Assessment of cluster homogeneity in fMRI data using Kendall's coefficient of concordance

In fMRI both model-led and exploratory data-driven methods are used to identify groups of voxels according to their correlation either with an external reference or with some similarity measure. Here we present a technique to assess intragroup homogeneity using Kendall’s coefficient of concordance W once groups have been identified. We show that the time-courses belonging to the group may be ranked according to their contribution to the overall concordance and describe an algorithm for group purification. We suggest the use of W as a cluster validation index in exploratory data analysis approaches, such as fuzzy or hard clustering, principal component analysis, independent component analysis and Kohonen maps.     

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.     

Improving the resolution of functional brain imaging: analyzing functional data in anatomical space

The accurate mapping of functional magnetic resonance imaging (fMRI) activations to anatomical structures is critical for fMRI studies of brain organization. In the commonly used functional space analysis method, functional images are realigned to a functional reference image and processed in low-resolution functional space. The average functional activations are then projected into high-resolution anatomical space for visualization. Here, we describe a new technique, anatomical space analysis (ASA), whereby low-resolution functional images are first coregistered and resampled directly into high-resolution anatomical space with all subsequent data processing performed in high-resolution space. A major advantage of ASA is that minor scanner sampling instabilities and small head movements can increase spatial resolution by providing multiple samples of the relationship between functional and anatomical space. Both simulations and analyses of real fMRI data show that ASA improves the precision, objectivity and reproducibility of functional brain mapping.     

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.     

Dynamical Analysis of the Dow Jones Index Using Dimensionality Reduction and Visualization

Time-series generated by complex systems (CS) are often characterized by phenomena such as chaoticity, fractality and memory effects, which pose difficulties in their analysis. The paper explores the dynamics of multidimensional data generated by a CS. The Dow Jones Industrial Average (DJIA) index is selected as a test-bed. The DJIA time-series is normalized and segmented into several time window vectors. These vectors are treated as objects that characterize the DJIA dynamical behavior. The objects are then compared by means of different distances to generate proper inputs to dimensionality reduction and information visualization algorithms. These computational techniques produce meaningful representations of the original dataset according to the (dis)similarities between the objects. The time is displayed as a parametric variable and the non-locality can be visualized by the corresponding evolution of points and the formation of clusters. The generated portraits reveal a complex nature, which is further analyzed in terms of the emerging patterns. The results show that the adoption of dimensionality reduction and visualization tools for processing complex data is a key modeling option with the current computational resources.     

Real-time functional magnetic resonance imaging: methods and applications

Functional magnetic resonance imaging (fMRI) has been limited by time-consuming data analysis and a low signal-to-noise ratio, impeding online analysis. Recent advances in acquisition techniques, computational power and algorithms increased the sensitivity and speed of fMRI significantly, making real-time analysis and display of fMRI data feasible. So far, most reports have focused on the technical aspects of real-time fMRI (rtfMRI). Here, we provide an overview of the different major areas of applications that became possible with rtfMRI: online analysis of single-subject data provides immediate quality assurance and functional localizers guiding the main fMRI experiment or surgical interventions. In teaching, rtfMRI naturally combines all essential parts of a neuroimaging experiment, such as experimental design, data acquisition and analysis, while adding a high level of interactivity. Thus, the learning of essential knowledge required to conduct functional imaging experiments is facilitated. rtfMRI allows for brain-computer interfaces (BCI) with a high spatial and temporal resolution and whole-brain coverage. Recent studies have shown that such BCI can be used to provide online feedback of the blood-oxygen-level-dependent signal and to learn the self-regulation of local brain activity. Preliminary evidence suggests that this local self-regulation can be used as a new paradigm in cognitive neuroscience to study brain plasticity and the functional relevance of brain areas, even being potentially applicable for psychophysiological treatment.     

Data planning and analysis for synthesis of multidimensional laws (nonlinear multifactor analysis)

The methodology of data planning and analysis for synthesis of multidimensional laws using visualization is described along with the ensuing method of numerical data approximation by functions with “separable” variables. The method is developed for the cases of source data presented as (a) a table where all cells are filled, (b) an orthogonal table where quite certain cells are filled, and (c) a table where, generally speaking, arbitrary cells are not filled. The method was successfully applied for different problems of nuclear science and technology.     

Applying functional MRI to the spinal cord and brainstem

Functional magnetic resonance imaging of the spinal cord (spinal fMRI) has facilitated the noninvasive visualization of neural activity in the spinal cord (SC) and brainstem of both animals and humans. This technique has yet to gain the widespread usage of brain fMRI, due in part to the intrinsic technical challenges spinal fMRI presents and to the narrower scope of applications it fulfills. Nonetheless, methodological progress has been considerable and rapid. To date, spinal fMRI studies have investigated SC function during sensory or motor task paradigms in spinal cord injury (SCI), multiple sclerosis (MS) and neuropathic pain (NP) patient populations, all of which have yielded consistent and sensitive results. The most recent study in our laboratory has successfully used spinal fMRI to examine cervical SC activity in a SCI patient with a metallic fixation device spanning the C₄ to C₆ vertebrae, a critical step in realizing the clinical utility of the technique. The literature reviewed in this article suggests that spinal fMRI is poised for usage in a wide range of patient populations, as multiple groups have observed intriguing, yet consistent, results using standard, readily available MR systems and hardware. The next step is the implementation of this technique in the clinic to supplement standard qualitative behavioral assessments of SCI. Spinal fMRI may offer insight into the subtleties of function in the injured and diseased SC, and support the development of new methods for treatment and monitoring.     

Comparison of functional MR-venography and EPI-BOLD fMRI at 1.5 t

Functional magnetic resonance imaging (fMRI) of the brain using blood oxygenation level dependent (BOLD) contrast relies on the changes of paramagnetic deoxyhemoglobin concentration, which affects brain parenchyma and draining venous vessels. These changes in deoxyhemoglobin concentration in venous vessels can also be monitored using a high-resolution susceptibility-based MR-venography technique. Four volunteers participated in the study in which functional MR-venograms were compared with conventional echo-planar imaging (EPI)-BOLD-fMRI. In all cases, small venous vessels could be identified close to the areas of activation detected by conventional fMRI. In the venograms, task performance (finger tapping) resulted in a loss of venous vessel contrast compared to the resting state, which is consistent with a local decrease of deoxyhemoglobin concentration. MR-venography allows a direct visualization of the BOLD-effect at high spatial resolution. In combination with conventional fMRI, this technique may help to separate the contribution of brain parenchyma and venous vessels in fMRI studies.     

Observations on maximum entropy processing of MR images

A maximum entropy (MAXENT) criteria for MR image processing optimizations has previously shown poor performance, but this note observes that there are two entirely different kinds of "data transmission" applications which appear to have been intermixed. In the two cases, "image entropy" actually refers to different kinds of data variables. The previous literature formulations are for transfer of data in which pixel-locations are the transmitted variable, and these pixels may be neither uniform nor constant. The second application concerns the MRI data set for display. Its data variables are image pixel-values of magnetization intensity, and the data transfer mode has the sense of visual display. When MAXENT criteria are modified to address an array of pixel-value intensities, and use a pixel-value information entropy rather than pixel-locations entropy, then successful data processing results. Restoring display visualization from highly nonuniform surface coils for lumbar spine scans are demonstrated, as an example of MAXENT usefulness.     

Multivariate analysis of fMRI time series: classification and regression of brain responses using machine learning

Machine learning and pattern recognition techniques are being increasingly employed in functional magnetic resonance imaging (fMRI) data analysis. By taking into account the full spatial pattern of brain activity measured simultaneously at many locations, these methods allow detecting subtle, non-strictly localized effects that may remain invisible to the conventional analysis with univariate statistical methods. In typical fMRI applications, pattern recognition algorithms "learn" a functional relationship between brain response patterns and a perceptual, cognitive or behavioral state of a subject expressed in terms of a label, which may assume discrete (classification) or continuous (regression) values. This learned functional relationship is then used to predict the unseen labels from a new data set ("brain reading"). In this article, we describe the mathematical foundations of machine learning applications in fMRI. We focus on two methods, support vector machines and relevance vector machines, which are respectively suited for the classification and regression of fMRI patterns. Furthermore, by means of several examples and applications, we illustrate and discuss the methodological challenges of using machine learning algorithms in the context of fMRI data analysis.     

Discussion on the choice of separated components in fMRI data analysis by spatial independent component analysis

By measuring the changes of magnetic resonance signals during a stimulation, the functional magnetic resonance imaging (fMRI) is able to localize the neural activation in the brain. In this report, we discuss the fMRI application of the spatial independent component analysis (spatial ICA), which maximizes statistical independence over spatial images. Included simulations show the possibility of the spatial ICA on discriminating asynchronous activations or different response patterns in an fMRI data set. An in vivo visual stimulation fMRI test was conducted, and the result shows a proper sum of the separated components as the final image is better than a single component, using fMRI data analysis by spatial ICA. Our result means that spatial ICA is a useful tool for the detection of different response activations and suggests that a proper sum of the separated independent components should be used for the imaging result of fMRI data processing.     

Hemodynamic response (BOLD/fMRI) in focal epilepsy with reference to benzodiazepine effect

We studied a new procedure of BOLD/fMRI acquisition in epilepsy. They use the benzodiazepine effect to achieve a more reliable baseline for statistical analysis. The method works only in the MR domain without EEG correlation. It compares the EPI images during interictal epileptic discharges and the images “inactivated” by benzodiazepine.

The results in five out of eight patients show that this procedure in comparison with the EEG/fMRI method gives a net improvement of spatial definition of BOLD areas. These preliminary results seem to confirm the hypothesis that the better BOLD/fMRI procedure in epilepsy is to make use of physical features of MR that, unlike EEG, is not influenced by the distance of intercerebral sources and consequently allows a more complete and undistorted display of BOLD areas.     

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.     

CORSICA: correction of structured noise in fMRI by automatic identification of ICA components

When applied to functional magnetic resonance imaging (fMRI) data, spatial independent component analysis (sICA), a data-driven technique that addresses the blind source separation problem, seems able to extract components specifically related to physiological noise and brain movements. These components should be removed from the data to achieve structured noise reduction and improve any subsequent detection and analysis of signal fluctuations related to neural activity. We propose a new automatic method called CORSICA (CORrection of Structured noise using spatial Independent Component Analysis) to identify the components related to physiological noise, using prior information on the spatial localization of the main physiological fluctuations in fMRI data. As opposed to existing spectral priors, which may be subject to aliasing effects for long-TR data sets (typically acquired with TR >1 s), such spatial priors can be applied to fMRI data, regardless of the TR of the acquisitions. By comparing the proposed automatic selection to a manual selection performed visually by a human operator, we first show that CORSICA is able to identify the noise-related components for long-TR data with a high sensitivity and a specificity of 1. On short-TR data sets, we validate that the proposed method of noise reduction allows a substantial improvement of the signal-to-noise ratio evaluated at the cardiac and respiratory frequencies, even in the gray matter, while preserving the main fluctuations related to neural activity.     

Realignment strategies for awake-monkey fMRI data

Functional magnetic resonance imaging (fMRI) experiments with awake nonhuman primates (NHPs) have recently seen a surge of applications. However, the standard fMRI analysis tools designed for human experiments are not optimal for NHP data collected at high fields. One major difference is the experimental setup. Although real head movement is impossible for NHPs, MRI image series often contain visible motion artifacts. Animal body movement results in image position changes and geometric distortions. Since conventional realignment methods are not appropriate to address such differences, algorithms tailored specifically for animal scanning become essential. We have implemented a series of high-field NHP specific methods in a software toolbox, fMRI Sandbox (http://kyb.tuebingen.mpg.de/~stoewer/), which allows us to use different realignment strategies. Here we demonstrate the effect of different realignment strategies on the analysis of awake-monkey fMRI data acquired at high field (7 T). We show that the advantage of using a nonstandard realignment algorithm depends on the amount of distortion in the dataset. While the benefits for less distorted datasets are minor, the improvement of statistical maps for heavily distorted datasets is significant.     

Wavelet domain de-noising of time-courses in MR image sequences

Magnetic resonance images acquired with high temporal resolution often exhibit large noise artifacts, which arise from physiological sources as well as from the acquisition hardware. These artifacts can be detrimental to the quality and interpretation of the time-course data in functional MRI studies. A class of wavelet-domain de-noising algorithms estimates the underlying, noise-free signal by thresholding (or 'shrinking') the wavelet coefficients, assuming the underlying temporal noise of each pixel is uncorrelated and Gaussian. A Wiener-type shrinkage algorithm is developed in this paper, for de-noising either complex- or magnitude-valued image data sequences. Using the de-correlation properties of the wavelet transform, as elucidated by Johnstone and Silverman, the assumption of i.i.d. Gaussian noise can be abandoned, opening up the possibility of removing colored noise. Both wavelet- and wavelet-packet based algorithms are developed, and the Wiener method is compared to the traditional Hard and Soft wavelet thresholding methods of Donoho and Johnstone. The methods are applied to two types of data sets. In the first, an artificial set of complex-valued images was constructed, in which each pixel has a simulated bimodal time-course. Gaussian noise was added to each of the real and imaginary channels, and the noise removed from the complex image sequence as well as the magnitude image sequence (where the noise is Rician). The bias and variance between the original and restored paradigms was estimated for each method. It was found that the Wiener method gives better balance in bias and variance than either Hard or Soft methods. Furthermore, de-noising magnitude data provides comparable accuracy of the restored images to that obtained from de-noising complex data. In the second data set, an actual in vivo complex image sequence containing unknown physiological and instrumental noise was used. The same bimodal paradigm as in the first data set was added to pixels in a small localized region of interest. For the paradigm investigated here, the smooth Daubechies wavelets provide better de-noising characteristics than the discontinuous Haar wavelets. Also, it was found that wavelet packet de-noising offers no significant improvement over the computationally more efficient wavelet de-noising methods. For the in vivo data, it is desirable that the groups of "activated" time-courses are homogeneous. It was found that the internal homogeneity of the group of time-courses increases when de-noising is applied. This suggests using de-noising as a pre-processing tool for both exploratory and inferential data analysis methods in fMRI.     

Spectroscopic imaging display and analysis.

A system for display of magnetic resonance (MR) spectroscopic imaging (SI) data is described which provides for efficient review and analysis of the multidimensional spectroscopic and spatial data format of this technique. Features include the rapid display of spectra from selected image voxels, formation of spectroscopic images, spectral and image data processing operations, methods for correlating spectroscopic image data with high resolution 1H MR images, and hardcopy facilities. Examples are shown for 31P and 1H spectroscopic imaging studies obtained in human and rat brain.