Abstract
The classical model of blood oxygen level-dependent (BOLD) responses by Buxton et al. [Buxton, R.B., Wong, E.C., Frank, L.R., 1998. Dynamics of blood flow and oxygenation changes during brain activation: the Balloon model. Magn. Reson. Med. 39, 855–864] has been very important in providing a biophysically plausible framework for explaining different aspects of hemodynamic responses. It also plays an important role in the hemodynamic forward model for dynamic causal modeling (DCM) of fMRI data. A recent study by Obata et al. [Obata, T., Liu, T.T., Miller, K.L., Luh, W.M., Wong, E.C., Frank, L.R., Buxton, R.B., 2004. Discrepancies between BOLD and flow dynamics in primary and supplementary motor areas: application of the Balloon model to the interpretation of BOLD transients. NeuroImage 21, 144–153] linearized the BOLD signal equation and suggested a revised form for the model coefficients. In this paper, we show that the classical and revised models are special cases of a generalized model. The BOLD signal equation of this generalized model can be reduced to that of the classical Buxton model by simplifying the coefficients or can be linearized to give the Obata model. Given the importance of hemodynamic models for investigating BOLD responses and analyses of effective connectivity with DCM, the question arises which formulation is the best model for empirically measured BOLD responses. In this article, we address this question by embedding different variants of the BOLD signal equation in a well-established DCM of functional interactions among visual areas. This allows us to compare the ensuing models using Bayesian model selection. Our model comparison approach had a factorial structure, comparing eight different hemodynamic models based on (i) classical vs. revised forms for the coefficients, (ii) linear vs. non-linear output equations, and (iii) fixed vs. free parameters, ε, for region-specific ratios of intra- and extravascular signals. Using fMRI data from a group of twelve subjects, we demonstrate that the best model is a non-linear model with a revised form for the coefficients, in which ε is treated as a free parameter.
Highlights
In many models of effective connectivity, like structural equation modeling (Horwitz et al, 1999; McIntosh and GonzalezLima, 1994; Büchel and Friston, 1997), psychophysiological interactions (Friston et al, 2007), or multivariate autoregression (Harrison et al, 2003; Goebel et al, 2003), coupling parameters are estimated directly from the measured time-series
Given the importance of hemodynamic modeling for investigations of blood oxygen level dependent (BOLD) responses and analyses of effective connectivity with dynamic causal modeling (DCM), the question arises: which formulation is a more appropriate model of empirically measured BOLD responses? In this article, we address this question by embedding different variants of the BOLD model” (BM) in a well-established DCM of functional interactions in the ventral stream of the visual cortex (Stephan et al, 2007a), which is fitted to BOLD responses that were measured in a group of twelve subjects (Stephan et al, 2003)
We first report the direct comparison between the classical Buxton model (CBMN) and the Obata model (RBML)
Summary
In many models of effective connectivity, like structural equation modeling (Horwitz et al, 1999; McIntosh and GonzalezLima, 1994; Büchel and Friston, 1997), psychophysiological interactions (Friston et al, 2007), or multivariate autoregression (Harrison et al, 2003; Goebel et al, 2003), coupling parameters are estimated directly from the measured time-series. In modeling dependencies among measured data, one implicitly assumes that neural activity can be observed directly. This is tenable for single neuron recordings, but not for non-invasive techniques like functional magnetic resonance imaging (fMRI) or electroencephalography (EEG). In fMRI, the relationship between neural activity and measured blood oxygen level dependent (BOLD) signals is complicated and not fully understood (Attwell and Iadecola, 2002; Lauritzen, 2004; Logothetis et al, 2001; Logothetis and Wandell, 2004). The interpretation of models of effective connectivity, which ignore the transformation from the neural activity to the BOLD measurements, can be difficult (Gitelman et al, 2003)
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