Latent Factor Analysis of High-Dimensional Brain Imaging Data

Recent advances in neuroimaging study, especially functional magnetic resonance imaging (fMRI), has become an important tool in understanding the human brain. Human cognitive functions can be mapped with the brain functional organization through the high-resolution fMRI scans. However, the high-dimensional data with the increasing number of scanning tasks and subjects pose a challenge to existing methods that wasn’t optimized for high-dimensional imaging data. In this thesis, I develop advanced data-driven methods to help utilize more available sources of information in order to reveal more robust brain-behavior relationship. In the first chapter, I provide an overview of the current related research in fMRI and my contributions to the field. In the second chapter, I propose two extensions to the connectome-based predictive modeling (CPM) method that is able to combine multiple connectomes when building predictive models. The two extensions are both able to generate higher prediction accuracy than using the single connectome or the average of multiple connectomes, suggesting the advantage of incorporating multiple sources of information in predictive modeling. In the third chapter, I improve CPM from the target behavioral measure’s perspective. I propose another two extensions for CPM that are able to combine multiple available behavioral measures into a composite measure for CPM to predict. The derived composite measures are shown to be predicted more accurately than any other single behavioral measure, suggesting a more robust brainbehavior relationship. In the fourth chapter, I propose a nonlinear dimensionality reduction framework to embed fMRI data from multiple tasks into a low-dimensional space. This framework helps reveal the common brain state in the multiple available tasks while also help discover the differences among these tasks. The results also provide valuable insights into the various prediction performance based on connectomes from different tasks. In the fifth chapter, I propose an another hyerbolic geometry-based brain graph edge embedding framework. The framework is based on Poincar´e embedding and is able to more accurately represent edges in the brain graph in a low-dimensional space than traditional Euclidean geometry-based embedding. Utilizing the embedding, we are able to cluster edges of the brain graph into disjoint clusters. The edge clusters can then be used to define overlapping brain networks and the derived metrics like network overlapping number can be used to investigate functional flexibility of each brain region. Overall, these work provide rich data-driven methods that help understand the brain-behavioral relationship through predictive modeling and low-dimensional data representation

Prediction of post-stroke motor recovery benefits from measures of sub-acute widespread network damages.

Following a stroke in regions of the brain responsible for motor activity, patients can lose their ability to control parts of their body. Over time, some patients recover almost completely, while others barely recover at all. It is known that lesion volume, initial motor impairment and cortico-spinal tract asymmetry significantly impact motor changes over time. Recent work suggested that disabilities arise not only from focal structural changes but also from widespread alterations in inter-regional connectivity. Models that consider damage to the entire network instead of only local structural alterations lead to a more accurate prediction of patients' recovery. However, assessing white matter connections in stroke patients is challenging and time-consuming. Here, we evaluated in a data set of 37 patients whether we could predict upper extremity motor recovery from brain connectivity measures obtained by using the patient's lesion mask to introduce virtual lesions in 60 healthy streamline tractography connectomes. This indirect estimation of the stroke impact on the whole brain connectome is more readily available than direct measures of structural connectivity obtained with magnetic resonance imaging. We added these measures to benchmark structural features, and we used a ridge regression regularization to predict motor recovery at 3 months post-injury. As hypothesized, accuracy in prediction significantly increased (R 2 = 0.68) as compared to benchmark features (R 2 = 0.38). This improved prediction of recovery could be beneficial to clinical care and might allow for a better choice of intervention

Relating resting-state fMRI and EEG whole-brain connectomes across frequency bands.

Whole brain functional connectomes hold promise for understanding human brain activity across a range of cognitive, developmental and pathological states. So called resting-state (rs) functional MRI studies have contributed to the brain being considered at a macroscopic scale as a set of interacting regions. Interactions are defined as correlation-based signal measurements driven by blood oxygenation level dependent (BOLD) contrast. Understanding the neurophysiological basis of these measurements is important in conveying useful information about brain function. Local coupling between BOLD fMRI and neurophysiological measurements is relatively well defined, with evidence that gamma (range) frequency EEG signals are the closest correlate of BOLD fMRI changes during cognitive processing. However, it is less clear how whole-brain network interactions relate during rest where lower frequency signals have been suggested to play a key role. Simultaneous EEG-fMRI offers the opportunity to observe brain network dynamics with high spatio-temporal resolution. We utilize these measurements to compare the connectomes derived from rs-fMRI and EEG band limited power (BLP). Merging this multi-modal information requires the development of an appropriate statistical framework. We relate the covariance matrices of the Hilbert envelope of the source localized EEG signal across bands to the covariance matrices derived from rs-fMRI with the means of statistical prediction based on sparse Canonical Correlation Analysis (sCCA). Subsequently, we identify the most prominent connections that contribute to this relationship. We compare whole-brain functional connectomes based on their geodesic distance to reliably estimate the performance of the prediction. The performance of predicting fMRI from EEG connectomes is considerably better than predicting EEG from fMRI across all bands, whereas the connectomes derived in low frequency EEG bands resemble best rs-fMRI connectivity

GEFF: Graph Embedding for Functional Fingerprinting

It has been well established that Functional Connectomes (FCs), as estimated from functional MRI (fMRI) data, have an individual fingerprint that can be used to identify an individual from a population (subject-identification). Although identification rate is high when using resting-state FCs, other tasks show moderate to low values. Furthermore, identification rate is task-dependent, and is low when distinct cognitive states, as captured by different fMRI tasks, are compared. Here we propose an embedding framework, GEFF (Graph Embedding for Functional Fingerprinting), based on group-level decomposition of FCs into eigenvectors. GEFF creates an eigenspace representation of a group of subjects using one or more task FCs (Learning Stage). In the Identification Stage, we compare new instances of FCs from the Learning subjects within this eigenspace (validation dataset). The validation dataset contains FCs either from the same tasks as the Learning dataset or from the remaining tasks that were not included in Learning. Assessment of validation FCs within the eigenspace results in significantly increased subject-identification rates for all fMRI tasks tested and potentially task-independent fingerprinting process. It is noteworthy that combining resting-state with one fMRI task for GEFF Learning Stage covers most of the cognitive space for subject identification. Thus, while designing an experiment, one could choose a task fMRI to ask a specific question and combine it with resting-state fMRI to extract maximum subject differentiability using GEFF. In addition to subject-identification, GEFF was also used for identification of cognitive states, i.e. to identify the task associated to a given FC, regardless of the subject being already in the Learning dataset or not (subject-independent task-identification). In addition, we also show that eigenvectors from the Learning Stage can be characterized as task- and subject-dominant, subject-dominant or neither, using two-way ANOVA of their corresponding loadings, providing a deeper insight into the extent of variance in functional connectivity across individuals and cognitive states

Building connectomes using diffusion MRI: why, how and but

Why has diffusion MRI become a principal modality for mapping connectomes in vivo? How do different image acquisition parameters, fiber tracking algorithms and other methodological choices affect connectome estimation? What are the main factors that dictate the success and failure of connectome reconstruction? These are some of the key questions that we aim to address in this review. We provide an overview of the key methods that can be used to estimate the nodes and edges of macroscale connectomes, and we discuss open problems and inherent limitations. We argue that diffusion MRI-based connectome mapping methods are still in their infancy and caution against blind application of deep white matter tractography due to the challenges inherent to connectome reconstruction. We review a number of studies that provide evidence of useful microstructural and network properties that can be extracted in various independent and biologically-relevant contexts. Finally, we highlight some of the key deficiencies of current macroscale connectome mapping methodologies and motivate future developments

Mapping neurotransmitter systems to the structural and functional organization of the human neocortex

Neurotransmitter receptors support the propagation of signals in the human brain. How receptor systems are situated within macro-scale neuroanatomy and how they shape emergent function remain poorly understood, and there exists no comprehensive atlas of receptors. Here we collate positron emission tomography data from more than 1,200 healthy individuals to construct a whole-brain three-dimensional normative atlas of 19 receptors and transporters across nine different neurotransmitter systems. We found that receptor profiles align with structural connectivity and mediate function, including neurophysiological oscillatory dynamics and resting-state hemodynamic functional connectivity. Using the Neurosynth cognitive atlas, we uncovered a topographic gradient of overlapping receptor distributions that separates extrinsic and intrinsic psychological processes. Finally, we found both expected and novel associations between receptor distributions and cortical abnormality patterns across 13 disorders. We replicated all findings in an independently collected autoradiography dataset. This work demonstrates how chemoarchitecture shapes brain structure and function, providing a new direction for studying multi-scale brain organization

Blending generative models with deep learning for multidimensional phenotypic prediction from brain connectivity data

Network science as a discipline has provided us with foundational machinery to study complex relational entities such as social networks, genomics, econometrics etc. The human brain is a complex network that has recently garnered immense interest within the data science community. Connectomics or the study of the underlying connectivity patterns in the brain has become an important field of study for the characterization of various neurological disorders such as Autism, Schizophrenia etc. Such connectomic studies have provided several fundamental insights into its intrinsic organisation and implications on our behavior and health. This thesis proposes a collection of mathematical models that are capable of fusing information from functional and structural connectivity with phenotypic information. Here, functional connectivity is measured by resting state functional MRI (rs-fMRI), while anatomical connectivity is captured using Diffusion Tensor Imaging (DTI). The phenotypic information of interest could refer to continuous measures of behavior or cognition, or may capture levels of impairment in the case of neuropsychiatric disorders. We first develop a joint network optimization framework to predict clinical severity from rs-fMRI connectivity matrices. This model couples two key terms into a unified optimization framework: a generative matrix factorization and a discriminative linear regression model. We demonstrate that the proposed joint inference strategy is successful in generalizing to prediction of impairments in Autism Spectrum Disorder (ASD) when compared with several machine learning, graph theoretic and statistical baselines. At the same time, the model is capable of extracting functional brain biomarkers that are informative of individual measures of clinical severity. We then present two modeling extensions to non-parametric and neural network regression models that are coupled with the same generative framework. Building on these general principles, we extend our framework to incorporate multimodal information from Diffusion Tensor Imaging (DTI) and dynamic functional connectivity. At a high level, our generative matrix factorization now estimates a time-varying functional decomposition. At the same time, it is guided by anatomical connectivity priors in a graph-based regularization setup. This connectivity model is coupled with a deep network that predicts multidimensional clinical characterizations and models the temporal dynamics of the functional scan. This framework allows us to simultaneously explain multiple impairments, isolate stable multi-modal connectivity signatures, and study the evolution of various brain states at rest. Lastly, we shift our focus to end-to-end geometric frameworks. These are designed to characterize the complementarity between functional and structural connectivity data spaces, while using clinical information as a secondary guide. As an alternative to the previous generative framework for functional connectivity, our representation learning scheme of choice is a matrix autoencoder that is crafted to reflect the underlying data geometry. This is coupled with a manifold alignment model that maps from function to structure and a deep network that maps to phenotypic information. We demonstrate that the model reliably recovers structural connectivity patterns across individuals, while robustly extracting predictive yet interpretable brain biomarkers. Finally, we also present a preliminary analytical and experimental exposition on the theoretical aspects of the matrix autoencoder representation

Geometric Data Analysis: Advancements of the Statistical Methodology and Applications

Data analysis has become fundamental to our society and comes in multiple facets and approaches. Nevertheless, in research and applications, the focus was primarily on data from Euclidean vector spaces. Consequently, the majority of methods that are applied today are not suited for more general data types. Driven by needs from fields like image processing, (medical) shape analysis, and network analysis, more and more attention has recently been given to data from non-Euclidean spaces–particularly (curved) manifolds. It has led to the field of geometric data analysis whose methods explicitly take the structure (for example, the topology and geometry) of the underlying space into account. This thesis contributes to the methodology of geometric data analysis by generalizing several fundamental notions from multivariate statistics to manifolds. We thereby focus on two different viewpoints. First, we use Riemannian structures to derive a novel regression scheme for general manifolds that relies on splines of generalized Bézier curves. It can accurately model non-geodesic relationships, for example, time-dependent trends with saturation effects or cyclic trends. Since Bézier curves can be evaluated with the constructive de Casteljau algorithm, working with data from manifolds of high dimensions (for example, a hundred thousand or more) is feasible. Relying on the regression, we further develop a hierarchical statistical model for an adequate analysis of longitudinal data in manifolds, and a method to control for confounding variables. We secondly focus on data that is not only manifold- but even Lie group-valued, which is frequently the case in applications. We can only achieve this by endowing the group with an affine connection structure that is generally not Riemannian. Utilizing it, we derive generalizations of several well-known dissimilarity measures between data distributions that can be used for various tasks, including hypothesis testing. Invariance under data translations is proven, and a connection to continuous distributions is given for one measure. A further central contribution of this thesis is that it shows use cases for all notions in real-world applications, particularly in problems from shape analysis in medical imaging and archaeology. We can replicate or further quantify several known findings for shape changes of the femur and the right hippocampus under osteoarthritis and Alzheimer's, respectively. Furthermore, in an archaeological application, we obtain new insights into the construction principles of ancient sundials. Last but not least, we use the geometric structure underlying human brain connectomes to predict cognitive scores. Utilizing a sample selection procedure, we obtain state-of-the-art results