Statistical analysis of functional MRI data in the wavelet domain

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.

Diffusion-informed spatial smoothing of fMRI data in white matter using spectral graph filters

Brain activation mapping using functional magnetic resonance imaging (fMRI) has been extensively studied in brain gray matter (GM), whereas in large disregarded for probing white matter (WM). This unbalanced treatment has been in part due to controversies in relation to the nature of the blood oxygenation level-dependent (BOLD) contrast in WM and its detectability. However, an accumulating body of studies has provided solid evidence of the functional significance of the BOLD signal in WM and has revealed that it exhibits anisotropic spatio-temporal correlations and structure-specific fluctuations concomitant with those of the cortical BOLD signal. In this work, we present an anisotropic spatial filtering scheme for smoothing fMRI data in WM that accounts for known spatial constraints on the BOLD signal in WM. In particular, the spatial correlation structure of the BOLD signal in WM is highly anisotropic and closely linked to local axonal structure in terms of shape and orientation, suggesting that isotropic Gaussian filters conventionally used for smoothing fMRI data are inadequate for denoising the BOLD signal in WM. The fundamental element in the proposed method is a graph-based description of WM that encodes the underlying anisotropy observed across WM, derived from diffusion-weighted MRI data. Based on this representation, and leveraging graph signal processing principles, we design subject-specific spatial filters that adapt to a subject's unique WM structure at each position in the WM that they are applied at. We use the proposed filters to spatially smooth fMRI data in WM, as an alternative to the conventional practice of using isotropic Gaussian filters. We test the proposed filtering approach on two sets of simulated phantoms, showcasing its greater sensitivity and specificity for the detection of slender anisotropic activations, compared to that achieved with isotropic Gaussian filters. We also present WM activation mapping results on the Human Connectome Project's 100-unrelated subject dataset, across seven functional tasks, showing that the proposed method enables the detection of streamline-like activations within axonal bundles.

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.

LARGE COVARIANCE ESTIMATION THROUGH ELLIPTICAL FACTOR MODELS

We propose a general Principal Orthogonal complEment Thresholding (POET) framework for large-scale covariance matrix estimation based on the approximate factor model. A set of high level sufficient conditions for the procedure to achieve optimal rates of convergence under different matrix norms is established to better understand how POET works. Such a framework allows us to recover existing results for sub-Gaussian data in a more transparent way that only depends on the concentration properties of the sample covariance matrix. As a new theoretical contribution, for the first time, such a framework allows us to exploit conditional sparsity covariance structure for the heavy-tailed data. In particular, for the elliptical distribution, we propose a robust estimator based on the marginal and spatial Kendall's tau to satisfy these conditions. In addition, we study conditional graphical model under the same framework. The technical tools developed in this paper are of general interest to high dimensional principal component analysis. Thorough numerical results are also provided to back up the developed theory.

Exploring the complementarity of THz pulse imaging and DCE-MRIs: Toward a unified multi-channel classification and a deep learning framework

We provide a comprehensive account of recent advances in biomedical image analysis and classification from two complementary imaging modalities: terahertz (THz) pulse imaging and dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI). The work aims to highlight underlining commonalities in both data structures so that a common multi-channel data fusion framework can be developed. Signal pre-processing in both datasets is discussed briefly taking into consideration advances in multi-resolution analysis and model based fractional order calculus system identification. Developments in statistical signal processing using principal component and independent component analysis are also considered. These algorithms have been developed independently by the THz-pulse imaging and DCE-MRI communities, and there is scope to place them in a common multi-channel framework to provide better software standardization at the pre-processing de-noising stage. A comprehensive discussion of feature selection strategies is also provided and the importance of preserving textural information is highlighted. Feature extraction and classification methods taking into consideration recent advances in support vector machine (SVM) and extreme learning machine (ELM) classifiers and their complex extensions are presented. An outlook on Clifford algebra classifiers and deep learning techniques suitable to both types of datasets is also provided. The work points toward the direction of developing a new unified multi-channel signal processing framework for biomedical image analysis that will explore synergies from both sensing modalities for inferring disease proliferation.

Wavelets and statistical analysis of functional magnetic resonance images of the human brain

Wavelets provide an orthonormal basis for multiresolution analysis and decorrelation or ‘whitening’ of nonstationary time series and spatial processes. Wavelets are particularly well suited to analysis of biological signals and images, such as human brain imaging data, which often have fractal or scale-invariant properties. We briefly define some key properties of the discrete wavelet transform (DWT) and review its applications to statistical analysis of functional magnetic resonance imaging (fMRI) data. We focus on time series resampling by ‘wavestrapping’ of wavelet coefficients, methods for efficient linear model estimation in the wavelet domain, and wavelet-based methods for multiple hypothesis testing, all of which are somewhat simplified by the decorrelating property of the DWT.

Anatomically-adapted graph wavelets for improved group-level fMRI activation mapping

A graph based framework for fMRI brain activation mapping is presented. The approach exploits the spectral graph wavelet transform (SGWT) for the purpose of defining an advanced multi-resolutional spatial transformation for fMRI data. The framework extends wavelet based SPM (WSPM), which is an alternative to the conventional approach of statistical parametric mapping (SPM), and is developed specifically for group-level analysis. We present a novel procedure for constructing brain graphs, with subgraphs that separately encode the structural connectivity of the cerebral and cerebellar gray matter (GM), and address the inter-subject GM variability by the use of template GM representations. Graph wavelets tailored to the convoluted boundaries of GM are then constructed as a means to implement a GM-based spatial transformation on fMRI data. The proposed approach is evaluated using real as well as semi-synthetic multi-subject data. Compared to SPM and WSPM using classical wavelets, the proposed approach shows superior type-I error control. The results on real data suggest a higher detection sensitivity as well as the capability to capture subtle, connected patterns of brain activity.

WAVELET-DOMAIN REGRESSION AND PREDICTIVE INFERENCE IN PSYCHIATRIC NEUROIMAGING

An increasingly important goal of psychiatry is the use of brain imaging data to develop predictive models. Here we present two contributions to statistical methodology for this purpose. First, we propose and compare a set of wavelet-domain procedures for fitting generalized linear models with scalar responses and image predictors: sparse variants of principal component regression and of partial least squares, and the elastic net. Second, we consider assessing the contribution of image predictors over and above available scalar predictors, in particular via permutation tests and an extension of the idea of confounding to the case of functional or image predictors. Using the proposed methods, we assess whether maps of a spontaneous brain activity measure, derived from functional magnetic resonance imaging, can meaningfully predict presence or absence of attention deficit/hyperactivity disorder (ADHD). Our results shed light on the role of confounding in the surprising outcome of the recent ADHD-200 Global Competition, which challenged researchers to develop algorithms for automated image-based diagnosis of the disorder.

Multi-resolution statistical analysis of brain connectivity graphs in preclinical Alzheimer's disease

There is significant interest, both from basic and applied research perspectives, in understanding how structural/functional connectivity changes can explain behavioral symptoms and predict decline in neurodegenerative diseases such as Alzheimer's disease (AD). The first step in most such analyses is to encode the connectivity information as a graph; then, one may perform statistical inference on various 'global' graph theoretic summary measures (e.g., modularity, graph diameter) and/or at the level of individual edges (or connections). For AD in particular, clear differences in connectivity at the dementia stage of the disease (relative to healthy controls) have been identified. Despite such findings, AD-related connectivity changes in preclinical disease remain poorly characterized. Such preclinical datasets are typically smaller and group differences are weaker. In this paper, we propose a new multi-resolution method for performing statistical analysis of connectivity networks/graphs derived from neuroimaging data. At the high level, the method occupies the middle ground between the two contrasts - that is, to analyze global graph summary measures (global) or connectivity strengths or correlations for individual edges similar to voxel based analysis (local). Instead, our strategy derives a Wavelet representation at each primitive (connection edge) which captures the graph context at multiple resolutions. We provide extensive empirical evidence of how this framework offers improved statistical power by analyzing two distinct AD datasets. Here, connectivity is derived from diffusion tensor magnetic resonance images by running a tractography routine. We first present results showing significant connectivity differences between AD patients and controls that were not evident using standard approaches. Later, we show results on populations that are not diagnosed with AD but have a positive family history risk of AD where our algorithm helps in identifying potentially subtle differences between patient groups. We also give an easy to deploy open source implementation of the algorithm for use within studies of connectivity in AD and other neurodegenerative disorders.

A versatile software package for inter-subject correlation based analyses of fMRI

In the inter-subject correlation (ISC) based analysis of the functional magnetic resonance imaging (fMRI) data, the extent of shared processing across subjects during the experiment is determined by calculating correlation coefficients between the fMRI time series of the subjects in the corresponding brain locations. This implies that ISC can be used to analyze fMRI data without explicitly modeling the stimulus and thus ISC is a potential method to analyze fMRI data acquired under complex naturalistic stimuli. Despite of the suitability of ISC based approach to analyze complex fMRI data, no generic software tools have been made available for this purpose, limiting a widespread use of ISC based analysis techniques among neuroimaging community. In this paper, we present a graphical user interface (GUI) based software package, ISC Toolbox, implemented in Matlab for computing various ISC based analyses. Many advanced computations such as comparison of ISCs between different stimuli, time window ISC, and inter-subject phase synchronization are supported by the toolbox. The analyses are coupled with re-sampling based statistical inference. The ISC based analyses are data and computation intensive and the ISC toolbox is equipped with mechanisms to execute the parallel computations in a cluster environment automatically and with an automatic detection of the cluster environment in use. Currently, SGE-based (Oracle Grid Engine, Son of a Grid Engine, or Open Grid Scheduler) and Slurm environments are supported. In this paper, we present a detailed account on the methods behind the ISC Toolbox, the implementation of the toolbox and demonstrate the possible use of the toolbox by summarizing selected example applications. We also report the computation time experiments both using a single desktop computer and two grid environments demonstrating that parallelization effectively reduces the computing time. The ISC Toolbox is available in https://code.google.com/p/isc-toolbox/

Improved compressed sensing-based algorithm for sparse-view CT image reconstruction

In computed tomography (CT), there are many situations where reconstruction has to be performed with sparse-view data. In sparse-view CT imaging, strong streak artifacts may appear in conventionally reconstructed images due to limited sampling rate that compromises image quality. Compressed sensing (CS) algorithm has shown potential to accurately recover images from highly undersampled data. In the past few years, total-variation-(TV-) based compressed sensing algorithms have been proposed to suppress the streak artifact in CT image reconstruction. In this paper, we propose an efficient compressed sensing-based algorithm for CT image reconstruction from few-view data where we simultaneously minimize three parameters: the ℓ₁ norm, total variation, and a least squares measure. The main feature of our algorithm is the use of two sparsity transforms—discrete wavelet transform and discrete gradient transform. Experiments have been conducted using simulated phantoms and clinical data to evaluate the performance of the proposed algorithm. The results using the proposed scheme show much smaller streaking artifacts and reconstruction errors than other conventional methods.

Statistical analysis of brain tissue images in the wavelet domain: wavelet-based morphometry

Wavelet-based methods have been developed for statistical analysis of functional MRI and PET data, where the wavelet transformation is employed as a tool for efficient signal representation. A number of studies using these approaches have reported better estimation capabilities, in terms of increased sensitivity and specificity, than the standard statistical analyses in the spatial domain. In line with these previous studies, the present report proposes a statistical analysis in the wavelet domain for the estimation of inter-group differences from structural MRI data. The procedure, called wavelet-based morphometry (WBM), was implemented under a voxel-based morphometry (VBM) style analysis. It was evaluated by comparing the gray-matter images of a group of 32 healthy subjects whose images were artificially altered to induce thinning of the cortex, with a different group of 32 healthy subjects whose images were unaltered. In order to quantify the performance of the reconstruction from a practical perspective, the same comparison was also conducted with standard VBM using SPM's Gaussian random fields and FSL's cluster-based statistics, family-wise error corrected, for datasets spatially-normalized via two different registration methods (i.e., SyN and FNIRT). The effect of using different amounts of smoothing, Battle-Lemarié filters and resolution levels in the wavelet transform was also investigated. Results support the proposed approach as a different and promising methodology to assess the structural morphometric differences between different populations of subjects.

The impact of denoising on independent component analysis of functional magnetic resonance imaging data

Independent component analysis (ICA) is a suitable method for decomposing functional magnetic resonance imaging (fMRI) activity into spatially independent patterns. Practice has revealed that low-pass filtering prior to ICA may improve ICA results by reducing noise and possibly by increasing source smoothness, which may enhance source independence; however, it eliminates useful information in high frequency features and it amplifies low signal fluctuations leading to independence loss. On the other hand, high-pass filtering may increase the independence by preserving spatial information, but its denoising properties are weak. Thus, such filtering strategies did not lead to simultaneous enhancements in independence and noise reduction; therefore, band-pass filtering or more sophisticated filtering methods are expected to be more appropriate. We used advanced wavelet filtering procedures, such as wavelet-based methods relying upon hard and soft coefficient thresholding and non-stationary Gaussian modelling based on geometrical prior information, to denoise artificial and real fMRI data. We compared the performance of these methods with the performance of traditional Gaussian smoothing techniques. First, we demonstrated both analytically and empirically the consistent performance increase of spatial filtering prior to ICA using spatial correlation and statistical sensitivity as quality measures. Second, all filtering methods were computationally efficient. Finally, denoising using low-pass filters was needed to improve ICA, suggesting that noise reduction may have a more significant effect on the component independence than the preservation of information contained within high frequencies.

Statistically significant contrasts between EMG waveforms revealed using wavelet-based functional ANOVA

We developed wavelet-based functional ANOVA (wfANOVA) as a novel approach for comparing neurophysiological signals that are functions of time. Temporal resolution is often sacrificed by analyzing such data in large time bins, increasing statistical power by reducing the number of comparisons. We performed ANOVA in the wavelet domain because differences between curves tend to be represented by a few temporally localized wavelets, which we transformed back to the time domain for visualization. We compared wfANOVA and ANOVA performed in the time domain (tANOVA) on both experimental electromyographic (EMG) signals from responses to perturbation during standing balance across changes in peak perturbation acceleration (3 levels) and velocity (4 levels) and on simulated data with known contrasts. In experimental EMG data, wfANOVA revealed the continuous shape and magnitude of significant differences over time without a priori selection of time bins. However, tANOVA revealed only the largest differences at discontinuous time points, resulting in features with later onsets and shorter durations than those identified using wfANOVA (P < 0.02). Furthermore, wfANOVA required significantly fewer (~1/4;×; P < 0.015) significant F tests than tANOVA, resulting in post hoc tests with increased power. In simulated EMG data, wfANOVA identified known contrast curves with a high level of precision (r(2) = 0.94 ± 0.08) and performed better than tANOVA across noise levels (P < <0.01). Therefore, wfANOVA may be useful for revealing differences in the shape and magnitude of neurophysiological signals (e.g., EMG, firing rates) across multiple conditions with both high temporal resolution and high statistical power.

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.

Modeling brain activation in fMRI using group MRF

Noise confounds present serious complications to functional magnetic resonance imaging (fMRI) analysis. The amount of discernible signals within a single dataset of a subject is often inadequate to obtain satisfactory intra-subject activation detection. To remedy this limitation, we propose a novel group Markov random field (GMRF) that extends each subject's neighborhood system to other subjects to enable information coalescing. A distinct advantage of GMRF over standard fMRI group analysis is that no stringent one-to-one voxel correspondence is required. Instead, intra- and inter-subject neighboring voxels are jointly regularized to encourage spatially proximal voxels to be assigned similar labels across subjects. Our proposed group-extended graph structure thus provides an effective means for handling inter-subject variability. Also, adopting a group-wise approach by integrating group information into intra-subject activation, as opposed to estimating a single average group map, permits inter-subject differences to be characterized and studied. GMRF can be elegantly implemented as a single MRF, thus enabling all subjects' activation maps to be simultaneously and collaboratively segmented with global optimality guaranteed in the case of binary labeling. We validate our technique on synthetic and real fMRI data and demonstrate GMRF's superior performance over standard fMRI analysis.

Extending local canonical correlation analysis to handle general linear contrasts for FMRI data

Local canonical correlation analysis (CCA) is a multivariate method that has been proposed to more accurately determine activation patterns in fMRI data. In its conventional formulation, CCA has several drawbacks that limit its usefulness in fMRI. A major drawback is that, unlike the general linear model (GLM), a test of general linear contrasts of the temporal regressors has not been incorporated into the CCA formalism. To overcome this drawback, a novel directional test statistic was derived using the equivalence of multivariate multiple regression (MVMR) and CCA. This extension will allow CCA to be used for inference of general linear contrasts in more complicated fMRI designs without reparameterization of the design matrix and without reestimating the CCA solutions for each particular contrast of interest. With the proper constraints on the spatial coefficients of CCA, this test statistic can yield a more powerful test on the inference of evoked brain regional activations from noisy fMRI data than the conventional t-test in the GLM. The quantitative results from simulated and pseudoreal data and activation maps from fMRI data were used to demonstrate the advantage of this novel test statistic.

Optimizing the performance of local canonical correlation analysis in fMRI using spatial constraints

The benefits of locally adaptive statistical methods for fMRI research have been shown in recent years, as these methods are more proficient in detecting brain activations in a noisy environment. One such method is local canonical correlation analysis (CCA), which investigates a group of neighboring voxels instead of looking at the single voxel time course. The value of a suitable test statistic is used as a measure of activation. It is customary to assign the value to the center voxel for convenience. The method without constraints is prone to artifacts, especially in a region of localized strong activation. To compensate for these deficiencies, the impact of different spatial constraints in CCA on sensitivity and specificity are investigated. The ability of constrained CCA (cCCA) to detect activation patterns in an episodic memory task has been studied. This research shows how any arbitrary contrast of interest can be analyzed by cCCA and how accurate P-values optimized for the contrast of interest can be computed using nonparametric methods. Results indicate an increase of up to 20% in detecting activation patterns for some of the advanced cCCA methods, as measured by ROC curves derived from simulated and real fMRI data.

TWave: high-order analysis of functional MRI

The traditional approach to functional image analysis models images as matrices of raw voxel intensity values. Although such a representation is widely utilized and heavily entrenched both within neuroimaging and in the wider data mining community, the strong interactions among space, time, and categorical modes such as subject and experimental task inherent in functional imaging yield a dataset with "high-order" structure, which matrix models are incapable of exploiting. Reasoning across all of these modes of data concurrently requires a high-order model capable of representing relationships between all modes of the data in tandem. We thus propose to model functional MRI data using tensors, which are high-order generalizations of matrices equivalent to multidimensional arrays or data cubes. However, several unique challenges exist in the high-order analysis of functional medical data: naïve tensor models are incapable of exploiting spatiotemporal locality patterns, standard tensor analysis techniques exhibit poor efficiency, and mixtures of numeric and categorical modes of data are very often present in neuroimaging experiments. Formulating the problem of image clustering as a form of Latent Semantic Analysis and using the WaveCluster algorithm as a baseline, we propose a comprehensive hybrid tensor and wavelet framework for clustering, concept discovery, and compression of functional medical images which successfully addresses these challenges. Our approach reduced runtime and dataset size on a 9.3GB finger opposition motor task fMRI dataset by up to 98% while exhibiting improved spatiotemporal coherence relative to standard tensor, wavelet, and voxel-based approaches. Our clustering technique was capable of automatically differentiating between the frontal areas of the brain responsible for task-related habituation and the motor regions responsible for executing the motor task, in contrast to a widely used fMRI analysis program, SPM, which only detected the latter region. Furthermore, our approach discovered latent concepts suggestive of subject handedness nearly 100× faster than standard approaches. These results suggest that a high-order model is an integral component to accurate scalable functional neuroimaging.

Unsupervised spatiotemporal fMRI data analysis using support vector machines

In this work we present a new support vector machine (SVM)-based method for fMRI data analysis. SVM has been shown to be a powerful, efficient data-driven tool in pattern recognition, and has been applied to the supervised classification of brain cognitive states in fMRI experiments. We examine the unsupervised mapping of activated brain regions using SVM. Specifically, the mapping process is formulated as an outlier detection problem of one-class SVM (OCSVM) that provides initial mapping results. These results are further refined by applying prototype selection and SVM reclassification. Multiple spatial and temporal features are extracted and selected to facilitate SVM learning. The proposed method was compared with correlation analysis (CA), t-test (TT), and spatial independent component analysis (SICA) methods using synthetic and experimental data. Our results show that the proposed method can provide more accurate and robust activation mapping than CA, TT and SICA, and is computationally more efficient than SICA. Besides its applicability to typical fMRI experiments, the proposed method is also a powerful tool in fMRI studies where a reliable quantification of activated brain regions is required.

Effects of temperature and handling conditions on lipid emulsion stability in veterinary parenteral nutrition admixtures during simulated intravenous administration

OBJECTIVE

To determine whether lipid particle coalescence develops in veterinary parenteral nutrition (PN) admixture preparations that are kept at room temperature (23 degrees C) for > 48 hours and whether that coalescence is prevented by admixture filtration, refrigeration, or agitation.

SAMPLE POPULATION

15 bags of veterinary PN solutions.

PROCEDURES

Bags of a PN admixture preparation containing a lipid emulsion were suspended and maintained under different experimental conditions (3 bags/group) for 96 hours while admixtures were dispensed to simulate IV fluid administration (rate, 16 mL/h). Bags were kept static at 4 degrees C (refrigeration); kept at 23 degrees C (room temperature) and continuously agitated; kept at room temperature and agitated for 5 minutes every 4 hours; kept static at room temperature and filtered during delivery; or kept static at room temperature (control conditions). Admixture samples were collected at 0, 24, 48, 72, and 96 hours and examined via transmission electron microscopy to determine lipid particle diameters. At 96 hours, 2 samples were collected at a location distal to the filter from each bag in that group for bacterial culture.

RESULTS

Distribution of lipid particle size in the control preparations and experimentally treated preparations did not differ significantly. A visible oil layer developed in continuously agitated preparations by 72 hours. Bacterial cultures of filtered samples yielded no growth.

CONCLUSIONS AND CLINICAL RELEVANCE

Data indicated that the veterinary PN admixtures kept static at 23 degrees C are suitable for use for at least 48 hours. Manipulations of PN admixtures appear unnecessary to prolong lipid particle stability, and continuous agitation may hasten lipid breakdown.

WSPM: Wavelet-based statistical parametric mapping

Recently, we have introduced an integrated framework that combines wavelet-based processing with statistical testing in the spatial domain. In this paper, we propose two important enhancements of the framework. First, we revisit the underlying paradigm; i.e., that the effect of the wavelet processing can be considered as an adaptive denoising step to "improve" the parameter map, followed by a statistical detection procedure that takes into account the non-linear processing of the data. With an appropriate modification of the framework, we show that it is possible to reduce the spatial bias of the method with respect to the best linear estimate, providing conservative results that are closer to the original data. Second, we propose an extension of our earlier technique that compensates for the lack of shift-invariance of the wavelet transform. We demonstrate experimentally that both enhancements have a positive effect on performance. In particular, we present a reproducibility study for multi-session data that compares WSPM against SPM with different amounts of smoothing. The full approach is available as a toolbox, named WSPM, for the SPM2 software; it takes advantage of multiple options and features of SPM such as the general linear model.

Resampling methods for improved wavelet-based multiple hypothesis testing of parametric maps in functional MRI

Two- or three-dimensional wavelet transforms have been considered as a basis for multiple hypothesis testing of parametric maps derived from functional magnetic resonance imaging (fMRI) experiments. Most of the previous approaches have assumed that the noise variance is equally distributed across levels of the transform. Here we show that this assumption is unrealistic; fMRI parameter maps typically have more similarity to a 1/f-type spatial covariance with greater variance in 2D wavelet coefficients representing lower spatial frequencies, or coarser spatial features, in the maps. To address this issue we resample the fMRI time series data in the wavelet domain (using a 1D discrete wavelet transform [DWT]) to produce a set of permuted parametric maps that are decomposed (using a 2D DWT) to estimate level-specific variances of the 2D wavelet coefficients under the null hypothesis. These resampling-based estimates of the "wavelet variance spectrum" are substituted in a Bayesian bivariate shrinkage operator to denoise the observed 2D wavelet coefficients, which are then inverted to reconstitute the observed, denoised map in the spatial domain. Multiple hypothesis testing controlling the false discovery rate in the observed, denoised maps then proceeds in the spatial domain, using thresholds derived from an independent set of permuted, denoised maps. We show empirically that this more realistic, resampling-based algorithm for wavelet-based denoising and multiple hypothesis testing has good Type I error control and can detect experimentally engendered signals in data acquired during auditory-linguistic processing.

Wavelet-based multi-resolution statistics for optical imaging signals: Application to automated detection of odour activated glomeruli in the mouse olfactory bulb

Optical imaging techniques offer powerful solutions to capture brain networks processing in animals, especially when activity is distributed in functionally distinct spatial domains. Despite the progress in imaging techniques, the standard analysis procedures and statistical assessments for this type of data are still limited. In this paper, we perform two in vivo non-invasive optical recording techniques in the mouse olfactory bulb, using a genetically expressed activity reporter fluorescent protein (synaptopHfluorin) and intrinsic signals of the brain. For both imaging techniques, we show that the odour-triggered signals can be accurately parameterized using linear models. Fitting the models allows us to extract odour specific signals with a reduced level of noise compared to standard methods. In addition, the models serve to evaluate statistical significance, using a wavelet-based framework that exploits spatial correlation at different scales. We propose an extension of this framework to extract activation patterns at specific wavelet scales. This method is especially interesting to detect the odour inputs that segregate on the olfactory bulb in small spherical structures called glomeruli. Interestingly, with proper selection of wavelet scales, we can isolate significantly activated glomeruli and thus determine the odour map in an automated manner. Comparison against manual detection of glomeruli shows the high accuracy of the proposed method. Therefore, beyond the advantageous alternative to the existing treatments of optical imaging signals in general, our framework propose an interesting procedure to dissect brain activation patterns on multiple scales with statistical control.

Bayesian fMRI data analysis with sparse spatial basis function priors

In previous work we have described a spatially regularised General Linear Model (GLM) for the analysis of brain functional Magnetic Resonance Imaging (fMRI) data where Posterior Probability Maps (PPMs) are used to characterise regionally specific effects. The spatial regularisation is defined over regression coefficients via a Laplacian kernel matrix and embodies prior knowledge that evoked responses are spatially contiguous and locally homogeneous. In this paper we propose to finesse this Bayesian framework by specifying spatial priors using Sparse Spatial Basis Functions (SSBFs). These are defined via a hierarchical probabilistic model which, when inverted, automatically selects an appropriate subset of basis functions. The method includes non-linear wavelet shrinkage as a special case. As compared to Laplacian spatial priors, SSBFs allow for spatial variations in signal smoothness, are more computationally efficient and are robust to heteroscedastic noise. Results are shown on synthetic data and on data from an event-related fMRI experiment.

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.

Estimation of false discovery rates for wavelet-denoised statistical parametric maps

Correction for multiple comparisons in neuroimaging data is an important area of research. Recently, wavelet-based methods have gained popularity and have been reported to achieve better sensitivity compared to spatial domain methods. However, these techniques produce smoothed statistical maps which are difficult to interpret. The generated maps have to be thresholded again in the spatial domain to delineate active from inactive regions. The selection of a proper threshold satisfying the required error rate control is not straightforward. In this paper, a framework is proposed for thresholding wavelet-denoised maps in which a rejection region is fixed, and the achieved false discovery rate (FDR) is estimated. This approach provides a meaningful strategy to choose thresholds for wavelet-denoised statistical parametric maps (SPMs). Two FDR estimation algorithms were used to assess the achieved error rate control when thresholding wavelet filtered SPMs at various rejection regions. Their performance was evaluated using both simulated and resting fMRI data. The proposed framework was also applied on in vivo data.

HBM functional imaging analysis contest data analysis in wavelet space

An analysis of the Functional Imaging Analysis Contest (FIAC) data is presented using spatial wavelet processing. This technique allows the image to be filtered adaptively according to the data itself, rather than relying on a predetermined filter. This adaptive filtering leads to better estimation of the parameters and contrasts in terms of mean squared error. It will be shown that by introducing a slight bias into the estimation, a large reduction in the variance can be achieved, leading to better overall mean squared error estimates. As no single filter needs to be preselected, results containing many scales of information can be found. In the FIAC data, it is shown that both small-scale and large-scale (smoother, more dispersed) effects occur. The combination of small- and large-scale effects detected in the FIAC data would be easy to miss using conventional single filter analysis.

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.

A wavelet-based statistical analysis of FMRI data: I. motivation and data distribution modeling

We propose a new method for statistical analysis of functional magnetic resonance imaging (fMRI) data. The discrete wavelet transformation is employed as a tool for efficient and robust signal representation. We use structural magnetic resonance imaging (MRI) and fMRI to empirically estimate the distribution of the wavelet coefficients of the data both across individuals and spatial locations. An anatomical subvolume probabilistic atlas is used to tessellate the structural and functional signals into smaller regions each of which is processed separately. A frequency-adaptive wavelet shrinkage scheme is employed to obtain essentially optimal estimations of the signals in the wavelet space. The empirical distributions of the signals on all the regions are computed in a compressed wavelet space. These are modeled by heavy-tail distributions because their histograms exhibit slower tail decay than the Gaussian. We discovered that the Cauchy, Bessel K Forms, and Pareto distributions provide the most accurate asymptotic models for the distribution of the wavelet coefficients of the data. Finally, we propose a new model for statistical analysis of functional MRI data using this atlas-based wavelet space representation. In the second part of our investigation, we will apply this technique to analyze a large fMRI dataset involving repeated presentation of sensory-motor response stimuli in young, elderly, and demented subjects.

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.

Varieties of attention-deficit/hyperactivity disorder-related intra-individual variability

Intra-individual variability in behavior and functioning is ubiquitous among children with attention-deficit/hyperactivity disorder (ADHD), but it has not been systematically examined or integrated within causal models. This article seeks to provide a conceptual, methodologic, and analytic framework as a foundation for future research. We first identify five key research questions and methodologic issues. For illustration, we examine the periodic structure of Eriksen Flanker task reaction time (RT) data obtained from 24 boys with ADHD and 18 age-matched comparison boys. Reaction time variability in ADHD differed quantitatively from control subjects, particularly at a modal frequency around .05 Hz (cycle length approximately 20 sec). These oscillations in RT were unaffected by double-blind placebo and were suppressed by double-blind methylphenidate. Together with converging lines of basic and clinical evidence, these secondary data analyses support the speculative hypothesis that the increased power of multisecond oscillations in ADHD RT data, and by inference, in attentional performance, represents a catecholaminergic deficit in the ability to appropriately modulate such oscillations in neuronal activity. These results highlight the importance of retaining time-series data and quantitatively examining intra-subject measures of variability as a putative endophenotype for ADHD.

ROC evaluation of statistical wavelet-based analysis of brain activation in [15O]-H2O PET scans

This paper presents and evaluates a wavelet-based statistical analysis of PET images for the detection of brain activation areas. Brain regions showing significant activations were obtained by performing Student's t tests in the wavelet domain, reconstructing the final image from only those wavelet coefficients that passed the statistical test at a given significance level, and discarding artifacts introduced during the reconstruction process. Using Receiver Operating Characteristic (ROC) curves, we have compared this statistical analysis in the wavelet domain to the conventional image-domain Statistical Parametric Mapping (SPM) method. For obtaining an accurate assessment of sensitivity and specificity, we have simulated realistic single subject [15O]-H2O PET studies with different hyperactivation levels of the thalamic region. The results obtained from an ROC analysis show that the wavelet approach outperforms conventional SPM in identifying brain activation patterns. Using the wavelet method, activation areas detected were closer in size and shape to the region actually activated in the reference image.

Unsupervised learning and mapping of active brain functional MRI signals based on hidden semi-Markov event sequence models

In this paper, a novel functional magnetic resonance imaging (fMRI) brain mapping method is presented within the statistical modeling framework of hidden semi-Markov event sequence models (HSMESMs). Neural activation detection is formulated at the voxel level in terms of time coupling between the sequence of hemodynamic response onsets (HROs) observed in the fMRI signal, and an HSMESM of the hidden sequence of task-induced neural activations. The sequence of HRO events is derived from a continuous wavelet transform (CWT) of the fMRI signal. The brain activation HSMESM is built from the timing information of the input stimulation protocol. The rich mathematical framework of HSMESMs makes these models an effective and versatile approach for fMRI data analysis. Solving for the HSMESM Evaluation and Learning problems enables the model to automatically detect neural activation embedded in a given set of fMRI signals, without requiring any template basis function or prior shape assumption for the fMRI response. Solving for the HSMESM Decoding problem allows to enrich brain mapping with activation lag mapping, activation mode visualizing, and hemodynamic response function analysis. Activation detection results obtained on synthetic and real epoch-related fMRI data demonstrate the superiority of the HSMESM mapping method with respect to a real application case of the statistical parametric mapping (SPM) approach. In addition, the HSMESM mapping method appears clearly insensitive to timing variations of the hemodynamic response, and exhibits low sensitivity to fluctuations of its shape.

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.

Spatiotemporal wavelet analysis for functional MRI

Characterizing the spatiotemporal behavior of the BOLD signal in functional Magnetic Resonance Imaging (fMRI) is a central issue in understanding brain function. While the nature of functional activation clusters is fundamentally heterogeneous, many current analysis approaches use spatially invariant models that can degrade anatomic boundaries and distort the underlying spatiotemporal signal. Furthermore, few analysis approaches use true spatiotemporal continuity in their statistical formulations. To address these issues, we present a novel spatiotemporal wavelet procedure that uses a stimulus-convolved hemodynamic signal plus correlated noise model. The wavelet fits, computed by spatially constrained maximum-likelihood estimation, provide efficient multiscale representations of heterogeneous brain structures and give well-identified, parsimonious spatial activation estimates that are modulated by the temporal fMRI dynamics. In a study of both simulated data and actual fMRI memory task experiments, our new method gave lower mean-squared error and seemed to result in more localized fMRI activation maps compared to models using standard wavelet or smoothing techniques. Our spatiotemporal wavelet framework suggests a useful tool for the analysis of fMRI studies.

Wavelet variance components in image space for spatiotemporal neuroimaging data

Neuroimaging studies place great emphasis on not only the estimation but also the standard error estimates of underlying parameters derived from a temporal model. This allows inferences to be made about the signal estimates and resulting conclusions to be drawn about the underlying data. It can often be advantageous to interrogate temporal models after spatial transformation of the data into the wavelet domain. Wavelet bases provide a multiresolution decomposition of the spatial data dimension and an ensuing reduction in spatial correlation. However, widespread acceptance of these wavelet techniques has been hampered by the limited ability to reconstruct both parametric and error estimates into the image domain after analysis of temporal models in the wavelet domain. This paper introduces a derivation and a fast implementation of a method for the calculation of the variance of the parametric images obtained from wavelet filters. The technique is proposed for a class of estimators that have been shown to be useful in neuroimaging studies. The techniques are demonstrated for both functional magnetic resonance imaging (fMRI) and positron emission tomography (PET) data sets.