Hierarchical clustering to measure connectivity in fMRI resting-state data
Introduction
Low frequency fluctuations of the cerebral hemodynamics with periods larger than 10 s have been observed in cortical and subcortical gray matter in the human brain with different imaging modalities such as fMRI [1], [2], [3], [4], near-infrared spectroscopy [5] and transcranial Doppler sonography [6]. Regions of the brain with similar functions, even when separated by a large distance have low frequency physiological fluctuations that show a zero phase relationship, implying a high degree of temporal coherence [7], [8]. This synchronicity of low frequency fluctuations in functionally related regions suggests the existence of neuronal connections characterizing a widespread cortical network. The underlying mechanism of this phase-locking behavior is still not understood. Some investigators hypothesize that synchronization between functionally connected regions might lead to a computational advantage in large distributed networks and thus keep the brain in a state of readiness in executing a future task [9], [10].
In functional connectivity MR imaging (fcMRI), functionally related regions of the brain are identified by measuring the temporal correlation of spontaneous low frequency fluctuations in their MR signals while the subject is in a “resting” state. Usually, the subject lies still with eyes closed for about 10 min during which no mental exercises are performed and echo-planar images are acquired in rapid succession. Unstructured random noise is seen in the MR signal together with cardiac and respiratory noise, and other oscillations below 0.1 Hz reflecting spontaneous, physiologically driven changes in local blood flow. To analyze signal time courses for correlations, the temporal correlation coefficient of a signal from a selected voxel (so called “seed voxel”) or voxels in a region of the brain is computed with signals from all other voxels in the brain. A statistical test is performed for each comparison to determine the strength of the correlation, and a suitable threshold is applied to create an image showing those regions of the brain with strong correlations to the selected seed voxels. Functional connectivity is hypothesized between the seed voxels and the regions with high temporal correlation to the fMRI response of the seed voxels.
While the feasibility of resting-state fMRI has been demonstrated in several papers, functional connectivity is incompletely characterized with the standard method. The seed voxel method is limited since each different seed voxel may provide a different functional connectivity map. Seed voxels are usually selected on the basis of anatomic information or previously performed functional activation maps. Partial volume effects where CSF and major blood vessels both contribute to the MR signal may confound the connectivity. Therefore, if adjacent voxels to the selected seed voxels are used, the resulting cross correlation maps can have completely different features [7], [8]. The seed voxel method can been criticized for bias in the selection of the seed voxels since there is no experimenter-independent selection standard.
To reduce reader bias, functional connectivity data could be analyzed by means of a model independent method. Exploratory data analysis methods have the attractive feature of being model free and thus allowing unbiased studies of brain signal responses. Examples in fMRI/PET include principal component analysis (PCA) [11], independent component analysis (ICA) [12] and cluster analysis [13], [14], [15]. PCA partitions data space into orthogonal components based on the covariance matrix. ICA relaxes the orthogonality constraint and determines components that are as statistically independent by reducing higher than second order statistical dependencies. While ICA has been applied to resting-state data [16], [17], [18], it is not clear how many of the components obtained are actually physiologic. In ICA Gaussian or near Gaussian distributions in physiological noise having a small Kurtoses cannot be separated and might contaminate other components, especially since the amplitude of low frequency oscillations is small. This is especially problematic. Furthermore, the necessary time independence of the weighting matrix as formulated in current ICA algorithms might not be true for a realistic description of resting-state data, since spatial pattern of resting-state activity might change during the long acquisition of the study. However, some successful applications have been reported recently [17].
In the present work we applied a hierarchical clustering algorithm [19], [20] based on the single link (nearest neighbor) method to find clusters whose voxel members have high cross correlation coefficients that indicate low frequency synchronous fluctuations in the fMRI signal. We use the synchrony to imply functional connectivity. This method does not require prior knowledge of cluster centers or the number of clusters present in the data. Our approach represents a first attempt to define an appropriate distance measure for analyzing resting-state data to partition all possible cross correlations coefficients from multi-slice data into meaningful patterns of functional connectivity. Furthermore, this approach permits an evaluation of the effects of hardware (i.e., gradient) instabilities and magnitudes of motion-induced correlations on connectivity data.
Section snippets
Data acquisition
Four normal male volunteers, ranging in age from 20–25 years and claiming to be in good health, participated in this study. Signed consent was obtained according to institutional guidelines (IRB approval). Head stabilization and motion control were achieved with foam pads. Each subject was instructed before the scanning session to be as motionless as possible during the EPI acquisitions, to keep his eyes closed and refrain from any cognitive exercise. MR scanning was performed in a commercial
Control studies
Artifacts resembling motion were present in all phantom data due to hardware instabilities. For the customized brain phantom [21] linear and angular displacements were required to register the data Fig. 3, Fig. 4. The linear displacement in the I-S direction is the dominant artifact. The scanner drift is present during the entire scan and has a constant slope of 0.067 mm/min. A slope of similar magnitude has also been found in human data. Fourier analysis (also evident in Fig. 4) shows that
Discussion
We have demonstrated the application of a clustering methodology based on temporal correlations in the low frequency range that reveals spontaneous hemodynamic processes in the resting brain. This approach does not rely on an Euclidean distance measure, which is often used in clustering Gaussian-distributed data [15]. Rather, our method is designed to explore correlations in structured non-Gaussian physiological noise without any contaminations from respiratory or cardiac effects. In order to
Conclusion
The present study demonstrates that physiologically predictable patterns of correlations in low-frequency oscillations can be found in resting-state fMRI data by a hierarchical clustering methodology. A requirement for measuring connectivity with the method has been described. The method is “data-driven,” meaning that the data themselves determine the natural divisions in the data set for functional connectivity. The approach is more powerful than the “seed-voxel” method in resting-state data
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