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

Anatomical Image Series Analysis in the Computational Anatomy Random Orbit Model

Serially acquired medical imagery plays an important role in the computational study of human anatomy. In this work, we describe the development of novel algorithms set in the large deformation diffeomorphic metric mapping framework for analyzing serially acquired imagery of two general types: spatial image series and temporal image series. In the former case, a critical step in the analysis of neural connectivity from serially-sectioned brain histology data is the reconstruction of spatially distorted image volumes and registration into a common coordinate space. In the latter case, computational methods are required for building low dimensional representations of the infinite dimensional shape space standard to computational anatomy. Here, we review the vast body of work related to volume reconstruction and atlas-mapping of serially-sectioned data as well as diffeomorphic methods for longitudinal data and we position our work relative to these in the context of the computational anatomy random orbit model. We show how these two problems are embedded as extensions to the classic random orbit model and use it to both enforce diffeomorphic conditions and analyze the distance metric associated to diffeomorphisms. We apply our new algorithms to histology and MRI datasets to study the structure, connectivity, and pathological degeneration of the brain

The Human Connectome Project's neuroimaging approach

Noninvasive human neuroimaging has yielded many discoveries about the brain. Numerous methodological advances have also occurred, though inertia has slowed their adoption. This paper presents an integrated approach to data acquisition, analysis and sharing that builds upon recent advances, particularly from the Human Connectome Project (HCP). The 'HCP-style' paradigm has seven core tenets: (i) collect multimodal imaging data from many subjects; (ii) acquire data at high spatial and temporal resolution; (iii) preprocess data to minimize distortions, blurring and temporal artifacts; (iv) represent data using the natural geometry of cortical and subcortical structures; (v) accurately align corresponding brain areas across subjects and studies; (vi) analyze data using neurobiologically accurate brain parcellations; and (vii) share published data via user-friendly databases. We illustrate the HCP-style paradigm using existing HCP data sets and provide guidance for future research. Widespread adoption of this paradigm should accelerate progress in understanding the brain in health and disease

Correction, Validation, and Characterization of Motion in Resting-State Functional Magnetic Resonance Images of Pediatric Patients

There are many scenarios, for both clinical and research applications, in which we would like to examine a patient's neurodevelopmental status. Generally, neurodevelopmental evaluations can be performed through psychological testing or in-person assessment with a psychologist. However, these approaches are not applicable in all cases, particularly for many pediatric populations. Researchers are beginning to turn to medical imaging approaches for objectively quantifying a patient's neurodevelopmental status. Resting-state functional magnetic resonance images (rs-fMRIs) can be used to study neuronal networks that are active even when a person is not performing a specific task or reacting to particular stimuli. These image sequences are highly sensitive to motion. Techniques have been developed to prevent patients from moving as well as monitor motion during the scan and correct for the patient's movement after the scan. We focus on the first step of retrospective motion correction: volume registration. The purpose of volume registration is to align the contents of all of the image volumes in the image sequence to the contents of a single volume. Traditionally, all image volumes are directly registered to the chosen stationary image volume. However, this approach does not account for significant differences in patient position between the stationary volume and the other volumes in the sequence. We developed a registration framework based on the concept of a directed acyclic graph. We treat the volumes in the sequence as nodes in a graph where pairs of subsequent volumes are connected via directed edges. This perspective allows us to model the relationships between subsequent volumes and account for them during registration. We applied both registration frameworks to a set of simulated images as well as neurological rs-fMRIs from three clinical populations. The clinical populations were preadolescent, neonatal, and fetal subjects who either were healthy or had congenital heart disease (CHD). The original and registered sequences were compared with respect to their local and global motion. The local motion was measured between every pair of image volumes $i$ and $i+1$ in each sequence using the framewise displacement (FD) and the derivative of the root mean square variance of the signal (DVARS). The global motion across each sequence was measured by calculating the similarity between every pair of image volumes in each sequence. The local motion parameters were compared to a pair of gold standard usability thresholds to determine how each registration framework impacted the usability of every image volume. Both the local and global motion parameters were used to determine how many sequences had statistically significant differences in their motion distributions before and after registration. Additionally, the local and global metrics of the original sequences were clustered to determine if a computer could identify groups of subjects based on their motion parameters. The registration frameworks had different effects on each age group of subjects. We found that the neonatal subjects contained the least amount of motion, while the fetal subjects contained the most motion. The DAG-based registration was most effective at reducing motion in the fetal images. Our clustering analysis showed that the different age groups have different global motion parameters, though lifespan-level patterns related to CHD status could not be detected

Modelling human choices: MADeM and decision‑making

Research supported by FAPESP 2015/50122-0 and DFG-GRTK 1740/2. RP and AR are also part of the Research, Innovation and Dissemination Center for Neuromathematics FAPESP grant (2013/07699-0). RP is supported by a FAPESP scholarship (2013/25667-8). ACR is partially supported by a CNPq fellowship (grant 306251/2014-0)