The Smoothing Artifact of Spatially Constrained Canonical Correlation Analysis in Functional MRI

Hindawi Publishing Corporation International Journal of Biomedical Imaging Volume 2012, Article ID 738283, 11 pages doi:10.1155/2012/738283 Research Article The Smoothing Artifact of Spatially Constrained Canonical Correlation Analysis in Functional MRI Dietmar Cordes,1, 2, 3 Mingwu Jin,3, 4 Tim Curran,2 and Rajesh Nandy5 1 Department of Physics, Ryerson University, Toronto, ON, Canada M5B 2K3 2 Department of Psychology and Neuroscience, University of Colorado, Boulder, CO 80309, USA 3 Department of Radiology, University of Colorado, Denver, CO 80045, USA 4 Department of Physics, University of Texas, Arlington, TX 76019, USA 5 Departments of Biostatistics and Psychology, UCLA, Los Angeles, CA 90095, USA Correspondence should be addressed to Dietmar Cordes, Received 19 March 2012; Revised 13 November 2012; Accepted 26 November 2012 Academic Editor: Carlos Alberola-Lopez Copyright © 2012 Dietmar Cordes et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. A wide range of studies show the capacity of multivariate statistical methods for fMRI to improve mapping of brain activations in a noisy environment. An advanced method uses local canonical correlation analysis (CCA) to encompass a group of neighboring voxels instead of looking at the single voxel time course. The value of a suitable test statistic is used as a measure of activation. It is customary to assign the value to the center voxel; however, this is a choice of convenience and without constraints introduces artifacts, especially in regions of strong localized activation. To compensate for these deficiencies, different spatial constraints in CCA have been introduced to enforce dominance of the center voxel. However, even if the dominance condition for the center voxel is satisfied, constrained CCA can still lead to a smoothing artifact, often called the “bleeding artifact of CCA”, in fMRI activation patterns. In this paper a new method is introduced to measure and correct for the smoothing artifact for constrained CCA methods. It is shown that constrained CCA methods corrected for the smoothing artifact lead to more plausible activation patterns in fMRI as shown using data from a motor task and a memory task. 1. Introduction Local canonical correlation analysis (CCA) is a multivariate statistical method in fMRI that uses the joint time course of a group of neighboring voxels, usually in a 3 × 3 inplane voxel grid, to determine the significance of activation. The value of a suitable test statistic is used as a measure of activation. Since the joint time course of the neighborhood is used, it is not immediately clear to which voxel the measure of activation should be assigned. For example, if a 3 × 3 voxel neighborhood is chosen and the measure of activation is significant, without further assumptions one can only conclude that activation occurred somewhere within the 3 × 3 voxel neighborhood. If the activation is assigned to all voxels of the neighborhood, loss of spatial specificity will occur. To increase spatial specificity, it has been proposed to assign the measure of activation to the center voxel of the 3 × 3 neighborhood [1, 2]. A center voxel assignment is usually justified by mathematical convenience but can also be reasoned on the fact that the fMRI BOLD response leads to patches of activation patterns that are most likely of convex shape and simple connectivity (without any holes in the interior neighborhood). However, this center voxel assignment proved to be prone to yield artifacts as activations tend to bleed to the neighboring voxels of strongly active voxels. The result is a loss of spatial specificity from this smoothing artifact. The smoothing artifact is not only common in conventional CCA, but also in any analysis technique that involves spatial low-pass filter kernels, such as univariate (single voxel) analysis where the data have been preprocessed using Gaussian spatial smoothing. In conventional data smoothing, the smoothing artifact has been intentionally “induced” to increase the signal-to-noise ratio at the cost of 2 International Journal of Biomedical Imaging reduced specificity and occurrence of typical spatial low-pass artifacts such as blurring of edges of activation patterns. To compensate for the smoothing artifact in conventional CCA, different assignment schemes were proposed. For example, a minimum relative weight for the center voxel was used to restrict false activations [3]. In another study using a more adaptive approach, the smoothing artifact was reduced by utilizing the spatial dependence among voxels as much as possible and assigning the significance of activation to the dominant voxel of local maxima [4]. This method was shown to be effective in eliminating the smoothing artifact in motor activation data that is known to have large contrast-to-noise ratio (CNR), however, in data where the activation is more subtle (such as hippocampal activation using an episodic memory paradigm), the method has the disadvantage of being less sensitive, according to our studies. To reduce the smoothing artifact in CCA, it is necessary to constrain the spatial weights properly and impose the condition that the center voxel always has the largest weight. Constrained CCA (cCCA) with positivity constraints have been proposed for fMRI. Friman et al. [5] as well as Ragnehed et al. [6] use nonnegative spatial weights with maximum weight of the center voxel in order to ensure spatial low-pass filter properties of cCCA. This has the additional benefit of constraining CCA to eliminate spurious correlations occurring in conventional CCA where spatial filters can have positive and negative coefficients. To our knowledge, the smoothing artifact in cCCA has never been studied. Recently, we provided a mathematical framework for cCCA and computed ROC properties of cCCA with different linear constraints and a nonlinear constraint for activation patterns of motor data and episodic memory data [7, 8]. In this paper we expand our previous research and investigate in detail the smoothing artifact that is associated with each spatial constraint in cCCA. Furthermore, we provide a novel approach of how to correct the measure of activation for the smoothing artifact. Results for motor activation data and episodic memory activation data are presented. Parts of this paper have been published in abstract form (one page) at a recent conference [9]. 2. Theory stimulus function). The coefficients αi and β j are the spatial and temporal weights, respectively, that are being determined and optimized by the data for each individual neighborhood using an optimization routine. The symbol ⊗ denotes spatial convolution and ε(t) is a Gaussian-distributed random error term. If the number of spatial basis functions is reduced to a single function, (1) becom (...truncated)