title: Efficiency, power, and entropy in event-related FMRI with multiple trial types. Part I: theory.
abstract: Experimental designs for functional magnetic resonance imaging (fMRI) experiments can be characterized by their estimation efficiency, which is a measure of the variance in the estimate of the hemodynamic response function (HRF), and their detection power, which is a measure of the variance in the estimate of the amplitude of functional activity. Previous studies have shown that there exists a fundamental trade-off between efficiency and power for experiments with a single trial type of interest. This paper extends the prior work by presenting a theoretical model for the relation between detection power and estimation efficiency in experiments with multiple trial types. It is shown that the trade-off between efficiency and power present in multiple-trial-type experiments is identical in form to that observed for single-trial-type experiments. Departures from the predicted trade-off due to the inclusion of basis function expansions and the assumption of correlated noise are examined. Finally, conditional entropy is introduced as measure for the randomness of a design, and an empirical relation between entropy and estimation efficiency is presented.
authors.affiliation: Center for Functional Magnetic Resonance Imaging, University of California San Diego, La Jolla, CA, USA. ttliu@ucsd.edu
authors.forename: Thomas T
authors.initials: TT
authors.lastname: Liu
authors.forename: Lawrence R
authors.initials: LR
authors.lastname: Frank
mesh_terms: D016477:Artifacts; D002540:Cerebral Cortex / Q000502:physiology*; D003198:Computer Simulation; D004526:Efficiency / Q000145:classification*; D019277:Entropy; D005071:Evoked Potentials / Q000502:physiology*; D006439:Hemodynamics / Q000502:physiology; D006801:Humans; D016014:Linear Models; D008279:Magnetic Resonance Imaging / Q000706:statistics & numerical data*; D009716:Numerical Analysis, Computer-Assisted; D012680:Sensitivity and Specificity