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Transient cells can be neurometrically sustained: the positional accuracy or retinal signals to moving targets
Abstract
The spatial accuracy inherent in retinal ganglion cell responses to moving targets was investigated by measuring trial-to-trial variability in response locus. When moving bars were used as stimuli, analysis of impulse trains showed that parafoveal cells of the magnocellular (MC) pathway provided a consistently accurate spatial signal over a range of target velocities up to ~8 deg/sec. Parvocellular (PC) pathway cells delivered less accurate signals even at low velocities, and their signals became even less accurate at higher target speeds. Human vernier performance in parafovea resembled the physiological MC-cell result, which suggests this feature of MC-cell behavior is functionally utilized. A similar result held with moving gratings; the highest signal-to-noise ratio for MC-cells occurred at low temporal frequencies. Psychophysical vernier thresholds to grating targets resembled phase variability of MC-cell responses as a function of temporal frequency. The analyses of physiological data utilized both the number of impulses a cell generates and their timing; MC-cells' responses may have low peak rates to slow moving stimuli compared to fast stimuli, but a spatially precise signal may be derived because many impulses are evoked at lower speeds. The results show that transient neurons can yield precise information about slowly moving stimuli, provided appropriate central mechanisms for extracting this information are present. Such central mechanisms would require either a long integration time or a suitable spatiotemporal filter that integrates over the ganglion array. Because accurate vernier performance can be achieved with brief presentations, the latter alternative is indicated.
History
Received November 5, 2001; published May 6, 2002
Citation
Ruttiger, L., Lee, B., & Sun, H. (2002). Transient cells can be neurometrically sustained: the positional accuracy or retinal signals to moving targets.
Journal of Vision, 2(3):3, 232-242,
Keywords
magnocellular, parvocellular, ganglion cell, vernier
Evidence for transient and sustained channels in the
human visual system was first derived from psychophysical observation
(Kulikowski & Tolhurst, 1973;
Legge, 1978;
Tolhurst, 1975). Such channel concepts
have since undergone significant modification
(Anderson & Burr, 1985;
Grossberg, 1991;
Lennie, 1980;
Stromeyer, Klein, Dawson, & Spillmann, 1982),
but there is physiological evidence for pathways with different temporal
properties at the subcortical level
(Dreher, Fukuda, & Rodieck, 1976;
Lee, Martin, & Valberg, 1989b;
Lee, Pokorny, Smith, Martin, & Valberg, 1990).
Cells of the magnocellular (MC) pathway display transient responses to a step
change in luminance whereas responses of cells of the parvocellular (PC) pathway
are more sustained. Cells of the MC-pathway exhibit a bandpass temporal
modulation transfer function, whereas such functions for cells of the PC-pathway
are more lowpass (Lee et al., 1990). It is
often assumed that transient channels can yield little information about slowly
changing or moving stimuli. Levi (1996)
showed that vernier thresholds for drifting gratings remained constant up to
about 8 Hz and then increased. He suggested that PC-pathway contributed to
thresholds at lower temporal frequencies and MC-pathway at higher temporal
frequencies. In another study, Kontsevich and
Tyler (2000) found that stereopsis was superior in a
sustained stimulus regime and concluded that the PC-pathway was involved. Here
we examine the assumption that the transient MC-pathway does not deliver
accurate localization information to slowly moving targets.
The strategy adopted in these experiments was to
measure ganglion cell responses to targets moving at different velocities and to
compare physiological results with human performance. We analyzed the spatial
variability of ganglion cell responses from trial to trial; the analysis
revealed an unexpected result. With moving bars, a consistently accurate spatial
signal was delivered by MC-cells up to ca. 8 deg/sec in parafovea. With moving
gratings, the variability in response phase is least for MC-cells at low
temporal frequencies. To compare psychophysical performance on a spatial task
with the cellular data, we chose vernier performance as a measure of human
spatial localization ability. The pattern of physiological results was similar
to psychophysical vernier performance of human observers with the same targets.
Signals from transient neurons can therefore yield more information about slowly
changing stimuli than has previously been assumed. Exactly how central cortical
mechanisms may extract this positional information remains to be determined.
Mechler and Victor (2000) recently
showed that some form of spatial comparison by central spatiotemporal filters is
necessary for vernier performance; temporal information alone is not sufficient.
The current results would be consistent with this suggestion, and we suggest
that evidence for transient and sustained channels in human vision reflects an
interaction of properties of the retinal output and those of central processing
mechanisms, rather than being derived from the properties of peripheral
mechanisms per
se.
Visual stimuli were generated on a CRT video display
(distance 2.26 m, frame rate 195 Hz). The luminance of the background was at 40
cd/m2 and chromaticity of the background was (0.45, 0.47) in CIE x, y
coordinates. Stimulus chromaticity was always identical to that of the
background. In Experiment 1, the stimulus was a rectangular bar (4
x 240 arc min) moving over cells'
receptive fields. The luminance contrast of the bar was fixed at 80% Michelson
contrast. The velocity of the bar was varied from 0.5 to 32 deg/sec (0.5, 1, 2,
4, 8, 16, and 32 deg/sec). Movement distance was 1 deg visual angle, which is
large compared to the size of receptive field centers (15 arc min) at the
eccentricities tested. In Experiment 2, the stimulus was a drifting sinusoidal
grating. The spatial frequency was 0.4 cycle/deg and luminance contrast 90%. The
temporal frequency varied from 0.5 to 26 Hz (0.54, 1.08, 2.17, 4.34, 8.68, 13,
17.4, and 26 Hz).
Ganglion cell recordings were obtained from the retinae
of five anesthetized macaques
(Lee et al., 1989b). Animal care procedures
were approved by the animal care committee of the State of Lower Saxony.
Neuronal activity was recorded directly from retinal ganglion cells by an
electrode inserted through a cannula entering the eye behind the limbus. Cell
identification was achieved through standard tests
(Lee et al., 1989b). These included
achromatic contrast sensitivity and responses to lights of different
chromaticity. Additional tests (e.g., measuring responses to heterochromatically
modulated lights)
(Smith, Lee, Pokorny, Martin, & Valberg, 1992)
were employed in rare cases when identification was equivocal. Receptive field
eccentricities were between 4 and 8 deg. The eyes were sutured to a ring during
preparation, which minimized eye movement. During each condition of measurement,
any residual systematic drifts of response position could be identified through
the analysis technique. Occasional systematic drifts of 1 to 2 min of arc were
found, and we assume them to be due to residual eye movements. These data were
discarded. A 3-mm artificial pupil was routinely used. Gas-permeable contact
lenses of the appropriate power were used to bring stimuli into focus on the
retina.
Times of spike occurrence were recorded to an accuracy
of 0.1 msec, and averaged histograms were simultaneously accumulated. For bar
stimuli, numbers of presentations were 20, 20, 40, 40, 40, 40, and 60 cycles
(for velocities 0.5, 1, 2, 4, 8, 16, and 32 deg/sec, respectively); binwidths of
histograms were 16, 12, 6, 3, 2, 1, and 1 msec, respectively. For grating
stimuli, numbers of presentations were 20, 20, 20, 40, 40, 40, 40, and 60 cycles
(for temporal frequencies 0.54, 1.08, 2.17, 4.34, 8.68, 13, 17.4, and 26 Hz,
respectively). For the bar stimuli, length of histograms recorded was 128 bins
(not all bins are shown in Figure 1). Duration of histograms was extended beyond
movement duration, to allow estimation of maintained firing and to capture
responses at high movement speeds, which are delayed due to response latency.
When stimulus presentation time is converted into retinal location, relative
retinal positions of the moving bar beyond one arc deg are thus virtual
values.
The same display system as in the physiological
experiments was used. The viewing distance was 3.60 m in Experiment 1 and 0.48 m
in Experiment 2. In Experiment 1, the vernier stimulus consisted of two vertical
bars (4 x 20 arc min) separated
vertically by 4 arc min. The two bars were presented 5 deg below a fixation
point. During the 185 msec presentation time, the bars were moved randomly from
left to right or vice versa. In Experiment 2, the vernier stimulus consisted of
two horizontal gratings (6.33 x 20
arc deg) separated horizontally by 11 or 5 arc min. The two gratings were
presented 5 deg to the right or left of the fixation point. During the 150 msec
presentation time, the gratings were drifted randomly upwards or downwards.
Except for the difference in spatial structure due to the presentation of two
targets, the luminance, chromaticity, and spatial frequencies of the stimuli and
background were the same as in physiological experiments. For bar stimuli, the
movement velocities were the same as in physiological experiment, and for
grating stimuli, the temporal frequencies were 0.5, 1, 2, 4, 8, 13, 17, and 26
Hz.
To achieve a subpixel resolution in Experiment 1, the
intensities of a row of pixels to the left and right of one of the bars were
adjusted so as to shift the centroid of the bar by the required amount
(Morgan & Aiba, 1985). To ensure that
relative positional information could not be derived from stimuli onset or
offset locations, in some set of experiments, 50-msec masking bars were
presented at both onset and offset of the bars. Presence or absence of the masks
had no effect on
thresholds.
Observers viewed the visual target monocularly and
pressed buttons to indicate the position of the leading bar (Experiment 1) or
which grating has a phase shift upward (Experiment 2). A two-alternative
forced-choice, random interleaved dual-staircase procedure was used; 71% correct
values were estimated from staircase reversals and psycho-metric functions. For
details see
Rüttiger and Lee (2000).
Five observers participated in one or both of the
experiments. Observers B.L., L.R., and H.S. are authors, and E.B. and J.K. are
naïve observers. E.B., J.K., L.R., and H.S. have normal color vision as
assessed with Neitz Anomaloscope, Ishihara pseudoisochromatic plates and
Farnsworth-Munsell 100-Hue Test. Observer B.L. is a deuteranope. Observer H.S.
is myopic and wore contact lens during
experiments.
We recorded responses to moving targets of macaque
retinal ganglion cells in parafovea. For each cell, the locus of the receptive
field was determined and the target movement centered around this point.
Figure 1a shows responses of a MC-pathway
cell to a moving bar at different movement velocities, with time as the
abscissa. Increasing target velocity causes the temporal duration of the
response to decrease, as does total impulse number, which is represented by the
area under the response histogram. Figure 1b
shows responses of the MC-cell with the abscissa expressed as retinal locus. As
movement speed increases, peak rate initially increases, and the spatial
position of the response shifts to the right due to response latency. The width
of the response curve remains similar at low target velocities at about 15 arc
min, which is the expected size of receptive field center diameters of MC-cells
at this retinal eccentricity
(Lee, Kremers, & Yeh, 1998). At the
highest speeds, the response begins to smear out spatially and decrease in
amplitude. This is due to the dwell time over the receptive field center, which
is ca. 25 msec at 10 deg/sec, becoming shorter than the duration of the initial
peak of cell's impulse response function (ca. 25 msec at the retinal illuminance
used
[Lee, Pokorny, Smith, & Kremers, 1994]).  Figure 1. Responses
of a MC-cell as a function of velocity. Averaged responses to an elongated bar
(80% contrast) moved across the receptive field at different velocities are
shown. a. The abscissa is expressed in time. b. The abscissa is expressed in
retinal position. Below each histogram is an example of an impulse train from a
single sweep. Distance of bar movement was 1 arc deg. At 16 and 32 deg/sec,
responses are delayed due to response latency, and the relative retinal position
of the moving bar greater than 1 arc deg is a virtual value.
Below each histogram in
Figure 1b is shown an example of an impulse
train of a single stimulus cycle. There are many impulses (30-40) at low
velocity (0.5 deg/sec), but at high velocities, only few impulses are
generated.
The relation of stimulus velocity to cells' peak firing
rate and to number of impulses per response is illustrated in
Figure 2, which includes averaged data from
11 MC- and 11 PC-cells from which complete data sets were obtained (consistent
partial data sets were obtained from similar numbers of cells). Details of
calculation of these measures are given in the legend. PC-cells generate weaker
responses to achromatic stimuli than MC-cells
(Kaplan & Shapley, 1986;
Lee, Martin, & Valberg, 1989a), and
their responses are more sustained, so that peak rate does not rise as markedly
with velocity as with MC-cells. The error bars in
Figure 2b represent the standard deviation
from cycle to cycle of number of impulses per response.
 Figure 2. Peak
rates (a) and number of impulses per response (b) as a function of velocity.
Mean data are shown for 11 MC- and 11 PC-cells. The error bars in
“b” indicate the standard deviation of the number of impulses per
response from sweep to sweep. Cells' firing rates were found by moving a 5-bin
(see “Methods” for binwidth) window to seek the peak response.
Numbers of impulses per response were counted within a window defined by the
period during which the response was above the maintained activity level. Both
of these measures were robust against minor changes in window width.
The accuracy of the spatial signal inherent in the
ganglion cell impulse train could be dependent on both number of impulses and
their timing. To quantify the spatial reliability of the response, we used a
template matching procedure
(Sun, Lee, & Rüttiger, 2002). For
each velocity, the response histogram was first smoothed with a Gaussian filter
to obtain a matching template, as in
Figure 3a. Each individual impulse train was
shifted over the template until the locus of maximum correlation was found. This
is illustrated in Figure 3b, where a number
of impulse trains from a MC-cell are displayed. Arrowheads indicate the best-fit
location of each train to the template. The scatter of the best-fit positions is
a fraction of the width of the template. We took the standard deviation of these
loci as a measure of the accuracy of spatial localization by the cell, and
termed it spatial variation. Temporal variation was calculated from the product
of spatial variation and stimulus speed. To investigate the robustness of the
analysis, we also tested a normal distribution as a template with similar width
to the actual response histogram. This did not significantly affect the spatial
variation obtained. We then tested the effect of varying the standard deviation
of the Gaussian distribution. The pattern of results was robust against this
manipulation until the width of the Gaussian was changed by a factor of more
than two. We conclude that the results are not an artifact of the template
matching
procedure.  Figure 3. A method
of defining precision of the spatial signal.
a. A response template was generated by smoothing the response histogram with a
Gaussian function (S.D. 4 bins).
b. Impulse trains from individual sweeps
were shifted over the template until the maximal correlation was found. A subset
of individual impulse trains are shown. Arrowheads indicate the locus of maximal
correlation. The standard deviation of these loci gives a measure of spatial
reliability (termed here spatial variation). Stimulus velocity was 4
deg/sec.
The outcome of the analysis is shown in
Figure 4. Spatial variation
(Figure 4a) remains similar up to ca. 8
deg/sec for MC-cells and then rises, which implies that cells of the MC-pathway
can yield a consistently accurate positional signal over a range of lower
velocities. Responses of PC-cells show larger spatial variation than those of
MC-cells even at the lowest target velocity, and spatial variation of PC-cell
signals increases rapidly with target velocity. Temporal variation
(Figure 4b) decreases as a function of
velocity for both MC- and PC-cells, and it reaches a minimum of 1 to 2 msec for
MC-cells.  Figure 4. Standard
deviations (SD) of response loci as a function of bar velocity in space (a) and
time (b). Mean data are shown for 11 MC- and 11 PC-cells; data from on- and
off-center cells were similar and have been combined; light bars were used for
on-center cells, dark bars for off-center cells.
c. Psychophysical vernier thresholds from three human observers as a function of
bar velocity.
For comparison with the physiological data, we measured
vernier thresholds as a function of velocity for a pair of bars at 5-deg retinal
eccentricity, and these are shown in
Figure 4c. Vernier thresholds remain
constant over a range of velocities, and then increase. The shape of the
relationship between vernier threshold and velocity strongly resembles MC-cell
data, and furthermore the psychophysical thresholds are similar in absolute
magnitude to the response precision of single MC-cells, as in other hyperacuity
tasks
(Lee, Wehrhahn, Westheimer, & Kremers, 1995;
Rüttiger & Lee, 2000). The
parafoveal vernier data resemble earlier foveal measurements. In the fovea,
Westheimer and McKee (1975) showed
that psychophysical thresholds for a vernier task involving pairs of moving
targets remained constant with target velocity up to about 4 deg/sec, and
subsequent work has confirmed this finding
(Levi, 1996;
Morgan, Watt, & McKee, 1983). In
parafovea, the plateau extends up to 8 deg/sec in both the psychophysical and
physiological MC-cell data, presumably due to the coarser retinal grain outside
the fovea. The rapid deterioration in PC-cell accuracy with velocity does not
match the psychophysical results.
One reason for the deterioration in cellular
performance above 8 deg/sec is likely to be the smearing out of the response. At
16 deg/sec, a single cell’s receptive field center diameter (15 arc min)
will be traversed by the bar in 15 msec, which is shorter than the duration of
the excitatory peak impulse response (about 25 msec
[Lee et al., 1994]). The statistics of the
impulse train making up the response are also likely to be a significant factor.
The invariant spatial accuracy of MC-cell signals
independent of target velocity was unexpected of a transient pathway and led us
to consider cell responses to other moving stimuli, such as gratings. Cell
responses were recorded to gratings drifted across the receptive field at
temporal frequencies from 0.54 to 26 Hz. The impulse train in response to the
grating varies from cycle to cycle. To estimate response variability, responses
to each cycle were Fourier analyzed, as in a previous study by
Croner, Purpura, and Kaplan (1993). In
Figure 5a, an example of a response to a
single cycle is shown and below are plotted real and imaginary components from
the Fourier analysis of a sample of cycles at a temporal frequency of 4.34 Hz.
As in Croner et al. (1993), noise was
calculated
as
where di is the vector difference between
response to cycle i and the mean
response, and N is the total number of cycles. Croner et al. showed that at a
fixed temporal frequency, the noise of the response was independent of contrast.
We confirmed their result, as shown in
Figure 5b. Response amplitude saturates as
contrast increases and has been fitted by a Naka-Rushton function. Noise is
almost independent of
contrast.  Figure 5. Analysis
of noise in grating responses. Each cycle (one example of an impulse train
shown) is Fourier analyzed to obtain real and imaginary response components.
When plotted on these axes (a), noise can be defined as indicated in the text
and in Equation 1. b. For a fixed temporal
and spatial frequency, response amplitude increases with contrast following a
saturating function, but response noise remains unchanged.
Figure 6 shows
single-cycle Fourier analyses for a MC-cell at different temporal frequencies.
The line segments indicate mean response vectors of each temporal frequency. As
frequency increases, the response vectors rotate clockwise due to response phase
delays. Both response amplitude and variability increase with temporal
frequency. Averaged data from a set of MC- and PC-cells are shown in
Figure 7. Response amplitude
(Figure 7a) of MC-cells increases with
temporal frequency more rapidly than that of PC-cells. Noise increases steeply
as a function of temporal frequency in a similar manner for both cell types
(Figure 7b).
Figure 7c shows the ratio of response
amplitude to noise. For both cell types, the highest ratio occurs at the lowest
temporal frequency. Although it is unexpected in view of the transient responses
of the MC-cells that the highest signal-to-noise ratio occurs with slowly moving
gratings, this result is consistent with the results with moving bars, in that
MC-cells potentially can yield precise information about slowly moving
stimuli.  Figure 6. Real and
imaginary components of a MC-cell's responses to gratings of different temporal
frequencies together with mean response vectors (only 20 cycles per frequency
are plotted for clarity). As frequency increases, the mean response vector
rotates due to phase delay. Response amplitude and noise both increase.
 Figure 7. a.
Response amplitude as a function of temporal frequency for MC- and PC-cell
samples. b. Noise as a function of temporal frequency is seen to increase
similarly for the two cell classes. c. The ratio of response amplitude to noise
is shown to be maximal at low temporal frequencies for both cell classes.
We tested if the results in
Figure 7 could be simulated by a simple
description of impulse statistics. Maintained activity of macaque ganglion cells
can be described by a low-order gamma process with refractory period
(Troy & Lee, 1994). The impulse
generation by the drifting grating was assumed to follow a sinusoidally
modulated Poisson process with a refractory period. Such a model does not
provide a complete description of neuron responsivity to repetitive stimuli
(Reich, Victor, & Knight, 1998), but
our goal was to test if such a simple model could capture the main features of
the data. Probability of impulse generation was modulated around a maintained
firing rate of 20 imp/sec with a 3-msec refractory period. The impulse trains so
generated were analyzed in the same way as for the actual data. The amplitude of
modulation of the probability of impulse generation was adjusted to give Fourier
response amplitudes similar to those observed for MC-cells. In the simulation,
noise increased steeply as a function of temporal frequency as in the actual
data and thus signal-to-noise ratio decreased. We conclude that the results of
Figure 7 do not require any special
mechanism of impulse generation but are a consequence of impulse
statistics.
It remained to be shown if the high signal-to-noise
ratio in MC-cell responses at low temporal frequencies is behaviorally utilized
by central mechanisms. We again consider this possibility in the context of a
vernier task. Response phase is assumed to be the relevant parameter for coding
spatial location. We therefore estimated the angular standard deviation of
response phase (Figure 8a) from the
following equation
(Batschelet, 1981).
where
φi is the vector angle
between cycle i and the mean response,
and N is the total number of cycles. Mean data for
MC- and PC-pathway cells are shown in
Figure 8b. For the MC-pathway, standard
deviations remain similar up to ca. 3 Hz and then increase, whereas for the
PC-pathway standard deviations are higher than the MC-pathway deviations by a
factor of 2 (i.e., spatial accuracy of the signal is lower) at the lowest
frequency tested and then increase steadily. Psychophysical vernier thresholds
for pairs of gratings at 5 deg eccentricity are shown in
Figure 8c. Vernier thresholds remained
unchanged up to ca. 4 Hz, and then increased with temporal frequency. This
result replicates foveal data obtained by other studies
(Levi, 1996). The psychophysical data thus
showed similar pattern to the MC-pathway cells, which is consistent with the
hypothesis that the information delivered by MC-cells is centrally
utilized.  Figure 8. a.
Angular standard deviation of response phase is calculated as in
Equation 2. b. Angular standard deviation
of response phase as a function of temporal frequency for MC- and PC-cells. c.
Psychophysical vernier thresholds from three human observers as a function of
grating temporal frequency.
The goal of the current study was to estimate the
spatiotemporal precision inherent in ganglion cells' signals. Vernier tasks, as
an unparalleled example of spatial localization, provide a psychophysical
benchmark against which cell data may be compared. Central mechanisms
responsible for vernier performance may take alternative forms, e.g.,
independent cortical filters for each vernier target or activation of a single
spatial filter by paired targets
(Beard, Levi, & Klein, 1997;
Burbeck & Yap, 1990;
Klein & Levi, 1987;
Levi & Klein, 1990;
Morgan & Regan, 1987;
Watt & Morgan, 1983;
Wilson, 1986). Signal-to-noise ratio of
the retinal output must provide a limiting factor for performance for both these
alternatives. Thus, it is the similarities of curve shape between physiological
and psychophysical data in Figures 4 and
8, rather than absolute level, which suggest
a link between the cellular and psychophysical performance.
It has been assumed
(Kontsevich & Tyler, 2000) that
the transient response of the MC-pathway would cause it to yield positional
information of low accuracy at slow stimulus speeds, but we show here that this
need not be the case. The MC-pathway data in
Figures 4 and
8 show that the MC-cells appear well adapted
to deliver consistently accurate positional signals over a range of slow target
velocities, and this pattern of behavior is consistent with human vernier
performance. The MC-pathway provides the main input to the parietal cortical
stream responsible for motion and positional processing
(Merigan & Maunsell, 1993), and the
velocity independence of the positional accuracy of MC-pathway signals is likely
to be valuable in other spatial contexts.
In contrast to MC-cells, the spatial information
delivered by PC-cells appears to degrade rapidly as target velocity increases
(Figure 4). The greater numerosity of cells
of the PC-pathway might provide the possibility of integrating over large
numbers of cells to compensate for the low positional accuracy of individual
neurons. However, it is unlikely that integration over large numbers of cells to
improve signal-to-noise ratio is compatible with maintaining high spatial
accuracy.
It is thought that visual information in neuronal spike
trains may be encoded either in response firing rate
(Shadlen & Newsome, 1996) or in
response structure, i.e., the timing of individual impulses
(McClurkin, Gawne, Optican, & Richmond, 1991).
At lower velocities, the MC-cells give extended response with many impulses.
Under these conditions, precise timing of individual impulses is not likely to
play an important role. At higher velocities, few impulses are delivered and the
timing of individual impulses is presumably critical in providing spatial
information. At 8 to 10 Hz, MC-cell signals can reach temporal precision of
about 1 to 2 msec (Figure 4b). This is
consistent with psychophysical studies
(Carney, Silverstein, & Klein, 1995;
Fahle & Poggio, 1981;
Levi, 1996;
Mechler & Victor, 2000;
Morgan et al., 1983), which suggest that
temporal accuracy in the millisecond range is involved in vernier performance at
high velocities. Neurophysiologically, a variety of recent studies have shown
that in central processing by cortical neurons temporal information can also be
signaled with millisecond accuracy
(Mainen & Sejnowski, 1995).
The resemblance between the accuracy of MC-cell
positional signals and psychophysical vernier performance suggests that this
information delivered by MC-cell is utilized by central mechanisms. How can this
be achieved at low velocities? The template matching and Fourier analyses use
time windows of hundreds of milliseconds or more, but human vernier thresholds
with moving targets do not improve much after presentation times exceed 50 to
100 msec (Morgan et al., 1983;
Westheimer & McKee, 1977). At
least two possible cortical mechanisms may be conceived. One possibility is that
a cortical mechanism uses an analysis window of fixed duration independent of
target velocity. We tested this possibility on our neurophysiological data and
found that, for example, with a Gaussian template of 50-msec standard deviation,
position of slow-moving targets was poorly estimated, and the match between
physiology and psychophysics became unsatisfactory. The second possibility is
that instead of deriving information from a single cell with a long time window,
some sophisticated spatiotemporal filter can be used to analyze the differential
output from a small group of cells within a brief time window. Recently,
Mechler and Victor (2000) reviewed some
of the requirements for central mechanisms for vernier tasks and concluded that
temporal asynchrony alone does not suffice. They concluded that tuned
spatiotemporal integrating mechanisms activated by motion signals are involved,
and spatial integration and comparison are essential. The current results would
be consistent with this view.
With low bar velocities and brief presentation times,
we estimated that only a few MC-cells would be swept during the psychophysical
exposure duration in the vernier task. For example, at 0.5 deg/sec, taking into
account coverage factor
(Grünert, Greferath, Boycott, & Wässle, 1993),
receptive fields of 4 to 8 cells would be swept by each (20 arc min) bar. If a
limited number of ganglion cells can contribute information, each cell must
contribute a signal of precision comparable to psychophysical performance,
because improvement by pooling over cells is limited. Our data are consistent
with this interpretation. When interaction between cell outputs occurs, a direct
relation between retinal physiological data and psychophysical thresholds may
break down. For example, psychophysical vernier thresholds tend to plateau at
very high contrasts, but
Rüttiger and Lee (2000) showed
that spatial precision of ganglion cell signals continues to increase with
contrast. Detailed comparisons of this sort, including both spatial and contrast
parameters, may help define more precisely cortical filters that handle the
retinal signal.
Response amplitude curves of MC-cells peak at fast
velocities (Figure 2a) and high temporal
frequencies (Figure 7a). The MC-pathway is
thought to provide the physiological basis of detection of uniform field
luminance modulation (Lee et al., 1990). In
such detection experiments, psychophysical thresholds are a bandpass function of
temporal frequency, and appear to correlate with cellular peak rate per se,
rather than signal-to-noise ratio. In comparison, we show here that
psychophysical vernier thresholds for bars and gratings are a lowpass function
of temporal frequency, and correlate with signal-to-noise ratio
(Figure 7c), rather than cellular peak rate.
This difference between luminance modulation detection and the spatial vernier
judgement presumably arises in the mode of operation of cortical detection
mechanisms. Two mechanisms with different spatiotemporal characteristics may be
involved in the two types of task. Alternatively, the same mechanism may be
involved but in the absence of spatial context it can operate only on the basis
of cells' peak firing rates. Introduction of spatial context, e.g., by adding a
surround, drastically changes the shape of the luminance detection temporal
characteristic (Brown, 1965;
Spehar & Zaidi, 1997;
Watson, 1986), but this might be
consistent with either alternative. Comparison of physiological and
psychophysical data in other spatiotemporal contexts may clarify this
issue.
Based on neurometric analysis of cell impulse trains,
signals from transient neurons, e.g., MC-cells, can yield significant
information about slowly changing stimuli. A close parallel between MC-cell data
and psychophysical vernier performance suggests that central cortical mechanisms
may extract this positional information from transient responses through the use
of appropriate spatiotemporal filters. We suggest that evidence for transient
and sustained channels in human vision reflects an interaction of properties of
the retinal output and those of central processing mechanisms, rather than being
derived from the properties of peripheral mechanisms per
se.
This work was supported by grant DFG Le-524/14-2 from
the Deutsche Forschungsgemeinschaft and by NEI R01-13112. Commercial
relationships:
None.
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