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The Journal of Neurophysiology Vol. 80 No. 5 November 1998, pp. 2446-2466
Copyright ©1998 by the American Physiological Society
1 Department of Anesthesiology, Yale University School of Medicine, New Haven, Connecticut 06510; and 2 Department of Mechanical Engineering, Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
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ABSTRACT |
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 Abstract
 Introduction
Methods
Results
Discussion
References
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LaMotte, R. H., R. M. Friedman, C. Lu, P. S. Khalsa, and M. A. Srinivasan. Raised object on a planar surface stroked across the fingerpad: responses of cutaneous mechanoreceptors to shape and orientation. J. Neurophysiol. 80: 2446-2466, 1998. The representations of orientation and shape were studied in the responses of cutaneous mechanoreceptors to an isolated, raised object on a planar surface stroked across the fingerpad. The objects were the top portions of a sphere with a 5-mm radius, and two toroids each with a radius of 5 mm along one axis and differing radii of 1 or 3 mm along the orthogonal axis. The velocity and direction of stroking were fixed while the orientation of the object in the horizontal plane was varied. Each object was stroked along a series of laterally shifted, parallel, linear trajectories over the receptive fields of slowly adapting, type I (SA), and rapidly adapting, type I (RA) mechanoreceptive afferents innervating the fingerpad of the monkey. "Spatial event plots" (SEPs) of the occurrence of action potentials, as a function of the location of each object on the receptive field, were interpreted as the responses of a spatially distributed population of fibers. That portion of the plot evoked by the curved object (the SEPc) provided a representation of the shape and orientation of the two-dimensional outline of the object in the horizontal plane in contact with the skin. For both SAs and RAs, the major vector of the SEPc, obtained by a principal components analysis, was linearly related to the physical orientation of the major axis of each toroid. The spatial distribution of discharge rates [spatial rate surface profiles (SRSs), after plotting mean instantaneous frequency versus spatial locus within the SEPc] represented object shape in a third dimension, normal to the skin surface. The shape of the SA SRSs, well fitted by Gaussian equations, better represented object shape than that of the RA SRSs. A cross-sectional profile along the minor axis [spatial rate profile (SRP)] was approximately triangular for SAs. After normalization for differences in peak height, the falling slopes of the SA SRPs increased, and the base widths decreased with curvature of the object's minor axis. These curvature-related differences in slopes and widths were invariant with changes in object orientation. It is hypothesized that circularity in object shape is coded by the constancy of slopes of SA SRPs between peak and base and that the constancy of differences in the widths and falling slopes evoked by different raised objects encodes, respectively, the differences in their sizes and shapes regardless of differences in their orientation on the skin.
The shape of an object is an intrinsic physical property that remains invariant with changes in orientation and translation in three-dimensional space. Within a smooth area, that has no edges or tears on the objects surface, the local shape at a point is completely defined by the curvatures and orientations of two orthogonal principal axes. For convex objects, both the principal curvatures are positive. In this paper, we investigate how cutaneous mechanoreceptors encode the orientation and shape of raised toroidal objects on a planar surface. Shape can be defined as the distribution of curvatures at any given point on the object's surface where the local curvature at that point is the reciprocal of the radius of a circle that can be fitted on a given cross-sectional surface profile of the object (Srinivasan and LaMotte 1991 Construction of raised objects of differing shape
Small, three-dimensional objects of differing shape were constructed and mounted on the center of a flat plate having a diameter of 25 mm (Fig. 1A). The objects were the top portions of a sphere with a 5-mm radius, and two toroids each with a radius of 5 mm along one axis and differing radii of 1 or 3 mm along the orthogonal axis. Their curvatures (inverse of radii) were 200, 333, and 1,000 m
Psychophysical testing with human subjects
A two-interval, two-alternative forced choice procedure was used to determine the discriminability of the shapes or orientations of the stimulus objects, for three human observers. Discriminations of shape and orientation were measured under conditions of active touch, wherein the subject actively stroked the object in a natural way. The stimulus object was placed on a raised circular platform (6 in. diam) in a slightly recessed position so that the edge of the planar surface on which the toroid or sphere was mounted rested flush with the surrounding surface of the platform. The subject's arm was supported so that the index finger was poised comfortably above the left side of the stimulus object before each stimulus presentation. At the start of each trial, the subject brought the finger down, approximately at a 25° angle to contact the platform. Using the fingerpad, a single stroke from left to right was made along a linear trajectory of 5 cm at a velocity of ~10 mm/s. The objects were presented in randomly determined order.
Method of applying objects to the skin during neurophysiological experiments
The hand was restrained, palm-up, in plasticine with the stimulated finger typically angled upward by ~25° with respect to the horizontal plane. A post was glued to the fingernail and sunk into the plasticine to maintain the position of the finger during tactile stimulation. A vertical post, mounted to the back of the plate containing the raised object (Fig. 1A, right), was inserted into the end of a lever containing strain gauges (Brock Research, Newton, MA) that allowed independent measurements of contact force on three axes (Fig. 2). The lever was mounted to a torque motor (Cambridge Technology, Watertown, MA) that maintained compressional force between the object and the skin at 15 ± 0.5 g during stroking (Fig. 2). The torque motor was mounted to a rotary platform that could change the orientation of the object within the horizontal plane (Fig. 1B). The platform was mounted to a three-axis, servo-controlled translation table (Anorad, Hauphaug, NY) that was used to stroke the object over the skin in the horizontal plane (X, Y) and make adjustments of the vertical position (Z) of the torque motor at the beginning of an experiment. The orientation of the stroke trajectories was orthogonal to the long axis of the finger and defined as 0°. The position, velocity, and acceleration for the four axes (X, Y, Z, and rotation) were under program control of a dedicated microprocessor (digital axis controller; Anorad) with positional resolution better than a micrometer. Before stroking, the object was rotated to the desired orientation and then stroked, forward and backward (x-axis in Fig. 1B), along a series of laterally shifted, parallel, linear trajectories over the fingerpad. Lateral shifts of the trajectories (y-axis in Fig. 1B) were either 0.1 mm, for the majority of fibers tested, or 0.2 mm. Trajectory lengths ranged from 6.0 to 10.0 mm. The areas encompassed by the stroking were always square. Thus a 6.0 × 6.0 mm area, centered on the fiber's receptive field, would be stimulated by having a trajectory length of 6.0 mm and 60 lateral shifts of 0.1 mm (a total of 120 strokes, 60 forward and 60 backward). The velocity of stroking was 10 mm/s. The orientation of the objects relative to the trajectory of stroking was varied from 0, 30, 60, and 90°.
Surgical preparation
Experiments were performed on anesthetized monkeys (Macaca fasicularis, n = 9) as has been described previously (e.g., LaMotte and Srinivasan 1987a Electrophysiological recordings
Mechanically sensitive afferents were sought whose receptive fields (RFs) were centrally located on the fingerpads of digits 2-4. The evoked neural responses were amplified (5K) and band-pass filtered (30-3,000 Hz). The neural responses of single afferents were isolated using a window discriminator. With the use of standard criteria, afferents were classified as either slowly (type I) or rapidly adapting (type I) afferents (SAs or RAs, respectively). In studies of shape coding, responses were recorded from 16 SAs and 11 RAs to objects of differing curvature and, for the toroids, a constant orientation of 90°. In studies of orientation coding, responses were recorded from a subset of these afferents, six SAs and five RAs, to different orientations of each two toroids and to a single orientation of the sphere.
Data collection
The sampling rates for all data collection were performed at 1 kHz. Indentation force and position were acquired from analog outputs from the indentation torque motor. The planar position of the stimulus was acquired from the digital axis controller. The time of occurrence of each action potential was acquired from the window discriminator. All data were displayed in real time by a computer and stored for subsequent analysis.
Data analysis of the neural representation of the
two-dimensional outline of an object's shape in the
horizontal plane
Each object was stroked from left to right and then from right to left along a series of parallel trajectories orthogonal to the long axis of the finger in the horizontal plane. The sequences of nerve impulses generated in response to each stroke, while collected as a temporal sequence, were plotted as spatial events and thus formed a "spatial event plot" (SEP) (Johnson and Lamb 1981
Data analysis of the neural representation of an object's orientation
A measure of the neural representation of the orientation of the object in the horizontal plane was obtained by using a principal components analysis (Morrison 1967 Data analyses of the neural representation of the third dimension of an object's shape, orthogonal to the surface of the skin
Two methods were used to analyze the neural coding of an object's shape in the vertical plane based on the spatial distributions of fiber discharge rates. The first method analyzed a fiber's spatial rate profile (SRP) defined as discharge rate (impulses/s) plotted as a function of distance along a line centrally located within the SEPc and parallel to the minor or the major axis of a toroid oriented at 90°. An SEPc obtained in response to an object whose orientation deviated from 90° was first rotated by an amount equal to the deviation. A rectangle was formed with sides that bordered the extreme edges of the SEPc (Fig. 3B, left). Two strips, each 1 mm wide and forming a cross, were centered within the rectangle. The mean IF was determined for successive bins of 0.2 × 1.0 mm in increments of 0.2 mm along the strip. For any given SEP, the SRPs evaluated the profiles of response to the major and minor axes of the object. The width of the central strip was chosen to be 1 mm because it represented 50% of the width of the smallest object, the 1 × 5 toroid, during stroking parallel to its major axis. We used this to compare the responses to the central region of curvature, without influences due to the edge of the curvature, between all the objects and all the orientations and trajectories.
Statistical analyses
Assessments of the significance of differences in parameters obtained from the principal components analyses, the SRPs, and the Gaussian surfaces for two or three object shapes, two stroke directions and four object orientations were performed with one- or two-way repeated measures analyses of variance (ANOVAs) or repeated measures ANOVAs on ranks. Post hoc analyses applied the Student-Newman-Keuls pairwise multiple comparison method. All statements referring to statistical significance were based on a probability criterion of P < 0.05.
Sensory discriminations of shape and orientation
Under conditions of active touch, each subject performed each discrimination task at levels that were well above the threshold criterion of 75%. For discriminations of shape, the two toroids were discriminated by a mean percentage correct of 98.7 and 84.7 at orientations of 90 and 0°, respectively. The corresponding percentages at the same orientations for the 3 × 5 and 5 × 5 mm objects were 91.7 and 89.0. For discriminations of object orientation, the mean percentages correct for 0 versus 30°, 30 versus 60°, and 60 versus 90° were each >90%. Orientation discrimination under passive touch was virtually identical to that under active touch. The mean percentages correct for 0 versus 30°, 30 versus 60°, and 60 versus 90° were each >90%. Thus human subjects could easily discriminate between the different orientations and shapes of the objects used in the neurophysiological experiments.
Neural coding of orientation
Both the orientation of the raised toroid and the two-dimensional outline of the contact region between the skin and the object were represented in the SEPs of single SA and RA responses. SEPs, evoked in a representative fiber of each type in response to the 1 × 5 mm toroid, are shown in Fig. 4. All strokes were in the "forward" direction (from left to right in the figure). The SAs often responded to the flat plate with a steady discharge that paused just before the leading edge (left side of the of the dense cluster) and just after the raised object moved over the most sensitive spot in the receptive field (Fig. 4A). The RAs typically responded in bimodal fashion to the object in a way that seemed to begin just before the object reached the most sensitive spot followed by a pause and another burst after it passed over this spot (Fig. 4C). Also shown, for the RA and SA, are the corresponding SEPcs after background responses to the plate were removed (Fig. 4, B and D). The major vector that described the spatial orientation of the cluster of action of action potentials was determined by principal components analysis and is superimposed on each SEPc. In general, the orientation of the major vector, termed the "response orientation," corresponded to the physical orientation of the shape equally well for SAs and RAs in response to the 1 × 5 mm toroid (Fig. 4).
Neural coding of shape
NEURAL REPRESENTATIONS OF THE TWO-DIMENSIONAL OUTLINE OF THE OBJECT IN THE HORIZONTAL PLANE.
Both the shape and the size of the two-dimensional outline of the raised object in contact with the skin are represented by the borders of activity of each SA and RA. The outline of the base of each object is superimposed on the SEP of the responses of typical SAs and RAs in Fig. 8 to each object and orientation, stroked in the forward direction (from left to right). The area of influence of the raised object on the responses of the RAs, as reflected in their SEPs was generally both wider and longer than the actual length and width of the base of the object and more extensive than on the responses of the SA. A Von Frey type filament (50 mN) was used to measure the widths of the receptive fields orthogonal to the long axis of the finger. A significant positive correlation (r = 0.61) was found between the widths of the receptive fields and the widths of the SEPcs, the latter measured through its middle cross-section, orthogonal to the finger axis for all three raised objects oriented at 90°. The mean widths of the receptive fields were 2.5 mm for the SAs and 3.08 mm for the RAs. This small difference in receptive-field width could not explain the difference in widths in the SEPcs of RAs and SAs. Rather, the greater widths of the RA SEPcs were due in large part to an earlier response onset and to a later offset in response.
NEURAL REPRESENTATIONS OF THE CROSS-SECTIONAL SHAPE OF THE OBJECT IN THE VERTICAL PLANE.
The neural representation of the profile of the object's shape in a third dimension was estimated by measuring the SRP along the minor and major axes of the SEPc of each fiber's response to each object (as described in Fig. 3B). The orientations of the object and stroke trajectory were fixed at 90 and 0°, respectively.
SPATIAL RATE PROFILES REPRESENTING THE CROSS-SECTIONAL PROFILE OF EACH OBJECT ALONG THE MINOR AXIS.
SRPs obtained from the responses of a typical SA and RA are shown in Fig. 9, A and C, respectively. The toroid having the greatest curvature on the minor axis evoked the highest discharge rate in each fiber, whereas the sphere elicited the lowest. That is, the mean peak discharge rate increased with increases in object curvature.
SPATIAL RATE PROFILES REPRESENTING A CROSS-SECTIONAL PROFILE OF EACH OBJECT ALONG THE MAJOR AXIS.
The SRPs representing a cross-sectional profile of the object along the major axis (always oriented at 90° to the stroke direction) are shown for the same SA and RA in Fig. 11, A and C, respectively. The overall shape of the SA's SRP was generally tentlike or triangular with a rounded top. The top portion was sharper for the 1 × 5 mm toroid and a little rounder and broader for the 3 × 5 mm toroid and the sphere (Fig. 11A). The overall shape of the RA SRP along the major axis was more rounded and moundlike for the 1 × 5 mm toroid, in comparison with that for the SA (Fig. 11C). The shape became flatter and slightly more irregular for the 3 × 5 mm toroid and the sphere. As already mentioned for the SRPs parallel to the minor axis, the mean maximal discharge rate, for SAs and RAs, i.e., the peak height of the SRP, increased with an increase in curvature on the minor axis. To analyze the effect of changes in curvature of the minor axis on the width of the response along the major axis, the SRPs for each SA and RA were normalized to the maximal discharge rate, obtained in response to the 1 × 5 mm toroid (Fig. 11, B and D). The mean width of the SRPs for all RAs was 1 mm greater than that for all SAs (5.6 vs. 4.6 mm) a difference equal to the difference in the mean length of the von Frey determined receptive field (4.65 vs. 3.64 mm for RAs and SAs, respectively). A repeated measures ANOVA of the widths of the normalized SRPs demonstrated that the differences in object curvature on the minor axis did not produce significant differences in the widths of the SRPs along the major axis for either fiber type and for either direction of stroking. In response to the sphere, the mean widths of the SRPs, parallel to the forward direction of stroking were 4.4 mm for SAs and 5.2 mm for RAs. These values were not significantly different from the mean widths of the SRP, orthogonal to the direction of stroking, 4.8 and 5.4 mm, respectively, nor significantly different from the mean SRP widths along the major axes obtained in response to the two toroids (paired t-tests). Similar results were obtained for strokes in the backward direction. Thus the size (length) of the major axis of each object is coded consistently in the width of the SRP along the major axis, regardless of changes in the width or curvature of the object along the minor axis.
NEURAL REPRESENTATIONS OF THE THREE-DIMENSIONAL SHAPE OF THE OBJECT.
To obtain a first estimate and overall visual impression of the neural coding of object shape in three dimensions, the responses of each fiber of a given type were combined as follows. The SEPcs obtained from the responses of each fiber to a given object stroked in the forward direction were aligned by their geometrically determined centers and then superimposed. Next, a matrix composed of areal instantaneous frequencies from each spatial cell (SRS) was obtained from the pooled responses and then smoothed as described in Fig. 3C, middle. These are shown for SAs and RAs without normalization both from an oblique view (Fig. 12, A and C, respectively), and from a frontal view, parallel to the minor axis, after normalization for peak discharge (Fig. 12, B and D). The shapes of these SRSs are qualitatively similar to most of those obtained, in similar fashion, from individual fibers (e.g., Fig. 3C, middle). The representation of the sphere in the SA SRS is approximately conical (with rounded apex). The cone becomes thinner along the minor axis with increasing object curvature, i.e., increasing deviation from sphericity. The representations of shape in the RA SRS are bimodal with the response to the leading edge greater in height than the response to the trailing edge. The heights of each portion of response increase with increasing object curvature and the spacing between the two portions decrease with the corresponding decrease in object width.
Effect of object orientation on neural representations of shape in SA responses
Before obtaining the Gaussian fitted SRS, the coordinates of SEPs obtained for objects whose orientations deviated from 90° were rotated by the amount of the deviation such that the SEP for a 0° orientation was rotated by 90°, the SEP for 30° by 60°, and the SEP for 60° by 30°. Asymmetric Gaussian surfaces were fitted to the SRSs obtained from the nonnormalized responses of six SAs to each orientation of each toroid stroked in each direction. Results obtained from the two stroke directions were averaged. The mean peak height is plotted in Fig. 14A as a function of orientation for strokes in the forward direction. The mean peak height obtained from the responses of the 5 × 5 mm object at a single orientation (0°) is also shown. Measures of width and slope were then obtained for each SA after normalizing the peak height of each SRS to the greatest peak height obtained. This was always obtained from the response to the 1 × 5 mm toroid oriented at 90°. The mean width, the mean rising slope, and the mean falling slope were each obtained from a cross-sectional profile through the Gaussian fitted surface along the minor axis. These are plotted for the sphere at a single orientation and for each toroid as a function of the orientation (Fig. 14).
When actively stroking a stationary object with a fingerpad, multiple sources of information about intended movements and their kinesthetic and cutaneous sensory consequences can be integrated to obtain knowledge of the object's orientation and shape on the skin. The goal of the present experiments was to investigate the sensory coding of the orientation and shape of an object stroked across the fingerpad in the responses of cutaneous afferent fibers. To eliminate information derived from active movement and confine the sensory input to cutaneous receptors alone, methods were developed to stroke objects of differing shape and orientation across the passive fingerpad while controlling the object's contact force and its velocity and direction of movement. It was determined that human observers could readily discriminate the orientations and shapes of the experimental objects regardless of whether the objects were actively explored or presented to the passive fingerpad under stimulus conditions employed in the neurophysiological experiments. Because the attributes of orientation and shape can be independently discriminated by humans via tactile cues alone, we explored candidate mechanisms by which each attribute could be independently coded in the responses of SA and RA afferents to objects stroked across the passive monkey fingerpad.
Neural coding of orientation
The relative contribution of SA and RA population responses to encoding the orientation of an object differs according to whether the object is stroked across or statically indented into the skin. For static indentation, SAs and not RAs encode the orientation of a toroid (Khalsa et al. 1998 Neural coding of two-dimensional shape parallel to the skin surface
Surface-parallel, spatial neural codes, based on responses of single fibers, have been proposed for discriminations of two-dimensional, raised patterns, such as Braille-sized raised letters, dots, and gratings stepped or stroked across the fingerpad of human (Phillips et al. 1990 Neural coding of two- and three-dimensional shape vertical to the skin surface
The shape of the spatial distribution of discharge rates of an estimated population of mechanoreceptors is an estimation of the geometry of an object in a third dimension, orthogonal to the surface of the skin. This representation is not isomorphic to the shape of the object. The raised spherical object was represented in the estimated SA population response as a cone with rounded apex and the toroid as a similar but elongated cone. Similar shapes were obtained in response to spherical objects of different curvature statically indented into the skin (Goodwin et al. 1995 SKIN-CURVATURE HYPOTHESIS.
With the use of a model proposed earlier (LaMotte and Srinivasan 1987a Effects of orientation on neural coding of shape
It is common experience that the shape and size of an object, perceived through the sense of touch, remain generally constant despite changes in its orientation on the skin. The present findings suggest that it is the constancy in the differences in the widths and falling slopes of the SRS and SRPs evoked in the SA population by different raised objects that encodes the constancy of their sizes and shapes regardless of differences in their orientation with respect to the direction of stroking. In contrast, the spatial responses of the RAs provide less reliable measures of shape, owing in part to the brevity of their responses to the onset of curvature and their responsiveness to skin movement produced by the effects of a moving object on the movement of the skin surrounding the object as opposed to the shape of the object. However, such responses provide a kind of negative image or shadow of the object's shape, the onset of which provides a preview of what is to be coded in the responses of the SAs.
INTRODUCTION
Abstract
Introduction
Methods
Results
Discussion
References
).
,b; Srinivasan and LaMotte 1987). RAs were predominantly sensitive to the indentation velocity and the rate of change in skin curvature, but only when the objects were stroked across the skin at a sufficiently high velocity. These observations were extended in studies of SA and RA responses to cylindrical bars (LaMotte and Srinivasan 1993; Srinivasan and LaMotte 1991), spheres (Goodwin et al. 1995), and toroids (Khalsa et al. 1998) statically indented into the skin and wavy surfaces, consisting of alternating convex and concave cylindrical bars of differing radii of curvature, stroked across the skin (LaMotte and Srinivasan 1996). It was generally concluded that the size and shape of an object are best represented by the size and shape of the spatially distributed pattern of peripheral neural discharge rates, particularly among the SA population.
) or spheres (Goodwin et al. 1995) and toroids (Khalsa et al. 1998) that were indented but not stroked. In contrast, there are many studies of the peripheral neural coding of spatial pattern and roughness that employed scanned planar surfaces containing two-dimensional raised elements (Connor et al. 1990; Connor and Johnson 1992; Johnson and Lamb 1981; LaMotte and Whitehouse 1986). These have focused primarily on the coding of spatial variations in the horizontal plane using raised elements with flat tops and sharp edges. Little is known of the neural coding of the orientation of single raised elements in the horizontal plane nor of the coding of the three-dimensional objects of such raised structures, of millimeter length scale, stroked across the skin, aside from preliminary observations (LaMotte et al. 1994, 1996).
METHODS
Abstract
Introduction
Methods
Results
Discussion
References
1. Each object and the plate on which it was mounted (Fig. 1A, right) were machined from clear, hard acrylic, were transparent, and had smooth surfaces. The flat plate allowed us to differentiate the neural response due the curvature of the objects from that due to a flat surface with no curvature. The heights of the objects ranged from 0.42 to 0.44 mm. At the base of the toroidal objects, the lengths of the major axes were 4.1 and 4.2 mm; the widths of the minor axes were 1.6 and 2.6 mm for the 1 × 5 and 3 × 5 mm toroids. The width of the base of the sphere was 4.3 mm in all directions.
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FIG. 1.
Procedures for constructing the stimulus object and for controlling its position and contact force as it was stroked over the fingerpad. A: a radius cutting tool was used to cut the toroid or sphere from a rotating cylinder. Then, with the axis of the object horizontal, the top was cutoff along a section parallel to the axis, ~0.4 mm from the peak. The resulting form, which, for each toroid had the shape of the top of an egg, was mounted on a flat plate (the "stimulus plate") shown at right. The curvatures for the 3 stimulus objects were identical along one axis but differed for the orthogonal axis. B: schematic of the tactile stimulator used to control the position and contact force of the stimulus object on the fingerpad. A stimulus plate (A, right) containing one of the objects was mounted, via its stem, to a lever, containing a 3-axis load cell and attached to a torque motor (Fig. 2A for expanded view that includes the finger). The motor was mounted on a 3-axis translation table that was used to control the motion of the stimulus object along a linear trajectory in the horizontal plane while the torque motor controlled the compressional force of the object against the skin. Video cameras (a) provided top and side views of stimulus object on the fingerpad (not shown). A stepper motor (b) rotated a transparent plate (c) to which the torque motor (d) was mounted by a bracket so that the stimulus object (e) could be rotated about its center before applying it to the fingerpad. The platform containing the rotary transparent plate (c) was attached to the z-axis (vertical) translator (f), which was mounted in turn to the y-axis translator (g) and the latter to the x-axis (h) translator. The translation system was bolted to a granite table (k). Dust covers (i) protected portions of the translation mechanisms for x and y. An adjustable platform (j) was used to support the subject's hand (not shown).
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FIG. 2.
Methods of force control and measurement with examples of typical force traces recorded when stroking the stimulus plate across the fingerpad. A: method of force control and measurement. The stimulus plate was mounted to a lever arm containing a 3-axis load cell that was used to obtain independent measurements of force along each axis (x, y, and z). Small changes in angular displacement of the lever arm produced by a torque motor (mounted to a translation table as shown in Fig. 1B) maintained the compressional force (z) constant as the stimulus plate was stroked across the fingerpad. A post was glued to the fingernail to hold the back of the finger against a Plexiglas holder (humans) or plasticine (monkeys). The stimulus plate, to which the stimulus object was mounted, was inscribed with marks (not shown) that allowed accurate orientation of the object in the horizontal plane and its alignment with the fiber's receptive field before stroking. B: superimposed force traces on each axis. These traces were obtained as the 1 × 5 mm toroid, oriented 90°, was stroked 6 times in each direction (forward and backward) along the same trajectory, parallel to the x-axis (0° orientation). Upward and downward arrows, respectively, indicate the beginning and end of stroking. Before the 1st stroke, the stimulus plate indented the center of the fingerpad and was then moved leftward to the start location of the forward stroke, resulting in an initial force on the x-axis of ~5 g.
). Briefly, an animal was sedated with ketamine hydrochloride (10 mg/kg im), and deep anesthesia (areflexic to painful cutaneous pinch but spontaneously breathing) was maintained with supplemental pentobarbital sodium (35 mg/kg iv). The animal was warmed to maintain body temperature (96 ± 2°F), and hydrated with lactated Ringer solution (100 ml/h). The elbow was clamped and the hand secured palm up. Short pegs were glued to the fingernails, and the dorsal aspect of the fingers were pressed into plasticine. Molding the plasticine around the fingers secured them so that they would not move during the subsequent mechanical stimuli. The median or ulnar nerve in the upper or lower arm, innervating the digits of a hand, was surgically exposed using sterile technique. Skin flaps were used to hold a pool of mineral oil covering the exposed nerve. Neural recordings were made from microdissected filaments of fascicles in the exposed nerve. At the end of the experiment, the mineral oil was removed and the incision site thoroughly cleansed. Muscle and facial layers were sutured in sequence, and the skin was sutured closed. Anesthesia was discontinued, and the animal was allowed to awake normally. Antibiotics to prevent infection were given starting 24 h before the experiment, and twice daily for 1 wk after the experiment and longer if any signs of infection were present. A minimum of 3 wk occurred between subsequent experiments. In total, an animal could have received up to eight experiments on the upper and lower, median and ulnar nerves in the left and right arms. On the final experiment, the animal was killed by overdose of anesthetic.
; Johnson and Hsaio 1992). An SEP obtained from strokes in a single direction was interpreted as indicating how a spatially distributed population of mechanoreceptors would respond to the two-dimensional outline of the object's shape in the horizontal plane, parallel to the surface of the skin. In the example shown in Fig. 3A, the object was stroked along each trajectory beginning with the flat plate on the left side of the figure and ended with the flat surface at the extreme right. To view the same events as a series of temporal sequences, the origin of time for each stroke would be at the left and the time scale obtained by dividing the distance by the stroke velocity (10 mm/s). A pattern of impulses generated by a given stroke can be viewed as a spatial sequence in two ways. If one imagines that the skin of the fingerpad moves at the given stroke velocity over the stationary object, each dot in the figure would represent the horizontal location of the center of a fiber's receptive field on the object's surface each time a nerve impulse occurred as the skin moved from left to right over the object. An alternative view, and the one we presently adopt, is to interpret the pattern of impulses (dots) as representing a snapshot of the instantaneous response of a hypothetical population of mechanoreceptors with identical neural and biomechanical response properties and spatially distributed over the fingerpad. The snapshot occurs at the moment in time when the object has reached a central location on the fingerpad along the stroke trajectory.
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FIG. 3.
Procedures for estimating the representation of object shape and orientation in the responses of a population of fibers based on the responses of a single fiber. Refer to METHODS for further details. A, left: spatial event plot (SEP) of the responses of a single slowly adapting, type I mechanoreceptive afferent (SA) fiber to the 1 × 5 mm toroid oriented 90° and stroked from left to right along a series of parallel trajectories orthogonal to the long axis of the finger in the horizontal plane. Each dot is the location of the center of the toroid when an action potential occurred. After each stroke from left to right the object was shifted proximal to distal (upward in the figure). The tic mark spacing on the coordinate axes is 1 mm. A, right: filtered version, (SEPc), of the SEP in A in which dots separated by distances more than a criterion amount, based on instantaneous frequency with respect to the preceding and subsequent dot, have been removed. Solid line is the major vector determined by a principal components analysis, representing the orientation of the cluster of dots. Left side of the response was evoked by the leading edge of the object as it moved from left to right. B: determination of the center of the SEPc and 2 central strips (superimposed on the SEP in the left panel) from which spatial rate profiles (SRPs) plotting discharge rate, in bins of 0.2 × 1.0 mm for successive increments of 0.2 mm along the strip, were derived for the minor and major axes (middle and right panels, respectively). From the 8th order polynomial fitted to each SRP, response widths (horizontal dashed lines) and average slopes of the rising and falling phases were obtained. C, left: mesh plot, from the SEP in A, left, of discharge rate (impulses/s) in areal bins of 0.04 mm2. C, middle: same mesh plot after smoothing by inverse distance interpolation (Sigma Plot 3.0 software from SPSS, Chicago, IL). C, right: asymmetric Gaussian surface fitted to the mesh plot obtained from the SEPc in A, right. D, left: cross-sectional profile (solid curve) through the center of the asymmetric Gaussian surface along the X-axis at the location indicated by the thick line in C, right. The vertical line through the peak amplitude (a) and the center of the Gaussian surface (b) indicates that the Gaussian surface was divided into 2 halves along the Y-axis, the left half fitted with one Gaussian equation (solid curve on the left, dotted on the right) while the right half was fitted with another (solid curve on the right, dotted on the left). Widths of the 2 Gaussians at 60.7% of the peak height are indicated by c and d. D, right: method used to measure slope. The smooth curve is the same asymmetric Gaussian profile represented by the solid curve in the left panel. The rising and falling slopes, Sr and Sf, were determined by linear extrapolation between points ( 
) that had amplitudes of 25 and 75% of the peak. Superimposed histogram represents the discharge rates in bins of 0.2 mm evoked by a single forward stroke as obtained from a center slice through the mesh plot in C, left.
) to determine the orientation of the cluster of dots in each individual SEPc (Fig. 3A, right) and each composite SEPc. This analysis determined the orientation of the vector that minimized the squared distances between it and the positions of the dots in the cluster.
![<IT>f</IT>(<IT>x<SUB>r</SUB></IT>) = <IT>a</IT>exp(−0.5{[(<IT>x − b</IT>)/<IT>c</IT>]<SUP>2</SUP>})](/content/vol80/issue5/fulltext/2446/img001.gif)
![<IT>f</IT>(<IT>x<SUB>f</SUB></IT>) = <IT>a</IT>exp(−0.5{[(<IT>x − b</IT>)/<IT>d</IT>]<SUP>2</SUP>})](/content/vol80/issue5/fulltext/2446/img002.gif)
![<IT>f</IT>(<IT>y<SUB>d</SUB></IT>) = <IT>a</IT>exp(−0.5{[(<IT>y − e</IT>)/<IT>f</IT>]<SUP>2</SUP>})](/content/vol80/issue5/fulltext/2446/img003.gif)
![<IT>f</IT>(<IT>y<SUB>p</SUB></IT>) = <IT>a</IT>exp(−0.5{[(<IT>y − e</IT>)/<IT>g</IT>]<SUP>2</SUP>})](/content/vol80/issue5/fulltext/2446/img004.gif)
This equation had several advantages. First, the form of the Gaussian surface equation allowed for asymmetries along a given axis as well as for the orthogonal axis. Second, the parameters of the equation could be directly related to the overall geometry of the SRS. The parameters (a
g) of the equation each have direct physical interpretations: a is the peak magnitude of the surface; b and e define the center of the Gaussian surface where it splits into halves along the X and Y axes; c and d define the widths of the rising and falling portions, respectively, of the Gaussian surface at 60.7% of the peak height and parallel to the X axis, respectively (Fig. 3D, left); and f and g define the widths of the rising and falling portions, respectively, of the Gaussian surface at 60.7% of the peak height and parallel to the Y axis. The conditional statements after the equations specify that for one axis only, one of the two Gaussian equations for that axis is used when fitting its part of the Gaussian surface. A third advantage is that the fitted Gaussian surface is similar to the general, nonlinear surface previously used by Goodwin et al. (1995) and Khalsa et al. (1998) to fit population responses obtained from peripheral mechanoreceptors. Fitting SRSs with the Gaussian surface equation was accomplished with commercially available software (TableCurve 3D, SPSS, Chicago, IL). Because the RA SRSs were bimodal in form, the Gaussian surface was fitted only to the leading half of the response.
RESULTS
Abstract
Introduction
Methods
Results
Discussion
References
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FIG. 4.
Spatial event plots of the responses of a single SA and rapidly adapting, type I mechanoreceptive afferent (RA) to different orientations of the toroidally shaped object with 1 × 5 mm radii. The toroid was oriented 90, 60, 30, and 0° to the direction of stroking that was from left to right, perpendicular to the long axis of the finger. A and C: SEPs representing raw data obtained from an SA and RA. B and D: filtered versions of same SEPs. Each panel contains an SEP from which background responses to the planar surround have been removed (SEPc) from the SEP shown directly above and on which is superimposed the major vector (solid line) that best describes the spatial orientation of the cluster of action potentials as determined by a principal components analysis (see Fig. 3A). Tic mark spacing on each axis is 1 mm.
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FIG. 5.
Spatial event plots of the responses of a single SA and RA fiber to different orientations of the 3 × 5 mm toroid. The SEPcs and superimposed major vectors were obtained from the same fibers and plotted in the same format as described for Fig. 4. A and B: responses of the SA. C and D: responses of the RA.
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FIG. 6.
Spatial event plots of the combined responses of a group of SAs and a group of RAs to different orientations of each toroidally shaped object. For each fiber type, the SEPcs obtained in response to a given orientation of the object, stroked from left to right, were aligned at their geometric centers (Fig. 3B, left panel) and superimposed. Solid line in each panel is the major vector, determined by a principal components analysis. Tic mark spacing on each axis is 1 mm. A and C: combined responses of 6 SAs to the toroids, with radii on the minor axis of 1 and 3 mm, respectively, oriented 90, 60, 30, and 0° to the direction of stroking. B and D: combined responses of 5 RAs to the same objects and orientations.
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FIG. 7.
Relationship between the physical orientation of the major axis of each toroid and the orientation of the major vector obtained from the spatially distributed responses of single fibers or a group of fibers of each type. A and C: mean major vectors, obtained by principal components analyses of the "individual SEPcs" evoked in single SAs ( 
) and RAs (- - -) produced in response to each orientation of the 1 × 5 mm toroid (A) and the 3 × 5 mm toroid (C). B and D: major vectors determined for "superimposed SEPcs," i.e., each combined SEPc, obtained from the superimposed responses of 6 SAs () and 5 RAs (- - -) to each orientation of the 1 × 5 mm toroid (B) and the 3 × 5 mm toroid (D). Error bars are SEs.
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FIG. 8.
Comparisons of the outline of the base of each object with the 2-dimensional shape of the SEP evoked by the object in typical SAs and RAs. The SEP in each panel was obtained in response to the object of stated radii (mm) and orientation. The outline of the base of each object on the flat plate is superimposed at an arbitrary position near the leading edge of the response. Spacing between tic marks on each axis is 1 mm. A: responses of SAs. B: responses of RAs. Each object was stroked from left to right.
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FIG. 9.
SRPs representing the middle cross-sectional shape of each object, along the minor axis. A: nonnormalized SRPs. Each panel displays the mean spatial discharge rate (impulses/s) along the middle section of the SEPc, as described in Fig. 3B, of the responses of an SA to the sphere, and to the 2 toroids each oriented at 90°. Each object was stroked from left to right. B: normalized SRPs. Each SRP in A was normalized to the peak discharge rate evoked by the 1 × 5 mm toroid and fitted with a polynomial function. The width of each function along the dashed horizontal line (at 25% of the peak height), and the rising and falling slopes were determined as described in Fig. 3B. C and D: SRPs of an RA displayed in the same format as described for the SA.
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FIG. 10.
Peak height, width, and slopes for the rising and falling phases of the middle, cross-sectional SRP along the minor axis. Mean values of each parameter for SAs ( ) and RAs (- - -) are plotted as a function of the curvature of the object on the minor axis. The orientation of each toroid was 90°. A: mean peak height of the SRP (peak discharge rate). B: mean width of the SRP. C and D: mean slopes of the rising and falling phases of the SRP.
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FIG. 11.
Spatial rate profiles representing the cross-sectional shape of each object along the major axis. Same format as in Fig. 9.
1.24 impulses/s/mm) obtained in response to the sphere, was not significantly different from the mean slope of the falling phase of the major axes obtained for this and the other two objects (1.2 to 1.3). Thus the constant shape of each object along the major axis was represented in a constant shape of the SA SRP along the major axis. A similar analysis was not reasonable for the RA SRPs due to their bimodal nature for the minor axis and, for the wider objects, their irregular or bimodal shape along the major axis.
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FIG. 12.
Smoothed mesh plots of the superimposed spatial discharge rate surfaces obtained from the combined responses of SAs and RAs to each object. A and C: oblique view of the nonnormalized spatial discharge rate surfaces (SRSs), fitted as described in Fig. 3C, middle, obtained from the combined responses of 16 SAs (A) and 11 RAs (C) to each object. The orientation of each toroid was 90°. B and D: frontal view of the same data as in the panel above, after normalization to the peak discharge rate obtained in response to the 1 × 5 mm toroid.
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FIG. 13.
Mesh plots and Gaussian surface fits of the spatial discharge rate surfaces obtained from the responses of a typical SA to each object. The orientation of each toroid was 90°. A: mesh plots of the nonnormalized spatial discharge rate surfaces (SRSs) obtained from the fiber's SEPcs (refer to Fig. 3C, left). B: Gaussian surface fit of each SRS in A after normalization to the peak discharge rate obtained in response to the 1 × 5 mm toroid. C: frontal view of the Gaussian surfaces in B.
View this table:
TABLE 1.
Mean values of goodness-of-fit and Gaussian parameters obtained from the Gaussian fitted SRSs of 16 SAs when each object was stroked in the forward direction
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TABLE 2.
Mean slope and mean width measures derived from cross-sectional profiles along the minor and major axes of Gaussian-fitted SRSs of 16 SAs
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FIG. 14.
Effects of changes in object orientation on the mean peak height, mean width, and mean slopes obtained from Gaussian surface fits of the SA spatial discharge rate surfaces (SRSs) obtained in response to objects of differing curvature. Radii of curvature are given in mm. The means were obtained from the SRSs of 6 SAs. A-D: results for height, width, rising slopes, and falling slopes, respectively.
DISCUSSION
Abstract
Introduction
Methods
Results
Discussion
References
; LaMotte and Srinivasan 1987a,b; Srinivasan and LaMotte 1987). An intensive response measure such as peak discharge rate, which we found can reflect differences in shape or in orientation when other stimulus parameters are held constant, is predicted to be less robust than spatial measures such as width and slope obtained from the responses of a population of fibers.
). Another approach, the one taken in the present experiments, is to estimate the population responses from the responses of single mechanoreceptive afferent fibers to different locations of the object with respect to the centers of their receptive fields. An estimation of the spatial distribution of neural activity, parallel to the surface of the skin, is obtained in the spatial event plot of the location of the object at each occurrence of an action potential. The two-dimensional shape and orientation of any part or all of this "surface parallel" distribution of activity (the SEP) can be interpreted as encoding the outline of the size, shape, and orientation of the corresponding portion of the object in contact with the skin (e.g., Goodwin et al. 1989; Johnson and Lamb 1981; LaMotte and Srinivasan 1987a,b, 1996; Phillips and Johnson 1981). The shape of a spatial discharge rate surface (SRS) obtained from these data not only contributes to orientation coding but also represents a third dimension of object shape, orthogonal to the surface of the skin (Goodwin et al. 1995; LaMotte et al. 1994, 1996). A vertical, cross-sectional profile or slice through this spatial distribution of discharge rates (SRP) is dominantly affected by the vertical cross-sectional shape of the object (Goodwin et al. 1995; LaMotte and Srinivasan 1996).
) or differences in the orientation of a cylinder (Dodson et al. 1998). For stroking, both SAs and RAs contribute to orientation coding. In the present study, the orientation of the major vector obtained from the estimated population responses (SEPcs) of SAs and RAs was found to be linearly related to the physical orientation of each toroidal object. This neural representation of the orientation of the major axis of curvature of an object stroked over the skin was also influenced both by the curvature of the object on the minor axis and by the orientation of the stroke trajectory. Clearly, when the object is more asymmetric, that is the greater the difference between its principal curvatures, its orientation on the skin should be more discernible. Our findings are consistent with this a priori prediction in that the neural representation of object orientation in the spatially distributed discharge rates of SAs and RAs was more variable for the 3 × 5 than the 1 × 5 mm toroid. Similarly, it was previously shown that the human capacity to identify a toroidal object's orientation becomes less accurate as the toroids become less asymmetric and more spherical (LaMotte et al. 1992).
,b; Srinivasan and LaMotte 1987). The length of skin experiencing a change in skin curvature and the magnitude and rate of change in curvature will be greater when the major axis of an object is orthogonal as opposed to parallel to the direction of stroking. These facts explain why the discharge rates of both SAs and RAs decreased and the shapes of their spatial distribution (SEPcs) in the horizontal plane became less asymmetric, i.e., more circular as the orientation of the major axis of each toroid was decreased from 90 to 0°. One might suppose that the shapes of the von Frey determined receptive fields, which were ~1 mm longer along the long axis of the finger than they were along the orthogonal axis, might have contributed to the decrease in asymmetry. However, a similar loss of asymmetry was observed in more circular receptive-field shapes. Another possible contribution to decreased asymmetry may result from the approximately cylindrical shape of the finger that is bound to influence the mechanics of contact and the mechanical state at receptor locations in the skin. However, the orientations of the major vectors of the spatially distributed responses of RAs and SAs were not determined solely by the shapes of the outline of activity in the horizontal plane but were also influenced by the spatial distribution of discharge rates within the active region. For example, the asymmetric shape in response outline might have sufficed in coding all orientations of the 1 × 5 mm toroid, whereas an asymmetric distribution of discharge rates within a more spherical outline was required for orientations of the 3 × 5 mm toroid. In any case, despite the spatial and intensive changes in discharge rate that occurred due in part to changes in skin curvature and its rate as object orientation was varied, the orientation of the principal component of the spatially distributed discharge rates in the activated RA and SA population was approximately linearly related to the physical orientation of the object.
; Pubols 1980; Talbot et al. 1968). RAs are poorer than SAs in coding the shapes of two-dimensional objects stroked across the skin (e.g., Johnson and Lamb 1981; LaMotte and Srinivasan 1987a,b). As shown in the present study, although RAs are poorer than SAs in coding the shapes of curved three-dimensional objects moving over the skin, they are superior in demarcating the locations of the trailing portions of the wider objects in addition to their anticipatory demarcations of the leading portions. This provided a longer spatial rate profile, and thus a slightly more accurate response orientation to a toroidal object as the orientation of the major axis of the object approached zero. The outline of this profile in the horizontal plane became a less important determinant of response orientation, and the spatial distribution of discharge rate became more important as the asymmetry in the outline's shape decreased with diminishing differences between major and minor principal curvatures of the object.
) and/or monkey (e.g., Johnson and Lamb 1981; Lamb 1983; Phillips and Johnson 1981). Isomorphic representations of each pattern were present in the responses of SAs and less accurately in responses of RAs but not those of pacinians or type II SAs. Recently, intensive, modal, and temporal neural codes were ruled out in favor of a spatial code for the roughness of embossed dots of varying dot diameter and spacing (Connor et al. 1990; Connor and Johnson 1992). The elements of the patterns in these studies had sharp edges and flat tops. For a given raised element, the transition from a flat surface to leading and trailing edges of high curvature provided an isomorphic image of the spatial extent of the raised element in the direction of stroking. The difference in magnitude of response between leading and trailing edges can be explained as due to a higher reaction force and rate of skin displacement by the leading edge (Blake et al. 1997).
).
). A broad-sided or a frontal view of the SA SRS (Fig. 12) reveals an approximately triangular shape as does the SRP representing the two-dimensional cross-sectional profile of the object along the major or minor axes. A sequence of triangular shapes was evoked in the SRP obtained for SAs in response to a wavy surface, consisting of cylindrically shaped surfaces of differing curvature, stroked across the fingerpad (LaMotte and Srinivasan 1996). The width of the base of the triangular shape, normalized for peak discharge (height), decreased with increasing curvature of the cylinder. Similarly, the convex, cylindrically shaped portion of a half-sinusoid step evoked a triangular-shaped SRP, whose base decreased as the wavelength or width of the steps was varied from gradual to steep (LaMotte and Srinivasan 1987a). It was hypothesized that the shape of each circular (cylindrical) object, defined by its constant curvature, was coded in the constancy of the slopes along the rising and declining phases of the corresponding triangular shape in the SRP. The size, or width, of the circular structure was coded in the width of the base of the triangle (LaMotte and Srinivasan 1996).
,b; Srinivasan and LaMotte 1987, 1991), it is possible to relate the shape of the raised object to the probable profile of skin deflection and the responses of each type of mechanoreceptor. It is hypothesized that SA responses are governed by not only the depth and velocity of indentation of the skin, but also the rate and amount of a positive change in the curvature of the skin at the most sensitive spot in the receptive field. RAs are primarily responsive to changes in the velocity of the skin at the most sensitive spot and the rate of change in the curvature of the skin. A change in skin curvature from its normally convex position to one more concave (as occurs during indentation) is defined as a positive change, whereas an increase in convexity is defined as negative. The planar surface produces an indentation with a small, positive change in skin curvature, resulting in a basal discharge in the SA. As the raised object approaches the most sensitive spot, before the skin contacts the object, the skin is lifted away from the plate, and there is then a negative change in curvature that can produce a pause in firing. The abrupt change in depth of indentation, together with a positive change in curvature, produces the rising phase of the SA's discharge as the raised object moves onto the most sensitive spot. This is followed by the effects of a reduced depth of indentation under the trailing half of the object and a negative change in curvature as the curved object continues to move over this most sensitive spot. RAs respond with a burst due to skin stretch caused by horizontal velocity as the planar surface begins its lateral translation and then a response to the negative vertical velocity of local skin retraction as the skin is lifted away from the most sensitive spot in front of the approaching object. This is followed by a response to the positive velocity of indentation by the object that ceases as the velocity approaches zero near the apex of the object. Another response is evoked by the negative velocity produced by the withdrawal of the object relative to the skin near the trailing edge. We are uncertain as to the extent to which curvature rate sensitivity contributes to these responses. However, it seems that the SRPs of the RAs appear to outline the spatial locations and velocities of the indentations and retractions of skin surrounding the object rather than provide an outline of the shape itself in the vertical plane. In contrast, the SAs provide a consistent spatial rate distribution that represents a third dimension of shape in addition to the outline of the shape in contact with the skin in the other two dimensions.
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ACKNOWLEDGEMENTS |
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The authors thank K. Greenquist and A. Klusch-Petersen for technical assistance.
This work was supported by National Institute of Neurological Disorders and Stroke Grant NS-15888 and Office of Naval Research Grant N00014-91-J-1566.
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FOOTNOTES |
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Address for reprint requests: R. H. LaMotte, Dept. of Anesthesiology, Yale University School of Medicine, 333 Cedar St., New Haven, CT 06510.
Received 8 October 1997; accepted in final form 16 July 1998.
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REFERENCES |
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Abstract
Introduction
Methods
Results
Discussion
References
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