Measuring Spatial Waves in Rivalry
H. Wilson, R. Blake, S-H. Lee

To study the dynamics of wave propogation in rivalry, we devised a technique allowing us to control the location at which a dominance wave originates and, therefore, to measure the speed at which that wave travels to other parts of the pattern. Our technique capitalizes on the well-established fact that an abrupt contrast increment reliably triggers the immediate dominance of a previously suppressed rival pattern. In our experiments the observer depressed and held the spacebar on the computer keyboard when the radial grating (or, on other blocks of trials, the concentric grating) was phenomenally suppressed, the spiral alone being visible. Very shortly after this keypress, a brief contrast increment was introduced at one location of the suppressed rival grating; the observer monitored the rivalry status of a specified portion of the grating, releasing the spacebar when that portion achieved dominance. Over trials, we varied the distance between the perturbing increment and the monitored portion of the grating.
Propogation time increases approximately linearly with angular distance, with no evidence for variations in speed with distance or with the location of the contrast increment. The abrupt appearance of the contrast increment ignites a wave of dominance that spreads in both directions away from the location of the increment.
In several ancillary experiments we examined the influence of stimulus variables on the speed of wave propogation (Table 1).

Table 1. Propogation time for different grating conditions. Each value is the mean of at least 30 observations, with the oerturbation site and monitored site always constant; values in parentheses are standard errors.
Observer c/deg contrast condition time (sec)
RB 3.24 .15 one pulse 1.63 (.06)
RB 3.24 .075 one pulse 2.05 (.12)
RB 3.24 .0375 one pulse 3.84 (.40)
RB 3.4 .15 Spiral contrast = .3 1.59 (.08)
HRW 3.24 .25 one pulse
HRW 6.48 .25 one pulse
HRW 1.62 .25 one pulse
RB 3.24 .15 Double pulse 1.05

Propogation time does not depend on grating spatial frequency nor on the contrast of the contralateral, spiral grating. Wave speed does, however, slow somewhat at low values of grating contrast. Indeed, at very low contrast levels, the local dominance ignited by a contrast increment often produces only a weak wave that dwindles and never reaches regions of the grating in another quadrant of the annulus. We also tried producing dominance waves using brief decrements in the contrast of the suppressed grating, but decrements proved ineffective at breaking suppression locally. Consequently, the measured durations associated with this condition were primarily those associated with spontaneous switches from suppression to dominance at the monitored location.
For all observers speed of propogation is considerably faster for the concentric grating than for the radial grating. This anisotropy may be related to long-range lateral connections among orientation-selective neurons in neighboring cortical columns. These long-range connections tend to be more extensive among orientation columns that are collinear in orientation preference compared to orientations parallel to one another. Collinearity also boosts the incidence of joint predominance of spatially distributed rivalry figures.
In another experiment, two contrast increments were introduced simultaneously within the suppressed grating, at locations on opposite sides of the circular annulus. As expected, dual perturbations ignited two waves of dominance that spread from their respective locations. The observer monitored the rival status of the grating at the midpoint of these two perturbation spots, releasing the spacebar whenever the first of these two waves reached the monitored location. The average propogation time for this condition was faster than that associated with perturbation at either point alone. In fact, this increase in speed is predicted from probability summation, the idea being that two stochastic processes will, on average, yield faster response times than will either process on its own.

Four observers (one naive) participated in these experiments. Annular rival patterns were generated on a 21" NEC RGB monitor (P104 phosphor; 1024 x 768 resolution; 100 Hz frame rate) controlled by a Power PC computer. All stimuli and trial-related events were programmed using Matlab software in conjunction with the Psychophysics Toolbox. The two circular patterns, each 3.6 deg visual angle in diameter, were viewed through a mirror stereoscope with the head stabilized by a chin and head rest. The central portion of each circular pattern comprised a concentric grating with a central fixation point. The peripheral, annular portion of one pattern comprised a spiral figure generated as the weighted sum of a radial and a concentric grating, with pitch angle equaling 45 deg. The corresponding, annular portion of the other rival pattern was either a radial grating (3.24 c/deg, unless otherwise specified) or a concentric grating (also 3.24 c/deg). Grating contrast was adjusted for each observer to find a value at which the spiral (100% contrast) was completely dominant for the majority of the viewing period; grating contrast varied among observers from .15 - .25.
For each experiment the observer first carefully adjusted the stereoscope mirrors to achieve accurate, relaxed binocular alignment. During the experiment, the observer maintained strict fixation in the center of the annular rival patterns (a region in which the two eyes viewed identical contours, which stabilized fusion). Once the grating was suppressed in its entirety, with the spiral alone dominant, the observer depressed the space bar on the computer keyboard. This produced a 100 msec increment (abrupt onset and offset, time locked to the video retrace) in the contrast of the grating at one of eight equally spaced locations around the circular grating. The increment comprised a gaussian spatial envelope the half-width of which was 18 arc min; the magnitude of the contrast increment was 0.70, a value sufficient to penetrate suppression locally on virtually every trial. With fixation maintained in the center of the pattern, the observer monitored the phenomenal status of a region of the grating demarcated by two nonius lines. Once that portion of the grating became dominant, the observer released the spacebar, thereby providing a measure of the time elapsing between presentation of the increment and reappearance of the grating at the monitored site. Trials were run in blocks of 30, with rest periods taken as needed. In several ancillary experiments, the location of the contrast increment was fixed relative to the monitored location of the grating; the purpose of these experiments was to measure the average propogation time for a fixed distance, typically as the function of some other stimulus variable.

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