Date of Award

Summer 2014

Document Type


Degree Name

Doctor of Philosophy (PhD)


Mathematics, Statistics and Computer Science


Computational Sciences

First Advisor

Rowe, Daniel B.

Second Advisor

Krenz, Gary S.

Third Advisor

Merrill, Stephen J.


Functional magnetic resonance imaging (fMRI) and functional connectivity MRI (fcMRI) use the physical principles of nuclear MR to provide high resolution representations of brain activity and connectivity. As the fMRI and fcMRI signals are detected from the excited hydrogen atoms in a magnetic field, the acquired data is determined by the underlying physical processes, such as the MR relaxivities. In fMRI and fcMRI, the Fourier encoded frequency space measurements are reconstructed into brain images, then spatiotemporal processing operations are applied before computing the brain activation and connectivity statistics. This dissertation seeks to utilize the magnetic resonance (MR) relaxivities at different stages of the fMRI pipeline, and aims to observe the statistical implications of the spatiotemporal processing operators on the fMRI and fcMRI data. We first develop a new statistical complex-valued nonlinear fMRI activation model that incorporates the MR relaxivities of gray matter into the brain activation statistics by utilizing the physical MR magnetization equation and the first scans of the fMRI data. We provide both theoretical and experimental comparison between the proposed model with the conventional linear magnitude-only and complex-valued fMRI activation models. Our statistical analysis results show that the new model provides better accuracy in computing brain activation statistics while theoretically eliminating false positives in non-gray matter areas. We then develop a linear Fourier reconstruction operator that incorporates the MR relaxivities into the image reconstruction process to account for their effects. The utilization of a linear system makes it achievable to theoretically compute the statistical implications of the use of the proposed operator. By focusing on longitudinal relaxation time, T1, to include into the image reconstruction, we show that the application of the proposed Fourier reconstruction operator provides better image contrast in the reconstructed images by recovering the information of the tissue characteristics that exist prior to T1 equilibrium. We finally examine the effects of time series preprocessing on computed functional correlations through the use of linear operators and provide ways of accounting for such effects in computing functional activity and connectivity statistics. Using both theoretical and experimentally acquired functional connectivity data, we examine the correlations induced by commonly used spatial and temporal processing operations. Furthermore, we provide the expansion of the statistical fcMRI and fMRI models to incorporate the quantified processing induced correlations in computing brain activity and connectivity statistics.