Feature Comparison

Because this representation of cortical variability is novel, and theoretically represents an efficient and overcomplete basis from which to represent the local features of each image, we hypothesized that we should be able to use our features to predict the values of other, more commonly used local features such as curvature, sulcal depth, cortical thickness, and gray/white contrast (as calculated using FreeSurfer) or measures of myelination, here calculated by dividing the Tintensity by the T2 intensity, as in  \cite{Glasser_2011}, then sampled onto the gray-white function surface.  Using our feature set as the input, quadratic regression models (ordinary least-squares) were estimated for each target metric using scikit-learn.  Model training and testing was performed in healthy controls using a 10-fold cross validation procedure.  Each fold was trained on all cortical vertices from 25 randomly selected healthy volunteers and tested on all cortical vertices from the remaining 5 subjects.  Performance was evaluated for each model using the coefficient of determination \(r{^2}\); effect size was reported as in \cite{cohen1988statistical}\(r=0.1\) as small\(r=0.3\) as medium, and \(r=0.5\) as large.

Similarity Estimation Across Subjects

Global Anomaly Detection

In our representation of cortical variability, we hypothesized that cortical lesions, but also possibly some normal cortical regions known to have atypical structural characteristics, would appear as global outliers in our feature space. To identify such regions of normal cortex, we calculated the average Mahalanobis distance for each cortical patch across all HVs (fig).  Specific outlier regions were identified by thresholding the average distance map across HVs at a threshold of 2.7, retaining 4.3% of the patches (equivalent to \(p=0.043\)), and clustering with a minimum of 30 nodes.  As exemplars, for further analysis we selected 2 of the resulting outlier regions of interest (ROI) in the anterior insula and primary motor cortex.

Directional Outliers and Similarity Maps 

Although some brain regions appear to be consistent global outliers across HVs, this does not mean that they are similar to each other.  In our representation, similarities or differences in combinations of features can be represented as differences in direction.  We explored this using our 2 exemplar outlier ROIs, defining the center and direction of each ROI as the average of the patches within that ROI across all HVs.  We similarly defined the average FCD ROI center and direction by averaging all of the patches within each MRI+ FCD mask (n=10), then averaging across the FCDs, to give each lesion equal weighting. Using the average direction of the insula ROI as the x-axis and the average direction of the motor ROI as the y-axis, we plotted the patches within each outlier ROI, the FCD ROI center, and 1000 randomly selected cortical patches for comparison (fig).