Technical NoteDynamic causal modeling: A generative model of slice timing in fMRI
Introduction
The aim of dynamic causal modeling (DCM) is to describe interactions among neuronal populations (Friston et al., 2003). DCM explains observed fMRI time-series by modeling interactions at a neuronal level and passing the ensuing neuronal states through a hemodynamic model to give region-specific blood oxygenation level-dependent (BOLD) signals (Buxton et al., 2004, Friston, 2002). The DCM is inverted using a variational Bayesian scheme to give posterior distributions of the model parameters. Inferences about a specific network are made using the posterior distributions of interesting parameters; e.g., the connectivity between areas or the modulation of connectivity by experimental manipulations. This makes DCM useful for testing hypotheses about modulatory effects; i.e., how experimental conditions change directed connections among areas. For example, it has been shown, using DCM, that the superior posterior parietal cortex (SPC) exerts a modulatory role, that mediates attentional effects, on V5 responses (Friston et al., 2003, Friston and Buchel, 2000). Other examples of DCM can be found in Mechelli et al., 2004, Noppeney et al., 2006, Stephan et al., 2005. DCM uses biophysically and physiologically inspired generative models.1 This makes it relatively simple to extend existing DCMs. The usefulness of changes to the model can then be assessed using model comparison (Penny et al., 2004).
Currently, DCM for fMRI assumes that data from all areas are acquired at the same time. Clearly, this is an approximation, because fMRI data are usually acquired slice by slice. For a typical fMRI study, it is likely that data from remote areas (orthogonal to slice orientation) are acquired with a slice-timing difference in the order of seconds. Friston et al. (2003) showed, for block designs that the model can cope with slice-timing differences of up to 1 s. This robustness rests on changes in (non-interesting) hemodynamic parameters, which explain away slice-timing effects.
The assumption of simultaneous data acquisition restricts the application of DCM to data that are acquired with slice-timing differences of less than a second. The typical repetition time (TR), i.e., the time needed for acquiring one volume, lies between 3 and 5 s. Note that the TR itself is not the limiting factor; the key factor is the timing differences among modeled areas. With a TR of several seconds, it is quite likely that some areas have slice-timing differences of more than 1 s. This questions the validity of DCM for such data. Furthermore, for event-related designs, the robustness of DCM to slice-timing differences has never been assessed. This is important, because event-related designs are prevalent in fMRI.
In this paper, we propose an extension that accommodates slice-timing differences: instead of assuming that data were acquired at the same time, we incorporate information about temporal sampling into the DCM. This is implemented using an informed integration scheme, which computes the predicted output given the model parameters and sampling times. The resulting DCM can be regarded as a three-level model. The first level models (interesting) interactions at a neuronal level. The second level models the hemodynamics. The third (and now explicit) level is the discrete temporal sampling of continuous second-level output. At this third level, we specify when the data were acquired from each area. The contribution of the present work is to show that this temporal sampling level is a useful extension to the model.
We establish the validity of this extension using simulations. By comparing models using their log-evidences, we show that the extended model is superior. We also compare the extended model with the current practice of ‘slice-timing correction’, i.e., aligning the data temporally (before using DCM) in an attempt to discount timing differences. Finally, we demonstrate, using real data, the importance of modeling slice-timing differences.
Section snippets
Dynamic causal modeling for fMRI: levels one and two
In this section we review briefly dynamic causal models of fMRI data (Friston et al., 2003). In the next section, we extend this model to accommodate slice timing (see Fig. 1 for an overview).
A dynamic causal model is a multiple-input multiple-output system that comprises Nu inputs and Nr outputs with one output per region. The Nu inputs correspond to designed causes (e.g., boxcar or impulse stimulus functions used in conventional analyses). Each region produces a measured output that
Synthetic data
In this section, we validate our model in terms of conditional inference and model comparison, using simulated data; in which the true parameters and models are known. We used two synthetic data sets. We generated the first from a system that was used by Friston et al. (2003) to validate the original DCM. The second was generated by a three-area network used in a visual attention study (Buchel and Friston, 1997, Friston et al., 2003). To generate synthetic data we selected some model parameters
Discussion
Our analyses indicate that event-related designs are the most susceptible to failures in modeling slice timing correctly. Our simulations suggest that even with a short TR of less than 2 s and a small difference in slice timing (between areas) of 0.5 s, one can get large deviations from the true connectivity parameters, for the fixed coupling and their modulations parameters (Fig. 4, Fig. 5). Model comparisons show that including slice-timing results in better models (Fig. 6). For block
Conclusion
We have presented an extension to dynamic causal modeling for functional magnetic resonance imaging data. Our analyses of synthetic and real data suggest that slice-timing differences between areas should and can be modeled. The extended model gives veridical estimates and higher model evidences, as compared to the original formulation. Furthermore, we can drop the former limitation that slice-timing differences between areas must not exceed 1 s. This makes DCM applicable to a much wider range
Acknowledgments
The Wellcome Trust funded this work. We thank Felix Blankenburg and Klaas Stephan for their helpful discussions.
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