Discussion

We used a novel normative modeling approach to compare local features of FCDs to those of normal cortex.  We found that FCDs on average are global outliers but not more so than some reproducible regions of normal cortex.  In addition, the features seen in FCDs appear quite similar to those found in some outlying cortical regions such as paralimbic and sensorimotor cortices.  After locally correcting for the expected appearance at each cortical location, FCD lesions become more easily distinguishable from normal cortex, with true positive clusters found in 13/15 patients, allowing for automated detection with 80% sensitivity and 70% specificity. 
The performance of any FCD detection method depends on the features used to create an effective representation of the data.  Here, we implemented a generic set of multiscale 3D rotationally-invariant derivative-based filters applied to T1, T2, and FLAIR images. Similar 2D filters have been used in computer vision applications such as texture synthesis and imaging denoising \cite{Portilla2003} and occasionally in biomedical applications such as brain tumor classification \cite{Zacharaki2009}, lung disease segmentation \cite{Joyseeree2018,Wang2018} and cerebral white matter lesion detection \cite{Selvaganesan2019}.  Most post-processing approaches to FCD detection to date have used features derived from voxel-based or surface-based morphometry (see review in \cite{Kini2016}), including a variety of measures of image intensity and blurring of the gray-white junction, similar to our Gaussian blurring and gradient amplitude metrics.  The second-derivative-based filters that we have employed contain information similar to the higher-order textural features implemented by Antel et al., who used gray-level co-occurrence matrices derived from T1-weighted images at a single spatial scale \cite{Antel2003}.  Our features extend this work by additionally containing information from multiple spatial scales, as well as multiple MR contrasts.  In our evaluation, we found that these features can be used to accurately predict other more commonly described features such as cortical thickness and myelination, as well as the Freesurfer-defined metric of blurring of the gray-white junction.
Detection of subtle cortical lesions is challenging, at least in part due to difficulties in accounting for the variability of both the cortex and the lesions.  Our normative model creates a single overall probabilistic representation of normal cortical variability that encompasses information from multiple local imaging features, spatial scales, and MR contrasts.  We found that while FCD lesions are on average global outliers in appearance compared to normal cortex as a whole, some normal regions are outliers to a similar degree.  FCDs also appear similar in their underlying average features to some of these normally outlying regions; the first component appears similar to regions such as the anterior insula and mesial temporal cortex, and the second appears similar to sensorimotor and posterior cingulate cortices.  These outlying regions generally consist of relatively thick agranular or dysgranular cortex  \cite{Amunts2015,Triarhou2007,Zilles2010} with relatively blurry gray-white junctions.  However, they are at opposite ends of the known gradients in myelination; primary sensorimotor regions are heavily myelinated while paralimbic cingulate and parahippocampal cortices are lightly myelinated \cite{Glasser2011,Nieuwenhuys2017,Paquola2019}. Accordingly, the precentral ROI similarity map parallels the myelination gradients, extending primarily toward the premotor regions, while the insula similarity map identifies the lightly myelinated, relatively thick anterior cingulate and parahippocampal cortices.  Commonalities between the FCD similarity maps is likely attributable to these shared features.
Local normalization procedures correct for the expected appearance of the cortex in a given location, thereby allowing FCDs to be more easily distinguished both from other normally outlying cortical regions.  Interestingly, we also observed that FCDs initially share some common features with their underlying homotopic cortical regions, with cosine similarities between FCDs and their respective homotopic regions being equal to that of other FCDs and significantly more similar than to random cortical areas. This finding is consistent with the fact that many of these lesions differ only subtly from surrounding cortex, which makes them difficult to appreciate visually.  This is no longer seen following local normalization.
Our automated detection procedure based on these locally-normalized FCD similarity maps allows  for detection of 80% of FCDs and 100% of visually identifiable FCDs with 70% specificity.  In patients with true positive clusters, the lesion of interest had the highest cluster weight in 11/13 (85%), thus providing an additional way of identifying lesions of higher interest in a given patient, similar to the approach used in Adler  et al. \cite{Adler2017}.  Many are also clearly identifiable by visual inspection of the FCD similarity maps, which can be reviewed similarly to the maps created using the MAP procedure \cite{Wang2015,Wagner2011}..  The performance of our automated classifier is similar to previously reported machine learning methods, which have achieved 58-74% sensitivity, with specificities ranging from not reported to 100% \cite{Adler2017,Ahmed2015,Hong2014,Jin2018}.  Comparisons of performance across methods continues to be challenging.  To our knowledge, no work to date has directly compared the performance of  different automated FCD methods in the same patient population.  Numerous factors may affect the performance, including the conspicuity of lesions studied, ranging from clearly MR+ to MR- patients, and size of the patient and healthy volunteer training sets utilized.  For supervised machine-learning methods, performance appears to improve significantly with increasing size of the healthy volunteer and patient training sets, which affect the accuracy of modeling of both pathological and normal cortical variability \cite{Jin2018}.  
There are several challenges to widespread adoption of these techniques into standard clinical practice, including: 1) MR scanning protocol variability, hardware, and software, which may impair generalization of any "learning" across centers; 2) limited availability of large patient and normative training sets at single institutions, particularly with ongoing evolution of acquisition protocols; and 3) significant technical expertise required to implement these approaches. This work, like others, is limited by the relatively small size of normative and lesional training sets.  Open source efforts such as this and the MELD Project (https://meldproject.github.io/) wil hopefully continue to increase adoption, allow for direct comparisons of methods, and allow for pooling of data across centers leading to improved performance \cite{Jin2018}

Conclusions

We implemented a novel normative modeling approach to FCD identification, providing a robust characterization of normal cortical variability for comparison with FCD lesions. In keeping with their often subtle appearance, FCD lesions are outliers but only to a similar degree as some normal cortical regions.  In our feature space, FCDs appear quite similar to some of these regions, such as paralimbic and sensorimotor cortices.  These similarities should be kept in mind when visually inspecting images to detect possible FCDs. They also help to explain the utility of local normalization procedures in reducing false positive detections.  Our resulting approach to automated FCD detection is 80% sensitive and 70% specific, AUC 0.91, similar to or better than many previously proposed methods, despite the relatively small size of the training and testing data.  Our normative modeling approach also has the potential to be of use in the detection of other types of pathology or to study normal cortical variability.

Acknowledgements

We are indebted to all patients and their families who have selflessly volunteered their time to participate in this study. 
Funding:  This work was supported by the Intramural Research Program of the National Institute of Neurological Disorders and Stroke, NIH.