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J Neurophysiol (November 1, 2002). 10.1152/jn.00858.2001
Submitted on 18 October 2001
Accepted on 2 August 2002
1Department of Biomedical Engineering, Technion, Israel Institute of Technology, Haifa 32000, Israel; 2Schepens Eye Research Institute, Boston, Massachusetts 02114; and 3Department of Ophthalmology, and 4Program in Neuroscience, Harvard Medical School, Boston, Massachusetts 02115
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ABSTRACT |
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 TOP
 ABSTRACT
 INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES
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Kagan, Igor,
Moshe Gur, and
D. Max Snodderly.
Spatial Organization of Receptive Fields of V1 Neurons of Alert
Monkeys: Comparison With Responses to Gratings.
J. Neurophysiol. 88: 2557-2574, 2002.
We studied the
spatial organization of receptive fields and the responses to gratings
of neurons in parafoveal V1 of alert monkeys. Activating regions (ARs)
of 228 cells were mapped with increment and decrement bars while
compensating for fixational eye movements. For cells with two or more
ARs, the overlap between ARs responsive to increments (INC) and ARs
responsive to decrements (DEC) was characterized by a quantitative
overlap index (OI). The distribution of overlap indices was bimodal.
The larger group (78% of cells) was composed of complex cells with
strongly overlapping ARs (OI 
0.5). The smaller group (14%) was
composed of simple cells with minimal spatial overlap of ARs (OI 
0.3). Simple cells were preferentially located in layers dominated
by the magnocellular pathway. A third group of neurons, the
monocontrast cells (8%), responded only to one sign of contrast and
had more sustained responses to flashed stimuli than other cells. One
hundred fourteen neurons were also studied with drifting sinusoidal
gratings of various spatial frequencies and window widths. For complex
cells, the relative modulation (RM, the ratio of the 1st harmonic to the mean firing rate), ranged from 0.6 ± 0.4 to 1.1 ± 0.5 (mean ± SD), depending on the stimulus conditions and the
mode of correction for eye movements. RM was not correlated with the
degree of overlap of ARs, indicating that the spatial organization of
receptive fields cannot reliably be predicted from RM values. In fact,
a subset of complex cells had RM > 1, the traditional criterion for identifying simple cells. However, unlike simple cells, even those
complex cells with high RM could exhibit diverse nonlinear responses
when the spatial frequency or window size was changed. Furthermore, the
responses of complex cells to counterphase gratings were predominantly
nonlinear even harmonics. These results show that RM is not a robust
test of linearity. Our results indicate that complex cells are the most
frequently encountered neurons in primate V1, and their behavior needs
to receive more emphasis in models of visual function.
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INTRODUCTION |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES
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Hubel and Wiesel (1962
,
1968) divided cells in the primary visual cortex of cats and
monkeys into two groups
simple and complex. They were distinguished by
the spatial organization of the receptive fields; simple cells had
small receptive fields with two or three separate ON or
OFF zones, whereas complex cells had larger receptive fields with less discrete zones or nonlinear summation properties. More
recent work has attempted to match the original dichotomy by
characterizing these two types according to their responses to
sinusoidal stimuli. A presumed index of linearity, the relative modulation (RM, the ratio of the response amplitude at the
temporal frequency of a drifting grating to the mean firing rate) was
proposed to be >1 for simple cells and <1 for complex cells
(De Valois et al. 1982; Movshon et al.
1978; Skottun et al. 1991). However, modulated
responses of complex cells have been reported by many authors
(Dean and Tolhurst 1983; Foster et al.
1985; Glezer et al. 1980, 1982; Hammond
et al. 1989; Holub and Morton-Gibson 1981; Kulikowski and Bishop 1982; Pollen and Ronner
1982; Pollen et al. 1978). Although the majority
view equates cell classification by spatial mapping and by relative
modulation criteria (Skottun et al. 1991), there are
exceptions to this opinion based on studies in cat V1 (Dean and
Tolhurst 1983; Hammond et al. 1989).
A stronger inconsistency is present in the literature on monkey visual
cortex, where results based on spatial mapping have designated a small
minority of V1 neurons (7-22%) as simple cells (Dow
1974; Foster et al. 1985; Gur et al.
1999b; Hubel and Wiesel 1968; Schiller et
al. 1976; Snodderly et al. 2000; see also
Conway 2001), but with one exception (Prince et
al. 2000), use of the relative modulation criterion has
resulted in roughly half of monkey V1 neurons (40-60%) being
designated as simple cells (De Valois et al. 1982;
O'Keefe et al. 1998; Sceniak et al. 1999, 2001). This conflict has not been resolved because no paper on monkey V1 has presented data comparing spatial mapping and relative modulation on the same sample of cells.
The dominance of simple cells in cat V1 and their linear properties
have influenced much of the theorizing on functional processing in
primary visual cortex (e.g., Artun et al. 1998;
Carandini and Heeger 1994; Carandini et al.
1997; Chance et al. 1998; Heeger 1993; Heeger et al. 1996; Reich et al.
2001; Troyer et al. 1998; Wielaard et al.
2001). Numerous studies have confirmed that simple cells can be
considered as basically linear (half-wave-rectified) spatiotemporal
operators (Carandini et al. 1999). Responses of such
operators are relatively easy to predict, analyze, and model. However,
if simple cells are a minor fraction of primate V1 neurons, as spatial
mapping studies indicate, then models of cortical function relevant to
human perception should incorporate more emphasis on other cell types.
These considerations led us to study the simple/complex dichotomy in V1 of alert monkeys. We found that spatial mapping divided most of our V1 sample into two groups. Simple cells (14%) had nonoverlapping increment (INC)- and decrement (DEC)-responsive zones, whereas complex cells (78%) had overlapping zones. The RM classification was not equivalent to the overlap/nonoverlap dichotomy. Thus for monkey V1, the relatively large number of simple cells found by modulation criteria appears to result from cells with extensively overlapping INC and DEC zones being designated as simple cells. Furthermore, complex cells with high RM values still exhibit essential nonlinearities. The dominance of nonlinear cells with overlapping INC and DEC regions implies that they should be important components in realistic models of visual cortex function.
Parts of this work have been presented in abstract form (Gur et
al. 1999b; Snodderly et al. 2000).
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METHODS |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES
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Five adult female monkeys (2 Macaca fascicularis and
3 M. mulatta) were used as subjects for spatial mapping, and
three of the monkeystwo M. mulatta and one M. fasciculariswere used for the grating experiments. Monkeys were
trained to fixate on a light-emitting diode (LED) for water reward.
Once the monkey learned the task, a head-holding implant and a
recording well were surgically attached to the skull under deep
anesthesia. All procedures complied with National Institutes of Health
guidelines and were approved by the Animal Care and Use Committee of
the Schepens Eye Research Institute.
Nerve-spike and eye-movement recording
Fiber electrodes made from quartz-insulated platinum-tungsten
alloy (Eckhorn and Thomas 1993) with bare tip lengths of
5 µm and impedance at 1 kHz of 3-4 M
were most frequently used to record single-unit activity. In some experiments, glass-insulated platinum-iridium electrodes (Snodderly 1973) with a tip
diameter of 1-1.5 µm, and bare tip length of 5-7 µm, were used.
Cells were assigned to cortical layers based on histological and/or
physiological criteria as previously described (Snodderly and
Gur 1995).
Position of the dominant eye was monitored by a double Purkinje image
eye tracker (2- to 3-minarc resolution; 100-Hz sampling rate) and
recorded in a computer file, together with spike arrival times (0.1-ms
time resolution) and spike shapes collected at 10-20 kHz (Gur
et al. 1999a). The trial started when the monkey correctly pressed the lever in response to the LED and continued for 5 s provided that the gaze remained within a predefined fixation window, usually about ±1.5°.
Stimulus presentation
Bar and grating stimuli were displayed on a Barco 7351 monitor
at a 60-Hz noninterlaced frame rate, with a Truevision ATVista video
graphics adapter. Bars were optimized for orientation, length, velocity, and color (green or red), 0.9 log units brighter or darker
than the background of 1 cd/m2. This luminance is
in the low photopic range and stimuli are vividly colored. Chromatic
stimuli were generated by activation of individual guns of the monitor.
Incremental (bright) bars were presented on a neutral gray background;
decremental (dark) bars were presented on a background of a single
color (Snodderly and Gur 1995). Because of limitations
in the experimental setup, dark bars with the same luminance decrement
for both colors could only be generated from colored backgrounds.
Preliminary tests with our new system showed no noticeable difference
between ARs mapped with luminance increments and decrements presented
on a color or a gray background.
Monochrome sine gratings of 50% luminance contrast, optimal orientation, length, and color were presented on backgrounds of the same color as the decrement bars, with a mean luminance of 1 or 5 cd/m2. Gratings had the same mean luminance as the background or were presented so that the maximal luminance corresponded to the luminance of the increment bar. We did not find any difference in responses to these similar luminance conditions.
After the ocular dominance was established, stimuli were viewed
binocularly, unless responses during monocular viewing were substantially stronger. The eye position signal for the dominant eye
was added to the stimulus position signal at the beginning of each
video frame (bars) or each second frame (gratings; "image stabilization," Gur and Snodderly 1987, 1997a,b;
Snodderly and Gur 1995). This was done to compensate for
changes in eye position during the intersaccadic intervals. Note that
the maximum delay between shifts in the eye position and subsequent
corrections could be as long as 28 ms for bars and 44 ms for gratings;
thus this procedure was not intended to compensate for the fast
saccadic eye movements. Epochs affected by saccades were automatically detected and excluded during data analysis using a velocity threshold of 10°/s (Snodderly et al. 2001) as described in
RESULTS.
Receptive field mapping
The width and location of receptive-field activating regions
(AR) was estimated with increment and decrement bars (2-16 minarc, mean: 7 ± 3 minarc) swept forward and back at 1.5-7°/s across the receptive field in a direction orthogonal to the optimal
orientation axis (Foster et al. 1985; Pettigrew
et al. 1968; Schiller et al. 1976). The
operational term "activating region" is used to distinguish regions
that respond to direct stimulation from other (covert) zones that may
modify the directly evoked response (e.g., side inhibition or
facilitation from subthreshold regions). To increase the precision of
measurement and minimize possible effects of response latency, we
calculated AR widths using the lowest velocity that elicited a strong
response in the data set for each cell.
Using image stabilization and appropriate eye movement corrections, we were able to obtain reliable measures of AR widths and locations in spite of inevitable variations in fixation (see RESULTS). Average peristimulus time histograms (PSTH) of responses were constructed, and a cumulative curve was superimposed (Fig. 1). The AR width was measured as 95% of the region defined by intersections of least-squares lines fitted to the cumulative curve for the response to motion in the preferred direction. Because our coordinates are referenced to the stimulus center, a quarter width of the bar was subtracted from each side to correct for occasional spikes elicited by incomplete entry and exit of the stimulus (we found that at least a quarter width of an optimal test bar was required to elicit a consistent response).
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An overlap index (OI) was calculated as (Schiller et al.
1976)
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(1) |
A directionality index (DI) was computed as 1 minus the ratio of the
response in the nonpreferred direction to the response in the preferred
direction, where the response is defined by the cumulative spike count
in the same manner as determining the AR. Like other authors, we
classified cells as direction selective when their DI was >0.5
(Snodderly and Gur 1995 and references therein). Except
for control experiments, the reported values of OI were always
estimated using the preferred direction.
Response latency and a transiency index (TI) (Snodderly et al.
2001) were also assessed for a subset of cells
(n = 101) stimulated with increment and decrement
stationary flashing bars.
Grating responses
Sinusoidal gratings were restricted in space by a rectangular
window of optimal length (same length as mapping bars), oriented parallel to the grating bars and centered on the CRF. The width of the
window in the direction perpendicular to the orientation axis varied
from a fraction of the CRF to a size much wider than the CRF (mean
window width: 56 ± 38 minarc; mean window to CRF ratio: 1.9 ± 2.3). Spatial frequency varied from 0.1 to 18 cycles/° (cpd), most
frequently from 0.5 to 5 cpd. Two types of gratingsdrifting and
counterphase (contrast-reversal)were used. Drifting gratings were
usually presented at a temporal frequency of 5 Hz. For directional cells, drift was always in the preferred direction. Counterphase gratings were temporally modulated by a 2-Hz square wave, and in most
cells more than one spatial phase was tested.
The fast Fourier transform (FFT) was used to compute the discrete
Fourier transform (DFT) of neuronal responses, using as input either
the raw concatenated spike train (sequence of 1 and 0 s, where
each 1 represents a spike in a spike train sampled at 1 kHz) or a
cumulative histogram of spike arrival times averaged over one stimulus
cycle. The two methods yielded very similar results for the frequency
range of interest. The magnitude (spikes/s) of the response harmonics
was extracted as Fk = (2/N)|DFTk|, k = 1...N, where N is the length of the DFT
vector. The relative modulation (RM) of the response to a drifting
grating [the ratio of the 1st harmonic (F1) to the mean firing rate
(F0) with baseline firing rate subtracted] was calculated as
(De Valois et al. 1982)
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(2) |
The phase (in degrees) of response harmonics was calculated as phase
= [angle(DFT)+
/2] · 180/, where
angle(DFT) = imag(log (DFT)) is the phase of the elements
in a complex DFT vector. To eliminate discontinuities (jumps) due to
phase wrapping, a simple "unwrapping" algorithm was applied. The
algorithm minimized the SD of a set by adding 2 to each phase (1 at
a time), re-calculating it, and then choosing the minimal SD.
Statistical analysis
Individual cells' PSTHs were plotted with a 10-ms binwidth. Statistical comparisons were based on the following tests: for non-Gaussian-distributed variables (e.g., OI), the Mann-Whitney U test and the Wilcoxon matched-pairs signed-rank test; for Gaussian variables (e.g., AR width), t-test and paired t-test. Correlations between variables were calculated using the Spearman r or the Pearson r. Values reported for individual parameters are means ± SD. Analyses were done with custom software written in Matlab 5.3 (MathWorks).
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RESULTS |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES
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A total of 228 V1 cells with receptive fields at 2-9° (mostly at 2-5°) eccentricity were studied. All cells were tested with sweeping bars, 101 cells were tested with flashing bars, and 114 were tested with sinusoidal gratings. Recording sites included a broad sample of all laminar locations.
We will refer to individual increment (INC)- and decrement (DEC)-responsive regions as activating regions (ARs) and the total region of space occupied by the activating regions as the classical receptive field (CRF). We describe first the spatial arrangement of the INC and DEC ARs within the CRF as measured with sweeping bars, along with information from flash responses. Then we consider the effects of fixational eye movements on the neuronal responses to sinusoidal gratings. Finally, we present a detailed analysis of the modulation of neuronal firing by gratings and its relationship to the spatial arrangements of the ARs.
Spatial organization of receptive fields
NEURONS WITH TWO OR THREE ACTIVATING REGIONS.
Previous studies have shown that saccadic eye movements modify
responses to sweeping bars (Gur and Snodderly
1997a; Gur et al. 1997; Snodderly
and Gur 1995), even while compensating for the eye movements of
fixation (image stabilization). Consistent with this observation, AR
widths measured when all time periods were included (32 ± 16 minarc; "all data") were inflated (P < 0.0001)
compared with widths calculated from time periods 150 ms after any
preceding saccade (28 ± 15 minarc, "no saccades"). Consequently, we base our spatial mapping results on the "no
saccades" mode of data selection, combined with image stabilization,
as the most straightforward method of correction for eye movements.
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0.3, n = 33, 14%)
will be referred to as simple cells (Hubel and Wiesel 1962,
1968). Nine of these were tripartite simple cells with three
ARs. In deference to common usage, cells with overlapping ARs (OI
0.5, n = 178, 78%) will be called complex cells even
though some of the original descriptions do not fit this category
(e.g., Hubel and Wiesel 1962, Fig. 7). Although many
laboratories have adopted weak response modulation to drifting gratings
as the criterion for identifying complex cells (Skottun et al.
1991), we show later in RESULTS that many cells
with spatially overlapping ARs have strongly modulated responses that
are inconsistent with the expected behavior of complex cells.
CONTROL EXPERIMENTS.
Because the measurement of AR and OI with moving bars is crucial to the
results of this paper, we present evidence that our spatial mapping is
not distorted by temporal effects. Although previous reports of
receptive field measurements in monkey (Dow et al. 1981;
Livingstone 1998; Schiller et al. 1976;
Snodderly and Gur 1995) and cat (Peterhans et al.
1985) V1 have found that flashed or moving stimuli give
comparable estimates of AR dimensions, the use of moving stimuli for
spatial mapping raises two potential problems: 1) the
relative positions of the INC and DEC ARs could be misjudged due to
differences in response latency, and 2) prolongation of the
response by temporal persistence could lead to an overestimate of the
AR width and OI.
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the AR widths either remained nearly the same or
decreased slightly with increasing sweep velocity from 3.5 ± 1.5 to 4.8 ± 1.6°/s (Fig. 3B). As a result, the OI
decreased slightly when going from lower to higher velocity (0.73 ± 0.37; 0.66 ± 0.36, P < 0.01). The responses
to the highest velocities in the set had quite short durations (87 ± 42 ms, in the smallest ARs as short as 30 ms), providing little evidence for persistence of the response. Consistent with the view that
receptive field dimensions measured with moving bars are not inflated,
a recent report (Jones et al. 2001) found that CRF
widths measured with drifting bars yield slightly smaller values than
widths based on area summation criteria. Indeed we find that mean CRF
and AR widths in our sample (Table 1) are either similar to (Born and Tootell 1991; Cumming
and Parker 1999; Schiller et al. 1976;
Vinje and Gallant 2002; Zhou at al. 2000) or smaller than (Foster et al. 1985; Li et al.
2000; Mazer et al. 2002; Rossi et al.
2001; Sceniak et al. 2001) measurements from
other studies in monkeys made at comparable eccentricities.
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50 ms) bursts of spikes in response
to fast (>10°/s) fixational saccades sweeping across a stationary
stimulus (Snodderly et al. 2001) and in response to very
fast flicker (Gur and Snodderly 1997b). Furthermore,
responses to flashes usually do not last longer than the stimulus
duration when latency is taken into account. Even cells that show some persistence in response to very brief flashes (e.g.,
"position/drift" cells) (Snodderly et al. 2001)
yield very consistent measures of AR width with different stimulus
velocities, which suggests that the responses to moving bars are cut
short by inhibitory influences when the stimulus passes from the CRF
into the surround. We suggest that in the presence of a constantly
moving retinal image, this kind of invariance in translating time to
space could be a useful feature for visual processing.
NEURONS WITH ONLY ONE ACTIVATING REGION.
A third group of 17 cells (8% of our sample) responded to only one
sign of contrast (monocontrast), either increment (n = 10) or decrement (n = 7). V1 cells responding to a
single sign of contrast have been reported previously but they were
only qualitatively described (Bullier and Henry 1980) or
described as nonoriented with sustained firing (T cells) or oriented
and predominantly direction selective (S1 cells) (Schiller et
al. 1976). Our monocontrast cells appear to differ from the
latter descriptions because they were all selective for orientation,
but only 4/17 (24%) were direction selective (mean DI 0.3 ± 0.28).
COMPARISONS AMONG CELL TYPES. Figure 4 displays histograms of AR widths (left) and CRF widths (right) for the three cell types and Table 1 gives numerical summaries. For cells with more than one AR, the mean AR width was used. The bottom row of Table 1 combines data from all cells, including those that could not be assigned to layers. Considering the entire sample, simple cells' mean AR widths were significantly smaller than the mean AR widths of complex cells (P < 0.0001). INC and DEC AR widths were highly correlated for both simple and complex cells (r = 0.88, P < 0.0001). The AR widths of monocontrast cells were similar to the AR widths of simple cells.
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). In the layer 4 group also, there was no significant
difference between CRF widths of simple and complex cells. In the
infragranular layers 5 and 6, simple cells' CRFs were much smaller
than those of complex cells (P < 0.01). A group of
very large complex cells (Fig. 4, bottom panels), all found
in layer 6 (cf. Schiller et al. 1976), contribute to
this relationship. We also found a small number of simple cells in the
upper layers 2/3 with larger CRFs than those of the complex cells
(P < 0.01). A larger sample of simple cells will be
needed to determine whether this is a general pattern.
In addition to moving stimuli, a subset of cells (n = 101) were tested with stationary flashing bars. Note that because we used both light (increment) and dark (decrement) stimuli, the terms
"increment/decrement" are not equivalent to the
"ON-OFF" terminology because an INC AR may give an
OFF response to extinguishing of a decrement stimulus and a
DEC AR will respond to the onset of a decrement stimulus. In
agreement with previous findings (e.g., Dean and Tolhurst
1983; Hubel and Wiesel 1962, 1968), most simple cells (7/9) gave only ON or OFF responses at
each spatial location, while most complex cells responded in an
ON-OFF fashion to both increment and decrement flashes.
Monocontrast cells (n = 9) gave only on responses to
stimuli of the appropriate contrast.
Monocontrast cells' responses to flashes were more sustained than the
responses of simple and complex cells. A transiency index (TI)
(Snodderly et al. 2001) that ranged from near zero for
perfectly sustained responses to 1 for very transient responses was
significantly smaller (P < 0.05) for monocontrast
cells (0.12 ± 0.33) than for simple cells (0.40 ± 0.41) and
complex cells (0.40 ± 0.33). This temporal difference in the
response of the monocontrast cells, along with the small sizes of their
ARs (Table 1) reinforces the idea that they should be treated as a
separate group.
Almost all cells (50/53) tested with flashing bars of increasing widths
exhibited strong side inhibition with a response reduction of 50% as
the stimulus was extended beyond the CRF.
Effects of eye movements on grating responses
It was apparent from inspecting the records that fixational eye movements considerably affect neuronal responses to gratings (Fig. 5). Almost all saccades and some slower eye movements were followed by spurious firing after a variable delay. For the complex cell illustrated in Fig. 5, responses to the drifting grating during stable fixation appeared mostly in the second half of the stimulus cycle, while eye movements shifted the responses in time or eliminated them.
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To analyze effects of eye movements, we used the stimulus combination
of spatial frequency and window size that evoked maximal RM. Each
behavioral trial was split into segments corresponding to one temporal
cycle of the grating. To quantify the effects of eye movements, the
relative modulation (RM) was calculated (see METHODS) using
two different modes of data selection as shown in Fig. 5A:
1) accepting all segments ("all") or 2)
automatically detecting fixational saccades by a velocity criterion and
discarding segments following saccades within 250 ms ("no
saccades"). Segments affected by saccades were discarded because our
compensation for eye movements (image stabilization) had too large a
delay to correct for saccades (see METHODS). Even during
the slower movements of the intersaccadic intervals, noise in the
eyetracker signal, small calibration errors, and small deviations from
linearity cause position errors of a few minutes of arc that are
difficult to eliminate. These residual position errors in image
stabilization result in phase jitter of the retinal image of sinusoidal
stimuli and corresponding jitter of the phases of the neuronal
responses (cf. Bridge and Cumming 2001). To correct for
the phase jitter, an additional measure of the relative modulation was
calculated by dividing the "no saccades" data into segments
corresponding to one temporal cycle of the grating and averaging the
RMs of individual segments. This calculation is equivalent to phase
alignment in the frequency domain ("aligned"). In principle,
alignment could be done in the time domain, but that would produce
erroneous results when applied to modulated responses that span
adjacent temporal cycles. Figure 5D shows how RM increased
as the effects of eye movements and the accompanying time jitter in the
response were progressively reduced.
As data selection became more stringent, the distributions of RM shifted toward more modulated values (Fig. 6, going from top to bottom). Simple cells and complex cells were similarly affected by saccades (Table 2). Elimination of data segments affected by saccades increased the mean RM by 22% for simple cells and by 29% for complex cells (Fig. 6, middle). Phase alignment increased the mean RM of simple cells by an additional 22% and of complex cells by an additional 42% (Fig. 6, bottom). The overall effect of removing both saccade influences and phase jitter was an increase in RM of 0.55 units (49%) for simple cells and 0.51 (84%) for complex cells. Thus RM increased by almost the same amount for both cell types but by a larger percentage for complex cells because they had a lower RM before data selection. Note that selecting data segments with minimal effects of saccades and then performing phase alignment resulted in a RM >1 for all simple cells, like the results from anesthetized animals. However, the same procedure resulted in 53/93 (57%) of the complex cells having an RM >1, which distinguishes them from the complex cells described in anesthetized preparations.
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Phase alignment to correct for eye movements has been previously
employed (Carandini et al. 1997; Cumming et al.
1999), and our results suggest that it helps to minimize the
effects of stabilization errors. One would predict that stabilization
errors should produce phase dispersion (SD of the phase of F1 across
response cycles) that is greater for cells with smaller CRFs and for
cells with higher optimal spatial frequencies. Consistent with this
prediction, we found that for complex cells, phase dispersion of the
"no saccades" data were negatively correlated with CRF width
(r = 
0.29, P < 0.005) and positively
correlated with optimal spatial frequency (r = 0.52, P < 0.0001). Also, as would be expected, the increases in the RM values for complex cells produced by aligning the segments were positively correlated with spatial frequency (r = 0.5, P < 0.0001). Trends were the same for simple
cells, but the sample was too small to reach statistical significance.
These results suggest that RM values derived from the "no saccades"
analyses are underestimates of the true values, especially for cells
with small receptive fields or high optimal spatial frequencies.
However, the RM values derived from analysis of the aligned segments
may be overestimates if there are significant phase shifts in the
neuronal responses due to other factors, such as intrinsic temporal
properties of the neurons (Garcia-Perez 1999). To
encompass the range of values that are our best estimates of the
properties of the neurons, we present the summary data with results
based on both methods of analysis.
Analysis of responses to gratings
When studying each neuron, several stimulus combinations of window
size and spatial frequency were presented. For comparison with previous
studies, the amplitude of the response harmonics F0 and F1 to drifting
gratings were calculated, and RM was calculated for the stimulus
condition generating the maximal harmonic of the entire set. If the
maximal harmonic in the set was F0, RM was <1, and if the maximal
harmonic was F1, RM was >1, which is the traditional criterion to
distinguish simple cells from complex cells based on sinusoidal
stimulation (De Valois et al. 1982; Skottun et
al. 1991).
In Fig. 7, typical responses to gratings
are illustrated for a simple cell and three complex cells. To be
conservative, the data for the figure have been analyzed in the "no
saccades" mode. The simple cell (A) and the first complex
cell (B) exhibit properties characteristic of simple and
complex classes found in anesthetized cats and monkeys. The simple cell
response was highly modulated, whereas the complex cell was almost
unmodulated. Many readers would expect this result, based on the
spatial overlap of the INC and DEC ARs (Skottun et al.
1991). However, for the other complex cells (C and
D) with similar OIs, drifting gratings evoked strong F1
modulation at the stimulus temporal frequency (5 Hz). Strong modulation
was relatively common among complex cells, and we show later in
RESULTS that the strength of the modulation was not related
to the spatial receptive field organization.
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Responses to counterphase gratings (middle left and
middle right) were similar to those described for
anesthetized preparations: the simple cell responded once during a
stimulus cycle, whereas the complex cells responded twice per cycle,
like typical complex cells (De Valois et al. 1982). Note
that the presence of a large, pseudolinear F1 harmonic (5 Hz) in the
response of the complex cells C and D to a
drifting grating is nevertheless associated with a large nonlinear F2
harmonic (4 Hz) in response to the stationary, counterphase grating.
Distributions of response modulation to drifting gratings
A total of 114 cells (93 complex, 16 simple, and 5 monocontrast)
were studied with drifting sinusoidal gratings. When choosing the
stimulus configuration for analyzing the responses to drifting gratings
we used two criteria. One was the stimulus evoking the largest F0 or
F1, as described in the preceding text. We refer to this as the
stimulus evoking the maximal harmonic. Because the relative modulation
may be a more important means of transmitting information than the
maximal harmonic (Reich et al. 2001), we also analyzed
responses to the stimulus producing the maximal RM.
For the examples of Fig. 7, and for 75% of simple cells and 57% of complex cells, the stimulus parameters evoking the maximal harmonic and the maximal RM were the same. For the rest of the simple and complex cells (n = 44), choosing the stimulus condition that produced the maximal RM reduced the amplitude of the maximal harmonic (F0 or F1) by 23 ± 19 spikes/s, or 34 ± 17%, but increased the mean RM by 47 ± 30%.
The value of RM was a function of both the choice of the stimulus and the mode of correction for eye movements (Table 3). In the most extreme two-way comparison, the mean RM assigned to complex cells for a stimulus eliciting the maximal RM analyzed with phase alignment of the response was nearly twice as large as the mean RM for a stimulus eliciting the largest single harmonic with only elimination of saccades.
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Figure 8 shows histograms illustrating the effects of these variables on RM values. For each condition, there was considerable overlap between the RM distributions of simple and of complex cells. Using the maximal harmonic as the traditional criterion for choice of stimulus and the conservative "no saccades" mode of data analysis (Fig. 8A), many complex cells showed a substantial degree of modulation and 14% had RM >1. Most simple cells (69%) had RM >1, although for five cells, RM was <1. When response phase was aligned (Fig. 8B), both complex and simple cell responses were more modulated; 37% of complex cells had RM >1 and 87% of simple cells had RM >1. Selecting the stimulus for maximal RM (Fig. 8, C and D) increased the number of complex cells with RM >1 to 26% and had an especially large effect on the complex cells when analyzed with phase alignment: more than half the complex cells (57%) had RM >1 and all simple cells had RM >1 (Fig. 8D).
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These results suggest an explanation for the discrepancy in the
literature between the small percentage (7-22%) (Dow
1974; Foster et al. 1985; Hubel and
Wiesel 1968; Schiller et al. 1976; see also
Conway 2001) of neurons in V1 designated as simple by spatial mapping and the relatively large percentage (40-60%)
(De Valois et al. 1982; O'Keefe et al.
1998; Sceniak et al. 1999, 2001) found by
relative modulation. By relative modulation criteria 14-37% of
complex cells identified by spatial mapping would be considered simple
cells, depending on the mode of analysis. Because complex cells
constitute the large majority of V1 cells (78% of our sample), the use
of RM >1 as a criterion for identifying simple cells will result in a
mixed population, a large fraction of which are complex cells by
spatial criteria.
Thus in our sample of V1 cells, RM would not be a reliable criterion for predicting the spatial organization of the CRF. Depending on the mode of analysis and stimulus conditions (eliciting the maximal harmonic or the maximal RM), 13-31 to 0-19% of the simple cells and 14-37 to 26-56% of the complex cells would be grouped with other cells with unlike spatial receptive fields.
We have not discussed the responses of monocontrast cells to drifting gratings because they were weak and variable, though well modulated (mean RM: 1.56). Even with stimuli selected for the maximal harmonic, the mean response amplitude was only 18 spikes/s (cf. complex cells: 54 spikes/s, simple cells: 36 spikes/s).
Relative modulation versus spatial organization
Scatter plots illustrating the relationship between the OI and the value of RM for each cell are shown in Fig. 9. For both maximal harmonic and maximal RM stimulus conditions, there was no statistically significant correlation, although there may be a weak negative relationship for the maximal harmonic condition. The weak relationship between INC and DEC overlap and RM reinforces the conclusion that factors other than spatial overlap must exert strong influences on the modulation behavior of the neurons.
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Two additional parameters that we measured do not appear to influence the modulation behavior of the cells. There was no correlation between RM and the CRF width in all conditions for both simple and complex cells (data not shown). Also, no significant correlation was found between RM and the transiency, TI, of responses to flashes.
Responses to counterphase gratings
Fifty-three complex cells were tested with counterphase gratings. For 25 cells, the spatial frequency of the counterphase grating was the same as the spatial frequency selected for one or both stimulus conditions used with the drifting grating; for the rest, the mean difference between the spatial frequency of the counterphase grating and the spatial frequency of the drifting grating (in either stimulus condition) was <1 cpd.
Forty-seven of 53 complex cells responded to counterphase gratings with
an F2 harmonic greater than the F1 harmonic and 40% of the F0
harmonic. Of the remaining six cells, five had little modulation and
one exceptional complex cell had a strong F1 response. The
prevalence of even harmonics in cells with overlapping INC and DEC ARs
suggests that the responses to counterphase gratings could prove more
consistent as counterparts for spatial mapping than the degree of
modulation to drifting gratings.
Only four simple cells were tested with counterphase gratings, so we cannot draw conclusions about population behavior.
Spatial frequency selectivity
For 102 cells (88 complex and 14 simple), data were collected with
gratings of several spatial frequencies covering a mean range of
2.2 ± 0.8 octaves. Spatial frequency selectivity curves were
analyzed using an automated procedure: for each curve, the maximum
response was normalized to 1 and if the response at low, high, or both
ends of the spatial frequency range was <71% of the maximum (1/
2),
the curve was considered as having a cutoff frequency. For 51% of the
cells, we reached both high- and low-frequency cutoffs or found no
clear attenuation with spatial frequency. Thus for half of our sample,
we had quantitative confirmation that we operated in a spatial
frequency range that was near the optimum for the cell. For the rest of
the cells, we reached one cutoff, but we did not obtain data for enough
spatial frequencies to cover the cell's entire bandwidth. We only had
time to collect data around the spatial frequency that we judged
qualitatively to elicit the strongest response. To confirm that for
this half of the sample we used spatial frequencies that were in a
nearly optimal range, we compared the distributions of the spatial
frequencies used for the two half-samples and the resulting complexity
indices (see following text). The two groups did not differ
significantly (P > 0.2 for both comparisons), so data
from all cells were combined.
Spatial frequencies for maximal harmonic and maximal RM stimulus
conditions are shown in Fig.
10A.
Simple and complex cells share the same distribution pattern, with a
mode at 1 cpd and mean ~1.5 cpd. The mean is slightly lower than the
values reported for anesthetized monkeys at comparable eccentricities
(cf. 2.2 cpd in Foster et al. 1985; 2.2-3.2 cpd in
De Valois et al. 1982). However, differences in
experimental conditions, including the lower stimulus luminance in our
experiments, may be responsible for these minor discrepancies.
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It has been suggested that modulated responses of complex cells could
result from "too-low spatial frequency" of the grating (Skottun et al. 1991). This was clearly not the case in
our experiments. For 74/93 complex cells, spatial frequencies for
maximal harmonic and maximal RM conditions either coincided or the
spatial frequency that elicited the maximal RM was higher
than the spatial frequency eliciting the maximal harmonic.
Complexity index (CI)
Distributions of the number of grating cycles within the CRF
(complexity index, CI) (Glezer et al. 1980)
for both the maximal harmonic and maximal RM conditions are shown in
Fig. 10B. The means of the distributions do not differ, so
in the remainder of RESULTS, we will use the maximal
harmonic condition analyzed in the "no saccades mode" for
comparisons with data of other authors.
The idea behind the complexity index is that it may reveal the presence
of preceding "subunits." We did not find evidence for multiple
subunits in most complex cells, unlike complex cells described in some
earlier papers (Movshon et al. 1978; Pollen and
Ronner 1983). Half of our complex cells, including those with RM >1, had a CI ~0.5, so that a half cycle of the grating filled the
CRF (Fig. 10C), and more than two-thirds of the cells had a CI 1. The mean CI was not different for simple cells (0.80 ± 0.68) and complex cells (0.76 ± 0.42), unlike the situation in cat, where complex cells had larger CIs than simple cells and most
cells had CI 1 (Glezer et al. 1980). Values of CI
reported for anesthetized monkeys are also larger than we have found
(Foster et al. 1985). In fact some cells in our sample
had values of CI 
0.5 that may be due to strong inhibitory surrounds
that encroach on the CRF center (Snodderly and Gur
1995), and conceal weak receptive field regions when narrow
single bars are used as probes (Carandini et al. 1999;
De Valois et al. 2000; Glezer and Gauzelman
1997). The absence of multiple (>3) spatial lobes in our
sample of simple cells is also consistent with concealment by powerful
inhibitory influences.
Spatial frequency and window size interactions
We also calculated how many grating cycles were optimal for a given condition. This measure is different from CI: it is the number of cycles that fit a grating window, not the CRF. For complex cells, 1.0 ± 0.8 cycles of a grating were optimal, and for simple cells it was 1.6 ± 1.3. These relationships are illustrated for the 40 complex cells nearest the mode of the CI distribution in Fig. 10C.
In 42/54 cells for which data with different grating windows were
collected, window size had a clear effect on the response amplitude.
The ratio of the most effective window widths to CRF widths was similar
for maximal harmonic (1.5) and maximal RM (1.6) conditions. In most
cases, window sizes slightly wider than the bar-responsive regions were
most effective, although for several cells, windows smaller than the
CRF were required to obtain a response to drifting gratings because of
strong side inhibition. These results are in agreement with Born
and Tootell (1991), who found that inhibition could occur
within the bar-responsive region as well as beyond the bar-responsive
region, as would be expected from a receptive field model with
overlapping center and surround mechanisms (Sceniak et al.
2001).
For the subset of 21 complex cells assigned to layers 2/3, the
number of grating cycles within the window was 1.2 ± 0.6, similar to that reported for supragranular complex cells of anesthetized monkeys (1.3 ± 0.6) (Born and Tootell 1991).
Moreover, side inhibition was common in other layers (cf.
Sceniak et al. 2001): in 27/42 cells, the response
declined when the grating width was extended 1.2-4 times beyond the
CRF. These results are in agreement with the conclusion that most
neurons in V1 are not tuned to extended periodic stimuli but rather to
spatially restricted object boundaries (Born and Tootell
1991; Sceniak et al. 2001; von der Heydt
et al. 1992).
For many complex cells, the harmonic content of the response strongly depended not only on the spatial frequency but also on the spatial window of the grating. An example of the spatial-frequency-window-size interaction for a complex cell is shown in Fig. 11A. Increasing spatial frequency with a fixed window, or increasing window size at a fixed spatial frequency, transformed the response from a frequency doubled to an F1-modulated response. The responses of several complex cells were similarly affected by increasing the grating width beyond the CRF borders, thus demonstrating that the surround may not only suppress or facilitate cells' responses but also have a strong effect on the form of the response. The surround influence was particularly powerful for 10 complex cells and 1 simple cell (of 54 cells tested), resulting in different window widths for maximal harmonic and for maximal RM stimulus conditions. Taken together, these data suggest that V1 neurons can be very context-sensitive and produce a variety of responses depending on stimulus parameters.
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The conditions under which frequency doubling occurs is another line of evidence that high RM values in complex cells did not result from too low a spatial frequency. Frequency doubling was defined as F2 > 0.85·F1 (where 0.85 is twice the F2/F1 ratio for a half-rectified sine function). We observed this feature in response to drifting gratings of low spatial frequency in 28/93 complex cells (and 1 simple cell). However, in 24 of 28 cells, RM was higher in response to higher spatial frequencies (n = 19) and/or another window size of the grating (n = 5). Most of these cells had significant F1 modulation: 16/24 cells had maximal RM >0.5 and 3 had maximal RM >1, "no saccades" mode. Another example of a cell whose RM decreased as spatial frequency was lowered is presented in Fig. 11B. In response to a grating of high spatial frequency, this cell was modulated at the grating's temporal frequency (1st row). With decreasing spatial frequency, the second harmonic appeared in the response (2nd and 3rd rows), and prevailed over the fundamental. Thus low spatial frequencies resulted in frequency doubling (F2) modulation and lower RM values.
Frequency dou
, simple cells;
, complex cells; mean OI values for
simple, 
(
(0.82 ± 0.12) cells.
, the mean RMs of complex and simple cell populations
for a given mode, respectively.
, simple cells;
, complex cells. Left:
"no saccades" analysis mode; right: "aligned"
mode. Top, A and B: maximal harmonic
condition. Correlation coefficients for complex cells,
r = 
