Empowering imaging biomarkers of Alzheimer's disease.

In a previous report, we proposed a method for combining multiple markers of atrophy caused by Alzheimer's disease into a single atrophy score that is more powerful than any one feature. We applied the method to expansion rates of the lateral ventricles, achieving the most powerful ventricular atrophy measure to date. Here, we expand our method's application to tensor-based morphometry measures. We also combine the volumetric tensor-based morphometry measures with previously computed ventricular surface measures into a combined atrophy score. We show that our atrophy scores are longitudinally unbiased with the intercept bias estimated at 2 orders of magnitude below the mean atrophy of control subjects at 1 year. Both approaches yield the most powerful biomarker of atrophy not only for ventricular measures but also for all published unbiased imaging measures to date. A 2-year trial using our measures requires only 31 (22, 43) Alzheimer's disease subjects or 56 (44, 64) subjects with mild cognitive impairment to detect 25% slowing in atrophy with 80% power and 95% confidence.

Maximizing power to track Alzheimer's disease and MCI progression by LDA-based weighting of longitudinal ventricular surface features.

We propose a new method to maximize biomarker efficiency for detecting anatomical change over time in serial MRI. Drug trials using neuroimaging become prohibitively costly if vast numbers of subjects must be assessed, so it is vital to develop efficient measures of brain change. A popular measure of efficiency is the minimal sample size (n80) needed to detect 25% change in a biomarker, with 95% confidence and 80% power. For multivariate measures of brain change, we can directly optimize n80 based on a Linear Discriminant Analysis (LDA). Here we use a supervised learning framework to optimize n80, offering two alternative solutions. With a new medial surface modeling method, we track 3D dynamic changes in the lateral ventricles in 2065 ADNI scans. We apply our LDA-based weighting to the results. Our best average n80-in two-fold nested cross-validation-is 104 MCI subjects (95% CI: [94,139]) for a 1-year drug trial, and 75AD subjects [64,102]. This compares favorably with other MRI analysis methods. The standard "statistical ROI" approach applied to the same ventricular surfaces requires 165 MCI or 94AD subjects. At 2 years, the best LDA measure needs only 67 MCI and 52AD subjects, versus 119 MCI and 80AD subjects for the stat-ROI method. Our surface-based measures are unbiased: they give no artifactual additive atrophy over three time points. Our results suggest that statistical weighting may boost efficiency of drug trials that use brain maps.

CUDA optimization strategies for compute- and memory-bound neuroimaging algorithms.

As neuroimaging algorithms and technology continue to grow faster than CPU performance in complexity and image resolution, data-parallel computing methods will be increasingly important. The high performance, data-parallel architecture of modern graphical processing units (GPUs) can reduce computational times by orders of magnitude. However, its massively threaded architecture introduces challenges when GPU resources are exceeded. This paper presents optimization strategies for compute- and memory-bound algorithms for the CUDA architecture. For compute-bound algorithms, the registers are reduced through variable reuse via shared memory and the data throughput is increased through heavier thread workloads and maximizing the thread configuration for a single thread block per multiprocessor. For memory-bound algorithms, fitting the data into the fast but limited GPU resources is achieved through reorganizing the data into self-contained structures and employing a multi-pass approach. Memory latencies are reduced by selecting memory resources whose cache performance are optimized for the algorithm's access patterns. We demonstrate the strategies on two computationally expensive algorithms and achieve optimized GPU implementations that perform up to 6× faster than unoptimized ones. Compared to CPU implementations, we achieve peak GPU speedups of 129× for the 3D unbiased nonlinear image registration technique and 93× for the non-local means surface denoising algorithm.

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.

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.

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.

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.

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.

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.

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.

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

Maps of local tissue compression or expansion are often computed by comparing magnetic resonance imaging (MRI) scans using nonlinear image registration. The resulting changes are commonly analyzed using tensor-based morphometry to make inferences about anatomical differences, often based on the Jacobian map, which estimates local tissue gain or loss. Here, we provide rigorous mathematical analyses of the Jacobian maps, and use themto motivate a new numerical method to construct unbiased nonlinear image registration. First, we argue that logarithmic transformation is crucial for analyzing Jacobian values representing morphometric differences. We then examine the statistical distributions of log-Jacobian maps by defining the Kullback-Leibler (KL) distance on material density functions arising in continuum-mechanical models. With this framework, unbiased image registration can be constructed by quantifying the symmetric KL-distance between the identity map and the resulting deformation. Implementation details, addressing the proposed unbiased registration as well as the minimization of symmetric image matching functionals, are then discussed and shown to be applicable to other registration methods, such as inverse consistent registration. In the results section, we test the proposed framework, as well as present an illustrative application mapping detailed 3-D brain changes in sequential magnetic resonance imaging scans of a patient diagnosed with semantic dementia. Using permutation tests, we show that the symmetrization of image registration statistically reduces skewness in the log-Jacobian map.