Statistical Design Issues for fMRI Studies: A Beginner’s Training Manual

Abstract

An experimental subject [patient] is presented with a mental stimulus such as a 1.5-second flickering checkerboard image or a painful heat stimulus at some of a total of n time points in the experiment. During this presentation, the patient absorbs a sequence of mental stimuli along with a provision for intermediate resting period as well. The measurement of a brain voxel at an instant is collected by an fMRI scanner. The purpose is to examine a collection of the response profiles to understand the nature and extent of local brain activity in response to the stimuli. Functional Magnetic Resonance Imaging (fMRI) is a technology for studying how our brains respond to mental stimuli. In recent times, researchers have paid attention to “modeling” the responses in terms of sequences of mental stimuli received during a given period including the “resting phase” as well. The simplest such model incorporates linear relation between mean response and the parameters describing the effects of the stimuli, applied at regularly spaced time points during the study period. There is a nuisance parameter and also those representing the unknown heights of the hemodynamic response function, HRF, at the stimulus onset time point and at some of the immediately preceding time points. Statistical design theorists have focused their attention to the study of design sequences for collecting most informative data in order to render most precise inference about these parameters under an assumed statistical model. We have noted that most experimental design researchers are not aware of this application of linear models and design considerations in fMRI studies. Accordingly, our primary consideration has been to introduce this application area and related concepts in simple terms. We have given illustrative examples at length. In the process, we have introduced the concept of “Clear Zero”. We thought this would create enough interest among researchers in the broad areas of linear models and DoE. In this paper, we review the linear model and discuss estimation issues and related concepts such as “orthogonality” and “balance”, as are applicable to fMRI research study. Incidentally, a concept termed “Clear 0” is introduced and studied at length. This is geared toward our understanding of comparison between two given design sequences from inferential aspects.