INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX REFERENCES

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.

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX REFERENCES

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.

View larger version (17K): [in this window] [in a new window]   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.

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).

View larger version (49K): [in this window] [in a new window]   Fig. 2. Deformed mesh of the finite element model (FEM) of skin overlying a compliant substrate with an applied load of 0.6 N.

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*x^0.3836, 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.

View larger version (13K): [in this window] [in a new window]   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.

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).

View larger version (14K): [in this window] [in a new window]   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.

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" (RF_C) 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 RF_C was observed). The most sensitive spot (MSS) within the RF_C was used for the center of the location of indentation. The RF_C 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 RF_C 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.

View larger version (20K): [in this window] [in a new window]   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.

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 (SPR_u) 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 SPR_u 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 SPR_u 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 (SPR_i) was developed from the SPR_u 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 SPR_u in 10-g-f increments (forming SPR_u,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, SPR_u,i's could be estimated at 70, 60, 50, and 40 g-f as well as the SPR_u that was recorded at 80 g-f. Each SPR_u,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 (SPR_a,i) was nonlinearly regressed in the same manner as described for the SPR_u,i. Third, the SPR_a,i was displayed as a surface plot. The horizontal extent (i.e., the widths and areas) of the "base" of the SPR_a,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., x_min to x_max) 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

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX REFERENCES

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).

View larger version (15K): [in this window] [in a new window]   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.

View larger version (9K): [in this window] [in a new window]   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).

Nociceptor receptive fields

Compressive receptive fields (RF_c), 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 RF_c 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 RF_c 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 RF_c. Although threshold and suprathreshold RF_c occasionally shared a boundary, the threshold RF_c always were enclosed by the suprathreshold RF_c. 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.

View larger version (15K): [in this window] [in a new window]   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.

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).

View larger version (13K): [in this window] [in a new window]   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).

View larger version (14K): [in this window] [in a new window]   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).

View larger version (12K): [in this window] [in a new window]   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).

Population encoding of noxious mechanical stimuli

Uniform spatial population responses (SPR_u) 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 SPR_u 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 (SPR_a,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 SPR_a,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.

View larger version (57K): [in this window] [in a new window]   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.

View larger version (22K): [in this window] [in a new window]   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).

View larger version (38K): [in this window] [in a new window]   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.

View larger version (48K): [in this window] [in a new window]   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 subpopulationSPRa,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).

View larger version (15K): [in this window] [in a new window]   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).

The center location of the stimulus was represented by x₀ and y₀, the offsets from 0 along the x and y axes for the SPR_a,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 SPR_a,i remained constant, the absolute areas (and widths) of the bases of the SPR_a,i enlarged with increasing load, saturating at 70 g-f (Fig. 17).

View larger version (21K): [in this window] [in a new window]   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).

	DISCUSSION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX REFERENCES

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 SPR_u 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 SPR_u (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 SPR_u 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 SPR_u 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.