Statistical properties of Jacobian maps and the realization of unbiased large-deformation nonlinear image registration

Increasing power for voxel-wise genome-wide association studies: the random field theory, least square kernel machines and fast permutation procedures

Imaging traits are thought to have more direct links to genetic variation than diagnostic measures based on cognitive or clinical assessments and provide a powerful substrate to examine the influence of genetics on human brains. Although imaging genetics has attracted growing attention and interest, most brain-wide genome-wide association studies focus on voxel-wise single-locus approaches, without taking advantage of the spatial information in images or combining the effect of multiple genetic variants. In this paper we present a fast implementation of voxel- and cluster-wise inferences based on the random field theory to fully use the spatial information in images. The approach is combined with a multi-locus model based on least square kernel machines to associate the joint effect of several single nucleotide polymorphisms (SNP) with imaging traits. A fast permutation procedure is also proposed which significantly reduces the number of permutations needed relative to the standard empirical method and provides accurate small p-value estimates based on parametric tail approximation. We explored the relation between 448,294 single nucleotide polymorphisms and 18,043 genes in 31,662 voxels of the entire brain across 740 elderly subjects from the Alzheimer's disease neuroimaging initiative (ADNI). Structural MRI scans were analyzed using tensor-based morphometry (TBM) to compute 3D maps of regional brain volume differences compared to an average template image based on healthy elderly subjects. We find method to be more sensitive compared with voxel-wise single-locus approaches. A number of genes were identified as having significant associations with volumetric changes. The most associated gene was GRIN2B, which encodes the N-methyl-d-aspartate (NMDA) glutamate receptor NR2B subunit and affects both the parietal and temporal lobes in human brains. Its role in Alzheimer's disease has been widely acknowledged and studied, suggesting the validity of the approach. The various advantages over existing approaches indicate a great potential offered by this novel framework to detect genetic influences on human brains.

Structural and functional neuroimaging phenotypes in dysbindin mutant mice

Schizophrenia is a highly heritable psychiatric disorder that is associated with a number of structural and functional neurophenotypes. DTNBP1, the gene encoding dysbindin-1, is a promising candidate gene for schizophrenia. Use of a mouse model carrying a large genomic deletion exclusively within the dysbindin gene permits a direct investigation of the gene in isolation. Here, we use manganese-enhanced magnetic resonance imaging (MEMRI) to explore the regional alterations in brain structure and function caused by loss of the gene encoding dysbindin-1. We report novel findings that uniquely inform our understanding of the relationship of dysbindin-1 to known schizophrenia phenotypes. First, in mutant mice, analysis of the rate of manganese uptake into the brain over a 24-hour period, putatively indexing basal cellular activity, revealed differences in dopamine rich brain regions, as well as in CA1 and dentate subregions of the hippocampus formation. Finally, novel tensor-based morphometry techniques were applied to the mouse MRI data, providing evidence for structural volume deficits in cortical regions, subiculum and dentate gyrus, and the striatum of dysbindin mutant mice. The affected cortical regions were primarily localized to the sensory cortices in particular the auditory cortex. This work represents the first application of manganese-enhanced small animal imaging to a mouse model of schizophrenia endophenotypes, and a novel combination of functional and structural measures. It revealed both hypothesized and novel structural and functional neural alterations related to dysbindin-1.

SMALL WORLD NETWORK MEASURES PREDICT WHITE MATTER DEGENERATION IN PATIENTS WITH EARLY-STAGE MILD COGNITIVE IMPAIRMENT

Alzheimer's Disease (AD) has long been considered a cortical degenerative disease, but impaired brain connectivity, due to white matter injury, may exacerbate cognitive problems. Predicting brain changes is critically important for early treatment. In a longitudinal diffusion tensor imaging study, we investigated white matter fiber integrity in 19 patients (mean age: 74.7 +/- 8.4 yrs at baseline) displaying early signs of mild cognitive impairment (eMCI). We first examined whether baseline average fractional anisotropy (FA) measures in the corpus callosum (CC) predicted changes in white matter integrity over the following 6 months. We then examined whether "small world" architecture measures - calculated from baseline connectivity maps - predicted white matter changes over the next 6 months. While average CC FA measures at baseline were not associated with future changes in FA, network measures were a sensitive biomarker for predicting white matter changes during this critical time before AD strikes.

DIFFUSION IMAGING PROTOCOL EFFECTS ON GENETIC ASSOCIATIONS

Large multi-site image-analysis studies have successfully discovered genetic variants that affect brain structure in tens of thousands of subjects scanned worldwide. Candidate genes have also associated with brain integrity, measured using fractional anisotropy in diffusion tensor images (DTI). To evaluate the heritability and robustness of DTI measures as a target for genetic analysis, we compared 417 twins and siblings scanned on the same day on the same high field scanner (4-Tesla) with two protocols: (1) 94-directions; 2mm-thick slices, (2) 27-directions; 5mm-thickness. Using mean FA in white matter ROIs and FA 'skeletons' derived using FSL, we (1) examined differences in voxelwise means, variances, and correlations among the measures; and (2) assessed heritability with structural equation models, using the classical twin design. FA measures from the genu of the corpus callosum were highly heritable, regardless of protocol. Genome-wide analysis of the genu mean FA revealed differences across protocols in the top associations.

Apolipoprotein E genotype is associated with temporal and hippocampal atrophy rates in healthy elderly adults: a tensor-based morphometry study

Apolipoprotein E (ApoE) ε4 genotype is a strong risk factor for developing Alzheimer's disease (AD). Conversely, the presence of the ε2 allele has been shown to mitigate cognitive decline. Tensor-based morphometry (TBM), a novel computational approach for visualizing longitudinal progression of brain atrophy, was used to determine whether cognitively intact elderly participants with the ε4 allele demonstrate greater volume reduction than those with the ε2 allele. Healthy "younger elderly" volunteers, aged 55-75, were recruited from the community and hospital staff. They were evaluated with a baseline and follow-up MRI scan (mean scan interval = 4.72 years, s.d. = 0.55) and completed ApoE genotyping. Twenty-seven participants were included in the study of which 16 had the ε4 allele (all heterozygous ε3ε4 genotype) and 11 had the ε2ε3 genotype. The two groups did not differ significantly on any demographic characteristics and all subjects were cognitively "normal" at both baseline and follow-up time points. TBM was used to create 3D maps of local brain tissue atrophy rates for individual participants; these spatially detailed 3D maps were compared between the two ApoE groups. Regional analyses were performed and the ε4 group demonstrated significantly greater annual atrophy rates in the temporal lobes (p = 0.048) and hippocampus (p = 0.016); greater volume loss was observed in the right hippocampus than the left. TBM appears to be useful in tracking longitudinal progression of brain atrophy in cognitively asymptomatic adults. Possession of the ε4 allele is associated with greater temporal and hippocampal volume reduction well before the onset of cognitive deficits.

Unbiased comparison of sample size estimates from longitudinal structural measures in ADNI

Structural changes in neuroanatomical subregions can be measured using serial magnetic resonance imaging scans, and provide powerful biomarkers for detecting and monitoring Alzheimer's disease. The Alzheimer's Disease Neuroimaging Initiative (ADNI) has made a large database of longitudinal scans available, with one of its primary goals being to explore the utility of structural change measures for assessing treatment effects in clinical trials of putative disease-modifying therapies. Several ADNI-funded research laboratories have calculated such measures from the ADNI database and made their results publicly available. Here, using sample size estimates, we present a comparative analysis of the overall results that come from the application of each laboratory's extensive processing stream to the ADNI database. Obtaining accurate measures of change requires correcting for potential bias due to the measurement methods themselves; and obtaining realistic sample size estimates for treatment response, based on longitudinal imaging measures from natural history studies such as ADNI, requires calibrating measured change in patient cohorts with respect to longitudinal anatomical changes inherent to normal aging. We present results showing that significant longitudinal change is present in healthy control subjects who test negative for amyloid-β pathology. Therefore, sample size estimates as commonly reported from power calculations based on total structural change in patients, rather than change in patients relative to change in healthy controls, are likely to be unrealistically low for treatments targeting amyloid-related pathology. Of all the measures publicly available in ADNI, thinning of the entorhinal cortex quantified with the Quarc methodology provides the most powerful change biomarker.

Clinical validation of a 4D-CT based method for lung ventilation measurement in phantoms and patients

BACKGROUND

Lung cancer patients referred to radiotherapy (RT) often present with regional lung function deficits, and it is therefore of interest to image their lung function prior to treatment. In this study a method was developed that uses a deformable image registration (DIR) between the peak-inhale and peak-exhale phases of a thoracic four-dimensional computed tomography (4D-CT) scan to extract ventilation information. The method calculates the displacement vector fields (DVFs) resulting from the DIR using the Jacobian map approach in order to extract information regarding regional lung volume change.

MATERIAL AND METHODS

The DVFs resulting from DIRs were analysed to compute the Jacobian determinant of vectors in the field, thus obtaining a map of the vector gradients of the entire registered CT image, i.e. voxel-wise local volume change. Geometric and quantitative validation was achieved using images of both phantoms and patients. In the phantom studies, translations and deformations of known size and direction were introduced to validate both the DIR algorithm and the method as a whole. Furthermore, five patients underwent 4D-CT for planning of stereotactic body RT (SBRT). The patients were immobilised in a stereotactic body frame (SBF) and for each patient, two thoracic 4D-CT scans were acquired, one scan with respiration restricted by an abdominal compression plate and the other under free breathing.

RESULTS

In the phantom studies deformation errors were found to be of the order of the expected precision of 3 mm, corresponding to the image slice distance, in lateral and vertical directions. For the longitudinal direction a more pronounced discrepancy was observed, with the algorithm predicting displacement lengths of less than half of the physically introduced deformation. Qualitatively the method performed as expected. In the patient study an inverse consistency test showed deviations of up to 5.8 mm, i.e. almost twice the image slice separation. Jacobian maps of the patient images indicated well-ventilated areas as anatomically expected.

CONCLUSION

The established method provides a means of using a (commercially available) DIR algorithm to obtain a quantitative measure of local lung volume change. With further phantom and patient validation studies, quantitative maps of specific ventilation should be possible to produce and use in a clinical setting.

DRAMMS: Deformable registration via attribute matching and mutual-saliency weighting

A general-purpose deformable registration algorithm referred to as "DRAMMS" is presented in this paper. DRAMMS bridges the gap between the traditional voxel-wise methods and landmark/feature-based methods with primarily two contributions. First, DRAMMS renders each voxel relatively distinctively identifiable by a rich set of attributes, therefore largely reducing matching ambiguities. In particular, a set of multi-scale and multi-orientation Gabor attributes are extracted and the optimal components are selected, so that they form a highly distinctive morphological signature reflecting the anatomical and geometric context around each voxel. Moreover, the way in which the optimal Gabor attributes are constructed is independent of the underlying image modalities or contents, which renders DRAMMS generally applicable to diverse registration tasks. A second contribution of DRAMMS is that it modulates the registration by assigning higher weights to those voxels having higher ability to establish unique (hence reliable) correspondences across images, therefore reducing the negative impact of those regions that are less capable of finding correspondences (such as outlier regions). A continuously-valued weighting function named "mutual-saliency" is developed to reflect the matching uniqueness between a pair of voxels implied by the tentative transformation. As a result, voxels do not contribute equally as in most voxel-wise methods, nor in isolation as in landmark/feature-based methods. Instead, they contribute according to the continuously-valued mutual-saliency map, which dynamically evolves during the registration process. Experiments in simulated images, inter-subject images, single-/multi-modality images, from brain, heart, and prostate have demonstrated the general applicability and the accuracy of DRAMMS.

Initial results on development and application of statistical atlas of femoral cartilage in osteoarthritis to determine sex differences in structure: data from the Osteoarthritis Initiative

PURPOSE

To create an average atlas of knee femoral cartilage morphology, to apply the atlas for quantitative assessment of osteoarthritis (OA), and to study localized sex differences.

MATERIALS AND METHODS

High-resolution 3D magnetic resonance imaging (MRI) data of the knee cartilage collected at 3 T as part of the Osteoarthritis Initiative (OAI) were used. An atlas was created based on images from 30 male Caucasian high-risk subjects with no symptomatic OA at baseline. A female cohort of age- and disease-matched Caucasian subjects was also selected from the OAI database. The Jacobian determinant was calculated from the deformation vector fields that nonlinearly registered each subject to the atlas. Statistical analysis based on the general linear model was used to test for regions of significant differences in the Jacobian values between the two cohorts.

RESULTS

The average Jacobian was larger in women (1.2 ± 0.078) than in men (1.08 ± 0.097), showing that after global scaling to the male template, the female cartilage was thicker in most regions. Regions showing significant structural differences include the medial weight bearing region, the trochlear (femoral) side of the patellofemoral compartment, and the lateral posterior condyle.

CONCLUSION

Sex-based differences in cartilage structure were localized using tensor based morphometry in a cohort of high-risk subjects.

Introducing the Jacobian-volume-histogram of deforming organs: application to parotid shrinkage evaluation

The Jacobian of the deformation field of elastic registration between images taken during radiotherapy is a measure of inter-fraction local deformation. The histogram of the Jacobian values (Jac) within an organ was introduced (JVH-Jacobian-volume-histogram) and first applied in quantifying parotid shrinkage. MVCTs of 32 patients previously treated with helical tomotherapy for head-neck cancers were collected. Parotid deformation was evaluated through elastic registration between MVCTs taken at the first and last fractions. Jac was calculated for each voxel of all parotids, and integral JVHs were calculated for each parotid; the correlation between the JVH and the planning dose-volume histogram (DVH) was investigated. On average, 82% (±17%) of the voxels shrinks (Jac < 1) and 14% (±17%) shows a local compression >50% (Jac < 0.5). The best correlation between the DVH and the JVH was found between V10 and V15, and Jac < 0.4-0.6 (p < 0.01). The best constraint predicting a higher number of largely compressing voxels (Jac0.5<7.5%, median value) was V15 ≥ 75% (OR: 7.6, p = 0.002). Jac and the JVH are promising tools for scoring/modelling toxicity and for evaluating organ/contour variations with potential applications in adaptive radiotherapy.

Nonlinear registration of longitudinal images and measurement of change in regions of interest

We describe here a method, Quarc, for accurately quantifying structural changes in organs, based on serial MRI scans. The procedure can be used to measure deformations globally or in regions of interest (ROIs), including large-scale changes in the whole organ, and subtle changes in small-scale structures. We validate the method with model studies, and provide an illustrative analysis using the brain. We apply the method to the large, publicly available ADNI database of serial brain scans, and calculate Cohen's d effect sizes for several ROIs. Using publicly available derived-data, we directly compare effect sizes from Quarc with those from four existing methods that quantify cerebral structural change. Quarc produced a slightly improved, though not significantly different, whole brain effect size compared with the standard KN-BSI method, but in all other cases it produced significantly larger effect sizes.

Accurate measurement of brain changes in longitudinal MRI scans using tensor-based morphometry

This paper responds to Thompson and Holland (2011), who challenged our tensor-based morphometry (TBM) method for estimating rates of brain changes in serial MRI from 431 subjects scanned every 6 months, for 2 years. Thompson and Holland noted an unexplained jump in our atrophy rate estimates: an offset between 0 and 6 months that may bias clinical trial power calculations. We identified why this jump occurs and propose a solution. By enforcing inverse-consistency in our TBM method, the offset dropped from 1.4% to 0.28%, giving plausible anatomical trajectories. Transitivity error accounted for the minimal remaining offset. Drug trial sample size estimates with the revised TBM-derived metrics are highly competitive with other methods, though higher than previously reported sample size estimates by a factor of 1.6 to 2.4. Importantly, estimates are far below those given in the critique. To demonstrate a 25% slowing of atrophic rates with 80% power, 62 AD and 129 MCI subjects would be required for a 2-year trial, and 91 AD and 192 MCI subjects for a 1-year trial.

Bias in tensor based morphometry Stat-ROI measures may result in unrealistic power estimates

A series of reports have recently appeared using tensor based morphometry statistically-defined regions of interest, Stat-ROIs, to quantify longitudinal atrophy in structural MRIs from the Alzheimer's Disease Neuroimaging Initiative (ADNI). This commentary focuses on one of these reports, Hua et al. (2010), but the issues raised here are relevant to the others as well. Specifically, we point out a temporal pattern of atrophy in subjects with Alzheimer's disease and mild cognitive impairment whereby the majority of atrophy in two years occurs within the first 6 months, resulting in overall elevated estimated rates of change. Using publicly-available ADNI data, this temporal pattern is also found in a group of identically-processed healthy controls, strongly suggesting that methodological bias is corrupting the measures. The resulting bias seriously impacts the validity of conclusions reached using these measures; for example, sample size estimates reported by Hua et al. (2010) may be underestimated by a factor of five to sixteen.

A nonconservative Lagrangian framework for statistical fluid registration-SAFIRA

In this paper, we used a nonconservative Lagrangian mechanics approach to formulate a new statistical algorithm for fluid registration of 3-D brain images. This algorithm is named SAFIRA, acronym for statistically-assisted fluid image registration algorithm. A nonstatistical version of this algorithm was implemented , where the deformation was regularized by penalizing deviations from a zero rate of strain. In , the terms regularizing the deformation included the covariance of the deformation matrices (Σ) and the vector fields (q) . Here, we used a Lagrangian framework to reformulate this algorithm, showing that the regularizing terms essentially allow nonconservative work to occur during the flow. Given 3-D brain images from a group of subjects, vector fields and their corresponding deformation matrices are computed in a first round of registrations using the nonstatistical implementation. Covariance matrices for both the deformation matrices and the vector fields are then obtained and incorporated (separately or jointly) in the nonconservative terms, creating four versions of SAFIRA. We evaluated and compared our algorithms' performance on 92 3-D brain scans from healthy monozygotic and dizygotic twins; 2-D validations are also shown for corpus callosum shapes delineated at midline in the same subjects. After preliminary tests to demonstrate each method, we compared their detection power using tensor-based morphometry (TBM), a technique to analyze local volumetric differences in brain structure. We compared the accuracy of each algorithm variant using various statistical metrics derived from the images and deformation fields. All these tests were also run with a traditional fluid method, which has been quite widely used in TBM studies. The versions incorporating vector-based empirical statistics on brain variation were consistently more accurate than their counterparts, when used for automated volumetric quantification in new brain images. This suggests the advantages of this approach for large-scale neuroimaging studies.

Heritability of White Matter Fiber Tract Shapes: A HARDI Study of 198 Twins

Genetic analysis of diffusion tensor images (DTI) shows great promise in revealing specific genetic variants that affect brain integrity and connectivity. Most genetic studies of DTI analyze voxel-based diffusivity indices in the image space (such as 3D maps of fractional anisotropy) and overlook tract geometry. Here we propose an automated workflow to cluster fibers using a white matter probabilistic atlas and perform genetic analysis on the shape characteristics of fiber tracts. We apply our approach to large study of 4-Tesla high angular resolution diffusion imaging (HARDI) data from 198 healthy, young adult twins (age: 20-30). Illustrative results show heritability for the shapes of several major tracts, as color-coded maps.

Tensor-based morphometry with stationary velocity field diffeomorphic registration: application to ADNI

Tensor-based morphometry (TBM) is an analysis technique where anatomical information is characterized by means of the spatial transformations mapping a customized template with the observed images. Therefore, accurate inter-subject non-rigid registration is an essential prerequisite for both template estimation and image warping. Subsequent statistical analysis on the spatial transformations is performed to highlight voxel-wise differences. Most of previous TBM studies did not explore the influence of the registration parameters, such as the parameters defining the deformation and the regularization models. In this work performance evaluation of TBM using stationary velocity field (SVF) diffeomorphic registration was performed in a subset of subjects from Alzheimer's Disease Neuroimaging Initiative (ADNI) study. A wide range of values of the registration parameters that define the transformation smoothness and the balance between image matching and regularization were explored in the evaluation. The proposed methodology provided brain atrophy maps with very detailed anatomical resolution and with a high significance level compared with results recently published on the same data set using a non-linear elastic registration method.

Differentiating prenatal exposure to methamphetamine and alcohol versus alcohol and not methamphetamine using tensor-based brain morphometry and discriminant analysis

Here we investigate the effects of prenatal exposure to methamphetamine (MA) on local brain volume using magnetic resonance imaging. Because many who use MA during pregnancy also use alcohol, a known teratogen, we examined whether local brain volumes differed among 61 children (ages 5-15 years), 21 with prenatal MA exposure, 18 with concomitant prenatal alcohol exposure (the MAA group), 13 with heavy prenatal alcohol but not MA exposure (ALC group), and 27 unexposed controls. Volume reductions were observed in both exposure groups relative to controls in striatal and thalamic regions bilaterally and in right prefrontal and left occipitoparietal cortices. Striatal volume reductions were more severe in the MAA group than in the ALC group, and, within the MAA group, a negative correlation between full-scale intelligence quotient (FSIQ) scores and caudate volume was observed. Limbic structures, including the anterior and posterior cingulate, the inferior frontal gyrus (IFG), and ventral and lateral temporal lobes bilaterally, were increased in volume in both exposure groups. Furthermore, cingulate and right IFG volume increases were more pronounced in the MAA than ALC group. Discriminant function analyses using local volume measurements and FSIQ were used to predict group membership, yielding factor scores that correctly classified 72% of participants in jackknife analyses. These findings suggest that striatal and limbic structures, known to be sites of neurotoxicity in adult MA abusers, may be more vulnerable to prenatal MA exposure than alcohol exposure and that more severe striatal damage is associated with more severe cognitive deficit.

A commonly carried allele of the obesity-related FTO gene is associated with reduced brain volume in the healthy elderly

A recently identified variant within the fat mass and obesity-associated (FTO) gene is carried by 46% of Western Europeans and is associated with an approximately 1.2 kg higher weight, on average, in adults and an approximately 1 cm greater waist circumference. With >1 billion overweight and 300 million obese persons worldwide, it is crucial to understand the implications of carrying this very common allele for the health of our aging population. FTO is highly expressed in the brain and elevated body mass index (BMI) is associated with brain atrophy, but it is unknown how the obesity-associated risk allele affects human brain structure. We therefore generated 3D maps of regional brain volume differences in 206 healthy elderly subjects scanned with MRI and genotyped as part of the Alzheimer's Disease Neuroimaging Initiative. We found a pattern of systematic brain volume deficits in carriers of the obesity-associated risk allele versus noncarriers. Relative to structure volumes in the mean template, FTO risk allele carriers versus noncarriers had an average brain volume difference of approximately 8% in the frontal lobes and 12% in the occipital lobes-these regions also showed significant volume deficits in subjects with higher BMI. These brain differences were not attributable to differences in cholesterol levels, hypertension, or the volume of white matter hyperintensities; which were not detectably higher in FTO risk allele carriers versus noncarriers. These brain maps reveal that a commonly carried susceptibility allele for obesity is associated with structural brain atrophy, with implications for the health of the elderly.

Measurement of hippocampal atrophy using 4D graph-cut segmentation: application to ADNI

We propose a new method of measuring atrophy of brain structures by simultaneously segmenting longitudinal magnetic resonance (MR) images. In this approach a 4D graph is used to represent the longitudinal data: edges are weighted based on spatial and intensity priors and connect spatially and temporally neighboring voxels represented by vertices in the graph. Solving the min-cut/max-flow problem on this graph yields the segmentation for all timepoints in a single step. By segmenting all timepoints simultaneously, a consistent and atrophy-sensitive segmentation is obtained. The application to hippocampal atrophy measurement in 568 image pairs (Baseline and Month 12 follow-up) as well as 362 image triplets (Baseline, Month 12, and Month 24) from the Alzheimer's Disease Neuroimaging Initiative (ADNI) confirms previous findings for atrophy in Alzheimer's disease (AD) and healthy aging. Highly significant correlations between hippocampal atrophy and clinical variables (Mini Mental State Examination, MMSE and Clinical Dementia Rating, CDR) were found and atrophy rates differ significantly according to subjects' ApoE genotype. Based on one year atrophy rates, a correct classification rate of 82% between AD and control subjects is achieved. Subjects that converted from Mild Cognitive Impairment (MCI) to AD after the period for which atrophy was measured (i.e., after the first 12 months) and subjects for whom conversion is yet to be identified were discriminated with a rate of 64%, a promising result with a view to clinical application. Power analysis shows that 67 and 206 subjects are needed for the AD and MCI groups respectively to detect a 25% change in volume loss with 80% power and 5% significance.

Brain structure changes visualized in early- and late-onset blind subjects

We examined 3D patterns of volume differences in the brain associated with blindness, in subjects grouped according to early and late onset. Using tensor-based morphometry, we mapped volume reductions and gains in 16 early-onset (EB) and 16 late-onset (LB) blind adults (onset <5 and >14 years old, respectively) relative to 16 matched sighted controls. Each subject's structural MRI was fluidly registered to a common template. Anatomical differences between groups were mapped based on statistical analysis of the resulting deformation fields revealing profound deficits in primary and secondary visual cortices for both blind groups. Regions outside the occipital lobe showed significant hypertrophy, suggesting widespread compensatory adaptations. EBs but not LBs showed deficits in the splenium and the isthmus. Gains in the non-occipital white matter were more widespread in the EBs. These differences may reflect regional alterations in late neurodevelopmental processes, such as myelination, that continue into adulthood.

Bias in estimation of hippocampal atrophy using deformation-based morphometry arises from asymmetric global normalization: an illustration in ADNI 3 T MRI data

Measurement of brain change due to neurodegenerative disease and treatment is one of the fundamental tasks of neuroimaging. Deformation-based morphometry (DBM) has been long recognized as an effective and sensitive tool for estimating the change in the volume of brain regions over time. This paper demonstrates that a straightforward application of DBM to estimate the change in the volume of the hippocampus can result in substantial bias, i.e., an overestimation of the rate of change in hippocampal volume. In ADNI data, this bias is manifested as a non-zero intercept of the regression line fitted to the 6 and 12 month rates of hippocampal atrophy. The bias is further confirmed by applying DBM to repeat scans of subjects acquired on the same day. This bias appears to be the result of asymmetry in the interpolation of baseline and followup images during longitudinal image registration. Correcting this asymmetry leads to bias-free atrophy estimation.

Optimizing power to track brain degeneration in Alzheimer's disease and mild cognitive impairment with tensor-based morphometry: an ADNI study of 515 subjects

Tensor-based morphometry (TBM) is a powerful method to map the 3D profile of brain degeneration in Alzheimer's disease (AD) and mild cognitive impairment (MCI). We optimized a TBM-based image analysis method to determine what methodological factors, and which image-derived measures, maximize statistical power to track brain change. 3D maps, tracking rates of structural atrophy over time, were created from 1030 longitudinal brain MRI scans (1-year follow-up) of 104 AD patients (age: 75.7+/-7.2 years; MMSE: 23.3+/-1.8, at baseline), 254 amnestic MCI subjects (75.0+/-7.2 years; 27.0+/-1.8), and 157 healthy elderly subjects (75.9+/-5.1 years; 29.1+/-1.0), as part of the Alzheimer's Disease Neuroimaging Initiative (ADNI). To determine which TBM designs gave greatest statistical power, we compared different linear and nonlinear registration parameters (including different regularization functions), and different numerical summary measures derived from the maps. Detection power was greatly enhanced by summarizing changes in a statistically-defined region-of-interest (ROI) derived from an independent training sample of 22 AD patients. Effect sizes were compared using cumulative distribution function (CDF) plots and false discovery rate methods. In power analyses, the best method required only 48 AD and 88 MCI subjects to give 80% power to detect a 25% reduction in the mean annual change using a two-sided test (at alpha=0.05). This is a drastic sample size reduction relative to using clinical scores as outcome measures (619 AD/6797 MCI for the ADAS-Cog, and 408 AD/796 MCI for the Clinical Dementia Rating sum-of-boxes scores). TBM offers high statistical power to track brain changes in large, multi-site neuroimaging studies and clinical trials of AD.

A deformation-based morphometry study of patients with early-stage Parkinson's disease

BACKGROUND AND PURPOSE

Previous volumetric magnetic resonance imaging (MRI) studies of Parkinson's disease (PD) utilized primarily voxel-based morphometry (VBM), and investigated mostly patients with moderate- to late-stage disease. We now use deformation-based morphometry (DBM), a method purported to be more sensitive than VBM, to test for atrophy in patients with early-stage PD.

METHODS

T1-weighted MRI images from 24 early-stage PD patients and 26 age-matched normal control subjects were compared using DBM. Two separate studies were conducted, where two minimally-biased nonlinear intensity-average were created; one for all subjects and another for just the PD patients. The DBM technique creates an average population-based MRI-average in an iterative hierarchical fashion. The nonlinear transformations estimated to match each subject to the MRI-average were then analysed.

RESULTS

The DBM comparison between patients and controls revealed significant contraction in the left cerebellum, and non-significant trends towards frontal, temporal and cingulate sulcal expansions with frontal and temporal white matter contractions. Within the patient group, the unified PD rating scores were highly correlated with local expansions in or near sulci bordering on frontal and temporal cortex.

CONCLUSION

Our results suggest that DBM could be a sensitive method for detecting morphological changes in early-stage PD.

Comparing registration methods for mapping brain change using tensor-based morphometry

Measures of brain changes can be computed from sequential MRI scans, providing valuable information on disease progression for neuroscientific studies and clinical trials. Tensor-based morphometry (TBM) creates maps of these brain changes, visualizing the 3D profile and rates of tissue growth or atrophy. In this paper, we examine the power of different nonrigid registration models to detect changes in TBM, and their stability when no real changes are present. Specifically, we investigate an asymmetric version of a recently proposed Unbiased registration method, using mutual information as the matching criterion. We compare matching functionals (sum of squared differences and mutual information), as well as large-deformation registration schemes (viscous fluid and inverse-consistent linear elastic registration methods versus Symmetric and Asymmetric Unbiased registration) for detecting changes in serial MRI scans of 10 elderly normal subjects and 10 patients with Alzheimer's Disease scanned at 2-week and 1-year intervals. We also analyzed registration results when matching images corrupted with artificial noise. We demonstrated that the unbiased methods, both symmetric and asymmetric, have higher reproducibility. The unbiased methods were also less likely to detect changes in the absence of any real physiological change. Moreover, they measured biological deformations more accurately by penalizing bias in the corresponding statistical maps.

Mjolnir: extending HAMMER using a diffusion transformation model and histogram equalization for deformable image registration

Image registration is a crucial step in many medical image analysis procedures such as image fusion, surgical planning, segmentation and labeling, and shape comparison in population or longitudinal studies. A new approach to volumetric intersubject deformable image registration is presented. The method, called Mjolnir, is an extension of the highly successful method HAMMER. New image features in order to better localize points of correspondence between the two images are introduced as well as a novel approach to generate a dense displacement field based upon the weighted diffusion of automatically derived feature correspondences. An extensive validation of the algorithm was performed on T1-weighted SPGR MR brain images from the NIREP evaluation database. The results were compared with results generated by HAMMER and are shown to yield significant improvements in cortical alignment as well as reduced computation time.

Active fibers: matching deformable tract templates to diffusion tensor images

Reliable quantitative analysis of white matter connectivity in the brain is an open problem in neuroimaging, with common solutions requiring tools for fiber tracking, tractography segmentation and estimation of intersubject correspondence. This paper proposes a novel, template matching approach to the problem. In the proposed method, a deformable fiber-bundle model is aligned directly with the subject tensor field, skipping the fiber tracking step. Furthermore, the use of a common template eliminates the need for tractography segmentation and defines intersubject shape correspondence. The method is validated using phantom DTI data and applications are presented, including automatic fiber-bundle reconstruction and tract-based morphometry.

Symmetric inverse consistent nonlinear registration driven by mutual information

A nonlinear viscoelastic image registration algorithm based on the demons paradigm and incorporating inverse consistent constraint (ICC) is implemented. An inverse consistent and symmetric cost function using mutual information (MI) as a similarity measure is employed. The cost function also includes regularization of transformation and inverse consistent error (ICE). The uncertainties in balancing various terms in the cost function are avoided by alternatively minimizing the similarity measure, the regularization of the transformation, and the ICE terms. The diffeomorphism of registration for preventing folding and/or tearing in the deformation is achieved by the composition scheme. The quality of image registration is first demonstrated by constructing brain atlas from 20 adult brains (age range 30-60). It is shown that with this registration technique: (1) the Jacobian determinant is positive for all voxels and (2) the average ICE is around 0.004 voxels with a maximum value below 0.1 voxels. Further, the deformation-based segmentation on Internet Brain Segmentation Repository, a publicly available dataset, has yielded high Dice similarity index (DSI) of 94.7% for the cerebellum and 74.7% for the hippocampus, attesting to the quality of our registration method.

Mutual information driven inverse consistent nonlinear registration

A fully symmetric nonlinear viscoelastic image registration method, under the demons paradigm is developed. The symmetric cost function includes mutual information (MI) as a similarity measure, regularization of the transformation, and inverse consistent constraint (ICC). Alternative strategy is used to minimize the divergent terms with different properties in the cost function to avoid the difficulties in balancing between the performance of registration and low Inverse Consistency Error (ICE). The diffeomorphism of the registration is achieved by the composition scheme. Validation studies show that the proposed method provides sub-voxel ICE. The improvement of registration performance is also demonstrated.

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.

Implicit reference-based group-wise image registration and its application to structural and functional MRI

In this study, an implicit reference group-wise (IRG) registration with a small deformation, linear elastic model was used to jointly estimate correspondences between a set of MRI images. The performance of pair-wise and group-wise registration algorithms was evaluated for spatial normalization of structural and functional MRI data. Traditional spatial normalization is accomplished by group-to-reference (G2R) registration in which a group of images are registered pair-wise to a reference image. G2R registration is limited due to bias associated with selecting a reference image. In contrast, implicit reference group-wise (IRG) registration estimates correspondences between a group of images by jointly registering the images to an implicit reference corresponding to the group average. The implicit reference is estimated during IRG registration eliminating the bias associated with selecting a specific reference image. Registration performance was evaluated using segmented T1-weighted magnetic resonance images from the Nonrigid Image Registration Evaluation Project (NIREP), DTI and fMRI images. Implicit reference pair-wise (IRP) registration-a special case of IRG registration for two images-is shown to produce better relative overlap than IRG for pair-wise registration using the same small deformation, linear elastic registration model. However, IRP-G2R registration is shown to have significant transitivity error, i.e., significant inconsistencies between correspondences defined by different pair-wise transformations. In contrast, IRG registration produces consistent correspondence between images in a group at the cost of slightly reduced pair-wise RO accuracy compared to IRP-G2R. IRG spatial normalization of the fractional anisotropy (FA) maps of DTI is shown to have smaller FA variance compared with G2R methods using the same elastic registration model. Analyses of fMRI data sets with sensorimotor and visual tasks show that IRG registration, on average, increases the statistical detectability of brain activation compared to G2R registration.

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.

Three-dimensional brain growth abnormalities in childhood-onset schizophrenia visualized by using tensor-based morphometry

Earlier studies revealed progressive cortical gray matter (GM) loss in childhood-onset schizophrenia (COS) across both lateral and medial surfaces of the developing brain. Here, we use tensor-based morphometry to visualize white matter (WM) growth abnormalities in COS throughout the brain. Using high-dimensional elastic image registration, we compared 3D maps of local WM growth rates in COS patients and healthy children over a 5-year period, based on analyzing longitudinal brain MRIs from 12 COS patients and 12 healthy controls matched for age, gender, and scan interval. COS patients showed up to 2.2% slower growth rates per year than healthy controls in WM (P = 0.02, all P values corrected). The greatest differences were in the right hemisphere (P = 0.006). This asymmetry was attributable to a right slower than left hemisphere growth rate mapped in COS patients (P = 0.037) but not in healthy controls. WM growth rates reached 2.6% per year in healthy controls (P = 0.0002). COS patients showed only a 1.3% per year trend for growth in the left hemisphere (P = 0.066). In COS, WM growth rates were associated with improvement in the Children's Global Assessment Scale (R = 0.64, P = 0.029). Growth rates were reduced throughout the brain in COS, but this process appeared to progress in a front-to-back (frontal-parietal) fashion, and this effect was not attributable to lower IQ. Growth rates were correlated with functional prognosis and were visualized as detailed 3D maps. Finally, these findings also confirm that the progressive GM deficits seen in schizophrenia are not the result of WM overgrowth.

Asymmetric and Symmetric Unbiased Image Registration: Statistical Assessment of Performance

Measures of brain changes can be computed from sequential MRI scans, providing valuable information on disease progression for neuroscientific studies and clinical trials. Tensor-based morphometry (TBM) creates maps of these brain changes, visualizing the 3D profile and rates of tissue growth or atrophy. In this paper, we examine the power of different nonrigid registration models to detect changes in TBM, and their stability when no real changes are present. Specifically, we investigate an asymmetric version of a recently proposed unbiased registration method, using mutual information as the matching criterion. We compare matching functionals (sum of squared differences and mutual information), as well as large deformation registration schemes (viscous fluid registration versus symmetric and asymmetric unbiased registration) for detecting changes in serial MRI scans of 10 elderly normal subjects and 10 patients with Alzheimer's Disease scanned at 2-week and 1-year intervals. We demonstrated that the unbiased methods, both symmetric and asymmetric, have higher reproducibility. The unbiased methods were also less likely to detect changes in the absence of any real physiological change. Moreover, they measured biological deformations more accurately by penalizing bias in the corresponding statistical maps.

Computational anatomical methods as applied to ageing and dementia

The cellular hallmarks of Alzheimer's disease (AD) accumulate in the living brain up to 30 years before the characteristic symptoms of dementia can be identified. Brain changes in AD are difficult to distinguish from those in normal ageing, and this has led to the development of powerful computational methods to extract statistical information on the brain changes that are characteristic of AD, mild cognitive impairment (MCI) and different dementia subtypes. Time-lapse maps can be built to show how the disease spreads in the brain, and where treatment affects the disease trajectory. Here, we review three computational approaches to map brain deficits in AD: cortical thickness maps, tensor-based morphometry and hippocampal/ventricular surface modelling. Anatomical structures, modelled as three-dimensional geometrical surfaces, are mathematically combined across subjects for group or interval comparisons. Mathematical concepts from computational surface modelling, fluid mechanics and multivariate statistics are exploited to distinguish disease from normal variations in brain structure. These methods yield insight into the dynamics of AD and MCI, showing where brain changes correlate with cognitive or behavioural changes such as language dysfunction or apathy. We describe cortical and hippocampal changes that distinguish dementia subtypes (such as Lewy-body dementia, HIV-associated dementia and AD), and we describe brain changes that predict recovery or decline in those at risk. Finally, we indicate which computational methods are powerful enough to track dementia in clinical trials, on the basis of their efficiency and sensitivity to early change, and the detail in the measures they provide.

Automated ventricular mapping with multi-atlas fluid image alignment reveals genetic effects in Alzheimer's disease

We developed and validated a new method to create automated 3D parametric surface models of the lateral ventricles in brain MRI scans, providing an efficient approach to monitor degenerative disease in clinical studies and drug trials. First, we used a set of parameterized surfaces to represent the ventricles in four subjects' manually labeled brain MRI scans (atlases). We fluidly registered each atlas and mesh model to MRIs from 17 Alzheimer's disease (AD) patients and 13 age- and gender-matched healthy elderly control subjects, and 18 asymptomatic ApoE4-carriers and 18 age- and gender-matched non-carriers. We examined genotyped healthy subjects with the goal of detecting subtle effects of a gene that confers heightened risk for Alzheimer's disease. We averaged the meshes extracted for each 3D MR data set, and combined the automated segmentations with a radial mapping approach to localize ventricular shape differences in patients. Validation experiments comparing automated and expert manual segmentations showed that (1) the Hausdorff labeling error rapidly decreased, and (2) the power to detect disease- and gene-related alterations improved, as the number of atlases, N, was increased from 1 to 9. In surface-based statistical maps, we detected more widespread and intense anatomical deficits as we increased the number of atlases. We formulated a statistical stopping criterion to determine the optimal number of atlases to use. Healthy ApoE4-carriers and those with AD showed local ventricular abnormalities. This high-throughput method for morphometric studies further motivates the combination of genetic and neuroimaging strategies in predicting AD progression and treatment response.

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.

3D pattern of brain abnormalities in Fragile X syndrome visualized using tensor-based morphometry

Fragile X syndrome (FraX), a genetic neurodevelopmental disorder, results in impaired cognition with particular deficits in executive function and visuo-spatial skills. Here we report the first detailed 3D maps of the effects of the Fragile X mutation on brain structure, using tensor-based morphometry. TBM visualizes structural brain deficits automatically, without time-consuming specification of regions-of-interest. We compared 36 subjects with FraX (age: 14.66+/-1.58 S.D., 18 females/18 males), and 33 age-matched healthy controls (age: 14.67+/-2.2 S.D., 17 females/16 males), using high-dimensional elastic image registration. All 69 subjects' 3D T1-weighted brain MRIs were spatially deformed to match a high-resolution single-subject average MRI scan in ICBM space, whose geometry was optimized to produce a minimal deformation target. Maps of the local Jacobian determinant (expansion factor) were computed from the deformation fields. Statistical maps showed increased caudate (10% higher; p = 0.001) and lateral ventricle volumes (19% higher; p = 0.003), and trend-level parietal and temporal white matter excesses (10% higher locally; p = 0.04). In affected females, volume abnormalities correlated with reduction in systemically measured levels of the Fragile X mental retardation protein (FMRP; Spearman's r < -0.5 locally). Decreased FMRP correlated with ventricular expansion (p = 0.042; permutation test), and anterior cingulate tissue reductions (p = 0.0026; permutation test) supporting theories that FMRP is required for normal dendritic pruning in fronto-striatal-limbic pathways. No sex differences were found; findings were confirmed using traditional volumetric measures in regions of interest. Deficit patterns were replicated by performing statistics after logarithmic transformation, which may be more appropriate for tensor-valued data. Investigation of how these anomalies emerge over time will accelerate our understanding of FraX and its treatment.