In this thesis, we conduct functional Magnetic Resonance Imaging (fMRI) data analysis with the aim of grouping the brain voxels depending on their responsiveness to a neural task. We mathematically treat the fMRI signals as the convolution of the neural stimulus with the hemodynamic response function (HRF). We first estimate a time series including HRFs for each of the observed fMRI signals from a given set and we cluster them in order to identify the groups of brain voxels. The HRF estimation problem is studied within the Bayesian framework through a blind deconvolution algorithm using MAP approach under completely unsupervised and model-free settings, i.e, stimulus is assumed to be unknown and also no particular shape is assumed for the HRF. Only using a given fMRI signal together with a weak Gaussian prior distribution imposed on HRF favoring &lsquo / smoothness&rsquo / , our method successfully estimates all the components of our framework: the HRF, the stimulus and the noise process. Then, we propose to use a modified version of Hausdorff distance to detect similarities within the space of HRFs, spectrally transform the data using Laplacian Eigenmaps and finally cluster them through EM clustering. According to our simulations, our method proves to be robust to lag, sampling jitter, quadratic drift and AWGN (Additive White Gaussian Noise). In particular, we obtained 100% sensitivity and specificity in terms of detecting active and passive voxels in our real data experiments. To conclude with, we propose a new framework for a mathematical treatment for voxel-based fMRI data analysis and our findings show that even when the HRF is unpredictable due to variability in cognitive processes, one can still obtain very high quality activation detection through the method proposed in this thesis.

Functional Magnetic Resonance Imaging (fMRI) is one of the most popular neuroimaging methods for investigating the activity of the human brain during cognitive tasks. The main objective of the thesis is to identify this underlying brain activation over time, using fMRI signal by detecting active and passive voxels. We performed two sub goals sequentially in order to realize the main objective. First, by using simple, data-driven Fourier Wavelet Regularized Deconvolution (ForWaRD) method, we extracted hemodynamic response function (HRF) which is the information that shows either a voxel is active or passive from fMRI signal. Second, the extracted HRFs of voxels are classified as active and passive using Laplacian Eigenmaps. By this, the active and passive voxels in the brain are identified, and so are the activation areas. The ForWaRD method is directly applied to fMRI signals for the first time. The extraction method is tested on simulated and real block design fMRI signals, contaminated with noise from a time series of real MR images. The output of ForWaRD contains the HRF for each voxel. After HRF extraction, using Laplacian Eigenmaps algorithm, active and passive voxels are classified according to their HRFs. Also with this study, Laplacian Eigenmaps are used for HRF clustering for the first time. With the parameters used in this thesis, the extraction and clustering methods presented here are found to be robust to changes in signal properties. Performance analyses of the underlying methods are explained in terms of sensitivity and specificity metrics. These measurements prove the strength of our presented methods against different kinds of noises and changing signal properties.

Thesis (M.S.)--James Madison University, 2009. / Includes bibliographical references.

Diss. (sammanfattning) Stockholm : Karolinska institutet, 2007. / Härtill 4 uppsatser.

Diss. (sammanfattning) Stockholm : Karolinska institutet, 2005. / Härtill 8 uppsatser.

Diss. (sammanfattning) Stockholm : Karol. inst., 2004. / Härtill 5 uppsatser.

Diss. (sammanfattning) Stockholm : Karol. inst., 2004. / Härtill 5 uppsatser.

Diss. (sammanfattning) Linköping : Linköpings universitet, 2005. / Härtill 4 uppsatser.

Diss. (sammanfattning) Stockholm : Karol. inst., 2006. / Härtill 5 uppsatser.

Diss. (sammanfattning) Stockholm : Karol. inst., 2006. / Härtill 4 uppsatser.