Topological Learning for Brain Networks

This paper proposes a novel topological learning framework that can integrate networks of different sizes and topology through persistent homology. This is possible through the introduction of a new topological loss function that enables such challenging task. The use of the proposed loss function bypasses the intrinsic computational bottleneck associated with matching networks. We validate the method in extensive statistical simulations with ground truth to assess the effectiveness of the topological loss in discriminating networks with different topology. The method is further applied to a twin brain imaging study in determining if the brain network is genetically heritable. The challenge is in overlaying the topologically different functional brain networks obtained from the resting-state functional MRI (fMRI) onto the template structural brain network obtained through the diffusion MRI (dMRI)

Inter-species cortical registration between macaques and humans using a functional network property under a spherical demons framework

Systematic evaluation of cortical differences between humans and macaques calls for inter-species registration of the cortex that matches homologous regions across species. For establishing homology across brains, structural landmarks and biological features have been used without paying sufficient attention to functional homology. The present study aimed to determine functional homology between the human and macaque cortices, defined in terms of functional network properties, by proposing an iterative functional network-based registration scheme using surface-based spherical demons. The functional connectivity matrix of resting-state functional magnetic resonance imaging (rs-fMRI) among cortical parcellations was iteratively calculated for humans and macaques. From the functional connectivity matrix, the functional network properties such as principal network components were derived to estimate a deformation field between the human and macaque cortices. The iterative registration procedure updates the parcellation map of macaques, corresponding to the human connectome project's multimodal parcellation atlas, which was used to derive the macaque's functional connectivity matrix. To test the plausibility of the functional network-based registration, we compared cortical registration using structural versus functional features in terms of cortical regional areal change. We also evaluated the interhemispheric asymmetry of regional area and its inter-subject variability in humans and macaques as an indirect validation of the proposed method. Higher inter-subject variability and interhemispheric asymmetry were found in functional homology than in structural homology, and the assessed asymmetry and variations were higher in humans than in macaques. The results emphasize the significance of functional network-based cortical registration across individuals within a species and across species.ope

Doctor of Philosophy

dissertationThe human brain is the seat of cognition and behavior. Understanding the brain mechanistically is essential for appreciating its linkages with cognitive processes and behavioral outcomes in humans. Mechanisms of brain function categorically represent rich and widely under-investigated biological substrates for neural-driven studies of psychiatry and mental health. Research examining intrinsic connectivity patterns across whole brain systems utilizes functional magnetic resonance imaging (fMRI) to trace spontaneous fluctuations in blood oxygen-level dependent (BOLD) signals. In the first study presented, we reveal patterns of dynamic attractors in resting state functional connectivity data corresponding to well-documented biological networks. We introduce a novel simulation for whole brain dynamics that can be adapted to either group-level analysis or single-subject level models. We describe stability of intrinsic functional architecture in terms of transient and global steady states resembling biological networks. In the second study, we demonstrate plasticity in functional connectivity following a minimum six-week intervention to train cognitive performance in a speed reading task. Long-term modulation of connectivity with language regions indicate functional connectivity as a candidate biomarker for tracking and measuring functional changes in neural systems as outcomes of cognitive training. The third study demonstrates utility of functional biomarkers in predicting individual differences in behavioral and cognitive features. We successfully predict three major domains of personality psychologyintelligence, agreeableness, and conscientiousnessin individual subjects using a large (N=475) open source data sample compiled by the National Institutes of Healths Human Connectome Project

Proceedings of the Third International Workshop on Mathematical Foundations of Computational Anatomy - Geometrical and Statistical Methods for Modelling Biological Shape Variability

International audienceComputational anatomy is an emerging discipline at the interface of geometry, statistics and image analysis which aims at modeling and analyzing the biological shape of tissues and organs. The goal is to estimate representative organ anatomies across diseases, populations, species or ages, to model the organ development across time (growth or aging), to establish their variability, and to correlate this variability information with other functional, genetic or structural information. The Mathematical Foundations of Computational Anatomy (MFCA) workshop aims at fostering the interactions between the mathematical community around shapes and the MICCAI community in view of computational anatomy applications. It targets more particularly researchers investigating the combination of statistical and geometrical aspects in the modeling of the variability of biological shapes. The workshop is a forum for the exchange of the theoretical ideas and aims at being a source of inspiration for new methodological developments in computational anatomy. A special emphasis is put on theoretical developments, applications and results being welcomed as illustrations. Following the successful rst edition of this workshop in 20061 and second edition in New-York in 20082, the third edition was held in Toronto on September 22 20113. Contributions were solicited in Riemannian and group theoretical methods, geometric measurements of the anatomy, advanced statistics on deformations and shapes, metrics for computational anatomy, statistics of surfaces, modeling of growth and longitudinal shape changes. 22 submissions were reviewed by three members of the program committee. To guaranty a high level program, 11 papers only were selected for oral presentation in 4 sessions. Two of these sessions regroups classical themes of the workshop: statistics on manifolds and diff eomorphisms for surface or longitudinal registration. One session gathers papers exploring new mathematical structures beyond Riemannian geometry while the last oral session deals with the emerging theme of statistics on graphs and trees. Finally, a poster session of 5 papers addresses more application oriented works on computational anatomy

Networked Data Analytics: Network Comparison And Applied Graph Signal Processing

Networked data structures has been getting big, ubiquitous, and pervasive. As our day-to-day activities become more incorporated with and influenced by the digital world, we rely more on our intuition to provide us a high-level idea and subconscious understanding of the encountered data. This thesis aims at translating the qualitative intuitions we have about networked data into quantitative and formal tools by designing rigorous yet reasonable algorithms. In a nutshell, this thesis constructs models to compare and cluster networked data, to simplify a complicated networked structure, and to formalize the notion of smoothness and variation for domain-specific signals on a network. This thesis consists of two interrelated thrusts which explore both the scenarios where networks have intrinsic value and are themselves the object of study, and where the interest is for signals defined on top of the networks, so we leverage the information in the network to analyze the signals. Our results suggest that the intuition we have in analyzing huge data can be transformed into rigorous algorithms, and often the intuition results in superior performance, new observations, better complexity, and/or bridging two commonly implemented methods. Even though different in the principles they investigate, both thrusts are constructed on what we think as a contemporary alternation in data analytics: from building an algorithm then understanding it to having an intuition then building an algorithm around it. We show that in order to formalize the intuitive idea to measure the difference between a pair of networks of arbitrary sizes, we could design two algorithms based on the intuition to find mappings between the node sets or to map one network into the subset of another network. Such methods also lead to a clustering algorithm to categorize networked data structures. Besides, we could define the notion of frequencies of a given network by ordering features in the network according to how important they are to the overall information conveyed by the network. These proposed algorithms succeed in comparing collaboration histories of researchers, clustering research communities via their publication patterns, categorizing moving objects from uncertain measurmenets, and separating networks constructed from different processes. In the context of data analytics on top of networks, we design domain-specific tools by leveraging the recent advances in graph signal processing, which formalizes the intuitive notion of smoothness and variation of signals defined on top of networked structures, and generalizes conventional Fourier analysis to the graph domain. In specific, we show how these tools can be used to better classify the cancer subtypes by considering genetic profiles as signals on top of gene-to-gene interaction networks, to gain new insights to explain the difference between human beings in learning new tasks and switching attentions by considering brain activities as signals on top of brain connectivity networks, as well as to demonstrate how common methods in rating prediction are special graph filters and to base on this observation to design novel recommendation system algorithms

Automated morphometric analysis and phenotyping of mouse brains from structural µMR images

In light of the utility and increasing ubiquity of mouse models of genetic and neurological disease, I describefully automated pipelines for the investigation of structural microscopic magnetic resonance images of mouse brains – for both high-throughput phenotyping, and monitoring disease. Mouse models offer unparalleled insight into genetic function and brain plasticity, in phenotyping studies; and neurodegenerative disease onset and progression, in therapeutic trials. I developed two cohesive, automatic software tools, for Voxel- and Tensor-Based Morphometry (V/TBM) and the Boundary Shift Integral (BSI), in the mouse brain. V/TBM are advantageous for their ability to highlight morphological differences between groups, without laboriously delineating regions of interest. The BSI is a powerful and sensitive imaging biomarker for the detection of atrophy. The resulting pipelines are described in detail. I show the translation and application of open-source software developed for clinical MRI analysis to mouse brain data: for tissue segmentation into high-quality, subject-specific maps, using contemporary multi-atlas techniques; and for symmetric, inverse-consistent registration. I describe atlases and parameters suitable for the preclinical paradigm, and illustrate and discuss image processing challenges encountered and overcome during development. As proof of principle and to illustrate robustness, I used both pipelines with in and ex vivo mouse brain datasets to identify differences between groups, representing the morphological influence of genes, and subtle, longitudinal changes over time, in particular relation to Down syndrome and Alzheimer’s disease. I also discuss the merits of transitioning preclinical analysis from predominately ex vivo MRI to in vivo, where morphometry is still viable and fewer mice are necessary. This thesis conveys the cross-disciplinary translation of up-to-date image analysis techniques to the preclinical paradigm; the development of novel methods and adaptations to robustly process large cohorts of data; and the sensitive detection of phenotypic differences and neurodegenerative changes in the mouse brai

Examining Resting-state Functional and Structural Connectivity of the Attention Networks after Early Brain Insults

Brain insults that occur early in life often lead to cognitive impairments, and sustained attention is highly vulnerable to the initial event as well as to the altered structural and functional brain development that follows. Sustained attention impairments are associated with neural changes in specific brain networks – default mode network (DMN) and central executive network (CEN) – that are crucial for proper attention functioning in healthy populations. Prior studies have, however, typically focused on adult cohorts, which is not applicable to understanding structural and functional changes in the developing brain. There are relatively few studies that have examined these networks in children with an early life injury with advanced quantitative neuroimaging techniques (structural magnetic resonance imaging (MRI) and functional MRI). Thus, the current thesis used these methods to investigate DMN and CEN changes following an early life brain insult in children with traumatic brain injury (TBI), epilepsy, or heterogeneous brain insults with the aim to identify shared neural changes in heterogeneous patient cohorts that underpin common attention impairments. The current thesis has reported reduced functional connectivity in the DMN regions (posterior cingulate cortex and medial prefrontal cortex) in children with TBI, and in the left parietal lobe in children with focal epilepsy as compared to controls at 2-years post-injury. Children with epilepsy however showed no differences in the structural covariance network when compared to controls. Children with heterogeneous brain insults also showed no significant functional and structural connectivity changes when imaging data were acquired in the acute post-insult period. This thesis is however limited by the lack of behavioural measures, and future studies should integrate neuropsychology and neuroimaging to better understand the relationships between the brain connectivity changes and attention deficits, therefore allowing the identification of children who would benefit most from early interventions that could improve their long-term neurocognitive outcomes

Data-Based And Theory-Based Network Models Of Perturbations To Neural Dynamics

Much of neuroscience is centered on uncovering simple principles that constrain the behavior of the brain. When considering the formation of neural architectures, similar structures can be recreated following the principles of minimizing wiring and maximizing topological complexity. However, a similar understanding of neural dynamics on top of these structural connections has not yet been achieved. One promising strategy for identifying underlying principles of neural dynamics is quantifying and modeling the response of neural systems to perturbation. Here, we use a spectrum of data- and theory-based network models to characterize the response of neural systems to different types of perturbations. We report how functional networks change in the context of pathological epileptic activity and brain-computer interface control. We also specifically test one possible principle: that activity is constrained to spread along connections in both the context of brain-computer interfaces and direct electrical stimulation. In the first study, we demonstrate across a wide variety of functional connectivity metrics and frequency bands that epileptic activity increases amplitude-based functional interactions, an observation that can now be incorporated into future theory-based models. In a second study, we determine that modeling activity that is constrained to spread along connections suggests why certain connections are important for brain-computer interface learning; specifically, these connections support sustained activity in attention regions. In our third study, we demonstrate that modeling activity changes from direct electrical stimulation using white matter connectivity explains more variance than models with rewired connections. This model generates testable predictions about which individuals, regions, and time points would lead to successful applications of direct electrical stimulation. Overall, this work demonstrates the potential uses of a range of data- and theory-based models for uncovering simple guiding principles that determine the behavior of a system. It also uses one specific principle - that activity is constrained to spread along connections - to understand the role of specific connections that may support learning, and provide a method to optimize individually tailored stimulation therapies for a specific outcome