Abstract: Diffusion imaging is a promising marker of microstructural damage in neurodegenerative disorders, but interpretation of its relationship with underlying neuropathology can be complex. Here, we examined both volumetric and brain microstructure abnormalities in 13 amnestic patients with mild cognitive impairment (MCI), who progressed to probable Alzheimer's disease (AD) no earlier than 2 years after baseline scanning, in order to focus on early, and hence more sensitive, imaging markers. We compared them to 22 stable amnestic MCI patients with similar cognitive performance and episodic memory impairment but who did not show progression of symptoms for at least 3 years. Significant group differences were mainly found in the volume and microstructure of the left hippocampus, while white matter group differences were also found in the body of the fornix, left fimbria, and superior longitudinal fasciculus (SLF). Diffusion index abnormalities in the SLF were the sign of a subtle microstructural injury not detected by standard atrophy measures in the corresponding gray matter regions. The microstructural measure obtained in the left hippocampus using diffusion imaging showed the most substantial differences between the two groups and was the best single predictor of future progression to AD. An optimal prediction model (91% accuracy, 85% sensitivity, 96% specificity) was obtained by combining MRI measures and CSF protein biomarkers. These results highlight the benefit of using the information of brain microstructural damage, in addition to traditional gray matter volume, to detect early, subtle abnormalities in MCI prior to clinical progression to probable AD and, in combination with CSF markers, to accurately predict such progression.
Abstract: To evaluate the percentage change in volume of prostate cancer, as assessed by T2-weighted MRI, following exposure to dutasteride (Avodart) 0.5mg daily for six months.
Abstract: OBJECTIVES: To evaluate dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) for characterising nasopharyngeal carcinoma (NPC). METHODS: Forty-five newly diagnosed NPC patients were recruited. The initial enhancement rate (E ( R )), contrast transfer rate (k ( ep )), elimination rate (k ( el )), maximal enhancement (MaxEn) and initial area under the curve (iAUC) were calculated from semiquantitative analysis. The K ( trans ) (volume transfer constant), v ( e ) (volume fraction) and k ( ep ) were calculated from quantitative analysis. Student's t-test was used to evaluate the differences among tumour stages. Pearson's correlation between the two sets of k ( ep ) was performed. RESULTS: Comparing tumours of T1/2 stage (n = 18) and T3/4 stage (n = 27), MaxEn (P = 0.030) and iAUC (P = 0.039) were both significantly different; however, the iAUC was the only independent variable with 69.6 % sensitivity and 76.5 % specificity respectively; v ( e ) was also significantly different (P = 0.010) with 69.6 % sensitivity and 70.6 % specificity respectively. No significant difference was found among N stages. The two sets of k ( ep )s were highly correlated (r = 0.809, P < 0.001). Forty-three patients had chemoradiation, one palliative chemotherapy and one radiotherapy only. In the four patients with poor outcome, k ( el, ) E ( R, ) MaxEn and iAUC tended to be higher. CONCLUSIONS: Neovasculature in higher T stage NPC exhibits some parameters of increased permeability and perfusion. Thus, DCE-MRI may be helpful as an adjunctive technique in evaluating NPC. KEY POINTS : • The correct assessment of nasopharyngeal carcinoma (NPC) is important for planning treatment. • Neovasculature in higher T stage NPC exhibits increased permeability and perfusion. • Correlation between quantitative and semi-quantitative analysis validates the robustness of DCE-MRI. • DCE-MRI may be helpful as an adjunctive parameter in evaluating NPC.
Abstract: Replications of the association between APOE-ε4 allele load and regional brain atrophy in Alzheimer's disease (AD) patients hold promise for future studies testing relationships between other disease risk gene variants and brain structure. A polymorphism, rs10868366, in the Golgi phosphoprotein 2 gene, GOLM1, was recently identified as an AD risk factor in a genome-wide association study. In a subset of the same AD cohort, we used voxel-based morphometry to test for association between the disease risk genotype and reduced regional gray matter (GM) volume in AD patients (n = 72). A mean 14% reduction in GM volume was observed in the left frontal gyrus with the higher risk GG genotype. A similar association was observed in an independent, dataset of nondemented subjects (n = 278), although with a smaller effect (1%). This replicated association with GM structural variation suggests that GOLM1 polymorphisms may be related to cognitive phenotypes. The greater effect size in AD patients also suggests that the GG genotype could be a risk factor for the expression of cognitive deficits in AD.
Abstract: Restless legs syndrome (RLS) is a common neurological disorder the pathophysiology of which is incompletely understood. Four studies have examined structural differences between the brains of RLS patients and healthy controls, using voxel-based morphometry (VBM). All 4 studies have provided different results.
Abstract: Many therapeutic approaches to cancer affect the tumour vasculature, either indirectly or as a direct target. Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) has become an important means of investigating this action, both pre-clinically and in early stage clinical trials. For such trials, it is essential that the measurement process (i.e. image acquisition and analysis) can be performed effectively and with consistency among contributing centres. As the technique continues to develop in order to provide potential improvements in sensitivity and physiological relevance, there is considerable scope for between-centre variation in techniques. A workshop was convened by the Imaging Committee of the Experimental Cancer Medicine Centres (ECMC) to review the current status of DCE-MRI and to provide recommendations on how the technique can best be used for early stage trials. This review and the consequent recommendations are summarised here. Key Points • Tumour vascular function is key to tumour development and treatment • Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) can assess tumour vascular function • Thus DCE-MRI with pharmacokinetic models can assess novel treatments • Many recent developments are advancing the accuracy of and information from DCE-MRI • Establishing common methodology across multiple centres is challenging and requires accepted guidelines.
Abstract: Two packages, oro.dicom and oro.nifti, are provided for the interaction with and manipulation of medical imaging data that conform to the DICOM standard or ANALYZE/NIfTI formats. DICOM data, from a single file or directory tree, may be uploaded into R using basic data structures: a data frame for the header information and a matrix for the image data. A list structure is used to organize multiple DICOM files. The S4 class framework is used to develop basic ANALYZE and NIfTI classes, where NIfTI extensions may be used to extend the fixed-byte NIfTI header. One example of this, that has been implemented, is an XML-based "audit trail" tracking the history of operations applied to a data set. The conversion from DICOM to ANALYZE/NIfTI is straightforward using the capabilities of both packages. The S4 classes have been developed to provide a user-friendly interface to the ANALYZE/NIfTI data formats; allowing easy data input, data output, image processing and visualization.
Abstract: The special volume on "Magnetic Resonance Imaging in R" features articles and packages related to a variety of imaging modalities: functional MRI, diffusion-weighted MRI, dynamic contrast-enhanced MRI, dynamic susceptibility-contrast MRI and structural MRI. The papers describe the methodology, software implementation and provide comprehensive examples and data.
Abstract: Though mild cognitive impairment is an intermediate clinical state between healthy aging and Alzheimer's disease (AD), there are very few whole-brain voxel-wise diffusion MRI studies directly comparing changes in healthy control, mild cognitive impairment (MCI) and AD subjects. Here we report whole-brain findings from a comprehensive study of diffusion tensor indices and probabilistic tractography obtained in a very large population of healthy controls, MCI and probable AD subjects. As expected from the literature, all diffusion indices converged to show that the cingulum bundle, the uncinate fasciculus, the entire corpus callosum and the superior longitudinal fasciculus are the most affected white matter tracts in AD. Significant differences between MCI and AD were essentially confined to the corpus callosum. More importantly, we introduce for the first time in a degenerative disorder an application of a recently developed tensor index, the "mode" of anisotropy, as well as probabilistic crossing-fibre tractography. The mode of anisotropy specifies the type of anisotropy as a continuous measure reflecting differences in shape of the diffusion tensor ranging from planar (e.g., in regions of crossing fibres from two fibre populations of similar density or regions of "kissing" fibres) to linear (e.g., in regions where one fibre population orientation predominates), while probabilistic crossing-fibre tractography allows to accurately trace pathways from a crossing-fibre region. Remarkably, when looking for whole-brain diffusion differences between MCI patients and healthy subjects, the only region with significant abnormalities was a region of crossing fibres in the centrum semiovale, showing an increased mode of anisotropy. The only white matter region demonstrating a significant difference in correlations between neuropsychological scores and a diffusion measure (mode of anisotropy) across the three groups was the same region of crossing fibres. Further examination using probabilistic tractography established explicitly and quantitatively that this previously unreported increase of mode and co-localised increase of fractional anisotropy was explained by a relative preservation of motor-related projection fibres (at this early stage of the disease) crossing the association fibres of the superior longitudinal fasciculus. These findings emphasise the benefit of looking at the more complex regions in which spared and affected pathways are crossing to detect very early alterations of the white matter that could not be detected in regions consisting of one fibre population only. Finally, the methods used in this study may have general applicability for other degenerative disorders and, beyond the clinical sphere, they could contribute to a better quantification and understanding of subtle effects generated by normal processes such as visuospatial attention or motor learning.
Abstract: High angular resolution diffusion imaging data is the observed characteristic function for the local diffusion of water molecules in tissue. This data is used to infer structural information in brain imaging. Nonparametric scalar measures are proposed to summarize such data, and to locally characterize spatial features of the diffusion probability density function (PDF), relying on the geometry of the characteristic function. Summary statistics are defined so that their distributions are, to first-order, both independent of nuisance parameters and also analytically tractable. The dominant direction of the diffusion at a spatial location (voxel) is determined, and a new set of axes are introduced in Fourier space. Variation quantified in these axes determines the local spatial properties of the diffusion density. Nonparametric hypothesis tests for determining whether the diffusion is unimodal, isotropic or multi-modal are proposed. More subtle characteristics of white-matter microstructure, such as the degree of anisotropy of the PDF and symmetry compared with a variety of asymmetric PDF alternatives, may be ascertained directly in the Fourier domain without parametric assumptions on the form of the diffusion PDF. We simulate a set of diffusion processes and characterize their local properties using the newly introduced summaries. We show how complex white-matter structures across multiple voxels exhibit clear ellipsoidal and asymmetric structure in simulation, and assess the performance of the statistics in clinically-acquired magnetic resonance imaging data.
Abstract: The package dcemriS4 provides a complete set of data analysis tools for quantitative assessment of dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI). Image processing is provided for the ANALYZE and NIfTI data formats as input with all parameter estimates being output in NIfTI format. Estimation of T1 relaxation from multiple flip-angle acquisitions, using either constant or spatially-varying flip angles, is performed via nonlinear regression. Both literature-based and data-driven arterial input functions are available and may be combined with a variety of compartmental models. Kinetic parameters are obtained from nonlinear regression, Bayesian estimation via Markov chain Monte Carlo or Bayesian maximum a posteriori estimation. A non-parametric model, using penalized splines, is also available to characterize the contrast agent concentration time curves. Estimation of the apparent diffusion coefficient (ADC) is provided for diffusion-weighted imaging. Given the size of multi-dimensional data sets commonly acquired in imaging studies, care has been taken to maximize computational efficiency and minimize memory usage. All methods are illustrated using both simulated and real-world medical imaging data available in the public domain.
Abstract: R is a language and environment for statistical computing and graphics. It can be considered an alternative implementation of the S language developed in the 1970s and 1980s for data analysis and graphics (Becker and Chambers, 1984; Becker et al., 1988). The R language is part of the GNU project and offers versions that compile and run on almost every major operating system currently available. We highlight several R packages built specifically for the analysis of neuroimaging data in the context of functional MRI, diffusion tensor imaging, and dynamic contrast-enhanced MRI. We review their methodology and give an overview of their capabilities for neuroimaging. In addition we summarize some of the current activities in the area of neuroimaging software development in R.
Abstract: There is limited evidence that imaging biomarkers can predict subsequent response to therapy. Such prognostic and/or predictive biomarkers would facilitate development of personalised medicine. We hypothesised that pre-treatment measurement of the heterogeneity of tumour vascular enhancement could predict clinical outcome following combination anti-angiogenic and cytotoxic chemotherapy in colorectal cancer (CRC) liver metastases.
Abstract: Pharmacokinetic parameters from dynamic contrast-enhanced MRI (DCE-MRI) were used to assess the perfusion effects due to treatment response using a tyrosine kinase inhibitor. A Bayesian hierarchical model (BHM) is proposed, as an alternative to voxel-wise estimation procedures, to test for a treatment effect while explicitly modeling known sources of variability.
Abstract: Here we report the first multi-center clinical trial in Alzheimer's disease (AD) using fluorodeoxyglucose positron emission tomography ([18F]FDG-PET) measures of brain glucose metabolism as the primary outcome. We contrasted effects of 12 months treatment with the PPARγ agonist Rosiglitazone XR versus placebo in 80 mild to moderate AD patients. Secondary objectives included testing for reduction in the progression of brain atrophy and improvement in cognition. Active treatment was associated with a sustained but not statistically significant trend from the first month for higher mean values in Kiindex and CMRgluindex, novel quantitative indices related to the combined forward rate constant for [18F]FDG uptake and to the rate of cerebral glucose utilization, respectively. However, neither these nor another analytical approach recently validated using data from the Alzheimer's Disease Neuroimaging Initiative indicated that active treatment decreased the progression of decline in brain glucose metabolism. Rates of brain atrophy were similar between active and placebo groups and measures of cognition also did not suggest clear group differences. Our study demonstrates the feasibility of using [18F]FDG-PET as part of a multi-center therapeutics trial. It suggests that Rosiglitazone is associated with an early increase in whole brain glucose metabolism, but not with any biological or clinical evidence for slowing progression over a 1 year follow up in the symptomatic stages of AD.
Abstract: Conventional time series analysis, focusing exclusively on a time series at a given scale, lacks the ability to explain the nature of the data-generating process. A process equation that successfully explains daily price changes, for example, is unable to characterize the nature of hourly price changes. On the other hand, statistical properties of monthly price changes are often not fully covered by a model based on daily price changes. In this paper, we simultaneously model regimes of volatilities at multiple time scales through wavelet-domain hidden Markov models. We establish an important stylized property of volatility across different time scales. We call this property asymmetric vertical dependence. It is asymmetric in the sense that a low volatility state (regime) at a long time horizon is most likely followed by low volatility states at shorter time horizons. On the other hand, a high volatility state at long time horizons does not necessarily imply a high volatility state at shorter time horizons. Our analysis provides evidence that volatility is a mixture of high and low volatility regimes, resulting in a distribution that is non-Gaussian. This result has important implications regarding the scaling behavior of volatility, and, consequently, the calculation of risk at different time scales.
Abstract: Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is an important tool for detecting subtle kinetic changes in cancerous tissue. Quantitative analysis of DCE-MRI typically involves the convolution of an arterial input function (AIF) with a nonlinear pharmacokinetic model of the contrast agent concentration. Parameters of the kinetic model are biologically meaningful, but the optimization of the nonlinear model has significant computational issues. In practice, convergence of the optimization algorithm is not guaranteed and the accuracy of the model fitting may be compromised. To overcome these problems, this paper proposes a semi-parametric penalized spline smoothing approach, where the AIF is convolved with a set of B-splines to produce a design matrix using locally adaptive smoothing parameters based on Bayesian penalized spline models (P-splines). It has been shown that kinetic parameter estimation can be obtained from the resulting deconvolved response function, which also includes the onset of contrast enhancement. Detailed validation of the method, both with simulated and in vivo data, is provided.
Abstract: Imaging in clinical oncology trials provides a wealth of information that contributes to the drug development process, especially in early phase studies. This article focuses on kinetic modeling in DCE-MRI, inspired by mixed-effects models that are frequently used in the analysis of clinical trials. Instead of summarizing each scanning session as a single kinetic parameter--such as median k(trans) across all voxels in the tumor ROI-we propose to analyze all voxel time courses from all scans and across all subjects simultaneously in a single model. The kinetic parameters from the usual nonlinear regression model are decomposed into unique components associated with factors from the longitudinal study; e.g., treatment, patient, and voxel effects. A Bayesian hierarchical model provides the framework to construct a data model, a parameter model, as well as prior distributions. The posterior distribution of the kinetic parameters is estimated using Markov chain Monte Carlo (MCMC) methods. Hypothesis testing at the study level for an overall treatment effect is straightforward and the patient- and voxel-level parameters capture random effects that provide additional information at various levels of resolution to allow a thorough evaluation of the clinical trial. The proposed method is validated with a breast cancer study, where the subjects were imaged before and after two cycles of chemotherapy, demonstrating the clinical potential of this method to longitudinal oncology studies.
Abstract: APOE epsilon4 is the best-established genetic risk factor for sporadic Alzheimer's disease (AD). However, while homozygotes show greater disease susceptibility and earlier age of onset than heterozygotes, they may not show faster rates of clinical progression. We hypothesize that there are differential APOE epsilon4 allele-load dependent influences on neuropathology across the brain. Our aim was to define the relationship between APOE epsilon4 allele load and regionally-specific brain cortical atrophy in Alzheimer's Disease (AD). For this reason voxel-based morphometry (VBM) was performed using T1-weighted MR images from 83 AD patients, contrasting regional cortical grey matter by APOE epsilon4 load according to either dominant or genotypic models. Patients fulfilled NINCDS-ADRDA criteria and were genotyped for APOE epsilon4 (15 epsilon4/epsilon4, 39 epsilon4/- and 29-/-). We observed that grey matter volume (GMV) decreased additively with increasing allele load in the medial (MTL) and anterior temporal lobes bilaterally. By contrast, a 2 degree-of-freedom genotypic model suggested a dominant effect of the APOE epsilon4 allele in the left temporal lobe. Brain regions showing a significant APOE epsilon4 allele load effect on GMV in AD included only some of those typically described as having greatest amyloid plaque deposition and atrophy. Temporal regions appeared to show a dominant effect of APOE epsilon4 allele load instead of the additive effect previously strongly associated with age of onset. Regional variations with allele load may be related to different mechanisms for effects of APOE epsilon4 load on susceptibility and disease progression.
Abstract: Variational Bayes (VB) has been proposed as a method to facilitate calculations of the posterior distributions for linear models, by providing a fast method for Bayesian inference by estimating the parameters of a factorized approximation to the posterior distribution. Here a VB method for nonlinear forward models with Gaussian additive noise is presented. In the case of noninformative priors the parameter estimates obtained from this VB approach are identical to those found via nonlinear least squares. However, the advantage of the VB method lies in its Bayesian formulation, which permits prior information to be included in a hierarchical structure and measures of uncertainty for all parameter estimates to be obtained via the posterior distribution. Unlike other Bayesian methods VB is only approximate in comparison with the sampling method of MCMC. However, the VB method is found to be comparable and the assumptions made about the form of the posterior distribution reasonable. Practically, the VB approach is substantially faster than MCMC as fewer calculations are required. Some of the advantages of the fully Bayesian nature of the method are demonstrated through the extension of the noise model and the inclusion of Automatic Relevance Determination (ARD) within the VB algorithm.
Abstract: The fundamental equations that model turbulent flow do not provide much insight into the size and shape of observed turbulent structures. We investigate the efficient and accurate representation of structures in two-dimensional turbulence by applying statistical models directly to the simulated vorticity field. Rather than extract the coherent portion of the image from the background variation, as in the classical signal-plus-noise model, we present a model for individual vortices using the non-decimated discrete wavelet transform. A template image, which is supplied by the user, provides the features to be extracted from the vorticity field. By transforming the vortex template into the wavelet domain, specific characteristics that are present in the template, such as size and symmetry, are broken down into components that are associated with spatial frequencies. Multivariate multiple linear regression is used to fit the vortex template to the vorticity field in the wavelet domain. Since all levels of the template decomposition may be used to model each level in the field decomposition, the resulting model need not be identical to the template. Application to a vortex census algorithm that records quantities of interest (such as size, peak amplitude and circulation) as the vorticity field evolves is given. The multiresolution census algorithm extracts coherent structures of all shapes and sizes in simulated vorticity fields and can reproduce known physical scaling laws when processing a set of vorticity fields that evolve over time.
Abstract: With expanding potential clinical applications of functional magnetic resonance imaging (fMRI) it is important to test how reliable different measures of fMRI activation are between subjects and sessions and between centres. This study compared variability across 17 patients with multiple sclerosis (MS) and 22 age-matched healthy controls (HC) in 5 European centres performing an fMRI block design with hand tapping. We recruited subjects from sites using 1.5 T scanners from different manufacturers. 5 healthy volunteers also were studied at each of 4 of the centres. We found that reproducibility between runs and sessions for single individuals was consistently much greater than between individuals. There was greater run-to-run variability for MS patients than for HC. Measurements of maximum signal change (MSC) appeared to provide higher reproducibility within individuals and greater sensitivity to differences between individuals than region of interest (ROI) suprathreshold voxel counts. The variability in measurements between centres was not as great as that between individuals. Consistent with these observations, we estimated that power should not be reduced substantially with use of multi-, as opposed to single-, centre study designs with similar numbers of subjects. Multi-centre interventional studies in which fMRI is used as an outcome measure thus appear practical even when implemented in conventional clinical environments.
Abstract: Estimation of noise-induced variability in diffusion tensor imaging (DTI) is needed to objectively follow disease progression in therapeutic monitoring and to provide consistent readouts of pathophysiology. The noise variability of nonlinear quantities of the diffusion tensor (e.g., fractional anisotropy, fiber orientation, etc.) have been quantified using the bootstrap, in which the data are resampled from the experimental averages, yet this approach is only applicable to DTI scans that contain multiple averages from the same sampling direction. It has been shown that DTI acquisitions with a modest to large number of directions, in which each direction is only sampled once, outperform the multiple averages approach. These acquisitions resist the traditional (regular) bootstrap analysis though. In contrast to the regular bootstrap, the wild bootstrap method can be applied to such protocols in which there is only one observation per direction. Here, we compare and contrast the wild bootstrap with the regular bootstrap using Monte Carlo numerical simulations for a number of diffusion scenarios. The regular and wild bootstrap methods are applied to human DTI data and empirical distributions are obtained for fractional anisotropy and the diffusion tensor eigensystem. Spatial maps of the estimated variability in the diffusion tensor principal eigenvector are provided. The wild bootstrap method can provide empirical distributions for tensor-derived quantities, such as fractional anisotropy and principal eigenvector direction, even when the exact distributions are not easily derived.
Abstract: Simple summary statistics of Dynamic Contrast-Enhanced MRI (DCE-MRI) parameter maps (e.g. the median) neglect the spatial arrangement of parameters, which appears to carry important diagnostic and prognostic information. This paper describes novel statistics that are sensitive to both parameter values and their spatial arrangement. Binary objects are created from 3-D DCE-MRI parameter maps by "extruding" each voxel into a fourth dimension; the extrusion distance is proportional to the voxel's value. The following statistics are then computed on these 4-D binary objects: surface area, volume, surface area to volume ratio, and box counting (fractal) dimension. An experiment using 4 low and 5 high grade gliomas showed significant differences between the two grades for box counting dimension computed for extruded v(e) maps, surface area of extruded K(trans) and v(e) maps and the volume of extruded v(e) maps (all p < 0.05). An experiment using 18 liver metastases imaged before and after treatment with a vascular endothelial growth factor (VEGF) inhibitor showed significant differences for surface area to volume ratio computed for extruded K(trans) and v(e) maps (p = 0.0013 and p = 0.045 respectively).
Abstract: 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.
Abstract: In pharmacological MRI (phMRI) studies tracking signal changes following the acute administration of a compound, the spatiotemporal pattern of response is often unknown a priori. Moreover, when analysed within a general linear model (GLM) framework, the experimental paradigm of a single injection point under-informs the construction of an appropriate signal model, and information from pharmacokinetics or ancillary in vivo studies may be unavailable or insufficient to accurately describe the dynamic signal changes observed following injection of the drug. Here, we extend the application of a data-driven clustering algorithm, wavelet cluster analysis (WCA), to phMRI data from one or more groups of subjects in a study. A WCA decomposition of spatially concatenated time series' provides a compact overview of spatiotemporal response patterns across cohorts, highlighting typical temporal signatures, brain regions implicated in the response and inter-subject variability. Further, we demonstrate the use of regressors based on selected temporal components as suitable signal models in GLM-based analyses, resulting in a close fit to dynamic phMRI signal changes. This approach is illustrated with simulated data and two representative in vivo phMRI studies in the rat (nicotine and apomorphine challenges).
Abstract: A semi-parametric bootstrap procedure is proposed for two-dimensional spatial processes on a finite lattice (images). Discrete wavelet transforms are used to produce coefficients that are approximately uncorrelated in space. For illustration, realizations of spatial processes from the Matern class of spectral density functions are analyzed. The goal is to obtain bootstrap realizations by applying the naive bootstrap to the approximately uncorrelated wavelet coefficients. The methodology is shown to be effective at reproducing moderate levels of spatial covariance on several simulated data sets as well as images taken from a functional magnetic resonance imaging (fMRI) experiment. An application to testing functional connectivity in fMRI is also presented. (c) 2005 Elsevier B.V. All rights reserved.
Abstract: Small-world properties have been demonstrated for many complex networks. Here, we applied the discrete wavelet transform to functional magnetic resonance imaging (fMRI) time series, acquired from healthy volunteers in the resting state, to estimate frequency-dependent correlation matrices characterizing functional connectivity between 90 cortical and subcortical regions. After thresholding the wavelet correlation matrices to create undirected graphs of brain functional networks, we found a small-world topology of sparse connections most salient in the low-frequency interval 0.03-0.06 Hz. Global mean path length (2.49) was approximately equivalent to a comparable random network, whereas clustering (0.53) was two times greater; similar parameters have been reported for the network of anatomical connections in the macaque cortex. The human functional network was dominated by a neocortical core of highly connected hubs and had an exponentially truncated power law degree distribution. Hubs included recently evolved regions of the heteromodal association cortex, with long-distance connections to other regions, and more cliquishly connected regions of the unimodal association and primary cortices; paralimbic and limbic regions were topologically more peripheral. The network was more resilient to targeted attack on its hubs than a comparable scale-free network, but about equally resilient to random error. We conclude that correlated, low-frequency oscillations in human fMRI data have a small-world architecture that probably reflects underlying anatomical connectivity of the cortex. Because the major hubs of this network are critical for cognition, its slow dynamics could provide a physiological substrate for segregated and distributed information processing.
Abstract: The combination of the long-acting beta2-agonist, salmeterol xinafoate (salmeterol) and inhaled corticosteroid, fluticasone propionate (FP) (Seretide/Advair) has shown enhanced efficacy compared with concurrent administration of the two drugs from individual inhalers at the same dose. A possible explanation for this increased effect is a higher degree of co-deposition of the two drugs from the combination (Seretide) inhaler compared with the component drugs administered separately. Raman laser spectroscopy, a technique capable of identifying individual drug particles, has been used with novel statistical methodology that we have developed, to determine whether there is any co-association between drug particles and whether this occurs in the Seretide formulation rather than by chance. Samples from a combined Seretide metered dose inhaler (MDI, 25/50 mcg) and salmeterol (25 mcg) with FP (50 mcg) from separate MDI's taken from Plate 4 of an Anderson Cascade Impactor were analysed. Using a statistical test based on the bootstrap technique, it was found that the co-deposition of FP and salmeterol particles from the combination MDI was significantly greater than from the separate inhalers group (p < 0.001). A higher degree of co-deposition on the same cells of the airways may possibly account for the increased efficacy observed in patients prescribed Seretide MDI.
Abstract: This paper proposes a new method for estimating kinetic parameters of dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) based on adaptive Gaussian Markov random fields. Kinetic parameter estimates using neighboring voxels reduce the observed variability in local tumor regions while preserving sharp transitions between heterogeneous tissue boundaries. Asymptotic results for standard errors from likelihood-based nonlinear regression are compared with those derived from the posterior distribution using Bayesian estimation with and without neighborhood information. Application of the method to the analysis of breast tumors based on kinetic parameters has shown that the use of Bayesian analysis combined with adaptive Gaussian Markov random fields provides improved convergence behavior and more consistent morphological and functional statistics.
Abstract: Current approaches to quantitative analysis of DCE-MRI with non-linear models involve the convolution of an arterial input function (AIF) with the contrast agent concentration at a voxel or regional level. Full quantification provides meaningful biological parameters but is complicated by the issues related to convergence, (de-)convolution of the AIF, and goodness of fit. To overcome these problems, this paper presents a penalized spline smoothing approach to model the data in a semi-parametric way. With this method, the AIF is convolved with a set of B-splines to produce the design matrix, and modeling of the resulting deconvolved biological parameters is obtained in a way that is similar to the parametric models. Further kinetic parameters are obtained by fitting a non-linear model to the estimated response function and detailed validation of the method, both with simulated and in vivo data is
Abstract: An analytic wavelet transform, based on Hilbert wavelet pairs, is applied to bivariate time-varying spectral estimation for neurophysiological time series. Under the assumption of an underlying block stationary process, both single-trial and ensemble Studies are amenable to this method. A bootstrap procedure, which samples with replacement blocks centered around the events of interest, is proposed to identify time points for which the event-averaged magnitude squared coherence is non-zero. Clinical data sets are used to compare the wavelet-based technique with the classical Fourier-based spectral measures and highlight its ability to detect time-varying coherence and phase properties. (c) 2005 Elsevier B.V. All rights reserved.
Abstract: MRI time series experiments produce a wealth of information contained in two or three spatial dimensions that evolve over time. Such experiments can, for example, localize brain response to pharmacological stimuli, but frequently the spatiotemporal characteristics of the cerebral response are unknown a priori and variable, and thus difficult to evaluate using hypothesis-based methods alone. Here we used features in the temporal dimension to group voxels with similar time courses based on a nonparametric discrete wavelet transform (DWT) representation of each time course. Applying the DWT to each voxel decomposes its temporal information into coefficients associated with both time and scale. Discarding scales in the DWT that are associated with high-frequency oscillations (noise) provided a straight-forward data reduction step and decreased the computational burden. Optimization-based clustering was then applied to the remaining wavelet coefficients in order to produce a finite number of voxel clusters. This wavelet-based cluster analysis (WCA) was evaluated using two representative classes of MRI neuroimaging experiments. In perfusion-weighted MRI, following occlusion of the middle cerebral artery (MCAO), WCA differentiated healthy tissue and different regions within the ischemic hemisphere. Following an acute cocaine challenge, WCA localized subtle differences in the pharmacokinetic profile of the cerebral response. We conclude that WCA provides a robust method for blind analysis of time series image data.
Abstract: This paper assesses the estimation of kinetic parameters from dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI). Asymptotic results from likelihood-based nonlinear regression are compared with results derived from the posterior distribution using Bayesian estimation, along with the output from an established software package (MRIW). By using the estimated error from kinetic parameters, it is possible to produce more accurate clinical statistics, such as tumor size, for patients with breast tumors. Further analysis has also shown that Bayesian methods are more accurate and do not suffer from convergence problems, but at a higher computational cost.
Abstract: In this paper we propose a new approach to estimating systematic risk (the beta of an asset). The proposed method is based on a wavelet multiscaling approach that decomposes a given time series on a scale-by-scale basis. The empirical results from different economies show that the relationship between the return of a portfolio and its beta becomes stronger as the wavelet scale increases. Therefore, the predictions of the CAPM model should be investigated considering the multiscale nature of risk and return. (C) 2004 Elsevier Ltd. All rights reserved.
Abstract: We are interested in methods for multiple hypothesis testing that optimize power to refute the null hypothesis while controlling the false discovery rate (FDR). The wavelet transform of a spatial map of brain activation statistics can be tested in two stages to achieve this objective: First, a set of possible wavelet coefficients to test is reduced, and second, each hypothesis in the remaining subset is formally tested. We show that a Bayesian bivariate shrinkage operator (BaybiShrink) for the first step provides a powerful and expedient alternative to a subband adaptive chi-squared test or an enhanced FDR algorithm based on the generalized degrees of freedom. We also investigate the dual-tree complex wavelet transform (CWT) as an alternative basis to the orthogonal discrete wavelet transform (DWT). We design and validate a test for activation based on the magnitude of the complex wavelet coefficients and show that this confers improved specificity for mapping spatial signals. The methods are applied to simulated and experimental data, including a pharmacological magnetic resonance imaging (MRI) study. We conclude that using BaybiShrink to define a reduced set of complex wavelet coefficients, and testing the magnitude of each complex pair to control the FDR, represents a competitive solution for multiple hypothesis mapping in fMRI.
Abstract: We introduce the multiscale analysis of seasonal persistent processes. that is, time series models with a singularity in their spectral density function at one or more frequencies in [0, 1/2]. The discrete wavelet packet transform (DWPT) and a nondecimated version of it known as the maximal overlap DWPT (MODWPT) are introduced as alternative methods to Fourier-based techniques for analyzing time series that exhibit seasonal long memory. The approximate log-linear relationship between the wavelet packet variance and frequency is used to produce a least squares estimator of the fractional difference parameter. Approximate maximum likelihood estimation is performed by replacing the variance/covariance matrix with a diagonalized matrix based on the DWPT. Simulations are performed to compare the wavelet-based techniques with the spectral estimate-based techniques for both least squares and maximum likelihood procedures. An application of this methodology to atmospheric and economic time series is used for demonstration purposes.
Abstract: 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.
Abstract: The efficient and accurate representation of two-dimensional turbulent fields is of interest in the geosciences because the fundamental equations that describe turbulence are difficult to handle directly. Rather than extract the coherent portion of the image from the background variation, as in the classical signal plus noise model, we present a statistical model for individual vortices using the non-decimated discrete wavelet transform. A template image, supplied by the user, provides the features we want to extract from the observed field. By transforming the vortex template into the wavelet domain specific characteristics present in the template, such as size and symmetry, are broken down into components associated with spatial frequencies. Multivariate multiple linear regression is used to fit the vortex template to the observed vorticity field in the wavelet domain.
Abstract: In this paper we propose to overcome the problem of spurious regression between fractionally differenced processes by applying the discrete wavelet transform (DWT) to both processes and then estimating the regression in the wavelet domain. The DWT is known to approximately decorrelate heavily autocorrelated processes and, unlike applying a first difference filter, involves a recursive two-step filtering and downsampling procedure. We prove the asymptotic normality of the proposed estimator and demonstrate via simulation its efficacy in finite samples. Copyright (C) 2003 John Wiley Sons, Ltd.
Abstract: In this paper we propose a new approach to estimating the systematic risk (the beta of an asset) in a capital asset pricing model (CAPM). The proposed method is based on a wavelet multiscaling approach that decomposes a given time series on a scale-by-scale basis. At each scale, the wavelet variance of the market return and the wavelet covariance between the market return and a portfolio are calculated to obtain an estimate of the portfolio's beta. The empirical results show that the relationship between the return of a portfolio and its beta becomes stronger as the wavelet scale increases. Therefore, the predictions of the CAPM model are more relevant in the medium long run as compared to short time horizons.
Abstract: We consider the problem of testing for homogeneity of variance in a time series with long memory structure. We demonstrate that a test whose null hypothesis is designed to be white noise can, in fact, be applied, on a scale by scale basis, to the discrete wavelet transform of long memory processes. In particular, we show that evaluating a normalized cumulative sum of squares test statistic using critical levels for the null hypothesis of white noise yields approximately the same null hypothesis rejection rates when applied to the discrete wavelet transform of samples from a fractionally differenced process. The point at which the test statistic, using a nondecimated version of the discrete wavelet transform, achieves its maximum value can be used to estimate the time of the unknown variance change. We apply our proposed test statistic on five time series derived from the historical record of Nile River yearly minimum water levels covering 622-1922 A.D., each series exhibiting various degrees of serial correlation including long memory. In the longest subseries, spanning 622-1284 A.D., the test confirms an inhomogeneity of variance at short time scales and identifies the change point around 720 A.D., which coincides closely with the construction of a new device around 715 A.D. for measuring the Nile River. The test also detects a change in variance for a record of only 36 years.
Abstract: in this paper, we investigate the scaling properties of foreign exchange volatility. Our methodology is based on a wavelet multi-scaling approach which decomposes the variance of a time series and the covariance between two time series on a scale by scale basis through the application of a discrete wavelet transformation. It is shown that foreign exchange rate volatilities follow different scaling laws at different horizons. Particularly, there is a smaller degree of persistence in intra-day volatility as compared to volatility at one day and higher scales. Therefore, a common practice in the risk management industry to convert risk measures calculated at shorter horizons into longer horizons through a global scaling parameter may not be appropriate. This paper also demonstrates that correlation between the foreign exchange volatilities is the lowest at the intra-day scales but exhibits a gradual increase up to a daily scare. The correlation coefficient stabilizes at scales one day and higher. Therefore, the benefit of currency diversification is the greatest at the intra-day scales and diminishes gradually at higher scales (lower frequencies). The wavelet cross-correlation analysis also indicates that the association between two volatilities is stronger at lower frequencies. (C) 2001 Elsevier Science B.V. All rights reserved.
Abstract: It is well documented that strong intraday seasonalities may induce distortions in the estimation of volatility models. These seasonalities are also the dominant source for the underlying misspecifications of the various volatility models. Therefore, an obvious route is to filter out the underlying intraday seasonalities from the data. In this paper, we propose a simple method for intraday seasonality extraction that is free of model selection parameters which may affect other intraday seasonality filtering methods. Our methodology is based on a wavelet multi-scaling approach which decomposes the data into its Iow- and high-frequency components through the application of a non-decimated discrete wavelet transform. It is simple to calculate, does not depend on a particular model selection criterion or model-specific parameter choices. The proposed filtering method is translation invariant, has the ability to decompose an arbitrary length series without boundary adjustments, is associated with a zero-phase filter and is circular. Being circular helps to preserve the entire sample unlike other two-sided filters where data loss occurs from the beginning and the end of the studied sample. (C) 2001 Elsevier Science B.V. All rights reserved.
Abstract: This article proposes a new method for simulating a Gaussian process, whose spectrum diverges at one or multiple frequencies in [0, 1/2] (not necessarily at zero). The method uses a generalization of the discrete wavelet transform, the discrete wavelet packet transform (DWPT), and requires only explicit knowledge of the spectral density function of the process-not its autocovariance sequence. An orthonormal basis is selected such that the spectrum of the wavelet coefficients is as flat as possible across specific frequency intervals, thus producing approximately uncorrelated wavelet coefficients. This method is compared to a popular time-domain technique based on the Levinson-Durbin recursions. Simulations show that the DWPT-based method performs comparably to the time-domain technique for a variety of sample sizes and processes-at significantly reduced computational time. The degree of approximation and reduction in computer time may be adjusted through selection of the orthonormal basis and wavelet filter.
Abstract: Multiscale analysis of univariate time series has appeared in the literature at an ever increasing rate. Here we introduce the multiscale analysis of covariance between two time series using the discrete wavelet transform. The wavelet covariance and wavelet correlation are defined and applied to this problem as an alternative to traditional cross-spectrum analysis. The wavelet covariance is shown to decompose the covariance between two stationary processes on a scale by scale basis. Asymptotic normality is established for estimators of the wavelet; covariance and correlation. Both quantities are generalized into the wavelet cross covariance and cross correlation in order to investigate possible lead/lag relationships. A thorough analysis of interannual variability for the Madden-Julian oscillation is performed using a 35+ year record of daily station pressure series. The time localization of the discrete wavelet transform allows the subseries, which are associated with specific physical time scales, to be partitioned into both seasonal periods (such as summer and winter) and also according to El Nine-Southern Oscillation (ENSO) activity, Differences in variance and correlation between these periods may then be firmly established through statistical hypothesis testing. The daily station pressure series used here show clear evidence of increased variance and correlation in winter across Fourier periods of 16-128 days, During warm episodes of ENSO activity, a reduced variance is observed across Fourier periods of 8-512 days for the station pressure series from Truk Island and little or no correlation between station pressure series for the same periods.
Abstract: Procedures for detecting change points in sequences of correlated observations (e.g., time series) can help elucidate their complicated structure. Current literature on the detection of multiple change points emphasizes the analysis of sequences of independent random variables. We address the problem of an unknown number of variance changes in the presence of long-range dependence (e.g., long memory processes). Our results are also applicable to time series whose spectrum slowly varies across octave bands. An iterated cumulative sum of squares procedure is introduced in order to look at the multiscale stationarity of a time series; that is, the variance structure of the wavelet coefficients on a scale by scale basis. The discrete wavelet transform enables us to analyze a given time series on a series of physical scales. The result is a partitioning of the wavelet coefficients into locally stationary regions. Simulations are performed to validate the ability of this procedure to detect and locate multiple variance changes. A 'time' series of vertical ocean shear measurements is also analyzed, where a variety of nonstationary features are identified.
