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.     

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.      

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 event-related fMRI data using best clustering bases

We explore a new paradigm for the analysis of event-related functional magnetic resonance images (fMRI) of brain activity. We regard the fMRI data as a very large set of time series x(i) (t), indexed by the position i of a voxel inside the brain. The decision that a voxel i(o) is activated is based not solely on the value of the fMRI signal at i(o), but rather on the comparison of all time series x(i) (t) in a small neighborhood Wi(o) around i(o). We construct basis functions on which the projection of the fMRI data reveals the organization of the time series x(i) (t) into activated and nonactivated clusters. These clustering basis functions are selected from large libraries of wavelet packets according to their ability to separate the fMRI time series into the activated cluster and a nonactivated cluster. This principle exploits the intrinsic spatial correlation that is present in the data. The construction of the clustering basis functions described in this paper is applicable to a large category of problems where time series are indexed by a spatial variable.     

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.     

Comparison of two exploratory data analysis methods for fMRI: unsupervised clustering versus independent component analysis

Exploratory data-driven methods such as unsupervised clustering and independent component analysis (ICA) are considered to be hypothesis-generating procedures, and are complementary to the hypothesis-led statistical inferential methods in functional magnetic resonance imaging (fMRI). In this paper, we present a comparison between unsupervised clustering and ICA in a systematic fMRI study. The comparative results were evaluated by 1) task-related activation maps, 2) associated time-courses, and 3) receiver operating characteristic analysis. For the fMRI data, a comparative quantitative evaluation between the three clustering techniques, self-organizing map, "neural gas" network, and fuzzy clustering based on deterministic annealing, and the three ICA methods, FastICA, Infomax and topographic ICA was performed. The ICA methods proved to extract features relatively well for a small number of independent components but are limited to the linear mixture assumption. The unsupervised Clustering outperforms ICA in terms of classification results but requires a longer processing time than the ICA methods.     

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.     

融合先验信息的脑功能图像分割

基于静息态功能磁共振图像(fMRI)的脑功能区分割广泛采用K均值聚类和谱聚类等无监督聚类算法。但这些算法对图像噪声较为敏感,可能会产生不可靠的脑区分割结果。文中提出了一种融合先验信息的半监督聚类算法,可以可靠地确定各子区间的边界,从而得到稳定的分割结果。提出的方法对人类右侧大脑的Broca区(BA44/45区)进行分割验证,实验结果表明,文中的方法不仅得到了可靠的功能子区边界,而且获得了较高的个体间一致性。     

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.     

Selection criteria for the analysis of data-driven clusters in cerebral FMRI

Functional MRI (fMRI) may be possible without a priori models of the cerebral hemodynamic response. First, such data-driven fMRI requires that all cerebral territories with distinct patterns be identified. Second, a systematic selection method is necessary to prevent the subjective interpretation of the identified territories. This paper addresses the second point by proposing a novel method for the automated interpretation of identified territories in data-driven fMRI. Selection criteria are formulated using: 1) the temporal cross-correlation between each identified territory and the paradigm and 2) the spatial contiguity of the corresponding voxel map. Ten event-design fMRI data sets are analyzed with one prominent algorithm, fuzzy c-means clustering, before applying the selection criteria. For comparison, these data are also analyzed with an established, model-based method: statistical parametric mapping. Both methods produced similar results and identified potential activation in the expected territory of the sensorimotor cortex in all ten data sets. Moreover, the proposed method classified distinct territories in separate clusters. Selected clusters have a mean temporal correlation coefficient of 0.39+/-0.07 (n=19) with a mean 2.7+/-1.4 second response delay. At most, four separate contiguous territories were observed in 87% of these clusters. These results suggest that the proposed method may be effective for exploratory fMRI studies where the hemodynamic response is perturbed during cerebrovascular disease.     

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.     

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。      

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.     

HRF estimation in fMRI data with an unknown drift matrix by iterative minimization of the Kullback-Leibler divergence

Hemodynamic response function (HRF) estimation in noisy functional magnetic resonance imaging (fMRI) plays an important role when investigating the temporal dynamic of a brain region response during activations. Nonparametric methods which allow more flexibility in the estimation by inferring the HRF at each time sample have provided improved performance in comparison to the parametric methods. In this paper, the mixed-effects model is used to derive a new algorithm for nonparametric maximum likelihood HRF estimation. In this model, the random effect is used to better account for the variability of the drift. Contrary to the usual approaches, the proposed algorithm has the benefit of considering an unknown and therefore flexible drift matrix. This allows the effective representation of a broader class of drift signals and therefore the reduction of the error in approximating the drift component. Estimates of the HRF and the hyperparameters are derived by iterative minimization of the Kullback-Leibler divergence between a model family of probability distributions defined using the mixed-effects model and a desired family of probability distributions constrained to be concentrated on the observed data. The performance of proposed method is demonstrated on simulated and real fMRI data, the latter originating from both event-related and block design fMRI experiments.     

基于BP神经网络的RSSI测距优化算法

基于接收信号强度指示(received signal strength indication, RSSI)测距的研究和应用领域很广泛,一直是物联网研究的热点. 为降低传统基于反向传播(back propagation,BP)神经网络的RSSI测距误差,文中提出一种基于K-means聚类算法对样本数据进行预处理的BP神经网络测距算法,来解决由于RSSI值衰减程度不同引起的不同距离区间RSSI值和真实距离之间映射关系不均匀的问题. 将K-means聚类算法应用于BP神经网络模型中,对样本数据进行距离区间划分,然后将已经分类好的数据分别输入BP神经网络建立网络模型并进行实验仿真. 结果显示:传统基于BP神经网络的RSSI测距算法的均方根误差为1.425 7 m;而经过K-means算法改进后的BP神经网络测距算法的均方根误差为1.288 7 m,降低了测距误差,并优化了目标RSSI值与真实距离的映射关系.     

Unsupervised robust nonparametric estimation of the hemodynamic response function for any fMRI experiment

This paper deals with the estimation of the blood oxygen level-dependent response to a stimulus, as measured in functional magnetic resonance imaging (fMRI) data. A precise estimation is essential for a better understanding of cerebral activations. The most recent works have used a nonparametric framework for this estimation, considering each brain region as a system characterized by its impulse response, the so-called hemodynamic response function (HRF). However, the use of these techniques has remained limited since they are not well-adapted to real fMRI data. Here, we develop a threefold extension to previous works. We consider asynchronous event-related paradigms, account for different trial types and integrate several fMRI sessions into the estimation. These generalizations are simultaneously addressed through a badly conditioned observation model. Bayesian formalism is used to model temporal prior information of the underlying physiological process of the brain hemodynamic response. By this way, the HRF estimate results from a tradeoff between information brought by the data and by our prior knowledge. This tradeoff is modeled with hyperparameters that are set to the maximum-likelihood estimate using an expectation conditional maximization algorithm. The proposed unsupervised approach is validated on both synthetic and real fMRI data, the latter originating from a speech perception experiment.     

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.     

Detection and visualization method of dynamic state transition for biological spatio-temporal imaging data

In the statistical analysis of functional brain imaging data, regression analysis and cross correlation analysis between time series data on each grid point have been widely used. The results can be graphically represented as an activation map on an anatomical image, but only activation signal, whose temporal pattern resembles the predefined reference function, can be detected. In the present study, we propose a fusion method comprising innovation approach in time series analysis and statistical test. Autoregressive (AR) models were fitted to time series data of each pixel for the range sufficiently before or after the state transition. Then, the remaining time series data were filtered using these AR parameters to obtain its innovation (filter output). The proposed method could extract brain neural activation as a phase transition of dynamics in the system without employing external information such as the reference function. The activation could be detected as temporal transitions of statistical test values. We evaluated this method by applying to optical imaging data obtained from the mammalian brain and the cardiac sino-atrial node (SAN), and demonstrated that our method can precisely detect spatio-temporal activation profiles in the brain or SAN.     

Model-free functional MRI analysis using Kohonen clustering neural network and fuzzy C-means

Conventional model-based or statistical analysis methods for functional MRI (fMRI) suffer from the limitation of the assumed paradigm and biased results. Temporal clustering methods, such as fuzzy clustering, can eliminate these problems but are difficult to find activation occupying a small area, sensitive to noise and initial values, and computationally demanding. To overcome these adversities, a cascade clustering method combining a Kohonen clustering network and fuzzy, means is developed. Receiver operating characteristic (ROC) analysis is used to compare this method with correlation coefficient analysis and t test on a series of testing phantoms. Results shown that this method can efficiently and stably identify the actual functional response with typical signal change to noise ratio, from a small activation area occupying only 0.2% of head size, with phase delay, and from other noise sources such as head motion. With the ability of finding activities of small sizes stably this method can not only identify the functional responses and the active regions more precisely, but also discriminate responses from different signal sources, such as large venous vessels or different types of activation patterns in human studies involving motor cortex activation. Even when the experimental paradigm is unknown in a blind test such that model-based methods are inapplicable, this method can identify the activation patterns and regions correctly.