Non-Euclidean, convolutional learning on cortical brain surfaces

In recent years there have been many studies indicating that multiple cortical features, extracted at each surface vertex, are promising in the detection of various neurodevelopmental and neurodegenerative diseases. However, with limited datasets, it is challenging to train stable classifiers with such high-dimensional surface data. This necessitates a feature reduction that is commonly accomplished via regional volumetric morphometry from standard brain atlases. However, current regional summaries are not specific to the given age or pathology that is studied, which runs the risk of losing relevant information that can be critical in the classification process. To solve this issue, this paper proposes a novel data-driven approach by extending convolutional neural networks (CNN) for use on non-Euclidean manifolds such as cortical surfaces. The proposed network learns the most powerful features and brain regions from the extracted large dimensional feature space; thus creating a new feature space in which the dimensionality is reduced and feature distributions are better separated. We demonstrate the usability of the proposed surface-CNN framework in an example study classifying Alzheimers disease patients versus normal controls. The high performance in the cross-validation diagnostic results shows the potential of our proposed prediction system

Identification of morphological fingerprint in perinatal brains using quasi-conformal mapping and contrastive learning

The morphological fingerprint in the brain is capable of identifying the uniqueness of an individual. However, whether such individual patterns are present in perinatal brains, and which morphological attributes or cortical regions better characterize the individual differences of ne-onates remain unclear. In this study, we proposed a deep learning framework that projected three-dimensional spherical meshes of three morphological features (i.e., cortical thickness, mean curvature, and sulcal depth) onto two-dimensional planes through quasi-conformal mapping, and employed the ResNet18 and contrastive learning for individual identification. We used the cross-sectional structural MRI data of 682 infants, incorporating with data augmentation, to train the model and fine-tuned the parameters based on 60 infants who had longitudinal scans. The model was validated on 30 longitudinal scanned infant data, and remarkable Top1 and Top5 accuracies of 71.37% and 84.10% were achieved, respectively. The sensorimotor and visual cortices were recognized as the most contributive regions in individual identification. Moreover, the folding morphology demonstrated greater discriminative capability than the cortical thickness, which could serve as the morphological fingerprint in perinatal brains. These findings provided evidence for the emergence of morphological fingerprints in the brain at the beginning of the third trimester, which may hold promising implications for understanding the formation of in-dividual uniqueness in the brain during early development

Role of deep learning in infant brain MRI analysis

Deep learning algorithms and in particular convolutional networks have shown tremendous success in medical image analysis applications, though relatively few methods have been applied to infant MRI data due numerous inherent challenges such as inhomogenous tissue appearance across the image, considerable image intensity variability across the first year of life, and a low signal to noise setting. This paper presents methods addressing these challenges in two selected applications, specifically infant brain tissue segmentation at the isointense stage and presymptomatic disease prediction in neurodevelopmental disorders. Corresponding methods are reviewed and compared, and open issues are identified, namely low data size restrictions, class imbalance problems, and lack of interpretation of the resulting deep learning solutions. We discuss how existing solutions can be adapted to approach these issues as well as how generative models seem to be a particularly strong contender to address them

CLASSIFICATION OF NEUROANATOMICAL STRUCTURES BASED ON NON-EUCLIDEAN GEOMETRIC OBJECT PROPERTIES

Studying the observed morphological differences in neuroanatomical structures between individuals with neurodevelopmental disorders and a control group of typically developing individuals has been an important objective. Researchers study the differences with two goals: to assist an accurate diagnosis of the disease and to gain insights into underlying mechanisms of the disease that cause such changes. Shape classification is commonly utilized in such studies. An effective classification is difficult because it requires 1) a choice of an object model that can provide rich geometric object properties (GOPs) relevant for a given classification task, and 2) a choice of a statistical classification method that accounts for the non-Euclidean nature of GOPs. I lay out my methodological contributions to address the aforementioned challenges in the context of early diagnosis and detection of Autism Spectrum Disorder (ASD) in infants based on shapes of hippocampi and caudate nuclei; morphological deviations in these structures between individuals with ASD and typically developing individuals have been reported in the literature. These contributions respectively lead to 1) an effective modeling of shapes of objects of interest and 2) an effective classification. As the first contribution for modeling shapes of objects, I propose a method to obtain a set of skeletal models called s-reps from a set of 3D objects. First, the method iteratively deforms the object surface via Mean Curvature Flow (MCF) until the deformed surface is approximately ellipsoidal. Then, an s-rep of the approximate ellipsoid is obtained analytically. Finally, the ellipsoid s-rep is deformed via a series of inverse MCF transformations. The method has two important properties: 1) it is fully automatic, and 2) it yields a set of s-reps with good correspondence across the set. The method is shown effective in generating a set of s-reps for a few neuroanatomical structures. As the second contribution with respect to modeling shapes of objects, I introduce an extension to the current s-rep for representing an object with a narrowing sharp tail. This includes a spoke interpolation method for interpolating a discrete s-rep of an object with a narrowing sharp tail into a continuous object. This extension is necessary for representing surface geometry of objects whose boundary has a singular point. I demonstrate that this extension allows appropriate surface modeling of a narrowing sharp tail region of the caudate nucleus. In addition, I show that the extension is beneficial in classifying autistic and non-autistic infants at high risk of ASD based on shapes of caudate nuclei. As the first contribution with respect to statistical methods, I propose a novel shape classification framework that uses the s-rep to capture rich localized geometric descriptions of an object, a statistical method called Principal Nested Spheres (PNS) analysis to handle the non-Euclidean s-rep GOPs, and a classification method called Distance Weighted Discrimination (DWD). I evaluate the effectiveness of the proposed method in classifying autistic and non-autistic infants based on either hippocampal shapes or caudate shapes in terms of the Area Under the ROC curve (AUC). In addition, I show that the proposed method is superior to commonly used shape classification methods in the literature. As my final methodological contribution, I extend the proposed shape classification method to perform the classifcation task based on temporal shape differences. DWD learns a class separation direction based on the temporal shape differences that are obtained by taking differences of the temporal pair of Euclideanized s-reps. In the context of early diagnosis and detection of ASD in young infants, the proposed temporal shape difference classification produces some interesting results; the temporal differences in shapes of hippocampi and caudate nuclei do not seem to be as predictive as the cross-sectional shape of these structures alone.Doctor of Philosoph

Learning from Complex Neuroimaging Datasets

Advancements in Magnetic Resonance Imaging (MRI) allowed for the early diagnosis of neurodevelopmental disorders and neurodegenerative diseases. Neuroanatomical abnormalities in the cerebral cortex are often investigated by examining group-level differences of brain morphometric measures extracted from highly-sampled cortical surfaces. However, group-level differences do not allow for individual-level outcome prediction critical for the application to clinical practice. Despite the success of MRI-based deep learning frameworks, critical issues have been identified: (1) extracting accurate and reliable local features from the cortical surface, (2) determining a parsimonious subset of cortical features for correct disease diagnosis, (3) learning directly from a non-Euclidean high-dimensional feature space, (4) improving the robustness of multi-task multi-modal models, and (5) identifying anomalies in imbalanced and heterogeneous settings. This dissertation describes novel methodological contributions to tackle the challenges above. First, I introduce a Laplacian-based method for quantifying local Extra-Axial Cerebrospinal Fluid (EA-CSF) from structural MRI. Next, I describe a deep learning approach for combining local EA-CSF with other morphometric cortical measures for early disease detection. Then, I propose a data-driven approach for extending convolutional learning to non-Euclidean manifolds such as cortical surfaces. I also present a unified framework for robust multi-task learning from imaging and non-imaging information. Finally, I propose a semi-supervised generative approach for the detection of samples from untrained classes in imbalanced and heterogeneous developmental datasets. The proposed methodological contributions are evaluated by applying them to the early detection of Autism Spectrum Disorder (ASD) in the first year of the infant’s life. Also, the aging human brain is examined in the context of studying different stages of Alzheimer’s Disease (AD).Doctor of Philosoph