We surveyed 170 published fMRI studies to characterize how the GLM is used to analyze imaging data. (A) Block and event-related designs were equally common. (B) Most event-related studies made inferences about a time-varying decision process. (C) Although response times were recorded in 82% of event-related studies with a decision component, only 9% actually used this information to construct a regression model for detecting brain activity. (D) Most studies assumed that there were no significant differences in HRF shape across subjects. (E) In event-related fMRI studies that made inferences about variable duration decision processes, a majority (95%) assumed that the shape of HDRs did not vary across trials or trial types, and 84% assumed that both shape and intensity did not vary across trials. (F) All of the major analysis platforms were represented and no obvious relationship between platform type and model type was found.

Each model was used to detect a simulated time-varying signal. Each data point consisted of 10,000 simulated runs. (A) The variable epoch model (blue) has significantly higher detection power as a function of effect size (Pearson’s correlation coefficient) than all the other models. Although the improvement in power is a function of run length, the results provide an estimate of the relative cost of using the other models in detecting time-varying signals. (B) All the models have similar false positive rates. (C) The variable impulse model (two regressors; green) has higher power than the variable epoch model (single regressor; blue) for small effect sizes. However, this comes at a substantial cost due to an increase in false positive rate (D). Error bars represent standard deviation (note: error bars are too small to be visible in A and C).

(A) When a neural process (in this case a flashing checkerboard) has variable duration across trials, the variable epoch model detects a greater number of significant voxels on each 5.5 min run than the other models. (B) The same pattern is true at the group level (mixed-effects analysis; n = 8 subjects). The variable impulse model has a much less consistent response across runs and across subjects, resulting in a large drop in sensitivity at the group level. (C) An example of the mixed-effects group level activation maps demonstrates that the variable epoch model showed higher Z-statistics and detects many more significant voxels than the other models. The unthresholded activation maps show that the variable impulse model has a similar, but non-significant, spatial distribution of activity in the visual cortex.

(A) A hypothetical event-related fMRI experiment in which the subject responded to the presentation of a stimulus. Assuming a linear time-invariant (LTI) system, the constant duration stimulus produces sensory neuronal responses and sensory BOLD responses that are also constant in duration. However, electrophysiological evidence (Janssen and Shadlen, 2005; Maimon and Assad, 2006; Ratcliff et al., 2007; Schall, 2003; Shadlen and Newsome, 2001; Snyder et al., 2006) shows that the same constant duration stimulus will typically produce variable duration decision-related neural responses, characterized by a subject’s RT distribution. An LTI system predicts that the decision-related BOLD response will vary in both shape and intensity from trial to trial. (B) We tested the efficacy of four regression models against a hypothetical decision-related cognitive/neural process that varied in duration on each trial. The constant impulse model consists of an impulse function positioned at the onset of each event. The constant epoch model consists of a 2 s epoch positioned on the TR nearest the onset of the neural event. The variable impulse model is a two-regressor model that uses a constant impulse regressor and a modulator regressor whose height is proportional to the demeaned durations of the process. All the models were convolved with a canonical double gamma hemodynamic response function.

(A) The canonical HRF was convolved with either an impulse of variable height (red) or an epoch of variable duration (0–4000 ms in 500 ms steps; blue). When only intensity is modulated, the shape of the HDR is constant, varies only in height, and is identical to the theoretical HRF (red). However, when duration is the critical variable, both the shape and height of the response vary (blue). (B) We calculated the Pearson’s correlation coefficient, R², between the impulse model (or HRF) and the variable duration HDRs. The percent of temporal variance explained by the impulse model decreases as a function of duration. When the duration of the neural process is 3 s, the impulse model can only explain half of the variance in the data. (C) Data from the visual cortex of a single subject viewing flashing checkerboards of variable contrast (5%, 10%, 20%, 40%) with a constant duration (0.25 s, left panel) and variable duration (0.25 s, 0.75 s, 1.3 s, 3.5 s) but constant intensity (5%, right panel). The circles indicate the peak intensity for each trial type. (D) As predicted by the LTI model in (A), the slope of the HDRs in (C, red) increases linearly with stimulus intensity (red). However, for stimulus durations greater than ~1.3 s, the slope of the HDRs in (C, blue) remains constant (blue). Error bars represent standard error. (E) As stimulus intensity increases, the time at which the HDRs reach their peak intensity remains constant (red), as predicted by the LTI model in (A). In contrast, the time to peak is linearly related to stimulus duration (blue). Error bars represent standard error.

(A) The variable epoch model generates a mean HRF estimate across subjects with lower variance than the constant impulse model. Shaded regions represent one standard deviation. (B) Levene’s Test for Equality of Variance was used to determine whether the variances were significantly different. The dotted line represents the significance threshold, set at p < 0.05, F(1,14) = 4.6. The majority of the time points have significantly higher variance for the impulse HRF estimate than for the variable epoch HRF estimate. Note that the crossover points at 7.5 s and 14.2 s are the only regions where the variance for the epoch HRF exceeds the variance for the impulse HRF.