Assessing Certainty of Activation or Inactivation in Test-Retest fMRI Studies

Functional Magnetic Resonance Imaging~(fMRI) is widely used to study activation in the human brain. In most cases, data are commonly used to construct activation maps corresponding to a given paradigm. Results can be very variable, hence quantifying certainty of identified activation and inactivation over studies is important. This paper provides a model-based approach to certainty estimation from data acquired over several replicates of the same experimental paradigm. Specifically, the $p$-values derived from the statistical analysis of the data are explicitly modeled as a mixture of their underlying distributions; thus, unlike methodology currently in use, there is no subjective thresholding required in the estimation process. The parameters governing the mixture model are easily obtained by the principle of maximum likelihood. Further, the estimates can also be used to optimally identify voxel-specific activation regions along with their corresponding certainty measures. The methodology is applied to a study involving a motor paradigm performed on a single subject several times over a period of two months. Simulation experiments used to calibrate performance of the method are promising. The methodology is also seen to be robust in determining areas of activation and their corresponding certainties.