Modeling hemodynamic response for analysis of functional MRI time‐series

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Abstract
The standard Gaussian function is proposed for the hemodynamic modulation function (HDMF) of functional magnetic resonance imaging (fMRI) time-series. Unlike previously proposed parametric models, the Gaussian model accounts independently for the delay and dispersion of the hemodynamic responses and provides a more flexible and mathematically convenient model. A suboptimal noniterative scheme to estimate the hemodynamic parameters is presented. The ability of the Gaussian function to represent the HDMF of brain activation is compared with Poisson and Gamma models. The proposed model seems valid because the lag and dispersion values of hemodynamic responses rendered by the Gaussian model are in the ranges of their previously reported values in recent optical and fMR imaging studies. An extension of multiple regression analysis to incorporate the HDMF is presented. The detected activity patterns exhibit improvements with hemodynamic correction. The proposed model and efficient parameter estimation scheme facilitated the investigation of variability of hemodynamic parameters of human brain activation. The hemodynamic parameters estimated over different brain regions and across different stimuli showed significant differences. Measurement of hemodynamic parameters over the brain during sensory or cognitive stimulation may reveal vital information on physiological events accompanying neuronal activation and functional variability of the human brain, and should lead to the investigation of more accurate and complex models.