Figure 1.
A. Stimuli. The stimuli used in experiments 1, 2&3. Stimulus motion was varied so that speeds were equal yet opposite in both eyes to produce symmetry across the eyes. Grating orientation was also opposite in both eyes. In exp. 1, the dial position was fixed at the top of the stimulus, whereas in exp. 2, the mark was placed at different positions around the entire upper half of the stimulus. B. Trial sequence. Subjects initiated the trials by depressing the space bar and ended them by releasing the space bar. First, the lower contrast half-image (carrier grating) was shown for 500 ms. Then, the higher contrast half-image (mask grating) was projected into the other eye, causing immediate perceptual dominance of the high-contrast mask annulus due to its higher contrast and the sudden onset of presentation. After another 500 ms, a 300 ms trigger in the lower contrast carrier grating annulus was used to initiate a wave-like transition at the 6 o'clock position that propagated upward in both directions across the annular stimulus. This strict timing sequence allowed precise control over the order of subjects' perceptual state during a trial.
Figure 2.
Results of Experiment 1, motion propels traveling waves.
A. Experiment 1: Rates of arrival directions at different stimulus speeds depend on stimulus motion direction. Scatter plot depicts the probability that the traveling wave reached the top of the annulus from the CCW direction. Each symbol type stands for data from one of five subjects. The ordinate represent CCW probability, sampled at a certain underlying stimulus speed (abcissa), positive speeds represent carrier grating motion in the CCW direction. The green dashed line is the best-fitting cumulative Gaussian distribution. The correlation between stimulus motion and CCW traveling wave probability is highly significant (Spearman's ρ 0.77, p<<0.001). B. Differences in arrival times between CW and CCW traveling waves. Arrival times from trials of experiment 1 were binned across stimulus speeds. Stimulus motion had a significant effect on the speeds at which CW and CCW traveling waves moved (p<0.01). These data indicate that the traveling waves' tendency to arrive from a certain direction was due to a change in traveling wave speed, confirming the arrival ratio data. Data represent the mean of the difference in CW and CCW arrival time across five subjects, error bars are ±1 SEM.
Figure 3.
Experiment 2: Spatial shift of arrival ratios across dial positions.
Underlying stimulus motion determines the position of the meeting point of the two traveling waves in both directions. Stimulus speeds in angular degrees per second are denoted along the ordinate, dial position along the abcissa. Gray lines are 9% iso-probability lines, the 3D profile is shown in the top-right inset. The black dashed line represents the line of equal μ of the best-fitting cumulative Gaussian in three dimensions. At stimulus speeds greater than approximately 75°/s in either direction the responses are dominated by the stimulus motion. In these cases, almost no reports of the traveling wave arriving in the direction opposite to the carrier grating motion occurred, even for the most extreme dial position. This means that the traveling wave moved more than three times faster in the direction of the carrier grating motion than it did in the opposite direction. Data points are the mean of 4 subjects. Inset 3D plot of the same data. The red line depicts data from the range used in experiment 1. These data mirror the data shown in figure 2A, showing that in the range of stimulus motion used in experiment 1 the results of experiment 2 show identical trends.
Figure 4.
Computational model: connectivity and simulations.
We adapted the model by Wilson et. al. (3) which incorporates spatially extended interocular inhibition and collinear facilitation, properties of the functional connectivity within striate cortex. A The model consists of two layers of cells, each of these layers receives input from one eye. Each cell interacts with neighboring cells in its own layer (collinear facilitation, +) and negatively interacts with retinotopically nearby cells in the opposing layer via inhibitory interneurons (−). B Illustration of the shape of excitatory (gray solid lines) and inhibitory (dashed lines) influences exerted by the layer that represents the Carrier -(C)- neurons. Stimulus motion causes an asymmetry in the inhibitory profile impinging on the Mask -(M)- neurons (green dashed curve), where a standstill stimulus causes a symmetric inhibition profile (red dashed curve). This direction-selective inhibition acts on the M-neurons, specifically those neurons that code for the opposite direction of motion. Thus, the increase of inhibition impinging on the M-neurons due to the rising activity of C-neurons is biased in the direction of the motion of the carrier grating. C The course of binocular rivalry traveling waves under the influence of stimulus motion, as predicted by the model. With greater stimulus speeds, the asymmetry of motion in the different directions increases and the traveling wave duration decreases. The top and bottom of the figures represent the bottom of the annular stimulus, and the sample positions used in experiment 2 are shown at the ordinate. Clearly, the point of arrival under conditions of the higher stimulus speeds lies farther than the 90° mark, meaning that the model accurately reproduces the psychophysical data. The bottom figure that represents a traveling wave under the influence of a high level of stimulus motion has a ratio between clockwise and counter-clockwise inhibition width of 4∶1.
Figure 5.
Experiment 3 and occlusion situation.
A. Effect of stimulus grating collinearity on the influence of stimulus motion on the traveling wave. In our model a change in spiral angle, i.e. the collinearity of the pattern, is represented by a change in excitatory influence on neighboring neurons in the same layer, whereas this change in spiral orientation causes the effects of stimulus motion to diminish. Simulations showed that these different elements jointly act in such a way that the influence of stimulus motion is hampered. We tested this prediction directly by changing the spiral angle of both carrier and mask gratings while keeping the angular velocity of rotational motion equal at 23°/s. Data from three subjects clearly confirms the prediction of a negative effect of stimulus grating collinearity on the influence of stimulus motion. The black solid line represents the mean across subjects (colored lines), error bars are ±1 SEM. B. Diagram of the functional relevance of the implementation of asymmetric inhibition. The figures represent a top view of a binocular occlusion situation at two times, t<t. A moving object may be occluded in one eye (R, t) and visible in the other (L, t). Direction-selective inhibition of the right-eye neurons in the path of the motion that is visible in the left eye allows direction-selective right-eye neurons to respond earlier to the appearance of the target moving leftward at t.