Fuzzy clustering of gradient-echo functional MRI in the human visual cortex. Part II: quantification

Analysis of fMRI Signals from Working Memory Tasks and Resting-State of Brain: Neutrosophic-Entropy-Based Clustering Algorithm

This study applies a neutrosophic-entropy-based clustering algorithm (NEBCA) to analyze the fMRI signals. We consider the data obtained from four different working memory tasks and the brain's resting state for the experimental purpose. Three non-overlapping clusters of data related to temporal brain activity are determined and statistically analyzed. Moreover, we used the Uniform Manifold Approximation and Projection (UMAP) method to reduce system dimensionality and present the effectiveness of NEBCA. The results show that using NEBCA, we are able to distinguish between different working memory tasks and resting-state and identify subtle differences in the related activity of brain regions. By analyzing the statistical properties of the entropy inside the clusters, the various regions of interest (ROIs), according to Automated Anatomical Labeling (AAL) atlas crucial for clustering procedure, are determined. The inferior occipital gyrus is established as an important brain region in distinguishing the resting state from the tasks. Moreover, the inferior occipital gyrus and superior parietal lobule are identified as necessary to correct the data discrimination related to the different memory tasks. We verified the statistical significance of the results through the two-sample t-test and analysis of surrogates performed by randomization of the cluster elements. The presented methodology is also appropriate to determine the influence of time of day on brain activity patterns. The differences between working memory tasks and resting-state in the morning are related to a lower index of small-worldness and sleep inertia in the first hours after waking. We also compared the performance of NEBCA to two existing algorithms, KMCA and FKMCA. We showed the advantage of the NEBCA over these algorithms that could not effectively accumulate fMRI signals with higher variability.

The dynamic functional connectome: State-of-the-art and perspectives

Resting-state functional magnetic resonance imaging (fMRI) has highlighted the rich structure of brain activity in absence of a task or stimulus. A great effort has been dedicated in the last two decades to investigate functional connectivity (FC), i.e. the functional interplay between different regions of the brain, which was for a long time assumed to have stationary nature. Only recently was the dynamic behaviour of FC revealed, showing that on top of correlational patterns of spontaneous fMRI signal fluctuations, connectivity between different brain regions exhibits meaningful variations within a typical resting-state fMRI experiment. As a consequence, a considerable amount of work has been directed to assessing and characterising dynamic FC (dFC), and several different approaches were explored to identify relevant FC fluctuations. At the same time, several questions were raised about the nature of dFC, which would be of interest only if brought back to a neural origin. In support of this, correlations with electroencephalography (EEG) recordings, demographic and behavioural data were established, and various clinical applications were explored, where the potential of dFC could be preliminarily demonstrated. In this review, we aim to provide a comprehensive description of the dFC approaches proposed so far, and point at the directions that we see as most promising for the future developments of the field. Advantages and pitfalls of dFC analyses are addressed, helping the readers to orient themselves through the complex web of available methodologies and tools.

Select and Cluster: A Method for Finding Functional Networks of Clustered Voxels in fMRI

Extracting functional connectivity patterns among cortical regions in fMRI datasets is a challenge stimulating the development of effective data-driven or model based techniques. Here, we present a novel data-driven method for the extraction of significantly connected functional ROIs directly from the preprocessed fMRI data without relying on a priori knowledge of the expected activations. This method finds spatially compact groups of voxels which show a homogeneous pattern of significant connectivity with other regions in the brain. The method, called Select and Cluster (S&C), consists of two steps: first, a dimensionality reduction step based on a blind multiresolution pairwise correlation by which the subset of all cortical voxels with significant mutual correlation is selected and the second step in which the selected voxels are grouped into spatially compact and functionally homogeneous ROIs by means of a Support Vector Clustering (SVC) algorithm. The S&C method is described in detail. Its performance assessed on simulated and experimental fMRI data is compared to other methods commonly used in functional connectivity analyses, such as Independent Component Analysis (ICA) or clustering. S&C method simplifies the extraction of functional networks in fMRI by identifying automatically spatially compact groups of voxels (ROIs) involved in whole brain scale activation networks.

Temporal-spatial mean-shift clustering analysis to improve functional MRI activation detection

Cluster analysis (CA) is often used in functional magnetic resonance imaging (fMRI) analysis to improve detection of functional activations. Commonly used clustering techniques typically only consider spatial information of a statistical parametric image (SPI) in their calculations. This study examines incorporating the temporal characteristics of acquired fMRI data with mean-shift clustering (MSC) for fMRI analysis to enhance activation detections. Simulated data and real fMRI data was used to compare the commonly used cluster analysis with MSC using a feature space containing temporal characteristics. Receiver Operating Characteristic curves show that improvements in low contrast to noise scenarios using MSC over CA and our previous MSC technique at all tested simulated activation sizes. The proposed MSC technique with a feature space using both temporal and spatial data characteristics shows improved activation detection for both simulated and real Blood oxygen level dependent (BOLD) fMRI data (approximately 60% increase). The proposed techniques are useful in techniques that inherently have low contrast to noise ratios, such as non-proton imaging or high resolution BOLD fMRI.

Scanning fast and slow: current limitations of 3 Tesla functional MRI and future potential

Functional MRI at 3T has become a workhorse for the neurosciences, e.g., neurology, psychology, and psychiatry, enabling non-invasive investigation of brain function and connectivity. However, BOLD-based fMRI is a rather indirect measure of brain function, confounded by physiology related signals, e.g., head or brain motion, brain pulsation, blood flow, intermixed with susceptibility differences close or distant to the region of neuronal activity. Even though a plethora of preprocessing strategies have been published to address these confounds, their efficiency is still under discussion. In particular, physiological signal fluctuations closely related to brain supply may mask BOLD signal changes related to "true" neuronal activation. Here we explore recent technical and methodological advancements aimed at disentangling the various components, employing fast multiband vs. standard EPI, in combination with fast temporal ICA. Our preliminary results indicate that fast (TR <0.5 s) scanning may help to identify and eliminate physiologic components, increasing tSNR and functional contrast. In addition, biological variability can be studied and task performance better correlated to other measures. This should increase specificity and reliability in fMRI studies. Furthermore, physiological signal changes during scanning may then be recognized as a source of information rather than a nuisance. As we are currently still undersampling the complexity of the brain, even at a rather coarse macroscopic level, we should be very cautious in the interpretation of neuroscientific findings, in particular when comparing different groups (e.g., age, sex, medication, pathology, etc.). From a technical point of view our goal should be to sample brain activity at layer specific resolution with low TR, covering as much of the brain as possible without violating SAR limits. We hope to stimulate discussion toward a better understanding and a more quantitative use of fMRI.

Application of mean-shift clustering to blood oxygen level dependent functional MRI activation detection

Background

Functional magnetic resonance imaging (fMRI) analysis is commonly done with cross-correlation analysis (CCA) and the General Linear Model (GLM). Both CCA and GLM techniques, however, typically perform calculations on a per-voxel basis and do not consider relationships neighboring voxels may have. Clustered voxel analyses have then been developed to improve fMRI signal detections by taking advantages of relationships of neighboring voxels. Mean-shift clustering (MSC) is another technique which takes into account properties of neighboring voxels and can be considered for enhancing fMRI activation detection.

Methods

This study examines the adoption of MSC to fMRI analysis. MSC was applied to a Statistical Parameter Image generated with the CCA technique on both simulated and real fMRI data. The MSC technique was then compared with CCA and CCA plus cluster analysis. A range of kernel sizes were used to examine how the technique behaves.

Results

Receiver Operating Characteristic curves shows an improvement over CCA and Cluster analysis. False positive rates are lower with the proposed technique. MSC allows the use of a low intensity threshold and also does not require the use of a cluster size threshold, which improves detection of weak activations and highly focused activations.

Conclusion

The proposed technique shows improved activation detection for both simulated and real Blood Oxygen Level Dependent fMRI data. More detailed studies are required to further develop the proposed technique.

Search for patterns of functional specificity in the brain: a nonparametric hierarchical Bayesian model for group fMRI data

Functional MRI studies have uncovered a number of brain areas that demonstrate highly specific functional patterns. In the case of visual object recognition, small, focal regions have been characterized with selectivity for visual categories such as human faces. In this paper, we develop an algorithm that automatically learns patterns of functional specificity from fMRI data in a group of subjects. The method does not require spatial alignment of functional images from different subjects. The algorithm is based on a generative model that comprises two main layers. At the lower level, we express the functional brain response to each stimulus as a binary activation variable. At the next level, we define a prior over sets of activation variables in all subjects. We use a Hierarchical Dirichlet Process as the prior in order to learn the patterns of functional specificity shared across the group, which we call functional systems, and estimate the number of these systems. Inference based on our model enables automatic discovery and characterization of dominant and consistent functional systems. We apply the method to data from a visual fMRI study comprised of 69 distinct stimulus images. The discovered system activation profiles correspond to selectivity for a number of image categories such as faces, bodies, and scenes. Among systems found by our method, we identify new areas that are deactivated by face stimuli. In empirical comparisons with previously proposed exploratory methods, our results appear superior in capturing the structure in the space of visual categories of stimuli.

Discovering structure in the space of fMRI selectivity profiles

We present a method for discovering patterns of selectivity in fMRI data for experiments with multiple stimuli/tasks. We introduce a representation of the data as profiles of selectivity using linear regression estimates, and employ mixture model density estimation to identify functional systems with distinct types of selectivity. The method characterizes these systems by their selectivity patterns and spatial maps, both estimated simultaneously via the EM algorithm. We demonstrate a corresponding method for group analysis that avoids the need for spatial correspondence among subjects. Consistency of the selectivity profiles across subjects provides a way to assess the validity of the discovered systems. We validate this model in the context of category selectivity in visual cortex, demonstrating good agreement with the findings based on prior hypothesis-driven methods.

Evaluation and optimization of fMRI single-subject processing pipelines with NPAIRS and second-level CVA

In functional magnetic resonance imaging (fMRI) analysis, although the univariate general linear model (GLM) is currently the dominant approach to brain activation detection, there is growing interest in multivariate approaches such as principal component analysis, canonical variate analysis (CVA), independent component analysis and cluster analysis, which have the potential to reveal neural networks and functional connectivity in the brain. To understand the effect of processing options on performance of multivariate model-based fMRI processing pipelines with real fMRI data, we investigated the impact of commonly used fMRI preprocessing steps and optimized the associated multivariate CVA-based, single-subject processing pipelines with the NPAIRS (nonparametric prediction, activation, influence and reproducibility resampling) performance metrics [prediction accuracy and statistical parametric image (SPI) reproducibility] on the Fiswidgets platform. We also compared the single-subject SPIs of univariate GLM with multivariate CVA-based processing pipelines from SPM, FSL.FEAT, NPAIRS.GLM and NPAIRS.CVA software packages (or modules) using a novel second-level CVA. We found that for the block-design data, (a) slice timing correction and global intensity normalization have little consistent impact on the fMRI processing pipeline, but spatial smoothing, temporal detrending or high-pass filtering, and motion correction significantly improved pipeline performance across all subjects; (b) the combined optimization of spatial smoothing, temporal detrending and CVA model parameters on average improved between-subject reproducibility; and (c) the most important pipeline choices include univariate or multivariate statistical models and spatial smoothing. This study suggests that considering options other than simply using GLM with a fixed spatial filter may be of critical importance in determining activation patterns in BOLD fMRI studies.

Spatial Patterns and Functional Profiles for Discovering Structure in fMRI Data

We explore unsupervised, hypothesis-free methods for fMRI analysis in two different types of experiments. First, we employ clustering to identify large-scale functionally homogeneous systems. We formulate a generative mixture model, derive the EM algorithm and apply it to delineate functional systems. We also investigate spectral clustering in application to this problem and demonstrate that both methods give rise to similar partitions of the brain based on resting state fMRI data. Second, we demonstrate how to extend this approach to include information about the experimental protocol. Specifically, we formulate a mixture model in the space of possible profiles of brain response to stimuli. In both applications, our methods confirm previously known results in brain mapping and point to new research directions for exploratory analysis of fMRI data.

Detection of spatial activation patterns as unsupervised segmentation of fMRI data

In functional connectivity analysis, networks of interest are defined based on correlation with the mean time course of a user-selected 'seed' region. In this work we propose to simultaneously estimate the optimal representative time courses that summarize the fMRI data well and the partition of the volume into a set of disjoint regions that are best explained by these representative time courses. Our approach offers two advantages. First, is removes the sensitivity of the analysis to the details of the seed selection. Second, it substantially simplifies group analysis by eliminating the need for a subject-specific threshold at which correlation values are deemed significant. This unsupervised technique generalizes connectivity analysis to situations where candidate seeds are difficult to identify reliably or are unknown. Our experimental results indicate that the functional segmentation provides a robust, anatomically meaningful and consistent model for functional connectivity in fMRI.

Data-driven clustering reveals a fundamental subdivision of the human cortex into two global systems

Global organizational principles are critical for understanding cortical functionality. Recently, we proposed a global sub-division of the posterior cortex into two large-scale systems. One system, labeled extrinsic, comprises the sensory-motor cortex, and is associated with the external environment. The second system, labeled intrinsic, overlaps substantially with the previously described "default-mode" network, and is likely associated with inner-oriented processing. This global partition of the cerebral cortex emerged from hemodynamic imaging data the analysis of which was constrained by pre-determined hypotheses. Here we applied a hypothesis-free, unsupervised two-class clustering algorithm (k-means) to a large set of fMRI data. The two clusters delineated by this unsupervised hypothesis-free procedure showed high anatomical consistency across individuals, and their cortical topography coincided largely with the previously determined extrinsic and intrinsic systems. These new clustering-based results confirm that the intrinsic-extrinsic subdivision constitutes a fundamental cortical divide.

Dissecting cognitive stages with time-resolved fMRI data: a comparison of fuzzy clustering and independent component analysis

In combination with cognitive tasks entailing sequences of sensory and cognitive processes, event-related acquisition schemes allow using functional MRI to examine not only the topography but also the temporal sequence of cortical activation across brain regions (time-resolved fMRI). In this study, we compared two data-driven methods--fuzzy clustering method (FCM) and independent component analysis (ICA)--in the context of time-resolved fMRI data collected during the performance of a newly devised visual imagery task. We analyzed a multisubject fMRI data set using both methods and compared their results in terms of within- and between-subject consistency and spatial and temporal correspondence of obtained maps and time courses. Both FCM and spatial ICA allowed discriminating the contribution of distinct networks of brain regions to the main cognitive stages of the task (auditory perception, mental imagery and behavioural response), with good agreement across methods. Whereas ICA worked optimally on the original time series, averaging with respect to the task onset (and thus introducing some a priori information on the stimulation protocol) was found to be indispensable in the case of FCM. On averaged time series, FCM led to a richer decomposition of the spatio-temporal patterns of activation and allowed a finer separation of the neurocognitive processes subserving the mental imagery task. This study confirms the efficacy of the two examined methods in the data-driven estimation of hemodynamic responses in time-resolved fMRI studies and provides empirical guidelines to their use.

Functional magnetic resonance imaging activation detection: fuzzy cluster analysis in wavelet and multiwavelet domains

PURPOSE

To present novel feature spaces, based on multiscale decompositions obtained by scalar wavelet and multiwavelet transforms, to remedy problems associated with high dimension of functional magnetic resonance imaging (fMRI) time series (when they are used directly in clustering algorithms) and their poor signal-to-noise ratio (SNR) that limits accurate classification of fMRI time series according to their activation contents.

MATERIALS AND METHODS

Using randomization, the proposed method finds wavelet/multiwavelet coefficients that represent the activation content of fMRI time series and combines them to define new feature spaces. Using simulated and experimental fMRI data sets, the proposed feature spaces are compared to the cross-correlation (CC) feature space and their performances are evaluated. In these studies, the false positive detection rate is controlled using randomization. To compare different methods, several points of the receiver operating characteristics (ROC) curves, using simulated data, are estimated and compared.

RESULTS

The proposed features suppress the effects of confounding signals and improve activation detection sensitivity. Experimental results show improved sensitivity and robustness of the proposed method compared to the conventional CC analysis.

CONCLUSION

More accurate and sensitive activation detection can be achieved using the proposed feature spaces compared to CC feature space. Multiwavelet features show superior detection sensitivity compared to the scalar wavelet features.

A quantitative comparison of functional MRI cluster analysis

The aim of this work is to compare the efficiency and power of several cluster analysis techniques on fully artificial (mathematical) and synthesized (hybrid) functional magnetic resonance imaging (fMRI) data sets. The clustering algorithms used are hierarchical, crisp (neural gas, self-organizing maps, hard competitive learning, k-means, maximin-distance, CLARA) and fuzzy (c-means, fuzzy competitive learning). To compare these methods we use two performance measures, namely the correlation coefficient and the weighted Jaccard coefficient (wJC). Both performance coefficients (PCs) clearly show that the neural gas and the k-means algorithm perform significantly better than all the other methods using our setup. For the hierarchical methods the ward linkage algorithm performs best under our simulation design. In conclusion, the neural gas method seems to be the best choice for fMRI cluster analysis, given its correct classification of activated pixels (true positives (TPs)) whilst minimizing the misclassification of inactivated pixels (false positives (FPs)), and in the stability of the results achieved.

A STAP algorithm approach to fMRI: a simulation study

PURPOSE

To adapt the space-time adaptive processing (STAP) algorithm, previously developed in the field of sensor array processing and applied to radar signal processing, for use in construction of brain activation maps in functional magnetic resonance imaging (fMRI).

MATERIALS AND METHODS

STAP is a two-dimensional filter in which both the spatial and temporal responses are controlled adaptively. It processes space-time data as a complete spatiotemporal set. Unlike presently used fMRI techniques, STAP locates activated regions both spatially and in frequency.

RESULTS

Computer simulations incorporating actual MRI noise indicate that STAP exhibits a high degree of accuracy in detecting the small signal intensity changes inherent in fMRI.

CONCLUSION

Because STAP processes space-time data as a single data matrix, it exhibits potential over currently available fMRI methods in providing a measure of the full spatiotemporal extent of a task-related activity.

Wavelet-based multifractal analysis of fMRI time series

Functional magnetic resonance imaging (fMRI) time series are investigated with a multifractal method based on the Wavelet Modulus Maxima (WTMM) method to extract local singularity ("fractal") exponents. The spectrum of singularity exponents of each fMRI time series is quantified by spectral characteristics including its maximum and the corresponding dimension. We found that the range of Hölder exponents in voxels with activation is close to 1, whereas exponents are close to 0.5 in white matter voxels without activation. The maximum dimension decreases going from white matter to gray matter, and is lower still for activated time series. The full-width-at-half-maximum of the spectra is higher in activated areas. The proposed method becomes particularly effective when combining these spectral characteristics into a single parameter. Using these multifractal parameters, it is possible to identify activated areas in the human brain in both hybrid and in vivo fMRI data sets without knowledge of the stimulation paradigm applied.

Independent component analysis of functional MRI: what is signal and what is noise?

Many sources of fluctuation contribute to the functional magnetic resonance imaging (fMRI) signal, complicating attempts to infer those changes that are truly related to brain activation. Unlike methods of analysis of fMRI data that test the time course of each voxel against a hypothesized waveform, data-driven methods, such as independent component analysis and clustering, attempt to find common features within the data. This exploratory approach can be revealing when the brain activation is difficult to predict beforehand, such as with complex stimuli and internal shifts of activation that are not time-locked to an easily specified sensory or motor event. These methods can be further improved by incorporating prior knowledge regarding the temporal and spatial extent of brain activation.

Fuzzy cluster analysis of high-field functional MRI data

Functional magnetic resonance imaging (fMRI) based on blood-oxygen level dependent (BOLD) contrast today is an established brain research method and quickly gains acceptance for complementary clinical diagnosis. However, neither the basic mechanisms like coupling between neuronal activation and haemodynamic response are known exactly, nor can the various artifacts be predicted or controlled. Thus, modeling functional signal changes is non-trivial and exploratory data analysis (EDA) may be rather useful. In particular, identification and separation of artifacts as well as quantification of expected, i.e. stimulus correlated, and novel information on brain activity is important for both, new insights in neuroscience and future developments in functional MRI of the human brain. After an introduction on fuzzy clustering and very high-field fMRI we present several examples where fuzzy cluster analysis (FCA) of fMRI time series helps to identify and locally separate various artifacts. We also present and discuss applications and limitations of fuzzy cluster analysis in very high-field functional MRI: differentiate temporal patterns in MRI using (a) a test object with static and dynamic parts, (b) artifacts due to gross head motion artifacts. Using a synthetic fMRI data set we quantitatively examine the influences of relevant FCA parameters on clustering results in terms of receiver-operator characteristics (ROC) and compare them with a commonly used model-based correlation analysis (CA) approach. The application of FCA in analyzing in vivo fMRI data is shown for (a) a motor paradigm, (b) data from multi-echo imaging, and (c) a fMRI study using mental rotation of three-dimensional cubes. We found that differentiation of true "neural" from false "vascular" activation is possible based on echo time dependence and specific activation levels, as well as based on their signal time-course. Exploratory data analysis methods in general and fuzzy cluster analysis in particular may help to identify artifacts and add novel and unexpected information valuable for interpretation, classification and characterization of functional MRI data which can be used to design new data acquisition schemes, stimulus presentations, neuro(physio)logical paradigms, as well as to improve quantitative biophysical models.

Human motor cortex activity during mental rotation

The functional role of human premotor and primary motor cortex during mental rotation has been studied using functional MRI at 3 T. Fourteen young, male subjects performed a mental rotation task in which they had to decide whether two visually presented cubes could be identical. Exploratory Fuzzy Cluster Analysis was applied to identify brain regions with stimulus-related time courses. This revealed one dominant cluster which included the parietal cortex, premotor cortex, and dorsolateral prefrontal cortex that showed signal enhancement during the whole stimulus presentation period, reflecting cognitive processing. A second cluster, encompassing the contralateral primary motor cortex, showed activation exclusively after the button press response. This clear separation was possible in 3 subjects only, however. Based on these exploratory results, the hypothesis that primary motor cortex activity was related to button pressing only was tested using a parametric approach via a random-effects group analysis over all 14 subjects in SPM99. The results confirmed that the stimulus response via button pressing causes activation in the primary motor cortex and supplementary motor area while parietal cortex and mesial regions rostral to the supplementary motor area are recruited for the actual mental rotation process.

Region growing method for the analysis of functional MRI data

Existing analytical techniques for functional magnetic resonance imaging (fMRI) data always need some specific assumptions on the time series. In this article, we present a new approach for fMRI activation detection, which can be implemented without any assumptions on the time series. Our method is based on a region growing method, which is very popular for image segmentation. A comparison of performance on fMRI activation detection is made between the proposed method and the deconvolution method and the fuzzy clustering method with receiver operating characteristic (ROC) methodology. In addition, we examine the effectiveness and usefulness of our method on real experimental data. Experimental results show that our method outperforms over the deconvolution method and the fuzzy clustering method on a number of aspects. These results suggest that our region growing method can serve as a reliable analysis of fMRI data.

Cluster analysis of muscle functional MRI data

Muscle functional magnetic resonance imaging (mfMRI) is frequently used to determine spatial patterns of muscle involvement in exercising humans. A frequent finding in mfMRI is that, even within synergistic muscle groups, signal intensity (SI) data from individual voxels can be quite heterogeneous. The purpose of this study was to develop a novel method for organizing heterogeneous mfMRI data into clusters whose members behave similarly to each other but distinctly from members of other clusters and apply it in studies of functional compartmentalization in the anterior compartment of the leg. An algorithm was developed that compared the SI time courses of adjacent voxels and grouped together voxels that were sufficiently similar. The algorithm's performance was verified by using simulated data sets with known regional differences in SI time courses that were then applied to experimental mfMRI data acquired from six male subjects (age 22.6 +/- 0.9 yr, mean +/- SE) who sustained isometric contractions of the dorsiflexors at 40% of maximum voluntary contraction. The experimental data were also characterized by using a traditional analysis (user-specified regions of interest from a single image), in which the relative change in SI and the contrast-to-noise ratio [CNR; 100%x(SI(RESTING) - SI(ACTIVE)/(noise standard deviation)] were measured. In general, clusters were found in areas in which the CNR exceeded 5. Cluster analysis made functional distinctions between regions of muscle that were not seen with traditional analysis. In conclusion, cluster analysis's use of the full SI time course provides more sensitivity to muscle functional compartmentation than traditional analysis.

Exploring regions of interest with cluster analysis (EROICA) using a spectral peak statistic for selecting and testing the significance of fMRI activation time-series

Much relevant information about activations and artifacts in a functional magnetic resonance imaging (fMRI) dataset can be obtained from an exploratory cluster analysis. In contrast to testing the significance of the measured experimental effect for a given model, unsupervised pattern recognition techniques, such as fuzzy clustering, often find unexpected behavior in addition to expected activations, allowing the exploitation of this element of surprise. The many artifact clusters often discovered might aid the experimenter in deciding whether the dataset is usable, whether some additional preprocessing step is required, or whether the one used has introduced spurious effects. However, clustering alone does not complete the analysis because the membership values that are generated are not indicative of the level of statistical significance with respect to the cluster activation patterns (centroids). This is of particular importance for fMRI datasets for which most time-series are "noise", with no activation patterns. We propose that an initial partition step should precede the clustering step. Only time-series that meet a certain statistical criterion (using a scaled version of Fisher's g-order statistic) are selected for clustering; this typically represents <5% of the whole brain region. The purpose of clustering is to generate a set of cluster centers that are the possible activation patterns; these are used in forming a linear model of all the time-series. The model parameter is tested for significance in both the time and frequency domains. We present a novel method of conducting these tests, which limits the number of false positives. We call the three-step process of initial partition, clustering and the two-domain significance test as exploring regions of interest with cluster analysis (EROICA).

Feature-space clustering for fMRI meta-analysis

Clustering functional magnetic resonance imaging (fMRI) time series has emerged in recent years as a possible alternative to parametric modeling approaches. Most of the work so far has been concerned with clustering raw time series. In this contribution we investigate the applicability of a clustering method applied to features extracted from the data. This approach is extremely versatile and encompasses previously published results [Goutte et al., 1999] as special cases. A typical application is in data reduction: as the increase in temporal resolution of fMRI experiments routinely yields fMRI sequences containing several hundreds of images, it is sometimes necessary to invoke feature extraction to reduce the dimensionality of the data space. A second interesting application is in the meta-analysis of fMRI experiment, where features are obtained from a possibly large number of single-voxel analyses. In particular this allows the checking of the differences and agreements between different methods of analysis. Both approaches are illustrated on a fMRI data set involving visual stimulation, and we show that the feature space clustering approach yields nontrivial results and, in particular, shows interesting differences between individual voxel analysis performed with traditional methods.

Contextual clustering for analysis of functional MRI data

We present a contextual clustering procedure for statistical parametric maps (SPM) calculated from time varying three-dimensional images. The algorithm can be used for the detection of neural activations from functional magnetic resonance images (fMRI). An important characteristic of SPM is that the intensity distribution of background (nonactive area) is known whereas the distributions of activation areas are not. The developed contextual clustering algorithm divides an SPM into background and activation areas so that the probability of detecting false activations by chance is controlled, i.e., hypothesis testing is performed. Unlike the much used voxel-by-voxel testing, neighborhood information is utilized, an important difference. This is achieved by using a Markov random field prior and iterated conditional modes (ICM) algorithm. However, unlike in the conventional use of ICM algorithm, the classification is based only on the distribution of background. The results from our simulations and human fMRI experiments using visual stimulation demonstrate that a better sensitivity is achieved with a given specificity in comparison to the voxel-by-voxel thresholding technique. The algorithm is computationally efficient and can be used to detect and delineate objects from a noisy background in other applications.

Functional MRI of the human motor cortex using single-shot, multiple gradient-echo spiral imaging

In this study, we combined the advantages of a fast multi-slice spiral imaging approach with a multiple gradient-echo sampling scheme at high magnetic field strength to improve quantification of BOLD and inflow effects and to estimate T2* relaxation times in functional brain imaging. Eight echoes are collected with echo time (TE) ranging from 5 to 180 ms. Acquisition time per slice and echo time is 25 ms for a nominal resolution of 4 x 4 x 4 mm3. Evaluation of parameter images during rest and stimulation yields no significant activation on the inflow sensitive spin-density images (rho or I0-maps) whereas clear activation patterns in primary human motor cortex (M1) and supplementary motor area (SMA) are detected on BOLD sensitive T2*-maps. The calculation of relaxation times and rates of the activated areas over all subjects yields an average T2* +/- standard deviation (SD) of 46.1+/-4.5 ms (R2* of 21.8+/-2.2 s(-1)) and an average increase (deltaT2* +/- SD) of 0.93+/-0.47 ms (deltaR2* of -0.4+/-0.14 s(-1)). Our findings demonstrate the usefulness of a multiple gradient echo data acquisition approach in separating various vascular contributions to brain activation in fMRI.

Plurality and resemblance in fMRI data analysis

We apply nine analytic methods employed currently in imaging neuroscience to simulated and actual BOLD fMRI signals and compare their performances under each signal type. Starting with baseline time series generated by a resting subject during a null hypothesis study, we compare method performance with embedded focal activity in these series of three different types whose magnitudes and time courses are simple, convolved with spatially varying hemodynamic responses, and highly spatially interactive. We then apply these same nine methods to BOLD fMRI time series from contralateral primary motor cortex and ipsilateral cerebellum collected during a sequential finger opposition study. Paired comparisons of results across methods include a voxel-specific concordance correlation coefficient for reproducibility and a resemblance measure that accommodates spatial autocorrelation of differences in activity surfaces. Receiver-operating characteristic curves show considerable model differences in ranges less than 10% significance level (false positives) and greater than 80% power (true positives). Concordance and resemblance measures reveal significant differences between activity surfaces in both data sets. These measures can assist researchers by identifying groups of models producing similar and dissimilar results, and thereby help to validate, consolidate, and simplify reports of statistical findings. A pluralistic strategy for fMRI data analysis can uncover invariant and highly interactive relationships between local activity foci and serve as a basis for further discovery of organizational principles of the brain. Results also suggest that a pluralistic empirical strategy coupled formally with substantive prior knowledge can help to uncover new brain-behavior relationships that may remain hidden if only a single method is employed.

Stability, repeatability, and the expression of signal magnitude in functional magnetic resonance imaging

In 23 fMRI studies on six subjects, we examined activation in visual and motor tasks. We modeled the expected activation time course by convolving a temporal description of the behavioral task with an empirically determined impulse response function. We evaluated the signal activation intensity as both the number of activated voxels over arbitrary correlation thresholds and as the slope of the regression line between our modeled time course and the actual data. Whereas the voxel counting was strikingly unstable (standard deviation 74% in visual trials at a correlation of 0.5), the slope was relatively constant across trials and subjects (standard deviation <14%). Using Monte Carlo methods, we determined that the measured slope was largely independent of the contrast-to-noise ratio. Voxel counting is a poor proxy for activation intensity, with greatly increased scatter, much reduced statistical power, and increased type II error. The data support an alternative approach to functional magnetic resonance imaging (fMRI) that allows for quantitative comparisons of fMRI response magnitudes across trials and laboratories.

A hierarchical clustering method for analyzing functional MR images

We introduce a novel method for detecting anatomic and functional structures in fMRI. The main idea is to divide the data hierarchically into smaller groups using k-means clustering. The separation is halted if the clusters contain no further structure that is verified by several independent tests. The resulting cluster centers are then used for computing the final results in one step. The procedure is flexible, fast to compute, and the numbers of clusters in the data are obtained in a data-driven manner. Applying the algorithm to synthetic fMRI data yields perfect separation of "anatomic," i.e., time-invariant, and "functional," i.e., time-varying, information for a standard off-on paradigm and a typical functional contrast-to-noise ratio of two and higher. In addition, an EPI-fMRI data set of the human motor cortex was analyzed to demonstrate the performance of this novel approach in vivo.

Dynamical cluster analysis of cortical fMRI activation

Localized changes in cortical blood oxygenation during voluntary movements were examined with functional magnetic resonance imaging (fMRI) and evaluated with a new dynamical cluster analysis (DCA) method. fMRI was performed during finger movements with eight subjects on a 1.5-T scanner using single-slice echo planar imaging with a 107-ms repetition time. Clustering based on similarity of the detailed signal time courses requires besides the used distance measure no assumptions about spatial location and extension of activation sites or the shape of the expected activation time course. We discuss the basic requirements on a clustering algorithm for fMRI data. It is shown that with respect to easy adjustment of the quantization error and reproducibility of the results DCA outperforms the standard k-means algorithm. In contrast to currently used clustering methods for fMRI, like k-means or fuzzy k-means, DCA extracts the appropriate number and initial shapes of representative signal time courses from data properties during run time. With DCA we simultaneously calculate a two-dimensional projection of cluster centers (MDS) and data points for online visualization of the results. We describe the new DCA method and show for the well-studied motor task that it detects cortical activation loci and provides additional information by discriminating different shapes and phases of hemodynamic responses. Robustness of activity detection is demonstrated with respect to repeated DCA runs and effects of different data preprocessing are shown. As an example of how DCA enables further analysis we examined activation onset times. In areas SMA, M1, and S1 simultaneous and sequential activation (in the given order) was found.

High-resolution, multiple gradient-echo functional MRI at 1.5 T

A multiple gradient echo, high resolution imaging method is proposed to better visualize different sources of activation in functional magnetic resonance imaging (fMRI) experiments. Eight echoes are collected from 30 ms to 205 ms with an echo spacing of 25 ms. All echoes show significant activation, but each echo reveals its own pattern of activation. From this variability, it appears that large vessel contributions can be separated from small vessel contributions using a fuzzy cluster analysis across echo times. The results demonstrate the importance of a multiple gradient echo data acquisition approach in localizing various vascular contributions to brain activation in fMRI.

On clustering fMRI time series

Analysis of fMRI time series is often performed by extracting one or more parameters for the individual voxels. Methods based, e.g., on various statistical tests are then used to yield parameters corresponding to probability of activation or activation strength. However, these methods do not indicate whether sets of voxels are activated in a similar way or in different ways. Typically, delays between two activated signals are not identified. In this article, we use clustering methods to detect similarities in activation between voxels. We employ a novel metric that measures the similarity between the activation stimulus and the fMRI signal. We present two different clustering algorithms and use them to identify regions of similar activations in an fMRI experiment involving a visual stimulus.

Quantification in functional magnetic resonance imaging: fuzzy clustering vs. correlation analysis

The potential of functional MRI (fMRI) data analysis using the paradigm independent fuzzy cluster analysis (FCA) applied in the time domain compared to frequently used paradigm based correlation analysis (CA) was studied with simulated and in vivo fMRI data. The performance of FCA and CA was investigated in a typical contrast-to-noise range for fMRI, ranging from 1.33 to 3.33. Using simulated fMRI data the methods were quantitatively compared in terms of generation of true positives, false positives, and the corresponding signal enhancement. Even without prior knowledge about the stimulation paradigm and the actual hemodynamic response function the performance of FCA was comparable to that of CA where extensive prior knowledge has to be added. Furthermore, discrimination of nonanticipated hemodynamic responses by FCA, such as different levels of activation and delayed response, are demonstrated in simulated and in vivo fMRI data. We demonstrate that using CA one cannot differentiate between these responses at least without extensive prior knowledge, i.e., FCA yields a more particular description of fMRI data. This may be worthwhile for analysis and optimization of data quality in fMRI as well as in the final data analysis.