Radial bias is not necessary for orientation decoding

Abstract

Multivariate pattern analysis can be used to decode the orientation of a viewed grating from fMRI signals in early visual areas. Although some studies have reported identifying multiple sources of the orientation information that make decoding possible, a recent study argued that orientation decoding is only possible because of a single source: a coarse-scale retinotopically organized preference for radial orientations. Here we aim to resolve these discrepant findings. We show that there were subtle, but critical, experimental design choices that led to the erroneous conclusion that a radial bias is the only source of orientation information in fMRI signals. In particular, we show that the reliance on a fast temporal-encoding paradigm for spatial mapping can be problematic, as effects of space and time become conflated and lead to distorted estimates of a voxel's orientation or retinotopic preference. When we implement minor changes to the temporal paradigm or to the visual stimulus itself, by slowing the periodic rotation of the stimulus or by smoothing its contrast-energy profile, we find significant evidence of orientation information that does not originate from radial bias. In an additional block-paradigm experiment where space and time were not conflated, we apply a formal model comparison approach and find that many voxels exhibit more complex tuning properties than predicted by radial bias alone or in combination with other known coarse-scale biases. Our findings support the conclusion that radial bias is not necessary for orientation decoding. In addition, our study highlights potential limitations of using temporal phase-encoded fMRI designs for characterizing voxel tuning properties.

Keywords: Area V1; MVPA; Orientation columns; Pattern classification; Phase encoding; Primary visual cortex.

Figure 1

Experimental stimuli and the resulting BOLD responses. Top row shows examples of the retinotopy wedge used in Experiments 1 and 3 (A), the oriented grating used in Experiments 1–3 (B) and the smoothed retinotopy wedge used in Experiment 2 (C). The middle row shows power spectrums of the BOLD signal in response to the wedge stimulus (D), oriented grating (E) and smoothed wedge (F), averaged over participants. The bottom row shows the corresponding BOLD signals from a representative participant to the wedge (G), grating (H) and smoothed wedge stimuli (I). The responses of individual voxels in V1 were phase locked to their retinotopic phase preference and averaged. The line shows the best-fitting cosine function to the data in each panel.

Figure 2

Decoding results from Experiments 1–3. The leftmost bar in each panel shows decoding performance for the original orientation data. The middle bar shows decoding performance after removal of the radial bias. The third bar shows the retinotopy baseline, which represents the amount of residual retinotopy information left over after removal of the retinotopy signal. If orientation decoding after removing the radial bias is higher than this retinotopy baseline, then there must be orientation information in the signal that is not due to radial bias. Error bars denote standard errors for orientation decoding with and without radial bias. For the retinotopy baseline, the error bars denote the .025 and .975 percentiles of the simulated distribution, averaged across participants.

Figure 3

Predicted effects of the hemodynamic response function on fMRI orientation signals. A) Hypothetical tuning curve that resembles a radial-bias like signal. B) The result of convolving the tuning curve in (A) with a hemodynamic response function (dashed curves), in which the oriented grating rotates through time over a 24 second period as in Freeman et al. and our Experiments 1 and 2. C) The result of convolving the hypothetical curve in (A) with the same HRF, but with a slower rotation period of 72 seconds. D) A hypothetical tuning curve that has a more complex signal, such as might reflect uneven sampling from the cortical columnar structure. E) In the 24-second design, convolution with the HRF filters out the complex aspects of the signal. F) Slowing the rotation period to 72 seconds greatly mitigates the filtering effect.

Figure 4

Examples of tuning curves for individual voxels. Each point depicts the BOLD response of an individual voxel to an individual block in Experiment 4. Lines denote the best-fitting single-cosine (blue), two-cosine (red), three-cosine (orange) and von Mises (magenta) models overlaid as lines. The von Mises curves have been shifted up slightly so that they are not obscured by other curves. Top, middle and bottom rows depict voxels that were fit best by the single, double and triple-cosine complexity, respectively, where fit was assessed using AIC.

Figure 5

Experiment 4 modeling results. A) Cross-validation performance (R²) for model M₂ plotted as a function of performance for model M₁ for each V1 voxel. Colors indicate whether models M₁ (red) or M₂ (gray) exhibited higher cross-validation performance. Color intensity indicates density of overlapping points. B) Cross-validation performance for model M₃ plotted as a function of model M₂. Colors indicate whether models M₂ (red) or M₃ (gray) exhibited higher cross-validation performance. C) Proportion of voxels in V1 for which each of the models provided the best fit, as measured with AIC (error bars denote standard errors across participants). D) Leave-one-run-out decoding accuracy (RMSE), using each model as a forward-encoding model. Note that model M₀ cannot be used for decoding as it predicts no orientation tuning, and is therefore omitted.

Figure 6

Results of simulation to evaluate the efficacy of identifying which model produced the simulated data, for model selection using AIC (A), cross-validation measuring proportion of variance explained (B), and cross-validated measures of orientation-decoding error (C).

Figure 7

Winning model for each voxel as measured with AIC, projected onto the flattened surface representation of early visual cortex for each of the four participants. The models have been collapsed into groups that reflect a gross orientation preference like the radial bias (red; M₁ or VM) and those that have a more complex orientation-tuning curve (yellow; M₂ or M₃).