Short CommunicationDetection of signal synchronizations in resting-state fMRI datasets
Introduction
Functional MR Imaging (fMRI) has been mainly used in detecting task-related metabolic activity related to neuronal activation. However, spontaneous signal fluctuations have also been described (Biswal et al., 1995, Cordes et al., 2001), and an important question about these fluctuations is their relationship with functional connectivity. Understanding these fluctuations may benefit activation studies that contrast a controlled activation state against the so-called resting state; the evolution of these fluctuations during learning or pathology may be particularly informative; moreover, they can characterize brain processes associated with attention and vigilance. Therefore, it is important to distinguish between different possible origins of the signal, e.g. acquisition/motion artifacts, or aliased respiratory and cardiac signals (Dodel et al., 2004), which potentially contribute to low-frequency fluctuations of the signal. A convenient way to overcome these difficulties consists in performing simultaneous acquisition of respiratory and cardiac rhythms (Dodel et al., 2004), or electro-encephalographic (EEG) activity (Goldman et al., 2002, Laufs et al., 2003). Besides the technical difficulty of these multimodal acquisition procedures, there remains the open issue of what the fMRI signal structure alone reveals about spontaneous activity.
Detection of resting-state activity (RSA) is a challenging task, because the resulting signals are confounded by physiological noise and there exist only weak spatial- and frequency-domain priors on the measurement artifacts. Frequency analysis of the individual time courses seems natural, since RSA has been shown to result in prominently low-frequency contributions; for instance, the Fast Fourier Transform (FFT) has been used by Kiviniemi et al. (2000), but this approach is not very accurate spatially (Kiviniemi et al., 2004). Cross-correlation analysis (Biswal et al., 1995, Cordes et al., 2001) requires the prior definition of a reference region, biasing the description towards subjective guess. The correlation between any two regions in the brain is also sensitive to physiological (motion-related, cardiac and respiratory) signals, which may induce strong correlations, even after adequate denoizing (Dodel et al., 2004). A frequency analysis of the cross-correlations might better separate the different contributions (Cordes et al., 2001). Finally, coherence analysis with reference or seed regions has also been proposed (Sun et al., 2004).
On the other hand, multivariate analysis builds on the spatially distributed structure of RSA. Principal Components Analysis (PCA) has been introduced for the analysis of the so-called functional connectivity (Friston et al., 1993), but spatial Independent Components Analysis (ICA) is known to be more successful in the separation of potential sources of signal (Kiviniemi et al., 2004). However, these methods face difficult dimension estimation issues (Beckmann and Smith, 2004). Moreover, the resulting components have to be further analyzed in order to select spatial- or frequency-domain components that match prior hypotheses on RSA. For instance, the average values of these maps can be recorded in regions of interest (van de Ven et al., 2004). Finally, the spatial maps have to be thresholded, which is usually performed by ad hoc procedures (z transforms and thresholding). These difficulties limit the reliability of these methods, while the lack of prior information may weaken their sensitivity. The present work is a novel combination of univariate methods (spectral coherence) and multivariate analysis (dimension reduction and clustering).
Our approach is based on the prior knowledge that RSA results in low-frequency coherent signals. Following Müller et al. (2001), we thus start by evaluating spectral coherence of the signals across all pairs of regions (or voxels).
Let Y(t) = [Y1(t),…,YN(t)] be the multivariate stochastic process that represents fMRI data. This process is assumed to be weakly stationary, i.e.:where ; stands for the expectation operator, and τ is an arbitrary time lag. Let C(τ) = (Cjk(τ)) be the Cross-Correlation matrix, and assume that it has a spectral representation that admits a density fjkwhere fjk(λ) measures the process covariance at frequency λ. The coefficientis known as the spectral coherence between Yj and Yk. Complete linear association of the two signals at the frequency λ holds when ρjk(λ) = 1, while ρjk(λ) = 0 indicates complete dissociation. The spectral lead of Yj(t) over Yk(t) at frequency λ is estimated aswhere Re() and Im() denote real and imaginary part, respectively. Note that – up to a normalization factor – the partial correlations used by Cordes et al. (2001) are the real part η of the complex coherence
In order to get robust estimators of (ρ,θ), we use the Parzen lag window method as suggested by Müller et al. (2001).
Following spectral coherence analysis, a difficult task consists in finding a simplified model of the pairwise interactions. In Müller et al. (2001), a direct thresholding is applied to the coherence matrix, and the set of mutually coherent voxel time courses are displayed. Besides the effect of more or less arbitrary thresholds, this does not handle the detection of multiple networks appropriately. In Cordes et al. (2002) a single-link hierarchical clustering technique was proposed, based on a pseudo-distance derived from partial correlation. However, such deterministic methods are sensitive to noise; they may yield inconsistent clusters (Stanberry et al., 2003) and require a lot of post hoc cluster validation. Lastly, they do not cope with the selection of the number of clusters better than standard methods.
To avoid these shortcomings, we turn to multivariate analysis, and introduce low-dimensional representations of the datasets based on the coherence matrix. These representations are intrinsically interesting since they give a geometrical representation of the global signal structure. Low-dimensional data can then be clustered more robustly and efficiently, using e.g. Gaussian Mixture Models (GMM) or C-means. Information criteria (e.g. BIC) provide then a data-tailored number q of clusters. These clusters can be interpreted as coherent modes of the dataset. If q is not too large, visual screening becomes an adapted exploration and validation procedure.
In what follows, we start by describing the datasets of our study. Then we develop the analysis procedure based on spectral coherence analysis suggested above. As in previous contributions on resting-state data analysis, we have not performed simulations of resting-state activity, since we have no real prior to build meaningful simulations. We show in the Results section that the networks found are interpretable in the view of neuroimaging literature, and discuss the inter-subject variability.
Section snippets
Datasets and pre-processing
Data were acquired using a Bruker 3 T System at MRI Center of La Timone, Marseille. For datasets 1 to 3, 1524 volumes of 6 contiguous slices were acquired (TR = 303 ms) on three different subjects. Although cardiac and respiratory measures were performed simultaneously (Dodel et al., 2004), we do not use these information here. Datasets 4 to 9 were recorded on the same three subjects (sessions 4–5, 6–7 and 8–9 from subjects 1, 2 and 3, respectively), with more conventional acquisition
Results
We first compare the three representation methods. Then, we detail the results obtained with the LE representation method across sessions.
Technical aspects
We proposed a self-contained framework for the detection of RSA networks, based on the derivation of representations of the coherence matrix, that could reproducibly detect spatially plausible networks in three subjects. Note that correlation-based analysis on these datasets had been confounded by the physiological (motion, heart, respiratory) signals, and had not been able to report such networks (Dodel et al., 2004) as clearly. Coherence analysis concentrates on a frequency band ([0.01 0.1]
Acknowledgments
We thank Philippe Ciuciu and Andreas Kleinschmidt for their suggestions and help in the writing of this document, and Jean-Luc Anton for his contribution in data acquisition and analysis. This work was partly funded by the French ministry of research through concerted actions ‘masse de données’, ‘neurosciences intégratives et computationnelles’ and ‘connectivité’.
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