A Bayesian hierarchical correlation model for fMRI cluster analysis

Data-driven cluster analysis is potentially suitable to search for, and discriminate between, distinct response signals in blood oxygenation level-dependent functional magnetic resonance imaging (BOLD fMRI), which appear during cerebrovascular disease. In contrast to model-driven methods, which test for a particular BOLD signal whose shape must be given beforehand, data-driven methods generate a set of BOLD signals directly from the fMRI data by clustering voxels into groups with correlated time signals. Here, we address the problem of selecting only the clusters that represent genuine responses to the experimental stimulus by modeling the correlation structure of the clustered data using a Bayesian hierarchical model. The model is empirically justified by demonstrating the hierarchical organization of the voxel correlations after cluster analysis. BOLD signal discrimination is demonstrated using: 1) simulations that contain multiple pathological BOLD response signals; and 2) fMRI data acquired during an event-related motor task. These demonstrations are compared with results from a model-driven method based on the general linear model. Our simulations show that the data-driven method can discriminate between the BOLD response signals, while the model-driven method only finds one signal. For fMRI, the data-driven method distinguishes between the BOLD signals appearing in the sensorimotor cortex and those in basal ganglia and putamen, while the model-driven method combines these signals into one activation map. We conclude that the proposed data-driven method provides an objective framework to identify and discriminate between distinct BOLD response signals.     

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.     

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 computational multiresolution BOLD fMRI model

Blood oxygenation level-dependent (BOLD) functional magnetic resonance imaging (fMRI) is a widely used method for brain mapping. BOLD fMRI signal detection is based on an intravoxel dephasing mechanism. This model involves bulk nuclear spin precession in a BOLD-induced inhomogeneous magnetic field within a millimeter-resolution voxel, that is, BOLD signal formation spans a huge spatial scale range from Angstrom to millimeter. In this letter, we present a computational model for multiresolution BOLD fMRI simulation, which consists of partitioning the nuclear spin pool into spin packets at a mesoscopic scale (～10(-6) m), and calculating multiresolution voxel signals by grouping spin packets at a macroscopic scale range (10(-5) to 10(-3) m). Under a small-angle approximation, we find that the BOLD signal intensity is related to its phase counterpart (or BOLD fieldmap) across two spatial resolution levels.     

Signal nonlinearity in fMRI: a comparison between BOLD and MION

In this paper, we introduce a methodology for comparing the nonlinearities present in sets of time series using four different nonlinearity measures, one of which, the "delay vector variance" method, is a novel approach to the characterization of a time series. It is then applied to examine the difference in nonlinearity between functional magnetic resonance imaging (fMRI) signals that have been recorded using different contrast agents. Recently, an exogenous contrast agent, monocrystalline iron oxide particle (MION), has been introduced for fMRI, which has been shown to increase the functional sensitivity compared with the traditional blood oxygen level dependent (BOLD) technique. The resulting fMRI signals are influenced by cerebral blood volume, whereas the more traditionally recorded BOLD signals are influenced not only by cerebral blood volume, but also by the cerebral blood flow and the metabolic rate of oxygen. The proposed methodology is applied to address the question whether this difference in the number of physiological variables is reflected in a difference in the degree of nonlinearity. We therefore analyze two sets of fMRI signals, one from a BOLD and the other from a MION monkey study with similar experimental designs. In the neuroimaging context, the proposed nonlinearity analyses are different from those described in the literature, since no a priori model is assumed: rather than pinpointing the source(s) of nonlinearity, nonparametric analyses are performed on BOLD and MION fMRI signals. Furthermore, we introduce a strategy for analyzing a population of fMRI signals, rather than focusing the analysis on one signal, as is traditionally done in the domain of nonlinear signal processing. Our results show that, overall, the BOLD signals are more nonlinear in nature than the MION ones, which is in agreement with current hypotheses.     

A New General Linear Convolution Model for fMRI Data Process

General linear model (GLM) is the most popular method for functional magnetic resource imaging (fMRI) data analysis. However, its theory is imperfect. The key of this model is how to constitute the design-matrix to model the interesting effects better and separate noises better. For the purpose of detecting brain function activation, according to the principle of GLM, a new convolution model is presented by a new dynamic function convolving with design-matrix, which combining with t-test can be used to detect brain active signal. The fMRI imaging result of visual stimulus experiment indicates that brain activities mainly concentrate among vland v2 areas of visual cortex, and also verified the validity of this technique.     

非线性脑区相关性分析及动态脑网络构建方法

针对静息态脑功能磁共振的血氧依赖水平信号中的非线性特征,在基于滑动窗口的动态数据分析技术的基础上,本文重点对构建全脑动态特征矩阵过程中的不同非线性相关分析方法展开了对比研究,并给出了构建脑网络中的阈值确定方法。脑网络降维和状态聚类实验结果显示,在阈值参数选择合理的前提下,采用三种非线性分析方法对BOLD信号进行的相关分析均可得到结构规模相似的脑网络,并且其状态转换结果均显现出相似的规律性,从而为下一步展开脑网络的动态特性分析和演化过程研究奠定了基础。      

Activelets: Wavelets for sparse representation of hemodynamic responses

We propose a new framework to extract the activity-related component in the BOLD functional magnetic resonance imaging (fMRI) signal. As opposed to traditional fMRI signal analysis techniques, we do not impose any prior knowledge of the event timing. Instead, our basic assumption is that the activation pattern is a sequence of short and sparsely distributed stimuli, as is the case in slow event-related fMRI.We introduce new wavelet bases, termed “activelets”, which sparsify the activity-related BOLD signal. These wavelets mimic the behavior of the differential operator underlying the hemodynamic system. To recover the sparse representation, we deploy a sparse-solution search algorithm.The feasibility of the method is evaluated using both synthetic and experimental fMRI data. The importance of the activelet basis and the non-linear sparse recovery algorithm is demonstrated by comparison against classical B-spline wavelets and linear regularization, respectively.     

Estimation of the hemodynamic response of fMRI Data using RBF neural network

Functional magnetic resonance imaging (fMRI) is an important technique for neuroimaging. The conventional system identification methods used in fMRI data analysis assume a linear time-invariant system with the impulse response described by the hemodynamic responses (HDR). However, the measured blood oxygenation level-dependent (BOLD) signals to a particular processing task (for example, rapid event-related fMRI design) show nonlinear properties and vary with different brain regions and subjects. In this paper, radial basis function (RBF) neural network (a powerful technique for modelling nonlinearities) is proposed to model the dynamics underlying the fMRI data. The equivalence of the proposed method to the existing Volterra series method has been demonstrated. It is shown that the first- and second-order Volterra kernels could be deduced from the parameters of the RBF neural network. Studies on both simulated (using Balloon model) as well as real event-related fMRI data show that the proposed method can accurately estimate the HDR of the brain and capture the variations of the HDRs as a function of the brain regions and subjects.     

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.     

An integrated neighborhood correlation and hierarchical clustering approach of functional MRI

Clustering analysis is a promising data-driven method for the analysis of functional magnetic resonance imaging (fMRI) time series, however, the huge computation load makes it difficult for practical use. In this paper, neighborhood correlation (NC) and hierarchical clustering (HC) methods are integrated as a new approach where fMRI data are processed first by NC to get a preliminary image of brain activations, and then by HC to remove some noises. In HC, to better use spatial and temporal information in fMRI data, a new spatio-temporal measure is introduced. A simulation study and an application to visual fMRI data show that the brain activations can be effectively detected and that different response patterns can be discriminated. These results suggest that the proposed new integrated approach could be useful in detecting weak fMRI signals.     

Specified-resolution wavelet analysis of activation patterns from BOLD contrast fMRI

Functional magnetic resonance (MR) MR imaging (fMRI) with blood-oxygenation-level-dependent (BOLD) contrast localizes neuronal processing of cognitive paradigms. As magnetic resonance signal responses are small, functional mapping requires statistical analysis of temporally averaged image data. Although voxels activating at the paradigm frequency can be identified from the Fourier power spectrum, such analyses collapse the temporal information that is useful to establish consistency of responses during the paradigm. The design of a set of nonorthogonal wavelets of specified frequency resolution within the power spectrum was investigated for extracting desired frequency responses from the noisy signal intensity of individual voxels. These wavelets separate the low-frequency cognitive response to the paradigm from the respiratory and cardiac responses at higher frequencies. The retention of the temporal information, possible by wavelet analysis, allows the MR signal changes to be compared to changes in behavioral responses over the duration of an entire paradigm. The amplitude and time delay of the wavelet specified by the paradigm identify quantitatively the size of the MR signal change and the temporal delay of the hemodynamic BOLD response, respectively. This specified-resolution wavelet analysis was demonstrated for individual voxels and maps through the frontal eye fields using a visually guided saccade paradigm.     

Independent Component Analysis Applied to fMRI Data: A Generative Model for Validating Results

Methods for testing and validating independent component analysis (ICA) results in fMRI are growing in importance as the popularity of this model for studying brain function increases. We introduce and apply a synthesis/analysis model for analyzing functional Magnetic Resonance Imaging (fMRI) data using ICA. Classes of signal types relevant to fMRI are described and a statistical approach for validation of simulation results is developed. Additionally, we propose an empirical version of our validation approach to test the performance of various ICA approaches in “hybrid” fMRI data, a mixture of real fMRI data and known (validatable) sources. The synthesis portion of the model assumes statistically independent spatial sources in the brain. We also assume that the fMRI scanner acquires overdetermined data such that there are more time points than hemodynamic brain sources. We propose several signal classes relevant to fMRI and discuss the properties of each. The analysis portion of the model includes several candidates for spatial smoothing, ICA algorithm, and data reduction. We use the Kullback-Leibler divergence between the estimated source distributions and the “true” distributions as a measure of the optimality of the final ICA decomposition. Using this model, we generate fMRI-like data and optimize the analysis stage as a function of ICA algorithm, data reduction scheme, and spatial smoothing. An example of how our synthesis/analysis model can be used in validating an fMRI experiment is demonstrated using simulations and “hybrid” fMRI data.     

Probabilistic framework for brain connectivity from functional MR images

This paper unifies our earlier work on detection of brain activation (Rajapakse and Piyaratna, 2001) and connectivity (Rajapakse and Zhou, 2007) in a probabilistic framework for analyzing effective connectivity among activated brain regions from functional magnetic resonance imaging (fMRI) data. Interactions among brain regions are expressed by a dynamic Bayesian network (DBN) while contextual dependencies within functional images are formulated by a Markov random field. The approach simultaneously considers both the detection of brain activation and the estimation of effective connectivity and does not require a priori model of connectivity. Experimental results show that the present approach outperforms earlier fMRI analysis techniques on synthetic functional images and robustly derives brain connectivity from real fMRI data.     

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.     

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.     

Clustered components analysis for functional MRI

A common method of increasing hemodynamic response (SNR) in functional magnetic resonance imaging (fMRI) is to average signal timecourses across voxels. This technique is potentially problematic because the hemodynamic response may vary across the brain. Such averaging may destroy significant features in the temporal evolution of the fMRI response that stem from either differences in vascular coupling to neural tissue or actual differences in the neural response between two averaged voxels. Two novel techniques are presented in this paper in order to aid in an improved SNR estimate of the hemodynamic response while preserving statistically significant voxel-wise differences. The first technique is signal subspace estimation for periodic stimulus paradigms that involves a simple thresholding method. This increases SNR via dimensionality reduction. The second technique that we call clustered components analysis is a novel amplitude-independent clustering method based upon an explicit statistical data model. It includes an unsupervised method for estimating the number of clusters. Our methods are applied to simulated data for verification and comparison to other techniques. A human experiment was also designed to stimulate different functional cortices. Our methods separated hemodynamic response signals into clusters that tended to be classified according to tissue characteristics.     

基于fMRI功能网络和贝叶斯矩阵分解的脑电源成像方法

脑电(EEG)是一种重要的脑功能成像技术,根据头皮记录的EEG信号重构皮层脑活动称为EEG源成像。然而脑源活动位置和尺寸的准确重构依然是一个挑战。为充分利用EEG和功能磁共振(fMRI)信号在时空分辨率上的互补信息,该文提出一个新的源成像方法——基于fMRI脑网络和时空约束的EEG源重构算法(FN-STCSI)。该方法在参数贝叶斯框架下,基于矩阵分解思想将源信号分解为若干时间基函数的线性组合。此外,为融合fMRI的高空间分辨率信息,FN-STCSI利用独立成分分析提取fMRI信号的功能网络,构建EEG源成像的空间协方差基,通过变分贝叶斯推断技术确定每个空间协方差基的相对贡献,实现EEG-fMRI融合。通过蒙特卡罗数值仿真和实验数据分析比较了FN-STCSI与现有算法在不同信噪比和不同先验条件下的性能,结果表明FN-STCSI能有效融合EEG-fMRI在时空上的互补信息,提高EEG弥散源成像的性能。