Granger mediation analysis of multiple time series with an application to functional magnetic resonance imaging

This paper presents Granger mediation analysis, a new framework for causal mediation analysis of multiple time series. This framework is motivated by a functional magnetic resonance imaging (fMRI) experiment where we are interested in estimating the mediation effects between a randomized stimulus time series and brain activity time series from two brain regions. The independent observation assumption is thus unrealistic for this type of time‐series data. To address this challenge, our framework integrates two types of models: causal mediation analysis across the mediation variables, and vector autoregressive (VAR) models across the temporal observations. We use “Granger” to refer to VAR correlations modeled in this paper. We further extend this framework to handle multilevel data, in order to model individual variability and correlated errors between the mediator and the outcome variables. Using Rubin's potential outcome framework, we show that the causal mediation effects are identifiable under our time‐series model. We further develop computationally efficient algorithms to maximize our likelihood‐based estimation criteria. Simulation studies show that our method reduces the estimation bias and improves statistical power, compared with existing approaches. On a real fMRI data set, our approach quantifies the causal effects through a brain pathway, while capturing the dynamic dependence between two brain regions.     

Splitting the spotlight of visual attention

Can the brain attend to more than a single location at one time? In this issue of Neuron, McMains and Somers report psychophysical and fMRI evidence showing that subjects can attend to two separate locations concurrently and that divided spatial attention leads to separate zones of attentional enhancement in early visual cortex.     

Magnetoencephalography and its Achilles' heel

Magnetoencephalography (MEG) has practically unlimited temporal resolution. Fundamental physical reasons, however, restrict the capability of MEG to separate simultaneously active sources. After a brief tutorial introduction into MEG, various aspects of spatial resolution are reviewed with the help of examples. First the estimation of a single current dipole is examined. A consideration of the resolution field shows that the spatial selectivity of the estimated dipole moment is highly dependent on methodological issues. A subsequent consideration of various two-dipole configurations illustrates how the topography of the magnetic field depends on the distance between the two dipoles and their relative orientations. The resolution fields associated with the estimation of the dipole moments reveal a strong interference for closely spaced dipoles. A simple model suggests that the standard deviations of the estimated moments are inversely proportional to the distance of the dipoles. Spatial information provided by techniques like functional magnetic resonance imaging (fMRI) could help to overcome problems resulting from the limited spatial resolution of MEG (multimodal integration). But a straightforward synthesis, according to the principle that fMRI provides the spatial structure of the sources and MEG adds the temporal information, is probably doomed to failure in many situations. A serious dilemma, among other problems, is that the fMRI signal generally represents a temporal integral over several seconds: The knowledge that a certain brain region was active sometime or other is not necessarily helpful for disentangling the MEG activity within a specified short time window. An intriguing fact is that the spatio-temporal pattern of the MEG signals can be considered as a signature of the brain which is suitable for hypothesis testing with high temporal and spatial resolution.     

Topographic Factor Analysis: A Bayesian Model for Inferring Brain Networks from Neural Data

The neural patterns recorded during a neuroscientific experiment reflect complex interactions between many brain regions, each comprising millions of neurons. However, the measurements themselves are typically abstracted from that underlying structure. For example, functional magnetic resonance imaging (fMRI) datasets comprise a time series of three-dimensional images, where each voxel in an image (roughly) reflects the activity of the brain structure(s)–located at the corresponding point in space–at the time the image was collected. FMRI data often exhibit strong spatial correlations, whereby nearby voxels behave similarly over time as the underlying brain structure modulates its activity. Here we develop topographic factor analysis (TFA), a technique that exploits spatial correlations in fMRI data to recover the underlying structure that the images reflect. Specifically, TFA casts each brain image as a weighted sum of spatial functions. The parameters of those spatial functions, which may be learned by applying TFA to an fMRI dataset, reveal the locations and sizes of the brain structures activated while the data were collected, as well as the interactions between those structures.     

Unsupervised clustering of fMRI and MRI time series

Unsupervised clustering represents a powerful technique for self-organized segmentation of biomedical image time series data describing groups of pixels exhibiting similar properties of local signal dynamics. The theoretical background is presented in the beginning, followed by several medical applications demonstrating the flexibility and conceptual power of these techniques. These applications range from functional MRI data analysis to dynamic contrast-enhanced perfusion MRI and breast MRI. For fMRI, these methods can be employed to identify and separate time courses of interest, along with their associated spatial patterns. When applied to dynamic perfusion MRI, they identify groups of voxels associated with time courses that are clinically informative and straightforward to interpret. In breast MRI, a segmentation of the lesion is achieved and in addition a subclassification is obtained within the lesion with regard to regions characterized by different MRI signal time courses. In the present paper, we conclude that unsupervised clustering techniques provide a robust method for blind analysis of time series image data in the important and current field of functional and dynamic MRI.     

Modeling the Spatial and Temporal Dependence in fMRI Data

Summary Functional magnetic resonance imaging (fMRI) data sets are large and characterized by complex dependence structures driven by highly sophisticated neurophysiology and aspects of the experimental designs. Typical analyses investigating task‐related changes in measured brain activity use a two‐stage procedure in which the first stage involves subject‐specific models and the second‐stage specifies group (or population) level parameters. Customarily, the first‐level accounts for temporal correlations between the serial scans acquired during one scanning session. Despite accounting for these correlations, fMRI studies often include multiple sessions and temporal dependencies may persist between the corresponding estimates of mean neural activity. Further, spatial correlations between brain activity measurements in different locations are often unaccounted for in statistical modeling and estimation. We propose a two‐stage, spatio‐temporal, autoregressive model that simultaneously accounts for spatial dependencies between voxels within the same anatomical region and for temporal dependencies between a subject's estimates from multiple sessions. We develop an algorithm that leverages the special structure of our covariance model, enabling relatively fast and efficient estimation. Using our proposed method, we analyze fMRI data from a study of inhibitory control in cocaine addicts.     

Repeated BOLD-fMRI Imaging of Deep Brain Stimulation Responses in Rats

Functional magnetic resonance imaging (fMRI) provides a picture of the global spatial activation pattern of the brain. Interest is growing regarding the application of fMRI to rodent models to investigate adult brain plasticity. To date, most rodent studies used an electrical forepaw stimulation model to acquire fMRI data, with α-chloralose as the anesthetic. However, α-chloralose is harmful to animals, and not suitable for longitudinal studies. Moreover, peripheral stimulation models enable only a limited number of brain regions to be studied. Processing between peripheral regions and the brain is multisynaptic, and renders interpretation difficult and uncertain. In the present study, we combined the medetomidine-based fMRI protocol (a noninvasive rodent fMRI protocol) with chronic implantation of an MRI-compatible stimulation electrode in the ventroposterior (VP) thalamus to repetitively sample thalamocortical responses in the rat brain. Using this model, we scanned the forebrain responses evoked by the VP stimulation repeatedly of individual rats over 1 week. Cortical BOLD responses were compared between the 2 profiles obtained at day1 and day8. We discovered reproducible frequency- and amplitude-dependent BOLD responses in the ipsilateral somatosensory cortex (S1). The S1 BOLD responses during the 2 sessions were conserved in maximal response amplitude, area size (size ratio from 0.88 to 0.91), and location (overlap ratio from 0.61 to 0.67). The present study provides a long-term chronic brain stimulation protocol for studying the plasticity of specific neural circuits in the rodent brain by BOLD-fMRI.     

Reconstructing visual experiences from brain activity evoked by natural movies

Quantitative modeling of human brain activity can provide crucial insights about cortical representations [1, 2] and can form the basis for brain decoding devices [3-5]. Recent functional magnetic resonance imaging (fMRI) studies have modeled brain activity elicited by static visual patterns and have reconstructed these patterns from brain activity [6-8]. However, blood oxygen level-dependent (BOLD) signals measured via fMRI are very slow [9], so it has been difficult to model brain activity elicited by dynamic stimuli such as natural movies. Here we present a new motion-energy [10, 11] encoding model that largely overcomes this limitation. The model describes fast visual information and slow hemodynamics by separate components. We recorded BOLD signals in occipitotemporal visual cortex of human subjects who watched natural movies and fit the model separately to individual voxels. Visualization of the fit models reveals how early visual areas represent the information in movies. To demonstrate the power of our approach, we also constructed a Bayesian decoder [8] by combining estimated encoding models with a sampled natural movie prior. The decoder provides remarkable reconstructions of the viewed movies. These results demonstrate that dynamic brain activity measured under naturalistic conditions can be decoded using current fMRI technology.     

Consistency of network modules in resting-state FMRI connectome data

At rest, spontaneous brain activity measured by fMRI is summarized by a number of distinct resting state networks (RSNs) following similar temporal time courses. Such networks have been consistently identified across subjects using spatial ICA (independent component analysis). Moreover, graph theory-based network analyses have also been applied to resting-state fMRI data, identifying similar RSNs, although typically at a coarser spatial resolution. In this work, we examined resting-state fMRI networks from 194 subjects at a voxel-level resolution, and examined the consistency of RSNs across subjects using a metric called scaled inclusivity (SI), which summarizes consistency of modular partitions across networks. Our SI analyses indicated that some RSNs are robust across subjects, comparable to the corresponding RSNs identified by ICA. We also found that some commonly reported RSNs are less consistent across subjects. This is the first direct comparison of RSNs between ICAs and graph-based network analyses at a comparable resolution.     

Spatiotemporal BOLD dynamics from a poroelastic hemodynamic model

A quantitative theory is developed for the relationship between stimulus and the resulting blood oxygen level dependent (BOLD) functional magnetic resonance imaging (fMRI) signal, including both spatial and temporal dynamics for the first time. The brain tissue is modeled as a porous elastic medium, whose interconnected pores represent the vasculature. The model explicitly incorporates conservation of blood mass, interconversion of oxygenated and deoxygenated hemoglobin, force balance within the blood and of blood pressure with vessel walls, and blood flow modulation due to neuronal activity. In appropriate limits it is shown to reproduce prior Balloon models of hemodynamic response, which do not include spatial variations. The regime of validity of such models is thereby clarified by elucidating their assumptions, and when these break down, for example when voxel sizes become small.     

Double‐wavelet transform for multisubject task‐induced functional magnetic resonance imaging data

The goal of this article is to model multisubject task‐induced functional magnetic resonance imaging (fMRI) response among predefined regions of interest (ROIs) of the human brain. Conventional approaches to fMRI analysis only take into account temporal correlations, but do not rigorously model the underlying spatial correlation due to the complexity of estimating and inverting the high dimensional spatio‐temporal covariance matrix. Other spatio‐temporal model approaches estimate the covariance matrix with the assumption of stationary time series, which is not always feasible. To address these limitations, we propose a double‐wavelet approach for modeling the spatio‐temporal brain process. Working with wavelet coefficients simplifies temporal and spatial covariance structure because under regularity conditions, wavelet coefficients are approximately uncorrelated. Different wavelet functions were used to capture different correlation structures in the spatio‐temporal model. The main advantages of the wavelet approach are that it is scalable and that it deals with nonstationarity in brain signals. Simulation studies showed that our method could reduce false‐positive and false‐negative rates by taking into account spatial and temporal correlations simultaneously. We also applied our method to fMRI data to study activation in prespecified ROIs in the prefontal cortex. Data analysis showed that the result using the double‐wavelet approach was more consistent than the conventional approach when sample size decreased.     

Exploiting the potential of three dimensional spatial wavelet analysis to explore nesting of temporal oscillations and spatial variance in simultaneous EEG-fMRI data

Synchronization of the activity in neural networks is a fundamental mechanism of brain function, putatively serving the integration of computations on multiple spatial and temporal scales. Time scales are thought to be nested within distinct spatial scales, so that whereas fast oscillations may integrate local networks, slow oscillations might integrate computations across distributed brain areas. We here describe a newly developed approach that provides potential for the further substantiation of this hypothesis in future studies. We demonstrate the feasibility and important caveats of a novel wavelet-based means of relating time series of three-dimensional spatial variance (energy) of fMRI data to time series of temporal variance of EEG. The spatial variance of fMRI data was determined by employing the three-dimensional dual-tree complex wavelet transform. The temporal variance of EEG data was estimated by using traditional continuous complex wavelets. We tested our algorithm on artificial signals with known signal-to-noise ratios and on empirical resting state EEG-fMRI data obtained from four healthy human subjects. By employing the human posterior alpha rhythm as an exemplar, we demonstrated face validity of the approach. We believe that the proposed method can serve as a suitable tool for future research on the spatiotemporal properties of brain dynamics, hence moving beyond analyses based exclusively in one domain or the other.     

Independent component analysis of functional MRI: what is signal and what is noise?

Many sources of fluctuation contribute to the functional magnetic resonance imaging (fMRI) signal, complicating attempts to infer those changes that are truly related to brain activation. Unlike methods of analysis of fMRI data that test the time course of each voxel against a hypothesized waveform, data-driven methods, such as independent component analysis and clustering, attempt to find common features within the data. This exploratory approach can be revealing when the brain activation is difficult to predict beforehand, such as with complex stimuli and internal shifts of activation that are not time-locked to an easily specified sensory or motor event. These methods can be further improved by incorporating prior knowledge regarding the temporal and spatial extent of brain activation.     

Functional Network Overlap as Revealed by fMRI Using sICA and Its Potential Relationships with Functional Heterogeneity,Balanced Excitation and Inhibition,and Sparseness of Neuron Activity

Functional magnetic resonance imaging (fMRI) studies traditionally use general linear model-based analysis (GLM-BA) and regularly report task-related activation, deactivation, or no change in activation in separate brain regions. However, several recent fMRI studies using spatial independent component analysis (sICA) find extensive overlap of functional networks (FNs), each exhibiting different task-related modulation (e.g., activation vs. deactivation), different from the dominant findings of GLM-BA. This study used sICA to assess overlap of FNs extracted from four datasets, each related to a different cognitive task. FNs extracted from each dataset overlapped with each other extensively across most or all brain regions and showed task-related concurrent increases, decreases, or no changes in activity. These findings indicate that neural substrates showing task-related concurrent but different modulations in activity intermix with each other and distribute across most of the brain. Furthermore, spatial correlation analyses found that most FNs were highly consistent in spatial patterns across different datasets. This finding indicates that these FNs probably reflect large-scale patterns of task-related brain activity. We hypothesize that FN overlaps as revealed by sICA might relate to functional heterogeneity, balanced excitation and inhibition, and population sparseness of neuron activity, three fundamental properties of the brain. These possibilities deserve further investigation.     

Generative embedding for model-based classification of fMRI data

Decoding models, such as those underlying multivariate classification algorithms, have been increasingly used to infer cognitive or clinical brain states from measures of brain activity obtained by functional magnetic resonance imaging (fMRI). The practicality of current classifiers, however, is restricted by two major challenges. First, due to the high data dimensionality and low sample size, algorithms struggle to separate informative from uninformative features, resulting in poor generalization performance. Second, popular discriminative methods such as support vector machines (SVMs) rarely afford mechanistic interpretability. In this paper, we address these issues by proposing a novel generative-embedding approach that incorporates neurobiologically interpretable generative models into discriminative classifiers. Our approach extends previous work on trial-by-trial classification for electrophysiological recordings to subject-by-subject classification for fMRI and offers two key advantages over conventional methods: it may provide more accurate predictions by exploiting discriminative information encoded in 'hidden' physiological quantities such as synaptic connection strengths; and it affords mechanistic interpretability of clinical classifications. Here, we introduce generative embedding for fMRI using a combination of dynamic causal models (DCMs) and SVMs. We propose a general procedure of DCM-based generative embedding for subject-wise classification, provide a concrete implementation, and suggest good-practice guidelines for unbiased application of generative embedding in the context of fMRI. We illustrate the utility of our approach by a clinical example in which we classify moderately aphasic patients and healthy controls using a DCM of thalamo-temporal regions during speech processing. Generative embedding achieves a near-perfect balanced classification accuracy of 98% and significantly outperforms conventional activation-based and correlation-based methods. This example demonstrates how disease states can be detected with very high accuracy and, at the same time, be interpreted mechanistically in terms of abnormalities in connectivity. We envisage that future applications of generative embedding may provide crucial advances in dissecting spectrum disorders into physiologically more well-defined subgroups.     

An fMRI Study of the Neural Systems Involved in Visually Cued Auditory Top-Down Spatial and Temporal Attention

Top-down attention to spatial and temporal cues has been thoroughly studied in the visual domain. However, because the neural systems that are important for auditory top-down temporal attention (i.e., attention based on time interval cues) remain undefined, the differences in brain activity between directed attention to auditory spatial location (compared with time intervals) are unclear. Using fMRI (magnetic resonance imaging), we measured the activations caused by cue-target paradigms by inducing the visual cueing of attention to an auditory target within a spatial or temporal domain. Imaging results showed that the dorsal frontoparietal network (dFPN), which consists of the bilateral intraparietal sulcus and the frontal eye field, responded to spatial orienting of attention, but activity was absent in the bilateral frontal eye field (FEF) during temporal orienting of attention. Furthermore, the fMRI results indicated that activity in the right ventrolateral prefrontal cortex (VLPFC) was significantly stronger during spatial orienting of attention than during temporal orienting of attention, while the DLPFC showed no significant differences between the two processes. We conclude that the bilateral dFPN and the right VLPFC contribute to auditory spatial orienting of attention. Furthermore, specific activations related to temporal cognition were confirmed within the superior occipital gyrus, tegmentum, motor area, thalamus and putamen.     

Spatial vs. Temporal Features in ICA of Resting-State fMRI – A Quantitative and Qualitative Investigation in the Context of Response Inhibition

Independent component analysis (ICA) can identify covarying functional networks in the resting brain. Despite its relatively widespread use, the potential of the temporal information (unlike spatial information) obtained by ICA from resting state fMRI (RS-fMRI) data is not always fully utilized. In this study, we systematically investigated which features in ICA of resting-state fMRI relate to behaviour, with stop signal reaction time (SSRT) in a stop-signal task taken as a test case. We did this by correlating SSRT with the following three kinds of measure obtained from RS-fMRI data: (1) the amplitude of each resting state network (RSN) (evaluated by the standard deviation of the RSN timeseries), (2) the temporal correlation between every pair of RSN timeseries, and (3) the spatial map of each RSN. For multiple networks, we found significant correlations not only between SSRT and spatial maps, but also between SSRT and network activity amplitude. Most of these correlations are of functional interpretability. The temporal correlations between RSN pairs were of functional significance, but these correlations did not appear to be very sensitive to finding SSRT correlations. In addition, we also investigated the effects of the decomposition dimension, spatial smoothing and Z-transformation of the spatial maps, as well as the techniques for evaluating the temporal correlation between RSN timeseries. Overall, the temporal information acquired by ICA enabled us to investigate brain function from a complementary perspective to the information provided by spatial maps.     

基于时间聚类分析和独立成分分析的癫痫fMRI盲分析方法

提出了一种基于时间聚类分析和独立成分分析的癫痫fMRI数据盲分析方法,并将两种方法有效联合,提取发作间期的癫痫fMRI激活时空信息.该方法首先由时间聚类分析得到与激活相关的时间峰度特征曲线,以此特征作为时间参考信息;再由空间独立成分分析分解fMRI信号得到空间独立成分;最后将每个独立成分所对应的时间曲线与参考曲线做相关分析提取相应脑激活图.提出的方法无需任何关于癫痫fMRI的先验假设信息,有效解决了独立成分的排序问题,实现了对数据的盲分析.仿真试验结果阐明了这一方法的有效性及可靠性,对癫痫数据的试验结果显示空间定位准确性优于统计参数图方法.     

Is Model Fitting Necessary for Model-Based fMRI?

Model-based analysis of fMRI data is an important tool for investigating the computational role of different brain regions. With this method, theoretical models of behavior can be leveraged to find the brain structures underlying variables from specific algorithms, such as prediction errors in reinforcement learning. One potential weakness with this approach is that models often have free parameters and thus the results of the analysis may depend on how these free parameters are set. In this work we asked whether this hypothetical weakness is a problem in practice. We first developed general closed-form expressions for the relationship between results of fMRI analyses using different regressors, e.g., one corresponding to the true process underlying the measured data and one a model-derived approximation of the true generative regressor. Then, as a specific test case, we examined the sensitivity of model-based fMRI to the learning rate parameter in reinforcement learning, both in theory and in two previously-published datasets. We found that even gross errors in the learning rate lead to only minute changes in the neural results. Our findings thus suggest that precise model fitting is not always necessary for model-based fMRI. They also highlight the difficulty in using fMRI data for arbitrating between different models or model parameters. While these specific results pertain only to the effect of learning rate in simple reinforcement learning models, we provide a template for testing for effects of different parameters in other models.