To image population responses in area V1 with the appropriate temporal resolution, we stained the cortex with a voltage-sensitive dye (VSD). VSD imaging delivers parallel recording from tens of square millimeters (Grinvald and Hildesheim, 2004
) with a resolution of ~100 μm in space (limited by light scatter in tissue) and few ms in time (limited by photon noise). The dyes fluoresce in proportion to membrane potential and bind to cell membrane mostly in superficial layers (Grinvald and Hildesheim, 2004
; Petersen et al., 2003b
). In addition to layer 1–3 neurons, these layers contain apical dendrites and axons from neurons in deeper layers.
A challenge with VSD signals is that they typically constitute < 1/1000 of the overall fluorescence, and are easily swamped by physiological noise arising from various sources. Some sources, e.g. respiration and heart beat, generate artifacts that are fairly repeatable (Shoham et al., 1999
). Other sources, e.g. slow variations in blood oxygenation, generate artifacts that are non-repeatable (Kalatsky and Stryker, 2003
). Additional variability arises from ongoing cortical activity (Arieli et al., 1996
Complex cells and the sources of VSD signals
We reasoned that the source of the VSD signal in area V1 should consist mostly of complex cells, because optical signals from multiple simple cells would approximately cancel out. Consider the membrane potential responses of idealized simple and complex cells to a stimulus that reverses in contrast sinusoidally (). A simple cell () will respond with an oscillation at the frequency of contrast reversal (Jagadeesh et al., 1993
; Movshon et al., 1978a
). A second simple cell with a receptive field of opposite polarity will respond with an oscillation of the opposite sign (). If these two cells contribute equally to the optical signal, their contributions will cancel out. On the other hand, complex cell responses are independent of spatial phase (Movshon et al., 1978c
), so a complex cell will respond with an oscillation at twice the frequency of the stimulus (). Critically, all complex cells will respond with the same temporal phase, so their contributions to the optical signal will summate rather than cancel. This cancellation argument is meant to hold on average; it does not require that the responses of simple cells be perfect sinusoids, or that each simple cell has an anti-cell that gives precisely the opposite response.
Figure 1 Responses of idealized simple and complex cells to a stimulus (a standing grating) whose contrast modulates sinusoidally in time. We illustrate the responses of three cells, whose receptive fields are shown in the left column. The dashed lines indicate (more ...)
This reasoning is confirmed by observing the VSD responses to stimuli that periodically reverse in contrast (). Gratings that contrast-reverse sinusoidally elicit responses that oscillate at twice the sinusoid’s frequency (). These 2nd harmonic responses can be accompanied by a 4th harmonic component (e.g. response to 5 Hz stimulus in ); indeed, the traces often resembled triangular waveforms more than sinusoids.
Figure 2 VSD responses to contrast-reversing stimuli, and basic properties of the 2nd harmonic response. (A) VSD signals measured in response to a blank screen, averaged over 10.6 mm2 of cortex. (B) VSD signals measured over the same area in response to a standing (more ...)
Similar oscillations could be observed in the field potential throughout the depth of cortex (Supplementary Figure 1
). Just as in VSD signals, in field potentials the 1st
harmonic responses are negligible, and the 2nd
harmonic responses are strong (Schroeder et al., 1991
Frequency-dependence of VSD noise
Seeking to elicit strong VSD signals that stand out from the noise, we turned our attention to the properties of the noise. We measured the VSD responses to a uniform gray screen (“noise”), and studied how their amplitude depends on frequency (). Noise in VSD measurements is largest at low temporal frequencies (Arieli et al., 1995
; Prechtl et al., 1997
). We found that its amplitude decreases with the inverse of frequency: it was well fitted by the expression 1/fx
, where f is frequency and the fitted exponent was x = 1.04 ± 0.06 (s.e., n = 6).
This dependence of noise on frequency agrees with the notion that most physiological sources of variability contribute power to low frequencies. Spontaneous vasomotor activity oscillates below 0.1 Hz (Kalatsky and Stryker, 2003
) and respiration oscillates at 0.3–0.6 Hz. In the higher range of frequencies lies the large artifact caused by heart beats (Shoham et al., 1999
), which oscillates at 2.5–4.2 Hz. These oscillations do not appear in the traces averaged across acquisition epochs () because our data are acquired randomly in relation to heart beats and the contribution from different epochs cancel each other out. The remaining amplitude spectrum is likely to reflect mostly the ongoing cortical activity, i.e. all neural signals that are not synchronous with the stimulus (Arieli et al., 1996
Amplitude spectra of the 1/f kind are commonly observed in human EEG (Pritchard, 1992
). Indeed we observed them also in field potentials (Supplementary Figure 1
). In response to a gray screen, the field potential shows large fluctuations, whose amplitude decreases with frequency. We fitted this amplitude with the same exponential expression as our VSD data, and found exponents of x = 1.00 ± 0.29 (s.e., n = 16).
Basic properties of 2nd harmonic responses
We then returned to the 2nd
harmonic responses and asked at which stimulus frequencies they are most distinct from noise. The relationship between 2nd
harmonic signal and noise depends on stimulus frequency (). Stimuli above 8–10 Hz typically elicited small responses, consistent with the preference of cat V1 neurons for frequencies <10 Hz (DeAngelis et al., 1993
; Movshon et al., 1978b
; Saul and Humphrey, 1992
). Responses elicited by stimuli below ~3 Hz, conversely, overlapped with large noise components and were thus not easily measured. Between these extremes lie the stimuli reversing at 4–8 Hz, which elicit 2nd
harmonic responses that are strong and have frequencies (8–16 Hz) high enough to clear the noise. On average, the optimal signal/noise was obtained at 5.2 ± 1.4 Hz (s.d. n = 5, ). For subsequent experiments, therefore, we generally chose to stimulate at 5 Hz and to measure responses at 10 Hz.
harmonic responses yield not only a measure of response magnitude, but also a measure of latency (). In sinusoidal responses, this latency can readily be measured from the sinusoid’s phase. For a pure delay, phase decreases linearly with frequency. Latencies are therefore estimated by fitting a line to graphs relating response phase to stimulus frequency. The slope of this line is known as integration time (Reid et al., 1992
) and indicates the latency between the stimulus onset and the bulk of the resulting response. We found it to be rather uniform across experiments, 82 ms for the example experiment () and 82 ± 5 ms on average (s.e., n = 4). Response latency in V1, however, is far from fixed and depends on factors such as contrast (Dean and Tolhurst, 1986
), temporal content (Reid et al., 1992
), and spatial content (Bredfeldt and Ringach, 2002
; Frazor et al., 2004
). Indeed, in a control experiment (not shown) we found the integration time to be ~60 ms longer at 10% contrast than at 100% contrast.
Maps of orientation selectivity from 2nd harmonic responses
harmonic responses yielded high-quality maps of orientation preference (). Stimuli of different orientation elicited the profiles of activity typical of cat V1 (Hübener and Bonhoeffer, 2002
), with orthogonal orientations yielding complementary maps (). These profiles of activity could be combined to produce the characteristic map of orientation preference ().
Figure 3 Maps of orientation preference obtained from 2nd harmonic responses. (AD) Amplitude of the 2nd harmonic responses to standing gratings with different orientations, whose contrast reversed at 5 Hz. For graphical purposes, these maps were corrected by subtracting (more ...)
The quality of these maps can be assessed from the population responses expressed as a function of preferred orientation (). Having labeled each pixel with an orientation preference (), we expressed the responses to individual stimulus orientations () as a function of preferred orientation (). As expected, the responses are strongest in the pixels selective for the stimulus orientation and weakest in the pixels selective for the orthogonal orientation.
These results can be summarized by a single population response profile, where orientation preference is expressed relative to stimulus orientation (). To quantify this profile we fitted it with a circular Gaussian (, curve
), and estimated the half width at half-height. The average value was 30 ± 5 deg (s.d., n = 14), comparable to the value (38 ± 15 deg) observed in the membrane potential of individual V1 neurons (Carandini and Ferster, 2000
). An additional effect of the stimulus is an elevation of responses that is independent of orientation (Sharon and Grinvald, 2002
): the trough in the profile of activation () is substantially higher than the responses to a blank screen (, open symbols). A similar effect is seen in the membrane potential of complex cells, which show some depolarization in response to all orientations, including those orthogonal to the preferred (Carandini and Ferster, 2000
harmonic responses () are much stronger and better tuned than the 1st
harmonic responses (). This observation confirms an assumption that we had made in our argument for the cancellation of simple cell responses (): that simple cells whose receptive fields have different polarity are not segregated over the scale resolved by VSD imaging (~100 μm). This assumption is reasonable because nearby simple cells can be selective for widely different spatial phases of a grating stimulus (DeAngelis et al., 1999
; Pollen and Ronner, 1981
The signals provided by the 2nd
harmonic responses () are also superior to those observed at the 0th
harmonic, the mean of the responses over time (). One might expect a strong signal at this harmonic because simple and complex cells respond to sinusoidal stimuli not only with a modulated response, but also with an elevation in mean potential (Carandini and Ferster, 2000
; Jagadeesh et al., 1993
). Indeed, visual stimuli increase the VSD amplitude at the lower frequencies (). However, this increase does not seem to be appropriate for mapping purposes, as it is noisy and not discernibly tuned for orientation (). The noisiness and lack of selectivity of the 0th
harmonic might result from this signal having to compete with the strong noise present at the low frequencies ().
Maps of retinotopy from 2nd harmonic responses
The 2nd harmonic responses could also be used to yield maps of retinotopy (). We measured these maps by stimulating with contrast-reversing gratings framed by elongated rectangular windows presented at various positions (). Moving the stimulus from left to right caused concomitant changes in the profile of the activity (). Moving the stimulus from high to low caused the activity to move from posterior to anterior (). By combining the responses to all these stimuli we computed a map of retinotopy, which relates the visual field () to the surface of the cortex ().
Figure 4 Maps of retinotopy obtained from 2nd harmonic responses and their relation to the orientation preference maps. (A–B) Stimuli were gratings windowed in narrow rectangles. (C–D) Amplitude of 2nd harmonic responses. The gray scale (white (more ...)
The function underlying our maps of retinotopy is simple, but suffices for the job at hand (). This mapping function relates a point in visual space to a point in cortex. It is linear and is specified by only 4 parameters: the two Cartesian coordinates of the area centralis in cortex, the angle of rotation, and the magnification factor (see Methods). A first limitation of this mapping function is that it is one-to-one, which is appropriate for area 17 or 18 but not for the region that spans the two, where a point in retina corresponds to two points in cortex (Tusa et al., 1978
). This concern is minor: our images mostly centered on one area, with at most a small region in the other area. A second limitation of our mapping function is that it is linear, which can only be appropriate in a local region of cortex; over the full extent of V1 the magnification factor shows great variation (Tusa et al., 1978
). A more realistic logarithmic mapping function (Balasubramanian et al., 2002
), however, costs additional parameters and did not noticeably improve the fits.
Relationship between retinotopy and orientation preference
The relationship between maps of orientation preference () and of retinotopy () has received substantial interest (Bosking et al., 2002
). An essential factor in the combination of these maps is the point spread function, the extent of cortex that is activated by a pointwise visual stimulus. The point spread function has been calculated from measurements of receptive field size and magnification factor (Hubel and Wiesel, 1974
); in cat its width averages 2.6 mm, regardless of eccentricity (Albus, 1975
). The structure of orientation preference maps, however, is finer than this scale. Therefore, as has been illustrated recently (Bosking et al., 2002
), a small oriented stimulus activates a region of cortex that is extended (because of the point spread function), but not uniform (because of the map of orientation preference). Indeed, our bar stimuli (), elicited responses that are broad and patchy (). The patchiness is due to the orientation map: when the combined responses to horizontal bars are subtracted from the combined responses to vertical bars, the result is a clear map of (horizontal vs. vertical) orientation preference ().
In summary, the pattern of activity elicited by an oriented stimulus must depend on the interplay of three factors, namely (1) the map of retinotopy; (2) the point spread function; and (3) the map of orientation preference. We asked what the exact rules of combination are for these three factors.
We tested a simple rule of combination. Our stimuli have uniform orientation and contrast inside a contour, and zero contrast outside the contour (). First, we predicted the representation of the contour in cortex based on the map of retinotopy (). The result is a tight region of activation with sharp borders. Second, we blurred this region of activation by convolving with the point spread function, which we modeled as a 2-dimensional Gaussian profile (). The result is a broad region of activation with blurred borders. Third, we multiplied point by point this region of activation with the map of preferred orientation, i.e. with the profile of activation expected for a large oriented stimulus (). The final result is a broad and patchy region of activation ().
This simple rule of combination provided good fits of the responses and allowed us to estimate the point spread function. The maps of activation predicted by the model () closely resembled the actual responses (). The model explained 78 % of the variance for the data in our example experiment (), and 74 ± 8 % of the variance on average (s.d., n = 7). The estimated point spread function had a width (standard deviation) of 0.7 mm for the example experiment (), and 1.1 ± 0.4 mm across experiments (s.d., n = 7). The overall width of the estimated point spread function (~2.2 mm at two standard deviations) is consistent with the value of ~2.6 mm estimated with electrodes (Albus, 1975
As a further validation of the model, we tested its performance on a new data set, one that was not used to obtain the model’s parameters (Supplementary Figure 2
). We first obtained the model parameters from an experiment like the one described above (). We then froze the parameters and asked whether the model could predict responses to a second stimulus set, which included not only horizontal and vertical gratings, but also diagonal ones. Reassuringly, the predictions of the model resembled the responses in all stimulus conditions (Supplementary Figure 2
Traveling waves in the spatial domain
The activity that we elicit with contrast reversal of focal visual stimuli oscillates at twice the reversal frequency. Does this activity propagate away from the retinotopic representation of the stimulus? In other words, can the activity be described as a traveling wave?
To answer this question we examined an additional attribute of the 2nd harmonic responses: response phase (). The 2nd harmonic responses are strong for the few stimuli placed near the optimal position, and decrease markedly as the stimulus is moved to more distal positions (). The phase of responses elicited distally differs from that of responses elicited proximally (): the color codes for phase are yellow and red when the stimulus excites the imaged region and progress towards purple, and cyan as the activated region becomes more distal and the associated response amplitudes become smaller. This progression is somewhat noisy due to small size of distal responses, but nonetheless suggests an increasing lag of the response as the distance between recorded regions and stimulated regions grows. This increasing lag is characteristic of a traveling wave.
Figure 5 The oscillations in the 2nd harmonic responses have different phases depending on stimulus position. (A) Stimuli are the same as . (B) Amplitude of 2nd harmonic responses (same data as in , only here it is shown in z-scores). (C) The (more ...)
To test the traveling wave hypothesis and characterize the speed of travel and other key properties, we summarized these data in a compact representation (). This representation concentrates on a single dimension of space, and collapses all the stimulus conditions into one graph, thus simplifying the analysis and increasing the signal/noise ratio of our measurements. Having fitted the model of retinotopy () we estimated the retinotopic location of the central axis of each stimulus, and expressed the amplitude of the 2nd
harmonic responses () as a function of distance from this location (Supplementary Figure 3
). We could then create a composite of the responses to different stimuli (). As expected, activity is strongest in the retinotopic location of the stimulus, and decays gracefully as distance from this location increases (). Pooling across space and across stimuli allows us to estimate the phase of the responses with high accuracy even when the associated amplitudes are weak (). Crucially, the phase changes linearly with distance from the retinotopic location of the stimulus, consistent with travel at a constant speed of 0.30 m/s ().
Figure 6 Traveling waves in the spatial domain. (A) Amplitude of the 2nd harmonic responses shown in , expressed as a function of distance from the retinotopic location of the stimulus. This representation collapses the two dimensions of cortex into one, (more ...)
To further test the traveling wave hypothesis, we asked whether the phase lag seen with increased distance from the stimulated region is due to a delay in the whole time course of the oscillating responses. We averaged the responses over one cycle of the stimulus period (), and found the delay both in the onset and in the offset of the responses, as would be expected by a traveling wave.
The results were highly repeatable across 6 experiments (). The decay in wave amplitude with increasing distance extended over a couple of millimeters (). The corresponding increase in delay with increasing distance was well fitted by a line of constant speed (). The average speed was 0.28 m/s, with a 75% confidence interval of 0.19 to 0.55 m/s. The cycle averages of the responses pooled across experiments showed a progressive delay with distance from the origin ()
These results prompt a number of questions. Firstly, does the traveling wave have a trivial explanation? Perhaps there is a fixed relationship between response amplitude and phase, such that weak amplitudes are always associated with lagged phases. Secondly, is the traveling wave specific to cortical sites that are selective for different stimulus positions, or is it also seen across sites that differ in orientation preference?
Standing waves in the orientation domain
We address these questions by asking whether waves of activity travel also in the orientation domain (). We consider the responses to contrast-reversing stimuli of different orientations, described earlier (), and examine not only the amplitude of the 2nd harmonic () but also its phase (). The analysis here is similar to the one performed in the spatial domain, except that we no longer consider the spatial dimension to be distance over the cortical surface but, rather, difference between preferred orientation and stimulus orientation.
Figure 7 Standing waves in the orientation domain. (A) Amplitude of the 2nd harmonic responses as a function of angle between the preferred orientation and the stimulus orientation (as in ). (B) Phase of these 2nd harmonic responses. (C) Space-time representation (more ...)
The results of this analysis indicate that in the orientation domain the oscillatory activity is a standing wave (). The phase of the 2nd harmonic responses is independent of orientation, indicating that there are no delays in the responses of subpopulations tuned to different orientations (). Indeed, the profile of activation does not sharpen nor broaden through time, as can be observed by inspecting the responses in a space-time plot (). This plot is conceptually similar to the one obtained earlier in the spatial domain (), but its appearance is markedly different, as it lacks any hint of propagation. We confirmed these observations by fitting to the data the model of a standing wave. A standing wave is a separable function of orientation and space (), i.e. the product of a function of preferred orientation () and a function of time (). This model fits the data well, as it leaves only a small residual () and accounts for 98 % of the variance in the data in this example.
These results were highly repeatable across our 23 experiments (). The phase of the pooled 2nd harmonic responses was not affected by orientation (), and the pooled activity resembled a standing wave (), with the separable model accounting for 99.7% of the variance (). In individual data sets, the model explained over 90% of the variance in the 20/23 data sets obtained at high signal/noise (average z score of 6.7 ± 3.1) and accounted for less variance only in the 3/23 experiments with poor signal/noise ratios (average z score of 1.9 ± 1.7). This effect suggests that the modest missing variance is predominantly due to noise rather than to deviations from separability.
The standing wave observed in the orientation domain is not simply explained by the short distances between sites of differing orientation preference (). Imagine that there were a traveling wave not only in the spatial domain but also in the orientation domain. This traveling wave might erroneously appear to us as a standing wave because the speeds are high and the cortical distances involved are short. To investigate this possibility we measured the average distance between sites in cortex as a function of difference in their preferred orientation. The average distance between a pixel and the closest pixel tuned to the orthogonal orientation is ~0.3 mm (). If activity in the orientation domain were a traveling wave propagating at 0.3 m/s (the speed seen in the spatial domain), the delay in activity between sites selective for orthogonal orientations would be ~1 ms. Could we detect such a small delay from our data? We simulated a wave that travels at 0.3 m/s across sites with different orientation preference, and compared these simulations to the data (). The two differ significantly: the measured delays lie on a flat line (consistent with a standing wave), and are all > 1 s.d. away from the predictions of the putative traveling wave. We can therefore reject the hypothesis of a wave that travels across the orientation domain.
Figure 8 The standing wave observed in the orientation domain is not simply explained by the short distances between sites of differing orientation preference. (A) Map of orientation selectivity for an example hemisphere (experiment 50.2.3). (B) A 60 deg stimulus (more ...)
The marked difference between the waves in the spatial domain () and in the orientation domain () has a number of consequences. First, the traveling wave seen in the spatial domain is not simply due to a putative delay that might accompany weaker responses; it is truly a function of distance in cortex. Second, the circuits that underlie spatial selectivity and orientation selectivity are fundamentally different. The former distributes neural activity to a progressively larger group of neurons. The latter, instead, is balanced, so that the profile of activity neither sharpens nor broadens through time.