Bayesian Local Smoothing Modeling and Inference for Pre-surgical FMRI Data.

Bayesian Local Smoothing Modeling and Inference for Pre-surgical FMRI Data by Zhuqing Liu Co-chairs: Dr. Timothy D. Johnson, Dr. Veronica J. Berrocal There is a growing interest in using fMRI measurements and analyses as tools for pre-surgical planning. One example is to map out essential functional brain regions of specific subjects via fMRI prior to surgery to facilitate tumor resection. For such applications, spatial precision and control over false negatives and false positives are vital, requiring careful design of an image smoothing method and a classification procedure. The standard smoothing method is to convolve the image with a Gaussian kernel, applying a fixed amount of smoothing to the entire image. This approach, however, cannot adapt to the spatially varying signal, causing some regions to be undersmoothed while others oversmoothed with a subsequent loss in spatial precision. In addition, while strict false positive control is usually desired in a neuroscientific fMRI study, controlling false negatives is of greater interest in pre-surgical planning. To this end, this dissertation seeks computationally efficient approaches to overcome the limitation of existing methods and address new challenges in pre-surgical fMRI analyses. In the first study, we develop a Bayesian solution for the pre-surgical analysis of a single fMRI brain image. Specifically, we propose a novel spatially adaptive conxi ditionally autoregressive model, i.e., the CWAS model, that adaptively and locally smooths the fMRI data. Our model provides more flexibility in characterizing the spatial variation of the fMRI data and introduces a parameter which offers an intuitive interpretation in controlling the degree of smoothing. We introduce a Bayesian theoretical decision approach that allows control of both false positives and false negatives to identify activated and deactivated brain regions. We benchmark the proposed solution to two existing spatially adaptive smoothing models, through simulation studies and two patients’ pre-surgical fMRI datasets. In the second study, we extend the idea of spatially adaptive smoothing to multiple fMRI brain images in order to leverage spatial correlations not only within images but also across multiple images. In particular, we propose three spatially adaptive multivariate conditional autoregressive models that can be considered as extensions of the multivariate conditional autoregressive (MCAR) model (Gelfand and Vounatsou, 2003), the CWAS model, and the model of Reich and Hodges (2008), respectively, and one mixed-effects model assuming that all observed fMRI images originate from one common image. We compare the performance of the proposed models with those from the MCAR and CWAS models using simulation studies and two sets of fMRI brain images, acquired either from the same patient, same paradigm or same patient, different paradigms. The last study is motivated by fMRI brain images acquired at two different spatial resolutions from the same patient. We develop a Bayesian hierarchical model with spatially varying coefficients to retain the spatial precision from the high resolution image while utilizing information from the low resolution image to improve estimation and inference. Comparisons between the proposed model and the CWAS model, which operates at a single spatial resolution, are performed on simulated data and a patient’s multi-resolution pre-surgical fMRI data. xii CHAPTER