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Computational and Mathematical Methods in Medicine
Volume 2013 (2013), Article ID 645043, 16 pages
Research Article

Development of the Complex General Linear Model in the Fourier Domain: Application to fMRI Multiple Input-Output Evoked Responses for Single Subjects

1Section of Brain Electrophysiology and Imaging, LCTS, NIAAA, National Institutes of Health, 10 Center Drive, MSC 1540, Bethesda, MD, USA
2Synergy Research Inc., 12051 Greystone Drive, Monrovia, MD, USA
3Laboratory of Neuroimaging and Genetics, Martinos Center for Biomedical Imaging, Massachusetts General Hospital, Charlestown, MA, USA

Received 6 February 2013; Revised 3 May 2013; Accepted 13 May 2013

Academic Editor: Lei Ding

Copyright © 2013 Daniel E. Rio et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A linear time-invariant model based on statistical time series analysis in the Fourier domain for single subjects is further developed and applied to functional MRI (fMRI) blood-oxygen level-dependent (BOLD) multivariate data. This methodology was originally developed to analyze multiple stimulus input evoked response BOLD data. However, to analyze clinical data generated using a repeated measures experimental design, the model has been extended to handle multivariate time series data and demonstrated on control and alcoholic subjects taken from data previously analyzed in the temporal domain. Analysis of BOLD data is typically carried out in the time domain where the data has a high temporal correlation. These analyses generally employ parametric models of the hemodynamic response function (HRF) where prewhitening of the data is attempted using autoregressive (AR) models for the noise. However, this data can be analyzed in the Fourier domain. Here, assumptions made on the noise structure are less restrictive, and hypothesis tests can be constructed based on voxel-specific nonparametric estimates of the hemodynamic transfer function (HRF in the Fourier domain). This is especially important for experimental designs involving multiple states (either stimulus or drug induced) that may alter the form of the response function.