Group analysis in functional neuroimaging: selecting subjects using similarity measures

Standard group analyses of fMRI data rely on spatial and temporal averaging of individuals. This averaging operation is only sensible when the mean is a good representation of the group. This is not the case if subjects are not homogeneous, and it is therefore a major concern in fMRI studies to assess this group homogeneity. We present a method that provides relevant distances or similarity measures between temporal series of brain functional images belonging to different subjects. The method allows a multivariate comparison between data sets of several subjects in the time or in the space domain. These analyses assess the global intersubject variability before averaging subjects and drawing conclusions across subjects, at the population level. We adapt the RV coefficient to measure meaningful spatial or temporal similarities and use multidimensional scaling to give a visual representation of each subject's position with respect to other subjects in the group. We also provide a measure for detecting subjects that may be outliers. Results show that the method is a powerful tool to detect subjects with specific temporal or spatial patterns, and that, despite the apparent loss of information, restricting the analysis to a homogeneous subgroup of subjects does not reduce the statistical sensitivity of standard group fMRI analyses.     

An automated method for neuroanatomic and cytoarchitectonic atlas-based interrogation of fMRI data sets

Analysis and interpretation of functional MRI (fMRI) data have traditionally been based on identifying areas of significance on a thresholded statistical map of the entire imaged brain volume. This form of analysis can be likened to a "fishing expedition." As we become more knowledgeable about the structure-function relationships of different brain regions, tools for a priori hypothesis testing are needed. These tools must be able to generate region of interest masks for a priori hypothesis testing consistently and with minimal effort. Current tools that generate region of interest masks required for a priori hypothesis testing can be time-consuming and are often laboratory specific. In this paper we demonstrate a method of hypothesis-driven data analysis using an automated atlas-based masking technique. We provide a powerful method of probing fMRI data using automatically generated masks based on lobar anatomy, cortical and subcortical anatomy, and Brodmann areas. Hemisphere, lobar, anatomic label, tissue type, and Brodmann area atlases were generated in MNI space based on the Talairach Daemon. Additionally, we interfaced these multivolume atlases to a widely used fMRI software package, SPM99, and demonstrate the use of the atlas tool with representative fMRI data. This tool represents a necessary evolution in fMRI data analysis for testing of more spatially complex hypotheses.     

Modeling state-related fMRI activity using change-point theory

The general linear model (GLM) approach has arguably become the dominant way to analyze functional magnetic resonance imaging (fMRI) data. It tests whether activity in a brain region is systematically related to some known input function. However, the GLM becomes impractical when the precise timing and duration of psychological events cannot be specified a priori. In this work, we introduce a new analysis approach that allows the predicted signal to depend non-linearly on the input. The approach uses ideas from statistical control theory and change-point theory to model slowly varying processes for which the onset times and durations of underlying psychological activity are uncertain. Our approach is exploratory in nature, while retaining the inferential capabilities of the more rigid modeling approach. It is a multi-subject extension of the exponentially weighted moving average (EWMA) method used in change-point analysis. We extend existing EWMA models for individual subjects (a single time series) so that they are applicable to fMRI data, and develop a group analysis using a hierarchical model, which we term HEWMA (Hierarchical EWMA). The HEWMA method can be used to analyze fMRI data voxel-wise throughout the brain, data from regions of interest, or temporal components extracted using ICA or similar methods. We validate the false-positive rate control of the method and provide power estimates using simulations based on real fMRI data. We further apply this method to an fMRI study (n=24) of state anxiety. A toolbox implementing all functions in Matlab is freely available from the authors.     

Integrated wavelet processing and spatial statistical testing of fMRI data

We introduce an integrated framework for detecting brain activity from fMRI data, which is based on a spatial discrete wavelet transform. Unlike the standard wavelet-based approach for fMRI analysis, we apply the suitable statistical test procedure in the spatial domain. For a desired significance level, this scheme has one remaining degree of freedom, characterizing the wavelet processing, which is optimized according to the principle of minimal approximation error. This allows us to determine the threshold values in a way that does not depend on data. While developing our framework, we make only conservative assumptions. Consequently, the detection of activation is based on strong evidence. We have implemented this framework as a toolbox (WSPM) for the SPM2 software, taking advantage of multiple options and functions of SPM such as the setup of the linear model and the use of the hemodynamic response function. We show by experimental results that our method is able to detect activation patterns; the results are comparable to those obtained by SPM even though statistical assumptions are more conservative.     

Learning functional structure from fMR images

We propose a novel method using Bayesian networks to learn the structure of effective connectivity among brain regions involved in a functional MR experiment. The approach is exploratory in the sense that it does not require an a priori model as in the earlier approaches, such as the Structural Equation Modeling or Dynamic Causal Modeling, which can only affirm or refute the connectivity of a previously known anatomical model or a hypothesized model. The conditional probabilities that render the interactions among brain regions in Bayesian networks represent the connectivity in the complete statistical sense. The present method is applicable even when the number of regions involved in the cognitive network is large or unknown. We demonstrate the present approach by using synthetic data and fMRI data collected in silent word reading and counting Stroop tasks.     

Dynamic connectivity regression: determining state-related changes in brain connectivity

Most statistical analyses of fMRI data assume that the nature, timing and duration of the psychological processes being studied are known. However, often it is hard to specify this information a priori. In this work we introduce a data-driven technique for partitioning the experimental time course into distinct temporal intervals with different multivariate functional connectivity patterns between a set of regions of interest (ROIs). The technique, called Dynamic Connectivity Regression (DCR), detects temporal change points in functional connectivity and estimates a graph, or set of relationships between ROIs, for data in the temporal partition that falls between pairs of change points. Hence, DCR allows for estimation of both the time of change in connectivity and the connectivity graph for each partition, without requiring prior knowledge of the nature of the experimental design. Permutation and bootstrapping methods are used to perform inference on the change points. The method is applied to various simulated data sets as well as to an fMRI data set from a study (N=26) of a state anxiety induction using a socially evaluative threat challenge. The results illustrate the method's ability to observe how the networks between different brain regions changed with subjects' emotional state.     

Real-time independent component analysis of fMRI time-series

Real-time functional magnetic resonance imaging (fMRI) enables one to monitor a subject's brain activity during an ongoing session. The availability of online information about brain activity is essential for developing and refining interactive fMRI paradigms in research and clinical trials and for neurofeedback applications. Data analysis for real-time fMRI has traditionally been based on hypothesis-driven processing methods. Off-line data analysis, conversely, may be usefully complemented by data-driven approaches, such as independent component analysis (ICA), which can identify brain activity without a priori temporal assumptions on brain activity. However, ICA is commonly considered a time-consuming procedure and thus unsuitable to process the high flux of fMRI data while they are acquired. Here, by specific choices regarding the implementation, we exported the ICA framework and implemented it into real-time fMRI data analysis. We show that, reducing the ICA input to a few points within a time-series in a sliding-window approach, computational times become compatible with real-time settings. Our technique produced accurate dynamic readouts of brain activity as well as a precise spatiotemporal history of quasistationary patterns in the form of cumulative activation maps and time courses. Results from real and simulated motor activation data show comparable performances for the proposed ICA implementation and standard linear regression analysis applied either in a sliding-window or in a cumulative mode. Furthermore, we demonstrate the possibility of monitoring transient or unexpected neural activities and suggest that real-time ICA may provide the fMRI researcher with a better understanding and control of subjects' behaviors and performances.     

A nonlinear identification method to study effective connectivity in functional MRI

In this paper we propose a novel approach for characterizing effective connectivity in functional magnetic resonance imaging (fMRI) data. Unlike most other methods, our approach is nonlinear and does not rely on a priori specification of a model that contains structural information of neuronal populations. Instead, it relies on a nonlinear autoregressive exogenous model and nonlinear system identification theory; the model’s nonlinear connectivities are determined using a least squares method. A statistical test was developed to quantify the significance of the influence that regions exert on one another. We compared this approach with a linear method and applied it to the human visual cortex network. Results show that this method can be used to model nonlinear interaction between different regions for fMRI data.     

Statistical shape modeling of low level visual area borders

This paper proposes a statistical modeling of functional landmarks delimiting low level visual areas which are highly variable across individuals. Low level visual areas are first precisely delineated by fMRI retinotopic mapping which provides detailed information about the correspondence between the visual field and its cortical representation. The model is then built by learning the variability within a given training set. It relies on an appropriate data representation and on the definition of an intrinsic coordinate system common to all visual maps. This allows to build a consistent training set on which a principal component analysis is eventually applied. Our approach constitutes a first step toward a functional landmark-based probabilistic atlas of low level visual areas.     

Posterior shape models

We present a method to compute the conditional distribution of a statistical shape model given partial data. The result is a “posterior shape model”, which is again a statistical shape model of the same form as the original model. This allows its direct use in the variety of algorithms that include prior knowledge about the variability of a class of shapes with a statistical shape model. Posterior shape models then provide a statistically sound yet easy method to integrate partial data into these algorithms. Usually, shape models represent a complete organ, for instance in our experiments the femur bone, modeled by a multivariate normal distribution. But because in many application certain parts of the shape are known a priori, it is of great interest to model the posterior distribution of the whole shape given the known parts. These could be isolated landmark points or larger portions of the shape, like the healthy part of a pathological or damaged organ. However, because for most shape models the dimensionality of the data is much higher than the number of examples, the normal distribution is singular, and the conditional distribution not readily available. In this paper, we present two main contributions: First, we show how the posterior model can be efficiently computed as a statistical shape model in standard form and used in any shape model algorithm. We complement this paper with a freely available implementation of our algorithms. Second, we show that most common approaches put forth in the literature to overcome this are equivalent to probabilistic principal component analysis (PPCA), and Gaussian Process regression. To illustrate the use of posterior shape models, we apply them on two problems from medical image analysis: model-based image segmentation incorporating prior knowledge from landmarks, and the prediction of anatomically correct knee shapes for trochlear dysplasia patients, which constitutes a novel medical application. Our experiments confirm that the use of conditional shape models for image segmentation improves the overall segmentation accuracy and robustness.     

Mapping directed influence over the brain using Granger causality and fMRI

We propose Granger causality mapping (GCM) as an approach to explore directed influences between neuronal populations (effective connectivity) in fMRI data. The method does not rely on a priori specification of a model that contains pre-selected regions and connections between them. This distinguishes it from other fMRI effective connectivity approaches that aim at testing or contrasting specific hypotheses about neuronal interactions. Instead, GCM relies on the concept of Granger causality to define the existence and direction of influence from information in the data. Temporal precedence information is exploited to compute Granger causality maps that identify voxels that are sources or targets of directed influence for any selected region-of-interest. We investigated the method by simulations and by application to fMRI data of a complex visuomotor task. The presented exploratory approach of mapping influences between a region of interest and the rest of the brain can form a useful complement to existing models of effective connectivity.     

Independent vector analysis (IVA): multivariate approach for fMRI group study

Independent component analysis (ICA) of fMRI data generates session/individual specific brain activation maps without a priori assumptions regarding the timing or pattern of the blood-oxygenation-level-dependent (BOLD) signal responses. However, because of a random permutation among output components, ICA does not offer a straightforward solution for the inference of group-level activation. In this study, we present an independent vector analysis (IVA) method to address the permutation problem during fMRI group data analysis. In comparison to ICA, IVA offers an analysis of additional dependent components, which were assigned for use in the automated grouping of dependent activation patterns across subjects. Upon testing using simulated trial-based fMRI data, our proposed method was applied to real fMRI data employing both a single-trial task-paradigm (right hand motor clenching and internal speech generation tasks) and a three-trial task-paradigm (right hand motor imagery task). A generalized linear model (GLM) and the group ICA of the fMRI toolbox (GIFT) were also applied to the same data set for comparison to IVA. Compared to GLM, IVA successfully captured activation patterns even when the functional areas showed variable hemodynamic responses that deviated from a hypothesized response. We also showed that IVA effectively inferred group-activation patterns of unknown origins without the requirement for a pre-processing stage (such as data concatenation in ICA-based GIFT). IVA can be used as a potential alternative or an adjunct to current ICA-based fMRI group processing methods.     

Computing personalized brain functional networks from fMRI using self-supervised deep learning

A novel self-supervised deep learning (DL) method is developed to compute personalized brain functional networks (FNs) for characterizing brain functional neuroanatomy based on functional MRI (fMRI). Specifically, a DL model of convolutional neural networks with an encoder-decoder architecture is developed to compute personalized FNs directly from fMRI data. The DL model is trained to optimize functional homogeneity of personalized FNs without utilizing any external supervision in an end-to-end fashion. We demonstrate that a DL model trained on fMRI scans from the Human Connectome Project can identify personalized FNs and generalizes well across four different datasets. We further demonstrate that the identified personalized FNs are informative for predicting individual differences in behavior, brain development, and schizophrenia status. Taken together, the self-supervised DL allows for rapid, generalizable computation of personalized FNs.     

Cross-covariance isolate detect: A new change-point method for estimating dynamic functional connectivity

Evidence of the non stationary behavior of functional connectivity (FC) networks has been observed in task based functional magnetic resonance imaging (fMRI) experiments and even prominently in resting state fMRI data. This has led to the development of several new statistical methods for estimating this time-varying connectivity, with the majority of the methods utilizing a sliding window approach. While computationally feasible, the sliding window approach has several limitations. In this paper, we circumvent the sliding window, by introducing a statistical method that finds change-points in FC networks where the number and location of change-points are unknown a priori. The new method, called cross-covariance isolate detect (CCID), detects multiple change-points in the second-order (cross-covariance or network) structure of multivariate, possibly high-dimensional time series. CCID allows for change-point detection in the presence of frequent changes of possibly small magnitudes, can assign change-points to one or multiple brain regions, and is computationally fast. In addition, CCID is particularly suited to task based data, where the subject alternates between task and rest, as it firstly attempts isolation of each of the change-points within subintervals, and secondly their detection therein. Furthermore, we also propose a new information criterion for CCID to identify the change-points. We apply CCID to several simulated data sets and to task based and resting state fMRI data and compare it to recent change-point methods. CCID may also be applicable to electroencephalography (EEG), magentoencephalography (MEG) and electrocorticography (ECoG) data. Similar to other biological networks, understanding the complex network organization and functional dynamics of the brain can lead to profound clinical implications. Finally, the R package ccid implementing the method from the paper is available from CRAN.     

A comparative evaluation of wavelet-based methods for hypothesis testing of brain activation maps

Wavelet-based methods for hypothesis testing are described and their potential for activation mapping of human functional magnetic resonance imaging (fMRI) data is investigated. In this approach, we emphasise convergence between methods of wavelet thresholding or shrinkage and the problem of hypothesis testing in both classical and Bayesian contexts. Specifically, our interest will be focused on the trade-off between type I probability error control and power dissipation, estimated by the area under the ROC curve. We describe a technique for controlling the false discovery rate at an arbitrary level of error in testing multiple wavelet coefficients generated by a 2D discrete wavelet transform (DWT) of spatial maps of fMRI time series statistics. We also describe and apply change-point detection with recursive hypothesis testing methods that can be used to define a threshold unique to each level and orientation of the 2D-DWT, and Bayesian methods, incorporating a formal model for the anticipated sparseness of wavelet coefficients representing the signal or true image. The sensitivity and type I error control of these algorithms are comparatively evaluated by analysis of "null" images (acquired with the subject at rest) and an experimental data set acquired from five normal volunteers during an event-related finger movement task. We show that all three wavelet-based algorithms have good type I error control (the FDR method being most conservative) and generate plausible brain activation maps (the Bayesian method being most powerful). We also generalise the formal connection between wavelet-based methods for simultaneous multiresolution denoising/hypothesis testing and methods based on monoresolution Gaussian smoothing followed by statistical testing of brain activation maps.     

Visualization of nonlinear kernel models in neuroimaging by sensitivity maps

There is significant current interest in decoding mental states from neuroimages. In this context kernel methods, e.g., support vector machines (SVM) are frequently adopted to learn statistical relations between patterns of brain activation and experimental conditions. In this paper we focus on visualization of such nonlinear kernel models. Specifically, we investigate the sensitivity map as a technique for generation of global summary maps of kernel classification models. We illustrate the performance of the sensitivity map on functional magnetic resonance (fMRI) data based on visual stimuli. We show that the performance of linear models is reduced for certain scan labelings/categorizations in this data set, while the nonlinear models provide more flexibility. We show that the sensitivity map can be used to visualize nonlinear versions of kernel logistic regression, the kernel Fisher discriminant, and the SVM, and conclude that the sensitivity map is a versatile and computationally efficient tool for visualization of nonlinear kernel models in neuroimaging.     

Multivariate analysis of neuronal interactions in the generalized partial least squares framework: simulations and empirical studies

Identification of spatiotemporal interactions within/between neuron populations is critical for detection and characterization of large-scale neuronal interactions underlying perception, cognition, and behavior. Univariate analysis has been employed successfully in many neuroimaging studies. However, univariate analysis does not explicitly test for interactions between distributed areas of activity and is not sensitive to distributed responses across the brain. Multivariate analysis can explicitly test for multiple statistical models, including the designed paradigm, and allows for spatial and temporal model detection. Here, we investigate multivariate analysis approaches that take into consideration the 4D (time and space) covariance structure of the data. Principal component analysis (PCA) and independent component analysis (ICA) are two popular multivariate approaches with distinct mathematical constraints. Common difficulties in using these two different decompositions include the following: classification of the revealed components (task-related signal versus noise), overall signal-to-noise sensitivity, and the relatively low computational efficiency (multivariate analysis requires the entire raw data set and more time for model identification analysis). Using both Monte Carlo simulations and empirical data, we derived and tested the generalized partial least squares (gPLS) framework, which can incorporate both PCA and ICA decompositions with computational efficiency. The gPLS method explicitly incorporates the experimental design to simplify the identification of characteristic spatiotemporal patterns. We performed parametric modeling studies of a blocked-design experiment under various conditions, including background noise distribution, sampling rate, and hemodynamic response delay. We used a randomized grouping approach to manipulate the degrees of freedom of PCA and ICA in gPLS to characterize both paradigm coherent and transient brain responses. Simulation data suggest that in the gPLS framework, PCA mostly outperforms ICA as measured by the receiver operating curves (ROCs) in SNR from 0.01 to 100, the hemodynamic response delays from 0 to 3 TR in fMRI, background noise models of Guassian, sub-Gaussian, and super-Gaussian distributions and the number of observations from 5, 10, to 20 in each block of a six-block experiment. Further, due to selective averaging, the gPLS method performs robustly in low signal-to-noise ratio (<1) experiments. We also tested PCA and ICA using PLS in a simulated event-related fMRI data to show their similar detection. Finally, we tested our gPLS approach on empirical fMRI motor data. Using the randomized grouping method, we are able to identify both transient responses and consistent paradigm/model coherent components in the 10-epoch block design motor fMRI experiment. Overall, studies of synthetic and empirical data suggest that PLS analysis, using PCA decomposition, provides a stable and powerful tool for exploration of fMRI/behavior data.