Contextual modeling of functional MR images with conditional random fields

This paper presents a conditional random field (CRF) approach to fuse contextual dependencies in functional magnetic resonance imaging (fMRI) data for the detection of brain activation. The interactions among both activation (activated/inactive) labels and observed data of brain voxels are unified in a probabilistic framework based on the CRF, where the interaction strength can be adaptively adjusted in terms of the data similarity of neighboring sites. Compared to earlier detection methods, including statistical parametric mapping and Markov random field, the proposed method avoids the suppression of high frequency information and relaxes the strong assumption of conditional independence of observed data. Experimental results show that the proposed approach effectively integrates contextual constraints within the detection process and robustly detects brain activities from fMRI data.     

Group replicator dynamics: a novel group-wise evolutionary approach for sparse brain network detection

Functional magnetic resonance imaging (fMRI) is increasingly used for studying functional integration of the brain. However, large inter-subject variability in functional connectivity, particularly in disease populations, renders detection of representative group networks challenging. In this paper, we propose a novel technique, "group replicator dynamics" (GRD), for detecting sparse functional brain networks that are common across a group of subjects. We extend the replicator dynamics (RD) approach, which we show to be a solution of the nonnegative sparse principal component analysis problem, by integrating group information into each subject's RD process. Our proposed strategy effectively coaxes all subjects' networks to evolve towards the common network of the group. This results in sparse networks comprising the same brain regions across subjects yet with subject-specific weightings of the identified brain regions. Thus, in contrast to traditional averaging approaches, GRD enables inter-subject variability to be modeled, which facilitates statistical group inference. Quantitative validation of GRD on synthetic data demonstrated superior network detection performance over standard methods. When applied to real fMRI data, GRD detected task-specific networks that conform well to prior neuroscience knowledge.     

Unified Framework for Robust Estimation of Brain Networks From fMRI Using Temporal and Spatial Correlation Analyses

There is a rapidly growing interest in the neuroimaging field to use functional magnetic resonance imaging (fMRI) to explore brain networks, i.e., how regions of the brain communicate with one another. This paper presents a general and novel statistical framework for robust and more complete estimation of brain functional connectivity from fMRI based on correlation analyses and hypothesis testing. In addition to the ability of examining the correlations with each individual seed as in the standard and existing methods, the proposed framework can detect functional interactions by simultaneously examining multiseed correlations via multiple correlation coefficients. Spatially structured noise in fMRI is also taken into account during the identification of functional interconnection networks through noncentral $F$ hypothesis tests. The associated issues for the multiple testing and the effective degrees-of-freedom are considered as well. Furthermore, partial multiple correlations are introduced and formulated to measure any additional task-induced but not stimulus-locked relation over brain regions so that we can take the analysis of functional connectivity closer to the characterization of direct functional interactions of the brain. Evaluation for accuracy and advantages, and comparisons of the new approaches in the presented general framework are performed using both realistic synthetic data and in vivo fMRI data.      

Unsupervised learning and mapping of active brain functional MRI signals based on hidden semi-Markov event sequence models

In this paper, a novel functional magnetic resonance imaging (fMRI) brain mapping method is presented within the statistical modeling framework of hidden semi-Markov event sequence models (HSMESMs). Neural activation detection is formulated at the voxel level in terms of time coupling between the sequence of hemodynamic response onsets (HROs) observed in the fMRI signal, and an HSMESM of the hidden sequence of task-induced neural activations. The sequence of HRO events is derived from a continuous wavelet transform (CWT) of the fMRI signal. The brain activation HSMESM is built from the timing information of the input stimulation protocol. The rich mathematical framework of HSMESMs makes these models an effective and versatile approach for fMRI data analysis. Solving for the HSMESM Evaluation and Learning problems enables the model to automatically detect neural activation embedded in a given set of fMRI signals, without requiring any template basis function or prior shape assumption for the fMRI response. Solving for the HSMESM Decoding problem allows to enrich brain mapping with activation lag mapping, activation mode visualizing, and hemodynamic response function analysis. Activation detection results obtained on synthetic and real epoch-related fMRI data demonstrate the superiority of the HSMESM mapping method with respect to a real application case of the statistical parametric mapping (SPM) approach. In addition, the HSMESM mapping method appears clearly insensitive to timing variations of the hemodynamic response, and exhibits low sensitivity to fluctuations of its shape.     

Convolution Power Spectrum Analysis for fMRI Data Based on Prior Image Signal

Functional MRI (fMRI) data-processing methods based on changes in the time domain involve, among other things, correlation analysis and use of the general linear model with statistical parametric mapping (SPM). Unlike conventional fMRI data analysis methods, which aim to model the blood-oxygen-level-dependent (BOLD) response of voxels as a function of time, the theory of power spectrum (PS) analysis focuses completely on understanding the dynamic energy change of interacting systems. We propose a new convolution PS (CPS) analysis of fMRI data, based on the theory of matched filtering, to detect brain functional activation for fMRI data. First, convolution signals are computed between the measured fMRI signals and the image signal of prior experimental pattern to suppress noise in the fMRI data. Then, the PS density analysis of the convolution signal is specified as the quantitative analysis energy index of BOLD signal change. The data from simulation studies and in vivo fMRI studies, including block-design experiments, reveal that the CPS method enables a more effective detection of some aspects of brain functional activation, as compared with the canonical PS SPM and the support vector machine methods. Our results demonstrate that the CPS method is useful as a complementary analysis in revealing brain functional information regarding the complex nature of fMRI time series.      

A sparse Bayesian method for determination of flexible design matrix for fMRI data analysis

The construction of a design matrix is critical to the accurate detection of activation regions of the brain in functional magnetic resonance imaging (fMRI). The design matrix should be flexible to capture the unknown slowly varying drifts as well as robust enough to avoid overfitting. In this paper, a sparse Bayesian learning method is proposed to determine a suitable design matrix for fMRI data analysis. Based on a generalized linear model, this learning method lets the data itself determine the form of the regressors in the design matrix. It automatically finds those regressors that are relevant to the generation of the fMRI data and discards the others that are irrelevant. The proposed approach integrates the advantages of currently employed methods of fMRI data analysis (the model-driven and the data-driven methods). Results from the simulation studies clearly reveal the superiority of the proposed scheme to the conventional t-test method of fMRI data analysis.     

Kernel Granger Causality Mapping Effective Connectivity on fMRI Data

Although it is accepted that linear Granger causality can reveal effective connectivity in functional magnetic resonance imaging (fMRI), the issue of detecting nonlinear connectivity has hitherto not been considered. In this paper, we address kernel Granger causality (KGC) to describe effective connectivity in simulation studies and real fMRI data of a motor imagery task. Based on the theory of reproducing kernel Hilbert spaces, KGC performs linear Granger causality in the feature space of suitable kernel functions, assuming an arbitrary degree of nonlinearity. Our results demonstrate that KGC captures effective couplings not revealed by the linear case. In addition, effective connectivity networks between the supplementary motor area (SMA) as the seed and other brain areas are obtained from KGC.      

Analysis of FMRI data using an integrated principal component analysis and supervised affinity propagation clustering approach

Clustering analysis is a promising data-driven method for analyzing functional magnetic resonance imaging (fMRI) time series data. The huge computational load, however, creates practical difficulties for this technique. We present a novel approach, integrating principal component analysis (PCA) and supervised affinity propagation clustering (SAPC). In this method, fMRI data are initially processed by PCA to obtain a preliminary image of brain activation. SAPC is then used to detect different brain functional activation patterns. We used a supervised Silhouette index to optimize clustering quality and automatically search for the optimal parameter p in SAPC, so that the basic affinity propagation clustering is improved by applying SAPC. Four simulation studies and tests with three in vivo fMRI datasets containing data from both block-design and event-related experiments revealed that functional brain activation was effectively detected and different response patterns were distinguished using our integrated method. In addition, the improved SAPC method was superior to the k -centers clustering and hierarchical clustering methods in both block-design and event-related fMRI data, as measured by the average squared error. These results suggest that our proposed novel integrated approach will be useful for detecting brain functional activation in both block-design and event-related experimental fMRI data.     

Model-independent method for fMRI analysis

This paper presents a fast method for delineation of activated areas of the brain from functional magnetic resonance imaging (fMRI) time series data. The steps of the work accomplished are as follows. 1) It is shown that the detection performance evaluated by the area under the receiver operating characteristic curve is directly related to the signal-to-noise ratio (SNR) of the composite image generated in the detection process. 2) Detection and segmentation of activated areas are formulated in a vector space framework. In this formulation, a linear transformation (image combination method) is shown to be desirable to maximize the SNR of the activated areas subject to the constraint of removing inactive areas. 3) An analytical solution for the problem is found. 4) Image pixel vectors and expected time series pattern (signature) for inactive pixels are used to calculate weighting vector and identify activated regions. 5) Signatures of the activated regions are used to segment different activities. 6) Segmented images by the proposed method are compared with those generated by the conventional methods (correlation, t-statistic, and z statistic). Detection performance and SNRs of the images are compared. The proposed approach outperforms the conventional methods of fMRI analysis. In addition, it is model-independent and does not require a priori knowledge of the fMRI response to the paradigm. Since the method is linear and most of the work is done analytically, numerical implementation and execution of the method are much faster than the conventional methods.     

Bayesian approach to segmentation of statistical parametric maps

A contextual segmentation technique to detect brain activation from functional brain images is presented in the Bayesian framework. Unlike earlier similar approaches [Holmes and Ford (1993) and Descombes et al. (1998)], a Markov random field (MRF) is used to represent configurations of activated brain voxels, and likelihoods given by statistical parametric maps (SPM's) are directly used to find the maximum a posteriori (MAP) estimation of segmentation. The iterative segmentation algorithm, which is based on a simulated annealing scheme, is fully data-driven and capable of analyzing experiments involving multiple-input stimuli. Simulation results and comparisons with the simple thresholding and the statistical parametric mapping (SPM) approaches are presented with synthetic images, and functional MR images acquired in memory retrieval and event-related working memory tasks. The experiments show that an MRF is a valid representation of the activation patterns obtained in functional brain images, and the present technique renders a superior segmentation scheme to the context-free approach and the SPM approach.     

Automatic identification of functional clusters in FMRI data using spatial dependence

In independent component analysis (ICA) of functional magnetic resonance imaging (fMRI) data, extracting a large number of maximally independent components provides a detailed functional segmentation of brain. However, such high-order segmentation does not establish the relationships among different brain networks, and also studying and classifying components can be challenging. In this study, we present a multidimensional ICA (MICA) scheme to achieve automatic component clustering. In our MICA framework, stable components are hierarchically grouped into clusters based on higher order statistical dependence--mutual information--among spatial components, instead of the typically used temporal correlation among time courses. The final cluster membership is determined using a statistical hypothesis testing method. Since ICA decomposition takes into account the modulation of the spatial maps, i.e., temporal information, our ICA-based approach incorporates both spatial and temporal information effectively. Our experimental results from both simulated and real fMRI datasets show that the use of spatial dependence leads to physiologically meaningful connectivity structure of brain networks, which is consistently identified across various ICA model orders and algorithms. In addition, we observe that components related to artifacts, including cerebrospinal fluid, arteries, and large draining veins, are grouped together and encouragingly distinguished from other components of interest.     

Group Study of Simulated Driving fMRI Data by Multiset Canonical Correlation Analysis

In this work, we apply a novel statistical method, multiset canonical correlation analysis (M-CCA), to study a group of functional magnetic resonance imaging (fMRI) datasets acquired during simulated driving task. The M-CCA method jointly decomposes fMRI datasets from different subjects/sessions into brain activation maps and their associated time courses, such that the correlation in each group of estimated activation maps across datasets is maximized. Therefore, the functional activations across all datasets are extracted in the order of consistency across different dataset. On the other hand, M-CCA preserves the uniqueness of the functional maps estimated from each dataset by avoiding concatenation of different datasets in the analysis. Hence, the cross-dataset variation of the functional activations can be used to test the hypothesis of functional-behavioral association. In this work, we study 120 simulated driving fMRI datasets and identify parietal-occipital regions and frontal lobe as the most consistently engaged areas across all the subjects and sessions during simulated driving. The functional-behavioral association study indicates that all the estimated brain activations are significantly correlated with the steering operation during the driving task. M-CCA thus provides a new approach to investigate the complex relationship between the brain functions and multiple behavioral variables, especially in naturalistic tasks as demonstrated by the simulated driving study.     

Analysis of fMRI data using improved self-organizing mapping and spatio-temporal metric hierarchical clustering

The self-organizing mapping (SOM) and hierarchical clustering (HC) methods are integrated to detect brain functional activation; functional magnetic resonance imaging (fMRI) data are first processed by SOM to obtain a primary merged neural nodes image, and then by HC to obtain further brain activation patterns. The conventional Euclidean distance metric was replaced by the correlation distance metric in SOM to improve clustering and merging of neural nodes. To improve the use of spatial and temporal information in fMRI data, a new spatial distance (node coordinates in the 2-D lattice) and temporal correlation (correlation degree of each time course in the exemplar matrix) are introduced in HC to merge the primary SOM results. Two simulation studies and two in vivo fMRI data that both contained block-design and event-related experiments revealed that brain functional activation can be effectively detected and that different response patterns can be distinguished using these methods. Our results demonstrate that the improved SOM and HC methods are clearly superior to the statistical parametric mapping (SPM), independent component analysis (ICA), and conventional SOM methods in the block-design, especially in the event-related experiment, as revealed by their performance measured by receiver operating characteristic (ROC) analysis. Our results also suggest that the proposed new integrated approach could be useful in detecting block-design and event-related fMRI data.      

A Connectivity-Based Method for Defining Regions-of-Interest in fMRI Data

In this paper, we describe a new methodology for defining brain regions-of-interset (ROIs) in functional magnetic resonance imaging (fMRI) data. The ROIs are defined based on their functional connectivity to other ROIs, i.e., ROIs are defined as sets of voxels with similar connectivity patterns to other ROIs. The method relies on 1) a spatially regularized canonical correlation analysis for identifying maximally correlated signals, which are not due to correlated noise; 2) a test for merging ROIs which have similar connectivity patterns to the other ROIs; and 3) a graph-cuts optimization for assigning voxels to ROIs. Since our method is fully connectivity-based, the extracted ROIs and their corresponding time signals are ideally suited for a subsequent brain connectivity analysis.      

A model selection method for nonlinear system identification based FMRI effective connectivity analysis

In this paper a model selection algorithm for a nonlinear system identification method is proposed to study functional magnetic resonance imaging (fMRI) effective connectivity. Unlike most other methods, this method does not need a pre-defined structure/model for effective connectivity analysis. Instead, it relies on selecting significant nonlinear or linear covariates for the differential equations to describe the mapping relationship between brain output (fMRI response) and input (experiment design). These covariates, as well as their coefficients, are estimated based on a least angle regression (LARS) method. In the implementation of the LARS method, Akaike's information criterion corrected (AICc) algorithm and the leave-one-out (LOO) cross-validation method were employed and compared for model selection. Simulation comparison between the dynamic causal model (DCM), nonlinear identification method, and model selection method for modelling the single-input-single-output (SISO) and multiple-input multiple-output (MIMO) systems were conducted. Results show that the LARS model selection method is faster than DCM and achieves a compact and economic nonlinear model simultaneously. To verify the efficacy of the proposed approach, an analysis of the dorsal and ventral visual pathway networks was carried out based on three real datasets. The results show that LARS can be used for model selection in an fMRI effective connectivity study with phase-encoded, standard block, and random block designs. It is also shown that the LOO cross-validation method for nonlinear model selection has less residual sum squares than the AICc algorithm for the study.     

Modeling brain activation in fMRI using group MRF

Noise confounds present serious complications to functional magnetic resonance imaging (fMRI) analysis. The amount of discernible signals within a single dataset of a subject is often inadequate to obtain satisfactory intra-subject activation detection. To remedy this limitation, we propose a novel group Markov random field (GMRF) that extends each subject's neighborhood system to other subjects to enable information coalescing. A distinct advantage of GMRF over standard fMRI group analysis is that no stringent one-to-one voxel correspondence is required. Instead, intra- and inter-subject neighboring voxels are jointly regularized to encourage spatially proximal voxels to be assigned similar labels across subjects. Our proposed group-extended graph structure thus provides an effective means for handling inter-subject variability. Also, adopting a group-wise approach by integrating group information into intra-subject activation, as opposed to estimating a single average group map, permits inter-subject differences to be characterized and studied. GMRF can be elegantly implemented as a single MRF, thus enabling all subjects' activation maps to be simultaneously and collaboratively segmented with global optimality guaranteed in the case of binary labeling. We validate our technique on synthetic and real fMRI data and demonstrate GMRF's superior performance over standard fMRI analysis.     

Classification of fMRI time series in a low-dimensional subspace with a spatial prior

We propose a new method for detecting activation in functional magnetic resonance imaging (fMRI) data. We project the fMRI time series on a low-dimensional subspace spanned by wavelet packets in order to create projections that are as non-Gaussian as possible. Our approach achieves two goals: it reduces the dimensionality of the problem by explicitly constructing a sparse approximation to the dataset and it also creates meaningful clusters allowing the separation of the activated regions from the clutter formed by the background time series. We use a mixture of Gaussian densities to model the distribution of the wavelet packet coefficients. We expect activated areas that are connected, and impose a spatial prior in the form of a Markov random field. Our approach was validated with in vivo data and realistic synthetic data, where it outperformed a linear model equipped with the knowledge of the true hemodynamic response.     

Min-max Extrapolation Scheme for Fast Estimation of 3D Potts Field Partition Functions. Application to the Joint Detection-Estimation of Brain Activity in fMRI

In this paper, we propose a fast numerical scheme to estimate Partition Functions (PF) of symmetric Potts fields. Our strategy is first validated on 2D two-color Potts fields and then on 3D two- and three-color Potts fields. It is then applied to the joint detection-estimation of brain activity from functional Magnetic Resonance Imaging (fMRI) data, where the goal is to automatically recover activated, deactivated and inactivated brain regions and to estimate region-dependent hemodynamic filters. For any brain region, a specific 3D Potts field indeed embodies the spatial correlation over the hidden states of the voxels by modeling whether they are activated, deactivated or inactive. To make spatial regularization adaptive, the PFs of the Potts fields over all brain regions are computed prior to the brain activity estimation. Our approach is first based upon a classical path-sampling method to approximate a small subset of reference PFs corresponding to prespecified regions. Then, we propose an extrapolation method that allows us to approximate the PFs associated to the Potts fields defined over the remaining brain regions. In comparison with preexisting methods either based on a path-sampling strategy or mean-field approximations, our contribution strongly alleviates the computational cost and makes spatially adaptive regularization of whole brain fMRI datasets feasible. It is also robust against grid inhomogeneities and efficient irrespective of the topological configurations of the brain regions.     

Order Selection of the Linear Mixing Model for Complex-Valued FMRI Data

Functional magnetic resonance imaging (fMRI) data are originally acquired as complex-valued images, which motivates the use of complex-valued data analysis methods. Due to the high dimension and high noise level of fMRI data, order selection and dimension reduction are important procedures for multivariate analysis methods such as independent component analysis (ICA). In this work, we develop a complex-valued order selection method to estimate the dimension of signal subspace using information-theoretic criteria. To correct the effect of sample dependence to information-theoretic criteria, we develop a general entropy rate measure for complex Gaussian random process to calibrate the independent and identically distributed (i.i.d.) sampling scheme in the complex domain. We show the effectiveness of the approach for order selection on both simulated and actual fMRI data. A comparison between the results of order selection and ICA on real-valued and complex-valued fMRI data demonstrates that a fully complex analysis extracts more meaningful components about brain activation.     

Toeplitz-Based Iterative Image Reconstruction for MRI With Correction for Magnetic Field Inhomogeneity

In some types of magnetic resonance (MR) imaging, particularly functional brain scans, the conventional Fourier model for the measurements is inaccurate. Magnetic field inhomogeneities, which are caused by imperfect main fields and by magnetic susceptibility variations, induce distortions in images that are reconstructed by conventional Fourier methods. These artifacts hamper the use of functional MR imaging (fMRI) in brain regions near air/tissue interfaces. Recently, iterative methods that combine the conjugate gradient (CG) algorithm with nonuniform FFT (NUFFT) operations have been shown to provide considerably improved image quality relative to the conjugate-phase method. However, for non-Cartesian k-space trajectories, each CG-NUFFT iteration requires numerous k-space interpolations; these are operations that are computationally expensive and poorly suited to fast hardware implementations. This paper proposes a faster iterative approach to field-corrected MR image reconstruction based on the CG algorithm and certain Toeplitz matrices. This CG-Toeplitz approach requires k-space interpolations only for the initial iteration; thereafter, only fast Fourier transforms (FFTs) are required. Simulation results show that the proposed CG-Toeplitz approach produces equivalent image quality as the CG-NUFFT method with significantly reduced computation time.