Local Normalization
Using our normative data, we explored several aspects of this normal cortical variability, both within and across individual healthy volunteers. Using our metrics of similarity (Euclidean distance and cosine similarity), we first hypothesized that, across healthy volunteers, pairs of patches at the same location (homotopic patches) should be more similar to each other than pairs of randomly selected patches at different locations (heterotopic patches). Using the same metrics, we also tested the hypothesis that homologous contralateral patches within individual subjects, as are commonly compared when calculating asymmetry indices, would be more similar to each other than randomly selected heterotopic patches. For each comparison, the mean and standard deviation of the included patches are reported. Welch's t-test was used to compare the distribution of Euclidean distances and cosine similarities between patches because both distributions were approximately normally distributed but often had unequal variances. Effect size was reported as in \cite{cohen1988statistical}: \(d=0.2\) as small , \(d=0.5\) as medium, and \(d=0.5\) as large.
Atypical Cortical Areas
To further explore the consistency of these metrics, we computed the Mahalanobis distances of all of the patches within each ROI in individual subjects and compared these to the distances obtained from a sample of 1000 randomly selected cortical patches (fig). We then defined the center and direction of each selected ROI as the average of the patches within that ROI across all healthy volunteers. To visualize the degree of similarity of these patches across subjects, we used the average direction of the insula ROI as the x-axis and the average direction of the motor ROI as the y-axis and plotted the average center of each patch within each ROI across healthy volunteers, as well as the centers of randomly selected cortical patches (fig).
Synthetic Contrasts
Finally, to explore the spatial distribution of similarity to each ROI, we created synthetic contrast maps by computing the projection of the mean feature vector for each patch onto the ROI direction. We calculated these synthetic contrast similarity maps for each healthy control and displayed the average synthetic contrast map on the cortical surface (fig).
FCD Characterization
By definition, our normative model was created using healthy volunteer data and generic features without regard to any specific type of pathology. We hypothesized that, in order to be visually identifiable, FCD patches would differ locally from their underlying homotopic patches in healthy volunteers and possibly globally if their characteristics were more unusual than those accounted for by normal cortical variability. We therefore first assessed whether FCD lesions identified as abnormal on visual inspection would appear as global outliers in our feature space, as there should be a low probability of similar patches being observed in the normative data. We therefore randomly selected 1000 patches from within manually labeled FCD lesions, and computed their distances from the center of the distribution. We compared these distances to those obtained from 1000 randomly selected patches of cortex from healthy volunteers, as well as from the previously identified outlier insular and motor cortex ROIs.
As described for the motor and insula ROIs, different regions can be global outliers but still have quite different characteristics and, thus, different locations in our feature space. To identify areas of normal cortex that appear similar to FCDs, we created FCD-based similarity maps, as done previously for the motor and insula ROIs. To compute the average FCD vector, we calculated the average of all patches included within each lesion mask for patients with a visibly-identifiable MRI lesion (n=10), then averaged these average vectors so that each individual lesion was weighted equally. Using this average FCD vector scaled to unit length, the lesion similarity at each patch was computed as the scalar projection of its feature vector onto the average FCD unit vector. The average FCD similarity map across healthy volunteers is shown in figure xxx.
Because several cortical regions reproducibly appear similar to FCDs, we implemented a local normalization procedure consisting of removal of the local mean at each patch calculated across all healthy volunteers. This was followed by variance normalization, with the local standard deviation for each patch calculated across healthy volunteers after removal of the local mean for each control subject individually. Following this local normalization procedure, we again calculated the distances from the center of the new normalized distribution of 1000 randomly selected FCD patches, 1000 randomly selected healthy control patches, and patches from the motor and insula outlier patches (fig xxx).
We expected that after local normalization, reproducible regional differences should no longer be present. However, the effect on FCD similarity (or dissimilarity) to normal cortex was unknown. To evaluate this, we computed the Euclidean distance and cosine similarity between 1000 randomly selected FCD patches and 1) 1000 homotypic patches that fell within the FCD mask in healthy volunteers, 2) 1000 heterotopic patches in healthy volunteers, and 3) to other non-overlapping FCD patches across patients. We also compared these distances to the similarities between 1000 pairs of homotopic patches and randomly selected heterotopic patches across healthy volunteers.
Finally, we wished to further visualize the distribution of FCDs after local normalization compared to normal cortex. We used a singular value decomposition (SVD) to select the 2 components explaining the most variance across the FCDs and used these as the x- and y-axes to create a 2D plot of the location of each FCD patch, along with the center of each individual FCD and the average FCD center across all subjects. We also plotted the centers of 1000 randomly sampled healthy control patches for comparison.
FCD Detection
We then sought to create an automated classification method to detect FCDs in our patient sample. As in \cite{Hong2014}, we used a two stage method to improve specificity, in this case using quadratic discriminant analysis as implemented in Scikit-learn. For training and evaluation of our classifier, we used a leave-one-out cross-validation strategy for each FCD patient and each healthy volunteer to build a subject specific model trained using the labeled data from the other subjects as follows:
- For the first stage, we randomly sampled with replacement: a) 1000 patches evenly across the healthy volunteers in the training set, and b) 1000 FCD samples from the FCD masks of the patients. We then fit a quadratic discriminant analysis (QDA) model to those 2000 samples to classify patches as FCD or HV.
- We applied this first stage QDA model to all of the patches in all of the training subjects. We then retained all clusters of patches that included more than 5 patches classified as FCD.
- For the second stage, we again sampled with replacement but only from clusters surviving the first stage: a) 1000 patches evenly across the healthy volunteers, and b) 1000 FCD samples from the patients' FCD masks, and fit a second QDA model.
- We then applied this second stage QDA model to all of the patches that survived the first stage model in the each test subject. We again retained all clusters of patches that included more than 5 patches classified as FCD.
- For each cluster surviving the second stage model, we computed a cluster weight, calculated as area \(\times\)mean FCD probability, as well as the cluster's rank among surviving clusters in that subject.
Performance of the classifier was assessed for all patients as well as for the patients with visually-identifiable lesions. We calculated a receiver operating characteristics (ROC) curve and area under the curve (AUC). True positives (or detections) were defined as MRI positive patients with co-localization of a detected cluster and the manual lesion mask or, for MRI negative patients, as overlap of a detected cluster with the resection mask. False positives were defined as healthy controls with clusters detected above a given threshold. The optimal threshold to apply to the resulting clusters was determined using the Youden Index (calculated as sensitivity + specificity - 1). Additionally, lesion detection and number of extralesional clusters were assessed for all patients and healthy volunteers individually. Extralesional clusters were defined as detected clusters that did not overlap with the manually drawn lesion or resection mask in patients or any detected cluster in healthy volunteers.
Results
Study Participants
A total of 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) were included in this study. FCDs were identified in the radiological reports in 6/15 patients. Post-hoc analysis identified FCDs that could be visually appreciated and traced on the T1 or FLAIR image in 10/15 patients. Seven of the patients had surgical resections, with pathological diagnosis of FCD type IIb in 3 and FCD type IIa in 4, with 4 additional patients having transmantle signs suggestive of FCD type IIb but no histological diagnosis as they did not undergo surgery. Patient demographics and further details are reported in Table (summary table).