Dietmar Cordes

Hierarchical clustering to measure connectivity in fMRI resting-state data

Low frequency oscillations, which are temporally correlated in functionally related brain regions, characterize the mammalian brain, even when no explicit cognitive tasks are performed. Functional connectivity MR imaging is used to map regions of the resting brain showing synchronous, regional and slow fluctuations in cerebral blood flow and oxygenation. In this study, we use a hierarchical clustering method to detect similarities of low-frequency fluctuations. We describe one measure of correlations in the low frequency range for classification of resting-state fMRI data. Furthermore, we investigate the contribution of motion and hardware instabilities to resting-state correlations and provide a method to reduce artifacts. For all cortical regions studied and clusters obtained, we quantify the degree of contamination of functional connectivity maps by the respiratory and cardiac cycle. Results indicate that patterns of functional connectivity can be obtained with hierarchical clustering that resemble known neuronal connections. The corresponding voxel time series do not show significant correlations in the respiratory or cardiac frequency band.

Cluster analysis of fMRI data using dendrogram sharpening.

The major disadvantage of hierarchical clustering in fMRI data analysis is that an appropriate clustering threshold needs to be specified. Upon grouping data into a hierarchical tree, clusters are identified either by specifying their number or by choosing an appropriate inconsistency coefficient. Since the number of clusters present in the data is not known beforehand, even a slight variation of the inconsistency coefficient can significantly affect the results. To address these limitations, the dendrogram sharpening method, combined with a hierarchical clustering algorithm, is used in this work to identify modality regions, which are, in essence, areas of activation in the human brain during an fMRI experiment. The objective of the algorithm is to remove data from the low‐density regions in order to obtain a clearer representation of the data structure. Once cluster cores are identified, the classification algorithm is run on voxels, set aside during sharpening, attempting to reassign them to the detected groups. When applied to a paced motor paradigm, task‐related activations in the motor cortex are detected. In order to evaluate the performance of the algorithm, the obtained clusters are compared to standard activation maps where the expected hemodynamic response function is specified as a regressor. The obtained patterns of both methods have a high concordance (correlation coefficient = 0.91). Furthermore, the dependence of the clustering results on the sharpening parameters is investigated and recommendations on the appropriate choice of these variables are offered. Hum. Brain Mapping 20:201–219, 2003.

Estimation of the intrinsic dimensionality of fMRI data.

A new method based on an autoregressive noise model of order 1 is introduced to the problem of detecting the number of components in fMRI data. Unlike current information-theoretic criteria like AIC, MDL, and related PPCA, which do not incorporate autocorrelations in the noise, the new method leads to more consistent estimates of the model order, as illustrated in simulated and real fMRI resting-state data.

BOLD-fMRI of PTZ-induced seizures in rats

PURPOSEnTo develop a non-invasive method for exploring seizure initiation and propagation in the brain of intact experimental animals.nnnMETHODSnWe have developed and applied a model-independent statistical method--Hierarchical Cluster Analysis (HCA)--for analyzing BOLD-fMRI data following administration of pentylenetetrazol (PTZ) to intact rats. HCA clusters voxels into groups that share similar time courses and magnitudes of signal change, without any assumptions about when and/or where the seizure begins.nnnRESULTSnEpileptiform spiking activity was monitored by EEG (outside the magnet) following intravenous PTZ (IV-PTZ; n=4) or intraperitoneal PTZ administration (IP-PTZ; n=5). Onset of cortical spiking first occurred at 29+/-16 s (IV-PTZ) and 147+/-29 s (IP-PTZ) following drug delivery. HCA of fMRI data following IV-PTZ (n=4) demonstrated a single dominant cluster, involving the majority of the brain and first activating at 27+/-23s. In contrast, IP-PTZ produced multiple, relatively small, clusters with heterogeneous time courses that varied markedly across animals (n=5); activation of the first cluster (involving cortex) occurred at 130+/-59 s. With both routes of PTZ administration, the timing of the fMRI signal increase correlated with onset of EEG spiking.nnnCONCLUSIONSnThese experiments demonstrate that fMRI activity associated with seizure activity can be analyzed with a model-independent statistical method. HCA indicated that seizure initiation in the IV- and IP-PTZ models involves multiple regions of sensitivity that vary with route of drug administration and that show significant variability across animal subjects. Even given this heterogeneity, fMRI shows clear differences that are not apparent with typical EEG monitoring procedures, in the activation patterns between IV and IP-PTZ models. These results suggest that fMRI can be used to assess different models and patterns of seizure activation.

Novel nonparametric approach to canonical correlation analysis with applications to low CNR functional MRI data

Detection of activation in functional MRI (fMRI) is often complicated by the low contrast‐to‐noise ratio (CNR) in the data. The primary source of the difficulty is the fact that for activities that are subtle the signal can be hidden inside the inherent noise in the data. Classical univariate methods based on t‐test or F‐test are susceptible to noise, as they fail to harness systematic correlations in evoked responses within neighboring voxels. Here the power of a multivariate statistical analysis tool known as canonical correlation analysis (CCA) in fMRI studies is demonstrated where the CNR is low. As a further illustration of the power of the method, a comparative study of CCA and ordinary correlation analysis using simulated data under various noise levels is also performed. A novel nonparametric approach is introduced to calculate the P‐values from the distribution of the complicated test statistic. The circumstances under which CCA is a better performer as well as when it is not the case are discussed. As an example, this method is applied to detect hippocampal activation from memory‐related tasks. Magn Reson Med 50:354–365, 2003.

Novel ROC‐type method for testing the efficiency of multivariate statistical methods in fMRI

The receiver operating characteristic (ROC) method is a useful and popular tool for testing the efficiency of various diagnostic tests applicable to functional MRI (fMRI) data. Typically, the diagnostic tests are applied on simulated and pseudo‐human fMRI data, and the area under the ROC curve is used as a measure of the efficiency of the diagnostic test. The effectiveness of such a method depends on how well the simulated data approximate the real data. For multivariate statistical methods, however, this technique is usually inadequate, as the spatial dependence among voxels is ignored for simulated data. In this work a modified ROC method using real fMRI data with a broader scope is proposed. This method can be applied to most fMRI postprocessing techniques, including multivariate analyses such as canonical correlation analysis (CCA). Also, the relationship of the modified ROC method with the conventional ROC method is discussed in detail. Magn Reson Med 49:1152–1162, 2003.

Improving the spatial specificity of canonical correlation analysis in fMRI

The contrast‐to‐noise ratio (CNR) is often very low in fMRI data, and standard univariate methods suffer from a loss of sensitivity in the context of noise. The increased power of a multivariate statistical analysis method known as canonical correlation analysis (CCA) in fMRI studies with low CNR was established previously. However, CCA in its conventional form has weak spatial specificity. In this work we propose a new assignment scheme to rectify this problem. It is shown that the new method has improved spatial specificity as well as sensitivity compared to conventional CCA for detecting activation patterns in fMRI. Magn Reson Med 52:947–952, 2004.

A semi-parametric approach to estimate the family-wise error rate in fMRI using resting-state data

One of the most important considerations in any hypothesis based fMRI data analysis is to choose the appropriate threshold to construct the activation maps, which is usually based on p-values. However, in fMRI data, there are three factors which necessitate severe corrections in the process of estimating the p-values. First, the fMRI time series at an individual voxel has strong temporal autocorrelation which needs to be estimated to obtain the corrected parametric p-value. The second factor is the multiple comparisons problem arising from simultaneously testing tens of thousands of voxels for activation. A common way in the statistical literature to account for multiple testing is to consider the family-wise error rate (FWE) which is related to the distribution of the maximum observed value over all voxels. The third problem, which is not mentioned frequently in the context of adjusting the p-value, is the effect of inherent low frequency processes present even in resting-state data that may introduce a large number of false positives without proper adjustment. In this article, a novel and efficient semi-parametric method, using resampling of normalized spacings of order statistics, is introduced to address all the three problems mentioned above. The new method makes very few assumptions and demands minimal computational effort, unlike other existing resampling methods in fMRI. Furthermore, it will be demonstrated that the correction for temporal autocorrelation is not critical in implementing the proposed method. Results using the proposed method are compared with SPM2.

Test-retest precision of functional magnetic resonance imaging processed with independent component analysis

This study was designed to compare the test-retest precision of functional magnetic resonance imaging (fMRI) data processed with independent component analysis (ICA) and the same data analyzed with a conventional model-dependent method (Students-t mapping). Volunteers underwent two or three iterations of visual and auditory stimuli, while data were collected for fMRI scans. The scan data were separately processed with ICA and with Students-t mapping (STM). As a measure of test-retest precision, concurrence ratios were calculated for each subject and each task as the number of voxels that were activated by two iterations of a task divided by the average number of voxels activated in each repetition. In 28 test-retest comparisons, the average concurrence ratio was 0.69±0.10 for ICA and 0.65±0.13 for the conventional method, a statistically insignificant difference. In fMR image data of block stimulus paradigms, ICA had similar test-retest precision to a conventional model-dependent method.

New approaches to receiver operating characteristic methods in functional magnetic resonance imaging with real data using repeated trials.

Receiver operating characteristic (ROC) methods are useful tools for evaluating the sensitivity and specificity of various postprocessing algorithms used in fMRI data analysis. New ROC methods using real fMRI data are proposed that improve a previously introduced method by Le and Hu (Le and Hu, NMR Biomed 1997;10:160–164). The proposed methods provide more accurate means of estimating the true ROC curve from real data and thereby aid in the comparative evaluation of a wide range of postprocessing tools in fMRI. The mathematical relationships between different ROC curves are explored for a comparison of different ROC methods. Examples using real and simulated data are provided to illustrate the ideas involved. Magn Reson Med 52:1424–1431, 2004.