Asymmetric and Symmetric Unbiased Image Registration: Statistical Assessment of Performance

A GPU-based symmetric non-rigid image registration method in human lung

Quantitative computed tomography (QCT) of the lungs plays an increasing role in identifying sub-phenotypes of pathologies previously lumped into broad categories such as chronic obstructive pulmonary disease and asthma. Methods for image matching and linking multiple lung volumes have proven useful in linking structure to function and in the identification of regional longitudinal changes. Here, we seek to improve the accuracy of image matching via the use of a symmetric multi-level non-rigid registration employing an inverse consistent (IC) transformation whereby images are registered both in the forward and reverse directions. To develop the symmetric method, two similarity measures, the sum of squared intensity difference (SSD) and the sum of squared tissue volume difference (SSTVD), were used. The method is based on a novel generic mathematical framework to include forward and backward transformations, simultaneously, eliminating the need to compute the inverse transformation. Two implementations were used to assess the proposed method: a two-dimensional (2-D) implementation using synthetic examples with SSD, and a multi-core CPU and graphics processing unit (GPU) implementation with SSTVD for three-dimensional (3-D) human lung datasets (six normal adults studied at total lung capacity (TLC) and functional residual capacity (FRC)). Success was evaluated in terms of the IC transformation consistency serving to link TLC to FRC. 2-D registration on synthetic images, using both symmetric and non-symmetric SSD methods, and comparison of displacement fields showed that the symmetric method gave a symmetrical grid shape and reduced IC errors, with the mean values of IC errors decreased by 37%. Results for both symmetric and non-symmetric transformations of human datasets showed that the symmetric method gave better results for IC errors in all cases, with mean values of IC errors for the symmetric method lower than the non-symmetric methods using both SSD and SSTVD. The GPU version demonstrated an average of 43 times speedup and ~5.2 times speedup over the single-threaded and 12-threaded CPU versions, respectively. Run times with the GPU were as fast as 2 min. The symmetric method improved the inverse consistency, aiding the use of image registration in the QCT-based evaluation of the lung.

Avoiding symmetry-breaking spatial non-uniformity in deformable image registration via a quasi-volume-preserving constraint

The choice of a reference image typically influences the results of deformable image registration, thereby making it asymmetric. This is a consequence of a spatially non-uniform weighting in the cost function integral that leads to general registration inaccuracy. The inhomogeneous integral measure--which is the local volume change in the transformation, thus varying through the course of the registration--causes image regions to contribute differently to the objective function. More importantly, the optimization algorithm is allowed to minimize the cost function by manipulating the volume change, instead of aligning the images. The approaches that restore symmetry to deformable registration successfully achieve inverse-consistency, but do not eliminate the regional bias that is the source of the error. In this work, we address the root of the problem: the non-uniformity of the cost function integral. We introduce a new quasi-volume-preserving constraint that allows for volume change only in areas with well-matching image intensities, and show that such a constraint puts a bound on the error arising from spatial non-uniformity. We demonstrate the advantages of adding the proposed constraint to standard (asymmetric and symmetrized) demons and diffeomorphic demons algorithms through experiments on synthetic images, and real X-ray and 2D/3D brain MRI data. Specifically, the results show that our approach leads to image alignment with more accurate matching of manually defined neuroanatomical structures, better tradeoff between image intensity matching and registration-induced distortion, improved native symmetry, and lower susceptibility to local optima. In summary, the inclusion of this space- and time-varying constraint leads to better image registration along every dimension that we have measured it.

Physical activity, inflammation, and volume of the aging brain

Physical activity influences inflammation, and both affect brain structure and Alzheimer's disease (AD) risk. We hypothesized that older adults with greater reported physical activity intensity and lower serum levels of the inflammatory marker tumor necrosis factor α (TNFα) would have larger regional brain volumes on subsequent magnetic resonance imaging (MRI) scans. In 43 cognitively intact older adults (79.3±4.8 years) and 39 patients with AD (81.9±5.1 years at the time of MRI) participating in the Cardiovascular Health Study, we examined year-1 reported physical activity intensity, year-5 blood serum TNFα measures, and year-9 volumetric brain MRI scans. We examined how prior physical activity intensity and TNFα related to subsequent total and regional brain volumes. Physical activity intensity was measured using the modified Minnesota Leisure Time Physical Activities questionnaire at year 1 of the study, when all subjects included here were cognitively intact. Stability of measures was established for exercise intensity over 9 years and TNFα over 3 years in a subset of subjects who had these measurements at multiple time points. When considered together, more intense physical activity intensity and lower serum TNFα were both associated with greater total brain volume on follow-up MRI scans. TNFα, but not physical activity, was associated with regional volumes of the inferior parietal lobule, a region previously associated with inflammation in AD patients. Physical activity and TNFα may independently influence brain structure in older adults.

Thalamic atrophy in antero-medial and dorsal nuclei correlates with six-month outcome after severe brain injury

The primary and secondary damage to neural tissue inflicted by traumatic brain injury is a leading cause of death and disability. The secondary processes, in particular, are of great clinical interest because of their potential susceptibility to intervention. We address the dynamics of tissue degeneration in cortico-subcortical circuits after severe brain injury by assessing volume change in individual thalamic nuclei over the first six-months post-injury in a sample of 25 moderate to severe traumatic brain injury patients. Using tensor-based morphometry, we observed significant localized thalamic atrophy over the six-month period in antero-dorsal limbic nuclei as well as in medio-dorsal association nuclei. Importantly, the degree of atrophy in these nuclei was predictive, even after controlling for full-brain volume change, of behavioral outcome at six-months post-injury. Furthermore, employing a data-driven decision tree model, we found that physiological measures, namely the extent of atrophy in the anterior thalamic nucleus, were the most predictive variables of whether patients had regained consciousness by six-months, followed by behavioral measures. Overall, these findings suggest that the secondary non-mechanical degenerative processes triggered by severe brain injury are still ongoing after the first week post-trauma and target specifically antero-medial and dorsal thalamic nuclei. This result therefore offers a potential window of intervention, and a specific target region, in agreement with the view that specific cortico-thalamo-cortical circuits are crucial to the maintenance of large-scale network neural activity and thereby the restoration of cognitive function after severe brain injury.

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Performed acute and chronic structural MRI in 25 severe TBI patients

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Tensor brain morphometry (TBM) shows localized thalamic acute-to-chronic atrophy.

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Anterior, medio- and lateral-dorsal nuclei are the most significant.

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Atrophy in these nuclei predicts 6-month outcome scores (GOSe).

Unbiased tensor-based morphometry: improved robustness and sample size estimates for Alzheimer's disease clinical trials

Various neuroimaging measures are being evaluated for tracking Alzheimer's disease (AD) progression in therapeutic trials, including measures of structural brain change based on repeated scanning of patients with magnetic resonance imaging (MRI). Methods to compute brain change must be robust to scan quality. Biases may arise if any scans are thrown out, as this can lead to the true changes being overestimated or underestimated. Here we analyzed the full MRI dataset from the first phase of Alzheimer's Disease Neuroimaging Initiative (ADNI-1) from the first phase of Alzheimer's Disease Neuroimaging Initiative (ADNI-1) and assessed several sources of bias that can arise when tracking brain changes with structural brain imaging methods, as part of a pipeline for tensor-based morphometry (TBM). In all healthy subjects who completed MRI scanning at screening, 6, 12, and 24months, brain atrophy was essentially linear with no detectable bias in longitudinal measures. In power analyses for clinical trials based on these change measures, only 39AD patients and 95 mild cognitive impairment (MCI) subjects were needed for a 24-month trial to detect a 25% reduction in the average rate of change using a two-sided test (α=0.05, power=80%). Further sample size reductions were achieved by stratifying the data into Apolipoprotein E (ApoE) ε4 carriers versus non-carriers. We show how selective data exclusion affects sample size estimates, motivating an objective comparison of different analysis techniques based on statistical power and robustness. TBM is an unbiased, robust, high-throughput imaging surrogate marker for large, multi-site neuroimaging studies and clinical trials of AD and MCI.

The Center for Computational Biology: resources, achievements, and challenges

The Center for Computational Biology (CCB) is a multidisciplinary program where biomedical scientists, engineers, and clinicians work jointly to combine modern mathematical and computational techniques, to perform phenotypic and genotypic studies of biological structure, function, and physiology in health and disease. CCB has developed a computational framework built around the Manifold Atlas, an integrated biomedical computing environment that enables statistical inference on biological manifolds. These manifolds model biological structures, features, shapes, and flows, and support sophisticated morphometric and statistical analyses. The Manifold Atlas includes tools, workflows, and services for multimodal population-based modeling and analysis of biological manifolds. The broad spectrum of biomedical topics explored by CCB investigators include the study of normal and pathological brain development, maturation and aging, discovery of associations between neuroimaging and genetic biomarkers, and the modeling, analysis, and visualization of biological shape, form, and size. CCB supports a wide range of short-term and long-term collaborations with outside investigators, which drive the center's computational developments and focus the validation and dissemination of CCB resources to new areas and scientific domains.

Mapping Alzheimer's disease progression in 1309 MRI scans: power estimates for different inter-scan intervals

Neuroimaging centers and pharmaceutical companies are working together to evaluate treatments that might slow the progression of Alzheimer's disease (AD), a common but devastating late-life neuropathology. Recently, automated brain mapping methods, such as tensor-based morphometry (TBM) of structural MRI, have outperformed cognitive measures in their precision and power to track disease progression, greatly reducing sample size estimates for drug trials. In the largest TBM study to date, we studied how sample size estimates for tracking structural brain changes depend on the time interval between the scans (6-24 months). We analyzed 1309 brain scans from 91 probable AD patients (age at baseline: 75.4+/-7.5 years) and 189 individuals with mild cognitive impairment (MCI; 74.6+/-7.1 years), scanned at baseline, 6, 12, 18, and 24 months. Statistical maps revealed 3D patterns of brain atrophy at each follow-up scan relative to the baseline; numerical summaries were used to quantify temporal lobe atrophy within a statistically-defined region-of-interest. Power analyses revealed superior sample size estimates over traditional clinical measures. Only 80, 46, and 39 AD patients were required for a hypothetical clinical trial, at 6, 12, and 24 months respectively, to detect a 25% reduction in average change using a two-sided test (alpha=0.05, power=80%). Correspondingly, 106, 79, and 67 subjects were needed for an equivalent MCI trial aiming for earlier intervention. A 24-month trial provides most power, except when patient attrition exceeds 15-16%/year, in which case a 12-month trial is optimal. These statistics may facilitate clinical trial design using voxel-based brain mapping methods such as TBM.

Comparing 3 T and 1.5 T MRI for tracking Alzheimer's disease progression with tensor-based morphometry

A key question in designing MRI-based clinical trials is how the main magnetic field strength of the scanner affects the power to detect disease effects. In 110 subjects scanned longitudinally at both 3.0 and 1.5 T, including 24 patients with Alzheimer's Disease (AD) [74.8 +/- 9.2 years, MMSE: 22.6 +/- 2.0 at baseline], 51 individuals with mild cognitive impairment (MCI) [74.1 +/- 8.0 years, MMSE: 26.6 +/- 2.0], and 35 controls [75.9 +/- 4.6 years, MMSE: 29.3 +/- 0.8], we assessed whether higher-field MR imaging offers higher or lower power to detect longitudinal changes in the brain, using tensor-based morphometry (TBM) to reveal the location of progressive atrophy. As expected, at both field strengths, progressive atrophy was widespread in AD and more spatially restricted in MCI. Power analysis revealed that, to detect a 25% slowing of atrophy (with 80% power), 37 AD and 108 MCI subjects would be needed at 1.5 T versus 49 AD and 166 MCI subjects at 3 T; however, the increased power at 1.5 T was not statistically significant (alpha = 0.05) either for TBM, or for SIENA, a related method for computing volume loss rates. Analysis of cumulative distribution functions and false discovery rates showed that, at both field strengths, temporal lobe atrophy rates were correlated with interval decline in Alzheimer's Disease Assessment Scale-cognitive subscale (ADAS-cog), mini-mental status exam (MMSE), and Clinical Dementia Rating sum-of-boxes (CDR-SB) scores. Overall, 1.5 and 3 T scans did not significantly differ in their power to detect neurodegenerative changes over a year. Hum Brain Mapp, 2010. (c) 2009 Wiley-Liss, Inc.

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.