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The use of functional magnetic resonance imaging in investigating pediatric anxiety disorders is studied. Functional magnetic resonance imaging can be utilized in demonstrating parallels between the neural architecture of difference in anxiety of humans and the neural architecture of attention-orienting behavior in nonhuman primates or rodents. Implications for anxiety disorder treatments are discussed.

Diffusion tensors are estimated from magnetic resonance images (MRIs) that are diffusion-weighted, and those images inherently contain noise. Therefore, noise in the diffusion-weighted images produces uncertainty in estimation of the tensors and their derived parameters, which include eigenvalues, eigenvectors, and the trajectories of fiber pathways that are reconstructed from those eigenvalues and eigenvectors. Although repetition and wild bootstrap methods have been widely used to quantify the uncertainty of diffusion tensors and their derived parameters, we currently lack theoretical derivations that would validate the use of these two bootstrap methods for the estimation of statistical parameters of tensors in the presence of noise. The aim of this paper is to examine theoretically and numerically the repetition and wild bootstrap methods for approximating uncertainty in estimation of diffusion tensor parameters under two different schemes for acquiring diffusion weighted images. Whether these bootstrap methods can be used to quantify uncertainty in some diffusion tensor parameters, such as fractional anisotropy (FA), depends critically on the morphology of the diffusion tensor that is being estimated. The wild and repetition bootstrap methods in particular cannot quantify uncertainty in the principal direction (PD) of isotropic (or oblate) tensor. We also examine the use of bootstrap methods in estimating tensors in a voxel containing multiple tensors, demonstrating their limitations when quantifying the uncertainty of tensor parameters in those locations. Simulation studies are also used to understand more thoroughly our theoretical results. Our findings raise serious concerns about the use of bootstrap methods to quantify the uncertainty of fiber pathways when those pathways pass through voxels that contain either isotropic tensors, oblate tensors, or multiple tensors. Index Terms--Acquisition scheme, bootstrap, diffusion tensor, fiber tracks, principal direction.

Computing the morphological similarity of diffusion tensors (DTs) at neighboring voxels within a DT image, or at corresponding locations across different DT images, is a fundamental and ubiquitous operation in the postprocessing of DT images. The morphological similarity of DTs typically has been computed using either the principal directions (PDs) of DTs (i.e., the direction along which water molecules diffuse preferentially) or their tensor elements. Although comparing PDs allows the similarity of one morphological feature of DTs to be visualized directly in eigenspace, this method takes into account only a single eigenvector, and it is therefore sensitive to the presence of noise ill the images that can introduce error intothe estimation of that vector. Although comparing tensor elements, rather than PDs, is comparatively more robust to the effects of noise, the individual elements of a given tensor do not directly reflect the diffusion properties of water molecules. We propose a measure for computing the morphological similarity of DTs that uses both their eigenvalues and eigenvectors, and that also accounts for the noise levels present in DT images. Our measure presupposes that DTs in a homogeneous region within or across DT images are random perturbations of one another in the presence of noise. The similarity values that are computed using our method are smooth (in the sense that small changes in eigenvalues and eigenvectors cause only small changes in similarity), and they are symmetric when differences in eigenvalues and eigenvectors are also symmetric. In addition, our method does not presuppose that the corresponding eigenvectors across two DTs have been identified accurately, an assumption that is problematic in the presence of noise. Because we compute the similarity between DTs using their eigenspace components, our similarity measure relates directly to both the magnitude and the direction of the diffusion of water molecules. The favorable performance characteristics of our measure offer the prospect of substantially improving additional postprocessing

To warp diffusion tensor fields accurately, tensors must be reoriented in the space to which the tensors are warped based on both the local deformation field and the orientation of the underlying fibers in the original image. Existing algorithms for warping tensors typically use forward mapping deformations in an attempt to ensure that the local deformations in the warped image remains true to the orientation of the underlying fibers; forward mapping, however, can also create 'seams' or gaps and consequently artifacts in the warped image by failing to define accurately the voxels in the template space where the magnitude of the deformation is large (e.g., |Jacobian| > 1). Backward mapping, in contrast, defines voxels in the template space by mapping them back to locations in the original imaging space. Backward mapping allows every voxel in the template space to be defined without the creation of seams, including voxels in which the deformation is extensive. Backward mapping, however, cannot reorient tensors in the template space because information about the directional orientation of fiber tracts is contained in the original, unwarped imaging space only, and backward mapping alone cannot transfer that information to the template space. To combine the advantages of forward and backward mapping, we propose a novel method for the spatial normalization of diffusion tensor (DT) fields that uses a bijection (a bidirectional mapping with one-to-one correspondences between image spaces) to warp DT datasets seamlessly from one imaging space to another. Once the bijection has been achieved and tensors have been correctly relocated to the template space, we can appropriately reorient tensors in the template space using a warping method based on Procrustean estimation. Index Terms--Bijection, diffusion tensor image (DTI), DTI warping, procrustean estimation.

It is well known that least absolute deviation (LAD) criterion or [L.sub.1]-norm used for estimation of parameters is characterized by robustness, i.e., the estimated parameters are totally resistant (insensitive) to large changes in the sampled data. This is an extremely useful feature, especially, when the sampled data are known to be contaminated by occasionally occurring outliers or by spiky noise. In our previous works, we have proposed the least absolute deviation neural network (LADNN) to solve unconstrained LAD problems. The theoretical proofs and numerical simulations have shown that the LADNN is Lyapunov-stable and it can globally converge to the exact solution to a given unconstrained LAD problem. We have also demonstrated its excellent application value in time-delay estimation. More generally, a practical LAD application problem may contain some linear constraints, such as a set of equalities and/or inequalities, which is called constrained LAD problem, whereas the unconstrained LAD can be considered as a special form of the constrained LAD. In this paper, we present a new neural network called constrained least absolute deviation neural network (CLADNN) to solve general constrained LAD problems. Theoretical proofs and numerical simulations demonstrate that the proposed CLADNN is Lyapunov stable and globally converges to the exact solution to a given constrained LAD problem, independent of initial values. The numerical simulations have also illustrated that the proposed CLADNN can be used to robustly estimate parameters for nonlinear curve fitting, which is extensively used in signal and image processing. Index Terms--Equality and inequality constraints, least absolute deviation (LAD), [L.sub.1]-norm optimization, neural network (NN), nonlinear curve fitting.

Methods for the analysis of brain morphology, including voxel-based morphology and surface-based morphometries, have been used to detect associations between brain structure and covariates of interest, such as diagnosis, severity of disease, age, IQ, and genotype. The statistical analysis of morphometric measures usually involves two statistical procedures: 1) invoking a statistical model at each voxel (or point) on the surface of the brain or brain subregion, followed by mapping test statistics (e.g., t test) or their associated p values at each of those voxels; 2) correction for the multiple statistical tests conducted across all voxels on the surface of the brain region under investigation. We propose the use of new statistical methods for each of these procedures. We first use a heteroscedastic linear model to test the associations between the morphological measures at each voxel on the surface of the specified subregion (e.g., cortical or subcortical surfaces) and the covariates of interest. Moreover, we develop a robust test procedure that is based on a resampling method, called wild bootstrapping. This procedure assesses the statistical significance of the associations between a measure of given brain structure and the covariates of interest. The value of this robust test procedure lies in its computationally simplicity and in its applicability to a wide range of imaging data, including data from both anatomical and functional magnetic resonance imaging (fMRI). Simulation studies demonstrate that this robust test procedure can accurately control the family-wise error rate. We demonstrate the application of this robust test procedure to the detection of statistically significant differences in the morphology of the hippocampus over time across gender groups in a large sample of healthy subjects. Index Terms--Heteroscedastic linear model, hippocampus, multiple hypothesis test, permutation test, robust test procedure.

Interest in the morphometric analysis of the brain and its subregions has recently intensified because growth or degeneration of the brain in health or illness affects not only the volume but also the shape of cortical and subcortical brain regions, and new image processing techniques permit detection of small and highly localized perturbations in shape or localized volume, with remarkable precision. An appropriate statistical representation of the shape of a brain region is essential, however, for detecting, localizing, and interpreting variability in its surface contour and for identifying differences in volume of the underlying tissue that produce that variability across individuals and groups of individuals. Our statistical representation of the shape of a brain region is defined by a reference region for that region and by a Gaussian random field (GRF) that is defined across the entire surface of the region. We first select a reference region from a set of segmented brain images of healthy individuals. The GRF is then estimated as the signed Euclidean distances between points on the surface of the reference region and the corresponding points on the corresponding region in images of brains that have been coregistered to the reference. Correspondences between points on these surfaces are defined through deformations of each region of a brain into the coordinate space of the reference region using the principles of fluid dynamics. The warped, coregistered region of each subject is then unwarped into its native space, simultaneously bringing into that space the map of corresponding points that was established when the surfaces of the subject and reference regions were tightly coregistered. The proposed statistical description of the shape of surface contours makes no assumptions, other than smoothness, about the shape of the region or its GRF. The description also allows for the detection and localization of statistically significant differences in the shapes of the surfaces across groups of subjects at both a fine and coarse scale. We demonstrate the effectiveness of these statistical methods by applying them to study differences in shape of the amygdala and hippocampus in a large sample of normal subjects and in subjects with attention deficit/hyperactivity disorder (ADHD). Index Terms--Conformal mapping, Gaussian random field, manifold, Riemannian curvature tensor, statistical shape analyses, students' E-statistics.

Corpus callosum (CC) white matter connectivity, as measured by the Fractional Anisotropy (FA) index from diffusion tensor images, is assessed in 20 clinically well-defined boys with Tourette syndrome (TS) and 20 age and gender-matched controls. Results suggest that reductions in FA in CC regions reflect either fewer interhemispheric fibers or reduced axonal myelination and FA values do not correlate significantly with the severity of the symptoms.

BACKGROUND. Previous studies have demonstrated that indomethacin lowers the incidence and decreases the severity of intraventricular hemorrhage, as well as improves the cognitive outcome, in prematurely born male infants. OBJECTIVE. The purpose of this work was to use functional magnetic resonance imaging to test the hypothesis that neonatal indomethacin treatment would differentially affect brain activation across genders in school-aged, prematurely born children during performance of a language task. METHODS. Forty-seven prematurely born children (600-1250-g birth weight) and 24 matched term control subjects were evaluated using a functional magnetic resonance imaging passive language task and neurodevelopmental assessments that included the Wechsler Intelligence Scale for Children-III and the Peabody Picture Vocabulary Test-Revised. Neural activity was assessed during both phonologic and semantic processing in the functional magnetic resonance imaging protocol. RESULTS. Neurodevelopmental assessments demonstrated significant differences in full-scale, verbal, and performance intelligence quotient, as well as Peabody Picture Vocabulary Test scores, between the preterm and term control subjects. Rates of perinatal complications did not differ significantly across preterm treatment groups, but male preterm subjects randomly assigned to saline tended to have lower Peabody Picture Vocabulary Test-Revised scores than did all of the other preterm groups. During phonological processing, a significant treatment-by-gender effect was demonstrated in 3 brain regions: the left inferior parietal lobule, the left inferior frontal gyrus (Broca's area), and the right dorsolateral prefrontal cortex. CONCLUSIONS. These data demonstrate a differential effect of indomethacin administration early in postnatal life on the subsequent development of neural systems that subserve language functioning in these male and female preterm infants. www.pediatrics.org/cgi/doi/10.1542/ peds.2005-2870 doi:10.15421peds.2005-2870 Key Words functional magnetic resonance imaging, premature, indomethacin, neurodevelopmental outcome Abbreviations IVH--intraventricular hemorrhage VLBW--very low birth weight CNS--central nervous system fMRI--functional magnetic resonance imaging PPVT--Peabody Picture Vocabulary Test IQ--intelligence quotient FSIQ--full-scale intelligence quotient VIQ--verbal intelligence quotient PIQ--performance intelligence quotient IPL--inferior parietal lobule IFG--inferior frontal gyrus DLPF--dorsolateral prefrontal cortex BA--Brodmann's area, INDOMETHACIN, A WELL-KNOWN inhibitor of cyclooxygenase, both lowers the incidence and decreases the severity of intraventricular hemorrhage (IVH) in very low birth-weight (VLBW) preterm infants. (1-4) In addition, indomethacin closes [...]

Objective. To compare regional brain volumes measured in term and preterm infants, and to correlate regional volumes with measures of neurodevelopmental outcome. Methods. High-contrast, high-resolution magnetic resonance imaging scans were acquired in 10 preterm and 14 term infants who were scanned near term. The cerebrum was segmented into cortical gray matter, white matter, cerebral ventricles, subcortical gray matter, cerebellum, and brainstem. The cortical gray matter, white matter, and ventricles were further divided into specific anatomic subregions, and the volumes were compared across groups. Measures of cognitive and motor development were acquired between 18 and 20 months of corrected age. Correlations of regional brain volumes with developmental outcome were assessed in the preterm group. Results. Volumes in preterm infants were reduced in parieto-occipital gray matter and increased in the midbody, occipital horn, and temporal horns of the lateral ventricles. Gray matter volumes were also less prominently reduced in the sensorimotor and inferior occipital cortices. Normal lateralization of white matter volumes were altered in the parieto-occipital region in the preterm infants, who had significantly larger left-sided and smaller right-sided structures. White matter volumes in the sensorimotor and midtemporal regions correlated strongly with measures of neurodevelopmental outcome. Conclusions. These findings of reduced volumes in sensorimotor and parieto-occipital regions in preterm infants, and the prospective correlations of regional volumes with cognitive outcome, confirm and extend findings previously reported in a cross-sectional study of 8-year-old prematurely born children. The data suggest that regional brain volumes near term are a promising marker for predicting disturbances of cognitive outcome in preterm infants. Further prospective, longitudinal studies of neonatal brain volumes and developmental indices into later childhood are required to confirm the utility of regional brain volumes as predictors of longer term outcome. Pediatrics 2003;111:939-948; magnetic resonance imaging; premature birth; development; cognition., ABBREVIATIONS. PVL, periventricular leukomalacia; CA, corrected age; MRI, magnetic resonance imaging; A-P, anterior-posterior; CSF, cerebrospinal fluid; PC, posterior commissure; AC, anterior commissure; PMA, postmenstrual age. Previous neuroimaging studies have shown [...]