Comparing hemodynamic models with DCM

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.

Bayesian Model Selection for Group Studies

“…We used this approach to demonstrate that hemodynamic models with nonlinear BOLD equations are superior to those with linear ones. This result is in accordance with previous studies that highlight the importance of nonlinearities in the BOLD signal (Deneux & Faugeras 2006;Friston et al 2000;Miller et al 2001;Stephan et al 2007c;Vazquez & Noll 1998;. However, in these earlier studies, this conclusion was based on comparisons of specific and single instances of linear and nonlinear hemodynamic models.…”

“…For example, the GBF has been used frequently to decide between competing dynamic causal models fitted to fMRI (Acs & Greenlee 2008;Allen et al 2008;Grol et al 2007;Heim et al 2008;Kumar et al 2007;Leff et al 2008;Smith et al 2006;Stephan et al 2007bStephan et al , 2007cSummerfield & Koechlin 2008) and EEG data (Garrido et al 2007(Garrido et al , 2008. While the GBF is a simple and straightforward index for model comparison at the group level, it assumes that all subjects' data are generated by the same model (i.e.…”

Reduced Prefrontal-Parietal Effective Connectivity and Working Memory Deficits in Schizophrenia

“…In DCM, the modeled neuronal dynamics need to be transformed into a measured response, in this case the BOLD signal. This is done by using a hemodynamic forward model (Friston et al, 2000;Stephan et al, 2007). Parameter estimation is performed in a Bayesian framework as described previously (Friston et al, 2003).…”

Generalised filtering and stochastic DCM for fMRI

“…each region (vasodilatory signal, blood flow, blood volume and deoxyhemoglobin content), as described by an extended version of the Balloon model (Buxton et al, 1998;Friston et al, 2003). A nonlinear mixture of volume and deoxyhemoglobin content provides the predicted BOLD response (Stephan et al, 2007). Here, the random state fluctuations ω (x) ∈ Ω (x) have an unknown precision (inverse variance) and smoothness that are hyperparameterised by π, σ ∈ γ such thatω x ð Þ e N 0; V σ ð Þ⊗Σ e −π ð Þ ð Þ .…”