Generalized tensor-based morphometry of HIV/AIDS using multivariate statistics on deformation tensors

A continuous STAPLE for scalar, vector, and tensor images: an application to DTI analysis

The comparison of images of a patient to a reference standard may enable the identification of structural brain changes. These comparisons may involve the use of vector or tensor images (i.e., 3-D images for which each voxel can be represented as an RN vector) such as diffusion tensor images (DTI) or transformations. The recent introduction of the Log-Euclidean framework for diffeomorphisms and tensors has greatly simplified the use of these images by allowing all the computations to be performed on a vector-space. However, many sources can result in a bias in the images, including disease or imaging artifacts. In order to estimate and compensate for these sources of variability, we developed a new algorithm, called continuous STAPLE, that estimates the reference standard underlying a set of vector images. This method, based on an expectation-maximization method similar in principle to the validation method STAPLE, also estimates for each image a set of parameters characterizing their bias and variance with respect to the reference standard. We demonstrate how to use these parameters for the detection of atypical images or outliers in the population under study. We identified significant differences between the tensors of diffusion images of multiple sclerosis patients and those of control subjects in the vicinity of lesions.

Mapping the regional influence of genetics on brain structure variability--a tensor-based morphometry study

Genetic and environmental factors influence brain structure and function profoundly. The search for heritable anatomical features and their influencing genes would be accelerated with detailed 3D maps showing the degree to which brain morphometry is genetically determined. As part of an MRI study that will scan 1150 twins, we applied Tensor-Based Morphometry to compute morphometric differences in 23 pairs of identical twins and 23 pairs of same-sex fraternal twins (mean age: 23.8+/-1.8 SD years). All 92 twins' 3D brain MRI scans were nonlinearly registered to a common space using a Riemannian fluid-based warping approach to compute volumetric differences across subjects. A multi-template method was used to improve volume quantification. Vector fields driving each subject's anatomy onto the common template were analyzed to create maps of local volumetric excesses and deficits relative to the standard template. Using a new structural equation modeling method, we computed the voxelwise proportion of variance in volumes attributable to additive (A) or dominant (D) genetic factors versus shared environmental (C) or unique environmental factors (E). The method was also applied to various anatomical regions of interest (ROIs). As hypothesized, the overall volumes of the brain, basal ganglia, thalamus, and each lobe were under strong genetic control; local white matter volumes were mostly controlled by common environment. After adjusting for individual differences in overall brain scale, genetic influences were still relatively high in the corpus callosum and in early-maturing brain regions such as the occipital lobes, while environmental influences were greater in frontal brain regions that have a more protracted maturational time-course.

Alzheimer's disease neuroimaging initiative: a one-year follow up study using tensor-based morphometry correlating degenerative rates, biomarkers and cognition

Tensor-based morphometry can recover three-dimensional longitudinal brain changes over time by nonlinearly registering baseline to follow-up MRI scans of the same subject. Here, we compared the anatomical distribution of longitudinal brain structural changes, over 12 months, using a subset of the ADNI dataset consisting of 20 patients with Alzheimer's disease (AD), 40 healthy elderly controls, and 40 individuals with mild cognitive impairment (MCI). Each individual longitudinal change map (Jacobian map) was created using an unbiased registration technique, and spatially normalized to a geometrically-centered average image based on healthy controls. Voxelwise statistical analyses revealed regional differences in atrophy rates, and these differences were correlated with clinical measures and biomarkers. Consistent with prior studies, we detected widespread cerebral atrophy in AD, and a more restricted atrophic pattern in MCI. In MCI, temporal lobe atrophy rates were correlated with changes in mini-mental state exam (MMSE) scores, clinical dementia rating (CDR), and logical/verbal learning memory scores. In AD, temporal atrophy rates were correlated with several biomarker indices, including a higher CSF level of p-tau protein, and a greater CSF tau/beta amyloid 1-42 (ABeta42) ratio. Temporal lobe atrophy was significantly faster in MCI subjects who converted to AD than in non-converters. Serial MRI scans can therefore be analyzed with nonlinear image registration to relate ongoing neurodegeneration to a variety of pathological biomarkers, cognitive changes, and conversion from MCI to AD, tracking disease progression in 3-dimensional detail.

Reward circuitry is perturbed in the absence of the serotonin transporter

The serotonin transporter (SERT) modulates the entire serotonergic system in the brain and influences both the dopaminergic and norepinephrinergic systems. These three systems are intimately involved in normal physiological functioning of the brain and implicated in numerous pathological conditions. Here we use high-resolution magnetic resonance imaging (MRI) and spectroscopy to elucidate the effects of disruption of the serotonin transporter in an animal model system: the SERT knock-out mouse. Employing manganese-enhanced MRI, we injected Mn(2+) into the prefrontal cortex and obtained 3D MR images at specific time points in cohorts of SERT and normal mice. Statistical analysis of co-registered datasets demonstrated that active circuitry originating in the prefrontal cortex in the SERT knock-out is dramatically altered, with a bias towards more posterior areas (substantia nigra, ventral tegmental area, and Raphé nuclei) directly involved in the reward circuit. Injection site and tracing were confirmed with traditional track tracers by optical microscopy. In contrast, metabolite levels were essentially normal in the SERT knock-out by in vivo magnetic resonance spectroscopy and little or no anatomical differences between SERT knock-out and normal mice were detected by MRI. These findings point to modulation of the limbic cortical-ventral striatopallidal by disruption of SERT function. Thus, molecular disruptions of SERT that produce behavioral changes also alter the functional anatomy of the reward circuitry in which all the monoamine systems are involved.

Computational anatomy with the SPM software

An overview of computational procedures for examining neuroanatomical variability is presented. The review focuses on approaches that can be applied using the SPM software package, beginning by explaining briefly how statistical parametric mapping is usually applied to functional imaging data. The review then proceeds to discuss volumetry, with an emphasis on voxel-based morphometry, and the pre-processing steps involved using the SPM software. Most volumetric studies involve univariate approaches, with a correction for some global measure, such as total brain volume. In contrast, the overall form of the brain may be more accurately modeled using multivariate approaches. Such models of anatomical variability may prove accurate enough for computer assisted diagnoses.

Deep gray matter atrophy in multiple sclerosis: a tensor based morphometry

Tensor based morphometry (TBM) was applied to determine the atrophy of deep gray matter (DGM) structures in 88 relapsing multiple sclerosis (MS) patients. For group analysis of atrophy, an unbiased atlas was constructed from 20 normal brains. The MS brain images were co-registered with the unbiased atlas using a symmetric inverse consistent nonlinear registration. These studies demonstrate significant atrophy of thalamus, caudate nucleus, and putamen even at a modest clinical disability, as assessed by the expanded disability status score (EDSS). A significant correlation between atrophy and EDSS was observed for different DGM structures: (thalamus: r=-0.51, p=3.85 x 10(-7); caudate nucleus: r=-0.43, p=2.35 x 10(-5); putamen: r=-0.36, p=6.12 x 10(-6)). Atrophy of these structures also correlated with 1) T2 hyperintense lesion volumes (thalamus: r=-0.56, p=9.96 x 10(-9); caudate nucleus: r=-0.31, p=3.10 x 10(-3); putamen: r=-0.50, p=6.06 x 10(-7)), 2) T1 hypointense lesion volumes (thalamus: r=-0.61, p=2.29 x 10(-10); caudate nucleus: r=-0.35, p=9.51 x 10(-4); putamen: r=-0.43, p=3.51 x 10(-5)), and 3) normalized CSF volume (thalamus: r=-0.66, p=3.55 x 10(-12); caudate nucleus: r=-0.52, p=2.31 x 10(-7), and putamen: r=-0.66, r=2.13 x 10(-12)). More severe atrophy was observed mainly in thalamus at higher EDSS. These studies appear to suggest a link between the white matter damage and DGM atrophy in MS.

Oriented morphometry of folds on surfaces

The exterior surface of the brain is characterized by a juxtaposition of crests and troughs that together form a folding pattern. The majority of the deformations that occur in the normal course of adult human development result in folds changing their length or width. Current statistical shape analysis methods cannot easily discriminate between these two cases. Using discrete exterior calculus and Tikhonov regularization, we develop a method to estimate a dense orientation fiel in the tangent space of a surface described by a triangulated mesh, in the direction of its folds. We then use this orientation field to distinguish between shape differences in the direction parallel to folds and those in the direction across them. We test the method quantitatively on synthetic data and qualitatively on a database consisting of segmented cortical surfaces of 92 healthy subjects and 97 subjects with Alzheimer's disease. The method estimates the correct fold directions and also indicates that the healthy and diseased subjects are distinguished by shape differences that are in the direction perpendicular to the underlying hippocampi, a finding which is consistent with the neuroscientific literature. These results demonstrate the importance of direction specific computational methods for shape analysis.

A tensor-based morphometry study of genetic influences on brain structure using a new fluid registration method

We incorporated a new Riemannian fluid registration algorithm into a general MRI analysis method called tensor-based morphometry to map the heritability of brain morphology in MR images from 23 monozygotic and 23 dizygotic twin pairs. All 92 3D scans were fluidly registered to a common template. Voxelwise Jacobian determinants were computed from the deformation fields to assess local volumetric differences across subjects. Heritability maps were computed from the intraclass correlations and their significance was assessed using voxelwise permutation tests. Lobar volume heritability was also studied using the ACE genetic model. The performance of this Riemannian algorithm was compared to a more standard fluid registration algorithm: 3D maps from both registration techniques displayed similar heritability patterns throughout the brain. Power improvements were quantified by comparing the cumulative distribution functions of the p-values generated from both competing methods. The Riemannian algorithm outperformed the standard fluid registration.

Mapping cerebellar degeneration in HIV/AIDS

Progressive brain atrophy in HIV/AIDS is associated with impaired psychomotor performance, perhaps partly reflecting cerebellar degeneration; yet little is known about how HIV/AIDS affects the cerebellum. We visualized the three-dimensional profile of atrophy in 19 HIV-positive patients (age: 42.9+/-8.3 years) versus 15 healthy controls (age: 38.5+/-12.0 years). We localized consistent patterns of subregional atrophy with an image analysis method that automatically deforms each patient's scan, in three dimensions, to match a reference image. Atrophy was greatest in the posterior cerebellar vermis (14.9% deficit) and correlated with depression severity (P=0.009, corrected), but not with dementia, alcohol/substance abuse, CD4+T-cell counts, or viral load. Profound cerebellar deficits in HIV/AIDS (P=0.007, corrected) were associated with depression, suggesting a surrogate disease marker for antiretroviral trials.

Diffeomorphic demons: efficient non-parametric image registration

We propose an efficient non-parametric diffeomorphic image registration algorithm based on Thirion's demons algorithm. In the first part of this paper, we show that Thirion's demons algorithm can be seen as an optimization procedure on the entire space of displacement fields. We provide strong theoretical roots to the different variants of Thirion's demons algorithm. This analysis predicts a theoretical advantage for the symmetric forces variant of the demons algorithm. We show on controlled experiments that this advantage is confirmed in practice and yields a faster convergence. In the second part of this paper, we adapt the optimization procedure underlying the demons algorithm to a space of diffeomorphic transformations. In contrast to many diffeomorphic registration algorithms, our solution is computationally efficient since in practice it only replaces an addition of displacement fields by a few compositions. Our experiments show that in addition to being diffeomorphic, our algorithm provides results that are similar to the ones from the demons algorithm but with transformations that are much smoother and closer to the gold standard, available in controlled experiments, in terms of Jacobians.

Adjusted exponentially tilted likelihood with applications to brain morphology

In this article, we develop a nonparametric method, called adjusted exponentially tilted (ET) likelihood, and apply it to the analysis of morphometric measures. The adjusted exponential tilting estimator is shown to have the same first-order asymptotic properties as that of the original ET likelihood. The adjusted ET likelihood ratio statistic is applied to test linear hypotheses of unknown parameters, such as the associations of brain measures (e.g., cortical and subcortical surfaces) with covariates of interest, such as age, gender, and gene. Simulation studies show that the adjusted exponential tilted likelihood ratio statistic performs as well as the t-test when the imaging data are symmetrically distributed, while it is superior when the imaging data have skewed distribution. We demonstrate the application of our new statistical methods to the detection of statistically significant differences in the morphology of the hippocampus between two schizophrenia groups and healthy subjects.

Tensor-based morphometry as a neuroimaging biomarker for Alzheimer's disease: an MRI study of 676 AD, MCI, and normal subjects

In one of the largest brain MRI studies to date, we used tensor-based morphometry (TBM) to create 3D maps of structural atrophy in 676 subjects with Alzheimer's disease (AD), mild cognitive impairment (MCI), and healthy elderly controls, scanned as part of the Alzheimer's Disease Neuroimaging Initiative (ADNI). Using inverse-consistent 3D non-linear elastic image registration, we warped 676 individual brain MRI volumes to a population mean geometric template. Jacobian determinant maps were created, revealing the 3D profile of local volumetric expansion and compression. We compared the anatomical distribution of atrophy in 165 AD patients (age: 75.6+/-7.6 years), 330 MCI subjects (74.8+/-7.5), and 181 controls (75.9+/-5.1). Brain atrophy in selected regions-of-interest was correlated with clinical measurements--the sum-of-boxes clinical dementia rating (CDR-SB), mini-mental state examination (MMSE), and the logical memory test scores - at voxel level followed by correction for multiple comparisons. Baseline temporal lobe atrophy correlated with current cognitive performance, future cognitive decline, and conversion from MCI to AD over the following year; it predicted future decline even in healthy subjects. Over half of the AD and MCI subjects carried the ApoE4 (apolipoprotein E4) gene, which increases risk for AD; they showed greater hippocampal and temporal lobe deficits than non-carriers. ApoE2 gene carriers--1/6 of the normal group--showed reduced ventricular expansion, suggesting a protective effect. As an automated image analysis technique, TBM reveals 3D correlations between neuroimaging markers, genes, and future clinical changes, and is highly efficient for large-scale MRI studies.

A NEW REGISTRATION METHOD BASED ON LOG-EUCLIDEAN TENSOR METRICS AND ITS APPLICATION TO GENETIC STUDIES

In structural brain MRI, group differences or changes in brain structures can be detected using Tensor-Based Morphometry (TBM). This method consists of two steps: (1) a non-linear registration step, that aligns all of the images to a common template, and (2) a subsequent statistical analysis. The numerous registration methods that have recently been developed differ in their detection sensitivity when used for TBM, and detection power is paramount in epidemological studies or drug trials. We therefore developed a new fluid registration method that computes the mappings and performs statistics on them in a consistent way, providing a bridge between TBM registration and statistics. We used the Log-Euclidean framework to define a new regularizer that is a fluid extension of the Riemannian elasticity, which assures diffeomorphic transformations. This regularizer constrains the symmetrized Jacobian matrix, also called the deformation (or strain) tensor. We applied our method to an MRI dataset from 40 fraternal and identical twins, to revealed voxelwise measures of average volumetric differences in brain structure for subjects with different degrees of genetic resemblance.

BEST INDIVIDUAL TEMPLATE SELECTION FROM DEFORMATION TENSOR MINIMIZATION

We study the influence of the choice of template in tensor-based morphometry. Using 3D brain MR images from 10 monozygotic twin pairs, we defined a tensor-based distance in the log-Euclidean framework [1] between each image pair in the study. Relative to this metric, twin pairs were found to be closer to each other on average than random pairings, consistent with evidence that brain structure is under strong genetic control. We also computed the intraclass correlation and associated permutation p-value at each voxel for the determinant of the Jacobian matrix of the transformation. The cumulative distribution function (cdf) of the p-values was found at each voxel for each of the templates and compared to the null distribution. Surprisingly, there was very little difference between CDFs of statistics computed from analyses using different templates. As the brain with least log-Euclidean deformation cost, the mean template defined here avoids the blurring caused by creating a synthetic image from a population, and when selected from a large population, avoids bias by being geometrically centered, in a metric that is sensitive enough to anatomical similarity that it can even detect genetic affinity among anatomies.

3D characterization of brain atrophy in Alzheimer's disease and mild cognitive impairment using tensor-based morphometry

Tensor-based morphometry (TBM) creates three-dimensional maps of disease-related differences in brain structure, based on nonlinearly registering brain MRI scans to a common image template. Using two different TBM designs (averaging individual differences versus aligning group average templates), we compared the anatomical distribution of brain atrophy in 40 patients with Alzheimer's disease (AD), 40 healthy elderly controls, and 40 individuals with amnestic mild cognitive impairment (aMCI), a condition conferring increased risk for AD. We created an unbiased geometrical average image template for each of the three groups, which were matched for sex and age (mean age: 76.1 years+/-7.7 SD). We warped each individual brain image (N=120) to the control group average template to create Jacobian maps, which show the local expansion or compression factor at each point in the image, reflecting individual volumetric differences. Statistical maps of group differences revealed widespread medial temporal and limbic atrophy in AD, with a lesser, more restricted distribution in MCI. Atrophy and CSF space expansion both correlated strongly with Mini-Mental State Exam (MMSE) scores and Clinical Dementia Rating (CDR). Using cumulative p-value plots, we investigated how detection sensitivity was influenced by the sample size, the choice of search region (whole brain, temporal lobe, hippocampus), the initial linear registration method (9- versus 12-parameter), and the type of TBM design. In the future, TBM may help to (1) identify factors that resist or accelerate the disease process, and (2) measure disease burden in treatment trials.

Brain mapping as a tool to study neurodegeneration

Alzheimer's disease (AD) is the most common neurodegenerative disorder for those 65 years or older; it currently affects 4.5 million in the United States and is predicted to rise to 13.2 million by the year 2050. Neuroimaging and brain mapping techniques offer extraordinary power to understand AD, providing spatially detailed information on the extent and trajectory of the disease as it spreads in the living brain. Computational anatomy techniques, applied to large databases of brain MRI scans, reveal the dynamic sequence of cortical and hippocampal changes with disease progression and how these relate to cognitive decline and future clinical outcomes. People who are mildly cognitively impaired, in particular, are at a fivefold increased risk of imminent conversion to dementia, and they show specific structural brain changes that are predictive of imminent disease onset. We review the principles and key findings of several new methods for assessing brain degeneration, including voxel-based morphometry, tensor-based morphometry, cortical thickness mapping, hippocampal atrophy mapping, and automated methods for mapping ventricular anatomy. Applications to AD and other dementias are discussed, with a brief review of related findings in other neurological and neuropsychiatric illnesses, including epilepsy, HIV/AIDS, schizophrenia, and disorders of brain development.