| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
|
|
|
|||||||
|
|||||||||
Group in Vision Science, School of Optometry and Helen Wills Neuroscience Institute, University of California, Berkeley, California 94720-2020
Submitted 24 October 2002; accepted in final form 24 February 2003
 |
ABSTRACT |
|---|
 TOP ABSTRACT INTRODUCTIONMETHODSRESULTSDISCUSSIONACKNOWLEDGMENTSREFERENCES |
|---|
|
INTRODUCTION |
|---|
|
TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONACKNOWLEDGMENTSREFERENCES |
|---|
,
1974). Behaviorally, oriented
detail is not uniformly resolvable. In particular, spatial detail with
vertical and horizontal orientations is more finely resolved than that with
oblique angles. This has been designated the "oblique effect"
(Appelle 1972). The classical
finding is that human subjects perform best on a spatial acuity test when the
visual targets are oriented horizontally or vertically
(Berkley et al. 1975;
Campbell and Kulikowski 1966;
Emsley 1925;
Higgins and Stultz 1950;
Jastrow 1893;
Taylor 1963). The general
finding applies to a variety of other measurements including contrast
sensitivity (Campbell and Kulikowski
1966; Mitchell et al.
1967), orientation selectivity (Andrews
1965,
1967;
Blake and Holopigian 1985;
Campbell and Kulikowski 1966;
Orban et al. 1984),
orientation discrimination (Bouma and
Andriessen 1968; Caelli et al.
1983; Coletta et al.
1993; Ferrera and Wilson
1990; Heeley and
Buchanan-Smith 1992; Heeley
and Timney 1988; Mustillo et
al. 1988; Orban et al.
1984; Regan and Price
1986; Vogels et al.
1984; Westheimer and Beard
1998), Vernier acuity
(Saarinen and Levi 1995;
Westheimer and Beard 1998),
motion discrimination (Ball and Sekuler
1980,
1982;
Coletta et al. 1993;
Gros et al. 1998;
Matthews and Welch 1997), and
reaction time (Attneave and Olson
1967; Essock 1980.
For reviews of the literature, see Appelle
1972; Howard 1982;
Howard and Templeton
1966.).
The oblique effect has also been studied in animal subjects. It has been
demonstrated behaviorally in the cat
(Orban and Kennedy 1979;
Parriss 1964;
Vandenbussche and Orban
1983), monkey (Bauer et al.
1979; Boltz et al.
1979; Nissen and McCulloch
1937) and other species
(Appelle 1972). However, the
oblique effect measured through animal psychophysics is not as consistent as
in humans. Some cat behavioral studies have failed to find significant effects
(Bisti and Maffei 1974;
Blake and Holopigian 1985;
De Weerd et al. 1990).
Early investigators attributed orientation anisotropies to physical
properties of the visual system such as asymmetric optics, sparser
photoreceptor packing in the retina along oblique angles, and frequent
microsaccade eye movements along the Cartesian axes. However, experimental
data demonstrate that these physical factors do not significantly contribute
to the effect (Higgins and Stultz
1950; Nachmias
1960). It is clear that the anisotropies have a neural basis
(Campbell and Kulikowski 1966;
Maffei and Campbell 1970;
Mitchell et al. 1967).
Some physiological single-cell studies in the primary visual cortex (V1) of
the monkey (De Valois et al.
1982; Mansfield
1974; Poggio and Fischer
1977) and the cat (Bauer and
Jordan 1993; Kalia and
Whitteridge 1973; Kennedy and
Orban 1979; Payne and Berman
1983; Pettigrew et al.
1968; Wilson and Sherman
1976) have reported that there are more cells tuned to horizontal
and vertical than oblique. However, other investigations, also in monkeys and
cats, failed to find significant differences in the numbers of cells tuned to
different orientations (Campbell et al.
1968; Finlay et al.
1976; Henry et al.
1974; Hubel and Wiesel
1968; Noda et al.
1970; Poggio et al.
1977; Rose and Blakemore
1974; Wilson and Sherman
1976). Visual evoked potential (VEP) studies, in monkeys and cats,
have also produced mixed results with some showing
(Bonds 1982;
Mansfield and Ronner 1978) and
others failing to show (Campbell et al.
1973) orientation anisotropies.
The unequal distribution of orientation preference is just one
characteristic that has been investigated. Differences in orientation tuning
specificity have also been studied. Neurons in V1 with horizontal or vertical
preferences have been reported to exhibit narrower orientation tuning widths
(Kennedy and Orban 1979;
Nelson et al. 1977;
Orban and Kennedy 1981;
Rose and Blakemore 1974).
However, in other work, orientation-specific differences in tuning width were
not observed (Finlay et al.
1976; Mansfield
1974; Wilson and Sherman
1976).
One possible explanation for why some physiological studies find an oblique
effect whereas others do not could be that anisotropies are only exhibited in
a subpopulation of neurons. For example, it has been reported that the
orientation preference anisotropy is exclusively due to simple cells
(Orban and Kennedy 1981;
Orban et al. 1984).
Orientation tuning width asymmetries have also been claimed to be limited to
simple cells (Nelson et al.
1977; Orban et al.
1984; Rose and Blakemore
1974). On the other hand, other studies have found pronounced
anisotropies in complex cells as well
(Albus 1975;
Henry et al. 1978;
Payne and Berman 1983).
Spatial characteristics might be another differentiating factor. Leventhal and
Hirsch (1977) reported that
only cells with small RF sizes exhibit orientation anisotropies. Other studies
find the effect only in the foveal region and not in the periphery
(Kennedy and Orban 1979;
Mansfield 1974;
Orban and Kennedy 1981). De
Valois et al. (1982) suggested
the RF size and fovea-parafovea distinctions are actually the result of
spatial frequency differences, although they did not have a large enough
sample size to substantiate this.
Several investigations have assumed that V1 is the site of origin for the
oblique effect. Electroretinogram (ERG) measurements have been unable to find
an effect at the retina level (Maffei and
Campbell 1970). Single-unit studies in cats (Orban and Kennedy
1979,
1981) and monkeys
(Levitt et al. 1994) have
reported anisotropies in area 17 but not 18, and functional magnetic resonance
imaging (fMRI) measurements in humans show an oblique effect only in V1 and
not in other visual areas (Furmanski and
Engel 2000). However, recent optical imaging studies of area 18
(Liu and Pettigrew 2003;
Wang et al. 2003) and
single-unit recordings from the inferior temporal cortex
(Orban and Vogels 1998)
demonstrate that orientation anisotropies can also be found outside of the
primary visual cortex. Furthermore, a study of the small orientation biases in
the cat lateral geniculate nucleus (LGN) has shown that a slight preference
for horizontal and vertical orientations is evident in the thalamus
(Vidyasagar and Urbas 1982).
The preference remains even with areas 17 and 18 lesioned, suggesting that the
feedforward connections from LGN neurons may play a significant role in
shaping the selectivity and preference for cardinal orientations in the
primary visual cortex.
Drawing solid conclusions from the existing research is difficult due to
conflicting results. This is confounded by the fact that each study used
different experimental techniques and analysis criteria. Furthermore, the
number of cells sampled was typically less than 100. Several studies have
attempted to get around the issue of limited sample size through imaging
techniques. Orientation anisotropies have been observed with optical imaging
(Chapman and Bonhoeffer 1998;
Coppola et al. 1998b;
Liu and Pettigrew 2003;
Wang et al. 2003;
Yu and Shou 2000), VEP
recordings (Arakawa et al.
2000; Bonds 1982;
Freeman 1975;
Frost and Kaminer 1975;
Maffei and Campbell 1970;
Mansfield and Ronner 1978;
Moskowitz and Sokol 1985;
Nelson et al. 1984;
Sokol et al. 1987), and fMRI
(Furmanski and Engel 2000).
However, these techniques do not provide a characterization of the response
properties of individual neurons. It is also not clear if observed
anisotropies are the result of differences in relative population size or
differences in the response amplitudes of individual neurons.
In the present study, we examine our database of physiological data from
thousands of cells to provide a more thorough analysis of the neural
correlates of perceptual orientation asymmetries. We have examined
selectivity, response characteristics, and the relative numbers of cells tuned
to different orientations as a function of cell type and spatial frequency
preference. We have also performed spatial and temporal analyses on a subset
of cells for which we measured two-dimensional (2D) space-time RFs. To test
the hypothesis that the orientation selectivity anisotropy found in V1 might
be formed by the feedforward connections from LGN cells, we examined the
linear and nonlinear contributions to the orientation tuning of simple cells
through a spatial RF analysis (Gardner et
al. 1999). This analysis makes use of a common model for simple
cells consisting of a linear filter followed by a static expansive
nonlinearity (Albrecht and Geisler
1991; Anzai et al.
1999; DeAngelis et al.
1993b; Emerson et al.
1989; Heeger 1992;
Movshon et al. 1978;
Tolhurst and Dean 1987). The
linear filter is believed to be formed from afferent LGN connections as well
as cortical contributions (Ferster
1988; Jagadeesh et al.
1997; Reid and Alonso
1995), while the expansive nonlinearity is assumed to arise solely
through intracortical mechanisms (Anzai et
al. 1999; Douglas et al.
1995; Gardner et al.
1999; Somers et al.
1995; Volgushev et al.
1996). If anisotropies in orientation tuning selectivity result
from feedforward LGN connections, they should be evident in the linear RF
analysis of simple cells.
|
METHODS |
|---|
|
TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONACKNOWLEDGMENTSREFERENCES |
|---|
Extracellular recordings are made from cells in the striate cortex of
anesthetized and paralyzed cats. Recordings from well-isolated single units
are obtained using multiple (2–4) tungsten-in-glass microelectrodes
(Levick 1972) (or commercial
models). Electrode penetrations are made along the medial bank of the
postlateral gyrus, 4 mm posterior and 2 mm lateral from the Horsley-Clarke
origin (Horsley and Clarke
1908) at an angle of 10° medial and 20° anterior. These
penetrations produce tracks that pass through multiple layers and orientation
columns within the central ±15° projection of the visual field
(DeAngelis et al. 1993a).
After a single unit is identified by the waveform of its response, the RF
size, optimal spatial frequency, and orientation are measured quantitatively
using sinusoidal gratings. Details of the surgical and experimental procedures
are described elsewhere (Anzai et al.
1999; DeAngelis et al.
1993a).
Orientation tuning curves are measured using drifting gratings at the optimal size and spatial frequency for each cell. Gratings are drifted at a temporal frequency of 2 Hz and are presented monocularly to the dominant eye. Contrast is chosen to elicit a robust response. A minimum of five orientation samples are spaced in 5–15° steps around the optimal value to produce a well-defined tuning curve. A no-stimulus condition (i.e., a blank screen) is used to obtain an estimate of spontaneous activity. Conditions are presented in random order and displayed for a 4-s duration with a 2- to 4-s inter-stimulus interval. The condition set is repeated four to five times.
2D spatial RFs are mapped using a sparse-noise reverse correlation
technique (DeBoer and Kuyper
1968; Eggermont et al.
1983; Jones and Palmer
1987; Sutter
1975). For details of the method as employed here, see DeAngelis
et al. (1993a). Briefly, a
rectangular stimulus patch is presented to the classical RF of the cell being
recorded. The patch is oriented along the preferred orientation and divided
into a 20 x 20 element grid. Individual bar stimuli of either high (32
cd/m2) or low (2 cd/m2) luminance are displayed one at a
time on random grid locations for a 40-ms duration with a mean background
luminance of 20 cd/m2. Cross-correlating the stimulus with the
response produces a linear approximation to the space-time RF profile.
Data analysis
Optimal orientation, response amplitude, and tuning width (full width at
half height) are estimated from a Gaussian fit to the orientation tuning data
[by use of a Levenberg-Marquardt least-squares fitting procedure
(Press et al. 1992)]. For
complex cells, fits are applied to the DC (mean firing rate minus the mean
spontaneous firing rate) of the peri-stimulus time histogram (PSTH). For
simple cells, fits are applied to the first harmonic (2 Hz) of the PSTH. Cells
are classified as simple or complex based on the classical criteria
(Hubel and Wiesel 1962) and
also on the ratio (F1/F0) of the first harmonic to the DC of the PSTH with
optimal stimulus parameters. Cells with an F1/F0 ratio ≥1 are classified as
simple (Skottun et al. 1991;
but see Mechler and Ringach
2002 for an alternative view of this classification system). The
ratio of 1 is the approximate middle point of the bimodal distribution of
F1/F0 ratios for our population of cells
(Fig. 1).
|
A spatial analysis is performed on a cell's measured RF to estimate linear
and nonlinear contributions to orientation selectivity using the method of
Gardner et al. (1999). A
summary of the method is as follows. We apply a discrete Fourier analysis to
the 2D spatial RF (as illustrated in Fig.
11A) at the optimal correlation delay to obtain a 2D
amplitude spectrum. The spectrum is then fit by a pair of 2D Gaussian
functions that are symmetric about the origin (see
Fig. 11B). The
orientation tuning curve predicted by the 2D RF is obtained by sampling points
in the spectrum at different angles at a fixed radius corresponding to the
same spatial frequency used in the grating measurements (see
Fig. 11C). The
predicted tuning curve is then fit with a Gaussian function to obtain
estimated tuning parameters. In general, the predicted tuning curve of simple
cells is broader than that measured using drifting gratings
(Gardner et al. 1999;
Volgushev et al. 1996). The
ratio of the measured and predicted tuning widths (as expressed by the
variances of the Gaussian fits) is an estimate of the magnitude of the cell's
expansive output nonlinearity (Gardner et
al. 1999).
|
The 
2 statistic is used when assessing the significance of
anisotropies in the distribution of cells tuned to different orientations. The
proportion Z test is applied when comparing the population sizes at
two selected orientations. Otherwise, estimates of the significance of
orientation anisotropies are obtained through the F test, one-way
ANOVA.
|
RESULTS |
|---|
|
TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONACKNOWLEDGMENTSREFERENCES |
|---|
The dataset that meets these criteria consists of 4,418 cells. We binned these cells into 16 groups according to their preferred orientations. Each bin is 22.5° wide to cover the full 360° orientation space. In our coordinate system, 0 and 180° correspond to horizontal orientations drifting downward and upward, respectively. Ninety and 270° correspond to vertical orientations drifting to the left and to the right, respectively.
Figure 2 (
) displays
the numbers of cells from the total population tuned to each orientation bin.
The plot has obvious peaks at horizontal and vertical orientations (0, 90,
180, and 270°) that are highly significant (P < 0.001,
2 test); 15.1% of the cells are tuned to horizontal
orientations, whereas a flat distribution would produce only 12.5%. A smaller
number, 13%, were tuned to vertical orientations, which is significantly less
than that for horizontal (P < 0.01, Z test). The oblique
orientations had the fewest numbers of cells with only 11% for 135 and
315°. These percentages are comparable with distributions of preferred
orientation across the cortical surface of area 17 as measured through optical
imaging (Chapman and Bonhoeffer
1998; Coppola et al.
1998b; Liu and Pettigrew
2003; Wang et al.
2003; Yu and Shou
2000). Figure 2
also shows the orientation distributions separately for simple cells (
)
and complex cells (
). From the figure, it is clear that most of the
anisotropy comes from simple cells. Complex cells are distributed more or less
equally across all orientations (P = 0.584, 2 test).
This is consistent with previous results, which indicate that the oblique
effect, in terms of orientation distribution, is limited to simple cells
(Nelson et al. 1977;
Orban and Kennedy 1981;
Pettigrew et al. 1968).
Nevertheless, the effect is still evident when analyzing simple and complex
cells together. This result is consistent with VEP measurements, optical
imaging, and fMRI studies that show an effect when pooling over large
populations of cells (Arakawa et al.
2000; Bonds 1982;
Campbell and Kulikowski 1966;
Chapman and Bonhoeffer 1998;
Coppola et al. 1998b;
Frost and Kaminer 1975;
Furmanski and Engel 2000;
Liu and Pettigrew 2003;
Mansfield and Ronner 1978;
Moskowitz and Sokol 1985;
Sokol et al. 1987;
Wang et al. 2003;
Yu and Shou 2000).
|
Because VEP and imaging techniques are presumably not only sensitive to
numbers of neurons but also to the level of neural activity, we performed an
analysis on the response amplitudes at different orientations to determine if
this is a contributing factor. This analysis was performed on the subset of
cells recorded with gratings of 50% contrast (n = 1848) to avoid
variations in response amplitude due to stimulus strength.
Figure 3 plots the mean firing
rate versus orientation for simple () and complex () cells. Complex
cells tend to exhibit larger response rates than simple cells (mean of 22.8
vs. 11.5 spikes/s), but we observe no significant variation across orientation
for either cell type. This result is consistent with previous reports from
single-cell recordings in the cat (Rose
and Blakemore 1974). This suggests that VEP and optical imaging
studies reporting an oblique effect
(Arakawa et al. 2000;
Chapman and Bonhoeffer 1998;
Coppola et al. 1998b;
Frost and Kaminer 1975;
Liu and Pettigrew 2003;
Moskowitz and Sokol 1985;
Wang et al. 2003;
Yu and Shou 2000) are likely
to be measuring differences in population sizes and not alterations in the
response amplitudes of individual cells.
|
Heightened orientation selectivity and discrimination at horizontal and
vertical orientations measured psychophysically in humans
(Campbell and Kulikowski 1966;
Furmanski and Engel 2000;
Heeley et al. 1997;
Maffei and Campbell 1970;
Mustillo et al. 1988;
Orban et al. 1984;
Taylor 1963) and cats
(Orban and Kennedy 1979;
Parriss 1964;
Vandenbussche and Orban 1983)
might be accounted for, at least in part, by the predominance of cells tuned
to these orientations. To determine if variations in the shape of orientation
tuning curves are also involved, we analyzed the width (full width at half
height) and maximum absolute slope of the curves as a function of
orientation.
Figure 4 plots the mean
tuning width for simple () and complex () cells as a function of
preferred orientation. Overall, tuning widths are comparable to values from
previous studies (e.g., Gizzi et al.
1990). Here we show that simple cells have significantly narrower
tuning at horizontal compared with other orientations (P <
0.00001, F test). The mean tuning width for simple cells preferring
horizontal is 28° compared with 35° for other orientations. Complex
cells have wider tuning widths (mean = 40°) with insignificant narrowing
at horizontal orientations (P = 0.179, F test). This finding
supports the view that an unequal distribution of tuning widths plays a role
in heightened orientation selectivity. As with the anisotropies in numbers of
cells, tuning width anisotropies are limited to simple cells.
|
Heightened orientation discrimination at cardinal angles can also
potentially arise from anisotropies in the shape of orientation tuning curves.
The equivalent of orientation discrimination for a single cell is optimal at
orientations where the slope of the orientation tuning curve is steepest
(Bradley et al. 1987;
Geisler and Albrecht 1997;
Vogels and Orban 1990). We
calculate these orientations by finding the peaks in the absolute value of the
derivative (dG/d
) of the Gaussian fits to the orientation
tuning curves, G(). The distribution of orientations at which
the steepest slope occurs (Fig.
5A) shows similar anisotropies to the distribution of
preferred orientations (Fig.
2). A disproportionate number of cells exhibit a maximum slope at
horizontal and vertical orientations (P < 0.00000001). This
anisotropy is more prominent in simple cells
(Fig. 5A, ) than
complex cells (). Because the derivative of a Gaussian curve is
characterized by two peaks, each cell is represented twice in
Fig. 5.
Figure 5B plots the
mean absolute value of the peak slope as a function of orientation. On
average, cells in the striate cortex exhibit a peak change in response of 0.91
spikes · s–1 ·
°–1 change in stimulus orientation. Slopes
tend to be steepest at horizontal orientations (1.04 spikes ·
s–1 · °–1).
Simple and complex cells show similar distributions of slope values as a
function of orientation.
|
Physiological and behavioral studies have suggested a variety of conditions
under which the oblique effect is observed. Some indicate that the effect is
limited to cells with RFs in the foveal region
(De Valois et al. 1982;
Mansfield 1974;
Orban and Kennedy 1981;
Wilson and Sherman 1976).
Others suggest that only cells with small RF size (Leventhal and Hirsch
1977,
1978) or high spatial
frequency preferences (Appelle
1972; Campbell and Kulikowski
1966; Kupersmith et al.
1984) are involved. Because all of our recordings are from a
fairly circumscribed region around the area centralis, we are not able to
analyze the effects of eccentricity. However, we are able to examine the
effects of spatial frequency (SF). To do this, we sorted the simple and
complex cells based on optimal SF, and categorized the top 25% and bottom 25%
of each type as high and low SF cells, respectively.
Figure 6A shows the
distribution of preferred orientation for high SF simple cells (SF >0.593
cycles/°; n = 637). These cells exhibit the same distribution
features as the overall population of simple cells with significant peaks at
horizontal and vertical orientations (P < 0.005, 2
test). The orientation distribution for low SF simple cells
(Fig. 6B; SF <0.25
cycles/°; n = 637) doesn't exhibit statistically significant
structure (P > 0.05, 2 test). Neither high
(Fig. 6C; SF >0.65
cycles/°, n = 512) nor low
(Fig. 6D; SF <0.268
cycles/°, n = 511) SF complex cells show significant variations
from a flat distribution with Poisson variance (P > 0.05,
2 test).
|
The narrower selectivity for horizontal orientations is also most pronounced for high SF simple cells. Figure 7A shows tuning width distributions for high (—) and low (- - -) SF simple cells. Only the high SF simple cells show significantly narrower tuning at 0 and 180° (P < 0.0001, F test). Low SF simple cells (Fig. 7A, - - -) and complex cells (Fig. 7B) don't show significant narrowing (P > 0.2, F test). Another relevant measurement is the slope of the orientation tuning curve. Analysis of this parameter shows that only cells tuned to high SF exhibit significant anisotropies. This is most significant for simple cells (Fig. 8A; P < 0.02), but complex cells also exhibit this in a significant way (Fig. 8B; P < 0.05). These findings demonstrate that within the central visual field, the oblique effect is limited to high SF.
|
|
To further characterize these orientation anisotropies, we analyzed the
linear 2D RF maps for 104 simple cells. These cells all had preferred spatial
frequencies >0.25 cycles/° and display the same anisotropies as the
larger population, as shown in Fig.
9. The top bar plot (Fig.
9A) shows the numbers of cells tuned to horizontal,
vertical and the two oblique orientations. The distribution is similar to the
larger population with a disproportionate number of cells preferring
horizontal and vertical compared with oblique (P < 0.003,
Z test). Here we used coarser binning due to the smaller sample size
(45 vs. 22.5°). Because the larger population of simple cells reveals no
directional asymmetries, the forward and reverse directions are combined. For
example, the horizontal category is comprised of both 0 and 180°
orientations. Figure
9B shows the orientation tuning width for horizontal,
vertical, and oblique orientations measured using drifting gratings. Here the
two oblique orientations are combined into one group because of limited
numbers. As is the case in the larger population, cells preferring horizontal
orientations have significantly narrower tuning widths (P < 0.05,
F test). In this analysis, oblique tuning widths are slightly
narrower than those for vertical orientations, but the difference is not
significant [P > 0.3, Tukey test
(Hochberg and Tamhane
1987)].
|
We performed a temporal analysis on this subset of cells with measured
space-time RFs to address psychophysical
(Essock 1980;
Olson and Attneave 1970) and
VEP (Essock 1980;
Moskowitz and Sokol 1985;
Olson and Attneave 1970;
Skrandies 1984;
Sokol et al. 1987) reports of
longer response latencies at oblique compared with horizontal and vertical
orientations. Response latency was determined by measuring the time delay of
the maximum response in the cell's spatial-temporal RF. Mean peak response
latencies for cells preferring horizontal, vertical and oblique orientations
are shown in Fig. 10. No
significant differences in latency are observed for these orientations
(P = 0.6, F test).
|
We performed a spatial analysis on the RFs to explore the relative roles of
linear and nonlinear mechanisms in shaping the narrower orientation tuning
width at horizontal orientations. The orientation tuning characteristics of
simple cells have been shown to be a result of both linear and nonlinear
mechanisms. A widely used model consists of a linear filter followed by a
static expansive nonlinearity (Albrecht and
Geisler 1991; Anzai et al.
1999; DeAngelis et al.
1993a; Heeger
1992; Movshon et al.
1978; Tolhurst and Dean
1987). The linear filter is composed mainly of feed-forward LGN
connections (Jagadeesh et al.
1997; Reid and Alonso
1995) but is also shaped by cortical circuitry
(Ferster 1988;
Pollen and Ronner 1982;
Troyer et al. 1998). The
expansive nonlinearity is assumed to be solely a result of cortical factors
such as spiking mechanisms and intercellular circuits. It has been shown
(Gardner et al. 1999;
Volgushev et al. 1996) that
nonlinear mechanisms play a major roll in sharpening the orientation tuning of
simple cells. Here, we ask if the narrower tuning at horizontal orientations
exhibited by simple cells is the result of linear or nonlinear mechanisms.
An example analysis is shown in Fig.
11. Figure
11A shows the measured 2D spatial RF at optimal
correlation delay for a cell tuned near horizontal (–18°). We fit
the frequency domain of this RF with two 2D Gaussian functions
(Fig. 11B). We
extracted points from the frequency domain fit as shown by the semicircle in
Fig. 11B, and the
resulting function is plotted in Fig.
11C. This was then fit by a Gaussian curve to obtain the
predicted tuning width. Figure
11D shows the tuning curve measured using drifting
gratings (—) and the Gaussian fit (- - -). For this cell, the predicted
tuning width is 
22% wider than the measured tuning width (42.5 vs.
34.7°). This difference is within the range found in our previous study
(Gardner et al. 1999).
The predicted tuning widths for all 104 cells are summarized in
Fig. 12. In
Fig. 12A, the mean
± SE are plotted for the same horizontal, vertical, and oblique groups
used in Fig. 9B. This
figure indicates that the predicted tuning widths from the linear RFs are
equal for all orientations (P > 0.3) and thus do not show the
oblique anisotropies exhibited by tuning widths measured with drifting
gratings (Fig. 9B).
Figure 12B shows a
scatter plot comparing predicted and measured tuning widths for each cell.
Cells with horizontal, vertical, and oblique orientation preferences are
plotted with , x, and , respectively. Most cells fall below
the diagonal line of slope 1. Cells preferring horizontal orientations ()
have clusters farthest below the line. The ratio between the predicted and
measured tuning widths is an estimate of the exponent of the expansive
nonlinearity exhibited at the output stage of simple cells
(Gardner et al. 1999). The
distribution of exponents estimated from our analysis is plotted in
Fig. 13. The average exponent
for all cells (geometric mean) is 2.17, which indicates a value approximated
by a squaring nonlinearity. Cells preferring horizontal orientations
(Fig. 13A) have a
mean exponent of 3.17, which is significantly higher (P < 0.01, F
test) than for vertical and oblique orientations (1.85 and 1.72,
respectively). This suggests that the narrower tuning widths of cells
preferring horizontal is the result of a larger expansive nonlinearity and
thus cannot be accounted for by linear processes such as the feedforward
connections from LGN to visual cortex. In other words, the neural origin of
the oblique effect is likely to be based primarily on differences in
intracortical connections.
|
|
|
DISCUSSION |
|---|
|
TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONACKNOWLEDGMENTSREFERENCES |
|---|
) reported that
"there is no clear tendency for one major axis to be represented by a
greater number of cells in the visual cortex." However, examination of
their data shows clearly that twice as many simple cells were tuned to
horizontal than to vertical or diagonal. This didn't reach statistical
significance because they only recorded from 39 simple cells. Other studies
found similarly strong trends that didn't reach statistical significance due
to limited sample sizes (De Valois et al.
1982; Finlay et al.
1976; Noda et al.
1970).
A second reason why some physiological studies may have failed to observe
significant anisotropies is that they didn't analyze separately different
classes of cells. Our data show that only simple cells tuned to relatively
high spatial frequencies exhibit significant meridional variations in cell
count and tuning width. Several studies that observed orientation based
effects provided separate analyses for simple and complex cells
(Kennedy and Orban 1979;
Nelson et al. 1977;
Orban and Kennedy 1981;
Pettigrew et al. 1968;
Rose and Blakemore 1974) or
for foveal versus parafoveal cells
(Mansfield 1974) or for small
versus large RF sizes (Leventhal and
Hirsch 1977; Payne and Berman
1983). Many of the studies that did not show an effect didn't
differentiate between simple and complex cells or between high and low spatial
frequency preference (Campbell et al.
1968; Henry et al.
1974; Wilson and Sherman
1976).
A third factor in previous examinations of meridional anisotropies is the
broad definition of cardinal and oblique angles. For example, many studies do
not differentiate between vertical and horizontal orientations. The early
behavioral oblique effect studies proposed that the visual system processes
both horizontal and vertical with a higher sensitivity than oblique. But our
current results indicate that there is a strong bias for mainly horizontal
orientations for which cells are both more numerous and more narrowly tuned.
Cells preferring vertical orientations have similar tuning widths as those
preferring oblique angles. Some studies that failed to show variations in
tuning width, grouped vertical and horizontal data together
(Finlay et al. 1976;
Mansfield 1974), and this
could have averaged out the effects seen exclusively at horizontal
orientations. Furthermore, most studies used 45–90° bin sizes for
categorizing orientations. The data reported here (using 22.5° bins)
indicate that the magnitude of the oblique effect already begins to decline by
11.25° away from cardinal and oblique angles.
The finding that orientation anisotropy is mostly a horizontal effect is
somewhat surprising. Contours of vertical orientations are used to process
horizontal disparity and this may be expected to be finely tuned to assist in
stereopsis. However, some previous results are compatible with those we
present here. Mustillo et al.
(1988) reported that
orientation discrimination thresholds in humans are significantly lower for
horizontal than for all other orientations including vertical. This effect
applies to both crossed and uncrossed disparities. Orban et al.
(1984) and Vandenbussche et
al. (1986) also noted that
orientation discrimination in humans is significantly better at horizontal
than at other orientations. Heeley and Buchanan-Smith
(1990) demonstrated that human
orientation detection thresholds are significantly lower for horizontal than
vertical. Spatial resolution (Coletta et
al. 1993) and contrast sensitivity
(Mitchell et al. 1967) are
also reportedly better at horizontal orientations. In terms of the
distributions of preferred orientations, the literature also suggests a higher
proportion of cells tuned to horizontal than vertical. Leventhal and Hirsch
(1980) reported that cells
with small RF sizes in area 17 of the cat had a disproportional preference for
horizontal and vertical orientations. But examination of their summary figure
(Fig. 11A) shows
clearly that most of this bias is toward horizontal orientations. They found
25% more cells tuned to horizontal than to vertical, which appears to be
significant (P < 0.05, Z test). Optical imaging
measurements from the primary visual cortex of the cat
(Liu and Pettigrew 2003;
Yu and Shou 2000) and the
ferret (Chapman and Bonhoeffer
1998; Coppola et al.
1998b) reveal that a larger area of cortical surface responds to
horizontal compared with vertical. fMRI recordings in humans also show greater
discrimination at horizontal than at vertical or oblique
(Furmanski and Engel
2000).
The functional reason for superior visual performance at horizontal
orientations is not clear. It could possibly play a role in postural stability
relative to the horizon, but we know of no behavioral evidence for this. There
is evidence that the orientation preference of cells in the visual cortex can
be influenced by the visual environment. In humans, it is clear that
uncorrected astigmatism can result in lasting meridional amblyopia
(Freeman 1975;
Freeman et al. 1972;
Mitchell et al. 1973). Cats
reared with visual stimuli of only one orientation tend to have cortical
orientation preferences of the same orientation
(Blakemore and Cooper 1970;
Freeman and Pettigrew 1973;
Hirsch and Spinelli 1970;
Muir and Mitchell 1973).
However, neurons selective to horizontal and vertical orientations tend to be
less affected by environmental factors than oblique
(Freeman and Pettigrew 1973;
Leventhal and Hirsch 1975).
And because an oblique effect is also found in the early development periods
of kittens (Fregnac and Imbert
1978), ferrets (Chapman and
Bonhoeffer 1998), and dark-reared animals
(Leventhal and Hirsch 1980),
it is unlikely that the oblique effect measured in adults is solely the result
of the disproportionate energy distribution at the cardinal orientations
characteristic of natural and "carpentered" scenes
(Annis and Frost 1973;
Coppola et al. 1998a;
Keil and Cristobal 2000;
Switkes et al. 1978;
Timney and Muir 1976).
An important step in explaining the origin and implications of the oblique
effect is determining where in the visual system the anisotropies are formed.
The evidence is clear that neither the optics of the eye nor the retina's
photoreceptor mosaic contribute to the oblique effect
(Campbell and Kulikowski 1966;
Maffei and Campbell 1970;
Mitchell et al. 1967). Eye
movements have also been shown to make no contribution
(Higgins and Stultz 1950;
Nachmias 1960). This
indicates that the oblique effect originates within the visual cortex or as a
result of feedforward LGN connections or both. There is anatomical evidence
suggesting that the unequal distribution of preferred orientations in V1
results from anisotropies in the retino-cortical projections
(Colonnier 1964;
Young 1960). However, the
narrower orientation tuning at horizontal orientations might be shaped through
intracortical mechanisms. A study of the small orientation biases in the cat
LGN has reported a preference for horizontal, and to a lesser extent vertical
orientations (Vidyasagar and Urbas
1982). The effect remains even after lesioning areas 17 and 18.
The report suggests that the biases of LGN neurons might explain the higher
selectivity for horizontal and vertical orientations found in V1. Our current
findings suggest that this is not the case. The tuning curves predicted from
the linear 2D RFs of simple cells cannot account for the observed sharpening
of tuning at horizontal orientations. The data reported here indicate that
cells preferring horizontal orientations exhibit superior selectivity due to a
larger expansive nonlinearity. This strongly suggests nonlinear intracortical
mechanisms rather than linear feedforward factors from LGN.
The finding that meridional anisotropies are found only in V1 simple cells
but not complex cells has some interesting implications for the classical
model of hierarchical visual processing where simple cells feed into complex
cells which in turn supply the input to higher stages of the visual system
(Hubel and Wiesel 1962,
1968). The clear implication
is that a substantial proportion of simple cells must have direct input to a
population of neurons in higher centers. It implies that all simple cells
don't feed into complex cells in a manner that preserves the distribution of
simple cell tuning characteristics. Furthermore, if perceptual measurements of
the oblique effect are indeed the result of unequal distributions of
orientation preference and selectivity, then the output of simple cells might
comprise a substantial proportion of the input to visual processing areas
mediating perception.
There have been different reports about the spatial conditions under which
the oblique effect is observed. It has been suggested that the effect is
primarily in the foveal region, and not found in the periphery
(Berkley et al. 1975;
Zoli 1973), and there is
physiological support for this (Kennedy
and Orban 1979; Mansfield
1974; Orban and Kennedy
1981). Leventhal and Hirsch
(1977) suggested that the
effect is only found for cells with small receptive fields. DeValois et al.
(1982) hypothesized that the
differentiating factor is spatial frequency. The data presented here are
consistent with the spatial frequency hypothesis. In our data set, only cells
with relatively high spatial frequency tuning are found to exhibit orientation
anisotropies. Because all of our cells were recorded from within the region
around the area centralis representation (central 15°), it is clear that
spatial frequency plays a significant role in limiting the oblique effect.
This is consistent with psychophysical
(Coletta et al. 1993;
Pointer 1996;
Westheimer 2003) and
physiological (Kalia and Whitteridge
1973; Wilson and Sherman
1976) evidence that the oblique effect exists in the periphery at
relatively high spatial frequencies and is absent in the fovea at low spatial
frequencies (Campbell and Kulikowski
1966). This, of course, doesn't rule out effects of eccentricity
on the oblique effect (Rovamo et al.
1982; Westheimer
2003).
The unequal distribution of preferred orientations in V1 can account, at
least qualitatively, for many of the perceptual phenomena that make up the
oblique effect. The classical effect is that spatial acuity is higher at
horizontal and vertical orientations
(Appelle 1972;
Campbell and Kulikowski 1966).
This agrees with the finding that there is a disproportionate number of cells
tuned to horizontal and vertical at high spatial frequencies. Simple
mathematical models of population coding predict that the observed unequal
distribution of preferred orientation can account for heightened sensitivity,
selectivity, and detection at cardinal orientations
(Green and Swets 1966;
Peterson et al. 1954;
Zhang and Sejnowski 1999).
These heigh
