Elsevier

NeuroImage

Volume 49, Issue 3, 1 February 2010, Pages 1943-1948
NeuroImage

Comments and Controversies
Against hyperacuity in brain reading: Spatial smoothing does not hurt multivariate fMRI analyses?

https://doi.org/10.1016/j.neuroimage.2009.02.047Get rights and content

Abstract

Recently it has been suggested that multivariate analyses of functional magnetic resonance imaging (fMRI) data can detect high spatial frequency components of cortical signals, like sub-millimeter columns. This ‘hyperacuity’ seems to be at odds with the common assumption that the fMRI signal has a low spatial resolution due to the spatial spread of the underlying hemodynamic events. To resolve this apparent contradiction, I checked a very straightforward prediction of the hyperacuity hypothesis: if multivariate analyses are picking up a small-scale functional organization, then it can be expected that smoothing will be detrimental to the ability to decode these fine-scale spatial signals. I tested this prediction using data obtained with two paradigms to which multivariate techniques have been applied previously, including the decoding of grating orientation from the pattern of activity in primary visual cortex. It was found that smoothing does not decrease the sensitivity of multivariate analyses. Further simulations in which the scale of cortical organization was known indicate that this effect of smoothing contradicts the idea that the patterns detected with multivariate techniques reflect a fine-scale spatial organization.

Introduction

Functional magnetic resonance imaging (fMRI) owes much of its success to its superior spatial resolution compared with other noninvasive techniques (e.g., event-related potentials). Nevertheless, its spatial resolution is still limited to the > mm range, so that even its smallest volumetric unit of measurement (a voxel) still contains many tens of thousands of neurons. This limited spatial resolution is mostly inherent to the hemodynamical events underlying the contrast measured with fMRI. For example, the most common situation, the measurement of gradient-echo blood-oxygenation-level-dependent (BOLD) contrast at a field strength of 3 T, is associated with a point-spread function of more than 3 mm full-width at half-maximal-height (FWHM) (Engel et al., 1997, Parkes et al., 2005, Shmuel et al., 2007).

This characteristic of the BOLD signal has been incorporated in the statistical pre-processing that is being performed in the major fMRI analysis software packages. A typical step during this pre-processing is smoothing the data with kernels of many millimeters (e.g., 8 mm FWHM in Statistical Parametric Mapping or SPM). Friston (2003) mentions several motivations for this smoothing step: the low spatial scale of the hemodynamic responses and the wish to use a smoothing kernel that matches the size of the anticipated effect (matched filter theorem); increasing the normality of the data and the validity of the assumptions behind the statistical tests; and reducing the effect of inter-individual differences in anatomy. Thus, a central part of this rationale is the idea that smoothing will not hurt given the intrinsically global scale of hemodynamic responses.

However, this rationale seems to be undercut by the results from a new multivariate approach to the analysis of imaging data. In this approach, it is assumed that there is important information in the pattern of response across voxels, necessitating the comparison of responses across voxels rather than considering each voxel as a separate entity (Haxby et al., 2001, Haynes and Rees, 2006, Norman et al., 2006, Peelen et al., 2006). These multi-voxel pattern analyses come in many flavors, so it is important to differentiate different sorts of analyses. The most straightforward analysis is to correlate the spatial activity pattern for one condition in a subset of the data with the activity pattern for that same or different conditions in another subset of the data (correlational multivariate analyses or CMA) (Downing et al., 2007, Op de Beeck et al., 2006, Op de Beeck et al., 2008a, Peelen et al., 2006). If this correlation is reliably higher for correlations between data from the same condition than for correlations between data from different conditions, then the activity pattern is said to be a reliable indicator of the differences between conditions (Haxby et al., 2001). These correlational analyses are common practice in the optical imaging literature, in which the patterns of activity are typically very reliable and correlations are high (Bonhoeffer and Grinvald, 1993, Fukuda et al., 2006). This is not always the case for the typical multivariate fMRI study. So many “brain decoding” fMRI papers turn to inventive pattern classifiers, like linear support vector machines (SVMs), to detect reliable patterns of activity (“decoding” multivariate analyses or DMA) (Haynes and Rees, 2005, Kamitani and Tong, 2005). In DMA, multiple subsets of the data are used to train a classifier to differentiate between two conditions, and an independent dataset is used to test the performance of the classifier with new data.

For both CMA and DMA the suggestion has been made that these techniques allow to differentiate patterns of activity at a finer scale than conventional univariate analyses (Downing et al., 2007, Haynes and Rees, 2005, Kamitani and Tong, 2005), and even lead to hyperacuity: sensitivity for differences at a finer scale than the voxel size. This argument has been made most fiercefully based on data showing that the orientation of a grating can be decoded from the pattern of activity in primary visual cortex scanned at a resolution of 3 × 3 × 3 mm (Haynes and Rees, 2005, Kamitani and Tong, 2005). The scale of orientation columns is very small, with all orientations being represented in less than 1 mm2 of cortex, so this conclusion is very extraordinary. The underlying idea is an unequal distribution of all the orientation in many voxels, so that even at the coarse voxel level there is a weak selectivity left that can be picked up reliably by looking at the signal across many voxels. Multivariate analyses have been used in other domains and brain regions, for example for the decoding of novel objects from the pattern of activity in object-selective cortex (lateral occipital cortex or LOC) (Op de Beeck et al., 2006, Op de Beeck et al., 2008a, Williams et al., 2007). While the underlying scale of functional organization is unknown, the V1 orientation data suggest that also in this case researchers might be picking up a sub-millimeter organization. One candidate is the existence of feature columns as shown in monkeys using optical imaging (Fujita et al., 1992, Op de Beeck et al., 2008b).

Section snippets

The effect of smoothing on multivariate analyses: some empirical data

If multivariate analyses pick up signals from such a fine scale, then it seems like a bad idea to smooth the data for these analyses. We would expect that decoding performance goes down when the data are smoothed. Nevertheless, two recent studies included some control analyses to look at the effect of smoothing on the results obtained with CMA in object-selective cortex, and found that smoothing strongly increases the size of these correlations (Op de Beeck et al., 2008a, Op de Beeck et al.,

The effect of smoothing on multivariate analyses: a simulation

The aforementioned empirical data suggest that smoothing does not decrease the ability of multivariate analyses to detect the organization for a particular feature. This finding was the same for grating orientation in V1 and for object categories in LOC. This finding is at least counterintuitive if the multivariate analyses would be picking up a functional organization at a finer scale than the voxel size. So, does this effect of smoothing contradict the hyperacuity hypothesis?

To answer this

Discussion

To summarize, I obtained the same findings with gratings and with objects. Information about grating orientation in area V1 was recovered at least as well with highly smoothed data as with unsmoothed data. Correlations in the selectivity patterns between runs were higher after smoothing, and SVM performance was not affected by smoothing. Likewise, information about object class in area LOC was preserved under high degrees of smoothing: correlations increased with smoothing and SVM performance

Acknowledgments

I thank R. Peeters, R. Goris, and T. Putzeys for technical support, and M. A. Williams and two anonymous reviewers for helpful comments on a previous version of the manuscript. This work was supported by a federal research action grant (IUAP P6/29), the Research Council of K.U.Leuven (CREA/07/004), the Fund for Scientific Research — Flanders (1.5.022.08), the Human Frontier Science Program (CDA 0040/2008), and by a Methusalem grant (METH/08/02) from the Flemish Government.

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