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The Journal of Neuroscience, January 1, 1999, 19(1):401-419
Velocity Invariance of Receptive Field Structure in Somatosensory
Cortical Area 3b of the Alert Monkey
James J.
DiCarlo and
Kenneth O.
Johnson
Krieger Mind/Brain Institute, Departments of Neuroscience and
Biomedical Engineering, Johns Hopkins University, Baltimore, Maryland
21218
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ABSTRACT |
This is the second in a series of studies of the neural
representation of tactile spatial form in cortical area 3b of the alert
monkey. We previously studied the spatial structure of 330 area 3b
neuronal receptive fields (RFs) on the fingerpad with random dot
patterns scanned at one velocity (40 mm/sec; DiCarlo et al., 1998 ).
Here, we analyze the temporal structure of 84 neuronal RFs by studying
their spatial structure at three scanning velocities (20, 40, and 80 mm/sec). As in the previous study, most RFs contained a single,
central, excitatory region and one or more surrounding or flanking
inhibitory regions. The mean time delay between skin stimulation and
its excitatory effect was 15.5 msec. Except for differences in mean
rate, each neuron's response and the spatial structure of its RF were
essentially unaffected by scanning velocity. This is the expected
outcome when excitatory and inhibitory effects are brief and
synchronous. However, that interpretation is consistent neither with
the reported timing of excitation and inhibition in somatosensory
cortex nor with the third study in this series, which investigates the
effect of scanning direction and shows that one component of inhibition
lags behind excitation. We reconcile these observations by showing that
overlapping (in-field) inhibition delayed relative to excitation can
produce RF spatial structure that is unaffected by changes in scanning
velocity. Regardless of the mechanisms, the velocity invariance of area
3b RF structure is consistent with the velocity invariance of tactile
spatial perception (e.g., roughness estimation and form recognition).
Key words:
receptive field; somatosensory; cortex; area 3b; SI; tactile; velocity; monkey; reverse correlation
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INTRODUCTION |
The study reported here concerns the
temporal and spatial response properties of neurons in area 3b of
primary somatosensory cortex. Previous studies of area 3b have shown
that each point in a neuron's cutaneous receptive field (RF) may give
rise to excitation, inhibition, or both (Mountcastle and Powell, 1959; Laskin and Spencer, 1979; Gardner and Costanzo, 1980b,c; DiCarlo et
al., 1998), that there is a delay between the cutaneous stimulus and
the response (Mountcastle and Powell, 1959; Laskin and Spencer, 1979;
Gardner and Costanzo, 1980a), that the excitatory and inhibitory effects may persist for variable periods (Laskin and Spencer, 1979;
Gardner and Costanzo, 1980b), and that the timing of excitation and
inhibition arising from a single cutaneous site may be different (Laskin and Spencer, 1979; Gardner and Costanzo, 1980b). Thus, area 3b
RFs have temporal, as well as spatial structure. Although the precise
relationship between the spatial and temporal parameters of a neuron's
response and the RF estimated with a scanned stimulus is complex (see
Appendix ), the general effects of temporal delay between the stimulus
and response are as follows. Because we do not initially know the delay
between the stimulus and each response component, our RF estimation
procedure assigns each response component to the stimulus location at
the time the response occurred. Thus, the location of delayed
excitation or inhibition in the estimated RF is displaced in the
scanning direction from its true location by a distance proportional to
the delay and the scanning velocity. If there is a difference in delay
between two components of the RF, the result is differential
displacement in the scanning direction that is proportional to the
scanning velocity. Similarly, a persistent temporal effect (excitatory
or inhibitory) appears as a spatial effect spread out in the scanning
direction over a distance proportional to the persistence and the
scanning velocity. Thus, both scanning velocity and scanning direction
are tools for investigating the temporal components in the neural
response. The effects of scanning velocity are reported in this paper;
the effects of scanning direction have been studied and will be
reported in a future paper.
Random dot patterns were scanned across the RFs of 84 area 3b neurons
at 20, 40, and 80 mm/sec. Although the mean firing rate usually
increased with increasing scanning velocity, the spatial patterning of
the neural responses and the RFs inferred from those responses were
almost completely unaffected by these changes in scanning velocity.
Although this result is not inconsistent with a brief temporal delay
between excitatory and inhibitory effects (see Discussion), it shows
that area 3b RFs are best described as spatial, rather than temporal,
filters and that the neural representation of tactile spatial stimuli
in area 3b (i.e., the population pattern of neural activity)
is largely insensitive to changes in scanning velocity. The responses
of a small sample of peripheral slowly adapting (SA1) and rapidly
adapting (RA) afferents to the same stimuli used in the cortical
studies show that part but not all of the inhibition in the area 3b RFs
might result from the response properties of SA1 afferents.
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MATERIALS AND METHODS |
Animals and surgery. Two male and one female rhesus
monkeys (Macaca mulatta) weighing 4-5 kg were used to study
the RF properties of neurons in area 3b. The effect of changes in
scanning velocity presented here came from the last monkey in the
series, a female weighing 5 kg. The animal was trained to perform a
visual detection task during the presentation of tactile stimuli, which
served to maintain the animal in a constant, alert state during
recording periods. After the animal was performing the task nearly
perfectly, which took a few weeks, surgery was performed to attach a
head-holding device and recording chamber to the skull. Surgical
anesthesia was induced with ketamine HCl (33 mg/kg, i.m.) and
maintained with pentobarbital (10 mg · kg 1 · hr1,
i.v.). All surgical procedures were done under sterile conditions and
in accordance with the guidelines of the Johns Hopkins Animal Care and
Use Committee and the Society for Neuroscience.
Recording. Electrophysiological recordings and histological
reconstruction of the recording sites were done using techniques described previously (DiCarlo et al., 1998). Briefly, we recorded from
neurons located in area 3b using a multielectrode microdrive (Mountcastle et al., 1991) loaded with seven quartz-coated
platinum/tungsten (90/10) electrodes (diameter, 80 µm; tip diameter,
4 µm; impedance, 1-5 M at 1000 Hz). Each electrode was coated
with one of three fluorescent dyes (DiI, DiI-C5, or DiO), which were
used later to identify the recording locations (DiCarlo et al., 1996).
A continuous record of stimulus location and the times of occurrences of action potentials, stimulus events, and behavioral events were stored in a computer with an accuracy of 0.1 msec (Johnson and Phillips, 1988). All neurons in area 3b that met the following criteria
were studied using the stimulus procedures described below: (1) the
neuron's action potentials were well isolated from the noise; (2) the
neural RF was located on one of the distal fingerpads (digits 2-5);
and (3) the stimulus drum and the hand (see below) could be positioned
so that the RF was centered on the portion of the fingerpad in contact
with the stimulus.
Stimuli. The stimulus pattern was an array of embossed dots
within a rectangular region 28 mm wide and 175 mm long (for details, see DiCarlo et al., 1998). Four hundred ninety dots were distributed randomly within this rectangular region with an average density of 10 dots/cm2. Each dot was 400 µm in height (relief
from the surface) and 500 µm in diameter at its top; its sides sloped
away at 60° relative to the surface of the stimulus pattern.
The dot pattern was wrapped around and glued to a cylindrical drum, 320 mm in circumference, which was mounted on a rotating drum stimulator
(Johnson and Phillips, 1988) (Fig. 1).
Random dot patterns are unbiased in the sense that all possible
patterns with the specified dot density are equally likely and the
probability of a repeated pattern is virtually zero.
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Figure 1.
Drum stimulator. The stimulus pattern consisted of
a field (28 mm wide × 175 mm long) of randomly distributed,
raised dots on a plastic surface, mounted on the surface of a drum, 320 mm in circumference. The dot pattern stimulated the skin through a thin
latex sheet positioned over the distal fingerpad that contained the
neural RF. The latex intermediate was tethered to a circular aperture
in a Mylar sheet supported by a Plexiglas frame. The hand and finger
were held fixed from below and the intermediate contacted the fingerpad
with a force of 10 gm. The purpose of the intermediate latex sheet was
to minimize lateral skin movement caused by tangential, frictional
forces between the surface and the skin; as a further precaution, these
forces were minimized by lubricating the pattern surface with glycerin.
The drum rotated with controlled normal force (30 gm), producing
surface pattern motion from proximal to distal over the fingerpad. The
scanning velocity was fixed at 20, 40, or 80 mm/sec for each scan
through the random dot pattern. After three drum rotations (one at each
scanning velocity), the drum was translated by 400 µm along its axis
of rotation. The data entering into the RF estimates were derived, on
average, from 25 scans at each velocity, which corresponded to 10 mm of
translation.
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After one or more neurons with overlapping RF locations were isolated
with one or more electrodes, the drum with the random dot pattern was
positioned over the fingerpad so that all the RFs were located in the
cutaneous region contacting the drum surface. The drum was rotated so
that the stimulus pattern was scanned in the proximal to distal
direction with a contact force of 30 gm (Johnson and Phillips,
1988). Scanning velocity was controlled by a direct-drive servomotor,
which could switch between the three velocities used in this study (20, 40, and 80 mm/sec) within 25 msec. The drum was positioned initially so
that the cutaneous contact region was wholly within the random dot
pattern and the center of the contact region was ~5 mm from the edge
of the long side of the pattern.
Before applying the drum stimulator to the fingerpad, a thin latex
sheet (Carter-Wallace, Cranbury, NJ) was positioned over the pad, and
glycerin was applied to the dot pattern to eliminate friction between
the pattern and the latex. The latex sheet was tethered in all
directions by gluing its edges to a 20-mm-diameter aperture in the
center of a thin (6 µm), 10 × 10 cm Mylar sheet (DuPont,
Wilmington, DE). The Mylar sheet was supported by a square Plexiglas
frame positioned horizontally over the fingerpad (Fig. 1). The frame
was lowered with a micrometer until the latex sheet contacted the skin
region containing the neural RFs with a normal force of 10 gm. The
purpose of the Mylar sheet, which was essentially inextensible, was to
prevent horizontal skin displacement when the scanning direction
changed. The thin latex intermediate allowed transmission of the
stimulus features to the skin. Control studies showed that the firing
rates, response structures, and RFs of most area 3b neurons were
unaffected by the presence of the latex intermediate (J. J. DiCarlo and K. O. Johnson, unpublished observations). The
Mylar-latex sheet was not needed for this study because the stimuli
were all scanned in the proximal-to-distal direction, and the skin of
the distal pad is anchored securely at the crease between the second
and third phalanges. It was used so the stimulus conditions would be
identical to those in a separate study in which scanning direction was varied.
To determine the effect of scanning velocity on the responses and the
RF of each neuron, the random dot pattern was scanned at 20, 40, and 80 mm/sec at each drum position. After the third scan the pattern was
stepped 400 µm in the direction orthogonal to the scanning direction
(i.e., along the drum's axis of rotation; see Fig. 1). To keep the
total recording time to a reasonable period (~15 min), the drum was
typically stepped over a distance of 10 mm (i.e., 25 steps). For some
neurons, the velocity sequence (20, 40, and 80 mm/sec) was repeated
(i.e., six drum revolutions at the same horizontal position) before
making the 400 µm step to the next horizontal position. The change
from one velocity to the next occurred over a scanning distance of 2 mm
at most and was always effected midway in the portion of the drum
surface (145 mm of the 320 mm total drum circumference) that did not
contain the random dot pattern. Two hundred marker impulses triggered at fixed, equal angular increments around the drum hub were used to
determine the stimulus position relative to the occurrence of each
action potential with an accuracy of 8 µm or better (Johnson and
Phillips, 1988).
Responses. The interleaved data segments collected at 20, 40, and 80 mm/sec from each neuron were divided into three data sets,
where each set was the response to the same pattern area (typically
10 × 175 mm) at a different scanning velocity. Within each of
these three data sets, the action potentials were assigned two-dimensional (x,y) locations relative to the
drum surface (Johnson and Phillips, 1988). The x location
(distance in the scanning direction from the beginning of the random
dot pattern) was determined by a digital shaft encoder. The
y location was determined by the axial (horizontal) position
of the drum. Each of the three resulting spatial rasters is referred to
as a spatial event plot (SEP). For example, Figure 3 shows SEPs of the
three data sets collected from a single area 3b neuron.
Receptive field estimation. The pattern of firing evoked by
the random dot stimulus at each scanning velocity was used to infer the
two-dimensional pattern of RF excitation and inhibition on the skin
surface (i.e., three RF estimates from each neuron). The details of the
implementation are specified in our previous paper (DiCarlo et al.,
1998). Here, we discuss the key theoretical features of the
method and the reasons for adopting them. The broad outline is as
follows: We use standard methods of multivariate regression (Draper and
Smith, 1998) with a modification to account for the neuron's threshold
nonlinearity (inability to produce negative spike rates). The first
step, which arises from the application of standard regression methods,
is reverse correlation (stacking and averaging spike-triggered
snapshots of the stimulus). However, stimulus autocorrelation distorts
the RF obtained by this operation. Correction for this distortion is
the purpose of the remaining steps of multivariate regression (solution
of the normal equations). When the method stops after this step
(reverse correlation) stimulus designs that minimize autocorrelation
(e.g., white noise stimuli and M-sequences) are critical. When the
method is carried to completion an unbiased estimate of the RF can be
obtained from any stimulus as long as the dimensions of the space
spanned by the stimuli exceed the number of RF parameters being
estimated. The details as they apply in our study follow.
To describe the RF on the skin surface, we assumed that each small
region of skin had a positive, negative, or zero effect on the firing
rate when stimulated and that the instantaneous firing rate was equal
to the sum of these effects. We subdivided a 10 × 10 mm square
region of skin containing the RF into a grid of 625 (25 × 25)
subregions, each 400 × 400 µm square. Multiple regression seeks
the 625 positive (excitatory) and negative (inhibitory) values that,
when convolved with the stimulus pattern, produce the best (least
squared error) approximation to the observed firing rates.
The regression method has three parts. The first involves the standard,
universal steps in formulating a multivariate model of a complex
process. When there are insufficient data to construct a mechanistic
model (which in this instance would be a model of the primary
afferents, dorsal column nucleus, thalamic, and cortical circuitry
underlying the responses we have observed), a widely used strategy for
estimating complex input-output relationships is to use a stepwise,
multivariate polynomial approximation (Marmarelis and Marmarelis,
1978). This approach starts with a linear model and successively adds
higher-order interactions when they yield a significantly improved fit
to the data (Draper and Smith, 1998). We showed in a previous paper
that the first, linear step in this process accounts for 10-75% of
the explainable response variance in area 3b neurons (DiCarlo et al.,
1998). We have not included nonlinear terms in the RF model because
they are generally not easily interpreted. The linear RF model that we
have adopted,
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(1)
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approximates the response at all times, t, by a
constant term, b0, and the sum of the
stimulus effects, xi(t), at 625 subregions, which taken together span a skin region larger than any
fingerpad RF that we have encountered in area 3b. The constants
b1 to b625 are zero when
they represent locations where stimuli have no linear (additive or
subtractive) effect on the response, positive at locations where
stimuli produce (on average) an increase in firing rate, and negative
at locations where stimuli produce a decrease in firing rate. The
number of responses required for an adequate solution is larger than
the number of unknown parameters (n = 626). Our
stimulus procedure produces a response histogram with ~20,000
responses (i.e., 20,000 bins). This yields 20,000 equations like the
one above, which can be expressed as a matrix equation:
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(2)
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where X is the stimulus matrix (20,000 × 626),
b is the vector of RF values (626 × 1), and
rlinear is the predicted impulse rate at each
time bin (20,000 × 1). Each row of X is a complete
representation of the stimulus (within the 10 × 10 mm region
specified above) at one time point.
The second step of the regression procedure, which we call zero
removal, accounts for the fact that neurons cannot produce negative
firing rates. If stimuli fall exclusively within the inhibitory part of
the receptive field, the correct model will predict a large negative
synaptic drive (i.e., a large negative rlinear
value) but will be penalized for doing so if this negative drive is
compared in a least squares manner with the observed impulse rate under
those conditions (zero rate). To avoid this, we remove all the
equations (rows of matrix Eq. 2) where an extended interval of zero
firing indicates that the neuron is inhibited. A neural net with a
thresholded activation function effectively does the same thing
(Johnson et al., 1995). We used the multivariate regression procedure
modified by zero removal because of its extensive theoretical
foundations and the error analysis that it allows (Draper and Smith,
1998).
The third step of the regression procedure solves for the RF. It begins
with reverse correlation and then corrects the result for the effects
of stimulus autocorrelation. The RF parameters, b, that
yield the best (in the least squared sense) approximation, rlinear, to the observed responses,
robserved, is obtained by solving the normal
equation (Draper and Smith, 1998):
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(3)
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The matrix operations effected on the right side of this
equation,
XTrobserved, are
the operations of reverse correlation (de Boer and Kuyper, 1968; Jones
and Palmer, 1987). The vector of 625 RF weights (plus a constant to
account for the mean rate) that this operation produces is the sum of
the stimulus snapshots (within the 10 × 10 mm region around the
RF) when action potentials occurred. The matrix product
XTX is the stimulus
autocorrelation matrix: each matrix element is the correlation between
stimulus values at two locations in the RF. Consequently, the matrix
product on the left side of the equation,
(XTX)b, is the
convolution of the RF (i.e., b) with the stimulus
autocorrelation function. Therefore, it can be seen that reverse
correlation produces an estimate not of the RF but rather of the RF
convolved with the stimulus autocorrelation function. Reverse
correlation yields an uncontaminated (i.e., least squares) estimate of
the RF only if the stimulus autocorrelation matrix is the identity
matrix (i.e., the stimulus pattern within the RF estimation grid is
uncorrelated with itself at all displacements). The standard regression
method, which we have used, determines the best estimate of the RF in
the general case by deconvolving the stimulus autocorrelation function
and the result of reverse correlation:
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(4)
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In our case the stimulus pattern was obtained with a random
number generator so that the pattern elements would be independent of
one another at all displacements and that the off-diagonal terms of the
autocorrelation matrix would be small. Therefore, the RFs that we
display are not very different from those obtained with reverse
correlation. However, that is no reason to forgo the deconvolution
step. Every pattern obtained by random sampling is autocorrelated to
some degree. Even stimulus sequences such as white-noise stimuli and
M-sequences (Sutter, 1987) designed to minimize autocorrelation have
some residual autocorrelation (Victor, 1992). The deconvolution step
eliminates the concern that correlation in the stimulus may have
affected the outcome. Furthermore, the deconvolution step allows a
least squared error solution for any stimulus. Insofar as RF estimation
is concerned, the only constraint on stimulus selection is the
robustness of the stimulus autocorrelation matrix (Golub and Van Loan,
1989).
A final small but very important aspect of our method, which we used in
our previous study (DiCarlo et al., 1998) as well as the current study,
is the use of singular value decomposition (SVD) for the deconvolution
(Golub and Van Loan, 1989). SVD provides a detailed description of the
stimulus autocorrelation structure (i.e., its eigenvalues and
eigenvectors). Because the deconvolution involves division by the
eigenvalues of the stimulus autocorrelation function, the magnitude of
those eigenvalues is critical. If any are near zero, they inordinately
amplify errors in the RF resulting from noise or distortion in the
response. In the SVD method those components can often be removed
before solution to minimize distortion. In our case, the ratio of
largest to smallest eigenvalues was 11.0, which is indicative of a
robust RF solution (Golub and Van Loan, 1989), and no components of the
deconvolution were removed.
Response alignment and measurement of temporal delays.
Because there is an (initially) unknown delay between the stimulus and
the neural response, alignment of the stimulus and the response is an
issue; however, exact alignment between the stimulus pattern and the
neural response is not critical. If the RF is estimated at two
different alignments, the same RF weight pattern emerges, except that
the pattern of excitatory and inhibitory weights is shifted within the
10 × 10 mm grid to reflect the difference in alignments. The
important consideration is that the entire RF fit within the 10 × 10 mm grid. In this study, the alignment was adjusted so the center of
excitation at 40 mm/sec was located at the center of the 10 × 10 grid. The same alignment was used to estimate the RFs at 20, 40, and 80 mm/sec. The conduction delay between skin stimulation and each RF
component produces an apparent displacement of each RF component in the
scanning direction that is proportional to the delay and the scanning
velocity (see Appendix ). Because the scanning velocities are known,
the delay can be estimated. The RF components estimated at 80 mm/sec
will all be displaced in the scanning direction (to the left in the RF
plots) relative to their position in the RF at 40 mm/sec; the RF
components at 20 mm/sec will be displaced to the right relative to
their position at 40 mm/sec. These relative displacements are used to
estimate the excitatory and inhibitory delays (see Fig. 8); they can be
seen on close inspection of the RFs in Figures 3-5.
The delays associated with the dominant RF regions of excitation and
inhibition were estimated by developing an objective method for
identifying their centers. This was done by constructing two circles
for each neuron, one for the excitatory region and one for the
inhibitory region, and finding the locations in the RF that included
the most excitation and inhibition. For excitation, the circle used to
find the center of excitation had a radius proportional to the square
root of the excitatory area (Ae):
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(5)
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The excitatory portion of the RF rarely involved more than a
single region and was generally circular or elliptical (DiCarlo et al.,
1998). The circle described by this radius
(re) typically encompassed one-third to
one-half the total excitatory area depending on its eccentricity.
Because the inhibitory regions were usually less concentrated, a
slightly different algorithm was used to determine the appropriate
radius. When inhibitory RF areas were less than ~15
mm2, they also consisted mainly of single compact
regions, and the same procedure worked well. However, inhibitory
regions with areas >15 mm2 tended to be more
elongated and often encompassed two or more sides of the excitatory
region (e.g., Figs. 3, 5E). When the region is more
elongated than circular, the radius required to encompass a constant
fraction of the total area grows linearly with area. So, we devised a
radius that grew as the square root of inhibitory area
(Ai) up to 15 mm2 and
then gradually tended toward proportionality:
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(6)
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These inhibitory radii captured 20-50% of the inhibitory
areas, depending on the shapes of the areas. The important point was to
include sufficient volume to locate the centers of the most intense
excitatory and inhibitory regions accurately while excluding the undue
influence of distant points. The same excitatory and inhibitory radii
(re and ri determined at
20 mm/sec) were used for RF estimates at all three velocities for each
neuron. The circle location enclosing the maximum excitatory (or
inhibitory) mass was determined by complete search of all positions in
each RF. Although the bin size of each RF was 400 × 400 µm, the
precision was increased by shifting the circle in 50 µm increments
(both directions) over the RF and including only the fraction of the mass in each bin that was within the circle.
Primary afferent recording. Recordings from primary
afferents were performed on anesthetized rhesus monkeys (M. mulatta) weighing 4-5 kg using standard methods (Mountcastle et
al., 1972). Single cutaneous mechanoreceptive fibers were dissected
from the median or ulnar nerves. Afferents were classified as SA1, RA,
or Pacinian on the basis of responses to indentation and vibration with
a point probe (Talbot et al., 1968). Only SA1 and RA afferents with RFs
located on one of the distal glabrous pads of digits 2-5 were studied.
All stimulus, data collection, and RF analysis methods were the same as
in the cortical experiments.
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RESULTS |
Eighty-four neurons in area 3b with RFs on a distal fingerpad were
studied with random dot patterns scanned from proximal to distal across
the fingerpad at 20, 40, and 80 mm/sec. These neurons were part of a
larger sample (330 neurons) studied at 40 mm/sec (DiCarlo et al.,
1998). A neuron with an RF located on one of the distal fingerpads was
excluded from the study only if the finger and the stimulator could not
be positioned to bring the RF, mapped with a manual probe, well within
the contact region between the skin and stimulus surface. Even neurons
that were marginally responsive to manual probing were studied with the idea that the random dot pattern might uncover responsiveness that was
not evident with simpler probing.
Average firing rate versus scanning velocity
Figure 2 shows the mean impulse
rates evoked by the random dot patterns at 20, 40, and 80 mm/sec. The
distribution of rates among neurons was broad, with mean impulse rates
varying by two orders of magnitude. In 90% of neurons, mean rates
increased with increasing velocity (arithmetic mean rates, 20.0, 24.3, and 28.0 impulses/sec (imp/sec); geometric mean rates, 11.5, 14.4, and 16.3 imp/sec at 20, 40, and 80 mm/sec, respectively; SD = 0.47 log10 units at all velocities). The slope of the log-log
relationship between mean firing rate and scanning velocity for each of
the 84 area 3b neurons is shown in the right panel of Figure 2. The mean slope is 0.252 (SD = 0.273), indicating that, on average, the
mean firing rate of area 3b neurons increased by 19% as the scanning
velocity doubled. With few exceptions, neurons with slopes <0 or >0.5
had response rates <10 imp/sec.
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Figure 2.
Effect of scanning velocity on firing rates. The
graph on the left shows the mean firing rate of each
area 3b neuron versus random dot scanning velocity. The graph on the
right shows velocity sensitivity versus overall mean
firing rate for individual neurons. The ordinate is the
log-log slope of mean impulse rate versus velocity (1.0 indicates a
linear, proportional relationship; 0.5, a square root relationship,
etc.). The abscissa is the geometric mean impulse rate
over all three velocities. Results from three primary afferent SA1
fibers (squares) and five primary afferent RA fibers
(triangles) are shown for comparison.
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The right panel of Figure 2 also shows the effect of scanning velocity
on the mean firing rates of three SA1 and five RA primary afferents for
comparison. Although the sample is small, the results are consistent
with previous studies (Johnson and Lamb, 1981; Lamb, 1983; Phillips et
al., 1992; Essick and Edin, 1995). The response rates of SA1 primary
afferents, like those of area 3b neurons, increased only slightly as
scanning velocity increased from 20 to 80 mm/sec (mean logarithmic
slope = 0.302; SD = 0.020). RA primary afferents were more
strongly affected by the same changes in scanning velocity (mean
logarithmic slope = 0.668; SD = 0.106). As shown in Figure 2,
the distribution of velocity effects on area 3b firing rates largely
overlaps the velocity effects on SA1 but not RA firing rates.
Typical responses and RFs versus scanning velocity
Figure 3 shows response rasters of a
typical area 3b neuron in the form of SEPs, where the horizontal axis
represents space rather than time. The stimulus pattern segment
illustrated in Figure 3 is ~40% of the whole pattern (75 mm segment
from the 175 mm pattern). Single sweeps across the pattern segment
shown in Figure 3 represent time periods of ~4, 2, and 1 sec at 20, 40, and 80 mm/sec, respectively. Although the impulse rate increased with increasing velocity, the increase was not enough to offset the
greatly decreased scan times over each pattern segment. This accounts
for the reduced spike density at higher velocities. Apart from this
change in spike density, the spatial structure of the response was very
similar across this fourfold change in scanning velocity, as can be
seen by close comparison of the three SEPs. RF estimates based on the
responses at the three scanning velocities are shown at the right sides
of the SEPs.
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Figure 3.
Effect of scanning velocity on the response and RF
of a single area 3b neuron. A portion of the random dot stimulus
pattern is shown at the top. Each dot
represents the location of a raised, truncated cone 400 µm in relief
and 500 µm in diameter at the top. Cone locations were determined by
a uniform, random number generator with a mean density of 10 dots/cm2. The stimulus autocorrelation in the
top right shows that there was no significant patterning
in the random dot locations (maximum correlation = 4.7% of center
peak). The stimulus pattern scanned from right to left across the
fingerpad. Responses at 20, 40, and 80 mm/sec are shown below the
stimulus. Each tick marks the occurrence of a single
action potential. The plotted position of each tick was determined by
the location of the stimulus pattern at the instant the spike occurred
(SEP). To the right is the RF determined from each SEP.
Each RF is the map (25 × 25 bins = 10 × 10 mm of skin
surface) of positive and negative weights that best describe (in a
least squares sense) the neuron's response at one scanning velocity
(see Materials and Methods). Black regions are positive
(excitatory); white regions are negative (inhibitory).
Each RF is plotted as if viewing the surface of the glabrous skin
through the back of the finger (i.e., from the neuron's point of view)
with the finger pointing to the left. Thus, the horizontal
axis, proceeding from right to
left in each RF plot, represents position along the
proximal-to-distal axis of the fingerpad (or increasing temporal
delay), and the vertical axis represents space along the
right-left axis of the finger as viewed through the back of the
finger. The RFs reveal that this neuron is most sensitive to stimuli
arranged in a slightly oblique, elongated region from NNE to SSW, and
that the neuron is inhibited by dot stimuli on either side of this
region. Examples of this stimulus selectivity are illustrated in the
boxes overlaid on the stimulus and response plots.
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The patterns of excitation and inhibition in the RFs at the three
scanning velocities illustrated in Figure 3, like the response patterns, are largely unaffected by changes in scanning
velocity. The three RF maps displayed in Figure 3 each reveal a
large, central, slightly oblique region of excitation flanked by two
regions of inhibition. In each RF map the excitatory and inhibitory
regions are ovoid with a slight, oblique (NNE to SSW) orientation. This indicates that the neuron should respond best to dots in slightly oblique clusters regardless of scanning velocity. As predicted, wherever a cluster of this kind occurs (by chance), the neuron fires
vigorously. The box in each SEP delineates the response to a region of
the random dot pattern that happens to have several such clusters.
Conversely, comparison of the stimulus pattern and the neural responses
shows that this neuron responds poorly or not at all to clusters in the
orthogonal (WNW to ESE) direction. Close inspection of this kind may
give the impression that the stimulus pattern happens to be dominated
by clusters of dots with a NNE to SSW orientation. However, this is not
so, as indicated by two-dimensional autocorrelation of this 75 mm
portion of the stimulus pattern, which is illustrated at the top right
corner of Figure 3, and by the responses of other neurons that respond to clusters in other orientations within the same stimulus pattern (Fig. 4).
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Figure 4.
Effect of scanning velocity on the response and RF
of a single area 3b neuron. See Figure 3. The RF of this neuron reveals
that it is most sensitive to dots arranged in an oblique, elongated
region from NW to SE. Examples of this stimulus selectivity are
illustrated in the boxes overlaid on the stimulus and
response plots.
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Figure 4 shows the responses of a neuron whose RF contains elongated
regions of excitation and inhibition with orientations almost
orthogonal to those of the previous example. Like the previous example,
the neuronal responses and the RF estimates are very similar at the
three scanning velocities. Unlike the previous example, the responses
correspond to dot clusters with a dominant orientation in the NW to SE direction.
Figure 5 shows the RFs of six other area
3b neurons estimated at the three scanning velocities. These RFs and
those shown in Figures 3 and 4 are typical examples of the effect of
velocity on the RFs of area 3b neurons. Changes in velocity had several effects, which can be seen in these RF plots and are analyzed below:
(1) the intensity of both excitation and inhibition increased with
increasing scanning velocity; (2) the intensity of inhibition increased
relative to excitation; and (3) the delay between the stimulus and the
arrival of excitation and inhibition produced a progressive distal
shift of the entire estimated RF location with increasing velocity.
However, in each example, as in the larger sample of 84 neurons, a
fourfold change in scanning velocity had no obvious effect on the
spatial pattern of excitation and inhibition. This subjective
assessment was supported by an analysis, which follows, of the pattern
of RF excitation and inhibition of a subset of neurons whose RF
estimates were sufficiently noise-free to allow precise, objective
characterization of the spatial structures of their excitatory and
inhibitory components.
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Figure 5.
Effect of scanning velocity on neural RFs. RFs
computed from the responses of six area 3b neurons to stimuli scanned
at 20, 40, and 80 mm/sec are shown on the left. The same
RFs are shown in the center three columns with
circles to identify the regions of maximum excitation
and inhibition, objectively determined (see Materials and
Methods). The white circle in each RF identifies
the region of maximum excitation; the black circle
identifies the region of maximum inhibition. The three
columns at the right display cross-sections
through the same receptive fields. The line defining
each cross-section (illustrated in the corresponding center
panel) passes through the centers of the circles
defining the regions of maximum excitation and inhibition. The
ordinate is the RF bin value, whose units represent
impulses per second per millimeter of indentation at the indicated
scanning velocity. The ordinates of the three histograms
for each neuron are scaled to include the absolute peak value across
all three scanning velocities (usually the excitatory RF peak at 80 mm/sec). The numbers above the upper and lower limits of
the right-most graphs are the RF values
represented by the extreme upper and lower ordinate values in each
group of three histograms.
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RF structure
The structural similarity between RFs estimated at different
scanning velocities was measured by computing the correlation between
estimates. Pearson's product-moment correlation coefficient computed
on a bin-by-bin basis between any two RFs provides a powerful measure
of their similarity; it compares all RF locations, and it is sensitive
to changes in both the pattern and relative magnitudes of the
excitatory and inhibitory effects, but it is unaffected by changes of
scale that affect all values equally. A further reason for using
correlation as a measure of structural similarity is that it was used
in the previous study to measure differences between independent,
repeated RF estimates at the same scanning velocity (DiCarlo et al.,
1998). Because some of the lack of structural similarity between RFs at
different velocities is due to RF noise, and we have measured this
effect, we can separate the loss of correlation that is due to velocity
effects from the loss due to noise in the repeated measures (see
Appendix ).
We used an RF noise estimate developed in our previous study (DiCarlo
et al., 1998) to restrict quantitative analyses to neurons whose RF
estimates were relatively noise-free. Briefly, the raw estimate of each
RF was filtered with a two-dimensional Gaussian filter whose SD (300 µm) was small relative to the spatial dimensions of interest. The
noise removed by the Gaussian filter was measured as the SD of the
difference between the raw and filtered RF estimates. The RF noise
index was defined as the ratio of this SD to the peak filtered RF
value. The previous study showed that very few RFs with noise indices
<0.30 had correlations between repeated estimates <0.75 (i.e., they
were highly repeatable). Because of the much longer time required to
collect data at 20, 40, and 80 mm/sec than at 40 mm/sec alone (3.5 times longer), the collection time at 40 mm/sec was much shorter
than in the previous study, and the RF estimates tended to be noisier.
Thirty-four of the 84 neurons (40%) had RF noise indices <0.30 at 40 mm/sec, and the analyses of RF structure were restricted to these
neurons. Because the collection time at 20 mm/sec was twice as long as at 40 mm/sec, and the number of action potentials was almost twice as
great, the noise index was always lower at 20 mm/sec than at 40 mm/sec.
This ensured highly reliable RF estimates from at least two scanning velocities.
Figure 6 illustrates correlation plots
between RF estimates at 20, 40, and 80 mm/sec for a typical area 3b
neuron (this neuron's RFs are plotted in Fig. 3). Before plotting two
RFs against one another on a bin-by-bin basis, the RF obtained at the
slower velocity was shifted distally to compensate for the effects of
conduction delay between skin stimulation and neural response (which
averaged 15 msec; see later). This required a shift of one to three
bins, depending on the difference in scanning velocities between the two RF estimates and the conduction delay. The correlation plots in
Figure 6 show that the RF bins at all three scanning velocities were
nearly colinear (correlations of 0.915, 0.884, and 0.873 for 20 vs 40 mm/sec, 40 vs 80 mm/sec, and 20 vs 80 mm/sec, respectively), indicating
that the RFs determined at each of the scanning velocities have nearly
identical patterns of excitation and inhibition. The correlation plots
also show that both excitation and inhibition became more intense
(larger RF bin values) as the scanning velocity increased. In the
example shown in Figure 6, the excitatory and inhibitory weights at
each RF location were approximately three times greater at 80 mm/sec
than at 20 mm/sec.
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Figure 6.
Bin-by-bin comparisons of RF estimates obtained at
three scanning velocities. The RF data are from the area 3b neuron
illustrated in Figure 3. Each point in each plot
represents bin values from corresponding bins in two RFs determined at
two of the three velocities. Before comparison, the RFs were aligned to
compensate for the small, progressive distal shifts produced by
conduction delay between the stimulus and the response. In this case,
the shifts were one, two, and four bins to the right at 20, 40, and 80 mm/sec (see Results). The bin values are in units of impulses
per second per millimeter of indentation at the specified scanning
velocity. The correlation coefficients from left to
right were 0.915, 0.884, and 0.872.
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Correlation coefficients between RFs obtained at 20 and 40 mm/sec and
at 40 and 80 mm/sec are shown in Figure 7
for each of the 34 neurons included in this analysis. The correlation
values are all large, confirming that the spatial structure of each
neuron's RF is largely unaffected by changes in scanning velocity.
Also, most points fall below the diagonal dashed line, indicating that RFs determined at 20 and 40 mm/sec are more similar than those at 40 and 80 mm/sec. However, that may simply reflect the fact that RF
estimates are noisier at 80 than at 20 mm/sec, as discussed above. In
fact, it is not clear that the data in Figure 7 signal any change in RF
structure with changes in scanning velocity; the lack of perfect
correlation could be attributable to RF noise alone.
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Figure 7.
Effect of scanning velocity on the RFs of area 3b
neurons. Left, The ordinate is the
correlation between RF estimates at 40 and 80 mm/sec. The
abscissa is the correlation between RF estimates at 20 and 40 mm/sec (see Fig. 6). Each point represents those
two correlations for a single neuron. Right, Difference
between observed correlations and expected correlations based on the
null hypothesis that velocity had no effect on the pattern of
excitation and inhibition in the RF. The method used to compute the
expected correlation is explained in Appendix .
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To test this hypothesis, we determined the correlation coefficient that
would be expected between repeated RF estimates at two velocities if
there was no change in the RF structure (see Appendix ). Figure 7
shows the difference between the observed and expected correlation
coefficients for each neuron (a negative difference indicates a loss of
correlation greater than that expected from noise alone). The
differences were distributed around zero, as can be seen in Figure 7,
but in each pairing the mean was slightly negative ( 0.028 for RFs at
20 and 40 mm/sec, 0.010 for 40 and 80 mm/sec, and 0.059 for 20 and
80 mm/sec). The difference was statistically significant
(p < 0.01, t test) for 20 versus 40 and 20 versus 80 but not for 40 versus 80 mm/sec. These very slight but
statistically significant differences are accounted for at least
partially by a difference in the rate of growth of inhibition and
excitation and a small growth of both excitatory and inhibitory area
with increasing velocity (see below).
Excitatory and inhibitory delays
Because we have no a priori knowledge of the delay
between a stimulus element and its excitatory or inhibitory effect on a neuron's discharge, the RF analysis assigns the effect to the stimulus
location at the time of the effect. Thus, the skin location that
appears to produce the effect will be displaced from its true site of
origin in the scanning direction by a distance that is proportional to
the delay and the scanning velocity; that is, the slope of the
relationship between this displacement and scanning velocity is the
delay (see Appendix ). Because we can measure the locations of the
centers of excitation and inhibition in the RF at each of the three
velocities, we can measure this slope and, therefore, estimate the
excitatory and inhibitory delays.
To do this, we sought an objective method for determining the locations
of the main centers of excitation and inhibition within each RF
estimate. Small regions of excitation or inhibition distant from the
centers of excitation and inhibition, like outliers in statistics, can
have an exaggerated effect on measures of location if they are
included. Consequently, we adopted a measure of location, which, like
statistically robust measures of central tendency, ignored the
locations of distant data. The method consisted of constructing a
circle that would capture, at most, 50% of the excitatory or
inhibitory area at 40 mm/sec (see Materials and Methods) and searching
the entire RF for the location that included the most excitatory or
inhibitory mass within the circle. The center of that circle was taken
as the center of excitation or inhibition. The important point was to
include sufficient mass to locate the centers of the most intense
excitatory and inhibitory regions accurately while excluding the undue
influence of distant points. The excitatory mass included in this
circle ranged from 33 to 50% of the total; the inhibitory mass ranged
from 20 to 50%. The radii differed between neurons but were fixed
within neurons at the value appropriate for the RF obtained at 20 mm/sec.
Results of the application of this algorithm are shown in Figure 5. The
white cross is the location of the center of the (white) circle
containing the most excitatory mass. The black cross (and circle)
defines the location containing maximum inhibitory mass. This algorithm
identified the same dominant excitatory and inhibitory foci at all
three scanning velocities in 85% (29 of 34) of the neurons.
Occasionally (5 of 34 neurons), when the RF contained two inhibitory
regions of near-equal strength, the algorithm identified one region at
two velocities and the other region at the other velocity; an example
is shown in Figure 5F. These five neurons were eliminated
from the analyses that follow.
Once the excitatory and inhibitory centers were located using the
circular windows, we plotted the proximal-to-distal position of the
centers and their relative proximal-to-distal separation as a function
of velocity (Fig. 8). The distal location
of each RF component is plotted as the offset from its
proximal-to-distal location at 20 mm/sec. The top left and center
panels of Figure 8 show that, with a few exceptions, the excitatory and
inhibitory centers moved distally in the RF map as velocity increased
from 20 to 80 mm/sec. The single neuron whose excitatory RF center was
more proximal at 80 than at 20 mm/sec is the neuron shown in Figure 4.
The explanation for this anomalous result can be seen by close
inspection of the RFs in Figure 4. The excitatory field is large, and,
although its overall boundaries shifted distally by a small amount, the
increasing excitatory strength that occurred with increasing velocity
(see later) occurred predominantly in the proximal part of the RF,
causing the measured center of excitation to move proximally rather
than distally. Similar effects explain the inhibitory responses that
appear to have moved proximally with increasing velocity.
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Figure 8.
Effect of scanning velocity on the locations of
the dominant excitatory and inhibitory RF component centers. The
two left plots of the top row show the
distal shifts of the apparent centers of excitation and inhibition
relative to their locations at 20 mm/sec. The top right
plot shows the differences between the inhibitory and
excitatory shifts. The middle row shows the geometric
means of the data in the top row (SEM brackets are too
small to be seen). The bottom row contains histograms of
the slopes of individual curves in the top row. In the
two left columns, those slopes are estimates of the
delay between skin stimulation and the centers of excitation and
inhibition. The bottom right graph is the histogram of
differences between the inhibitory and excitatory delays (see
Results).
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Because the distal offset caused by delay is the product of the delay
and the scanning velocity (Eq. A3), the slopes of the relationships
between excitatory and inhibitory distal location and velocity
illustrated in the top row of Figure 8 are direct estimates of the
excitatory and inhibitory delays (see Appendix ). Those slopes for
individual neurons are shown in the histograms in the bottom row of
Figure 8. The mean excitatory and inhibitory delays, 15.5 and 11.4 msec, respectively, are both significantly different from zero
(two-tailed t test, p < 0.001). These
delays are consistent with previously reported response latencies in
area 3b (Mountcastle and Powell, 1959; Gardner and Costanzo,
1980a).
The difference between excitatory and inhibitory distal offsets in
individual neurons is displayed in the top right panel of Figure 8.
Each point in this plot is the difference between points displayed in
the middle and left top panels of Figure 8 for a single neuron. This
plot shows that separation between excitatory and inhibitory centers in
the scanning direction was not strongly affected by changes in scanning
velocity. The distribution of the slopes of these lines is shown in the
bottom right panel of Figure 8 and is expressed as the delay of the
center of inhibition relative to the center of excitation. The mean of
the distribution, 4.2 msec, is not significantly different from zero
(p > 0.05, two-tailed t test). This
result indicates that RF excitation and inhibition appear to act nearly
simultaneously (i.e., without significant relative temporal delay) at
scanning velocities between 20 and 80 mm/sec (but see Discussion).
RF mass
To investigate the effects of scanning velocity further and to
compare the RFs described in this study with those in the previous study (DiCarlo et al., 1998), we analyzed RF area and mass. Excitatory (inhibitory) mass is a measure of the total strength of the excitatory (inhibitory) effects within the RF. As in the previous study, excitatory mass was calculated as the sum of the excitatory (positive) RF bin values, and inhibitory mass was calculated as the sum of the
absolute values of the inhibitory (negative) RF bin values. Both
excitatory and inhibitory mass have units of impulses per second per
millimeter of stimulus relief, and both increased significantly with
increasing scanning velocity (Fig. 9).
The excitatory mass almost doubled between 20 and 80 mm/sec (geometric
mean excitatory masses were 2937, 3810, and 5475 mass units at 20, 40, and 80 mm/sec, respectively). The inhibitory masses more than doubled (1897, 2925, and 4635 mass units at 20, 40, and 80 mm/sec,
respectively). The mean slope of the logarithm of excitatory mass
versus log velocity was 0.449 (SD = 0.306 log10
units); the comparable inhibitory slope was 0.644 (SD = 0.334 log10 units). Both were significantly different from zero
(p < 0.001, t test).
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Figure 9.
RF mass versus scanning velocity. Top
panels show results for individual neurons; bottom
panels show geometric means (brackets indicate SEM). Excitatory
(inhibitory) mass was calculated as the sum of the values of the
positive (negative) RF bins. The E/I
ratio is the ratio of the total excitatory and inhibitory masses shown
in the left two panels.
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Relative changes in excitatory and inhibitory strength with changes in
velocity were assessed by computing the ratios of excitatory to
inhibitory mass, which are shown in the two right panels of Figure 9.
At 40 mm/sec, the excitatory mass was, on average, 30% greater than
the inhibitory mass (the geometric mean mass ratio was 1.302), which is
consistent with the ratio in the larger sample (1.247) (DiCarlo et al.,
1998). However, inhibition grew more rapidly than excitation with
increasing scanning velocity, as indicated by a declining mass ratio
(mean of slopes = 0.195; t = 2.75;
p < 0.01). On average, the inhibitory mass grew from 65% of the excitatory mass at 20 mm/sec to 85% at 80 mm/sec. This effect is apparent on close inspection of the RFs shown in Figures 3-5. In most of the RFs shown in these figures, some of the RF
inhibition appears to deepen (i.e., become lighter on the RF plots) as
scanning velocity increases. This effect of scanning velocity on the
ratio of excitation to inhibition was particularly pronounced for the RF regions that trail the excitatory region (e.g., Figs. 3,
5A).
RF area
As in the previous study (DiCarlo et al., 1998), the excitatory
and inhibitory areas in each RF were calculated as the number of
excitatory and inhibitory RF bins in the RF grid exceeding a threshold
(10% of the peak excitatory or inhibitory value) and multiplied by the
area covered by each RF bin (0.16 mm2). As in the
larger study (DiCarlo et al., 1998), RF excitatory and inhibitory areas
were both widely distributed (Fig. 10).
The mean excitatory and inhibitory areas both grew 20% from 20 to 80 mm/sec (the geometric mean excitatory areas at 20, 40, and 80 mm/sec
were 18.2, 18.7, and 21.8 mm2, respectively; the
inhibitory areas were 18.5, 20.4, and 22.2 mm2,
respectively). The mean excitatory and inhibitory areas at 40 mm/sec
are slightly larger than the mean areas in the larger sample (14 and 18 mm2, respectively; DiCarlo et al., 1998). The means
of the slopes of log excitatory and inhibitory area versus log velocity
were 0.131 (SD = 0.217) and 0.133 (SD = 0.303). Although
slight, the mean slopes were statistically significant (excitatory:
t = 3.50; p < 0.001; inhibitory:
t = 2.55; p = 0.016). The ratio of
excitatory RF area to inhibitory RF area, shown in the top right panel
of Figure 10, is not affected by changes in scanning velocity (mean of
slopes = 0.002; t = 0.31; p = 0.98).
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Figure 10.
RF area versus scanning velocity. Top
panels show results for individual neurons; bottom
panels show geometric means (brackets indicate SEM). Excitatory
(inhibitory) area was calculated as the area covered by all the
positive (negative) bins within the RF whose values exceeded 10% of
the peak positive (negative) value. The
E/I ratio is the ratio of the total
excitatory and inhibitory areas shown in the left two
panels.
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The growth of excitatory and inhibitory area provides a basis for
estimating the persistence of excitation and inhibition in much the
same way that progressive displacement of the centers of excitation and
inhibition provided a basis for estimating the delay between the
stimulus and excitation and inhibition. If, for example, the excitation
persisted for 50 msec, the effect would be spread out over 1 mm at 20 mm/sec and over 4 mm at 80 mm/sec, which would have resulted in an
increase of 3 mm in the proximal-to-distal RF dimensions. No growth of
that magnitude was evident, so the persistence was obviously much less.
This relationship between persistence and RF structure is analyzed in
Appendix , where it is shown that the growth in excitatory and
inhibitory area illustrated in Figure 10 is very close to that expected
from excitatory and inhibitory persistence of  10 msec. If any part of
the increase in measured area is attributable to an effect other than
excitatory or inhibitory persistence (e.g., increased RF noise at the
higher scanning velocities may result in some artifactual increase in
RF area), then excitatory and inhibitory persistence is <10 msec.
Primary afferent RFs
Studies using complex spatial stimuli show that primary afferents,
particularly SA1 afferents, exhibit response properties very much like
those attributed to spatially separated excitation and inhibition in
the CNS: skin indentation by any stimulus (e.g., a point, bar,
or edge) evokes a smaller response when there is skin indentation at a
neighboring region than when the stimulus indents the skin alone
(Johnson and Lamb, 1981; Phillips and Johnson, 1981a; Phillips et al.,
1992). This raises the question, what part of the area 3b RF inhibition
reported here is attributable to the response properties of primary
afferents? To address this, we studied 11 SA1 and 11 RA primary
afferents using the same random dot patterns and RF estimation methods
as were used in the cortical studies. Three SA1 and five RA afferents
were studied using scanning velocities of 20, 40, and 80 mm/sec. The
remainder were studied only at 40 mm/sec because of the abundant
evidence that the spatial structure of primary afferent responses is
unaffected by scanning velocity over the range from 20 to 80 mm/sec
(Johnson and Lamb, 1981; Johnson et al., 1991; Phillips et al., 1992).
Because the term inhibition implies synaptic mediation, we refer to the
negative regions in primary afferent RFs as suppressive rather than
inhibitory regions. The general features of SA1 and RA primary afferent
RFs can be seen in the examples shown in Figure
11. All 11 SA1 primary afferent fibers
yielded RFs with regions of significant suppression that trailed behind
the excitation, as can be seen in Figure 11 (i.e., the response evoked
by a dot trailing closely behind another dot was suppressed relative to
the response evoked by an isolated dot). The mean SA1 excitatory and
suppressive areas at 40 mm/sec were 5.5 (range, 4.0-7.2) and 6.8 (range, 1.9-10.2) mm2, respectively; the mean
excitatory and suppressive masses were 4490 (range, 1530-7890) and
1920 (range, 640-2900) mass units, respectively. A suppressive region
was detected in most RA afferents (9 of 11), but its magnitude was
negligible compared with the excitation. The mean RA excitatory and
suppressive areas at 40 mm/sec were 10.5 (range, 8.0-14.4) and 2.9 (range, 0-9.9) mm2, respectively; the mean
excitatory and suppressive masses were 6060 (range, 2570-9740) and 350 (range, 0-800) mass units, respectively. For comparison, the mean
excitatory and inhibitory RF areas for the 247 area 3b neurons studied
with the same random dot stimuli were 14.3 (range, 3-43) and 18.0 (range, 1-47) mm2, respectively; the geometric mean
excitatory and inhibitory cortical RF masses were 2140 (range,
210-10,300) and 1620 (range, 125-6830) mass units, respectively
(DiCarlo et al., 1998). As in the area 3b RFs reported here, the
spatial structure of the primary afferent RFs was largely unaffected by
changes in scanning velocity. The excitatory mass increased with
increasing scanning velocity for both afferent types, as did the
suppressive mass for the SA1 afferents. These data indicate that some
part of the trailing "inhibition" observed in area 3b RFs may be
attributable to trailing suppression in the responses of SA1 but not RA
afferents. However, none of the primary afferent RFs contained
significant regions of suppression that did not trail the central
excitation (e.g., as in Fig. 11). This indicates that nontrailing
inhibitory regions in the area 3b RFs reported here and in the previous
study (DiCarlo et al., 1998) must be attributable to mechanisms
operating in the central pathways (i.e., dorsal column nucleus,
thalamus, and/or SI cortex).
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Figure 11.
Effect of scanning velocity on typical SA1 and RA
primary afferent RFs. The stimulus and methods used to determine the
primary afferent RFs were identical to those used to determine the area
3b RFs in this study and the previous study (DiCarlo et al., 1998). The
RF display is the same as in Figure 5.
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DISCUSSION |
The main result of this study is that the spatial structure of
area 3b RFs is largely unaffected by changes in scanning velocity, but
their excitatory and inhibitory intensities are affected strongly. Excitatory and inhibitory RF mass both nearly doubled as velocity increased from 20 to 80 mm/sec, and neural firing rates increased 42%.
Correlations between RF estimates at different scanning velocities were
often as high as correlations between repeated estimates at a single
velocity. This indicates that the neural representation of a stimulus
in area 3b is affected little by changes in scanning velocity. Analysis
of the progressive shift in the apparent locations of the excitatory
and inhibitory parts of the RFs with increasing velocity suggests that
excitation and inhibition arrive nearly synchronously with a delay of
~15 msec. Analysis of the growth of excitatory and inhibitory area
showed that both components persist for 10 msec (SD) at most. Analysis
of the RFs of primary afferents showed that some of the area 3b RF
inhibition that trails behind the excitation might arise in the
response properties of SA1 afferents.
Previous studies and mechanistic implications
Previous studies of the effect of scanning velocity on area 3b
firing rates evoked by textured patterns (Burton and Sinclair, 1994;
Tremblay et al., 1996) and brush stimuli (Whitsel et al., 1972; Essick
and Whitsel, 1985) show that impulse rates generally rise with
increasing scanning velocity. There are no previous studies of the
effect of scanning velocity on the structure of somatosensory cortical RFs.
The results of this study considered in isolation would suggest that
the excitatory and inhibitory effects that constitute the RF of an area
3b neuron arrive nearly synchronously, 10-15 msec after the stimulus
that evokes them, and that their spatial structures are independent of
scanning velocity. However, those inferences are consistent neither
with the literature on the timing of excitation and inhibition in the
somatosensory cortex nor with other results from our studies, which
both suggest that some inhibition lags behind excitation. Previous
studies indicate that there is substantial spatial overlap between
excitatory and inhibitory effects (Laskin and Spencer, 1979; Gardner
and Costanzo, 1980b) and that inhibitory effects are typically delayed
relative to excitatory effects (Andersson, 1965; Whitehorn and Towe,
1968; Innocenti and Manzoni, 1972; Laskin and Spencer, 1979; Gardner and Costanzo, 1980b) by 10-20 msec (Laskin and Spencer, 1979; Gardner
and Costanzo, 1980b). Our own studies (DiCarlo and Johnson, unpublished
observations) show that when scanning direction is varied, area 3b RFs
change shape in a way that suggests that some inhibitory effects are
delayed relative to the excitatory effects. The question is how to
reconcile these data and the results of the current study.
Figure 12 illustrates how overlapping
excitation and inhibition can produce near-velocity invariance even
when the inhibition is delayed substantially relative to excitation.
The top two rows contain an exaggeratedly simplified RF model that
illustrates the key points. The model consists of uniform, rectangular
regions of excitation and inhibition that overlap in space but not in time: both the excitatory and inhibitory effects arise from the same
skin region, but the inhibitory effect arrives 20 msec after the
excitatory effect. When mapped with a scanned stimulus, this model
matches qualitatively the RF features described in this study: (1)
inhibition appears to trail excitation in the scanning direction
(compare Figs. 3-5) because its temporal delay appears as a spatial
offset in the scanning velocity (see Appendix ); (2) excitatory and
inhibitory areas grow with increasing scanning velocity (compare Fig.
10) because the increasing, apparent displacement between excitation
and inhibition with increasing velocity reduces the cancellation
between them; (3) net excitatory and inhibitory intensities (masses)
increase with increasing scanning velocity (compare Fig. 9) for the
same reason; and (4) the distance between the apparent centers of
excitation and inhibition is fixed and independent of scanning velocity
(compare Fig. 8) because it is determined by the widths of the
overlapping excitation and inhibition, not by the temporal delay.
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Figure 12.
One- and two-dimensional models illustrating
possible effects of scanning velocity on RF geometry. The purpose of
these models is to show how inhibition can be delayed relative to
excitation but result in either no shift of the center of inhibition
relative to the center of excitation as scanning velocity varies (as in
A) or only a minimal shift (as in B). The
illustrative models assume inhibition whose origins on the skin overlap
the region giving rise to excitation perfectly but whose effect is
delayed by 20 msec relative to the excitation. Profiles above (below)
the line in each panel represent profiles of excitation
(inhibition). The horizontal axis in each panel
represents the location on the skin surface where the excitation or
inhibition appears to have arisen. When the stimulus moves at a
constant velocity and there is an unknown delay between the stimulus
event on the skin and the effect on the neuronal discharge, then the
effect appears to have arisen from a location that is displaced from
the true location by an amount proportional to the delay and the
scanning velocity (see Appendix ). When the delay to inhibition is 20 msec greater than the delay to excitation, then the skin region giving
rise to inhibition appears to be displaced by 0.02*velocity mm relative
to the apparent location of the excitation (0.4 mm at 20 mm/sec, 1.6 mm
at 80 mm/sec). A, The top row illustrates
this effect at scanning velocities of 20 and 80 mm/sec in both the
proximal and distal scanning directions. The second row
illustrates the net effect (i.e., the observed RF) after accounting for
the canceling effects of overlapping excitation and inhibition (assumed
to be additive). Rectangular profiles, 3 mm wide, are illustrated for
simplicity. Note how the offset between the observed centers of
excitation and inhibition is unaffected by changes in scanning velocity
(compare Fig. 8) and how the observed excitatory and inhibitory volumes
(masses) increase in intensity (compare Fig. 9). B, Same
effects with Gaussian excitatory and inhibitory profiles meant to
simulate more closely the RF profiles observed in this study. The
inhibitory peak value is 10% less than the excitatory peak value, but
its width is increased relative to the excitatory width so that they
have equal mass. As in the simpler case illustrated above, the relative
displacement between observed excitation and inhibition is affected
little by changes in scanning velocity, and both excitation and
inhibition become more intense with increasing velocity.
C, Gray scale plots of the RFs that would be observed in
B. The correlation of the RFs illustrated at 20 and 80 mm/sec is 0.95. The offset of the inhibition from the excitation is 2.3 mm at both 20 and 80 mm/sec, indicating apparent synchrony with the
excitation (compare Fig. 8), whereas the actual relative delay was 20 msec.
|
|
The bottom two rows of Figure 12 are like the top two rows, except that
the excitatory and inhibitory effects are more like the regions of
excitation and in-field inhibition reported previously (Mountcastle and
Powell, 1959; Gardner and Costanzo, 1980b). In this model, as in our
results (compare Figs. 9, 10), net excitatory and inhibitory
intensities (masses) increase much more with increasing velocity than
do the excitatory and inhibitory areas. When the centers of excitation
and inhibition and their displacements in the scanning direction are
measured exactly the same way as in our study, the relative
displacement between the centers is unchanged even though the relative
displacement between the centers of the overlapped excitation and
inhibition increased by 1.2 mm. If these data had been entered into our
analysis of temporal delays (compare Fig. 8), we would have inferred
that inhibition was synchronous with the excitation, whereas the true
delay is 20 msec.
In summary, Figure 12 shows that overlapping excitation and inhibition
can largely mask the effects of differences in delay between excitation
and inhibition so that RF spatial structure is affected little by large
changes in scanning velocity. However, this mechanism only accounts for
the invariance of the relationship between excitation and trailing
inhibition. Correlation analyses (Fig. 7) and visual inspection showed
that the entire RF including "nontrailing" inhibitory regions was
invariant, which suggests that a large part of the inhibition arrives
synchronously with the excitation.
Primary afferent RF properties
Area 3b RF spatial and temporal structure is the result of
peripheral as well as central mechanisms. Previous studies have shown
that the spatial structure of SA1 and RA primary afferent responses to
scanned dot patterns (Johnson and Lamb, 1981; Phillips et al., 1992),
scanned embossed letters (Phillips et al., 1988; Johnson et al., 1991),
and brushed stimuli (Edin et al., 1995) are unaffected over a wide
range scanning velocities. Also, SA1 and RA impulse rates both rise
with increasing raised pattern (Johnson and Lamb, 1981; Lamb, 1983;
Phillips et al., 1992) and brushstroke (Whitsel et al., 1972; Franzen
et al., 1984; Essick and Edin, 1995) velocity. Area 3b firing
rates rise at nearly the same rate as primary SA1 firing rates and more
slowly than primary RA firing rates (Fig. 2; Lamb, 1983; Phillips et
al., 1992; Essick and Edin, 1995), which raises the intriguing
possibility that area 3b neurons are driven largely by the SA1 primary
afferent population and therefore are likely to play a critical role in form recognition (Johnson and Hsiao, 1992) and roughness perception (Blake et al., 1997a).
In the current study we showed that SA1 RFs have a trailing suppressive
component that might contribute in part to the cortical inhibition that
we have reported. In our previous study of area 3b RFs (DiCarlo et al.,
1998), the inhibitory RF mass was, on average, almost as large (76%)
as the excitatory mass. The mass of the SA1 trailing suppression
averaged 43% of the excitatory mass, so a significant part, but not
all, of the cortical trailing inhibition that we have reported could be
accounted for by SA1 trailing suppression. Most RA RFs exhibited some
trailing suppression, but its mass, 6% of the excitatory RA mass on
average, was too small to account for more than a minor fraction of the
cortical inhibition that we have reported.
SA1 and RA primary afferent transduction models based on homogeneous,
isotropic elastic continua (Phillips and Johnson, 1981b; Srinivasan and
Dandekar, 1996) provide a reasonable explanation of trailing
suppression. The static skin deformation profile surrounding two dots
separated by ~3 mm in the scanning direction (the distance producing
maximum trailing suppression) is like an inverted tent (with two
supports) with deformation extending 3-4 mm in all directions from
each of the dots (Phillips and Johnson, 1981b; Srinivasan, 1989; Connor
et al., 1990; Phillips et al., 1992; Blake et al., 1997b). Both SA1 and
RA afferents are much more sensitive to the rate of change of
deformation than its absolute value (Pubols and Pubols, 1976). The rate
of change of skin deformation is proportional to the spatial
deformation gradient in the scanning direction and the velocity. Thus,
an explanation for the reduced response to the trailing dot is that the
skin is suspended between the dots, and therefore the spatial gradients
leading up to the second dot are smaller than those leading up to the
first dot (i.e., the indentation rates are less, and therefore the
response is less).
The relative lack of trailing suppression in the RA RFs may have two
explanations. One is that the RA RFs mapped by scanned dots are
approximately twice as large as SA1 RFs (two times in the current
study; Johnson and Lamb, 1981; Phillips et al., 1992) and that this
masks any suppressive effect at a 3 mm separation. A second major
factor is that RA but not SA1 afferents respond to the withdrawal of
deformation (i.e., upward rate of deformation) (Talbot et al., 1968;
Knibestöl, 1973; Pubols, 1980). Because the rate of withdrawal in
the wake of the second dot is similar to the rate of indentation
leading the first dot, the RA may respond well to both dots.
Functional implications of velocity invariance
The acquisition of tactile spatial information by scanning
movements compensates for the very limited field of view provided by a
single fingerpad. It is clearly an advantage to be able to scan one's
fingers over an object or a surface rapidly without loss of spatial
acuity. However, temporal factors such as reduced time in which to
respond to each stimulus element at higher scanning velocities,
differences in latency between different response components,
persistence of excitatory and inhibitory effects, and even conduction
velocity dispersion in the afferent pathways (Johnson and Lamb, 1981)
tend to degrade the spatial integrity of a moving neural image.
Nonetheless, psychophysical experiments demonstrate little loss of
spatial acuity at scanning rates from 20 mm/sec up to at least 80 mm/sec (Vega-Bermudez et al., 1991). This, in turn, implies that
mechanisms at all levels within the pathways leading to perception
maintain the integrity of spatial information over this broad range of
scanning velocities. The increased firing rates that accompany
increased scanning velocities compensate to some extent for the reduced
dwell time over each stimulus feature. The primary significance of
overlapping inhibition and excitation in the neural RFs may be to
minimize the effects of differences in delay between the excitatory and
inhibitory components of the RF. Whether this is so or not, the data
presented here demonstrate that area 3b responses are essentially
invariant over a wide range of scanning velocities. This invariance is
consistent with the hypothesis that area 3b plays a critical role in
tactile spatial perception, including roughness estimation and form
recognition, which are also unaffected by changes in scanning
velocity (Katz, 1925; Lederman, 1974, 1983; Vega-Bermudez et al.,
1991).
| |
FOOTNOTES |
Received June 24, 1998; revised Oct. 9, 1998; accepted Oct. 15, 1998.
This study was supported by National Institutes of Health Grant NS18787
and by the W. M. Keck Foundation. We thank Drs. S. Hsiao, V. Mountcastle, D. Pawluk, G. Poggio, P. Steinmetz, and E. Young for
helpful advice and criticism. John Lane, Steve Patterson, and David
O'Shaughnessy provided invaluable technical support.
Correspondence should be addressed to Kenneth O. Johnson, 338 Krieger
Hall, Johns Hopkins University, 3400 North Charles Street, Baltimore,
MD 21218.
| |
APPENDIX A |
Relationship between a neuron's full spatiotemporal RF and its RF
estimated with a scanned stimulus
In this appendix we derive the relationship between the neuron's
true spatiotemporal RF and the RF that we have estimated with a scanned
stimulus in this and the previous study (DiCarlo et al., 1998). We
assume that except for the threshold nonlinearity that arises because a
neuron cannot produce a negative discharge rate, the mechanisms are
linear. If they are not, the formulation applies to the response
fraction that is accounted for by linear mechanisms. The instantaneous
discharge rate, r(t), produced by a general
stimulus that varies in both time and space,
s(x,y,t), is determined by
the weighting assigned to all the stimuli that affect its discharge
(e.g., Marmarelis and Marmarelis, 1978):
|
(A1)
|
when the result is positive and zero otherwise. The weighting
function w(x,y, ) is the
neuron's spatiotemporal RF, which describes the effect of stimulation
of each location (x,y) in the neuron's RF at
each time lag () after the stimulus was presented. When a stimulus
pattern with constant spatial structure,
p(u,v), is scanned across the RF at a
constant velocity, the stimulus within the RF at any instant of time is
given by s(x,y,t) = p(x0 + x vxt, y0 + y vyt), where
x0 and y0 specify the
stimulus location in contact with the center of the RF at time
t = 0. The object is to determine the unknown
w(x,y,). However, the
two-dimensional data provided by neural responses to a pattern scanned
at a single velocity and scanning direction are not sufficient to
determine the three-dimensional structure of
w(x,y,) (because spatial and
temporal effects are confounded in the scanning direction). To see
this, we define new variables: x' = x + vx and y' = y + vy . Then, by substituting x' vx for x and y' vy for y, the convolution integral (Eq. A1) can be reformulated as:
|
(A2)
|
h(x',y') is the
two-dimensional RF that we have estimated at vx = 20, 40, and 80 mm/sec and vy = 0.
The effects of delay and persistence can be seen by examining the RF
estimates produced by scanning a stimulus across a spatiotemporal, excitatory RF that is Gaussian in space and time [i.e., by assuming that w(x,y,) in Eq. A1 is a
three-dimensional Gaussian]. Assume the spatial distribution of the
Gaussian is described by a center (µx,µy) and the spread by
( x and y), and that it has a mean delay of
delay (temporal "center"), and persistence
characterized by a temporal spread, t. We assume a scanning
velocity, v, in the x direction. The
y' dimensions of the two-dimensional RF obtained by
integrating the three-dimensional RF are the same as for
w(y' = y). The mean
location and spread in the x direction are given by:
|
(A3)
|
The shift of the RF component caused by temporal delay is
manifested in the product,
vx*delay, in Equation A3.
Larger delays or larger scanning velocities produce larger shifts in the RF component from its true spatial center (µx). If the
delay is assumed to be constant, then Equation A3 shows that the slope
of the measured spatial center (µx') versus
velocity is a direct measure of the delay (see Fig. 8). The smearing of
the RF component caused by persistence is manifested in the product,
vx2*t2, in
Equation A3. Larger temporal persistence or larger scanning velocities
produces larger spatial extent in the measured RF spread (x'). Our method of calculating RF area (all RF regions exceeding 10% of the peak value) includes all RF area within
±2.15 SD of the center of a Gaussian RF; thus the area of the measured
RF h(x',y') is:
|
(A4)
|
A typical excitatory area of 20 mm2 (see Fig.
10) would be produced by x = y = 1.2 mm. The
growth in area produced by persistence can be seen by examining the
effect of various persistence values, t. In fact, a
persistence of 10 msec (t = 10 msec) matches the observed
increases in RF area closely. It predicts a 4% growth in area between
20 and 40 mm/sec and 20% growth between 20 and 80 mm/sec. The observed increases in area were 3 and 20% for excitatory area and 10 and 20%
for inhibitory area.
| |
APPENDIX B |
Compensation for velocity effects unrelated to RF structure
Changes in scanning velocity had two effects on the estimated RF
unrelated to its structure, and we took measures to compensate for both
effects in the computation of RF correlation. One was progressive RF
displacement in the scanning direction with increasing velocity because
of conduction delays between the stimulus and the cortex. This effect
is accounted for as described in Results. The other was an increase in
RF noise with increasing scanning velocity because of the reduced
recording times at higher velocities. When the scanning velocity
doubled (e.g., from 20 to 40 imp/sec) the mean impulse rates increased,
on average, by 25%, but the recording time was cut in half. As a
result, the number of action potentials entering into the RF estimate
at the higher velocity dropped by 38% on average, and the noise in
the RF estimates increased substantially. The null hypothesis is
that scanning velocity had no effect on the spatial structure of the
RFs and therefore that the decline in correlation between two estimates
at different scanning velocity is determined by the noise in the two
estimates. The following is the method used to determine the expected
correlation when the noise levels in the two estimates are different.
The previous paper showed that repeated RF estimates based on data from
interleaved sweeps at the same scanning velocity were highly correlated
and that the correlation coefficient was related in a systematic way to
the RF noise index, which is illustrated in Figure
13. It is difficult to imagine any
systematic differences in the RF related to the interleaved sweeps, so
we assume that the loss of correlation (values <1.0) was entirely due
to noise in the two RF estimates that entered into each correlation
value. If the noise indices of the two RF estimates obtained at
different velocities were similar, the expected correlation could be
obtained from Figure 13, but they typically were not, as indicated
above. However, the expected correlation can still be estimated as the product of the square roots of the correlations associated with each of
the noise indices. That relationship is derived as follows.
View larger version (18K):
[in this window]
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|
Figure 13.
Correlations of repeated estimates of the same RF
(from DiCarlo et al., 1998). The ordinate represents the
correlation of two independent estimates of the same area 3b RF
obtained from alternating sweeps of the random dot pattern across the
RF at 40 mm/sec. The abscissa represents the average
noise index of the two RF estimates (see DiCarlo et al., 1998,
Results). The solid line is a running average produced
by a 100-point-wide boxcar filter.
|
|
Each RF estimate can be written as the sum of RF signal (i.e., the
expected value of the RF bins) and RF noise (i.e., fluctuations in the
RF bins caused by variability in the neural processes leading up to the
spikes from which the RF is estimated):
|
(B1)
|
where RF(i) is the estimate in the ith RF
bin, S(i) is the expected (i.e., true) RF value
in the ith bin, and N(i) is the noise
in the estimate of the ith RF bin. Defined this way, the noise (N) is uncorrelated with the signal
(S) so that the variance of the observed RF is equal
to the sum of their individual variances:
|
(B2)
|
The expected Pearson's correlation coefficient of any two RF
estimates, RF1 and RF2, is:
|
(B3)
|
We have assumed by the null hypothesis that two RFs estimated from
the same neuron at different scanning velocities have identical
underlying structure (i.e., S1 = S2 = S). When the noise variances are
identical, as we assume they are in estimates based on
interleaved sweeps at the same velocity, the correlation between estimates of the same RF (RF1 vs RF1) is
given by:
|
(B4)
|
Thus, it can be seen that the expected correlation between two
estimates of the same RF with different noise variances (Eq. B3 above)
is given by:
|
(B5)
|
where  11 and 22 are the expected
correlations for repeated measures of RFs with noise variances
2N1 and
2N2. The noise variances are
not known but the noise indices are, and they can be used to get
estimates of the expected correlations for repeated RF estimates
(11 and 22).
To do this, the data in Figure 13 were smoothed using a 100-point-wide
boxcar filter; the result is shown as a solid line. For each RF
estimate at each scan velocity, an estimate of the correlation
coefficient of that RF and another RF estimate obtained under identical
stimulus conditions (i.e., 11 in Eq. B5) was determined using the noise index of the RF estimate and the curve in Figure 13.
Thus, for two RFs estimated from the same neuron at different scanning
velocities, the expected correlation under the null hypothesis of
identical underlying RF structures but possibly different noise variances (i.e., 12 in Eqs. B3 and B5) was determined
from Equation B5, with 11 and 22
determined from the noise indices of each RF estimate.
| |
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D. T. Blake and M. M. Merzenich
Changes of AI Receptive Fields With Sound Density
J Neurophysiol,
December 1, 2002;
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[Abstract]
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R. N. S. Sachdev and K. C. Catania
Receptive Fields and Response Properties of Neurons in the Star-Nosed Mole's Somatosensory Fovea
J Neurophysiol,
May 1, 2002;
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2602 - 2611.
[Abstract]
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K. O. Johnson, S. S. Hsiao, and T. Yoshioka
Book Review: Neural Coding and the Basic Law of Psychophysics
Neuroscientist,
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111 - 121.
[Abstract]
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T. Yoshioka, B. Gibb, A. K. Dorsch, S. S. Hsiao, and K. O. Johnson
Neural Coding Mechanisms Underlying Perceived Roughness of Finely Textured Surfaces
J. Neurosci.,
September 1, 2001;
21(17):
6905 - 6916.
[Abstract]
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J. J. DiCarlo and K. O. Johnson
Spatial and Temporal Structure of Receptive Fields in Primate Somatosensory Area 3b: Effects of Stimulus Scanning Direction and Orientation
J. Neurosci.,
January 1, 2000;
20(1):
495 - 510.
[Abstract]
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Top
Abstract
Introduction
