Similarity Estimation
Having observed significant overlap in outlierness between FCDs and some normal cortical regions, we explored the similarity in underlying features between FCDs and normal cortex. In one approach, we created similarity maps to our average FCD and exemplar normal outlier ROIs by computing the scalar projection of the mean feature vector for each cortical patch onto the ROI average unit vector and projecting it onto the cortical surface (see Figure 2). This metric highlights outlying patches with similar underlying features to the exemplar ROI.
To assess similarity between cortical patches \(p_{i}\) and \(p_{j}\) without regard to degree of outlierness, we assessed the cosine similarity between their directions \(s_{ij}=\hat{u}_{i}\cdot\hat{u}_{j}\). Using this metric, patches with similar relative combinations of underlying features will appear more similar regardless of their distance from the center of the distribution. Based on known patterns of cortical variability, we hypothesized that local image features would vary across the cortical sheet in a somewhat reproducible fashion across HVs and therefore patches in the same locations would appear more similar to each other than patches in different locations. To assess this, we defined patches as being in homotopic (same) or heterotopic (different) locations as defined by the standard surface mesh and computed the cosine similarity between 1000 randomly sampled heterotopic patches and 1000 homotopic patches across HVs. To determine how similar FCD lesions appeared to normal cortex, we then compared the cosine similarity of 1000 non-overlapping FCD patches to each other, as well as to 1000 randomly selected heterotopic and then homotopic patches across HVs.
Local Normalization
Because FCDs were not more globally anomalous and also appeared to have similar features to some normal cortical regions, we hypothesized that to be identifiable, FCDs must differ from the expected appearance at their underlying location, or homotopic region, in HVs. We implemented a local normalization procedure by removing the local mean, calculated across homotopic patches in HVs. We expected that after local normalization, reproducible regional differences in normal cortex should no longer be present. However, the effect on FCDs was unknown. Therefore, following normalization, we again compared the Mahalanobis distances of normal cortex, the outlier ROIs, and FCDs as above, as well as the cosine similarity between FCD patches and heterotopic and homotopic normal cortical patches.
Automated FCD Detection
We created an automated FCD detection method based on locally normalized FCD similarity maps. We used a leave-one-out cross-validation strategy to build a subject specific model for each FCD patient and HV. In each subject, we computed the scalar projection of the mean feature vector for each patch onto the FCD average unit vector (Figure 4b). We then applied a threshold to identify the top 1% of vertices and retained clusters with 5 or more adjacent remaining vertices, a minimal size threshold meant to eliminate isolated outlying vertices. For each surviving cluster, we computed the mean FCD similarity.
Statistical Analysis
All statistical analyses were carried out in Python. For the feature prediction models, performance was evaluated for each model using the coefficient of determination \(r{^2}\). To estimate the extent of the differences between the measured and predicted models, we report effect size as in \cite{cohen1988statistical}: \(r=0.1\) as small; \(r=0.3\) as medium; and \(r=0.5\) as large. For distance-wise comparisons between patches, we used Welch's unequal variance t-test to assess significance and to estimate the effect size of the differences, reported as in \cite{cohen1988statistical}: \(d=0.2\) as small; \(d=0.5\) as medium; and \(d=0.5\) as large.
Sensitivity of the automated FCD detection procedure was assessed initially for MRI+ patients and then for all patients. We calculated a receiver operating characteristics (ROC) curve and area under the curve (AUC) based on the patients with manual lesion labels that were included in the leave-one-out analysis. True positives were defined as co-localization of a detected cluster with the manual lesion mask for MRI+ patients and as overlap of a detected cluster with the resection mask for MRI- patients. False positives were defined as HVs with clusters detected above a given threshold. The optimal threshold for the final detection was determined using the Youden Index (calculated as sensitivity + specificity - 1 for each threshold) in the patients with lesion masks. Lesion detection and number of extralesional clusters (outside of the lesion and resection masks or in HVs) were assessed for all patients and HVs individually.
Results
Study Participants
This study includes 15 patients with drug resistant focal epilepsy and FCD (median age 27, range 15-53, 11 females) and 30 healthy controls (median age 23, range 8-63, 12 females). FCDs were identified in the radiological reports in 6/15 patients; an additional five patients had lesions identifiable on post-hoc analysis (MRI+ n=11) (details in Table 1).