Voxel Time Series Research Articles

Increased interhemispheric resting‐state functional connectivity in functional dyspepsia: a pilot study

Recent brain imaging studies have emphasized the role of regional brain activity abnormalities in the pathophysiology of functional dyspepsia (FD). However, whether the functional connectivity between brain regions is changed, especially between the cerebral hemispheres, in patients with FD remains unknown. Thus, the present study aimed to examine the interhemispheric resting-state functional connectivity (RSFC) changes in patients with FD. Resting-state functional MRI (fMRI) was performed in 26 patients with FD and in 20 matched healthy controls. An interhemispheric RSFC map was obtained by calculating the Pearson correlation (Fisher Z transformed) between each pair of homotopic voxel time series for each subject. The between-group difference in interhemispheric RSFC was then examined at global and voxelwise levels separately. The global difference in interhemispheric RSFC between groups was tested using the independent two-sample t-test. Voxelwise comparisons were carried out using a permutation-based nonparametric test, and multiple comparisons across space were corrected using the threshold-free cluster enhancement (TFCE) method. The results showed that patients with FD had higher global interhemispheric RSFC than healthy controls (p < 0.01). Furthermore, voxelwise analysis revealed that patients with FD had increased interhemispheric RSFC in brain regions including the anterior cingulate cortex, insula and thalamus (p < 0.01, TFCE corrected). Our findings provide preliminary evidence of interhemispheric correlation abnormalities in patients with FD and contribute to a better understanding of the pathophysiology of the disease.

Activation Detection on fMRI Time Series Using Hidden Markov Model

This paper introduces two unsupervised learning methods for analyzing functional magnetic resonance imaging (fMRI) data based on hidden Markov model (HMM). HMM approach is focused on capturing the first-order statistical evolution among the samples of a voxel time series, and it can provide a complimentary perspective of the BOLD signals. Two-state HMM is created for each voxel, and the model parameters are estimated from the voxel time series and the stimulus paradigm. Two different activation detection methods are presented in this paper. The first method is based on the likelihood and likelihood-ratio test, in which an additional Gaussian model is used to enhance the contrast of the HMM likelihood map. The second method is based on certain distance measures between the two state distributions, in which the most likely HMM state sequence is estimated through the Viterbi algorithm. The distance between the on-state and off-state distributions is measured either through a t-test, or using the Kullback-Leibler distance (KLD). Experimental results on both normal subject and brain tumor subject are presented. HMM approach appears to be more robust in detecting the supplemental active voxels comparing with SPM, especially for brain tumor subject.

Synchronization-based approach for detecting functional activation of brain

In this paper, we investigate a synchronization-based, data-driven clustering approach for the analysis of functional magnetic resonance imaging (fMRI) data, and specifically for detecting functional activation from fMRI data. We first define a new measure of similarity between all pairs of data points (i.e., time series of voxels) integrating both complete phase synchronization and amplitude correlation. These pairwise similarities are taken as the coupling between a set of Kuramoto oscillators, which in turn evolve according to a nearest-neighbor rule. As the network evolves, similar data points naturally synchronize with each other, and distinct clusters will emerge. The clustering behavior of the interaction network of the coupled oscillators, therefore, mirrors the clustering property of the original multiple time series. The clustered regions whose cross-correlation coefficients are much greater than other regions are considered as the functionally activated brain regions. The analysis of fMRI data in auditory and visual areas shows that the recognized brain functional activations are in complete correspondence with those from the general linear model of statistical parametric mapping, but with a significantly lower time complexity. We further compare our results with those from traditional K-means approach, and find that our new clustering approach can distinguish between different response patterns more accurately and efficiently than the K-means approach, and therefore more suitable in detecting functional activation from event-related experimental fMRI data.

The equivalence of linear Gaussian connectivity techniques

The theoretical basis of linear Gaussian connectivity methods for the analysis of fMRI data is examined in this article, resulting in a clarification of methodological dependencies between techniques. In particular, Granger causality connectivity procedures, which describe instantaneous and directed influence between sets of voxel timeseries, are shown to be remappings of correlation-based metrics. Furthermore, the statistical inference tests applied to pairwise Granger causality measures are theoretically shown to be equivalent to inference tests applied to correlation-based metrics. These results are demonstrated empirically using receiver operating characteristic curves derived from vector autoregressive models of various lags, sample size, and noise covariance values. The equivalence of linear Granger causality and correlation-based methods, in both metric and test statistic, renders linear Granger causality a restatement of traditional data-driven methodologies in the context of brain connectivity studies. Furthermore, the equivalence highlights the centrality of partial correlation and partial variance in linear connectivity analyses and bridges the gap between functional and effective connectivity techniques. Consequently, rather than a distinction rooted in methodological difference, the dichotomy between functional and effective connectivity methods is ultimately a function of model configuration realized in choices such as the selection of nodes, the choice to model instantaneous and/or directed influence, and the choice to employ many bivariate models or a single multivariate model. While these theoretical results may be unsurprising to the reader with advanced statistical knowledge, they highlight the importance of a clear understanding of the theoretical basis of connectivity analysis methods for human brain mapping researchers.

Improved decoding of neural activity from fMRI signals using non-separable spatiotemporal deconvolutions

The goal of most functional Magnetic Resonance Imaging (fMRI) analyses is to investigate neural activity. Many fMRI analysis methods assume that the temporal dynamics of the hemodynamic response function (HRF) to neural activation is separable from its spatial dynamics. Although there is empirical evidence that the HRF is more complex than suggested by space-time separable canonical HRF models, it is difficult to assess how much information about neural activity is lost when assuming space-time separability. In this study we directly test whether spatiotemporal variability in the HRF that is not captured by separable models contains information about neural signals. We predict intracranially measured neural activity from simultaneously recorded fMRI data using separable and non-separable spatiotemporal deconvolutions of voxel time series around the recording electrode. Our results show that abandoning the spatiotemporal separability assumption consistently improves the decoding accuracy of neural signals from fMRI data. We compare our findings with results from optical imaging and fMRI studies and discuss potential implications for classical fMRI analyses without invasive electrophysiological recordings.

A supervised method to assist the diagnosis and monitor progression of Alzheimer's disease using data from an fMRI experiment

The aim of this work is to provide a supervised method to assist the diagnosis and monitor the progression of the Alzheimer's disease (AD) using information which can be extracted from a functional magnetic resonance imaging (fMRI) experiment. The proposed method consists of five stages: (a) preprocessing of fMRI data, (b) modeling of the fMRI voxel time series using a generalized linear model, (c) feature extraction from the fMRI experiment, (d) feature selection, and (e) classification using the random forests algorithm. In the last stage we employ features that were extracted from the fMRI and other features such as demographics, behavioral and volumetric measures. The aim of the classification is twofold: first to diagnose AD and second to classify AD as very mild and mild. The method is evaluated using data from 41 subjects. The stage of AD is established using the Washington University Alzheimer's Disease Research Center recruitment and assessment procedures. The method classifies a patient as healthy or demented with 84% sensitivity and 92.3% specificity, and the stages of AD with 81% and 87% accuracy for the three class and the four class problem, respectively. The method is advantageous since it is fully automated and for the first time the diagnosis and staging of the disease are addressed using fMRI.

Detection and characterization of single‐trial fMRI bold responses: Paradigm free mapping

This work presents a novel method of mapping the brain's response to single stimuli in space and time without prior knowledge of the paradigm timing: paradigm free mapping (PFM). This method is based on deconvolution of the hemodynamic response from the voxel time series assuming a linear response and using a ridge-regression algorithm. Statistical inference is performed by defining a spatio-temporal t-statistic and by controlling for multiple comparisons using the false discovery rate procedure. The methodology was validated on five subjects who performed self-paced and visually cued finger tapping at 7 Tesla, with moderate (TR = 2 s) and high (TR = 0.4 s) temporal resolution. The results demonstrate that detection of single-trial BOLD events is feasible without a priori information on the stimulus paradigm. The proposed method opens up the possibility of designing temporally unconstrained paradigms to study the cortical response to unpredictable mental events.

A multiscale analysis of the temporal characteristics of resting-state fMRI data

In this paper, we conduct an investigation of the null hypothesis distribution for functional magnetic resonance imaging (fMRI) time series using multiscale analysis tools, SiZer (significance of zero crossings of the derivative) and wavelets. Most current approaches to the analysis of fMRI data assume simple models for temporal (short term or long term) dependence structure. Such simplifications are to some extent necessary due to the complex, high-dimensional nature of the data, but to date there have been few systematic studies of the dependence structures under a range of possible null hypotheses, using data sets gathered specifically for that purpose. We aim to address some of these issues by analyzing the detrended data with a long enough time horizon to study possible long-range temporal dependence. Our multiscale approach shows that even for resting-state data, data, i.e. “null” or ambient thought, some voxel time series cannot be modeled by white noise and need long-range dependent type error structure. This finding suggests the use of different time series models in different parts of the brain in fMRI studies.

A Bayesian multilevel model for fMRI data analysis

Bayesian approaches have been proposed by several functional magnetic resonance imaging (fMRI) researchers in order to overcome the fundamental limitations of the popular statistical parametric mapping method. However, the difficulties associated with subjective prior elicitation have prevented the widespread adoption of the Bayesian methodology by the neuroimaging community. In this paper, we present a Bayesian multilevel model for the analysis of brain fMRI data. The main idea is to consider that all the estimated group effects (fMRI activation patterns) are exchangeable. This means that all the collected voxel time series are considered manifestations of a few common underlying phenomena. In contradistinction to other Bayesian approaches, we think of the estimated activations as multivariate random draws from the same distribution without imposing specific prior spatial and/or temporal information for the interaction between voxels. Instead, a two-stage empirical Bayes prior approach is used to relate voxel regression equations through correlations between the regression coefficient vectors. The adaptive shrinkage properties of the Bayesian multilevel methodology are exploited to deal with spatial variations, and noise outliers. The characteristics of the proposed model are evaluated by considering its application to two real data sets.

A six stage approach for the diagnosis of the Alzheimer’s disease based on fMRI data

The aim of this work is to present an automated method that assists in the diagnosis of Alzheimer’s disease and also supports the monitoring of the progression of the disease. The method is based on features extracted from the data acquired during an fMRI experiment. It consists of six stages: (a) preprocessing of fMRI data, (b) modeling of fMRI voxel time series using a Generalized Linear Model, (c) feature extraction from the fMRI data, (d) feature selection, (e) classification using classical and improved variations of the Random Forests algorithm and Support Vector Machines, and (f) conversion of the trees, of the Random Forest, to rules which have physical meaning. The method is evaluated using a dataset of 41 subjects. The results of the proposed method indicate the validity of the method in the diagnosis (accuracy 94%) and monitoring of the Alzheimer’s disease (accuracy 97% and 99%).

Functional magnetic resonance imaging brain activation directly from k-space.

In functional magnetic resonance imaging (fMRI), the process of determining statistically significant brain activation is commonly performed in terms of voxel time series measurements after image reconstruction and magnitude-only time series formation. The image reconstruction and statistical activation processes are treated separately. In this manuscript, a framework is developed so that statistical analysis is performed in terms of the original, prereconstruction, complex-valued k-space measurements. First, the relationship between complex-valued (Fourier) encoded k-space measurements and complex-valued image measurements from (Fourier) reconstructed images is reviewed. Second, the voxel time series measurements are written in terms of the original spatiotemporal k-space measurements utilizing this k-space and image relationship. Finally, voxelwise fMRI activation can be determined in image space in terms of the original k-space measurements. Additionally, the spatiotemporal covariance between reconstructed complex-valued voxel time series can be written in terms of the spatiotemporal covariance between complex-valued k-space measurements. This allows one to utilize the originally measured data in its more natural, acquired state rather than in a transformed state. The effects of modeling preprocessing in k-space on voxel activation and correlation can then be examined.

Effects of model-based physiological noise correction on default mode network anti-correlations and correlations

Previous studies have reported that the spontaneous, resting-state time course of the default-mode network is negatively correlated with that of the “task-positive network”, a collection of regions commonly recruited in demanding cognitive tasks. However, all studies of negative correlations between the default-mode and task-positive networks have employed some form of normalization or regression of the whole-brain average signal (“global signal”); these processing steps alter the time series of voxels in an uninterpretable manner as well as introduce spurious negative correlations. Thus, the extent of negative correlations with the default mode network without global signal removal has not been well characterized, and it is has recently been hypothesized that the apparent negative correlations in many of the task-positive regions could be artifactually induced by global signal pre-processing. The present study aimed to examine negative and positive correlations with the default-mode network when model-based corrections for respiratory and cardiac noise are applied in lieu of global signal removal. Physiological noise correction consisted of (1) removal of time-locked cardiac and respiratory artifacts using RETROICOR (Glover, G.H., Li, T.Q., Ress, D., 2000. Image-based method for retrospective correction of physiological motion effects in fMRI: RETROICOR. Magn. Reson. Med. 44, 162–167), and (2) removal of low-frequency respiratory and heart rate variations by convolving these waveforms with pre-determined transfer functions (Birn et al., 2008; Chang et al., 2009) and projecting the resulting two signals out of the data. It is demonstrated that negative correlations between the default-mode network and regions of the task-positive network are present in the majority of individual subjects both with and without physiological noise correction. Physiological noise correction increased the spatial extent and magnitude of negative correlations, yielding negative correlations within task-positive regions at the group-level (p<0.05, uncorrected; no regions at the group level were significant at FDR=0.05). Furthermore, physiological noise correction caused region-specific decreases in positive correlations within the default-mode network, reducing apparent false positives. It was observed that the low-frequency respiratory volume and cardiac rate regressors used within the physiological noise correction algorithm displayed significant (but not total) shared variance with the global signal, and constitute a model-based alternative to correcting for non-neural global noise.

Relationship between respiration, end-tidal CO2, and BOLD signals in resting-state fMRI

A significant component of BOLD fMRI physiological noise is caused by variations in the depth and rate of respiration. It has previously been demonstrated that a breath-to-breath metric of respiratory variation (respiratory volume per time; RVT), computed from pneumatic belt measurements of chest expansion, has a strong linear relationship with resting-state BOLD signals across the brain. RVT is believed to capture breathing-induced changes in arterial CO2, which is a cerebral vasodilator; indeed, separate studies have found that spontaneous fluctuations in end-tidal CO2 (PETCO2) are correlated with BOLD signal time series. The present study quantifies the degree to which RVT and PETCO2 measurements relate to one another and explain common aspects of the resting-state BOLD signal. It is found that RVT (particularly when convolved with a particular impulse response, the “respiration response function”) is highly correlated with PETCO2, and that both explain remarkably similar spatial and temporal BOLD signal variance across the brain. In addition, end-tidal O2 is shown to be largely redundant with PETCO2. Finally, the latency at which PETCO2 and respiration belt measures are correlated with the time series of individual voxels is found to vary across the brain and may reveal properties of intrinsic vascular response delays.

Analyzing brain networks with PCA and conditional Granger causality

Identifying directional influences in anatomical and functional circuits presents one of the greatest challenges for understanding neural computations in the brain. Granger causality mapping (GCM) derived from vector autoregressive models of data has been employed for this purpose, revealing complex temporal and spatial dynamics underlying cognitive processes. However, the traditional GCM methods are computationally expensive, as signals from thousands of voxels within selected regions of interest (ROIs) are individually processed, and being based on pairwise Granger causality, they lack the ability to distinguish direct from indirect connectivity among brain regions. In this work a new algorithm called PCA based conditional GCM is proposed to overcome these problems. The algorithm implements the following two procedures: (i) dimensionality reduction in ROIs of interest with principle component analysis (PCA), and (ii) estimation of the direct causal influences in local brain networks, using conditional Granger causality. Our results show that the proposed method achieves greater accuracy in detecting network connectivity than the commonly used pairwise Granger causality method. Furthermore, the use of PCA components in conjunction with conditional GCM greatly reduces the computational cost relative to the use of individual voxel time series.

Assessment of brain interactivity in the motor cortex from the concept of functional connectivity and spectral analysis of fMRI data

Functional magnetic resonance imaging (fMRI) was used to assess the contributions of movement preparation and execution of a visuomotor task in a cerebral motor network. The functional connectivity of the voxel time series between brain regions in the frequency space was investigated by performing spectral analysis of fMRI time series. The regional interactivities between the two portions of the supplementary motor area (pre-SMA and SMA-proper) and the primary motor cortex (M1), defined as a seed region, were evaluated. The spectral parameter of coherence was used to describe a correlation structure in the frequency domain between two voxel-based time series and to infer the strength of the functional interaction within our presumed motor network of connections. The results showed meaningful differences of the functional interactions between the two portions of the SMA and the M1 area depending on the task conditions. This approach demonstrated the existence of a functional dissociation between the pre-SMA and SMA-proper subregions. We therefore conclude that spectral analysis is useful for identifying functional interactions of brain regions and might provide a powerful tool to quantify changes in connectivity profiles associated with various components of an experimental task.

REX: Response Exploration for Neuroimaging Datasets

Neuroimaging technologies produce large and complex datasets. The challenge of comprehensively analysing the recorded dynamics remains an important field of research. The whole-brain linear modelling of hypothesised response dynamics and experimental effects must utilise simple basis sets, which may not detect unexpected or complex signal effects. These unmodelled effects can influence statistical mapping results, and provide important additional clues to the underlying neural dynamics. They can be detected via exploration of the raw signal, however this can be difficult. Specialised visualisation tools are required to manage the huge number of voxels, events and scans. Many effects can be occluded by noise in individual voxel time-series. This paper describes a visualisation framework developed for the assessment of entire neuroimaging datasets. While currently available tools tend to be tied to a specific model of experimental effects, this framework includes a novel metadata schema that enables the rapid selection and processing of responses based on easily-adjusted classifications of scans, brain regions, and events. Flexible event-related averaging and process pipelining capabilities enable users to investigate the effects of preprocessing algorithms and to visualise power spectra and other transformations of the data. The framework has been implemented as a MATLAB package, REX (Response Exploration), which has been utilised within our lab and is now publicly available for download. Its interface enables the real-time control of data selection and processing, for very rapid visualisation. The concepts outlined in this paper have general applicability, and could provide significant further functionality to neuroimaging databasing and process pipeline environments.

Processing the acute cocaine FMRI response in human brain with Bayesian source separation

Pharmacological FMRI in humans involves BOLD signal acquisition before, during and after the administration of a drug, and often results in a heterogeneous pattern of drug-induced hemodynamic responses in the brain. Exploratory techniques, including blind source separation, can be useful for BOLD data that contains patterns of cross-dependencies. Bayesian source separation (BSS) is a multivariate technique used to calculate the presence of unobserved signal sources in measured FMRI data, as well as the covariance between data voxels and between reference waveforms. Unlike conventional univariate regression analysis, BSS does not assume independence between voxel time series or source components. In this study, BOLD measurement of the acute effect of an intravenous dose of cocaine, a substance shown previously to engage multiple sites within the orbitofrontal cortex, was processed with BSS. The utility of BSS in pharmacological FMRI applications was demonstrated in multiple examples featuring single-ROI, multiple-ROI and whole-slice data. The flexibility of the BSS technique was shown by choosing different modeling strategies to form the prior reference functions, including approximating the pharmacokinetics of cocaine, interpolating simultaneously measured behavioral data and using observed BOLD responses from known subcortical afferents to the cortex of interest.

Characterizing phase-only fMRI data with an angular regression model

FMRI voxel time series are complex-valued with real and imaginary parts that are usually converted to magnitude-phase polar coordinates. Magnitude-only data models that discard the phase portion of the data have dominated fMRI analysis. However, when such analyses are performed, the data that is discarded may contain valuable biologic information that is not in the magnitude data. This biologic information from BOLD fMRI data may be vascular [Menon RS. Postacquisition suppression of large-vessel BOLD signals in high-resolution fMRI. Magn Reson Med 2002;47(1):1–9] or neuronal [Bodurka J, Jesmanowicz A, Hyde JS, Xu H, Estowski L, Li S-J. Current-induced magnetic resonance phase imaging. J Magn Reson 1999;137(1):265–71] in origin. When phase-only time series that discard the magnitude portion of the data have been analyzed, ordinary least squares (OLS) regression has been the technique of choice. However, OLS models may fit poorly when phase-wrap or low signal-to-noise ratio (SNR) is present. We have explored alternatives to the OLS model which will account for the angular response of the phase while also allowing us the flexibility to develop similar hypothesis tests. We adopt an angular regression model by Fisher and Lee [Fisher NI, Lee AJ. Regression models for an angular response. Biometrics 1992;48:665–77] for our analysis and show its improvement over the OLS model at low SNR in terms of both parameter estimation and inferences. We found an improvement in parameter estimation along with modeling for the Fisher and Lee method in simulated data while detailing potential benefits when used with experimentally acquired data. Finally, we look at a map of the statistics testing the association of the observed voxel phase time course and the reference function in our acquired data. This shows the possible detection of biological information in the generally discarded phase.

Detecting functional nodes in large‐scale cortical networks with functional magnetic resonance imaging: A principal component analysis of the human visual system

This study aimed to demonstrate how a regional variant of principal component analysis (PCA) can be used to delineate the known functional subdivisions of the human visual system. Unlike conventional eigenimage analysis, PCA was carried out as a second-level analysis subsequent to model-based General Linear Model (GLM)-type functional activation mapping. Functional homogeneity of the functional magnetic resonance imaging (fMRI) time series within and between clusters was examined on several levels of the visual network, starting from the level of individual clusters up to the network level comprising two or more distinct visual regions. On each level, the number of significant components was identified and compared with the number of clusters in the data set. Eigenimages were used to examine the regional distribution of the extracted components. It was shown that voxels within individual clusters and voxels located in bilateral homologue visual regions can be represented by a single component, constituting the characteristic functional specialization of the cluster(s). If, however, PCA was applied to time series of voxels located in functionally distinct visual regions, more than one component was observed with each component being dominated by voxels in one of the investigated regions. The model of functional connections derived by PCA was in accordance with the well-known functional anatomy and anatomical connectivity of the visual system. PCA in combination with conventional activation mapping might therefore be used to identify the number of functionally distinct nodes in an fMRI data set in order to generate a model of functional connectivity within a neuroanatomical network.

Determining significant connectivity by 4D spatiotemporal wavelet packet resampling of functional neuroimaging data

An active area of neuroimaging research involves examining functional relationships between spatially remote brain regions. When determining whether two brain regions exhibit significant correlation due to true functional connectivity, one must account for the background spatial correlation inherent in neuroimaging data. We define background correlation as spatiotemporal correlation in the data caused by factors other than neurophysiologically based functional associations such as scanner induced correlations and image preprocessing. We develop a 4D spatiotemporal wavelet packet resampling method which generates surrogate data that preserves only the average background spatial correlation within an axial slice, across axial slices, and through each voxel time series, while excluding the specific correlations due to true functional relationships. We also extend an amplitude adjustment algorithm which adjusts our surrogate data to closely match the amplitude distribution of the original data. Our method improves upon existing wavelet-based methods and extends them to 4D. We apply our resampling technique to determine significant functional connectivity from resting state and motor task fMRI datasets.