Many studies have investigated the linearity of the relationship between BOLD signal changes and measured or inferred neural activity and have found that neurohemodynamic coupling behaves, by and large, as a linear system that obeys the principles of superposition and scaling (Boynton et al., 1996, 1999; Logothetis et al., 2001; Heckman et al., 2007; Zhang et al., 2008). Because these previous studies have used full-field or extended visual stimuli, which stimulate large regions of cortex, the present study was designed to test the linearity of the BOLD response to isolated Gabor patches that produce well-localized patches of neural activity (approximately 5 mm in diameter) in early visual areas. These relatively weak stimuli could potentially unveil non-linear aspects of the hemodynamic response, such as local oxygen consumption without concomitant increases in local blood flow (resulting in a lower-than-predicted BOLD response to low-contrast stimuli), or over-perfusion at low contrast due to a lack of fine resolution in local blood flow recruitment. The expected finding for this experiment is a linear relationship when the BOLD contrast response is compared against the neural contrast response estimated from psychophysical data.

As an alternative to the more common gradient echo (GE) BOLD techniques that use T₂*-weighted images to maximize sensitivity to magnetic field perturbations in and near veins (Ogawa et al., 1993; Bandettini et al., 1994), spin echo (SE) BOLD techniques use T₂-weighted images to bias BOLD sensitivity toward small venules and capillaries (Norris et al., 2002; Duong et al., 2003; Yacoub et al., 2003; Hulvershorn et al., 2005; Parkes et al., 2005). At low field strengths (1.5 T), the spatial specificity of SE BOLD is limited by intravascular blood signal from large veins (Oja et al., 1999), but at high field strength (e.g., 7 T), the short T₂ of venous blood removes this residual contribution from large veins (Duong et al., 2003). We therefore measured the BOLD contrast response with both GE and SE techniques at 7 T to discover whether any non-linearities in the BOLD response are more likely attributable to large-diameter or small-diameter vascular compartments.

In our first experiment, we measured the GE and SE BOLD contrast response functions for isolated Gabor patches. First, GE BOLD and SE BOLD block-design localizers were used to define two sets of ROIs (Figure 3A). Each set of ROIs in each subject consisted of four sub-ROIs, corresponding to the four cortical representations of the four Gabor patches. The SE BOLD-derived ROIs were smaller than the GE BOLD-derived ROIs, as would be expected either from the lower CNR of the SE BOLD technique (Olman et al., 2010) or from the decreased blurring due to dominance of the small-diameter vascular compartment. The average volume of a SE BOLD sub-ROI was 137 ± 9.7 mm³ (mean ± SEM, 18 sub-ROIs); the average volume of a GE BOLD sub-ROI was 288 ± 22 mm³. The SE ROIs were also largely contained within the larger GE ROIs: 9.2 ± 2.5% (mean ± SEM, 18 sub-ROIs) of the voxels selected by SE localizers were not included in the GE ROIs, while 54 ± 3.6% of the voxels in GE ROIs were outside of the smaller SE ROIs. Assuming a cortical thickness of 3 mm, and a cortical representation for each Gabor patch approximately 5–8 mm in diameter, the predicted stimulated cortical volume in each location is approximately 60–150 mm³.

We then estimated GE BOLD and SE BOLD event-related HRFs within each ROI for Gabor patches presented at 5, 10, 30, and 90% luminance contrast. Estimated HRFs for the SE and GE BOLD response in the SE and GE BOLD-defined ROIs in one representative subject are shown in Figure 3B. The primary analyses of interest are the GE BOLD response in the GE BOLD-defined ROIs (upper right panel) and the SE BOLD response in the SE BOLD-defined ROIs (lower left panel). However, the crossed analyses (GE BOLD response in voxels selected by SE BOLD localizer, and vice versa, thin dashed lines in Figure 3B) were also performed. It is worth noting that both the GE BOLD and the SE BOLD HRFs are larger in the more-selective SE BOLD-derived ROIs (right column).

The average GE and SE BOLD responses to Gabor patches of increasing contrast are shown in Figure 4A. Because the underlying V1 neural response saturates with increasing contrast, a linear increase in amplitude with increasing contrast is not expected. However, in neither the GE nor the SE data was the response to 5% contrast significantly lower than the response to 10% contrast. In the SE data, there was a trend in the expected direction (t₄ = 1.74, p = 0.08, one-tailed paired t-test), but no distinction in the GE data (t₄ = 0.22, p = 0.58). Normalized BOLD response is plotted against psychophysically estimated neural response for individual subjects in Figure 4B and illustrates the variability within and between subjects that contributed to our failure to measure 5% contrast responses that were significantly less than 10% contrast responses.

In a control experiment, we tested whether the lack of reliability in the estimated BOLD response to low contrast targets was a consequence of the small stimulus size or of the rapid event-related experiment design. The rapid event-related design (average ISI of 4.5 s) assumes linearity (specifically, superposition) of the hemodynamic response; if this assumption is not valid, it could produce unreliable behavior, particularly in the weaker responses. Therefore, with an experiment design and analysis identical to the previous, we measured the BOLD response to larger patches of sinusoidal gratings (2° radius) centered at the same eccentricity (3°) as the four Gabor patches in the main experiment. Four of the subjects who participated in the main experiment participated in this control. As shown in Figure 4B, the GE BOLD response at 10% contrast was significantly larger than the response at 5% (t₃ = −4.04, p = 0.014, one-tailed paired t-test). The SE BOLD response at 10% contrast was also higher than the response to 5% contrast (t₃ = −2.32, p = 0.052).

To investigate the contribution of voxel selection to the unreliable estimates of the BOLD response to isolated Gabor patches, we estimated HRFs for individual voxels in the GE BOLD ROIs from the main experiment (Figure 5). As expected, since the stimulus contrast is highest in the center of the Gabor patch and decreases toward the edges, response magnitude decreased with distance from the center of the cortical representation of each Gabor patch (Figure 5A). What is unexpected, however, is the spatial dependence of the ratio between the 10 and 5% contrast responses (Figure 5B). In every subject, this ratio was fit by a linear trend with negative slope (GE data: t₄ = −4.3, p = 0.013; SE data: t₄ = −2.7, p = 0.052). The average intercept was greater than 1 (GE data: 1.24 ± 0.35 (SD); SE data: 1.3 ± 0.27), indicating that the 10%:5% ratio is greater than 1 in the center of the ROI, but decreases with distance from the center of the ROI. Therefore, the exact spatial extent of the ROI can have a strong effect on the estimated amplitude of the response to a 5% contrast target, relative to a 10% contrast target, which can explain the variability between subjects observed in the ROI analysis. Using the y-intercept of the linear fits illustrated in Figure 5A as an estimate of the amplitude of the BOLD response to the Gabor patch improves the linearity of the contrast response functions recovered for both GE and SE BOLD (Figure 5C): 95% confidence intervals (shaded regions) are 14% smaller in the top panel for the GE data, and 18% smaller in the top panel for the SE data.

Our main finding is that the average response in a selected ROI is not the most reliable method of estimating the BOLD response for isolated stimuli that produce small patches of cortical activation, particularly for GE BOLD. In an ROI-based analysis, we found that the GE BOLD response to small image patches presented at 5% contrast was not significantly smaller than the response to patches presented at 10% contrast. The difficulty in distinguishing 5 and 10% contrast responses was not an artifact of the experiment design, because the GE BOLD response to extended sinusoidal grating patches presented at 10% contrast was significantly larger than the response to 5% contrast gratings. Nor was it a consequence of low CNR in the data, because subjects with low CNR or high fit residuals were excluded from analysis, and the non-monotonic behavior observed in some subjects was more pronounced in the GE BOLD data, which had higher CNR than the SE BOLD data. The larger-than-expected GE BOLD response in the ROI-based analysis appeared to be a consequence of spatial heterogeneity in the cortical response to small stimuli. Specifically, we observed a relative amplification of the 5% contrast response at the edges of the cortical representation of the stimuli. Improved contrast response estimates were obtained, particularly for the GE BOLD data, by fitting individual voxels and estimating the magnitude of the BOLD response at the center of the ROI.

Our finding of an amplification of the GE BOLD ROI response at very low contrast is not without precedent. Murray (2008) measured the effect of attention on V1 contrast response functions for relatively small patches of sinusoidal gratings; the main finding was that the effects of attention to patches of sinusoidal gratings presented in the four visual quadrants could be described by a baseline shift. Close inspection of Figure 3 in that paper, however, shows that the GE BOLD response to the 3% contrast stimulus is larger than the BOLD response to the 6% contrast grating, most notably in the unattended condition. The stimuli in the Murray experiment subtended 6° of visual angle, centered at 8° eccentricity, so the predicted size of the cortical representation of those stimuli should be intermediate between the Gabor patches and the larger sinusoidal gratings used in this experiment.

This is also not the first time we have observed that voxel selection, or spatial heterogeneity in the GE BOLD responses in V1, can have an impact on interpretations of the relationship between BOLD and stimulus geometry or psychophysical measurements. We have observed previously that some voxels produce negative hemodynamic impulse responses to the presentation of a spatially restricted checkerboard (Olman et al., 2007), even though the stimulus is presented in the voxel's receptive field (i.e., the voxel is inside a ROI defined by a differential localizer that clearly reflects retinotopic location within V1). The local dominance of the negative BOLD in that study was explained by mislocalization of signal by large veins, which brought surrounding negative BOLD signal into voxels in the cortical territory representing the stimulus. More recently, we have shown that surround suppression of the BOLD response to isolated Gabors cannot be predicted from psychophysical measurements of the suppressed visual response to the target Gabors (Schumacher and Olman, 2010). When a target Gabor was flanked by parallel Gabor elements at higher contrast, we measured a localized V1 GE BOLD signal that decreased as the contrast of the target Gabor increased. Those two studies, in combination with the present findings, indicate that accurate inference of spatially heterogeneous neural activity from high-resolution BOLD data requires a model for neurohemodynamic coupling that is more complex than a Gaussian pooling kernel (Engel et al., 1997; Parkes et al., 2005). These experiments also suggest the necessity of a model that takes into account more complex spatiotemporal characteristics of vascular pooling (Kriegeskorte et al., 2009).

One possible neurohemodynamic explanation for the unexpected decrease in the ratio of 10%:5% contrast responses with distance from the center of the cortical representation of each patch is a spatial broadening of the cortical perfusion in response to 5% contrast stimuli. If the hemodynamic response becomes more narrowly targeted (better matched to the locus of neural activity) as contrast increases, then voxels at the edge of a generously defined ROI would show more positive BOLD response for 5% contrast than 10% contrast stimuli. This explanation for the data is essentially an argument in favor of hemodynamic spatial uncertainty for low-contrast stimuli, i.e., hemodynamic resources that are directed to an overly large region of cortex for small, low-contrast stimuli. The GE BOLD ROIs, sensitive to signals from larger veins that pool over a larger cortical territory, would be particularly sensitive to excessive perfusion of flanking cortical territory.

While spatially untargeted perfusion might explain our pattern of results (i.e., variability between subjects in the relative amplitudes of responses to 5% contrast and 10% contrast Gabors in an ROI-based analysis), this is certainly not a general expectation for fMRI experiments. There has been ample demonstration that the arterial blood supply as well as GE BOLD and SE BOLD responses are regulated on a spatial scale fine enough to enable visualization of individual cortical columns – a scale much finer than the resolution required for the present experiment (Cheng et al., 2001; Duong et al., 2001; Yacoub et al., 2008). However, these studies that show excellent targeting of perfusion have been performed with large stimuli using a differential, block-design protocol that minimizes the contribution of large veins and measures only perturbations of the blood supply from a high-response state.

As an alternative to the hemodynamic explanation above, subjects’ eye-movements could conceivably explain the relative increase in the strength of the BOLD response to 5% contrast stimuli in voxels far from the ROI center. If subjects are more likely to make micro-saccades in the direction of one of the target stimuli when the stimuli are near detection threshold (and therefore harder to see), then the cortical representation for the 5% contrast stimuli would be blurred or expanded. Thus, in voxels several millimeters from the ROI center, where the BOLD responses to high-contrast stimuli (with more stable fixation) are decreasing, the response to 5% contrast stimuli (spread by fixation instability) would be inordinately large. Eye-tracking equipment is not currently available at our 7 T scanner, so we do not have data regarding fixation stability on each trial. In addition to repeating this experiment with eye-tracking, another way to distinguish the hyperperfusion hypothesis from the micro-saccade hypothesis is perfusion measurements. With independent measurement of BOLD response and perfusion responses, we could determine whether the balance of perfusion and oxygen consumption differs across the cortical territory for near-threshold and supra-threshold stimuli.

Finally, as another alternative explanation for our data, it is possible that the amplification of the observed BOLD response to 5% contrast is driven by attention or anticipation. Robust V1 BOLD responses occasionally represent perception, rather than actual stimulus presence or contrast (Ress and Heeger, 2003; Maier et al., 2008). A recent optical imaging study also found that anticipation of a stimulus produced a robust hemodynamic response that was not accompanied by measured neural responses (Sirotin and Das, 2009). Since response rates for 5% contrast Gabors were lower than for the higher contrast patterns (80–85% instead of 95–100%), perhaps the sheer difficulty of reliably perceiving 5% contrast Gabors at 3° eccentricity resulted in a unique neural modulation akin to modulation by attention (Buracas and Boynton, 2007; Murray, 2008). Therefore modulation by attention, in spite of the assigned contrast discrimination task, could disproportionately amplify the neural (and BOLD) response at 5% contrast under the particular conditions of the experiment we conducted. However, there are several reasons that such cognitive differences are not likely to explain the observed pattern. First, it would be difficult to explain why an attention or anticipation effect would be observed more strongly in the GE BOLD signal than in the SE BOLD signal. Using attention to explain the full pattern of results we observed would require invoking an attention-based non-linearity in the pooling of blood from small-diameter venous compartments to large-diameter venous compartments, which returns us to an argument similar to the hyperperfusion argument presented above. Second, Murray (2008) found an amplification of the BOLD response to 3% contrast stimuli in both the unattended and attended conditions, further suggesting that mechanisms related to perceptual awareness are not responsible for the pattern observed. Finally, our ITI was randomized, so subjects could not anticipate the onset timing for low-contrast trials.

For comparing the BOLD data against the underlying neural response in this study, we used psychophysical data to estimate neural contrast response functions in V1. While the use of contrast discrimination threshold measurements to estimate V1 contrast response functions has been validated in the past (Boynton et al., 1999; Zenger-Landolt and Heeger, 2003), it is nonetheless an indirect estimate of the neural population response. Electrophysiological data from non-human primates suggests that the population contrast response function can be fit by a power law with exponent ∼0.6 (Heeger et al., 2000); this power law predicts a ratio of 1.5 between the magnitude of the neural population responses to 10 and 5% contrast gratings. The psychophysical data predict an average ratio of 1.6. Both ratios are more consistent with the BOLD response estimated by the extrapolated intercept at the center of the cortical representations of the patches [voxel-based analysis, GE data: 1.24 ± 0.35 (standard deviation); SE data: 1.3 ± 0.27] than with the ROI-based analysis of the GE data (0.95 ± 0.50, Figure 4A). Presumably due to the smaller ROI size and reduced contribution of large vein data to the SE signal, the SE ROI-based analysis provided more reliable estimates of the underlying neural responses (than the GE ROI-based analysis) and was most consistent with the psychophysical data and the voxel-based analysis (1.43 ± 0.52).

The ROI-based analysis provided a more reliable estimate of the underlying neural response to isolated Gabor patches when applied to the SE BOLD data than when applied to the GE BOLD data. In part this was because the SE-defined ROIs were more spatially restricted (roughly half the volume of the GE-defined ROIs), and in part this was because the spatial heterogeneity was not as pronounced (the negative trend for the 10%:5% response ratio was present but not significant across subjects). All of the potential explanations presented above for the overly large response to 5% contrast stimuli we observed at the periphery of the sub-ROIs should affect SE data as well as GE data. However, because the GE data contain a stronger signal contribution from large veins, which pool signal over a larger cortical territory, it is likely that this spatial filtering (blurring) in the GE data amplifies local variations in the BOLD response.

While the main experiment suggests that smaller ROIs (limited to just the center of the stimulated cortical region) would provide better estimates of the BOLD response, using small ROIs is problematic because they are difficult to localize accurately and because ROIs that include just a few voxels are generally quite noisy. The approach used in this paper – to define a generous ROI and then fit the individual voxel responses to estimate the response at the center – addresses both the problem of localization and the need to combine data from a large number of voxels to beat down noise. This approach is only relevant for ROIs in which the BOLD response is expected to vary significantly throughout the ROI. With large stimuli, only a small percentage of the voxels selected for analysis might be on the edge (i.e., in cortical territory where the neural response magnitude varies strongly as a function of spatial position), but with small stimuli, the neural response magnitude varies consistently throughout even a conservatively defined ROI.

To summarize, the GE BOLD response to parafoveal Gabor elements presented at 5% contrast is not reliably smaller than the response to 10% contrast elements in an analysis based on the average response in an ROI. The ratio of 10%:5% responses decreases with cortical distance from the center of the ROI – exactly opposite the pattern predicted if the size of the cortical representation of a Gabor patch increases with contrast. Either eye movements or poor spatial targeting of perfusion for weak stimuli (vascular spatial uncertainty) could explain this result, which was more pronounced for GE BOLD than for SE BOLD data. While it appears likely that the limitations observed in the GE BOLD ROI-based analysis would be encountered only rarely – response estimation was more reliable with higher contrast stimuli and when stimuli are increased to subtend several degrees of visual angle – this study offers an important cautionary note for the interpretation of high-resolution GE BOLD measurements of the cortical representation of finely detailed visual stimuli.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.