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.     

Spatio-temporal modeling of localized brain activity

Functional neuroimaging, including positron emission tomography (PET) and functional magnetic resonance imaging (fMRI), plays an important role in identifying specific brain regions associated with experimental stimuli or psychiatric disorders such as schizophrenia. PET and fMRI produce massive data sets that contain both temporal correlations from repeated scans and complex spatial correlations. Several methods exist for handling temporal correlations, some of which rely on transforming the response data to induce either a known or an independence covariance structure. Despite the presence of spatial correlations between the volume elements (voxels) comprising a brain scan, conventional methods perform voxel-by-voxel analyses of measured brain activity. We propose a two-stage spatio-temporal model for the estimation and testing of localized activity. Our second-stage model specifies a spatial auto-regression, capturing correlations within neural processing clusters defined by a data-driven cluster analysis. We use maximum likelihood methods to estimate parameters from our spatial autoregressive model. Our model protects against type-I errors, enables the detection of both localized and regional activations (including volume of interest effects), provides information on functional connectivity in the brain, and establishes a framework to produce spatially smoothed maps of distributed brain activity for each individual. We illustrate the application of our model using PET data from a study of working memory in individuals with schizophrenia.     

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.     

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.     

Bayesian Spatiotemporal Inference in Functional Magnetic Resonance Imaging

Mapping of the human brain by means of functional magnetic resonance imaging (fMRI) is an emerging field in cognitive and clinical neuroscience. Current techniques to detect activated areas of the brain mostly proceed in two steps. First, conventional methods of correlation, regression, and time series analysis are used to assess activation by a separate, pixelwise comparison of the fMRI signal time courses to the reference function of a presented stimulus. Spatial aspects caused by correlations between neighboring pixels are considered in a separate second step, if at all. The aim of this article is to present hierarchical Bayesian approaches that allow one to simultaneously incorporate temporal and spatial dependencies between pixels directly in the model formulation. For reasons of computational feasibility, models have to be comparatively parsimonious, without oversimplifying. We introduce parametric and semiparametric spatial and spatiotemporal models that proved appropriate and illustrate their performance applied to visual fMRI data.     

Inferences about population dynamics from count data using multistate models: a comparison to capture–recapture approaches

Wildlife populations consist of individuals that contribute disproportionately to growth and viability. Understanding a population's spatial and temporal dynamics requires estimates of abundance and demographic rates that account for this heterogeneity. Estimating these quantities can be difficult, requiring years of intensive data collection. Often, this is accomplished through the capture and recapture of individual animals, which is generally only feasible at a limited number of locations. In contrast, N‐mixture models allow for the estimation of abundance, and spatial variation in abundance, from count data alone. We extend recently developed multistate, open population N‐mixture models, which can additionally estimate demographic rates based on an organism's life history characteristics. In our extension, we develop an approach to account for the case where not all individuals can be assigned to a state during sampling. Using only state‐specific count data, we show how our model can be used to estimate local population abundance, as well as density‐dependent recruitment rates and state‐specific survival. We apply our model to a population of black‐throated blue warblers (Setophaga caerulescens) that have been surveyed for 25 years on their breeding grounds at the Hubbard Brook Experimental Forest in New Hampshire, USA. The intensive data collection efforts allow us to compare our estimates to estimates derived from capture–recapture data. Our model performed well in estimating population abundance and density‐dependent rates of annual recruitment/immigration. Estimates of local carrying capacity and per capita recruitment of yearlings were consistent with those published in other studies. However, our model moderately underestimated annual survival probability of yearling and adult females and severely underestimates survival probabilities for both of these male stages. The most accurate and precise estimates will necessarily require some amount of intensive data collection efforts (such as capture–recapture). Integrated population models that combine data from both intensive and extensive sources are likely to be the most efficient approach for estimating demographic rates at large spatial and temporal scales.     

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.     

High-resolution functional magnetic resonance imaging of the animal brain

To fully understand brain function, one must look beyond the level of a single neuron. By elucidating the spatial properties of the columnar and laminar functional architectures, information regarding the neural processing in the brain can be gained. To map these fine functional structures noninvasively and repeatedly, functional magnetic resonance imaging (fMRI) can be employed. In this article the basic principles of fMRI are introduced, including specific hardware requirements and the equipment necessary for animal magnetic resonance research. Since fMRI measures a change in secondary hemodynamic responses induced by neural activity, it is critical to understand the principles and potential pitfalls of fMRI techniques. Thus, the underlying physics of conventional blood oxygenation, cerebral blood flow, and cerebral blood volume-based fMRI techniques are extensively discussed. Tissue-specific signal change is close to the site of neural activity, while signals from large vessels can be distant from the actual active site. Thus, methods to minimize large vessel contributions and to maximize tissue signals are described. The fundamental limitation of fMRI spatial resolution is the intrinsic hemodynamic response. Based on our high-resolution fMRI studies, the hemodynamic response is regulated at submillimeter functional domains and thus spatial resolution can be achieved to an order of 100 microm. Since hemodynamic responses are sluggish, it is difficult to obtain very high temporal resolution. By using an approach with multiple experiments with different stimulus conditions, temporal resolution can be improved on the order of 100 ms. With current fMRI technologies, submillimeter columnar- and laminar-specific specific functional images can be obtained from animal brains.     

Modeling Inter‐Subject Variability in fMRI Activation Location: A Bayesian Hierarchical Spatial Model

Summary The aim of this article is to develop a spatial model for multi‐subject fMRI data. There has been extensive work on univariate modeling of each voxel for single and multi‐subject data, some work on spatial modeling of single‐subject data, and some recent work on spatial modeling of multi‐subject data. However, there has been no work on spatial models that explicitly account for inter‐subject variability in activation locations. In this article, we use the idea of activation centers and model the inter‐subject variability in activation locations directly. Our model is specified in a Bayesian hierarchical framework which allows us to draw inferences at all levels: the population level, the individual level, and the voxel level. We use Gaussian mixtures for the probability that an individual has a particular activation. This helps answer an important question that is not addressed by any of the previous methods: What proportion of subjects had a significant activity in a given region. Our approach incorporates the unknown number of mixture components into the model as a parameter whose posterior distribution is estimated by reversible jump Markov chain Monte Carlo. We demonstrate our method with a fMRI study of resolving proactive interference and show dramatically better precision of localization with our method relative to the standard mass‐univariate method. Although we are motivated by fMRI data, this model could easily be modified to handle other types of imaging data.     

Smooth individual level covariates adjustment in disease mapping

Spatial models for disease mapping should ideally account for covariates measured both at individual and area levels. The newly available “indiCAR” model fits the popular conditional autoregresssive (CAR) model by accommodating both individual and group level covariates while adjusting for spatial correlation in the disease rates. This algorithm has been shown to be effective but assumes log‐linear associations between individual level covariates and outcome. In many studies, the relationship between individual level covariates and the outcome may be non‐log‐linear, and methods to track such nonlinearity between individual level covariate and outcome in spatial regression modeling are not well developed. In this paper, we propose a new algorithm, smooth‐indiCAR, to fit an extension to the popular conditional autoregresssive model that can accommodate both linear and nonlinear individual level covariate effects while adjusting for group level covariates and spatial correlation in the disease rates. In this formulation, the effect of a continuous individual level covariate is accommodated via penalized splines. We describe a two‐step estimation procedure to obtain reliable estimates of individual and group level covariate effects where both individual and group level covariate effects are estimated separately. This distributed computing framework enhances its application in the Big Data domain with a large number of individual/group level covariates. We evaluate the performance of smooth‐indiCAR through simulation. Our results indicate that the smooth‐indiCAR method provides reliable estimates of all regression and random effect parameters. We illustrate our proposed methodology with an analysis of data on neutropenia admissions in New South Wales (NSW), Australia.     

Investigating the neural basis for functional and effective connectivity. Application to fMRI

Viewing cognitive functions as mediated by networks has begun to play a central role in interpreting neuroscientific data, and studies evaluating interregional functional and effective connectivity have become staples of the neuroimaging literature. The neurobiological substrates of functional and effective connectivity are, however, uncertain. We have constructed neurobiologically realistic models for visual and auditory object processing with multiple interconnected brain regions that perform delayed match-to-sample (DMS) tasks. We used these models to investigate how neurobiological parameters affect the interregional functional connectivity between functional magnetic resonance imaging (fMRI) time-series. Variability is included in the models as subject-to-subject differences in the strengths of anatomical connections, scan-to-scan changes in the level of attention, and trial-to-trial interactions with non-specific neurons processing noise stimuli. We find that time-series correlations between integrated synaptic activities between the anterior temporal and the prefrontal cortex were larger during the DMS task than during a control task. These results were less clear when the integrated synaptic activity was haemodynamically convolved to generate simulated fMRI activity. As the strength of the model anatomical connectivity between temporal and frontal cortex was weakened, so too was the strength of the corresponding functional connectivity. These results provide a partial validation for using fMRI functional connectivity to assess brain interregional relations.     

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.     

Inferring recent historic abundance from current genetic diversity

Recent historic abundance is an elusive parameter of great importance for conserving endangered species and understanding the pre‐anthropogenic state of the biosphere. The number of studies that have used population genetic theory to estimate recent historic abundance from contemporary levels of genetic diversity has grown rapidly over the last two decades. Such assessments often yield unexpectedly large estimates of historic abundance. We review the underlying theory and common practices of estimating recent historic abundance from contemporary genetic diversity, and critically evaluate the potential issues at various estimation steps. A general issue of mismatched spatio‐temporal scales between the estimation itself and the objective of the estimation emerged from our assessment; genetic diversity–based estimates of recent historic abundance represent long‐term averages, whereas the objective typically is an estimate of recent abundance for a specific population. Currently, the most promising approach to estimate the difference between recent historic and contemporary abundance requires that genetic data be collected from samples of similar spatial and temporal duration. Novel genome‐enabled inference methods may be able to utilize additional information of dense genome‐wide distributions of markers, such as of identity‐by‐descent tracts, to infer recent historic abundance from contemporary samples only.     

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.     

Decoding Multiple Sound Categories in the Human Temporal Cortex Using High Resolution fMRI

Perception of sound categories is an important aspect of auditory perception. The extent to which the brain’s representation of sound categories is encoded in specialized subregions or distributed across the auditory cortex remains unclear. Recent studies using multivariate pattern analysis (MVPA) of brain activations have provided important insights into how the brain decodes perceptual information. In the large existing literature on brain decoding using MVPA methods, relatively few studies have been conducted on multi-class categorization in the auditory domain. Here, we investigated the representation and processing of auditory categories within the human temporal cortex using high resolution fMRI and MVPA methods. More importantly, we considered decoding multiple sound categories simultaneously through multi-class support vector machine-recursive feature elimination (MSVM-RFE) as our MVPA tool. Results show that for all classifications the model MSVM-RFE was able to learn the functional relation between the multiple sound categories and the corresponding evoked spatial patterns and classify the unlabeled sound-evoked patterns significantly above chance. This indicates the feasibility of decoding multiple sound categories not only within but across subjects. However, the across-subject variation affects classification performance more than the within-subject variation, as the across-subject analysis has significantly lower classification accuracies. Sound category-selective brain maps were identified based on multi-class classification and revealed distributed patterns of brain activity in the superior temporal gyrus and the middle temporal gyrus. This is in accordance with previous studies, indicating that information in the spatially distributed patterns may reflect a more abstract perceptual level of representation of sound categories. Further, we show that the across-subject classification performance can be significantly improved by averaging the fMRI images over items, because the irrelevant variations between different items of the same sound category are reduced and in turn the proportion of signals relevant to sound categorization increases.     

Spatiotemporal mapping of brain activity by integration of multiple imaging modalities

Functional magnetic resonance imaging (fMRI) and positron emission tomography measure local changes in brain hemodynamics induced by cognitive or perceptual tasks. These measures have a uniformly high spatial resolution of millimeters or less, but poor temporal resolution (about 1s). Conversely, electroencephalography (EEG) and magnetoencephalography (MEG) measure instantaneously the current flows induced by synaptic activity, but the accurate localization of these current flows based on EEG and MEG data alone remains an unsolved problem. Recently, techniques have been developed that, in the context of brain anatomy visualized with structural MRI, use both hemodynamic and electromagnetic measures to arrive at estimates of brain activation with high spatial and temporal resolution. These methods range from simple juxtaposition to simultaneous integrated techniques. Their application has already led to advances in our understanding of the neural bases of perception, attention, memory and language. Further advances in multi-modality integration will require an improved understanding of the coupling between the physiological phenomena underlying the different signal modalities.     

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.     

Resting-State Temporal Synchronization Networks Emerge from Connectivity Topology and Heterogeneity

Spatial patterns of coherent activity across different brain areas have been identified during the resting-state fluctuations of the brain. However, recent studies indicate that resting-state activity is not stationary, but shows complex temporal dynamics. We were interested in the spatiotemporal dynamics of the phase interactions among resting-state fMRI BOLD signals from human subjects. We found that the global phase synchrony of the BOLD signals evolves on a characteristic ultra-slow (<0.01Hz) time scale, and that its temporal variations reflect the transient formation and dissolution of multiple communities of synchronized brain regions. Synchronized communities reoccurred intermittently in time and across scanning sessions. We found that the synchronization communities relate to previously defined functional networks known to be engaged in sensory-motor or cognitive function, called resting-state networks (RSNs), including the default mode network, the somato-motor network, the visual network, the auditory network, the cognitive control networks, the self-referential network, and combinations of these and other RSNs. We studied the mechanism originating the observed spatiotemporal synchronization dynamics by using a network model of phase oscillators connected through the brain’s anatomical connectivity estimated using diffusion imaging human data. The model consistently approximates the temporal and spatial synchronization patterns of the empirical data, and reveals that multiple clusters that transiently synchronize and desynchronize emerge from the complex topology of anatomical connections, provided that oscillators are heterogeneous.     

The genetics of phenotypic plasticity. XII. Temporal and spatial heterogeneity

To understand empirical patterns of phenotypic plasticity, we need to explore the complexities of environmental heterogeneity and how it interacts with cue reliability. I consider both temporal and spatial variation separately and in combination, the timing of temporal variation relative to development, the timing of movement relative to selection, and two different patterns of movement: stepping‐stone and island. Among‐generation temporal heterogeneity favors plasticity, while within‐generation heterogeneity can result in cue unreliability. In general, spatial variation more strongly favors plasticity than temporal variation, and island migration more strongly favors plasticity than stepping‐stone migration. Negative correlations among environments between the time of development and selection can result in seemingly maladaptive reaction norms. The effects of higher dispersal rates depend on the life history stage when dispersal occurs and the pattern of environmental heterogeneity. Thus, patterns of environmental heterogeneity can be complex and can interact in unforeseen ways to affect cue reliability. Proper interpretation of patterns of trait plasticity requires consideration of the ecology and biology of the organism. More information on actual cue reliability and the ecological and developmental context of trait plasticity is needed.