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.
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, retaining 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+ patients with co-localization of a detected cluster and the manual lesion mask, and for MRI- patients, as overlap of a detected cluster with the resection mask. False positives were defined as HVs with detected 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 (outside of the lesion or resection masks or in HVs) were assessed for all patients and HVs individually.
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).