RESUMO
We explore functional connectivity in nine subjects measured with 1.5T fMRI-BOLD in a longitudinal study of recovery from unilateral stroke affecting the motor area (Small et al., 2002). We found that several measures of complexity of covariance matrices show strong correlations with behavioral measures of recovery. In Schmah et al. (2010), we applied Linear and Quadratic Discriminants (LD and QD) computed on a principal components (PC) subspace to classify the fMRI volumes into "early" and "late" sessions. We demonstrated excellent classification accuracy with QD but not LD, indicating that potentially important differences in functional connectivity exist between the early and late sessions. Motivated by Mclntosh et al. (2008), who showed that EEG brain-signal variability and behavioral performance both increased with age during development, we investigated complexity of the covariance matrix for this longitudinal stroke recovery data set. We used three complexity measures: the sphericity index described by Abdi (2010); "unsupervised dimensionality", which is the number of PCs that minimizes unsupervised generalization error of a covariance matrix (Hansen et al., 1999); and "QD dimensionality", which is the number of PCs that minimizes the classification accuracy of QD. Although these approaches measure different kinds of complexity, all showed strong correlations with one or more behavioral tests: nine-hole peg test, hand grip test and pinch test. We could not demonstrate that either sphericity or unsupervised dimensionality were significantly different for the "early" and "late" sessions using a paired Wilcoxon test. However, the amount of relative behavioral improvement was correlated with sphericity of the overall covariance matrix (pooled across all sessions), as well as with the divergence of the eigenspectra between the "early" and "late" covariance matrices. Complexity measures that use the number of PCs (which optimize QD classification or unsupervised generalization) were correlated with the behavioral performance of the final session, but not with the relative improvement. These are suggestive, but limited, results given the sample size, restricted behavioral measurements and older 1.5T BOLD data sets. Nevertheless, they indicate one potentially fruitful direction for future data-driven fMRI studies of stroke recovery in larger, better-characterized longitudinal stroke data sets recorded at higher field strength. Finally, we produced sensitivity maps (Kjems et al., 2002) corresponding to both linear and quadratic discriminants for the "early" vs. "late" classification. These maps measure the influence of each voxel on the class assignments for a given classifier. Differences between the scaled sensitivity maps for the linear and quadratic discriminants indicate brain regions involved in changes in functional connectivity. These regions are highly variable across subjects, but include the cerebellum and the motor area contralateral to the lesion.
