Dorsal Horn Spatial Representation of Simple Cutaneous Stimuli
PAUL B. BROWN, RONALD MILLECCHIA, JEFFREY J. LAWSON, STEPHANIE STEPHENS,
PAUL HARTON, AND JAMES C. CULBERSON
Departments of Physiology and Anatomy, West Virginia University Health Sciences Center, Morgantown,
West Virginia 26506
INTRODUCTION
Stimulation of different sites on the body surface evokes
responses at different loci in somatosensory nuclei (somatotopic organization). Therefore, stimulus locations and geometries must be reproduced to some extent by the spatial
patterns of responding neurons, providing a spatial representation of stimuli. Reciprocally, the locations of responding
neurons should be an adequate indication of the location
of the stimulus (place code). In principle, spatial relations
between or within stimuli may be sufficiently well preserved
in this representation that discriminations can be performed
by looking for features of the stimulus pattern in the central
representation ( feature preservation). Under this scheme,
for example, size (area) of stimulus may be reflected in size
of representation (number of responding neurons) and two
point discrimination could be mediated by detecting separate
peaks of neural activity separated by an area with less activity. We wish to determine the degree to which this assumption is tenable for the spinal dorsal horn. To examine place
coding in the dorsal horn, we have chosen to model the
spatial pattern of responses to simple stimuli, as predicted
by the excitatory low-threshold receptive fields (RFs) of
cells in dorsal horn laminae III and IV. These cells receive
almost exclusively input from low-threshold cutaneous
mechanoreceptors (e.g., Brown et al. 1977, 1978 1980, 1981;
Fyffe 1992); they are organized in a single somatotopic map
in the rostrocaudal (RC), mediolateral (ML) plane (e.g.,
Brown and Fuchs 1975; Brown et al. 1992); and some of
them project to rostral somatosensory centers via pathways
that are adequate to perform tactile spatial discriminations
in the absence of the alternative path to the cortex, the dorsal
columns (Noordenbos and Wall 1976; Vierck 1973, 1977).
We would like to be able to use a small sample, e.g., 500
neurons, as a basis for modeling the representations of stimuli
by the entire population. These modeled representations then
can be used to predict localization, size, and two-point discrimination on the basis of various putative discrimination
mechanisms acting on them. First, we have approximated RFs
of observed cells as ellipses, which can be described with five
parameters. In a second stage, these five parameters were
described as mean and variance surfaces in the RC, ML plane
according to the locations of the cells, so that the entire population of Ç122,000 cell RFs (Wang et al. 1997) could be
simulated according to their locations in the plane. The following measures of goodness of fit of the model were obtained: fractional overlaps of best-fitting ellipses and real RFs;
spatial correlations of the segmental representations of sampled and simulated cells; fractional overlaps of the RFs of
observed cells and cells simulated at the same RC, ML locations; and spatial correlations of geometric properties (area
and length/width ratio) of the RFs of simulated and observed
cells as a function of their RF locations on the hindlimb.
In this preliminary investigation, only the place coding
capacity of the dorsal horn was examined. It was not the
purpose of this research to determine the roles of discharge
patterns (e.g., action potential patterns elicited during movement of a stimulus across the skin), or variations in discharge rate elicited by stimuli impinging on different portions of cells’ RFs. We have simulated representations of
stimuli with varying location, size, and two-point separation
to determine whether the dorsal horn spatial representations
of the stimuli reflect these three stimulus properties.
A preliminary report of these results has been published
in abstract form (Brown et al. 1996).
0022-3077/98 $5.00 Copyright q 1998 The American Physiological Society
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Brown, Paul B., Ronald Millecchia, Jeffrey J. Lawson, Stephanie Stephens, Paul Harton, and James C. Culberson. Dorsal
horn spatial representation of simple cutaneous stimuli. J. Neurophysiol. 79: 983–998, 1998. A model of lamina III–IV dorsal horn
cell receptive fields (RFs) has been developed to visualize the
spatial patterns of cells activated by light touch stimuli. Lowthreshold mechanoreceptive fields (RFs) of 551 dorsal horn neurons recorded in anesthetized cats were characterized by location
of RF center in cylindrical coordinates, area, length/width ratio,
and orientation of long axis. Best-fitting ellipses overlapped actual
RFs by 90%. Exponentially smoothed mean and variance surfaces
were estimated for these five variables, on a grid of 40 points
mediolaterally by 20/segment rostrocaudally in dorsal horn segments L4 –S1. The variations of model RF location, area, and
length/width ratio with map location were all similar to previous
observations. When elliptical RFs were simulated at the locations
of the original cells, the RFs of real and simulated cells overlapped
by 64%. The densities of cell representations of skin points on the
hindlimb were represented as pseudocolor contour plots on dorsal
view maps, and segmental representations were plotted on the standard views of the leg. Overlap of modeled and real segmental
representations was at the 84% level. Simulated and observed RFs
had similar relations between area and length/width ratio and location on the hindlimb: r( A) Å 0.52; r( L/W ) Å 0.56. Although the
representation of simple stimuli was orderly, and there was clearly
only one somatotopic map of the skin, the representation of a single
point often was not a single cluster of active neurons. When twopoint stimuli were simulated, there usually was no fractionation of
response zones or addition of new zones. Variation of stimulus
size (area of skin contacted) produced less variation of representation size (number of cells responding) than movement of stimuli
from one location to another. We conclude that stimulus features
are preserved poorly in their dorsal horn spatial representation and
that discrimination mechanisms that depend on detection of such
features in the spatial representation would be unreliable.
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BROWN, MILLECCHIA, LAWSON, STEPHENS, HARTON, AND CULBERSON
METHODS
Combining data across animals
Single-unit recording
Additional cells were recorded from adult cats of either sex,
anesthetized with 0.3 mg/kg ketamine and 0.025 mg/kg xylazine
or with 0.17 mg/kg telazol (Fort Dodge Laboratories). This was
replaced with °30 mg/kg alpha chloralose as the original anesthetic wore off. In later animals, we maintained cardiac function with
0.05 mg/kg glycopyrrolate im every 3 h to counteract the cardiodepressant effects of the drugs used for induction. The fur of the
hindlimb was clipped to a length of Ç1 mm. Intubations of trachea,
internal carotid artery, and jugular vein were used for artificial
respiration and expired CO2 monitoring, blood pressure measurement, and the administration of drugs, respectively. Expired CO2
was maintained at 4% by controlling respirator parameters. Temperature was maintained at 387C via rectal probe-controlled heating
pad and heat lamps. The animal was mounted on a rigid frame and
the lumbosacral enlargement was exposed at the bottom of a mineral oil pool. Paralysis was induced with 20 mg gallamine triethiodide (Flaxedil), maintained with 10-mg supplements every half
hour. Maintenance doses of 0.1 times the initial dose of chloralose
were administered intravenously every 2 h or earlier when blood
pressure responded to surgical manipulations. A slow lactated
Ringer drip was used to maintain fluid volume. When necessary,
mean blood pressure was maintained at 90 mg Hg with slow infusions of dopamine.
Single units were recorded using stainless-steel microelectrodes
in segments L4 –S2 in rows of tracks spaced 200 mm apart across
the width of the dorsal horn, at quarter-segment intervals. Each
excitatory RF was characterized with hand-held probes, applying
mechanical stimuli that barely displaced the skin, defining the perimeter of the RF to an accuracy of approximately {1 mm. The
excitatory RFs of lamina III–IV cells are defined sharply, and
different investigators can obtain quantitatively repeatable measures of their sizes, shapes, and locations. The RFs were transferred
to standard leg drawings using distances of borders from bony
landmarks. Each RF was drawn as a planar projection with the
center placed at the location of the RF center on that view of the
leg where the center was closest to the transverse midline of the
leg drawing. Each recording site was marked by passing 01 mA,
200 s 01 square waves through the metal electrode for 30 s, producing a small area of coagulation that could be seen in dark field.
At the end of each experiment, animals were perfused with 1 l
387C physiological saline, followed by 2 l of 10% formalin at
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Generation of the descriptive model
SHIFTING DATA. The procedure for shifting animals to eliminate
interanimal variation due to pre- and postfixation has been explained in detail elsewhere (Wang et al. 1997). All the data from
an animal were shifted in trial steps of 0.1 segment rostral and
caudal. At each shift, the unshifted data D (RC, ML) from all
animals were combined and exponential smoothing was used to
obtain model D * (RC, ML) at each shifted recording site in order
measure the deviation of each shifted D (RC, ML) from the model
D * (RC, ML). The shift at which the root mean square deviation
of D (RC, ML) from D * (RC, ML) was minimized was taken as
the best shift for aligning the animal’s data with the aggregate of
all animals. This process was repeated for each animal. Then all
animals’ data were shifted by their best shifts, and the process of
modeling and shifting was repeated until the best shifts were all
zero; shifts converged to zero in no more than four iterations.
GEOMETRIC DESCRIPTION OF RFs. One objective in modeling
RFs was for individual RFs to be represented by geometric figures
that have a high fractional overlap with the original RFs. To model
RFs as best fitting geometric figures, we chose to use ellipses,
which can be described by five parameters. We chose as parameters
three measures that we have used already for analysis of RFs plus
two new ones. We already are using D, distance of RF center from
tips of toes; A, area; and L/W, length/width ratio (e.g., Brown et
al. 1975). In addition, we need another position parameter u, the
circumferential angle of RF center around the leg, and f, the
orientation of the ellipse. RFs were translated from the standard
leg drawings to an unfolded skin representation of the leg, and D
and u were measured as y and x positions, respectively, on the
unfolded skin drawing (Fig. 1A).
Each RF was approximated as an ellipse as follows (Fig. 1B):
the ellipse center was placed at the RF geometric center. The
location of the RF center on the leg was expressed as y (unfolded
skin coordinate, identical to D, the distance from tips of toes), and
x, the horizontal position on the unfolded skin drawing. The ellipse
area A (cm2 ) was set equal to the RF area and the ratio of major/
minor axis was set equal to the ratio of the longest axis of the RF
(longest line from 1 edge to the other, through the center) to the
perpendicular axis (longest line perpendicular to the long axis,
from 1 edge to the other, not necessarily through the center of the
RF). The angle of orientation of the ellipse f was equal to the
angle of the long axis of the ellipse relative to the x axis of the
standard skin outline. Goodness of fit was determined by placing
a grid of points i, j with 0.5-mm spacing on the skin outline,
and setting values within each area (original RF and elliptical
approximation) equal to 1, values outside each area equal to 0.
The fractional overlap f was determined as follows:
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s
fÅ
where
and
Rij Å
Sij Å
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H
S
(( Rij Sij
ij
D
2
(( R 2ij (( S 2ij
ij
ij
1:
original RF covers grid point i, j
0:
original RF doesn’t cover grid point i, j,
1:
simulated RF covers grid point i, j
0:
simulated RF doesn’t cover grid point i, j
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It is not possible, using present techniques, for us to characterize
the RFs and reconstruct recording sites of 500 neurons in one
animal. Therefore single-unit data must be combined across animals. One requirement for combining data across animals is the
need to compensate for random rostral and caudal shifts of the
map due to random RC shifts of dorsal root dermatomes. To compensate for these shifts, we have devised a method of shifting data
from individual animals relative to the aggregate of data across
animals, for best fit of each animal’s RF locations (D, distance of
RF center from tips of toes) as a function of RC and ML cell
locations (Koerber and Brown 1995; Koerber et al. 1993; Wang
et al. 1997). Such shifting procedures require enough cells in each
animal to obtain a goodness-of-fit measure [root mean square deviation of D (RC, ML) in an individual animal relative to the model
surface for all animals combined]. We have chosen as a rule of
thumb at least six cells with characterized RFs and reconstructed
recording sites per animal. Using these criteria, 356 cells were
available from previous studies (Koerber and Brown 1995;
Koerber et al. 1993; Wang et al. 1998).
room temperature. Relevant segments were removed and blocked
at intersegmental boundaries, and stored in 10% formalin for ¢1
wk. Frozen transverse sections were cut and mounted on subbed
slides. Sections were stained with Cresyl Echt violet and Luxol
fast blue (Kluver-Barrera). Electrode tracks and lesions were visualized under dark field, and the relative ML, RC, and laminar
locations were determined.
DORSAL HORN PLACE CODING OF SIMPLE STIMULI
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where 07 was taken as the left edge and 3607 the right edge, of the
skin outline at y corresponding to D, the distance of the RF center
from the tips of the toes. Mean and variance u’s were computed
and translated back to values of x. Clearly, it was mandatory that
trends in the RC, ML plane for these variables should agree with
trends already reported in the literature. Covariances among the
five parameters as a function of RC, ML were not adjusted for.
Although such adjustments might improve the accuracy of the
model, the accuracy obtained was adequate for our purposes.
SIMULATION OF MODEL RFs. Using the mean and variance surfaces, it was possible to generate populations of elliptical RFs at
each grid square, the number of simulated RFs at each square being
equal to the number of cells estimated from cell counts of laminae
III and IV (Wang et al. 1997). At each grid square, each simulated
RF parameter was generated by adding the fitted mean to a random
variable with variance equal to the fitted variance, for the required
number of cells.
FIG . 1. Approximation of receptive fields (RFs) as ellipses. A: typical
RFs on 3 standard views of the leg (posterior view: small RF on plantar
foot; lateral view: larger RF on dorsal foot; medial view: larger RF on
medial thigh), and their translation to an unfolded skin representation. Thin
line on the lateral and medial views represents the ‘‘zipper,’’ which forms
the lateral and medial edges of the unfolded skin view. B: 5 ellipse parameters used to describe approximate RF geometries. A, area (stippled); y, y
axis location of RF center on unfolded skin diagram (same as D, distance
from tips of toes); x, x axis location on the unfolded skin diagram; L/W,
length/width ratio; and f, angle of the major axis of the ellipse relative to
the x axis.
AGGREGATE RFs. To test the aggregate simulated RFs against the
aggregate RFs of the data sample, we compared the segmental
distribution of RFs for observed and simulated populations. Different smoothing factors (space constants used to produce the five
parameter surfaces) were tested to determine which gave the best
match between observed and simulated segmental representations.
This was done by computing spatial correlations of stacked RFs,
plotted on a grid with 0.5-mm spacing on the unfolded skin. Each
grid point on the grid was initialized to zero and was incremented
by one for each RF that overlapped it. This is equivalent to stacking
all the RFs on the skin, each RF contributing unit elevation, and
counting the number of RFs stacked at each grid point. Separate
stacked RFs were generated for the observed and simulated populations. The stack height at each point on the simulated and observed
set of RFs then were cross-correlated.
INDIVIDUAL RFs. Because the representations of stimuli are dependent on adequate modeling of individual RFs, it was desirable
to know how well individual RFs compared with modeled RFs at
the same RC, ML locations. Values of means of the five descriptive
parameters at recording sites were estimated from values at grid
squares in the model, and these means were used to simulate RFs
at these sites. Fractional overlap was computed using different
space constants for smoothing of the parameter surfaces.
RF GEOMETRIES AS A FUNCTION OF POSITION ON THE LEG.
where the best fractional overlap Å 1 (perfect congruence), worst
fractional overlap Å 0 (no overlap). This is the Pearson productmoment correlation, equivalent to the overlapping area divided by
the geometric mean of the two areas.
MEAN AND VARIANCE SURFACES. For each of the five parameters of the ellipses, surfaces were fitted to the data using exponential
smoothing to describe the mean and variance of each variable as
a function of RC, ML. Different degrees of smoothing, determined
by length constants lRC and lML , were tried. We have described
the details of this procedure elsewhere (Wang et al. 1997). Briefly,
the RC, ML plane was divided into 4,000 grid squares, and the
value of the mean at each grid point i, j was computed using all
the data points g, h, the weight of each datum declining exponentially with distance between (RCi , MLj ) and (RCg , MLh ). Exponentially weighted means at the locations of data points were computed in the same manner. Deviations of data points from smoothed
means at those points were computed. Then variances at all grid
points were calculated from the deviations at the data points by
exponential smoothing. Mean and variance for x, horizontal position on the unfolded skin drawing, was calculated by converting x
to u, the angular position of x on the circumference of the leg,
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As a final test of the model, we assessed the ability of the model
to predict RF geometries as a function of location on the leg. Area
A and length width ratio L/W were plotted for all cells in the
observed and simulated populations as a function of x and y, the
RF center locations on the leg. These properties of the cell RFs
were determined in the modeled cells entirely by their locations in
the RC, ML plane, and there should be poor agreement if the model
is not accurate. The variables A and L/W therefore were averaged
at grid points on the leg corresponding to their RF centers, and
values then were interpolated by exponential smoothing on the
unfolded skin. Corresponding grid points obtained from the observed and simulated data then were cross-correlated in the same
fashion as the stacked RFs used to compare observed and simulated
segmental representations.
Dorsal horn spatial representations of simple stimuli
The immediate purpose of these simulations was to model the
spatial representation of simple stimuli. This was accomplished by
placing simulated stimuli on the unfolded skin and determining
which cells’ RFs overlapped the stimuli. If a grid point was overlapped by both a cell’s RF and a stimulus, the cell was excited by
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Validation of the model
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Validation of the model
FIG . 2. Overlap of original RFs and their best-fitting ellipses. A: greatest
overlap. B: least overlap. C: average overlap. D: distribution of spatial
fractional overlaps (percent overlaps, equivalent to Pearson correlation coefficients) of RFs and best-fitting ellipses.
the stimulus. The number of cells at each grid square in the RC,
ML plane of the dorsal horn that were activated by the stimulus
was counted, and these response densities were taken as the dorsal
horn spatial representation of the stimulus.
Four sets of stimuli were simulated to assess the general organization of the representation of the skin, the representation of single
points at different locations on the skin, the effect of varying stimulus size (contact area), and the representation of two-point stimuli.
RESULTS
Single-unit recording
Recording sites were reconstructed successfully for 195
characterized cells. These were added to the original database of 356 cells, and the optimal shifts for all animals were
determined, as described in METHODS . The resulting database
had 3 cells in L3, 20 in L4, 81 in L5, 209 in L6, 150 in L7,
83 in S1, and 5 in S2. Because of small sample sizes in
L3 and S2, only segments L4 –S1 were used for modeling
purposes.
Generation of the descriptive model
Original RFs and their fitted ellipses based on the five
RF parameters are illustrated in Fig. 2, A– C, for the best
and worst-fitting ellipses, and an ellipse the fit of which
was equal to the average fit. Average fractional overlap of
best fitting ellipses and original RFs was 0.90 { 0.092
( SD ). The distribution of fractional overlaps is illustrated
in Fig. 2 D.
The five parameters for all the observed cells are plotted
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SEGMENTAL REPRESENTATIONS. Stacked RFs are illustrated
in Fig. 5 for the five segments studied. In each set of four
stacked representations, the segmental span of dorsal horn
cells sampled is illustrated (left). In each segmental representation, the four unfolded skin outlines, going from a to
d, are observed data, least ( lRC Å 0.03, lML Å 0.01), intermediate ( lRC Å 0.15, lML Å 0.05), and greatest ( lRC Å 0.3,
lML Å 0.1) smoothing. Fractional overlap analysis revealed
that the smallest smoothing factor produced the highest fractional overlap (0.84) between observed and simulated segmental representations (Table 1). In the three greatest
smoothings, the highest fractional overlap was observed
when the calculated variances were used rather than 10 times
or one-tenth the variances. In the least smoothing, all three
variances gave essentially identical results. This indicates
that covariance among the five parameters is not an important factor for our purposes. Zero l’s would produce the
best fractional overlap, perfect except for the nonelliptical
shapes of original RFs and in rare instances where differing
RFs were encountered at the same RC, ML location in the
shifted original data.
INDIVIDUAL RFs. To test similarity of individual simulated and
observed RFs, cells’ RFs were simulated at each of the sites
where observed cells were recorded with the smallest smoothing
factors (second smallest of Table 1) of Fig. 5. A fraction of
the original RFs are plotted in the figurine drawing of Fig. 6
in colored cyan. For this figure, all RFs were scaled to the same
plotting area, and placed so that their centers fell at the RC,
ML locations of the cells’ recording sites. Then a portion of
the appropriate figurine was added, similarly scaled and properly
positioned relative to the RF, to fill a fixed window size on the
plot. If a figurine’s window overlapped one already plotted by
more than one-third, it was not illustrated. Modeled RFs at the
same locations, scaled the same as original RFs, are illustrated
in the figurine drawing, colored light brown. Areas of overlap
between original and simulated RFs are colored magenta. Because the purpose here was to compare individual RFs with
their simulated counterparts, only the mean values of the parameters were used to simulate RFs without any variance. Original
RFs and not their best-fitting ellipses were used for observed
RFs. This should decrease the average fractional overlap by a
factor of Ç0.9 because original RFs are not perfectly correlated
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as five sets of elevations as a function of RC, ML in Fig. 3.
Even though the 551 data points plotted in this way generate
chaotic pictures, certain trends are apparent. The lowest values of D (shown as Y ), A, and L/W are found in medial
dorsal horn of segments L6 and L7 where the toes are represented, and X varies with segmental location reflecting the
shift from preaxial to postaxial skin from rostral to caudal.
These trends all agree with earlier reports (e.g., Brown et
al. 1975).
Surface plots of model means and variances for the five
ellipse parameters are plotted as functions of RC, ML in
Fig. 4, plotted using lRC Å 0.03, lML Å 0.01. These were
the surfaces used to simulate the RFs of dorsal horn cells.
For each simulated cell, the values of the variables’ means
and variances at the cell’s RC, ML locations were obtained
from these surfaces.
DORSAL HORN PLACE CODING OF SIMPLE STIMULI
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with their best fitting ellipses. Visual inspection reveals a very
close agreement among most of the original and simulated RFs,
on a cell by cell basis, although there are a few instances where
original and simulated RFs do not overlap at all.
For purposes of quantitative analysis, corresponding observed and modeled RFs were compared by computation of
fractional overlap. All observed and modeled cell pairs were
compared, regardless of whether they were included in Fig.
6. The distribution of fractional overlaps is plotted in Fig.
7 for all the smoothing factors of Table 1 (the 2nd smallest
smoothing of Fig. 7 was the 1 used to generate Fig. 6).
Again, best fractional overlaps were obtained with lowest
smoothing (Fig. 7A). The distribution in Fig. 7A was bimodal: the mean of the bimodal distribution is 0.64 and the
higher mode peaks between 0.80 and 1.0. Small fractional
overlaps were produced where there were clusters of two or
more cells very close together in the original data, and their
parameter values described nonoverlapping RFs. The mean
locations computed from these cells produced RFs that were
intermediate in location and that overlapped the original RFs
poorly if at all. The peak at zero overlap consists of 116
cells or Ç21% of the total. The high fractional overlaps were
found at locations where cells were relatively isolated from
other cells or clustered cells had similar RFs so that the
observed and simulated RFs overlapped well.
The second smallest smoothing, Fig. 7B, was the one used
for Fig. 4. The peak at zero overlap consists of 174 cells or
Ç26% of the total; the rest of the distribution is relatively
flat, and the mean for the histogram was 0.49.
RF GEOMETRIES AS A FUNCTION OF POSITION ON THE LEG.
The final test of the validity of the descriptive model was
perhaps the most challenging: a comparison of simulated
and observed RF area and length/width ratio as a function
of RF position on the skin. These relationships were not
direct consequences of the model because none of the five
parameters was modeled as a function of any of the others
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(specifically, A and L/W were not modeled as a function
of D and u ). Therefore these relations are only indirectly
determined by the model, in that the four parameters A,
L/W, D, and u were all modeled as functions of RC, ML.
Figure 8 illustrates A and L/W as a function of position on the
leg, using pseudocolor for A and L/W . The space constant lxy
for smoothing on the unfolded skin was 5 mm (10 grid
points). Visual inspection indicates a high degree of similarity, which correlation analysis confirms: r( A) Å 0.50, r( L/
W ) Å 0.66.
Spatial representation of simple stimuli
OVERALL ORGANIZATION OF THE MAP STUDIED WITH SIMULATED STIMULATION OF BANDS OF SKIN. Figure 9 illus-
trates the spatial distributions of dorsal horn cells responding
to simulated stimulation of bands of skin. The 4 panels in
the left portion of A–D, represent the densities of responding
original cells (left to right) at all grid points and the densities
of modeled cells using least smoothing, intermediate, and
most smoothing of Fig. 5, respectively. The band on each
skin outline represents the simulated stimulus, 5 cm in proximodistal extent, with distal edges at 0, 7, 14, and 21 cm
from tips of toes. Note that, as the band is moved up the
leg, the pattern of responding cells moves from the toe region
in medial L7 and S1 to more lateral, rostral, and caudal locations, as would be expected from previous studies (e.g.,
Brown and Fuchs 1975). This indicates an orderly organization of the map that is similar for original and simulated
cells. Note that the representations of bands of skin consist
of discontinuous clusters of responding cells (patchy representation) for the two most proximal stimuli.
As would be expected from an orderly map in which some
RFs are bound to overlap more than one stimulus band, the
degree of overlap between representations decreased as a function of distance between bands. However, it should be noted
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FIG . 3. Plots of the original RF parameters as a function of location in the horizontal [rostrocaudal (RC), mediolateral
(ML)] plane. Elevations represent data from single cells except in rare cases where ú1 cell was recovered from the same
grid square.
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BROWN, MILLECCHIA, LAWSON, STEPHENS, HARTON, AND CULBERSON
that even widely spaced bands (e.g., on toes and thigh) had for punctate stimuli. Figure 10 illustrates the responses of
some overlap of their representations, presumably because of dorsal horn cells to simulated 2 1 2 mm stimuli at 32 differvariances in the location parameters (D and u ) and large RFs. ent locations on the leg. To accommodate 32 dorsal views
The degree of spatial correlation of the different representations in a single figure, only the intermediate smoothing of Figs.
was calculated (Table 2). The two most similar representations, 4–7 was used. Note that, at several sites, a single point on
for bands 14 and 21 cm from tips of toes, have a positive the skin is represented by more than one cluster of recorrelation of 0.49. These areas have the lowest map scale and sponding cells. Also these constant-area stimuli clearly do
the largest RFs, so it is not surprising that they have the most not activate equivalent numbers of cells (Table 3: cells
similar representations. Poorly overlapping representations counts based on modeled cells used for dorsal views).
(e.g., 0 and 7, 7 and 14 cm) have essentially zero correlations. REPRESENTATION OF STIMULUS SIZE. The representations of
Representations that are roughly complementary (e.g., 0 and punctate stimuli of Fig. 10 are discernibly smaller (involve
14; 0 and 21) have strong negative correlations. Generally, fewer responding neurons) than the representations of Fig. 9,
correlations become less positive (or more negative) with in- as expected from the fact that the simulated stimuli are much
creasing distance between stimuli.
smaller and therefore overlap fewer RFs. To study explicitly
the effect of stimulus size on representation size (number of
REPRESENTATION OF PUNCTATE STIMULI. The simulation of
Fig. 9 involved the use of large simulated stimuli to study responding neurons), the simulated stimulus area was varied
overall organization of the representation of the hindlimb. at three different locations on the hindlimb over a 100-fold
It is also of interest to know the effect of stimulus location range, from 0.5 1 0.5 to 5 1 5 mm, and representations were
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FIG . 4. Exponentially smoothed means and variances of the 5 ellipse parameters based on original data (least smoothing:
lRC Å 0.03, lML Å 0.01). A, C, E, G, and I: mean surfaces for y, x, A, L/W, and f, respectively. B, D, F, H, and J: variance
surfaces for the same variables.
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FIG . 5. Segmental representations for each of the 5 segments. A: L4; B: L5; C: L6; D: L7; E: S1. In A–E, the bar on the
left represents the segment sampled; the 4 unfolded skin representations (a–d in A) are original data, least smoothing,
intermediate smoothing, and most smoothing. In each unfolded skin representation, the RFs are stacked and autoscaled, and
depth of stack at each point is indicated by pseudocolor (pseudocolor scale on right).
989
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TABLE
BROWN, MILLECCHIA, LAWSON, STEPHENS, HARTON, AND CULBERSON
1.
Correlations of stacked RFs for real vs. simulated RFs
ML Å 0.001, RC Å 0.003
ML Å 0.010, RC Å 0.030
ML Å 0.050, RC Å 0.150
ML Å 0.100, RC Å 0.300
Lambdas
var-wt
0.1
1
10
0.1
1
10
0.1
1
10
0.1
1
10
L4
L5
L6
L7
S1
Average
0.72
0.90
0.87
0.87
0.85
0.84 { 0.07
0.73
0.85
0.88
0.89
0.87
0.84 { 0.07
0.73
0.82
0.87
0.89
0.88
0.84 { 0.06
0.60
0.65
0.60
0.59
0.78
0.64 { 0.08
0.60
0.70
0.67
0.70
0.81
0.70 { 0.08
0.59
0.66
0.64
0.55
0.71
0.63 { 0.06
0.24
0.12
0.23
0.31
0.47
0.27 { 0.13
0.38
0.54
0.63
0.53
0.45
0.51 { 0.10
00.03
00.12
0.32
0.31
0.04
0.10 { 0.20
00.18
0.00
0.14
0.25
0.25
0.09 { 0.18
00.07
0.47
0.61
0.44
0.28
0.35 { 0.26
00.05
00.19
0.24
0.25
0.03
0.06 { 0.19
Spatial fractional overlaps (Pearson correlation) of segmental representations for real versus modeled data, showing variation of fractional overlap with segment, smoothing, and different multiples of
observed variances. RF, receptive fields; ML, mediolateral; RC, rostrocaudal.
the proximal limb. In fact, there is greater variation of representation size with stimulus placement than with stimulus area
over the ranges tested.
REPRESENTATION OF TWO-POINT STIMULI. One common assumption about two-point discrimination is that the central
representation preserves spatial relations among stimulus
features sufficiently well that a two-point stimulation can
be recognized by detection of two separate peaks in the
FIG . 6. Figurine drawings of a representative sample of original RFs (cyan) and simulated RFs (light brown) at the same
RC, ML locations. Areas of overlap between original and simulated RFs are colored magenta. Dorsal view of left dorsal
horn, segments L5 –S1. Left edge, lateral edge; right edge, medial edge. Normalized RC and ML dimensions. All cells,
regardless of which side they were recorded, are plotted as left side.
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depicted on dorsal views (Fig. 11). Although there is clearly
some effect of stimulus size, the representation size does not
change as much as the stimulus size. This is illustrated quantitatively in Fig. 12, where it can be seen that for a 100-fold
range of stimulus area, there is only a 1.6-fold range of representation size for a given site on the leg. Representation size
also varies as a function of location: more dorsal horn cells
respond to a given area stimulus on the distal limb than on
DORSAL HORN PLACE CODING OF SIMPLE STIMULI
991
FIG . 7. Fractional overlaps of original/
modeled cell pairs using least, intermediate,
and greatest smoothing.
DISCUSSION
Adequacy of the model
For most purposes, this first-order model should be an
adequate simulation of ‘‘average’’ dorsal horn cells’ RFs
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and their variation with location in the map of the hindlimb. The simple elliptical approximation of RFs is good
enough, for example, so that simulations of the spatial
distribution of cells responding to tactile stimuli is in good
agreement with the spatial distributions based on real data.
Insofar as the model is based on actual distributions of
cells rather than a potentially biased distribution of sampled cells ( e.g., due to surface blood vessel patterns ) , the
simulated distributions of responding cells actually may
be more realistic than that deduced directly from the sample of observed cells.
There are, however, some known sources of error that
might produce artifactual results in simulations of spatial
patterns of responding cells. First, not all interanimal variation has been eliminated. Ideally, the representation of an
‘‘average’’ animal’s map should include the average withinanimal variation but should exclude interanimal variations.
We have eliminated some of the interanimal variation due
to pre- and postfixation by shifting data from individual
animals, but we have not eliminated variation that cannot
be compensated for by shifting. In principle, this could be
done with appropriate analysis of variance. Our initial analysis (Koerber et al. 1993) indicates that intra-animal variation
is about one-third of the total variance measured in data
combined across animals, so this could have a significant
effect.
Our samples of the most rostral and caudal segments with
very proximal hindlimb input are not yet adequate for modeling. This deficit can be remedied by more extensive sampling
in these segments. In the meantime, conclusions about the
spatial patterns of cells activated by stimulation of the proximal leg only should be accepted tentatively.
Although elliptical approximations have a fractional
overlap of 0.9 with the original RFs, it may be that in
some applications a higher approximation is required. In
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representation. To test this concept with regard to the dorsal
horn representation, we simulated two-point stimuli on the
leg and the corresponding representations (Fig. 13). Stimuli
were placed on the plantar foot and posterior knee; twopoint stimuli were compared with separate presentations of
the two points for pairs with distoproximal and mediolateral
orientations. The feature preservation hypothesis would predict different single-zone responses for the two points presented separately and a combination resulting in two discernible zones of responses when the pair is presented simultaneously. This was not the case for any of the four stimulus
pairs, even though paired stimulus representations were always recognizable as composites of the representations of
individual point stimuli.
The surprising conclusion is that a discrimination mechanism operating on the representations of Fig. 13 could not
use a peak detecting procedure to determine whether one or
two points is (are) being stimulated. Many one-point stimuli
give rise to multiple zones of discharge, (e.g., medial point
on foot, medial and lateral points on knee, distal point on
foot, proximal and distal points on knee), and addition of a
second point does not result in the addition of a new zone
or fragmentation of an old response zone. In fact, two-point
representations sometimes appear more continuous than single-point ones (e.g., medial / lateral vs. medial foot) or
very similar to one of the single point representations (e.g.,
medial / lateral vs. lateral knee). We must conclude that
insufficient information about the structure of the stimulus
is preserved in the simulated spatial representation for such
a discrimination mechanism to work.
992
BROWN, MILLECCHIA, LAWSON, STEPHENS, HARTON, AND CULBERSON
that case, additional RF descriptors will be required, such
as curvature of the principal axis of the ellipse or shifting
of the center of the minor axis away from the center of
the major axis.
One clear source of potential error is the presence of covariation of RF parameters. The L/W, A, and D tend to
covary, so independent simulation of their variances could
introduce more scatter in the geometries of RFs than actually
exists. A covariance model would be needed to compensate
for such effects.
This model does not include dynamic factors such as
differences of discharge pattern ( including rate ) evoked
by stimulating different parts of a cell’s RF, inhibitory
portions of RFs, or spatial interactions. Although there
is little doubt that such factors are important in spatial
discriminations ( e.g., Johnson and Phillips 1981; LaMotte
and Srinavasan 1993; Loomis 1979; Wheat et al. 1995 ) ,
our first objective is to study the adequacy of classical
place coding for such discriminations. Any inadequacies
in a simple place code would suggest either that other
types of representation are involved or that the dorsal
horn does not have an adequate representation for some
discriminations.
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Multiple zones of response to single-point stimuli
A large fraction of the single-point stimulus simulations
produced multiple response zones in the dorsal horn. We do
not believe that this implies multiple maps of the skin because of the orderly migration of response zones as circumferential stimuli are moved up the leg. The most obvious
cause of such fractionation is the discontinuity required to
represent a closed surface (the skin) on an open surface
(the horizontal plane of the dorsal horn). The discontinuity
appears to approximate the boundary between pre- and postaxial skin (viz., Brown et al. 1992). Individual dorsal horn
cell RFs overlap the axial line, both in the pre- and postaxial
portions of the skin representation. Therefore it is necessary
for substantial projections of preaxial skin near the axial line
into postaxial areas of the map and for some postaxial skin
to project into preaxial map. This should be discernible in
axonal marking studies. Although it is evident in the projections of some cutaneous nerves (Koerber and Brown 1980,
1982), there are no reports of two-part projections of individual axons (Brown et al. 1977, 1978, 1980, 1981). This
may mean that the discontinuity is bridged by postsynaptic
axons or axonal marking methods have not been adequate
to reveal existing two-part projections.
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FIG . 8. L/W and A as a function of location on the leg for original and simulated cells. A: original unsmoothed L/W .
B: original smoothed L/W . C: simulated unsmoothed L/W . D: simulated smoothed L/W . E: original unsmoothed A. F:
original smoothed A. G: simulated unsmoothed A. H: simulated smoothed A.
DORSAL HORN PLACE CODING OF SIMPLE STIMULI
993
2. Fractional overlap of cell representations from
stimulating 5-cm bands of skin
TABLE
Distances From Tips of Toes, cm
0
7
14
21
0
7
14
21
1.00
00.06
00.62
00.53
00.06
1.00
0.18
00.37
00.62
0.18
1.00
0.49
00.53
00.37
0.49
1.00
Fractional overlap of dorsal horn representations of simulated stimulation
of 5-cm bands of skin, corresponding to the simulations of Fig. 7.
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Although the single-point stimuli that give rise to clearly
separated pre- and postaxial responses are most commonly
near the axial line, there are other, smaller clusters and voids
in the response patterns that may be due to experimental
errors in localization of cells in the dorsal horn (including
recordings from dorsal horn cell axons) or RFs on the skin
or that may represent real anomalies. A larger sample might
reveal that such ‘‘anomalies’’ are more ubiquitous than these
data suggest, in which case they should simply be considered
part of the normal variation of somatotopy.
The multiple patches of cells activated by some small
stimuli and the small changes produced by the introduction
of a second punctate stimulus suggest that a literal interpretation of one model of two-point discrimination, where the
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FIG . 9. Simulated spatial distributions of responding cells activated by simulated annular stimuli applied at different
distances from tips of toes. In each portion of the figure, the 4 dorsal views at the left represent densities of responding cells
based on original data, least smoothing, intermediate, and greatest smoothing ( left to right). Unfolded skin representation at
right depicts simulated stimulus location. Each dorsal view is autoscaled to the same maximum; pseudocolor scale at right
indicates range of colors from minimum to maximum.
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DORSAL HORN PLACE CODING OF SIMPLE STIMULI
3. Stimulus locations for the 32 standard stimulation
sites of Fig. 12 and the numbers of responding cells using the
intermediate smoothing
TABLE
Xmin
Xmax
Ymin
Ymax
Responding
Cells
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
70
82
93
103
114
127
139
149
78
100
121
141
94
104
121
137
84
104
122
138
63
98
121
146
36
82
121
160
24
77
129
191
72
84
95
105
116
129
141
151
80
102
123
143
96
106
123
139
86
106
124
140
65
100
123
148
38
84
123
162
26
79
131
193
5
7
8
9
7
6
7
7
24
24
25
25
58
58
59
60
99
99
99
99
142
142
141
142
184
183
182
180
242
242
242
241
7
9
10
11
9
8
9
9
26
26
27
27
60
60
61
62
101
101
101
101
144
144
143
144
186
185
184
182
244
244
244
243
498
1,548
3,004
4,989
6,308
4,913
2,558
1,293
1,025
5,272
8,997
4,265
4,413
8,166
10,990
7,013
5,754
9,676
9,198
4,900
4,199
7,667
5,182
1,319
2,774
4,802
2,366
341
1,270
2,192
552
30
Xmin and Xmax and Ymin and Ymax are in millimeters.
CNS detects two clusters of responding cells (Mountcastle
and Darian-Smith 1968), is not tenable, especially if such
fragmentation exists in other somatosensory nuclei. However, the CNS still could perform two-point discriminations
if a ‘‘same/different’’ judgment is made regarding distributions of cells responding to a one-point standard versus a
two-point comparison stimulus or if a mechanism exists for
construction of a central representation in which features
such as numbers of stimulus points are well preserved. Thus
the CNS could judge whether there is a significant difference
in the distribution of responding cells engaged by one or
two points: such a difference measure presumably would
increase with distance between points, as the sets of cells
activated by standard and comparison stimuli diverged.
Application of the model to studies of discrimination
A long-standing interest regarding the function of the dorsal horn concerns the extent to which it contributes to spatial
tactile discriminations such as localization and two-point
discrimination (e.g., Noordenbos and Wall 1976; Vierck
1973, 1977). This can be broken down into two questions:
what is the representation of stimuli in the dorsal horn and
what use is made of this representation by the nervous system in performing discriminations? We have begun to address the first question in this account so as to address the
second question in later studies.
We are interested initially in studying the neural correlates
of localization and two-point discrimination, two elementary
discriminations that have been tested in a variety of lesioned
preparations and in human (e.g., Adani et al. 1994; Brown
et al. 1989; DeMaio-Feldman 1996; Fuchs and Brown 1984;
Keunen and Slooff 1983; Kim and Choi-Kwon 1996; Matsen
et al. 1986; McCracken 1975; Ogunro 1984; Poppen et al.
1979; Shimokata and Kuzuya 1995; Song et al. 1993; Van
Boven and Johnson 1994; Wilson and Wilson 1967). It classically has been supposed that the primary representation of
stimulus location and shape is the spatial pattern of neurons
driven to discharge (place code). Our results indicate that
the assumption that the spatial representation of even simple
stimuli, however, is not necessarily a simple transformation
of the stimulus pattern. It is therefore likely that we cannot
perform simulated discriminations such as two-point discrimination by looking for features in the representation that
mirror similar features of the stimulus, such as presence of
two peaks of activity corresponding to two discrete stimulated points. However, we can ask whether there is a quantitative relation between the performance of subjects asked to
make same/different judgments about two stimuli and the
degree of similarity of the spatial representations evoked by
the two stimuli.
Application of the first-order model to studies of
development and plasticity
We have proposed a developmental model that is amenable to quantitative testing (Brown et al. 1997). Among its
other features, this model postulates invariant divergence/
convergence ratios for the connections of primary afferent
to dorsal horn cells. Recent quantitative analyses have supported this postulate for annular rings of skin 1 cm in proximodistal length for the full length of the leg (Wang et al.
1997). In these analyses, we showed that the calculated
ratio of map scale to innervation density was invariant for
different D. We proposed that initial (‘‘prototype’’) RFs are
formed during the initial ingrowth of peripheral axons and
that these prototype RFs then are modified to some unknown
extent by further ramification of afferent axons, activitydependent competitive mechanisms, and such sculpting influences as pre- and postsynaptic inhibition. We also suggested that the map scale and geometries of prototype RFs
at any level of the dorsal horn are determined by the distribution of afferent input available through axons growing into
the gray matter at that level. It soon will be possible to
model the prototype RF formation once we have determined
afferent input densities (analogous to innervation densities)
of primary axons growing in at different rostrocaudal levels
FIG . 10. Simulated responses to 2 1 2 mm stimuli applied at 32 standard locations on the hindlimb. In each portion of
the figure, the dorsal view is the modeled response obtained with intermediate smoothing, and the unfolded drawing represents
the stimulus location (stimulus enlarged for visibility). Each portion of the figure is autoscaled; pseudocolor scale at right.
The illustrated stimuli are enlarged for easier visibility.
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Site No.
995
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BROWN, MILLECCHIA, LAWSON, STEPHENS, HARTON, AND CULBERSON
in the adult. These prototype RFs then can be compared
statistically [e.g., using the distributed t-test, which we recently have validated (Brown and Millecchia 1997b)] with
the model developed here to determine the magnitude of
changes that would be necessary to go from the predicted
prototype RFs to the adult RFs.
It is striking that no strong theories of the mechanisms
underlying plastic change in the dorsal horn have been established. One reason may be the lack of agreement concerning
the sorts of changes that occur as result of such maneuvers as
partial deafferentation, spinal transection, and spinal injury.
Another may be the lack of good quantitative methods of
describing changes that do occur and the absence of a model
of the normal organization of the dorsal horn. Such a model
now exists, and appropriate statistical methods are now
available (Brown and Millecchia 1997b). The only requirement for quantitative descriptions of changes of somatotopy
and dorsal horn RF geometries is a sample of perhaps 500
neurons from an appropriate animal model with at least half
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a dozen cells recorded from the normal side of the spinal
cord in each animal to shift data into register across animals.
Such quantitative descriptions are essential before we can
pose testable hypotheses about changes occurring during reorganization.
Implications for spatial discriminations based on place
code
The most startling conclusion from this simulation study
is that the classical place code isn’t much good for discrimination of numbers of stimuli placed on the skin. The assumption that spatial features of the stimulus are reflected accurately in corresponding features of the representation is not
correct. Localization, size (area) discrimination, and twopoint discrimination all would be served poorly by a discrimination mechanism that performs feature detection on the
spatial representation.
It can be argued that somatotopic organization is not re-
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FIG . 11. Simulated variation of stimulus size (area of skin contacted). Columns, left to right: plantar foot, posterior calf,
posterior thigh. Rows, top to bottom: 0.5 1 0.5 mm, 1 1 1 mm, 2 1 2 mm, 5 1 5 mm. Figurines are scaled so stimulus is
shown same size in each simulation, and leg drawing is scaled to fit stimulus.
DORSAL HORN PLACE CODING OF SIMPLE STIMULI
997
FIG . 12. Log-log plot of representation
size (number of responding cells) as a
function of stimulus size (area of skin contacted) for the simulations of Fig. 14. Separate curves for stimulus/response relationships for foot, calf, and thigh.
strating that feature preservation in the somatotopic map of
the skin is not adequate for spatial discriminations known
to be subserved by the dorsal horn. It would be of great
interest to know whether this is the case for other somatosensory nuclei; we are inclined to suspect that it is, given the
similarities of somatotopic organization and RF geometries.
The lack of feature preservation in the spatial patterns of
discharge evoked by simulated cutaneous stimuli does not,
of course, preclude a role for a dorsal horn place code in
spatial discriminations. The dorsal horn cell spatial patterns
of discharge must contain the information necessary for
higher somatosensory nuclei to perform spatial discrimina-
FIG . 13. Comparison of representations of simulated 1- and 2-point stimuli. Rows, top to bottom:
plantar foot mediolateral orientation of stimulus
pair; posterior knee, mediolateral orientation of stimulus pair; plantar foot, proximodistal orientation of
stimulus pair; posterior knee, proximodistal orientation of stimulus pair. Columns, left to right: single
stimulus, lateral or distal of pair; single stimulus,
medial or proximal of pair; both stimuli combined.
Each dorsal horn representation is autoscaled.
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quired for representation of the spatial features of tactile
stimuli. This is verified easily by a simple thought experiment: shuffle the locations of cells in a somatotopic map
without changing any of their afferent or efferent connections. Because all the cells still have the same connections,
they will have the same RFs and the same projections, so
their function will not be altered, in spite of the fact that their
spatial organization has been changed from somatotopic to
random. We have suggested, instead (Brown et al. 1991,
1997), that somatotopic organization is a remnant of developmental processes responsible for the formation of concise
RFs. The results of this investigation go further by demon-
998
BROWN, MILLECCHIA, LAWSON, STEPHENS, HARTON, AND CULBERSON
tions because cats and humans with dorsal column sections
still can perform such discriminations. An alternative worth
investigating is the possibility that the central representation
actually used for discrimination is an aggregate of the RFs
of cells activated by a stimulus, which we have called the
referred representation (Brown and Millecchia 1997a).
This work was supported by National Institute of Neurological Disorders
and Stroke Grant 1 R01 NS-29997.
Address reprint requests to P. B. Brown.
Received 15 July 1997; accepted in final form 14 October 1997.
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