Spatiotemporal wavelet analysis for functional MRI

Double-wavelet transform for multi-subject resting state functional magnetic resonance imaging data

Conventional regions of interest (ROIs)-level resting state fMRI (functional magnetic resonance imaging) response analyses do not rigorously model the underlying spatial correlation within each ROI. This can result in misleading inference. Moreover, they tend to estimate the temporal covariance matrix with the assumption of stationary time series, which may not always be valid. To overcome these limitations, we propose a double-wavelet approach that simplifies temporal and spatial covariance structure because wavelet coefficients are approximately uncorrelated under mild regularity conditions. This property allows us to analyze much larger dimensions of spatial and temporal resting-state fMRI data with reasonable computational burden. Another advantage of our double-wavelet approach is that it does not require the stationarity assumption. Simulation studies show that our method reduced false positive and false negative rates by properly taking into account spatial and temporal correlations in data. We also demonstrate advantages of our method by using resting-state fMRI data to study the difference in resting-state functional connectivity between healthy subjects and patients with major depressive disorder.

Spatiotemporal multiscale ICA could invariantly extract task (motor) modes from wavelet subbands of fMRI data

BACKGROUND AND OBJECTIVE

. Given a timeseries of task-evoked functional MRI (fMRI) images (4D spatiotemporal data), we can extract the task mode by statistical independent component analysis (ICA). If the 4D data are spatiotemporally decomposed into subbands (multiresolutions in both time and space), is ICA still capable of extracting the task modes at multiscales? We answer this question using the well-established fingertapping motor-task experiments at 3T and 7T. The positive answer informs that a brain task is spatiotemporal separable at ICA decomposition and shift invariant at multiscales during activation over a finite region.

METHODS

. We collected a set of task fMRI datasets from sixteen subjects performing fingertapping at 3T and one single dataset from a different subject at 7T. For each 4D fMRI dataset, we first performed temporal wavelet transform (1D WT) at 3 levels using different wavelets (e.g. 'db1','db2', and 'sym4'), then extracted the task modes from the WT subbands via ICA (as called multi-timescale ICA). Meanwhile, we also performed task mode extraction by applying ICA to 3D spatial WT subbands (as called multi-spacescale ICA). Upon the multiscale ICA results, we identified the primary motor task modes in the motor cortex, in comparison to the raw fMRI data analysis (at level 0).

RESULTS

. In the 7T experiment, the multiscale ICA across 3 timescale levels and 2 spacescale levels could extract the primary task modes at a tasktcorr of 0.90 and 0.86, respectively, compared to 0.87 for the ICA task extraction from raw data. In the 3T experiment, the multiscale could extract the primary task mode with 0.92 and 0.91, while the ICA task extraction from raw data was 0.91.

CONCLUSION

. ICA could extract the primary motor task modes from wavelet-decomposed multi-timescale and multi-spacescale subbands, construing the broad spatial activation (extent >>voxel size) of the brain motor task performed in a long duration (>>TR). Our experimental results show the brain functional activity signal is spatiotemporal separable as well as shift invariant at multiscales in both time and space.

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.

SACICA: a sparse approximation coefficient-based ICA model for functional magnetic resonance imaging data analysis

Independent component analysis (ICA) has been widely used in functional magnetic resonance imaging (fMRI) data to evaluate the functional connectivity, which assumes that the sources of functional networks are statistically independent. Recently, many researchers have demonstrated that sparsity is an effective assumption for fMRI signal separation. In this research, we present a sparse approximation coefficient-based ICA (SACICA) model to analyse fMRI data, which is a promising combination model of sparse features and an ICA technique. The SACICA method consists of three procedures. The wavelet packet decomposition procedure, which decomposes the fMRI data into wavelet tree nodes with different degrees of sparsity, is first. Then, the sparse approximation coefficients set formation procedure, in which an effective Lp norm is proposed to measure the sparse degree of the distinct wavelet tree nodes, is second. The ICA decomposition and reconstruction procedure, which utilises the sparse approximation coefficients set of the fMRI data, is last. The hybrid data experimental results demonstrated that the SACICA method exhibited the stronger spatial source reconstruction ability with respect to the unsmoothed fMRI data and better detection sensitivity of the functional signal on the smoothed fMRI data than the FastICA method. Furthermore, task-related experiments also revealed that SACICA was not only effective in discovering the functional networks but also exhibited a better detection sensitivity of the visual-related functional signal. In addition, the SACICA combined with Fast-FENICA proposed by Wang et al. (2012) was demonstrated to conduct the group analysis effectively on the resting-state data set.

Paradigm free mapping with sparse regression automatically detects single-trial functional magnetic resonance imaging blood oxygenation level dependent responses

The ability to detect single trial responses in functional magnetic resonance imaging (fMRI) studies is essential, particularly if investigating learning or adaptation processes or unpredictable events. We recently introduced paradigm free mapping (PFM), an analysis method that detects single trial blood oxygenation level dependent (BOLD) responses without specifying prior information on the timing of the events. PFM is based on the deconvolution of the fMRI signal using a linear hemodynamic convolution model. Our previous PFM method (Caballero-Gaudes et al., 2011: Hum Brain Mapp) used the ridge regression estimator for signal deconvolution and required a baseline signal period for statistical inference. In this work, we investigate the application of sparse regression techniques in PFM. In particular, a novel PFM approach is developed using the Dantzig selector estimator, solved via an efficient homotopy procedure, along with statistical model selection criteria. Simulation results demonstrated that, using the Bayesian information criterion to select the regularization parameter, this method obtains high detection rates of the BOLD responses, comparable with a model-based analysis, but requiring no information on the timing of the events and being robust against hemodynamic response function variability. The practical operation of this sparse PFM method was assessed with single-trial fMRI data acquired at 7T, where it automatically detected all task-related events, and was an improvement on our previous PFM method, as it does not require the definition of a baseline state and amplitude thresholding and does not compromise on specificity and sensitivity.

Bayesian hierarchical multi-subject multiscale analysis of functional MRI data

We develop a methodology for Bayesian hierarchical multi-subject multiscale analysis of functional Magnetic Resonance Imaging (fMRI) data. We begin by modeling the brain images temporally with a standard general linear model. After that, we transform the resulting estimated standardized regression coefficient maps through a discrete wavelet transformation to obtain a sparse representation in the wavelet space. Subsequently, we assign to the wavelet coefficients a prior that is a mixture of a point mass at zero and a Gaussian white noise. In this mixture prior for the wavelet coefficients, the mixture probabilities are related to the pattern of brain activity across different resolutions. To incorporate this information, we assume that the mixture probabilities for wavelet coefficients at the same location and level are common across subjects. Furthermore, we assign for the mixture probabilities a prior that depends on a few hyperparameters. We develop an empirical Bayes methodology to estimate the hyperparameters and, as these hyperparameters are shared by all subjects, we obtain precise estimated values. Then we carry out inference in the wavelet space and obtain smoothed images of the regression coefficients by applying the inverse wavelet transform to the posterior means of the wavelet coefficients. An application to computer simulated synthetic data has shown that, when compared to single-subject analysis, our multi-subject methodology performs better in terms of mean squared error. Finally, we illustrate the utility and flexibility of our multi-subject methodology with an application to an event-related fMRI dataset generated by Postle (2005) through a multi-subject fMRI study of working memory related brain activation.

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.

Wavelet-based fMRI analysis: 3-D denoising, signal separation, and validation metrics

We present a novel integrated wavelet-domain based framework (w-ICA) for 3-D denoising functional magnetic resonance imaging (fMRI) data followed by source separation analysis using independent component analysis (ICA) in the wavelet domain. We propose the idea of a 3-D wavelet-based multi-directional denoising scheme where each volume in a 4-D fMRI data set is sub-sampled using the axial, sagittal and coronal geometries to obtain three different slice-by-slice representations of the same data. The filtered intensity value of an arbitrary voxel is computed as an expected value of the denoised wavelet coefficients corresponding to the three viewing geometries for each sub-band. This results in a robust set of denoised wavelet coefficients for each voxel. Given the de-correlated nature of these denoised wavelet coefficients, it is possible to obtain more accurate source estimates using ICA in the wavelet domain. The contributions of this work can be realized as two modules: First, in the analysis module we combine a new 3-D wavelet denoising approach with signal separation properties of ICA in the wavelet domain. This step helps obtain an activation component that corresponds closely to the true underlying signal, which is maximally independent with respect to other components. Second, we propose and describe two novel shape metrics for post-ICA comparisons between activation regions obtained through different frameworks. We verified our method using simulated as well as real fMRI data and compared our results against the conventional scheme (Gaussian smoothing+spatial ICA: s-ICA). The results show significant improvements based on two important features: (1) preservation of shape of the activation region (shape metrics) and (2) receiver operating characteristic curves. It was observed that the proposed framework was able to preserve the actual activation shape in a consistent manner even for very high noise levels in addition to significant reduction in false positive voxels.

HomER: a review of time-series analysis methods for near-infrared spectroscopy of the brain

Near-infrared spectroscopy (NIRS) is a noninvasive neuroimaging tool for studying evoked hemodynamic changes within the brain. By this technique, changes in the optical absorption of light are recorded over time and are used to estimate the functionally evoked changes in cerebral oxyhemoglobin and deoxyhemoglobin concentrations that result from local cerebral vascular and oxygen metabolic effects during brain activity. Over the past three decades this technology has continued to grow, and today NIRS studies have found many niche applications in the fields of psychology, physiology, and cerebral pathology. The growing popularity of this technique is in part associated with a lower cost and increased portability of NIRS equipment when compared with other imaging modalities, such as functional magnetic resonance imaging and positron emission tomography. With this increasing number of applications, new techniques for the processing, analysis, and interpretation of NIRS data are continually being developed. We review some of the time-series and functional analysis techniques that are currently used in NIRS studies, we describe the practical implementation of various signal processing techniques for removing physiological, instrumental, and motion-artifact noise from optical data, and we discuss the unique aspects of NIRS analysis in comparison with other brain imaging modalities. These methods are described within the context of the MATLAB-based graphical user interface program, HomER, which we have developed and distributed to facilitate the processing of optical functional brain data.

DWT-CEM: an algorithm for scale-temporal clustering in fMRI

The number of studies using functional magnetic resonance imaging (fMRI) has grown very rapidly since the first description of the technique in the early 1990s. Most published studies have utilized data analysis methods based on voxel-wise application of general linear models (GLM). On the other hand, temporal clustering analysis (TCA) focuses on the identification of relationships between cortical areas by measuring temporal common properties. In its most general form, TCA is sensitive to the low signal-to-noise ratio of BOLD and is dependent on subjective choices of filtering parameters. In this paper, we introduce a method for wavelet-based clustering of time-series data and show that it may be useful in data sets with low signal-to-noise ratios, allowing the automatic selection of the optimum number of clusters. We also provide examples of the technique applied to simulated and real fMRI datasets.

Hidden Markov multiple event sequence models: A paradigm for the spatio-temporal analysis of fMRI data

This paper presents a novel, completely unsupervised fMRI brain mapping method that addresses the three problems of hemodynamic response function (HRF) variability, hemodynamic event timing, and fMRI response non-linearity. Spatial and temporal information are directly taken into account into the core of the activation detection process. In practice, activation detection at voxel v is formulated in terms of temporal alignment between sequences of hemodynamic response onsets (HROs) detected in the fMRI signal at v and in the spatial neighborhood of v, and the input sequence of stimuli or stimulus onsets. Event-related and epoch paradigms are considered. The multiple event sequence alignment problem is solved within the probabilistic framework of hidden Markov multiple event sequence models (HMMESMs), a new class of hidden Markov models. Results obtained on real and synthetic data significantly outperform those obtained with the popular statistical parametric mapping (SPM2) method without requiring any prior definition of the expected activation patterns, the HMMESM mapping approach being completely unsupervised.

The multiscale character of evoked cortical activity

Both the architecture and the dynamics of the brain have characteristic features at different spatial scales. However, the existence, nature and function of dynamical interdependencies between such scales have not been investigated. We studied the multiscale properties of functional magnetic resonance imaging (fMRI) data acquired while human subjects viewed a visual image. Traditional "region of interest" analysis of this data set revealed evoked activity in primary and extrastriate visual cortex. Wavelet transform in the spatial domain provides a multiscale representation of this evoked brain activity. Studying the correlation structure of this representation revealed strong and novel interdependencies in these data within and between different spatial scales. We found that such correlations are stronger than those evident in the original data and comparable in magnitude to those obtained after Gaussian smoothing. However, analysis of the data in the wavelet domain revealed additional structure such as positive correlations, strong anti-correlations and phase-lagged interdependencies. Statistical significance of these effects was inferred through nonparametric bootstrap techniques. We conclude that the spatial analysis of functional neuroimaging data in the wavelet domain provides novel information which may reflect complex spatiotemporal neuronal activity and information encoding. It also affords a quantitative means of testing hierarchical and multiscale models of cortical activity.

Emotional task-dependent low-frequency fluctuations and methylphenidate: Wavelet scaling analysis of 1/f-type fluctuations in fMRI of the cerebellar vermis

Ion channel currents, neural firing patterns, and brain BOLD signals display 1/f-type fluctuations or fractal properties in time. By design, fMRI methods attempt to minimize the contribution of variance from low-frequency physiological 1/f-noise. New fMRI methods are described to visualize and measure 1/f-type BOLD fluctuations in volunteers recalling affectively neutral or emotional memories or meditating (i.e., attending to breathing) then retrospectively rating emotional content. A wavelet scaling exponent (alpha) was used to characterize signals from 0.015625 to 0.5Hz in cerebellar lobules VIII to X of the vermis (posterior inferior vermis; PIV), a region coordinating balance, eye tracking, locomotion, and vascular tone, and a possible site of pathology in attention deficit hyperactivity disorder (ADHD).

RESULTS

Changes in alpha and emotional measures were correlated in PIV voxels (r = 0.622, d.f .= 14, P < 0.0005), but not other regions examined. In contrast, conventional means and standard deviations of PIV voxels were unchanged. Methylphenidate, shown to decrease slow oscillations in rodent basal ganglia [Ruskin DN, Bergstrom DA, Shenker A, Freeman LE, Baek D, Walters JR. Drugs used in the treatment of attention-deficit/hyperactivity disorder affect postsynaptic firing rate and oscillation without preferential dopamine autoreceptor action. Biol Psychiatry 2001;49:340-50.], abolished task-dependent alpha changes in the PIV of an adult with ADHD. Wavelet analysis of long BOLD time series appears well suited to fractal physiology and studies of pharmacologically modulated cerebellar-thalamic-cortical function in ADHD or other psychiatric disorders.

Nonstationary noise estimation in functional MRI

An important issue in functional MRI analysis is accurate characterisation of the noise processes present in the data. Whilst conventional fMRI noise representations often assume stationarity (or time-invariance) in the noise generating sources, such approaches may serve to suppress important dynamic information about brain function. As an alternative to these fixed temporal assumptions, we present in this paper two time-varying procedures for examining nonstationary noise structure in fMRI data. In the first procedure, we approximate nonstationary behaviour by means of a collection of simple but numerous time-varying parametric models. This is accomplished through the derivation of a locally parametric AutoRegressive (AR) plus drift model which tracks temporal covariance by allowing the model parameters to evolve over time. Before exploring time variation in these parameters, window-widths (bandwidths) that are well suited to the latent time-varying noise structure must be determined. To do this, we employ a bandwidth selection mechanism based on Stein's Unbiased Risk Estimator (SURE) criterion. In the second procedure, we describe the fMRI noise using a nonparametric method based on Functional Data Analysis (FDA). This process generates well-conditioned nonstationary covariance estimates that reflect temporal continuity in the underlying data structure whilst penalizing effective model dimension. We demonstrate both methods on simulated data and investigate the presence of nonstationary noise in resting fMRI data using the whitening capabilities of the locally parametric procedure. We evaluate the comparative behaviour of the stationary and nonstationary AR-based methods on data acquired at 1.5, 3 and 7 T magnetic field strengths and show that incorporation of time variation in the AR parameters leads to an overall decrease in the level of residual structure in the data. The FDA noise modelling technique is formulated within an activation mapping procedure and compared to the SPM (Statistical Parametric Mapping) toolbox on a cognitive face recognition task. Both the SPM and FDA methods show good sensitivity on this task, but we find that inclusion of the nonstationary FDA noise model seems to improve detection power in important task-related medial temporal regions.

Wavelets and functional magnetic resonance imaging of the human brain

The discrete wavelet transform (DWT) is widely used for multiresolution analysis and decorrelation or "whitening" of nonstationary time series and spatial processes. Wavelets are naturally appropriate for analysis of biological data, such as functional magnetic resonance images of the human brain, which often demonstrate scale invariant or fractal properties. We provide a brief formal introduction to key properties of the DWT and review the growing literature on its application to fMRI. We focus on three applications in particular: (i) wavelet coefficient resampling or "wavestrapping" of 1-D time series, 2- to 3-D spatial maps and 4-D spatiotemporal processes; (ii) wavelet-based estimators for signal and noise parameters of time series regression models assuming the errors are fractional Gaussian noise (fGn); and (iii) wavelet shrinkage in frequentist and Bayesian frameworks to support multiresolution hypothesis testing on spatially extended statistic maps. We conclude that the wavelet domain is a rich source of new concepts and techniques to enhance the power of statistical analysis of human fMRI data.