Group Analysis of Self-organizing Maps based on Functional MRI using Restricted Frechet Means

Studies of functional MRI data are increasingly concerned with the estimation of differences in spatio-temporal networks across groups of subjects or experimental conditions. Unsupervised clustering and independent component analysis (ICA) have been used to identify such spatio-temporal networks. While these approaches have been useful for estimating these networks at the subject-level, comparisons over groups or experimental conditions require further methodological development. In this paper, we tackle this problem by showing how self-organizing maps (SOMs) can be compared within a Frechean inferential framework. Here, we summarize the mean SOM in each group as a Frechet mean with respect to a metric on the space of SOMs. We consider the use of different metrics, and introduce two extensions of the classical sum of minimum distance (SMD) between two SOMs, which take into account the spatio-temporal pattern of the fMRI data. The validity of these methods is illustrated on synthetic data. Through these simulations, we show that the three metrics of interest behave as expected, in the sense that the ones capturing temporal, spatial and spatio-temporal aspects of the SOMs are more likely to reach significance under simulated scenarios characterized by temporal, spatial and spatio-temporal differences, respectively. In addition, a re-analysis of a classical experiment on visually-triggered emotions demonstrates the usefulness of this methodology. In this study, the multivariate functional patterns typical of the subjects exposed to pleasant and unpleasant stimuli are found to be more similar than the ones of the subjects exposed to emotionally neutral stimuli. Taken together, these results indicate that our proposed methods can cast new light on existing data by adopting a global analytical perspective on functional MRI paradigms.Comment: 23 pages, 5 figures, 4 tables. Submitted to Neuroimag

On Frequency Variation of Dynamic Resting-state Functional Brain Network Activation and Connectivity with Applications to both Healthy and Clinical Populations

One of the earliest and fundamental observation in scientific study of the brain was discovering the relation between activities in different local regions of brain and some core functions of the brain. This was later followed by observing that not only local activities of regions but also synchronous activities between distributed brain regions play a key role in high-level brain functions. Synchronous activity related to the functions of the brain is commonly referred to as functional connectivity (FC) and is studied in the form of connectivity states of the brain which measure degree of interactions between distributed parts of the brain. Functional connectivity has been studied with different imaging modalities such as electroencephalogram (EEG), magnetoencephalography (MEG) and functional magnetic resonance imaging (fMRI). The latter has the advantage of having relatively higher spatial resolution of the underlying functional regions and is our choice for the source of the data in this work. Functional connectivity analysis of the human brain in fMRI researches focuses on identifying meaningful brain networks that have coherent activity either during a task or in the resting state. These networks are generally identified either as collections of voxels whose time series correlate strongly with a pre-selected region or voxel, or using data-driven methodologies such as independent component analysis (ICA) that compute sets of maximally spatially independent voxel weightings (component spatial maps (SMs)), each associated with a single time course (TC). Recent studies of functional connectivity have shed light on new aspects of functional connectivity. For example, connectivity during a resting state (RS) of the brain had long been know to constitute a single state of connectivity and just recently it is argued that RS-connectivity, varies in time and has a dynamic nature. In this work, we investigate new aspects of RS-connectivity jointly with its dynamic aspect. As part of the new observations, we discuss that RS-connectivity is in fact frequency dependent in addition to be temporally dynamic. This discovery allows to capture RS-coonectivity at a given time as the superposition of multiple connectivity states along frequency dimension. Later, we also show that interaction between fMRI networks is not only frequency dependent and temporally dynamic but also may occur cross different frequency spectra which is the first evidennce of cross-frequency depenence between fMRI functional networks. We also discuss that all of these observations would enable us to design novel measures to explain RS-connectivity variation among different group of subjects such as healthy and diseased or males and females which would have clinical diagnosis applications and could possibly serve as new bio-markers to study underlying functions of the brain

Fusing Novel Statistical Methods and Network Science to Understand Brain Function

Analyzing brain networks has long been a prominent research topic in neuroimaging. However, statistical methods to detect differences between these networks and relate them to phenotypic traits are still sorely needed. Our previous work developed a novel permutation testing framework to detect differences between two groups. In chapter two, we advance that work to allow both assessing differences by continuous phenotypes and controlling for confounding variables. To achieve this, we propose an innovative regression framework to relate distances (or similarities) between brain network features to functions of absolute differences in continuous covariates and indicators of difference for categorical variables. In chapter three, motivated by a retest subset from the Human Connectome Project (HCP), we extend the framwork to allow for multiple brain networks for each individual. In chapter four, the framework is adapted to allow for multilevel modeling (motivated by the HCP’s inclusion of siblings and twins). We explore several similarity metrics for comparing distances (or similarities) between nodal degree vectors and connection matrices, and adapt several standard methods for estimation and inference within our framework. Via simulation studies, we assess all approaches for estimation and inference while comparing them with existing Multivariate Distance Matrix Regression (MDMR) methods. We then illustrate the utility of our framework by analyzing the relationship between fluid intelligence and brain network distances in Human Connectome Project data.Doctor of Philosoph

Informed Segmentation Approaches for Studying Time-Varying Functional Connectivity in Resting State fMRI

The brain is a complex dynamical system that is never truly “at rest”. Even in the absence of explicit task demands, the brain still manifests a stream of conscious thought, varying levels of vigilance and arousal, as well as a number of postulated ongoing “under the hood” functions such as memory consolidation. Over the past decade, the field of time-varying functional connectivity (TVFC) has emerged as a means of detecting dynamic reconfigurations of the network structure in the resting brain, as well as uncovering the relevance of these changing connectivity patterns with respect to cognition, behavior, and psychopathology. Since the nature and timescales of the underlying resting dynamics are unknown, methodologies that can detect changing temporal patterns in connectivity without imposing arbitrary timescales are required. Moreover, as the study of TVFC is still in its infancy, rigorous evaluation of new and existing methodologies is critical to better understand their behavior when applied in resting data, which lacks ground truth temporal landmarks against which accuracy can be assessed. In this dissertation, I contribute to the methodological component of the TVFC discourse. I propose two distinct, yet related, approaches for identifying TVFC using an informed segmentation framework. This data-driven framework bridges instantaneous and windowed approaches for studying TVFC, in an attempt to mitigate the limitations of each while simultaneously leveraging the advantages of both. I also present a comprehensive, head-to-head comparative analysis of several of the most promising TVFC methodologies proposed to date, which does not exist in the current body of literature.PHDBioinformaticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/170046/1/marlenad_1.pd

The Association of Aerobic Fitness with Resting State Functional Connectivity and Verbal Learning and Memory in Healthy Young Adults

The beneficial effects of exercise and cardiopulmonary fitness on general health, quality of life, and reduction of mortality are well known in older adults. There is evidence to support the positive effects of exercise and aerobic fitness on psychiatric and neurocognitive function in children, adults, and older adults. Indeed, many studies have explored the positive effects of aerobic fitness on slowing cognitive decline associated with normal and pathological aging. However, comparatively fewer empirical studies in the literature exist to support and understand the effects of aerobic fitness on the developing brain, particularly during adolescence and young adulthood, especially as it relates to resting state functional connectivity during this dynamic stage of development. The current study investigated the association of aerobic fitness on functional connectivity with the left hippocampus in healthy young adults and the degree to which differential resting state functional connectivity is associated with verbal learning and memory. The sample was comprised of healthy young adults with varying degrees of aerobic fitness as part of a larger study of the effects of cardiorespiratory health on neurocognitive performance, brain structure and function. Results of the study indicated that better aerobic fitness is associated with increased functional connectivity to the left parahippocampal gyrus, a region known for its role in working memory and encoding. Results from this study contribute to a better understanding of the factors that may underlie the beneficial effects of exercise on brain health and neurocognition and further offer insights into the value of early preventive health behaviors to reduce the risk of later of cognitive decline and impairment

Probing the topological properties of complex networks modeling short written texts

In recent years, graph theory has been widely employed to probe several language properties. More specifically, the so-called word adjacency model has been proven useful for tackling several practical problems, especially those relying on textual stylistic analysis. The most common approach to treat texts as networks has simply considered either large pieces of texts or entire books. This approach has certainly worked well -- many informative discoveries have been made this way -- but it raises an uncomfortable question: could there be important topological patterns in small pieces of texts? To address this problem, the topological properties of subtexts sampled from entire books was probed. Statistical analyzes performed on a dataset comprising 50 novels revealed that most of the traditional topological measurements are stable for short subtexts. When the performance of the authorship recognition task was analyzed, it was found that a proper sampling yields a discriminability similar to the one found with full texts. Surprisingly, the support vector machine classification based on the characterization of short texts outperformed the one performed with entire books. These findings suggest that a local topological analysis of large documents might improve its global characterization. Most importantly, it was verified, as a proof of principle, that short texts can be analyzed with the methods and concepts of complex networks. As a consequence, the techniques described here can be extended in a straightforward fashion to analyze texts as time-varying complex networks

Study of circadian mental fatigue by fMRI

Master'sMASTER OF SCIENC

Special Topics in Latent Variable Models with Spatially and Temporally Correlated Latent Variables

The term latent variable model (LVM) refers to any statistical procedure that utilizes information contained in a set of observed variables to construct a set of underlying latent variables that drive the observed values and associations. Independent component analysis (ICA) is a LVM that separates recorded mixtures of signals into independent source signals, called independent components (ICs). ICA is popular tool for separating brain signals of interest from artifacts and noise in electroencephalogram (EEG) data. Due to challenges in the estimation of uncertainties in ICA, standard errors are not generally estimated alongside ICA estimates and thus ICs representing brain signals of interest cannot be distinguished through a statistical hypothesis testing framework. In Chapter 2 of this dissertation, we propose a bootstrapping algorithm for ICA that produces bootstrap samples that retain critical correlation structures in the data. These are used to compute uncertainties for ICA parameter estimates and to construct a hypothesis test to identify ICs representing brain activity, which we demonstrate in the context of EEG functional connectivity. In Chapter 3, we extend this bootstrapping approach to accommodate pre-ICA dimension reduction procedures, and we use the resulting method to compare popular strategies for pre-ICA dimension reduction in EEG research. In the final chapter, we turn our attention to another LVM, factor analysis, which utilizes the covariance structure of a set of correlated observed variables to model a smaller number of unmeasured underlying variables. A spatial factor analysis (SFA) model can be used to quantify the social vulnerability of communities based on a set of observed social variables. Current SFA methodology is ill-equipped to handle spatial misalignment in the observed variables. We propose a joint spatial factor analysis model that identifies a common set of latent variables underlying spatially misaligned observed variables and produces results at the level of the smallest spatial units, thereby minimizing loss of information. We apply this model to spatially misaligned data to construct an index of community social vulnerability for Louisiana, which we integrate with Louisiana flood data to identify communities at high risk during natural disasters, based on both social and geographic features.Doctor of Philosoph

Spatio-temporal Deep Learning Architectures for Data-Driven Learning of Brain’s Network Connectivity

Brain disorders are often linked to disruptions in the dynamics of the brain\u27s intrinsic functional networks. It is crucial to identify these networks and determine disruptions in their interactions to classify, understand, and possibly cure brain disorders. Brain\u27s network interactions are commonly assessed via functional (network)\ connectivity, captured as an undirected matrix of Pearson correlation coefficients. Functional connectivity can represent static and dynamic relations. However, often these are modeled using a fixed choice for the data window. Alternatively, deep learning models may flexibly learn various representations from the same data based on the model architecture and the training task. The representations produced by deep learning models are often difficult to interpret and require additional posthoc methods, e.g., saliency maps. Also, deep learning models typically require many input samples to learn features and perform the downstream task well. This dissertation introduces deep learning architectures that work on functional MRI data to estimate disorder-specific brain network connectivity and provide high classification accuracy in discriminating controls and patients. To handle the relatively low number of labeled subjects in the field of neuroimaging, this research proposes deep learning architectures that leverage self-supervised pre-training to increase downstream classification. To increase the interpretability and avoid using a posthoc method, deep learning architectures are proposed that expose a directed graph layer representing the model\u27s learning about relevant brain connectivity. The proposed models estimate task-specific directed connectivity matrices for each subject using the same data but training different models on their own discriminative tasks. The proposed architectures are tested with multiple neuroimaging datasets to discriminate controls and patients with schizophrenia, autism, and dementia, as well as age and gender prediction. The proposed approach reveals that differences in connectivity among sensorimotor networks relative to default-mode networks are an essential indicator of dementia and gender. Dysconnectivity between networks, especially sensorimotor and visual, is linked with schizophrenic patients. However, schizophrenic patients show increased intra-network default-mode connectivity compared to healthy controls. Sensorimotor connectivity is vital for both dementia and schizophrenia prediction, but the differences are in inter and intra-network connectivity