| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
|
|
|
|||||||
|
|||||||||
1 Department of Anesthesiology, Yale University School of Medicine, New Haven, Connecticut 06510; and 2 Department of Physiology, University of Massachusetts Medical School, Worcester, Massachusetts 01655
 |
ABSTRACT |
|---|
 Abstract
 Introduction
Methods
Results
Discussion
References
|
|---|
Khalsa, Partap S., Robert H. LaMotte, and Peter Grigg. Tensive and compressive responses of nociceptors in rat hairy skin. J. Neurophysiol. 78: 492-505, 1997. Mechanically sensitive nociceptor afferents were studied in a preparation of isolated skin from rat leg. Each neuron was studied while the skin was subjected to tensile and compressive loading. The experiment was designed to create highly uniform states of stress in both tension and compression. Tensile loads were applied by pulling on the edges of the sample. Applied loads were used to determine the tensile stresses. Surface displacements were used to determine tensile strains. Compressive loads were applied by indenting the surface of the skin with flat indenter tips applied under force control. The skin was supported by a flat, hard substrate. Compressive stresses were determined from the applied loads and tip geometry. Compressive strains were determined from skin thickness and tip excursions. All nociceptors were activated by both tensile and compressive loading. There was no interaction between the responses to compressive and tensile stimuli (i.e., the responses were simply additive). Responses of nociceptors were better related to tensile and compressive stresses than to strains. Nociceptors responded better to tensile loading than to compressive loading. Response thresholds were lower and sensitivities were higher for tensile stress than for compressive stress. The response to compression was better related to compressive stress than to other stimulus parameters (i.e., load/circumference or simply load). Indentations of intact skin over a soft substrate such as muscle would be expected to cause widespread activation of nociceptors because of tensile stresses.
Mechanosensitive nociceptors undoubtedly play an important role in the genesis of mechanically evoked pain. Yet, quantitative empirical and theoretical studies of the biomechanical basis for their activation are lacking. Cutaneous mechanonociceptors have received the greatest attention from neurophysiologists primarily because of greater accessibility and greater ease in relating nociceptor functional properties to sensations of mechanically evoked pain in humans. The most common method of stimulation is to vary the force of an indenting probe, or probes of differing diameter, and obtain either the threshold for evoking a response or a stimulus response function relating magnitude of discharge to force. Nociceptors with myelinated or unmyelinated axons (A or C fibers) are typically responsive not only to mechanical stimuli but also to noxious heat (termed AMHs and CMHs) and/or to cold (similarly, AMCs and CMCs) or irritant chemicals. As well, they have force thresholds that are roughly similar and generally exceed those of sensitive low-threshold mechanoreceptors with myelinated axons (e.g., Adriaensen et al. 1983 Preparation
Experiments were performed with the use of isolated skin-nerve specimens that were obtained from the ventral surface of the hindlimb of adult Sprague-Dawley rats of either sex. The location of the specimen on the leg is shown in Fig. 1A. This preparation has been described in detail elsewhere (Grigg 1996
Stretching and compression apparatus
Tensile loads were applied to the skin specimen with the use of an apparatus (Fig. 1B) consisting of 12 linear actuators and load cells, arranged three along each side of the skin specimen. The apparatus has been described in detail previously (Khalsa et al. 1996
Nerve recording, identification, and classification
The nerve was drawn into an oil-filled compartment for recording. Loose connective tissue was dissected free, and the nerve was immersed in a 1.5% solution of collagenase (Worthington Biochemical). After 30 min the collagenase was removed and the nerve was rinsed with artificial interstitial fluid. The nerve was then dissected into small filaments with the use of fine forceps. Individual filaments were placed on a fine gold wire electrode for recording. An indifferent electrode was located in the saline bath. Neural signals were amplified and filtered with the use of conventional methods. Action potentials were identified as unitary spikes on the basis of a template matching paradigm (SPS Systems, Prospect, South Australia). Times of occurrence of action potentials were recorded. The neural response to a stimulus 10 s in duration was characterized with the use of the total number of evoked action potentials. This single measure of the neural response was chosen because of the high variability of the response. The total number of action potentials represented a measure of response common to all afferents.
Experimental procedure
When a suitable afferent was found, it was studied while the skin was mechanically loaded with the use of tensile stimuli alone, compressive stimuli alone, or combinations of tensile and compressive stimuli. Three levels of tensile load (0.01, 0.04, and 0.08 N per tab) were used to characterize each afferent.
Data analysis
The three-dimensional state of stress and strain was evaluated at the mechanoreceptor location. Plane (tensile) stresses were estimated from the tab loads and the cross-sectional area of the tabs. Tab cross-sectional area was calculated from the widths, measured from a video image of the preparation, and with the use of a value of 0.3 mm for skin thickness (Grigg 1996 Estimation of the responses of a population of nociceptors due to skin indentation in the intact limb
The section of skin studied in these experiments overlies muscle. Thus, when it is indented in situ, large indentations can result, with the development of both tensile and compression stresses and strains. We wished to determine the relative magnitudes of the compression and tensile stresses caused by indentations in situ to estimate how a population of nociceptors located in the skin would respond to the indentation.
Recording of neurons
Ninety-eight C or A
Responses to tensile loading
Each neuron was studied while the tabs were actuated, creating in-plane stresses and strains. An example of data recorded during a single trial is shown in Fig. 3. In this trial, the neural response averaged ~5 imp/s, which was typical for the C afferents. As can be seen, all tab loads were approximately equal. Every neuron was tested with the use of uniform tab loads of 0.00, 0.01, 0.04, and 0.08 N per tab, although some were studied with the use of more load levels. Because applied loads were the controlled variables, the tensile stresses were approximately equal in both directions. However, because the skin in this region of the leg is slightly orthotropic (Grigg 1996
Responses to compression loading
All mechanically sensitive afferents were activated by compressive stimuli. When afferents had multiple receptive fields in the skin, we used the most excitable spot for compressive loading. Each afferent was studied with at least four (including 0) levels of compressive load. Figure 4, C and D, shows the average response of six CM neurons (same neurons as in Fig. 4, A and B) to compressive stress and strain. It should be noted that by convention, tensile stresses are positive and compressive stresses are negative in sign. However, to allow easier comparisons, we have graphed tension and compression with the use of the same scales. Thus Fig. 4C shows compressive stresses as being positive, and similarly, Fig. 4D shows compressive strains as being positive. The large degree of variability in Fig. 4C arises because 1) not every afferent was studied at each stress or strain level and 2) the stimulus levels that were used differed somewhat between experiments. The variability observed in compressive strains (Fig. 4D) reflects the above as well as the fact that strains (as described in METHODS) were strongly influenced by viscoelastic responses of the skin. In every experiment, compression stresses were much higher than tensile stresses, so that the response was saturated in many experiments (Fig. 4C).
Quantitative relationships between neuronal response and the magnitudes of mechanical states in the skin
Each experimental trial resulted in stresses and strains in both tension and compression. It was of interest to determine the relationship between the neural response and the magnitudes of those variables. We first wished to identify those variables that were most closely related to the response of the neuron. For example, either stress or strain might be considered to be the independent variable in exciting neurons. Relationships between the response of a neuron and the magnitudes of various mechanical states were explored with the use of correlation analysis. In these analyses, correlation coefficients were calculated between neuronal response levels and the magnitude of various candidate mechanical variables. The resulting correlation coefficients were lumped together across all neurons (Figs. 5 and 6). As was previously found for other mechanosensitive neurons (Fuller et al. 1991
Thresholds and sensitivity to tensile and compression stresses
Of the 37 neurons, 33 yielded both threshold and sensitivity values in compression, and 16 yielded both threshold and sensitivity values in tension. Afferents were characterized with the use of a minimum of three levels (4, including 0)of pure tension or compression loading (i.e., not combination trials). The resulting data (i.e., see Fig. 4) allowed us to estimate both the threshold and sensitivity (i.e., the slope of the curve in Fig. 4, A and C) of each neuron for both tensile and compression stresses. The thresholds for tensile stresses were much lower than those for compressive stress (Table 2). In addition, the sensitivity to tensile stress was much higher than for compressive stress (Table 2).
Dependence of neuronal response on compressive stress versus compressive load
We wished to determine whether the neural response to compressive loading was best related to the compression load, the resulting compressive stress, or the load/circumference of the indenter (cf. Garell et al. 1996
Interaction between tensile and compressive responses
To determine whether there was any interaction between the responses to tensile and compressive loading, each neuron was studied with the use of combinations of compression and tensile loadings. We attempted to record the responses of each afferent while presenting all combinations of the set of tensile and compressive loads that were used with that neuron. Thus, ideally, each neuron was studied with the use of 15 experimental runs that represented each combination of tensile and compressive loading. Results were obtained from 37 afferents. Data obtained from one neuron are shown in Fig. 10. To test whether there was a significant interaction between the responses to tension and compression, an analysis of variance (ANOVA) was performed, in which tensile and compressive stresses were independent variables. The resulting ANOVA revealed that the tension × compression interaction was not significant (P > 0.50) for any type of afferent. Thus the responses to simultaneously applied tension and compression are simply additive.
In vivo tensile and compressive stresses caused by indenting intact skin over muscle
In five experiments, the indenter was used to apply compressive loads to the middle of the sampled area (Fig. 1). The loads used were in the same range as those used in the in vitro experiments. Because the skin overlies muscle, large indentations resulted. With an applied load of 0.3 N, the indentation was ~12 mm. The tensile strains observed along the X and Y directions are summarized in Table 4. They were greatest near the indenter, and decreased with distance from the indenter. The depth of the indentation was determined mainly by the magnitude of the indenting load; changing the diameter of the indenter had only a minor effect on the depth of the indentation. The profile of this indentation is shown three-dimensionally in Fig. 11. The asymmetry of the skin indentation profile resulted at least in part from the skin anisotropy (i.e., the skin was stiffer along the Y-axis than the X-axis) (Grigg 1996
Others (Bove and Light 1995
INTRODUCTION
Abstract
Introduction
Methods
Results
Discussion
References
; Bessou and Perl 1969; Burgess and Perl 1967; Campbell et al. 1979; Georgopoulos 1977; Handwerker et al. 1987; Kumazawa and Perl 1977; Lynn and Carpenter 1982; Perl 1968; Van Hees and Gybels 1972). Both A and C fiber types exhibit increased discharge rates as a function of force, although the A fibers generally exhibit higher discharge rates in response to a given force than the C fibers (Garell et al. 1996; Handwerker et al. 1987; Reeh et al. 1987) and greater differentiation in their responses to small probes of different diameter (Garell et al. 1996).
; Cooper et al. 1991; Garell et al. 1996; Lynn and Carpenter 1982; Meyer et al. 1991). It is controversial as to whether such differences imply the existence of separate subpopulations of mechanonociceptors or just a single population with a wide range of response sensitivities (e.g., Burgess and Perl 1967; Cooper et al. 1991; Garell et al. 1996; for review, see Lynn 1992). The major problem one faces in addressing this question is that the nociceptor does not respond directly to the externally applied stimulus itself (e.g., indentation force or probe geometry) but to the changes of the internally produced stresses and strains in the tissue brought about by that stimulus. These changes depend in large part on the biomechanical properties of the tissue, such as its compliance. For example, tensile stresses and strains (in the plane of the skin) will be relatively low in relation to compressive stresses and strains (normal to the skin) for indentations of skin lying directly over a hard substrate such as bone. In contrast, both tensile and compressive stresses and strains may be significant when indenting skin lying over soft substrates such as fat and muscle.
; Handwerker et al. 1987; Reeh et al. 1987), there have been no tests of the hypothesis because there were no practical means of obtaining separate stimulus control of these two mechanical quantities. Now, however, a method has been developed in which tensile and compressive loading can be independently applied to an isolated patch of skin (Grigg 1996) or joint capsule (Khalsa et al. 1996) and the resulting stresses and strains directly measured during simultaneous recording of evoked discharges in single low-threshold mechanoreceptive afferent nerve fibers. The purpose of the present study is to determine the sensitivities of nociceptive mechanoreceptive afferents to tensile and compressive stresses and strains with the use of the same methodology.
METHODS
Abstract
Introduction
Methods
Results
Discussion
References
). Briefly, rats were anesthetized with pentobarbital sodium (50 mg/kg ip). The hair on the hindlimb was clipped and removed with a chemical depilatory (Nair). The area to be studied was marked by gluing an array of nine surface markers (0.3-mm black disks) on the skin (Fig. 1A). The markers in the array were 7 mm apart, and the selected area was 14 mm square. In addition to defining the area selected for study, the markers were also used during the experiment to track surface displacements associated with stretching the skin. The orientation of the sample was defined by a 10th marker that was placed along the X direction (along the axis of the tibia, Fig. 1A). The locations of the markers were recorded so that the in situ geometry of the specimen could be reproduced when it was excised and in vitro (Fig. 1B). The edges of the specimen, along which it would be cut, were then drawn on the skin. The edges were laid out as tabs (7 × 10 mm) that were subsequently used to couple the skin to actuators that applied tensile loads. The skin was excised from the hindlimb by cutting along the marked boundaries. The nerve branches innervating the specimen were identified, dissected centrally to the sartorius nerve, and cut in the inguinal fossa. The isolated skin-nerve specimen was removed to an apparatus (Fig. 1B), where it was maintained (epidermis up) in artificial interstitial fluid (Bretag 1969). The fluid was kept at room temperature (20°C), gassed with 95% O2-5% CO2, and circulated with a pump.
View larger version (28K):
[in a new window]
FIG. 1.
A: area of skin studied. Rat is ventral side up; sample was cut from right hindlimb along the line drawn. Three tabs are cut along each edge. Dots: markers glued on skin surface. B: skin sample mounted in apparatus. Each tab is coupled to a linear actuator and a load cell (L1-L12). Rotary actuator (C) applies compression loads by actuating the arm (A). N, nerve is threaded into chamber for recording.
). Each actuator/load cell was coupled to a skin tab via a length of suture with a miniature fishhook at the end. Each hook was engaged in a hole punched in the end of a tab. Thus, when an actuator was operated, a load was developed at the point of application of its hook. When loaded, the skin tabs had an aspect ratio (length/width) > 2, so that the applied point loads were approximately uniformly distributed at the end of the tab (Khalsa et al. 1996). The skin was stretched until the distances between the markers closely approximated their in vivo configuration. Typically, this resulted in an initial preload of ~0.01 N per tab.
View larger version (24K):
[in a new window]
FIG. 2.
Side view of apparatus. A: tip of compression stimulator. B: chamber. C: skin sample. D: plastic platform supporting underside of skin. E: physiological saline bath. F: arm coupling DC motor (G) to compression tip (A).
z = (L1 
L0)/L0] was used for strain calculation. In this method, all strain measures are referenced to the skin thickness (L0) measured in the first trial. L0 was measured by lowering the indenter to the skin surface until it measured a minimal load (0.001 N), and recording its location. Later, after all indentation trials were completed, the skin was moved aside, and the location of the platform surface was recorded. The difference between the skin surface and the platform surface was the value of thickness used for L0. The value of L1 used for any given trial was determined from the difference between the location of the platform and the location of the indenter during the trial. L1 was measured during the last 0.5 s of the 10-s static load, when the creep response was at a minimum.
) to correct for the slowing effect of the relatively cold preparation. We classified afferents with corrected conduction velocities <2.0 m/s as C fibers and faster afferents as A fibers.
2.0 mm diam. The intertrial interval was 4 min, based on previous observations that C mechanoreceptors in skin had stable responses when repeatedly stimulated at this or shorter intervals (Bessou et al. 1971; Garell et al. 1996).
View larger version (17K):
[in a new window]
FIG. 3.
Representative data from a single trial in which both tensile and compressive loads were applied to the skin. A: tensile loads from the 12 actuator/load cells and the 1 compressive load. Note positive and negative sign conventions for tensile and compressive loads, respectively. B: time of occurrence of each action potential. C: instantaneous frequency computed from spike train.
). Tensile stresses were measured with high accuracy (Khalsa et al. 1996). Plane (tensile) strains were calculated from the displacements of the array of surface markers (Hoffman and Grigg 1984). Each marker formed a node of a quadrilateral. Tensile strains were calculated at each node. Tensile strains at the location of the mechanoreceptor ending were linearly interpolated from the nodal strains of the quadrilateral encompassing the mechanoreceptor ending. Nodal strains were measured with an accuracy of ±0.002. Compressive stress was calculated from the indenter load and the tip geometry and was accurate to within ±1%. Compressive strain was calculated from indenter displacements and was accurate to within ±0.001.
), it was surmised that neural response might be related to a mechanical quantity whose magnitude is not dependent on the orientation of an arbitrary coordinate system. Thus relationships were sought between neural response and coordinate-independent variables. For example, strain energy density is a scalar quantity that is the sum of the products of stress and strain along each of the three principle axes. Its magnitude is independent of the orientation of the coordinate system in which it is expressed. The other coordinate-independent quantities that we used were similar to those described for the two-dimensional situation in Khalsa et al. (1996). The expressions used to compute these quantities in three dimensions are given in the APPENDIX.
). In addition, the depth of the indentation directly under the indenter tip was measured directly from the actuator. From the resulting data we determined the uniaxial tensile strains between each pair of markers as well as between the edge of the indenter and the first marker.
).
RESULTS
Abstract
Introduction
Methods
Results
Discussion
References
-afferent neurons were recorded in 25 successful experiments. Corrected conduction velocities averaged 0.3 and 3.7 m/s for the C and A-afferents, respectively. Afferents that lacked mechanical sensitivity were not suitable for this investigation, and many units that were mechanically sensitive were not recorded for long enough to allow for them to be adequately characterized. Thus the results are based on recordings from 37 mechanically sensitive afferents (Table 1) for which sufficient data were available to undertake an analysis of their mechanical sensitivity. The neural response in each trial, changes in firing rate, and adaptation of response was analyzed for attributes that might be related to the stimuli. No relationship was found, so the total number of action potentials that occurred was used as the response measure for each trial.
View this table:
TABLE 1.
Numbers of afferents of different types
), strains were not equal in both directions. Both stresses and strains varied slightly between experiments because of differences in geometry of the specimens. Every mechanically sensitive afferent was activated by tensile loading. Figure 4, A and B, shows the averaged response of six C mechanoreceptor not sensitive to cold or heat (CM) afferents to tensile loading along the X direction. Because the loading was uniform and biaxial, similar plots could also be constructed for stress and strain along the Y direction. Because stress was the controlled variable in these experiments, there was little variability in the stress levels used with different neurons, resulting in the narrow horizontal error bars of Fig. 4A. In contrast, the (resulting) tensile strains that were observed in those experiments were quite variable, resulting in the broad horizontal error bars of Fig. 4B. Because of limitations of the apparatus, we never achieved tensile stresses >30 kPa. Reflecting this low level of loading, saturation of neural response was never observed with the use of tensile loading.
View larger version (27K):
[in a new window]
FIG. 4.
Pooled response of 12 CM units to tensile and compressive stresses and strains. A: tensile stress. B: tensile strain. C: compressive stress. D: compressive strain. By convention, compressive stresses and strains are negative in sign. However, to facilitate comparison with tensile stresses and strains, we have graphed them both with the use of positive scales.
; Grigg 1996; Khalsa et al. 1996), neuronal response levels were more highly correlated with stress variables than strain variables. Overall, the highest correlation was with the compressive stress, followed by the tensile stresses and then tensile strains. There was essentially no correlation between the neural response and shear strains. The neural response was more highly correlated with the coordinate invariant mechanical quantities composed solely of stress tensor components, termed "stress invariants," than with those composed solely of strain tensor components (Fig. 6). The neural response was approximately as well correlated with the strain energy density as with the stress invariants.
View larger version (51K):
[in a new window]
FIG. 5.
Mean value, across all neurons, of correlation coefficient between neuronal response level and magnitude of individual components of stress and strain tensors. Sx and Sy: tensile strength in the X and Y directions. Sz: compressive stress. Ex and Ey: tensile strains in the X and Y directions. Ez: compressive strain. Exy: in-plane shear strain.
View larger version (73K):
[in a new window]
FIG. 6.
Mean value, across all neurons, of correlation coefficient between neuronal response level and magnitude of variables whose magnitude is independent of orientation of coordinate system. I1-I3: 1st-3rd invariants, respectively, of stress tensor. J2 and J3: 2nd and 3rd invariants of stress deviatoric tensor. MSS, maximum shear stress; SED, strain energy density. E1-E3: 1st-3rd invariants, respectively, of strain tensor. F2 and F3: 2nd and 3rd invariants of strain deviatoric tensor. MSSr, maximum shear strain.
View this table:
TABLE 2.
Mean thresholds and sensitivities
) and slowly adapting type IIs (SAIIs) and C mechanoreceptors in rat hairy skin (Grigg 1996).
View larger version (13K):
[in a new window]
FIG. 7.
Histogram of thresholds of nociceptors. Value (mean ± SE) ofthreshold for activation of each nociceptor submodality forcompressive and tensile loading. AMC, A -mechanoreceptor sensitive to cold; CM, C mechanoreceptor; CMC, cold-sensitive CM; CMH, heat-sensitive CM; CMHC, heat- and cold-sensitive CM.
View larger version (30K):
[in a new window]
FIG. 8.
Histogram of sensitivity of afferents. Value (mean ± SE) of sensitivity of each type of afferent for tensile and compressive loading. Abbreviations as in Fig. 7.
). Eight neurons were studied during indentation trials in which the diameter of the indenter tip was varied between 1.4 and 3.0 mm. The compressive load was varied so that approximately equivalent stress levels were generated with each tip. No tensile loads were used in these trials. Results from one neuron are shown in Fig. 9. The strength of the relationship between the neural response (total number of action potentials per 10 s) and each variable was determined by calculating the correlation coefficient, R, between the neural response and the variable. R2, which expresses the percentage of variance in the dependent variable that is accounted for by the independent variable, was calculated for each variable for each neuron (Table 3).
View larger version (17K):
[in a new window]
FIG. 9.
Effect of tip diameter on response to compressive loading. A: response vs. compressive load. B: response vs. load/circumference of indenter. C: response vs. compressive stress.
View this table:
TABLE 3.
R2 values
View larger version (54K):
[in a new window]
FIG. 10.
Interaction between responses for 1 neuron when subjected to pure tensile loading, pure compressive loading, and combinations of tensile and compressive loading. Surface representing neural response was forced to pass through data points (symbols on surface) and was interpolated between these points.
).
View this table:
TABLE 4.
Tensile strains measured along the X and Y directions during an 0.3-N compressive load
View larger version (16K):
[in a new window]
FIG. 11.
Plots of tensile stress vs. tensile strain, measured in experiments in which skin was biaxially loaded. Solid line: best fit to data with the use of a power relationship (see text).
X = 1051.7X and Y = 1551.6Y, where is the stress and is the strain, respectively, for the X and Y directions. Tensile stresses underneath the indenter were calculated from the stresses in segment 1 (Table 4) and the geometry of the skin next to the indenter, which formed angles of 0.94 and 0.34 rad along the X and Y directions, respectively (Fig. 12).
View larger version (64K):
[in a new window]
FIG. 12.
Skin deformation and modeled neuronal response resulting from an in situ indentation with the use of an 0.3-Nload with a 2-mm-diam cylinder applied to the intact skin. Contour: shape of indentation in the skin. Colors: estimated neural response of nociceptors throughout the patch of skin, on the basis of the compressive and tensile stress under the indenter tip, and estimates of tensile stress in skin surrounding tip.
DISCUSSION
Abstract
Introduction
Methods
Results
Discussion
References
) have shown that nociceptors are sensitive to stretch. This is the first report that shows that nociceptors have a significant and substantial sensitivity to tensile loading of skin. In experiments in which both tensile and compression stress and strain were measured, we found that all nociceptors were better activated by tensile than by compressive loading. They had lower thresholds and higher sensitivity to tensile stress than compressive stresses. These results have important ramifications in the study of mechanical nociception. If compressive stimuli are applied to skin that lies over soft tissue such as muscle, substantial indentations can result. Large indentations can cause substantial tensile loading around the indenting stimulus. In previous studies, any such tensile component developed during mechanical loading could not be measured or controlled. Thus, when nociceptors have been activated by compressive stimuli applied to skin overlying soft tissue, any neural response would be confounded by (and potentially even dominated by) the response to the resulting tensile stresses. The higher responsiveness to tensile as compared with compressive components of loading, was observed in all submodalities of nociceptors.
and Garell et al. (1996). They found that the thresholds for pain in humans, and responses of nociceptors in cat hairy skin, were better related to the applied force/circumference than to applied force/area (i.e., compressive stress) of the stimulus. We find those results difficult to interpret, because compressive force scaled according to the circumference of the indenter has no physical meaning and would be unique to any particular indenter geometry. However, the above findings could be accounted for by the tensile component of nociceptor responses, which were not accounted for in either study.
, their Fig. 7), where the response magnitude is ordered directly in inverse order of tip size. A similar outcome is shown in Greenspan and McGillis (1991, their Fig. 3a), in which the pain threshold is lower with larger indenter tips. In our experiment, when the tensile component of the response was eliminated by applying only pure compression, the resulting neuronal response was closely related to the compressive stress.
). Very small tips also create problems for stress determination, because shear stresses and strains will be present around the edges. These stresses and strains cannot be evaluated, and the neuron ending may be close enough to the edges to be influenced by them. However, by controlling for the effects of tensile loads and by avoiding problems associated with the above types of tips, we have shown that responses to compressive loading are caused by the resulting compressive stress.
; Grigg 1996; Khalsa et al. 1996) showing that stretch-sensitive afferents appear to function as tensile stress sensors. Second, it was observed that the threshold for activation by tensile stress in nociceptors (~5 kPa) is similar in magnitude to that observed for SAII afferents and C mechanoreceptors in rat hairy skin (Grigg 1996) and stretch sensors in cat knee capsule (Khalsa et al. 1996).
; White et al. 1991). Thus, at the highest compression loads for the smallest-diameter indenters, these stimuli would be noxious and, most likely, also painful.
; Gynther et al. 1992; Jarvilehto et al. 1981; Macefield et al. 1990; Vallbo et al. 1995). These would be unprecedented roles for nociceptive afferents. However, the above finding may be unique to the skin studied in this experiment. In the region of the rat leg that we studied, neither SAII afferents nor nociceptors were spontaneously active, and neither would be activated during any rotations of the leg (Grigg 1996). The tensile threshold would, we estimate, be reached only when large tractions are applied or when large indentations are made into the skin. The fact that nociceptors and SAII afferents in rat hindlimb had similar thresholds for stretch should not, we feel, be generalized to other sites or other animals without circumspection, and the sensory role played by the stretch responses of nociceptors should be evaluated exclusively for any specific site. It is unclear whether the properties that we describe would apply (for example) to the cat hindlimb, where there might be substantial differences in the mechanical properties of the skin and possibly phenotypic differences in the properties of neurons. In the rat hindlimb, at least, there is no evidence of a proprioceptive role for nociceptors. However, the stretch responses caused by indentations would serve to amplify the population response of nociceptors to a strong indenting stimulus that could cause a penetrating injury. Furthermore, the strains caused by the stress levels that we employed were well beyond the range of what might be called "physiological" (Grigg 1996).
). In contrast, our measures of stress and strain are based on modeling the skin as a continuum material. However, notwithstanding the shortcomings of using a continuum model for determining skin stresses and strains, these variables were highly predictive of neuronal responses. The difference in threshold and sensitivity between tensile and compressive stresses, and the fact that there was no interaction between their effects, suggests that tensile and compressive stimuli may be coupled to a single transducer mechanism through different constituents of the skin.
; Grigg and Hoffman 1984; Khalsa et al. 1996; Srinivasan and Dandekar 1996) have postulated that strain energy density is the local mechanical state that is encoded by mechanically sensitive afferents. If a uniform stress or strain field is applied to a material like skin that has structural components with spatially varying orientations, stress or strain vectors would differ in various regions according to the local orientations of collagen fibrils. The magnitude of such a stress or strain field could be signaled by neurons that encode coordinate-independent variables (e.g., strain energy density). However, we found no evidence to support such a model. On the other hand, the magnitude of such a spatially varying state would also be encoded by neurons that signal stress and are not directionally tuned. The nociceptors in our study appeared to be indistinguishable from the C mechanoreceptors observed by Grigg (1996), which were not directionally selective. Our data would then support this latter model.
| |
ACKNOWLEDGEMENTS |
|---|
The authors thank A. Allard for building the apparatus and C. Packard for computer programming.
This study was partially funded by Foundation for Chiropractic Education and Research research fellowship 95-RR-02 to P. S. Khalsa and by National Institute of Neurological Disorders and Stroke Grants NS-10783 to P. Grigg and NS-14624 to R. H. LaMotte.
| |
APPENDIX: DESCRIPTION OF THE INVARIANT MECHANICAL QUANTITIES |
|---|
The three-dimensional stress () and strain () at the location of a terminal ending of a nociceptive afferent ending can be described with the use of tensor notation as
![<B>σ</B>= [σ<SUB>ij</SUB>] = <FENCE><AR><R><C>σ<SUB>11</SUB></C><C>σ<SUB>12</SUB></C><C>σ<SUB>13</SUB></C></R><R><C>σ<SUB>21</SUB></C><C>σ<SUB>22</SUB></C><C>σ<SUB>23</SUB></C></R><R><C>σ<SUB>31</SUB></C><C>σ<SUB>32</SUB></C><C>σ<SUB>33</SUB></C></R></AR></FENCE>= <FENCE><AR><R><C>σ<SUB>xx</SUB></C><C>σ<SUB>xy</SUB></C><C>σ<SUB>xz</SUB></C></R><R><C>σ<SUB>yx</SUB></C><C>σ<SUB>yy</SUB></C><C>σ<SUB>yz</SUB></C></R><R><C>σ<SUB>zx</SUB></C><C>σ<SUB>zy</SUB></C><C>σ<SUB>zz</SUB></C></R></AR></FENCE>](/content/vol78/issue1/fulltext/492/img001.gif)
|
(1) |
![<B>ε</B>= [ε<SUB>ij</SUB>] = <FENCE><AR><R><C>ε<SUB>11</SUB></C><C>ε<SUB>12</SUB></C><C>ε<SUB>13</SUB></C></R><R><C>ε<SUB>21</SUB></C><C>ε<SUB>22</SUB></C><C>ε<SUB>23</SUB></C></R><R><C>ε<SUB>31</SUB></C><C>ε<SUB>32</SUB></C><C>ε<SUB>33</SUB></C></R></AR></FENCE>= <FENCE><AR><R><C>ε<SUB>xx</SUB></C><C>ε<SUB>xy</SUB></C><C>ε<SUB>xz</SUB></C></R><R><C>ε<SUB>yx</SUB></C><C>ε<SUB>yy</SUB></C><C>ε<SUB>yz</SUB></C></R><R><C>ε<SUB>zx</SUB></C><C>ε<SUB>zy</SUB></C><C>ε<SUB>zz</SUB></C></R></AR></FENCE>](/content/vol78/issue1/fulltext/492/img002.gif)
|
(2) |
11, 22, and 33). In addition to the strains along the diagonal of the strain tensor (i.e., 11, 22, and 33), we were also able to measure one of the planar shear strains (i.e., 12).
From the stress and strain tensors, it was possible to calculate a number of scalar quantities that were invariant to the orientation of the external imposed coordinate system. Individual mechanoreceptors have been shown to align themselves to the local orientation of collagen fibers (Halata et al. 1985). Therefore a population of receptors within a large enough volume of tissue would be expected to have different orientations. Thus a uniformly applied stress (or strain) field would result in different stresses (or strains) depending on the orientation of the receptors. However, the magnitude of the tensor invariants would be the same irrespective of receptor orientations. Thus the tensor invariants were attractive candidates for being the mechanical quantity(s) that might be encoded by mechanically sensitive nociceptors.
Stress tensor invariants are commonly defined by first describing the principal stresses. The same process is directly used to described strain tensor invariants and will not be repeated for sake of brevity. Principal stresses are defined as those, for a particular coordinate system orientation, in which the shear stresses are nonexistent (i.e., ij = 0, for i 
j). The determination of the principal stresses and their directions is solved by the standard calculation of the eigenvalues and eigenvectors. Not all of the invariant quantities that arise from the characteristic equation that is used to solve the eigenvalues and eigenvectors have direct relationships with easily described physical states. However, they form the mathematical basis of much of material failure and plasticity theories (Chen and Han 1988). The following is a description of the invariants evaluated in this study.
I1, I2, and I3 are the first, second, and third invariants, respectively, of the stress tensor. I1 is related to the stresses responsible for pure dilation of an elastic volume. I2 and I3 do not have easily identifiable physical correlates. Their equation are given as follows
|
(3) |
|
(4) |
|
(5) |
![<IT>J</IT><SUB>2</SUB> = <FR><NU>1</NU><DE>6</DE></FR>[(σ<SUB>11</SUB> − σ<SUB>22</SUB>)<SUP>2</SUP> + (σ<SUB>22</SUB> − σ<SUB>33</SUB>)<SUP>2</SUP> + (σ<SUB>33</SUB> − σ<SUB>11</SUB>)<SUP>2</SUP>]](/content/vol78/issue1/fulltext/492/img006.gif)
|
|
(6) |
|
(7) |
12 = 13 = 23 = 0). The stresses tangential to these planes are termed principal shear stresses. Assuming that the principal axes are aligned with the global coordinate system, the maximum of these shearing stresses is
|
(8) |
formulation was used, which takes into account the stresses present in an initially stressed material such as skin in vivo, where Sij are the initial stresses
|
(9) |
|
(10) |
|
(11) |
|
(12) |
|
(14) |
![<IT>F</IT><SUB>2</SUB> = <FR><NU>1</NU><DE>6</DE></FR>[(ε<SUB>11</SUB> − ε<SUB>22</SUB>)<SUP>2</SUP> + (ε<SUB>22</SUB> − ε<SUB>33</SUB>)<SUP>2</SUP> + (ε<SUB>33</SUB> − ε<SUB>11</SUB>)<SUP>2</SUP>] + ε<SUP>2</SUP><SUB>12</SUB> + ε<SUP>2</SUP><SUB>23</SUB> + ε<SUP>2</SUP><SUB>31</SUB>](/content/vol78/issue1/fulltext/492/img015.gif)
|
|
(13) |
|
(15) |
| |
FOOTNOTES |
|---|
Address for reprint requests: P. S. Khalsa, Dept. of Anesthesiology, Yale University, 333 Cedar St., New Haven, CT 06510.
Received 9 September 1996; accepted in final form 4 March 1997.
| |
REFERENCES |
|---|
|
Abstract
Introduction
Methods
Results
Discussion
References
|
|---|
This article has been cited by other articles:
|
|
 |
|
  A. P. Sripati, S. J. Bensmaia, and K. O. Johnson A Continuum Mechanical Model of Mechanoreceptive Afferent Responses to Indented Spatial Patterns J Neurophysiol, June 1, 2006; 95(6): 3852 - 3864. [Abstract] [Full Text] [PDF]
|
|
|
|
 |
|
 R. M. Slugg, J. N. Campbell, and R. A. Meyer The Population Response of A- and C-Fiber Nociceptors in Monkey Encodes High-Intensity Mechanical Stimuli J. Neurosci., May 12, 2004; 24(19): 4649 - 4656. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
P. Grigg and D. R. Robichaud II Rat Cutaneous RA Afferents Activated by Two-Dimensional Skin Stretch J Neurophysiol, January 1, 2004; 92(1): 484 - 491. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
D. R. Robichaud II, Z. Del Prete, and P. Grigg Stretch Sensitivity of Cutaneous RA Mechanoreceptors in Rat Hairy Skin J Neurophysiol, September 1, 2003; 90(3): 2065 - 2068. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
Z. Del Prete, S. P. Baker, and P. Grigg Stretch Responses of Cutaneous RA Afferent Neurons in Mouse Hairy Skin J Neurophysiol, March 1, 2003; 89(3): 1649 - 1659. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
D. Levy and A. M. Strassman Mechanical Response Properties of A and C Primary Afferent Neurons Innervating the Rat Intracranial Dura J Neurophysiol, December 1, 2002; 88(6): 3021 - 3031. [Abstract] [Full Text] [PDF]
|
|
|
|
 |
|
 D Levy and A M Strassman Distinct sensitizing effects of the cAMP-PKA second messenger cascade on rat dural mechanonociceptors J. Physiol., January 15, 2002; 538(2): 483 - 493. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
R. M. Slugg, R. A. Meyer, and J. N. Campbell Response of Cutaneous A- and C-Fiber Nociceptors in the Monkey to Controlled-Force Stimuli J Neurophysiol, April 1, 2000; 83(4): 2179 - 2191. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
Z. D. Prete and P. Grigg Responses of Rapidly Adapting Afferent Neurons to Dynamic Stretch of Rat Hairy Skin J Neurophysiol, August 1, 1998; 80(2): 745 - 754. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
A. M. Strassman, D. Levy, and A.M. Strassman Distinct sensitizing effects of the cAMP-PKA second messenger cascade on rat dural mechanonociceptors J. Physiol., December 3, 2001; (2001) 200101317. [Abstract] [PDF]
|
|
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
| Visit Other APS Journals Online |
