Statistical methods for detecting activated regions in functional MRI of the brain

Two statistical tests for detecting activated pixels in functional MRI (fMRI) data are presented. The first test (t-test) is the optimal solution to the problem of detecting a known activation signal in Gaussian white noise. The results of this test are shown to be equivalent to the cross-correlation method that is widely used for activation detection in fMRI. The second test (F test) is the optimal solution when the measured data are modeled to consist of an unknown activation signal that lies in a known lower dimensional subspace of the measurement space with added Gaussian white noise. A model for the signal subspace based on a truncated trigonometric Fourier series is proposed for periodic activation-baseline imaging paradigms. The advantage of the second method is that it does not assume any information about the shape or delay of the activation signal, except that it is periodic with the same period as the activation-baseline pattern. The two models are applied to experimental echo-planar fMRI data sets and the results are compared.