An application of the complex general linear model to analysis of fMRI single subjects multiple stimuli input data

ABSTRACT The general linear model (GLM) has been extensively applied to fMRI data in the time domain. However, traditionally time series data can be analyzed in the Fourier domain wher e the assumptions made as to the noise in the signal can be less restrictive and statistical tests are mathematically more rigorous. A complex form of the GLM in the Fourier domain has been applied to the analysis of fMRI (BOLD) data. This methodology has a number of advantages over temporal methods: 1. Noise in the fMRI data is modeled more generally and closer to that actually seen in the data. 2. Any input function is allowed regardless of the timing. 3. Non-parametric estimation of the transfer functions at each voxel are possible. 4. Rigorous statistical inference of single subjects is possible. This is demonstrated in the analysis of an experimental design with random exponentially distributed stimulus inputs (a two way ANOVA design with input stimuli images of alcohol, non-alcohol beverage and positive or negative images) sampled at 400 milliseconds. This methodology applied to a pair of subjects showed precise and interesting results (e.g. alcoholic beverage images attenuate the response of negative images in an alcoholic as compared to a control subject). Keywords: fMRI (BOLD), time series analysis, Fourier domain, statistical analysis, complex general linear model, single subject analysis, alcoholic research