December, 2011
Many existing methods for estimating the hemodynamic response functions (HRF) break down when analyzing multi-subject fMRI data from multi-stimulus designs due to the large and inhomogeneous variances across subjects. Within the context of the General Linear Model, we propose two new nonparametric estimators of the HRF for fMRI data arising from such designs. We first introduce a kernel-smoothed nonparametric estimator, based on which we conduct hypothesis tests to identify task relevant neural activity. To cope with the inherent large data variance, we further impose a Tikhonov regularization to the kernel-smoothed HRF estimator, on top of which a bias-correction procedure is introduced by utilizing the multi-subject averaged HRF. A fast algorithm with linear computational time is also developed to select optimal regularization and smoothing parameters. We apply these methods to the fMRI data collected under a psychology design employing the monetary incentive task. The proposed tests successfully identify the neural activation related to affective responses to monetary incentives and penalties. The HRF estimates reveal that the magnitude of the penalty-related neural activity is significantly correlated with an individual state anxiety measure.
Keywords: general linear model, hemodynamic response function, kernel smoothing, regularization.
The manuscript is available in PDF formats.