Independent Component Analysis Applied to fMRI Data: A Generative Model for Validating Results

Methods for testing and validating independent component analysis (ICA) results in fMRI are growing in importance as the popularity of this model for studying brain function increases. We introduce and apply a synthesis/analysis model for analyzing functional Magnetic Resonance Imaging (fMRI) data using ICA. Classes of signal types relevant to fMRI are described and a statistical approach for validation of simulation results is developed. Additionally, we propose an empirical version of our validation approach to test the performance of various ICA approaches in “hybrid” fMRI data, a mixture of real fMRI data and known (validatable) sources. The synthesis portion of the model assumes statistically independent spatial sources in the brain. We also assume that the fMRI scanner acquires overdetermined data such that there are more time points than hemodynamic brain sources. We propose several signal classes relevant to fMRI and discuss the properties of each. The analysis portion of the model includes several candidates for spatial smoothing, ICA algorithm, and data reduction. We use the Kullback-Leibler divergence between the estimated source distributions and the “true” distributions as a measure of the optimality of the final ICA decomposition. Using this model, we generate fMRI-like data and optimize the analysis stage as a function of ICA algorithm, data reduction scheme, and spatial smoothing. An example of how our synthesis/analysis model can be used in validating an fMRI experiment is demonstrated using simulations and “hybrid” fMRI data.