Comparison of two exploratory data analysis methods for fMRI: fuzzy clustering vs. principal component analysis

Exploratory data-driven methods such as Fuzzy clustering analysis (FCA) and Principal component analysis (PCA) may be considered as hypothesis-generating procedures that are complementary to the hypothesis-led statistical inferential methods in functional magnetic resonance imaging (fMRI). Here, a comparison between FCA and PCA is presented in a systematic fMRI study, with MR data acquired under the null condition, i.e., no activation, with different noise contributions and simulated, varying "activation." The contrast-to-noise (CNR) ratio ranged between 1-10. We found that if fMRI data are corrupted by scanner noise only, FCA and PCA show comparable performance. In the presence of other sources of signal variation (e.g., physiological noise), FCA outperforms PCA in the entire CNR range of interest in fMRI, particularly for low CNR values. The comparison method that we introduced may be used to assess other exploratory approaches such as independent component analysis or neural network-based techniques.     

Controlling the false positive rate in fuzzy clustering using randomization: application to fMRI activation detection

Despite its potential advantages for fMRI analysis, fuzzy C-means (FCM) clustering suffers from limitations such as the need for a priori knowledge of the number of clusters, and unknown statistical significance and instability of the results. We propose a randomization-based method to control the false-positive rate and estimate statistical significance of the FCM results. Using this novel approach, we develop an fMRI activation detection method. The ability of the method in controlling the false-positive rate is shown by analysis of false positives in activation maps of resting-state fMRI data. Controlling the false-positive rate in FCM allows comparison of different fuzzy clustering methods, using different feature spaces, to other fMRI detection methods. In this article, using simulation and real fMRI data, we compare a novel feature space that takes the variability of the hemodynamic response function into account (HRF-based feature space) to the conventional cross-correlation analysis and FCM using the cross-correlation feature space. In both cases, the HRF-based feature space provides a greater sensitivity compared to the cross-correlation feature space and conventional cross-correlation analysis. Application of the proposed method to finger-tapping fMRI data, using HRF-based feature space, detected activation in sub-cortical regions, whereas both of the FCM with cross-correlation feature space and the conventional cross-correlation method failed to detect them.     

Improvement of spectral density-based activation detection of event-related fMRI data

For event-related data obtained from an experimental paradigm with a periodic design, spectral density at the fundamental frequency of the paradigm has been used as a template-free activation detection measure. In this article, we build and expand upon this detection measure to create an improved, integrated measure. Such an integrated measure linearly combines information contained in the spectral densities at the fundamental frequency as well as the harmonics of the paradigm and in a spatial correlation function characterizing the degree of co-activation among neighboring voxels. Several figures of merit are described and used to find appropriate values for the coefficients in the linear combination. Using receiver-operating characteristic analysis on simulated functional magnetic resonance imaging (fMRI) data sets, we quantify and validate the improved performance of the integrated measure over the spectral density measure based on the fundamental frequency as well as over some other popular template-free data analysis methods. We then demonstrate the application of the new method on an experimental fMRI data set. Finally, several extensions to this work are suggested.     

Derivative temporal clustering analysis: detecting prolonged neuronal activity

Temporal clustering analysis (TCA) and independent component analysis (ICA) are promising data-driven techniques in functional magnetic resonance imaging (fMRI) experiments to obtain brain activation maps in conditions with unknown temporal information regarding the neuronal activity. Although comparable to ICA in detecting transient neuronal activities, TCA fails to detect prolonged plateau brain activations. To eliminate this pitfall, a novel derivative TCA (DTCA) method was introduced and its algorithms with different subtraction intervals were tested on simulated data with a pattern of prolonged plateau brain activation. It was found that the best performance of DTCA method in generating functional maps could be obtained if the subtraction interval is equal to or larger than the length of the rising time of the fMRI response. The DTCA method and its theoretical predication were further investigated and validated using in vivo fMRI data sets. By removing the limitations in the previous TCA, DTCA has shown its powerful capability in detecting prolonged plateau neuronal activities.     

A signal subspace approach for modeling the hemodynamic response function in fMRI

Many fMRI analysis methods use a model for the hemodynamic response function (HRF). Common models of the HRF, such as the Gaussian or Gamma functions, have parameters that are usually selected a priori by the data analyst. A new method is presented that characterizes the HRF over a wide range of parameters via three basis signals derived using principal component analysis (PCA). Covering the HRF variability, these three basis signals together with the stimulation pattern define signal subspaces which are applicable to both linear and nonlinear modeling and identification of the HRF and for various activation detection strategies. Analysis of simulated fMRI data using the proposed signal subspace showed increased detection sensitivity compared to the case of using a previously proposed trigonometric subspace. The methodology was also applied to activation detection in both event-related and block design experimental fMRI data using both linear and nonlinear modeling of the HRF. The activated regions were consistent with previous studies, indicating the ability of the proposed approach in detecting brain activation without a priori assumptions about the shape parameters of the HRF. The utility of the proposed basis functions in identifying the HRF is demonstrated by estimating the HRF in different activated regions.     

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.     

Investigating the neural basis for fMRI-based functional connectivity in a blocked design: application to interregional correlations and psycho-physiological interactions

This paper investigates how well different kinds of fMRI functional connectivity analysis reflect the underlying interregional neural interactions. This is hard to evaluate using real experimental data where such relationships are unknown. Rather, we use a biologically realistic neural model to simulate both neuronal activities and multiregional fMRI data from a blocked design. Because we know how every element in the model is related to every other element, we can compare functional connectivity measurements across different spatial and temporal scales. We focus on (1) psycho-physiological interaction (PPI) analysis, which is a simple brain connectivity method that characterizes the activity in one brain region by the interaction between another region's activity and a psychological factor, and (2) interregional correlation analysis. We investigated the neurobiological underpinnings of PPI using simulated neural activities and fMRI signals generated by a large-scale neural model that performs a visual delayed match-to-sample task. Simulated fMRI data are generated by convolving integrated synaptic activities (ISAs) with a hemodynamic response function. The simulation was done under three task conditions: high-attention, low-attention and a control task ('passive viewing'). We investigated how biological and scanning parameters affect PPI and compared these with functional connectivity measures obtained using correlation analysis. We performed correlational and PPI analyses with three types of time-series data: ISA, fMRI and deconvolved fMRI (which yields estimated neural signals) obtained using a deconvolution algorithm. The simulated ISA can be considered as the 'gold standard' because it represents the underlying neural activity. Our main findings show (1) that evaluating the change in an interregional functional connection using the difference in regression coefficients (as is essentially done in the PPI method) produces results that better reflect the underlying changes in neural interrelationships than does evaluating the functional connectivity difference as a change in correlation coefficient; (2) that using fMRI and deconvolved fMRI data led to similar conclusions in the PPI-based functional connectivity results, and these generally agreed with the nature of the underlying neural interactions; and (3) the functional connectivity correlation measures often led to different conclusions regarding significance for different scanning and hemodynamic parameters, but the significances of the PPI regression parameters were relatively robust. These results highlight the way in which neural modeling can be used to help validate the inferences one can make about functional connectivity based on fMRI data.     

Neuronal event detection in fMRI time series using iterative deconvolution techniques

An iterative estimation algorithm for deconvolution of neuronal activity from Blood Oxygen Level Dependent (BOLD) time series data is presented. The algorithm requires knowledge of the hemodynamic impulse response function but does not require knowledge of the stimulation function. The method uses majorization-minimization of a cost function to find an optimal solution to the inverse problem. The cost function includes penalties for the l₁ norm, total variation and negativity. The algorithm is able to identify the occurrence of neuronal activity bursts from BOLD time series accurately. The accuracy of the algorithm was tested in simulations and experimental fMRI data using blocked and event-related designs. The simulations revealed that the algorithm is most sensitive to contrast-to-noise ratio levels and to errors in the assumed hemodynamic model and least sensitive to autocorrelation in the noise. Within normal fMRI conditions, the method is effective for event detection.     

Correlations and dissociations between BOLD signal and P300 amplitude in an auditory oddball task: a parametric approach to combining fMRI and ERP

A parametric method is proposed to examine the relationship between neuronal activity, measured with event related potentials (ERPs), and the hemodynamic response, observed with functional magnetic resonance imaging (fMRI), during an auditory oddball paradigm. After verifying that the amplitude of the evoked response P300 increases as the probability of oddball target presentation decreases, we explored the corresponding effect of target frequency on the fMRI signal. We predicted and confirmed that some regions that showed activation changes following each oddball are affected by the rate of presentation of the oddballs, or the probability of an oddball target. We postulated that those regions that increased activation with decreasing probability might be responsible for the corresponding changes in the P300 amplitude. fMRI regions that correlated with the amplitude of the P300 wave were supramarginal gyri, thalamus, insula and right medial frontal gyrus, and are presumably sources of the P300 wave. Other regions, such as anterior and posterior cingulate cortex, were activated during the oddball paradigm but their fMRI signal changes were not correlated with the P300 amplitudes. This study thus shows how combining fMRI and ERP in a parametric design identifies task-relevant sources of activity and allows separation of regions that have different response properties.     

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.     

A novel local PCA-based method for detecting activation signals in fMRI.

A novel local principal component analysis (LPCA) technique is presented for activation signal detection in functional magnetic resonance imaging (fMRI) without explicit knowledge about the shape of the model activation signal. Unlike the traditional PCA methods, our LPCA algorithm is based on a measure of separation between two clusters formed by the signal segments in active periods and inactive periods, which is computed in an eigen-subspace. In addition, we only applied PCA to the temporal sequence of each individual voxel instead of applying PCA to the fMRI data set. In our algorithm, we first applied a linear regression procedure to alleviate the baseline drift artifact. Then, the baseline-corrected temporal signals were partitioned into active and inactive segments according to the paradigm used for the fMRI data acquisition. Principal components were computed from all these segments for each voxel by PCA. By projecting the segments of each voxel onto a linear subspace formed by the corresponding most dominant principal components, two separate clusters were formed from active and inactive segments. An activation measure was defined based on the degree of separation between these two clusters in the projection space. We show experimental results on the activation signal detection from various sets of fMRI data with different types of stimulation by using the proposed LPCA algorithm and the standard t-test method for comparison. Our experiments indicate that the LPCA algorithm in general provides substantial signal-to-noise ratio improvement over the t-test method.     

A data post-processing protocol for dynamic MRI data to discriminate brain activity from global physiological effects

All fMRI techniques measure stimulus induced focal metabolic and physiological changes in activated brain areas. During the entire fMRI experiment it is necessary to maintain the general physiological condition of the subject as stable as possible. This is not always an easy task. The typical block design in standard fMRI experiments minimizes most of the problems related with these general physiological changes. However in some fMRI experiments, like pharmacological MRI, the experimental setup makes the use of a blocked design impossible. Therefore signal correction algorithms have been developed to correct for these physiological signal instabilities. These algorithms often require elaborate calculation efforts and the data interpretation is often very difficult if no prior knowledge on the nature of the changes exists.In this work we present an algorithm, which has the advantage of being low in calculation effort and the resulting data after correction are easy to interpret. It makes use of a datafit between the general physiological and focal activation related signal changes to eliminate the generalized effects. This algorithm has been tested on simulated and experimentally obtained signal traces suffering both from substantial general signal changes overwhelming the smaller focal activation induced signal changes.     

Decoding neural events from fMRI BOLD signal: A comparison of existing approaches and development of a new algorithm

Neuroimaging methodology predominantly relies on the blood oxygenation level dependent (BOLD) signal. While the BOLD signal is a valid measure of neuronal activity, variances in fluctuations of the BOLD signal are not only due to fluctuations in neural activity. Thus, a remaining problem in neuroimaging analyses is developing methods that ensure specific inferences about neural activity that are not confounded by unrelated sources of noise in the BOLD signal. Here, we develop and test a new algorithm for performing semiblind (i.e., no knowledge of stimulus timings) deconvolution of the BOLD signal that treats the neural event as an observable, but intermediate, probabilistic representation of the system's state. We test and compare this new algorithm against three other recent deconvolution algorithms under varied levels of autocorrelated and Gaussian noise, hemodynamic response function (HRF) misspecification and observation sampling rate. Further, we compare the algorithms' performance using two models to simulate BOLD data: a convolution of neural events with a known (or misspecified) HRF versus a biophysically accurate balloon model of hemodynamics. We also examine the algorithms' performance on real task data. The results demonstrated good performance of all algorithms, though the new algorithm generally outperformed the others (3.0% improvement) under simulated resting-state experimental conditions exhibiting multiple, realistic confounding factors (as well as 10.3% improvement on a real Stroop task). The simulations also demonstrate that the greatest negative influence on deconvolution accuracy is observation sampling rate. Practical and theoretical implications of these results for improving inferences about neural activity from fMRI BOLD signal are discussed.     

Nonlinear responses of cerebral blood volume, blood flow and blood oxygenation signals during visual stimulation

Hemodynamic-based functional magnetic resonance imaging (fMRI) techniques provide a great utility for noninvasive functional brain mapping. However, because the hemodynamic signals reflect underlying neural activity indirectly, characterization of these signals following brain activation is essential for experimental design and data interpretation. In this report, the linear (or nonlinear) responses to neuronal activation of three hemodynamic parameters based primarily on changes of cerebral blood volume, blood flow and blood oxygenation were investigated by testing these hemodynamic responses' additivity property. Using a recently developed fMRI technique that acquires vascular space occupancy (VASO), arterial spin labeling (ASL) perfusion and blood oxygenation level-dependent (BOLD) signals simultaneously, the additivity property of the three hemodynamic responses in human visual cortex was assessed using various visual stimulus durations. Experiments on healthy volunteers showed that all three hemodynamic-weighted signals responded nonlinearly to stimulus durations less than 4 s, with the degree of nonlinearity becoming more severe as the stimulus duration decreased. Vascular space occupancy and ASL perfusion signals showed similar nonlinearity properties, whereas the BOLD signal was the most nonlinear. These data suggest that caution should be taken in the interpretation of hemodynamic-based signals in fMRI.     

Performance evaluation of nonnegative matrix factorization algorithms to estimate task-related neuronal activities from fMRI data

Nonnegative matrix factorization (NMF) is a blind source separation (BSS) algorithm which is based on the distinct constraint of nonnegativity of the estimated parameters as well as on the measured data. In this study, according to the potential feasibility of NMF for fMRI data, the four most popular NMF algorithms, corresponding to the following two types of (1) least-squares based update [i.e., alternating least-squares NMF (ALSNMF) and projected gradient descent NMF] and (2) multiplicative update (i.e., NMF based on Euclidean distance and NMF based on divergence cost function), were investigated by using them to estimate task-related neuronal activities. These algorithms were applied firstly to individual data from a single subject and, subsequently, to group data sets from multiple subjects. On the single-subject level, although all four algorithms detected task-related activation from simulated data, the performance of multiplicative update NMFs was significantly deteriorated when evaluated using visuomotor task fMRI data, for which they failed in estimating any task-related neuronal activities. In group-level analysis on both simulated data and real fMRI data, ALSNMF outperformed the other three algorithms. The presented findings may suggest that ALSNMF appears to be the most promising option among the tested NMF algorithms to extract task-related neuronal activities from fMRI data.     

Activation detection in event-related fMRI data based on spatio-temporal properties.

Template-based activation detection methods, such as cross-correlation, could be difficult to apply in event-related functional MRI data because accurate a priori knowledge about the activation signal patterns is often not available. As a result, several categories of template-free data analysis techniques have been introduced in the fMRI literature. One previously described template-free activation detection technique is based on the feature that activated voxels yield reproducible time course patterns as the subject undergoes the same simulation in repeated epochs. In this paper, spatial information is incorporated as a second feature and a combined univariate measure is formed. The resulting method is shown to offer measurable improvement in detecting activation regions in simulated data in a highly computationally efficient manner. Its practical utility is demonstrated with an experimental data set obtained with a visually guided motor paradigm.     

Graphical display of fMRI data: visualizing multidimensional space

Visualization of multidimensional data is an integral part of computational statistics and exploratory data analysis (EDA). We show how visualization of fMRI time-courses may be used to reveal the fMRI data structure. We consider fMRI time-courses (TCs) as points in multidimensional space. In simulated and in vivo data, we show that minimum spanning tree (MST)-based sequencing of multivariate time-courses, in combination with a homogeneity map visualization, allows for effective and useful graphical display of the groups of coactivated time-courses obtained by temporal clustering. This display may serve as a tool for investigation of brain connectivity. We also suggest a simple overall display of the entire fMRI data set.     

Nonlinear blood oxygen level-dependent responses for transient activations and deactivations in V1 - insights into the hemodynamic response function with the balloon model

We report studies of the nonlinear nature of blood oxygen level-dependent (BOLD) responses to short transient deactivations in human visual cortex. Both functional magnetic resonance imaging (fMRI) and near-infrared spectroscopy (NIRS) have been used to compare and contrast the hemodynamic response functions (HRFs) associated with transient activation and deactivation in primary visual cortex. We show that signal decreases for short duration deactivations are smaller than corresponding signal increases in activation studies. Moreover, the standard balloon model of BOLD effects may be modified to account for the observed nonlinear nature of deactivations by appropriate changes to simple hemodynamic parameters without recourse to new assumptions about the nature of the coupling between activity and oxygen use.     

Principal component analysis of the dynamic response measured by fMRI: a generalized linear systems framework.

Principal component analysis (PCA) is one of several structure-seeking multivariate statistical techniques, exploratory as well as inferential, that have been proposed recently for the characterization and detection of activation in both PET and fMRI time series data. In particular, PCA is data driven and does not assume that the neural or hemodynamic response reaches some steady state, nor does it involve correlation with any pre-defined or exogenous experimental design template. In this paper, we present a generalized linear systems framework for PCA based on the singular value decomposition (SVD) model for representation of spatio-temporal fMRI data sets. Statistical inference procedures for PCA, including point and interval estimation will be introduced without the constraint of explicit hypotheses about specific task-dependent effects. The principal eigenvectors capture both the spatial and temporal aspects of fMRI data in a progressive fashion; they are inherently matched to unique and uncorrelated features and are ranked in order of the amount of variance explained. PCA also acts as a variation reduction technique, relegating most of the random noise to the trailing components while collecting systematic structure into the leading ones. Features summarizing variability may not directly be those that are the most useful. Further analysis is facilitated through linear subspace methods involving PC rotation and strategies of projection pursuit utilizing a reduced, lower-dimensional natural basis representation that retains most of the information. These properties will be illustrated in the setting of dynamic time-series response data from fMRI experiments involving pharmacological stimulation of the dopaminergic nigro-striatal system in primates.