In our representation, the similarity between two patches \(p_{i}\) and \(p_{j}\) can be assessed using simple metrics, such as the cosine similarity between their directions \(s_{ij}=\hat{u}_{i}\cdot\hat{u}_{j}\).  Based on known patterns of cortical variability, we first hypothesized that our features would vary across the cortical sheet in a somewhat reproducible fashion across HVs.  To assess this, we defined patches as being in homotopic (same) or heterotopic (different) locations as defined by the standard surface mesh (Figure 4a),  and computed the cosine similarity between 1000 randomly sampled heterotopic patches and 1000 heterotopic patches across HVs.  We then wished to determine how similar FCD lesions appeared to normal cortex.  We therefore compared the cosine similarity of 1000 non-overlapping FCD patches to each other, as well as to 1000 randomly selected heterotopic HV patches, and 1000 homotopic patches that fell within the FCD mask in 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.

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. 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. For each surviving cluster, we computed the mean FCD similarity.  

Statistical Analysis

All statistical analysis was 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).