Bayesian analysis of functional magnetic resonance imaging data with spatially varying auto‐regressive orders

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/148250/1/rssc12320.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/148250/2/rssc12320_am.pd

Statistical Techniques For Addressing The Clinico-Radiological Paradox In Multiple Sclerosis

Medical imaging technology has allowed for unparalleled insight into the structure and function of the human brain, giving clinicians powerful new tools for disease diagnosis and monitoring. Yet the complex and high-dimensional nature of imaging data makes computational analysis challenging. In multiple sclerosis (MS), this complexity is typically simplified by identifying regions of visible tissue damage and measuring spatial extent. However, many common radiological measures have been shown to be only weakly associated with clinical outcomes (a discovery that has been referred to as “the clinico-radiological paradox”). We attempt to bridge this gap by developing statistical methods capable of extracting clinically relevant information from MRI scans in MS. Here, we discuss three such techniques: a texture modeling approach to improve research on lesion dynamics; a biomarker detection algorithm to support diagnostic decision-making; and a flexible multi-modal group differences test to facilitate exploration of subtle disease processes. The performance of these methods is illustrated using simulated and real data, and the opportunities and obstacles for their clinical use are discussed

PREDICTION OF RESPIRATORY MOTION

Radiation therapy is a cancer treatment method that employs high-energy radiation beams to destroy cancer cells by damaging the ability of these cells to reproduce. Thoracic and abdominal tumors may change their positions during respiration by as much as three centimeters during radiation treatment. The prediction of respiratory motion has become an important research area because respiratory motion severely affects precise radiation dose delivery. This study describes recent radiotherapy technologies including tools for measuring target position during radiotherapy and tracking-based delivery systems. In the first part of our study we review three prediction approaches of respiratory motion, i.e., model-based methods, model-free heuristic learning algorithms, and hybrid methods. In the second part of our work we propose respiratory motion estimation with hybrid implementation of extended Kalman filter. The proposed method uses the recurrent neural network as the role of the predictor and the extended Kalman filter as the role of the corrector. In the third part of our work we further extend our research work to present customized prediction of respiratory motion with clustering from multiple patient interactions. For the customized prediction we construct the clustering based on breathing patterns of multiple patients using the feature selection metrics that are composed of a variety of breathing features. In the fourth part of our work we retrospectively categorize breathing data into several classes and propose a new approach to detect irregular breathing patterns using neural networks. We have evaluated the proposed new algorithm by comparing the prediction overshoot and the tracking estimation value. The experimental results of 448 patients’ breathing patterns validated the proposed irregular breathing classifier

Bayesian Computation with Application to Spatial Models and Neuroimaging

Analysis of Neuroimaging data has experienced great strides over the last few decades. Two key aspects of Neuroimaging data are its high-dimensionality and complex spatio-temporal autocorrelation. Classical approaches are somewhat limited in dealing with these two issues, as a result, Bayesian approaches are being utilized more frequently due to their flexibility. Despite their flexibility, there are several challenges for Bayesian approaches with respect to the required computation. First, the need for an efficient posterior computation method is paramount. Second, even in conjugate models, statistical accuracy in Bayesian computation may be hard to achieve. Since accuracy is of primary concern when studying the human brain, a careful and innovative exploration of Bayesian models and computation is necessary. In this dissertation, we address some of these issues by looking at various Bayesian computational algorithms in terms of both accuracy and speed in the context of Neuroimaging data. The algorithms we study are the Hamiltonian Monte Carlo (HMC), Variational Bayes (VB), and integrated nested Laplace approximation (INLA) algorithms. HMC is a MCMC method that's particularly powerful for sampling in high-dimensional space with highly correlated parameters. It's robust and accurate, yet not as fast as some approximate Bayesian methods, for example, Variational Bayes (VB). However, since there is no theoretical guarantee that the resulting posterior derived from VB is accurate, its performance has to be analyzed on a case-by-case basis. INLA is another extremely fast method based on numerical integration with Laplace approximations but, like VB, there are no generally applicable theoretical guarantees of accuracy. In Chapter II we focus on a particular spatial point process model, namely the log Gaussian Cox Process (LGCP), and consider applications to ecological and neuroimaging data. Inference for the LGCP is challenging due to its non-conjugacy and doubly stochastic property. We develop HMC and VB algorithms for the LGCP model and make comparisons with INLA. In Chapter III, we turn our focus to the general linear model with autoregressive errors (GLM-AR) which is widely used in analyzing fMRI single subject data. We derive an HMC algorithm and compare it with the VB algorithm and the mass univariate approach using the Statistical Parametric Mapping (SPM) software program. In Chapter IV, we extend the original GLM-AR model to a new model where the order of the AR coefficients can varying spatially across the brain and call it GLM with spatially varying autoregressive orders (SVARO). Using simulations and real data we compare our SVARO model with GLM-AR model implemented under both our MCMC sampler and the SPM VB algorithm. Our results shed light on several important issues. While HMC almost always yields the most accurate results, the performance of VB is strongly model specific. INLA is a fast alternative to MCMC methods but we observe some limitations when examining its accuracy in certain settings. Furthermore, our new SVARO model performs better than the GLM-AR model in a number of ways. Not surprisingly, more accurate algorithms generally require more computational time. By systematically evaluating the pros and cons of each method, we believe our work to be practically useful for those researchers considering the use of these methods.PHDBiostatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/138616/1/tengming_1.pd