Figure 3. BOLD summation in the absence of neural nonlinearity associated with stimulus summation, with the 6-s stimuli.

(See Figure 3—figure supplement 1 for results obtained with the 1-s stimuli, which are qualitatively identical.) (A) The stimuli used in the BOLD summation experiment. The full stimulus display subtended 24°(w) x 19°(h). Stimulus types A and B are single-sided stimuli, while type A+B is a double-sided stimulus. BOLD responses associated with the outer checkerboard discs were extracted from the corresponding ROIs. These outer discs were of diameter 4° and centered at an eccentricity of 7°. (B) Estimated peristimulus time courses from V1-V3 for the three stimulus types at five different contrast levels. Red and magenta represent responses (lines) and ± SE (bands) to the single-sided stimuli, and green represents responses to the double-sided stimuli. Black dashed lines represent the predictions of linear BOLD summation, which overestimated the measured responses (green bands). Gray bars on the abscissa indicate the duration of the stimulus (6 s). (C) The contrast response functions of V1-V3 as defined by the amplitudes of the time courses. The amplitude of a time course was taken to be the average response between 7–9 s post-stimulus onset when the response typically reached its peak. The red lines represent the average single-sided response amplitudes as a function of luminance contrast. The green lines represent the average double-sided response amplitudes. The gray bands represent the predicted responses (68.2% confidence interval) evoked with the double-sided stimulus under the assumption of linear BOLD summation (i.e. the summed response to conditions A and B), and the magenta bands represent the prediction of contrast summation – the equivalent contrast of a double-sided stimulus being twice that of the corresponding single-sided stimulus. The measured double-sided responses were significantly lower than the predictions of linear BOLD summation and higher than that of contrast summation.

DOI: http://dx.doi.org/10.7554/eLife.09600.007

Figure 3—figure supplement 1. fMRI BOLD summation with a 1-s stimulus duration.

(A) Estimated peri-stimulus BOLD time courses from V1-V3 for the three stimulus types at five contrast levels. Red and magenta curves represent, respectively, the BOLD responses (lines) and ± SE (bands) to the single-sided stimuli, and the green curves represents BOLD responses to the double-sided stimuli. Black dashed lines represent the predictions of linear BOLD summation, which overestimated the measured responses (green bands). Gray bars on the abscissa indicate the duration of the stimulus presentation (1 s). (B) The contrast response functions of V1-V3 as defined by the amplitudes of the time courses. The amplitude of a time course was taken to be the estimated response at 5 s post stimulus onset, when the response typically reached its peak. The red lines represent the averaged response amplitudes to the single-sided stimuli as a function of luminance contrast. Green lines represent the responses to the double-sided stimuli. The dark bands represent the predicted response amplitudes (and 68.2% confidence intervals) evoked with the double-sided stimuli assuming linear BOLD summation, while the magenta bands represent the prediction of contrast summation. Neither of these predictions fits the data. These results are qualitatively identical to those obtained with the 6 s stimulus (Figure 3).

DOI: http://dx.doi.org/10.7554/eLife.09600.008

Figure 3—figure supplement 2. Results of the 6-s BOLD summation experiment with and without removing the global noise components.

The experiment with a 1 s stimulus duration does not have a sufficient signal-to-noise ratio to yield reliable results with conventional deconvolution analysis (using finite-impulse-response basis). The GLM denoising method of Kay et al. (2013) was used to estimate and remove the most prominent principle components of the noise that were shared across voxels. To confirm that this denoising method did not lead to any systematic bias, we applied the same denoising method to the data obtained with the 6 s stimulus duration experiment, for which conventional deconvolution analysis is applicable (Figure 3). The red and magenta colors represent single-sided responses and the green color represents double-sided responses (see also Figure 3). Solid lines, which are identical to those in Figure 3, represent time courses estimated using the conventional deconvolution analysis without adding the estimated global noise components as regressors of no interest (see methods). Square symbols represent the time courses inferred with the global noise components removed by representing them as regressors of no interest. The two methods yielded virtually identical results for the 6-s stimulus.

DOI: http://dx.doi.org/10.7554/eLife.09600.009

Figure 3—figure supplement 3. Results of the 1-s and 6-s BOLD summation experiments obtained from the corresponding retinotopically-defined V1 ROI in the left hemisphere of the achiasmic subject.

Red and magenta represent responses (lines) and ± SE (bands) to the single-sided stimuli, and green represents responses to the double-sided stimuli. Since the achiasmic subject viewed the stimuli with only his right eye, there was no stimulus-evoked response in the early visual areas of the left hemisphere. If there were any anticipatory and endogenous response, we should be able to observe the response in the left hemisphere. We found no such response – the peri-stimulus time courses from the left hemisphere do not deviate significantly from zero.

DOI: http://dx.doi.org/10.7554/eLife.09600.010