Detection of time-varying signals in event-related fMRI designs

Abstract

In neuroimaging research on attention, cognitive control, decision-making, and other areas where response time (RT) is a critical variable, the temporal variability associated with the decision is often assumed to be inconsequential to the hemodynamic response (HDR) in rapid event-related designs. On this basis, the majority of published studies model brain activity lasting less than 4 s with brief impulses representing the onset of neural or cognitive events, which are then convolved with the hemodynamic impulse response function (HRF). However, electrophysiological studies have shown that decision-related neuronal activity is not instantaneous, but in fact, often lasts until the motor response. It is therefore possible that small differences in neural processing durations, similar to human RTs, will produce noticeable changes in the HDR, and therefore in the results of regression analyses. In this study we compare the effectiveness of traditional models that assume no temporal variance with a model that explicitly accounts for the duration of very brief epochs of neural activity. Using both simulations and fMRI data, we show that brief differences in duration are detectable, making it possible to dissociate the effects of stimulus intensity from stimulus duration, and that optimizing the model for the type of activity being detected improves the statistical power, consistency, and interpretability of results.

Introduction

Over the past two decades, the development of functional magnetic resonance imaging (fMRI) technology has generated near exponential growth in neuroimaging research and its clinical applications (Bandettini, 2007). The most commonly used method for analyzing the blood oxygenation level-dependent (BOLD) changes in fMRI is based on the general linear model (GLM). A typical experiment consists of generating a hypothetical cognitive or neural model of brain activity and using multiple linear regression to search for voxels correlated with the predicted response. In classic block designs, the duration of each regressor in the regression model matches the duration of the stimulus block. As blocks shorten to 4 s or less, the current convention is to switch to using ‘impulse functions’ of arbitrarily short duration, rather than simply continue shortening blocks to match the length of the stimulus. While this may produce accurate results when the cognitive/neural events are of constant duration (20% of event-related studies; Fig. 1B), the majority (80%) of event-related studies involves choice-related neural processes that can vary in duration with the subject's RT. In 95% of event-related studies containing a decision process (Fig. 1E), the duration of the decision period is assumed to be constant and is typically modeled by the convolution of a constant height, finite impulse function (i.e. a Kronecker delta function) positioned at event onset with a canonical hemodynamic response function (Friston, 2003, Friston et al., 1994, Henson, 2003, Josephs et al., 1997).

Although this method can often detect task-related fMRI activity, it makes the implicit assumption that the underlying neural or cognitive process is a brief, essentially zero duration, event (i.e. an impulse). This simplification is generally thought to have little or no impact on the results. In fact, due to the low-pass filtering properties of the BOLD response (Zarahn et al., 1997), it has been argued that the shape of the physiological hemodynamic response (HDR) to brief stimuli (< 4 s) is equal to the theoretical hemodynamic impulse response function (HRF), making the constant impulse model a good approximation to the actual BOLD response (Henson, 2003). However, it has been shown that stimulus durations as small as 34 ms (Glover, 1999, Rosen et al., 1998, Savoy et al., 1995) and onset asynchronies as low as 50 ms (Bellgowan et al., 2003, Henson et al., 2002, Kim et al., 1997, Menon et al., 1998, Miezin et al., 2000, Richter et al., 2000) can elicit detectable BOLD responses, suggesting that small differences in the onset or duration of modeled events may be important.

If the assumption of equivalence between impulse functions and short (100 ms–4 s) blocks (or boxcars) does not hold, then it should be possible to dissociate the effects of stimulus intensity from stimulus duration in event-related designs. Moreover, any discriminable differences between these models would suggest that the shape of the BOLD response should be optimized for the type of activity being detected. For example, impulse functions might best model neural activity at stimulus onset, whereas brief epochs might best capture activity that is sustained throughout stimulus processing. Potential differences between impulse- and short epoch-based models may be magnified by the fact that response times (RTs) in many studies vary across trials. Such variations have been shown in animal research to be related to the variations in the duration of decision-related neuronal firing (Janssen and Shadlen, 2005, Maimon and Assad, 2006, Ratcliff et al., 2007, Schall, 2003, Shadlen and Newsome, 2001, Snyder et al., 2006), and such variability in response time is the basis for a variety of decision-making models (Ratcliff, 2005). In addition, several fMRI studies have demonstrated that the HDR to a decision process is likely to vary with the time it takes to elicit the subject's response (Connolly et al., 2005, Formisano et al., 2002, Kruggel et al., 2000, Menon et al., 1998). Importantly, temporal variability is rarely an explicit experimental manipulation, but nevertheless exists implicitly as a distribution of response times. RTs for simple, suprathreshold detection tasks (simple RTs) typically range from 200 to 500 ms, whereas choice responses between multiple options (choice RTs) start at around 400 ms and can range up to tens of seconds depending on speed-accuracy tradeoffs, task complexity, arousal, age, clinical status, etc (Verhaeghen et al., 2006, Verhaeghen et al., 2003). Thus, decision-related behavioral responses to many types of brief stimuli—such as those elicited by attention, memory, cognitive control, language, and decision-making processes—are likely to elicit neural activity that (a) persists over much of the time between stimulus presentation and response, and (b) varies in duration from trial to trial (Fig. 2A).

It has been proposed that modeling temporal variability in the data increases statistical power and captures an important source of information about the relationship between brain activity and psychophysical performance (Buchel et al., 1998, Friston, 2003, Henson, 2003, Josephs and Henson, 1999). Models that incorporate information about trial-to-trial variation in RT (or other psychophysiological parameters) into the GLM are often called ‘parametric modulation’ models. In the parametric (or variable impulse) approach, a participant's mean-centered RTs are used to modulate the amplitude of an impulse function. The modulated impulse function is then convolved with the HRF and added as an additional regressor in the GLM. Brain regions for which the amplitude of the primary, unmodulated regressor is significantly non-zero are interpreted as task-related. Conversely, brain regions for which the amplitude of the modulated regressor is significant are interpreted as being sensitive to trial-to-trial variations in RT.

An alternative method is the variable epoch approach, which involves modeling each trial with a boxcar epoch function whose duration is equal to the RT of the trial. A single regressor is then constructed from these boxcars to use in the GLM. This approach makes the critical assumption that the cognitive and neural basis of decision-related activity is accurately represented by the diffusion (or race) model of decision-making (Ratcliff, 2005, Ratcliff et al., 2007). The diffusion model is supported by electrophysiological studies in humans (Philiastides et al., 2006) and non-human primates (Janssen and Shadlen, 2005, Maimon and Assad, 2006, Ratcliff et al., 2007, Schall, 2003, Shadlen and Newsome, 2001, Snyder et al., 2006) in which neuronal activity (or firing rate) is sustained or even increases up to the time of the behavioral response. Thus, compared to the constant impulse approach, the variable epoch model attempts to more faithfully represent the physiological processes related to decision-making in many brain regions. In our previous work, we used this model to locate RT-sensitive brain regions in a decision-making task and confirmed model accuracy using model-free (GLM-free) analysis methods (Grinband et al., 2006).

In the current study, the variable epoch model was compared against three other models: a constant impulse model (the most common model, used in 70% of event-related studies in our survey; Fig. 1E), the variable impulse model that includes a mean-centered parametric modulator (11% of event-related studies), and a constant epoch model (a variation of the constant impulse approach in which the impulses are binned within each 2 s TR; 14% of event-related studies). This paper uses simulations and fMRI data to explore the differences in the predictions made by these models and demonstrates that, even for brief events, they are not equivalent. Our data suggest that when detecting time-varying signals, such as those generated by a behavioral response, the variable epoch model is physiologically plausible, and has higher power and reliability for detecting brain activation.