Diffusion-based spatial priors for functional magnetic resonance images

We recently outlined a Bayesian scheme for analyzing fMRI data using diffusion-based spatial priors [Harrison, L.M., Penny, W., Ashburner, J., Trujillo-Barreto, N., Friston, K.J., 2007. Diffusion-based spatial priors for imaging. NeuroImage 38, 677-695]. The current paper continues this theme, applying it to a single-subject functional magnetic resonance imaging (fMRI) study of the auditory system. We show that spatial priors on functional activations, based on diffusion, can be formulated in terms of the eigenmodes of a graph Laplacian. This allows one to discard eigenmodes with small eigenvalues, to provide a computationally efficient scheme. Furthermore, this formulation shows that diffusion-based priors are a generalization of conventional Laplacian priors [Penny, W.D., Trujillo-Barreto, N.J., Friston, K.J., 2005. Bayesian fMRI time series analysis with spatial priors. NeuroImage 24, 350-362]. Finally, we show how diffusion-based priors are a special case of Gaussian process models that can be inverted using classical covariance component estimation techniques like restricted maximum likelihood [Patterson, H.D., Thompson, R., 1974. Maximum likelihood estimation of components of variance. Paper presented at: 8th International Biometrics Conference (Constanta, Romania)]. The convention in SPM is to smooth data with a fixed isotropic Gaussian kernel before inverting a mass-univariate statistical model. This entails the strong assumption that data are generated smoothly throughout the brain. However, there is no way to determine if this assumption is supported by the data, because data are smoothed before statistical modeling. In contrast, if a spatial prior is used, smoothness is estimated given non-smoothed data. Explicit spatial priors enable formal model comparison of different prior assumptions, e.g., that data are generated from a stationary (i.e., fixed throughout the brain) or non-stationary spatial process. Indeed, for the auditory data we provide strong evidence for a non-stationary process, which concurs with a qualitative comparison of predicted activations at the boundary of functionally selective regions.     

Bayesian fMRI data analysis with sparse spatial basis function priors

In previous work we have described a spatially regularised General Linear Model (GLM) for the analysis of brain functional Magnetic Resonance Imaging (fMRI) data where Posterior Probability Maps (PPMs) are used to characterise regionally specific effects. The spatial regularisation is defined over regression coefficients via a Laplacian kernel matrix and embodies prior knowledge that evoked responses are spatially contiguous and locally homogeneous. In this paper we propose to finesse this Bayesian framework by specifying spatial priors using Sparse Spatial Basis Functions (SSBFs). These are defined via a hierarchical probabilistic model which, when inverted, automatically selects an appropriate subset of basis functions. The method includes non-linear wavelet shrinkage as a special case. As compared to Laplacian spatial priors, SSBFs allow for spatial variations in signal smoothness, are more computationally efficient and are robust to heteroscedastic noise. Results are shown on synthetic data and on data from an event-related fMRI experiment.     

Investigation of spatial resolution, partial volume effects and smoothing in functional MRI using artificial 3D time series

This work addresses the balance between temporal signal-to-noise ratio (tSNR) and partial volume effects (PVE) in functional magnetic resonance imaging (fMRI) and investigates the impact of the choice of spatial resolution and smoothing. In fMRI, since physiological time courses are monitored, tSNR is of greater importance than image SNR. Improving SNR by an increase in voxel volume may be of negligible benefit when physiological fluctuations dominate the noise. Furthermore, at large voxel volumes, PVE are more pronounced, leading to an overall loss in performance. Artificial fMRI time series, based on high-resolution anatomical data, were used to simulate BOLD activation in a controlled manner. The performance was subsequently quantified as a measure of how well the resulted activation matched the simulated activation. The performance was highly dependent on the spatial resolution. At high contrast-to-noise ratio (CNR), the optimal voxel volume was small, i.e. in the region of 2(3) mm(3). It was also shown that using a substantially larger voxel volume in this case could potentially negate the CNR benefits. The optimal smoothing kernel width was dependent on the CNR, being larger at poor CNR. At CNR >1, little or no smoothing proved advantageous. The use of artificial time series gave an opportunity to quantitatively investigate the effects of partial volume and smoothing in single subject fMRI. It was shown that a proper choice of spatial resolution and smoothing kernel width is important for fMRI performance.     

Evaluation and comparison of GLM- and CVA-based fMRI processing pipelines with Java-based fMRI processing pipeline evaluation system

Activation patterns identified by fMRI processing pipelines or fMRI software packages are usually determined by the preprocessing options, parameters, and statistical models used. Previous studies that evaluated options of GLM (general linear model)--based fMRI processing pipelines are mainly based on simulated data with receiver operating characteristics (ROC) analysis, but evaluation of such fMRI processing pipelines on real fMRI data is rare. To understand the effect of processing options on performance of GLM-based fMRI processing pipelines with real fMRI data, we investigated the impact of commonly-used fMRI preprocessing steps; optimized the associated GLM-based single-subject processing pipelines; and quantitatively compared univariate GLM (in FSL.FEAT and NPAIRS.GLM) and multivariate CVA (canonical variates analysis) (in NPAIRS.CVA)-based analytic models in single-subject analysis with a recently developed fMRI processing pipeline evaluation system based on prediction accuracy (classification accuracy) and reproducibility performance metrics. For block-design data, we found that with GLM analysis (1) slice timing correction and global intensity normalization have little consistent impact on fMRI processing pipelines, spatial smoothing and high-pass filtering or temporal detrending significantly increases pipeline performance and thus are essential for robust fMRI statistical analysis; (2) combined optimization of spatial smoothing and temporal detrending improves pipeline performance; and (3) in general, the prediction performance of multivariate CVA is higher than that of the univariate GLM, while univariate GLM is more reproducible than multivariate CVA. Because of the different bias-variance trade-offs of univariate and multivariate models, it may be necessary to consider a consensus approach to obtain more accurate activation patterns in fMRI data.     

The problem of low variance voxels in statistical parametric mapping; a new hat avoids a 'haircut'

Statistical parametric mapping (SPM) locates significant clusters based on a ratio of signal to noise (a ‘contrast’ of the parameters divided by its standard error) meaning that very low noise regions, for example outside the brain, can attain artefactually high statistical values. Similarly, the commonly applied preprocessing step of Gaussian spatial smoothing can shift the peak statistical significance away from the peak of the contrast and towards regions of lower variance. These problems have previously been identified in positron emission tomography (PET) (Reimold et al., 2006) and voxel-based morphometry (VBM) (Acosta-Cabronero et al., 2008), but can also appear in functional magnetic resonance imaging (fMRI) studies. Additionally, for source-reconstructed magneto- and electro-encephalography (M/EEG), the problems are particularly severe because sparsity-favouring priors constrain meaningfully large signal and variance to a small set of compactly supported regions within the brain. (Acosta-Cabronero et al., 2008) suggested adding noise to background voxels (the ‘haircut’), effectively increasing their noise variance, but at the cost of contaminating neighbouring regions with the added noise once smoothed. Following theory and simulations, we propose to modify - directly and solely - the noise variance estimate, and investigate this solution on real imaging data from a range of modalities.     

Deriving the optimal number of events for an event-related fMRI study based on the spatial extent of activation

Event-related fMRI is a powerful tool for localising psychological functions to specific brain areas. However, the number of events required to produce stable activation maps is a poorly investigated and understood problem. Huettel and McCarthy [Huettel, S.A., McCarthy, G., 2001. The effects of single-trial averaging upon the spatial extent of fMRI activation. NeuroReport 12, 2411-2416] have shown that the spatial extent of activation increases monotonically with the number of events in an analysis. In the present paper, this result is replicated and shown to be a consequence of the cross-correlation technique used to determine active voxels and does not hold, for example, for a GLM analysis. Another analysis technique, that does not depend on goodness-of-fit to the data, is also proposed. This technique calculates an impulse response function (IRF) for each voxel, finds the best fitting haemodynamic shape to the IRF and returns an area-under-the-curve (%AUC) activation measure. Using spatial extent as a measure, asymptotic behaviour is evident after as few as 25 events for the %AUC analysis technique in a finger-tapping task with non-overlapping haemodynamic responses and for both the GLM and %AUC techniques in a similar task that allows responses to overlap. The experimental validity of the %AUC technique to identify active brain regions while minimising false positive levels is demonstrated in a group study with 25 participants.     

Whole brain high-resolution functional imaging at ultra high magnetic fields: an application to the analysis of resting state networks

Whole-brain functional magnetic resonance imaging (fMRI) allows measuring brain dynamics at all brain regions simultaneously and is widely used in research and clinical neuroscience to observe both stimulus-related and spontaneous neural activity. Ultrahigh magnetic fields (7T and above) allow functional imaging with high contrast-to-noise ratios and improved spatial resolution and specificity compared to clinical fields (1.5T and 3T). High-resolution 7T fMRI, however, has been mostly limited to partial brain coverage with previous whole-brain applications sacrificing either the spatial or temporal resolution. Here we present whole-brain high-resolution (1, 1.5 and 2mm isotropic voxels) resting state fMRI at 7T, obtained with parallel imaging technology, without sacrificing temporal resolution or brain coverage, over what is typically achieved at 3T with several fold larger voxel volumes. Using Independent Component Analysis we demonstrate that high resolution images acquired at 7T retain enough sensitivity for the reliable extraction of typical resting state brain networks and illustrate the added value of obtaining both single subject and group maps, using cortex based alignment, of the default-mode network (DMN) with high native resolution. By comparing results between multiple resolutions we show that smaller voxels volumes (1 and 1.5mm isotropic) data result in reduced partial volume effects, permitting separations of detailed spatial features within the DMN patterns as well as a better function to anatomy correspondence.     

Support vector machines for temporal classification of block design fMRI data

This paper treats support vector machine (SVM) classification applied to block design fMRI, extending our previous work with linear discriminant analysis [LaConte, S., Anderson, J., Muley, S., Ashe, J., Frutiger, S., Rehm, K., Hansen, L.K., Yacoub, E., Hu, X., Rottenberg, D., Strother S., 2003a. The evaluation of preprocessing choices in single-subject BOLD fMRI using NPAIRS performance metrics. NeuroImage 18, 10-27; Strother, S.C., Anderson, J., Hansen, L.K., Kjems, U., Kustra, R., Siditis, J., Frutiger, S., Muley, S., LaConte, S., Rottenberg, D. 2002. The quantitative evaluation of functional neuroimaging experiments: the NPAIRS data analysis framework. NeuroImage 15, 747-771]. We compare SVM to canonical variates analysis (CVA) by examining the relative sensitivity of each method to ten combinations of preprocessing choices consisting of spatial smoothing, temporal detrending, and motion correction. Important to the discussion are the issues of classification performance, model interpretation, and validation in the context of fMRI. As the SVM has many unique properties, we examine the interpretation of support vector models with respect to neuroimaging data. We propose four methods for extracting activation maps from SVM models, and we examine one of these in detail. For both CVA and SVM, we have classified individual time samples of whole brain data, with TRs of roughly 4 s, thirty slices, and nearly 30,000 brain voxels, with no averaging of scans or prior feature selection.     

Optimal spatial regularisation of autocorrelation estimates in fMRI analysis

In the General Linear Model (GLM) framework for the statistical analysis of fMRI data, the problem of temporal autocorrelations in the residual signal (after regression) has been frequently addressed in the open literature. There exist various methods for correcting the ensuing bias in the statistical testing, among which the prewhitening strategy, which uses a prewhitening matrix for rendering the residual signal white (i.e., without temporal autocorrelations). This correction is only exact when the autocorrelation structure of the noise-generating process is accurately known, and the estimates derived from the fMRI data are too noisy to be used for correction. Recently, Worsley and co-workers proposed to spatially smooth the noisy autocorrelation estimates, effectively reducing their variance and allowing for a better correction. In this article, a systematic study into the effect of the smoothing kernel width is performed and a method is introduced for choosing this bandwidth in an "optimal" manner. Several aspects of the prewhitening strategy are investigated, namely the choice of the autocorrelation estimate (biased or unbiased), the accuracy of the estimates, the degree of spatial regularisation and the order of the autoregressive model used for characterising the noise. The proposed method is extensively evaluated on both synthetic and real fMRI data.     

Spatial accuracy of fMRI activation influenced by volume- and surface-based spatial smoothing techniques

As improvements in cortical surface modeling allowed accurate cortical topology in brain imaging studies, surface-based methods for the analysis of functional magnetic resonance imaging (fMRI) were introduced to overcome the topological deficiency of commonly used volume-based methods. The difference between the two methods is mainly due to the smoothing techniques applied. For practical applications, the surface-based methods need to quantitatively validate the accuracy of localizing activation. In this study, we evaluated the spatial accuracy of activation detected by the volume- and surface-based methods using simulated blood oxygenation level-dependent (BOLD) signals and MRI phantoms focusing on the influence of their smoothing techniques. T1- and T2-weighted phantoms were acquired from BrainWeb () and used to extract cortical surfaces and to generate echo planar imaging (EPI) data. Simulated BOLD signals as the gold standard of activation in our experiment were applied to the surfaces and projected to the volume space with random noise. Three-dimensional isotropic Gaussian kernel smoothing and two-dimensional heat kernel smoothing were applied to the volume- and surface-based methods. Sensitivity and 1-specificity, which are truly and falsely detected activations, and similarity measures, which are spatially and statistically similar for the gold standard and detected activations, were calculated. In the results, the surface-based method showed the sensitivity and similarity scores of about 12% higher than the volume-based method. In conclusion, the surface-based method guarantees better spatial accuracy for the localization of BOLD signal sources within the cortex than the volume-based method.     

Characterization of groups using composite kernels and multi-source fMRI analysis data: application to schizophrenia

Pattern classification of brain imaging data can enable the automatic detection of differences in cognitive processes of specific groups of interest. Furthermore, it can also give neuroanatomical information related to the regions of the brain that are most relevant to detect these differences by means of feature selection procedures, which are also well-suited to deal with the high dimensionality of brain imaging data. This work proposes the application of recursive feature elimination using a machine learning algorithm based on composite kernels to the classification of healthy controls and patients with schizophrenia. This framework, which evaluates nonlinear relationships between voxels, analyzes whole-brain fMRI data from an auditory task experiment that is segmented into anatomical regions and recursively eliminates the uninformative ones based on their relevance estimates, thus yielding the set of most discriminative brain areas for group classification. The collected data was processed using two analysis methods: the general linear model (GLM) and independent component analysis (ICA). GLM spatial maps as well as ICA temporal lobe and default mode component maps were then input to the classifier. A mean classification accuracy of up to 95% estimated with a leave-two-out cross-validation procedure was achieved by doing multi-source data classification. In addition, it is shown that the classification accuracy rate obtained by using multi-source data surpasses that reached by using single-source data, hence showing that this algorithm takes advantage of the complimentary nature of GLM and ICA.     

A method for functional network connectivity among spatially independent resting-state components in schizophrenia

Functional connectivity of the brain has been studied by analyzing correlation differences in time courses among seed voxels or regions with other voxels of the brain in healthy individuals as well as in patients with brain disorders. The spatial extent of strongly temporally coherent brain regions co-activated during rest has also been examined using independent component analysis (ICA). However, the weaker temporal relationships among ICA component time courses, which we operationally define as a measure of functional network connectivity (FNC), have not yet been studied. In this study, we propose an approach for evaluating FNC and apply it to functional magnetic resonance imaging (fMRI) data collected from persons with schizophrenia and healthy controls. We examined the connectivity and latency among ICA component time courses to test the hypothesis that patients with schizophrenia would show increased functional connectivity and increased lag among resting state networks compared to controls. Resting state fMRI data were collected and the inter-relationships among seven selected resting state networks (identified using group ICA) were evaluated by correlating each subject's ICA time courses with one another. Patients showed higher correlation than controls among most of the dominant resting state networks. Patients also had slightly more variability in functional connectivity than controls. We present a novel approach for quantifying functional connectivity among brain networks identified with spatial ICA. Significant differences between patient and control connectivity in different networks were revealed possibly reflecting deficiencies in cortical processing in patients.     

Effect of initial fMRI data modeling on the connectivity reported between brain areas

Nearly all neuroimaging data analysis rests upon some form of variance partitioning. Conventional analyses, with a general linear model (GLM), partition the variance in the measured response variable into partitions described by a design matrix of explanatory variables. This approach can also be adopted in the initial modeling of the data in studies using data-led methods to summarize functional connectivity, such as principle component analysis, or studies of effective connectivity, using for example structural equation modeling. The point made in this technical note is that the partition of the original time series has to be precisely described to qualify the sources of variations that are taken into account. For conventional analyses using the GLM, the partition investigated corresponds to the subspaces of the design matrix that are tested. However, in the analyses of functional and effective connectivity, the particular subspaces considered are not always specified explicitly. Here we show that selecting different subspaces, or variance partitions, can have a profound effect, both qualitatively and quantitatively, on the sample covariances and the ensuing inferences about connectivity. We will illustrate this using simulated data that include condition and block-related effects and their interactions. We will use these three subspaces to show how the correlation between two voxels depends on which sub-partitions are examined. We will also show how the partition of the design matrix influences the resulting correlation matrix observed when studying correlations between error terms. We will finally demonstrate, quantitatively, the effect of the variance partitions considered on the correlations between two regions using a real fMRI study of biological motion.     

Dynamic discrimination analysis: a spatial-temporal SVM

Recently, pattern recognition methods (e.g., support vector machines (SVM)) have been used to analyze fMRI data. In these applications the fMRI scans are treated as spatial patterns and statistical learning methods are used to identify statistical properties of the data that discriminate between brain states (e.g., task 1 vs. task 2) or group of subjects (e.g., patients and controls). We propose an extension of these approaches using temporal embedding. This makes the dynamic aspect of fMRI time series an explicit part of the classification. The proposed pattern recognition approach uses both spatial and temporal information. Temporal embedding was implemented by defining spatiotemporal fMRI observations and applying a support vector machine to these temporally extended observations. This produces a discriminating weight vector encompassing both voxels and time. The resulting vector furnishes discriminating responses, at each voxel without imposing any constraints on their temporal form.     

Enhancing reproducibility of fMRI statistical maps using generalized canonical correlation analysis in NPAIRS framework

Common fMRI data processing techniques usually minimize a temporal cost function or fit a temporal model to extract an activity map. Here, we focus on extracting a highly, spatially reproducible statistical parametric map (SPM) from fMRI data using a cost function that does not depend on a model of the subjects' temporal response. Based on a generalized version of canonical correlation analysis (gCCA), we propose a method to extract a highly reproducible map by maximizing the sum of pair-wise correlations between some maps. In a group analysis, each map is calculated from a linear combination of fMRI scans of a subset of subjects under study. The proposed method is applied to BOLD fMRI datasets without any spatial smoothing from 10 subjects performing a simple reaction time (RT) task. Using the NPAIRS split-half resampling framework with a reproducibility measure based on SPM correlations, we compare the proposed approach with canonical variate analysis (CVA) and a simple general linear model (GLM). gCCA provides statistical parametric maps with higher reproducibility than CVA and GLM with correlation reproducibilities across independent split-half SPMs of 0.78, 0.46, and 0.41, respectively. Our results show that gCCA is an efficient approach for extracting the default mode network, assessing brain connectivity, and processing event-related and resting-state datasets in which the temporal BOLD signal varies from subject to subject.     

Task fMRI data analysis based on supervised stochastic coordinate coding

Task functional magnetic resonance imaging (fMRI) has been widely employed for brain activation detection and brain network analysis. Modeling rich information from spatially-organized collection of fMRI time series is challenging because of the intrinsic complexity. Hypothesis-driven methods, such as the general linear model (GLM), which regress exterior stimulus from voxel-wise functional brain activity, are limited due to overlooking the complexity of brain activities and the diversity of concurrent brain networks. Recently, sparse representation and dictionary learning methods have attracted increasing interests in task fMRI data analysis. The major advantage of this methodology is its promise in reconstructing concurrent brain networks systematically. However, this data-driven strategy is, to some extent, arbitrary and does not sufficiently utilize the prior information of task design and neuroscience knowledge. To bridge this gap, we here propose a novel supervised sparse representation and dictionary learning framework based on stochastic coordinate coding (SCC) algorithm for task fMRI data analysis, in which certain brain networks are learned with known information such as pre-defined temporal patterns and spatial network patterns, and at the same time other networks are learned automatically from data. Our proposed method has been applied to two independent task fMRI datasets, and qualitative and quantitative evaluations have shown that our method provides a new and effective framework for task fMRI data analysis.     

Combining spatial priors and anatomical information for fMRI detection

In this paper, we analyze Markov Random Field (MRF) as a spatial regularizer in fMRI detection. The low signal-to-noise ratio (SNR) in fMRI images presents a serious challenge for detection algorithms, making regularization necessary to achieve good detection accuracy. Gaussian smoothing, traditionally employed to boost SNR, often produces over-smoothed activation maps. Recently, the use of MRF priors has been suggested as an alternative regularization approach. However, solving for an optimal configuration of the MRF is NP-hard in general. In this work, we investigate fast inference algorithms based on the Mean Field approximation in application to MRF priors for fMRI detection. Furthermore, we propose a novel way to incorporate anatomical information into the MRF-based detection framework and into the traditional smoothing methods. Intuitively speaking, the anatomical evidence increases the likelihood of activation in the gray matter and improves spatial coherency of the resulting activation maps within each tissue type. Validation using the receiver operating characteristic (ROC) analysis and the confusion matrix analysis on simulated data illustrates substantial improvement in detection accuracy using the anatomically guided MRF spatial regularizer. We further demonstrate the potential benefits of the proposed method in real fMRI signals of reduced length. The anatomically guided MRF regularizer enables significant reduction of the scan length while maintaining the quality of the resulting activation maps.     

Reducing inter-subject anatomical variation: Effect of normalization method on sensitivity of functional magnetic resonance imaging data analysis in auditory cortex and the superior temporal region

Conventional group analysis of functional MRI (fMRI) data usually involves spatial alignment of anatomy across participants by registering every brain image to an anatomical reference image. Due to the high degree of inter-subject anatomical variability, a low-resolution average anatomical model is typically used as the target template, and/or smoothing kernels are applied to the fMRI data to increase the overlap among subjects' image data. However, such smoothing can make it difficult to resolve small regions such as subregions of auditory cortex when anatomical morphology varies among subjects. Here, we use data from an auditory fMRI study to show that using a high-dimensional registration technique (HAMMER) results in an enhanced functional signal-to-noise ratio (fSNR) for functional data analysis within auditory regions, with more localized activation patterns. The technique is validated against DARTEL, a high-dimensional diffeomorphic registration, as well as against commonly used low-dimensional normalization techniques such as the techniques provided with SPM2 (cosine basis functions) and SPM5 (unified segmentation) software packages. We also systematically examine how spatial resolution of the template image and spatial smoothing of the functional data affect the results. Only the high-dimensional technique (HAMMER) appears to be able to capitalize on the excellent anatomical resolution of a single-subject reference template, and, as expected, smoothing increased fSNR, but at the cost of spatial resolution. In general, results demonstrate significant improvement in fSNR using HAMMER compared to analysis after normalization using DARTEL, or conventional normalization such as cosine basis function and unified segmentation in SPM, with more precisely localized activation foci, at least for activation in the region of auditory cortex.     

Classifying brain states and determining the discriminating activation patterns: Support Vector Machine on functional MRI data

In the present study, we applied the Support Vector Machine (SVM) algorithm to perform multivariate classification of brain states from whole functional magnetic resonance imaging (fMRI) volumes without prior selection of spatial features. In addition, we did a comparative analysis between the SVM and the Fisher Linear Discriminant (FLD) classifier. We applied the methods to two multisubject attention experiments: a face matching and a location matching task. We demonstrate that SVM outperforms FLD in classification performance as well as in robustness of the spatial maps obtained (i.e. discriminating volumes). In addition, the SVM discrimination maps had greater overlap with the general linear model (GLM) analysis compared to the FLD. The analysis presents two phases: during the training, the classifier algorithm finds the set of regions by which the two brain states can be best distinguished from each other. In the next phase, the test phase, given an fMRI volume from a new subject, the classifier predicts the subject's instantaneous brain state.