Abstract
Peak-based meta-analyses of neuroimaging studies create, for each study, a brain map of effect size or peak likelihood by convolving a kernel with each reported peak. A kernel is a small matrix applied in order that voxels surrounding the peak have a value similar to, but slightly lower than that of the peak. Current kernels are isotropic, i.e., the value of a voxel close to a peak only depends on the Euclidean distance between the voxel and the peak. However, such perfect spheres of effect size or likelihood around the peak are rather implausible: a voxel that correlates with the peak across individuals is more likely to be part of the cluster of significant activation or difference than voxels uncorrelated with the peak. This paper introduces anisotropic kernels, which assign different values to the different neighboring voxels based on the spatial correlation between them. They are specifically developed for effect-size signed differential mapping (ES-SDM), though might be easily implemented in other meta-analysis packages such as activation likelihood estimation (ALE). The paper also describes the creation of the required correlation templates for gray matter/BOLD response, white matter, cerebrospinal fluid, and fractional anisotropy. Finally, the new method is validated by quantifying the accuracy of the recreation of effect size maps from peak information. This empirical validation showed that the optimal degree of anisotropy and full-width at half-maximum (FWHM) might vary largely depending on the specific data meta-analyzed. However, it also showed that the recreation substantially improved and did not depend on the FWHM when full anisotropy was used. Based on these results, we recommend the use of fully anisotropic kernels in ES-SDM and ALE, unless optimal meta-analysis-specific parameters can be estimated based on the recreation of available statistical maps. The new method and templates are freely available at http://www.sdmproject.com/.
Highlights
In order to help summarize and integrate the results of the evergrowing number of neuroimaging studies, some groups have developed methods to conduct voxel-based meta-analyses solely relying on the information reported in the papers, namely the peaks of the clusters where there were statistically significant activations or where patients and controls showed statistically significant differences
As shown in Figure 6, the optimal full-width at half-maximum (FWHM) in this particular dataset ranged from 40–45 mm in the absence of anisotropy, to 100 mm when anisotropy was 0.4 or higher
As expected from Eq 2, the effects of FWHM were null when recreations were conducted with full anisotropy, whereas there was still a substantial decrease of mean square error (MSE) (MSE = 92%, p = 0.030)
Summary
In order to help summarize and integrate the results of the evergrowing number of neuroimaging studies, some groups have developed methods to conduct voxel-based meta-analyses solely relying on the information reported in the papers, namely the peaks of the clusters where there were statistically significant activations or where patients and controls showed statistically significant differences. Activation likelihood estimation (ALE) [1,2,3,4], (effect-size) signed differential mapping (ES-SDM) [5,6,7] and (multilevel) kernel density analysis (M-KDA) [8, 9] are commonly used methods that have already been applied to meta-analyze a wide range of normal brain functions [10,11,12] and abnormalities in neurological [13,14,15] and psychiatric disorders [16,17,18] As briefly introduced, these methods differ substantially in their algorithms [for a deeper review, see Ref. All voxels at 1 cm of a peak would have the same effect size, independently of whether they are in the same brain region or not
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