True Spatio-Temporal Detection and Estimation for Functional Magnetic Resonance Imaging.

Abstract

The development of fast imaging in magnetic resonance imaging (MRI) makes it possible for researchers in various fields to investigate functional activities of the human brain with a unique combination of high spatial and temporal resolution. A significant task in functional MRI data analysis is to develop a detection statistic for activation, showing subject’s localized brain responses to pre-specified stimuli. With rare exceptions in FMRI, these detection statistics have been derived from a measurement model under two main assumptions: spatial independence and space-time separability of background noise.

One of the main goals of this thesis is to remove these assumptions which have been widely used in existing approaches. This thesis makes three main contributions:(1) a development of a detection statistic based on a spatiotemporally correlated noise model without space-time separability, (2) signal and noise modeling to implement the proposed detection statistic, (3) a development of a detection statistic that is robust to signal-to-noise ratio (SNR), Rician activation detection.

For the first time in FMRI, we develop a properly formulated spatiotemporal detection statistic for activation, based on a spatiotemporally correlated noise model without space-time separability. The implementation of the developed detection statistic requires joint signal and noise modeling in three or four dimensions, which is non-trivial statistical model estimation. We complete the implementation with the parametric cepstrum, allowing dramatic reduction of computations in model fitting. These two are totally new contributions to FMRI data analysis. As byproducts, a novel test procedure for space-time separability is proposed and its asymptotic power is analyzed. The developed detection statistic and conventional statistics involving spatial smoothing by Gaussian kernel are compared through a model comparison technique and asymptotic relative efficiency.

Most methods in FMRI data analysis are based on magnitude voxel time courses and their approximation by a Gaussian distribution. Since the magnitude images, in fact, obey Rician distribution and the Gaussian approximation is valid under a high SNR assumption, Gaussian modeling may perform poorly when SNR is low. In this thesis, we develop a detection statistic from a Rician distributed model, allowing a robust activation detection regardless of SNR.