane of
the skin (i.e., the x-y plane). zz and
xx are the magnitudes of the stresses along the
z and x axis, respectively;
xz is the out-of-plane shear stress; and SED is the
strain energy density, a scalar term being the product of the stress
and strain components (Khalsa et al. 1997 ).
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Population encoding of noxious mechanical stimuli
Uniform spatial population responses (SPRu)
were estimated from each nociceptor, and two representative nociceptors
are shown using contour and surface plots (Fig.
12) and fitted with Gaussian surfaces
(Fig. 13). Whereas most
SPRu demonstrated a single peak at, or near, the
location of the indentation, three exhibited more than one distinct
peak (Fig. 14) and five others
exhibited multiple, but very small, peaks. Averaged spatial population
responses (SPRa,i) for the A
and C
subpopulations at compression stimulus intensities ranging from 40 to
90 g-f are shown fitted with Gaussian surfaces (Fig.
15). The intensity of the stimulus was
represented by the peak neural response of the
SPRa,i, which increased monotonically over the
range of compressive stimuli (Fig. 15). The relationships between peak
response and compressive load (Fig.
16A) were significant (ANOVA, P < 0.001 and P = 0.015 for
A
- and C-mechano-nociceptor subpopulations, respectively) and well
described by exponential curves (R2 = 0.98 and 0.94, respectively). The curves were of the form
y = f(x) = y0 + a(1
e
bx)where
y0, a, and b
were parameters to be fit during nonlinear regression (respectively,
A
:
611.0, 678.0, and 0.07; and C:
1141.5, 1258.0, and 0.07). On
average, for a given stimulus intensity, the peak neural response was
greater for the C than the A
subpopulation.

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Fig. 12.
Uniform spatial population responses (SPRu) represented as
contour and surface plots for representative A and C
mechano-nociceptors. A: contour plot for AMC.
B: surface plot for AMC. C: contour plot
for CM. D: surface plot for CM. +, locations of all the
indentations performed for that nociceptor.
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Fig. 13.
Uniform spatial population responses (SPRu) for typical A
and C mechano-nociceptors represented by Gaussian surfaces using the
same data shown in Fig. 12. Filled circles are the actual data, and the
surfaces were considered to fit the data well
(R2 = 0.86 and 0.82, respectively).
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Fig. 14.
SPRu, displayed as a contour plot, for an AMC nociceptor.
The highest neural response (spikes/10 s, indicated by the color bar)
occurred close to the edge of the indenter (3- mm diam) along the
x axis not at the indenter's center. See text for
interpretation of this phenomenon.
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Fig. 15.
Averaged spatial population responses (SPRa,i) for the A
and C mechano-nociceptor subpopulations to compression with a 3-mm-diam
cylinder at loads ranging from 40 to 90 g-f. Red dots represent the
actual data superimposed onto the Gaussian surfaces obtained through
nonlinear regression. A: A
subpopulation SPRa,i were comprised of different numbers
of nociceptors due to different thresholds and saturation levels
(number of nociceptors were 8, 9, 10,11, 11, and 6, respectively).
B: C subpopulations (number of neurons were 6, 6, 6, 7, and 4, respectively).
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Fig. 16.
Parameters of nonlinear regression using an equation for a Gaussian
surface of the spatial population responses for the A and C
mechano-nociceptor populations plotted as functions of compressive
load. A: peak discharges of the SPR were significantly
different between and within groups (ANOVA, P < 0.05); B: widths of the SPR, at 60.7% from the peak, were
not significantly different (ANOVA, P > 0.05);
C: x, y location of the peak of the SPR.
Actual indentation occurred at 0,0. Only the A x0 was
significantly different from the other offsets (ANOVA,
P < 0.05).
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The center location of the stimulus was represented by
x0 and
y0, the offsets from 0 along the
x and y axes for the
SPRa,i, and the offsets remained constant with
increasing compressive load for both the A
and C subpopulations
(ANOVA, P > 0.05, Fig. 16C). The
x offset was significantly different from the y
offset for the A
subpopulation (ANOVA, P < 0.001),
but not for the C subpopulation (ANOVA, P > 0.05).
The shape of the stimulus (i.e., the cylinder) was represented by the
widths of the population response (parameters b and c, the widths of the Gaussian surface at 60.7% from the
peak along the x and y axes, respectively). The
widths remained constant with increasing compressive load for both
subpopulations (ANOVA, P < 0.05, Fig. 16B).
Neither of the widths was significantly different from each other for
their respective A
and C subpopulations (ANOVA, P > 0.05), but the means were significantly different between the two
subpopulations (2.61 and 2.14 mm, respectively; ANOVA, P < 0.001). Although the proportional widths of the
SPRa,i remained constant, the absolute areas (and
widths) of the bases of the SPRa,i enlarged with
increasing load, saturating at 70 g-f (Fig. 17).

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Fig. 17.
Mean (±SE) areas and widths of the Gaussian fits of the spatial
population responses (SPRu,i) at the same magnitude of
neural response (10 spikes/10 s). Greater than 40-g indentation load,
the differences between the A and C subpopulations were not
significant (ANOVA, P > 0.05).
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DISCUSSION |
Vallbo et al. (1993)
were the first to report a
spatial event plot for a mechanically sensitive C afferent; however,
they stated that the afferent was not nociceptive as it had a threshold of <4 g-f. The current study is the first report of a SPR of
mechanically sensitive nociceptors to noxious indentation. The
population response was created by combining the data obtained from
individual mechano-nociceptors from different rats, though from the
same area of skin. This method of sampling likely introduced
variability in the data that would not have been present had an actual
population of mechano-nociceptors been recorded. Further, the protocol
required obtaining the data over long time periods (
7 h) to represent
how a population would respond to a single indentation (lasting only
10 s). However, our data indicate that there was no significant
difference in spatial extent of the population response from different
rats. In addition, the sensitivity of nociceptors to mechanical stimuli has been shown to be relatively constant over long recording periods in
cats (Garell et al. 1996
), rats (Khalsa et al.
1997
), and in the current study.
The type of indenter used in this study also contributed somewhat to
the variability of the data. Rather than a linear actuator, indentation
was performed used a force-controlled torque motor that actuated a
lever arm. For small displacements, like occurred during indentations
of the skin overlying the hard platform, off-axis loads have previously
been shown to be insignificant (Khalsa et al. 1997
).
However, for indentations of skin overlying the compliant platform, the
displacements of the lever arm would be relatively large and the
resultant force vector would develop an increasing angle proportional
to the displacement. This was partially compensated for by allowing the
indenter tip to be "self-centering" relative to the force vector
(Khalsa et al. 1997
). The angle of the resultant force
vector may partially explain the offset of the SPR along the
y axis. However, such a resultant force angle vector would only occur in the yz plane and should not have influenced
the observed x axis offset.
The location of the noxious indentation was unambiguously encoded in
the SPR. The x, y position of the peak magnitude of the SPR
always was located underneath the indenter, although it did exhibit an
offset from the center of the indenter. An explanation for this offset,
in addition to experiment variability discussed previously, may be that
it was encoding the most noxious portion of the indentation. From a
mechanical perspective, the most damaging or noxious state would be
where there was the highest energy. Strain energy density (SED)
represents the energy developed in tissue due to an applied load, and
it has been proposed as a mechanical quantity encoded by low-threshold
mechanoreceptors (Dandekar and Srinivasan 1995
;
Grigg and Hoffman 1984
; Srinivasan and Dandekar 1996
) and mechano-nociceptors (Khalsa et al.
1997
). The finite-element model of the in vitro skin and
compliant platform predicted that, during indentation, the highest SED
in the skin occurred near the edge, rather than in the center, of the
indenter (Fig. 11). If mechano-nociceptors are responding to SED, then
this would tend to shift the peak of the SPR from the center toward the
edge of the indenter.
The intensity of the noxious indentation also was encoded in the SPR.
Increasing compressive load was encoded by increasing peak neural
response of the SPR, and this relationship was observed even with
nociceptors of different sensitivities, thresholds, and saturations and
in both the A
and C subpopulations. For both subpopulations, the
peak neural response tended to saturate approaching a compressive force
of 70 g-f (or, given the area of the indenter tip, a compressive stress
of 221 kPa). This stimulus magnitude was considerably lower than that
which produced suprathreshold pain rated as moderate to intense in
human dental mucosa (Cooper et al. 1993
). Unfortunately,
there are few other studies of mechanically evoked suprathreshold pain
(cf. Greenspan and McGillis 1991
) and none that have
examined it in hairy skin. Hence, we can only speculate on an
explanation for this difference. One possibility is that it simply
reflects a species difference. Another possibility is that it was due
to the large deformations produced during the indentation that resulted
in a three-dimensional combination of tension, compression, and shear.
Hence, while the compressive force (or stress) may have been smaller
than that necessary to produce moderate pain in humans (dental mucosa),
the total state of stress and strain would have been relatively large
in magnitude. The neural responses of single nociceptors in rat, hairy
skin have been shown to correlate well with strain energy density, a
scalar quantity reflecting the total energy developed in a volume of
material during loading (Khalsa et al. 1997
). Thus in
the current experiments, the SPR may likely have been responding to the
strain energy density, or a similar quantity, rather than simply to the compressive force (or stress).
The peak neural responses of the SPR were higher in the C than in A
subpopulations. This corresponded to the average higher compressive
sensitivities of the C mechano-nociceptors that comprised the
population studied. Other studies have found that A
mechano-nociceptors respond to indentation at higher rates than do C
mechano-nociceptors (Garell et al. 1996
;
Handwerker et al. 1987
). However, when the effects of
tension were removed explicitly from those of compression, some classes
of C mechano-nociceptors were more sensitive to compression and tension
than A
mechano-nociceptors (Khalsa et al. 1997
). Hence combinations of tensile and compressive stimuli could produce higher response rates in C than A
mechano-nociceptor populations, as
was found in the current study.
The overall "form" (peak, slopes, and base area) of the SPR was
comparable with that previously predicted in a first-order model
(Khalsa et al. 1997
). All three form features would be
scaled by the sensitivities of an actual population. For example, a
reduced tensile sensitivity would decrease the peak neural response and the areal extent of the base of the SPR as was seen in the current study. The areal extent, representing the portion of a population of
neurons responding to a given stimulus, of any SPR will be dependent
not only on the relative tensile compliance of the skin region, but
also the bulk compliance and geometry of the underlying tissue (e.g., muscle).
The SPR had a central high point (i.e., a peak), and the neural
responses at all other locations were lower. This contrasts with the
prediction of Khalsa et al. (1997)
of the largest neural responses being next to the edges of the indenter along the
x axis rather than toward its center. That prediction was
based on measurements of high tensile sensitivity of nociceptors and the highest tensile strains occurring next to the indenter. The finite-element model in the current study also estimated that the
maximum tensile stresses occurred next to the edge of the indenter
(Fig. 11). A few SPRu did exhibit bilateral peaks
next to the edge of the indenter (Fig. 14), although more commonly only a single peak was observed and on average it was offset from the center
almost 1 mm. Another explanation for the phenomena (shown in Fig. 14)
would be that shear stress (or strain) caused the high neural response
at the edge of the indenter. The finite-element model estimates that
both shear stress and strain are maximal at the edge of the indenter
(Fig. 11). For the SPRu (shown in Fig. 14), the
edge of the indenter would be positioned, in principle, over the most
sensitive spot of the neuron's receptive field when the indenter was
centered at ±1.5 mm along the x or y axes. If there was a symmetrical response to the indentation, this would produce
a SPRu formed similar to a "volcano" with the
maxima along the edges of the central crater. The data from this study
do not allow making a determination as to whether the observed
phenomena was due to high tensile stress, high shear stress, or some
combination of both. Finally, multiple terminal endings of single
nociceptors also would tend to broaden the SPRu
and make the peak solitary rather than annular.
The SPR suggests a possible mechanism for encoding some aspects of
shape of a noxious mechanical stimulus. Not only was the SPR well fit
with a Gaussian surface, but the widths of SPR (i.e., the b
and c parameters and hence area) remained unchanged, as was
the area of the indenter, with increases of compressive load. Evidence
to support this conjecture comes from two different venues. First,
Vallbo et al. (1999)
recently have demonstrated that
mechanically sensitive C afferents can encode nonnoxious tactile
stimuli. Low-threshold C mechanoreceptors encoded dynamic loads during
indentation using probes with both rounded and sharp tips. In both
cases, there was a noticeable time lag between the stimulus and the
neural response, but the response was proportional to the stimulus.
High-threshold C mechanosensitive afferents, presumably
mechano-nociceptors, showed proportional response to noxious
indentation. They also documented that low-threshold C mechanoreceptors
can encode movement of objects, although the correlation was better at
low than high velocities. Second, population responses of A
,
low-threshold, slowly adapting mechanoreceptors have been shown to
encode object curvature during indentation in monkey fingerpad
(Goodwin et al. 1995
;Khalsa et al. 1998
),
human glabrous skin (Goodwin et al. 1991
, 1997
) and
during stroking in the monkey fingerpad (Friedman et al.
1998
). All these population responses were also well described by Gaussian surfaces. Thus taken together, these previous studies and
the current study suggest a possible role for C mechano-nociceptors to
encode some aspects of object shape during noxious stimulus and
particularly during noxious indentation.
This study did not measure the actual number of mechano-nociceptors
innervating the region of skin (i.e., the innervation density) that was
mechanically stimulated nor the size and extent of overlap of their
receptive fields. Our estimate of a SPR to noxious indentation is based
on an assumption of relative uniform distribution of the terminal
endings of mechano-nociceptors. If an actual population was distributed
nonuniformly, our data suggest that noxious indentation by a
symmetrical object would result in a SPR the form of which would be
skewed and its peak location significantly offset from the actual site
of indentation. However, the effect of innervation density should only
be to improve the accuracy of encoding magnitude and location with
increasing density. Similarly, increasing innervation density also
should improve the postulated ability to encode object shape.
In conclusion, this study found that the location and intensity of
noxious, compressive stimuli were encoded in the spatial population
responses of A
and C mechano-nociceptors.
Conceptually, to implement the FEM two separate but related processes
are undertaken: the geometry of the tissue is mathematically described
by a finite number of small "elements" (i.e., connected regions or
volumes) and a mathematical expression is formulated that describes the
stiffness (i.e., resistance to deformation) of the elements so that
when loaded, the displacements of various points within the global
structure can be calculated. The stiffness of each element is
determined from both its geometric properties (shape) and from the
material behavior that is assigned to each element. Mechanical stresses
and strains then can be calculated for each element from the structural
displacements. When the formulation that describes the material is the
same function as the shape function used to define the element
geometry, as was done in these experiments, this function and the
family of elements are called isoparametric.
Soft tissues, like skin, derive their tensile strength primarily from
collagen fibers, and secondarily from elastin, embedded in the
extracellular matrix (Lanir 1976
, 1979
). The collagen
and elastin fibers are individually linearly elastic, but the
bulk-stress-strain relationship of skin is nonlinear due to the
inhomogeneous composite nature of its structure (Maurel et al.
1998
). After preconditioning (Fung 1993
), the
short-time stress-strain relationship is pseudoelastic, meaning that
one can model the response ignoring its viscous components. However,
skin undergoes relatively large deformations for small loads. In the
FEM, a material exhibiting nonlinear, large deformations not dependent
on the rate of loading is termed "hyperelastic," and its
constitutive behavior is defined as a total stress-total strain
relationship as follows (Maurel et al. 1998
):
A hyperelastic material strain-stress relationship can be derived from
an internal strain energy function. For purpose of experimentation, the
strain energy functions are more appropriate expressed using the strain
invariants Ic = I1,
IIc = I2, IIIc = I3, which can be determined by the
extension ratios
1,
2,
3
Once this strain energy function is formed, then the principal
components of the Lagrangian stress tensor T are derived as
(Allaire et al. 1977
):
The authors thank Peter Grigg, PhD, of the University of
Massachussetts Medical School for generously donating equipment to help
perform the experiments, and Robert Friedman, PhD, of the Yale
University School of Medicine for reading and critically assessing the manuscript.
Address for reprint requests: P. S. Khalsa, Dept. of Orthopaedics,
S.U.N.Y. at Stony Brook, HSC T18-030, Stony Brook, NY 11794-8181.
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.