Misconceptions in the use of the General Linear Model applied to functional MRI: a tutorial for junior neuro-imagers

Most brain research to date have focused on studying the amplitude of evoked fMRI responses, though there has recently been an increased interest in measuring onset, peak latency and duration of the responses as well. A number of modeling procedures provide measures of the latency and duration of fMRI responses. In this work we compare several techniques that vary in their assumptions, model complexity, and interpretation. For each method, we introduce methods for estimating amplitude, peak latency, and duration and for performing inference in a multi-subject fMRI setting. We then assess the techniques' relative sensitivity and their propensity for mis-attributing task effects on one parameter (e.g., duration) to another (e.g., amplitude). Finally, we introduce methods for quantifying model misspecification and assessing bias and power-loss related to the choice of model. Overall, the results show that it is surprisingly difficult to accurately recover true task-evoked changes in BOLD signal and that there are substantial differences among models in terms of power, bias and parameter confusability. Because virtually all fMRI studies in cognitive and affective neuroscience employ these models, the results bear on the interpretation of hemodynamic response estimates across a wide variety of psychological and neuroscientific studies.

An important challenge in the design and analysis of event-related or single-trial functional magnetic resonance imaging (fMRI) experiments is to optimize statistical efficiency, i.e., the accuracy with which the event-related hemodynamic response to different stimuli can be estimated for a given amount of imaging time. Several studies have suggested that using a fixed inter-stimulus-interval (ISI) of at least 15 sec results in optimal statistical efficiency or power and that using shorter ISIs results in a severe loss of power. In contrast, recent studies have demonstrated the feasibility of using ISIs as short as 500 ms while still maintaining considerable efficiency or power. Here, we attempt to resolve this apparent contradiction by a quantitative analysis of the relative efficiency afforded by different event-related experimental designs. This analysis shows that statistical efficiency falls off dramatically as the ISI gets sufficiently short, if the ISI is kept fixed for all trials. However, if the ISI is properly jittered or randomized from trial to trial, the efficiency improves monotonically with decreasing mean ISI. Importantly, the efficiency afforded by such variable ISI designs can be more than 10 times greater than that which can be achieved by fixed ISI designs. These results further demonstrate the feasibility of using identical experimental designs with fMRI and electro-/magnetoencephalography (EEG/MEG) without sacrificing statistical power or efficiency of either technique, thereby facilitating comparison and integration across imaging modalities.

This article considers the efficiency of event-related fMRI designs in terms of the optimum temporal pattern of stimulus or trial presentations. The distinction between "stochastic" and "deterministic" is used to distinguish between designs that are specified in terms of the probability that an event will occur at a series of time points (stochastic) and those in which events always occur at prespecified time (deterministic). Stochastic designs may be "stationary," in which the probability is constant, or nonstationary, in which the probabilities change with time. All these designs can be parameterized in terms of a vector of occurrence probabilities and a prototypic design matrix that embodies constraints (such as the minimum stimulus onset asynchrony) and the model of hemodynamic responses. A simple function of these parameters is presented and used to compare the relative efficiency of different designs. Designs with slow modulation of occurrence probabilities are generally more efficient than stationary designs. Interestingly the most efficient design is a conventional block design. A critical point, made in this article, is that the most efficient design for one effect may not be the most efficient for another. This is particularly important when considering evoked responses and the differences among responses. The most efficient designs for evoked responses, as opposed to differential responses, require trial-free periods during which baseline levels can be attained. In the context of stochastic, rapid-presentation designs this is equivalent to the inclusion of "null events." Copyright 1999 Academic Press.