Learning nonparametric ordinary differential equations from noisy data.

Learning nonparametric systems of Ordinary Differential Equations (ODEs) x˙=f(t,x) from noisy data is an emerging machine learning topic. We use the well-developed theory of Reproducing Kernel Hilbert Spaces (RKHS) to define candidates for f for which the solution of the ODE exists and is unique. Learning f consists of solving a constrained optimization problem in an RKHS. We propose a penalty method that iteratively uses the Representer theorem and Euler approximations to provide a numerical solution. We prove a generalization bound for the L2 distance between x and its estimator. Experiments are provided for the FitzHugh-Nagumo oscillator, the Lorenz system, and for predicting the Amyloid level in the cortex of aging subjects. In all cases, we show competitive results compared with the state-of-the-art.

Longitudinal changes in Alzheimer's-related plasma biomarkers and brain amyloid.

INTRODUCTION: Understanding longitudinal plasma biomarker trajectories relative to brain amyloid changes can help devise Alzheimer's progression assessment strategies. METHODS: We examined the temporal order of changes in plasma amyloid-ß ratio ( A ß 42 / A ß 40 ${{\rm A}\beta }_{42}/{{\rm A}\beta }_{40}$ ), glial fibrillary acidic protein (GFAP), neurofilament light chain (NfL), and phosphorylated tau ratios ( p-tau181 / A ß 42 $\text{p-tau181}/\mathrm{A}{\beta}_{42}$ , p-tau231 / A ß 42 $\text{p-tau231}/\mathrm{A}{\beta}_{42}$ ) relative to 11 C-Pittsburgh compound B (PiB) positron emission tomography (PET) cortical amyloid burden (PiB-/+). Participants (n = 199) were cognitively normal at index visit with a median 6.1-year follow-up. RESULTS: PiB groups exhibited different rates of longitudinal change in A ß 42 / A ß 40 ( ß = 5.41 × 10 - 4 , SE = 1.95 × 10 - 4 , p = 0.0073 ) ${{\rm A}\beta }_{42}/{{\rm A}\beta }_{40}\ ( {\beta \ = \ 5.41 \times {{10}}^{ - 4},{\rm{\ SE\ }} = \ 1.95 \times {{10}}^{ - 4},\ p\ = \ 0.0073} )$ . Change in brain amyloid correlated with change in GFAP (r = 0.5, 95% CI = [0.26, 0.68]). The greatest relative decline in A ß 42 / A ß 40 ${{\rm A}\beta }_{42}/{{\rm A}\beta }_{40}$ (-1%/year) preceded brain amyloid positivity by 41 years (95% CI = [32, 53]). DISCUSSION: Plasma A ß 42 / A ß 40 ${{\rm A}\beta }_{42}/{{\rm A}\beta }_{40}$ may begin declining decades prior to brain amyloid accumulation, whereas p-tau ratios, GFAP, and NfL increase closer in time. HIGHLIGHTS Plasma A ß 42 / A ß 40 ${{\rm A}\beta }_{42}/{{\rm A}\beta }_{40}$ declines over time among PiB- but does not change among PiB+. Phosphorylated-tau to Aß42 ratios increase over time among PiB+ but do not change among PiB-. Rate of change in brain amyloid is correlated with change in GFAP and neurofilament light chain. The greatest decline in A ß 42 / A ß 40 ${{\rm A}\beta }_{42}/{{\rm A}\beta }_{40}$ may precede brain amyloid positivity by decades.

Longitudinal changes in Alzheimer's-related plasma biomarkers and brain amyloid.

INTRODUCTION: Understanding longitudinal plasma biomarker trajectories relative to brain amyloid changes can help devise Alzheimer's progression assessment strategies. METHODS: We examined the temporal order of changes in plasma amyloid-ß ratio (Aß 42 /Aß 40 ), glial fibrillary acidic protein (GFAP), neurofilament light chain (NfL), and phosphorylated tau ratios (p-tau181/Aß 42 , p-tau231/Aß 42 ) relative to 11 C-Pittsburgh compound B (PiB) positron emission tomography (PET) cortical amyloid burden (PiB-/+). Participants (n = 199) were cognitively normal at index visit with a median 6.1-year follow-up. RESULTS: PiB groups exhibited different rates of longitudinal change in Aß 42 /Aß 40 (ß = 5.41 × 10^ -4 , SE = 1.95 × 10 -4 , p = 0.0073). Change in brain amyloid was correlated with change in GFAP (r = 0.5, 95% CI = [0.26, 0.68]). Greatest relative decline in Aß 42 /Aß 40 (-1%/year) preceded brain amyloid positivity onset by 41 years (95% CI = [32, 53]). DISCUSSION: Plasma Aß 42 /Aß 40 may begin declining decades prior to brain amyloid accumulation, whereas p-tau ratios, GFAP, and NfL increase closer in time.

Multi-method investigation of factors influencing amyloid onset and impairment in three cohorts.

Alzheimer's disease biomarkers are becoming increasingly important for characterizing the longitudinal course of disease, predicting the timing of clinical and cognitive symptoms, and for recruitment and treatment monitoring in clinical trials. In this work, we develop and evaluate three methods for modelling the longitudinal course of amyloid accumulation in three cohorts using amyloid PET imaging. We then use these novel approaches to investigate factors that influence the timing of amyloid onset and the timing from amyloid onset to impairment onset in the Alzheimer's disease continuum. Data were acquired from the Alzheimer's Disease Neuroimaging Initiative (ADNI), the Baltimore Longitudinal Study of Aging (BLSA) and the Wisconsin Registry for Alzheimer's Prevention (WRAP). Amyloid PET was used to assess global amyloid burden. Three methods were evaluated for modelling amyloid accumulation using 10-fold cross-validation and holdout validation where applicable. Estimated amyloid onset age was compared across all three modelling methods and cohorts. Cox regression and accelerated failure time models were used to investigate whether sex, apolipoprotein E genotype and e4 carriage were associated with amyloid onset age in all cohorts. Cox regression was used to investigate whether apolipoprotein E (e4 carriage and e3e3, e3e4, e4e4 genotypes), sex or age of amyloid onset were associated with the time from amyloid onset to impairment onset (global clinical dementia rating ≥1) in a subset of 595 ADNI participants that were not impaired before amyloid onset. Model prediction and estimated amyloid onset age were similar across all three amyloid modelling methods. Sex and apolipoprotein E e4 carriage were not associated with PET-measured amyloid accumulation rates. Apolipoprotein E genotype and e4 carriage, but not sex, were associated with amyloid onset age such that e4 carriers became amyloid positive at an earlier age compared to non-carriers, and greater e4 dosage was associated with an earlier amyloid onset age. In the ADNI, e4 carriage, being female and a later amyloid onset age were all associated with a shorter time from amyloid onset to impairment onset. The risk of impairment onset due to age of amyloid onset was non-linear and accelerated for amyloid onset age >65. These findings demonstrate the feasibility of modelling longitudinal amyloid accumulation to enable individualized estimates of amyloid onset age from amyloid PET imaging. These estimates provide a more direct way to investigate the role of amyloid and other factors that influence the timing of clinical impairment in Alzheimer's disease.

Structured layer surface segmentation for retina OCT using fully convolutional regression networks.

Optical coherence tomography (OCT) is a noninvasive imaging modality with micrometer resolution which has been widely used for scanning the retina. Retinal layers are important biomarkers for many diseases. Accurate automated algorithms for segmenting smooth continuous layer surfaces with correct hierarchy (topology) are important for automated retinal thickness and surface shape analysis. State-of-the-art methods typically use a two step process. Firstly, a trained classifier is used to label each pixel into either background and layers or boundaries and non-boundaries. Secondly, the desired smooth surfaces with the correct topology are extracted by graph methods (e.g., graph cut). Data driven methods like deep networks have shown great ability for the pixel classification step, but to date have not been able to extract structured smooth continuous surfaces with topological constraints in the second step. In this paper, we combine these two steps into a unified deep learning framework by directly modeling the distribution of the surface positions. Smooth, continuous, and topologically correct surfaces are obtained in a single feed forward operation. The proposed method was evaluated on two publicly available data sets of healthy controls and subjects with either multiple sclerosis or diabetic macular edema, and is shown to achieve state-of-the art performance with sub-pixel accuracy.

Fully Convolutional Boundary Regression for Retina OCT Segmentation.

A major goal of analyzing retinal optical coherence tomography (OCT) images is retinal layer segmentation. Accurate automated algorithms for segmenting smooth continuous layer surfaces, with correct hierarchy (topology) are desired for monitoring disease progression. State-of-the-art methods use a trained classifier to label each pixel into background, layer, or surface pixels. The final step of extracting the desired smooth surfaces with correct topology are mostly performed by graph methods (e.g. shortest path, graph cut). However, manually building a graph with varying constraints by retinal region and pathology and solving the minimization with specialized algorithms will degrade the flexibility and time efficiency of the whole framework. In this paper, we directly model the distribution of surface positions using a deep network with a fully differentiable soft argmax to obtain smooth, continuous surfaces in a single feed forward operation. A special topology module is used in the deep network both in the training and testing stages to guarantee the surface topology. An extra deep network output branch is also used for predicting lesion and layers in a pixel-wise labeling scheme. The proposed method was evaluated on two publicly available data sets of healthy controls, subjects with multiple sclerosis, and diabetic macular edema; it achieves state-of-the art sub-pixel results.

Deep learning based topology guaranteed surface and MME segmentation of multiple sclerosis subjects from retinal OCT.

Optical coherence tomography (OCT) is a noninvasive imaging modality that can be used to obtain depth images of the retina. Patients with multiple sclerosis (MS) have thinning retinal nerve fiber and ganglion cell layers, and approximately 5% of MS patients will develop microcystic macular edema (MME) within the retina. Segmentation of both the retinal layers and MME can provide important information to help monitor MS progression. Graph-based segmentation with machine learning preprocessing is the leading method for retinal layer segmentation, providing accurate surface delineations with the correct topological ordering. However, graph methods are time-consuming and they do not optimally incorporate joint MME segmentation. This paper presents a deep network that extracts continuous, smooth, and topology-guaranteed surfaces and MMEs. The network learns shape priors automatically during training rather than being hard-coded as in graph methods. In this new approach, retinal surfaces and MMEs are segmented together with two cascaded deep networks in a single feed forward propagation. The proposed framework obtains retinal surfaces (separating the layers) with sub-pixel surface accuracy comparable to the best existing graph methods and MMEs with better accuracy than the state-of-the-art method. The full segmentation operation takes only ten seconds for a 3D volume.

Predicting time to dementia using a quantitative template of disease progression.

INTRODUCTION: Characterization of longitudinal trajectories of biomarkers implicated in sporadic Alzheimer's disease (AD) in decades before clinical diagnosis is important for disease prevention and monitoring. METHODS: We used a multivariate Bayesian model to temporally align 1369 Alzheimer's disease Neuroimaging Initiative participants based on the similarity of their longitudinal biomarker measures and estimated a quantitative template of the temporal evolution of cerebrospinal fluid A ß 1 - 42 , p- ta u 181 p , and t-tau and hippocampal volume, brain glucose metabolism, and cognitive measurements. We computed biomarker trajectories as a function of time to AD dementia and predicted AD dementia onset age in a disjoint sample. RESULTS: Quantitative template showed early changes in verbal memory, cerebrospinal fluid Aß1-42 and p-tau181p, and hippocampal volume. Mean error in predicted AD dementia onset age was < 1.5 years. DISCUSSION: Our method provides a quantitative approach for characterizing the natural history of AD starting at preclinical stages despite the lack of individual-level longitudinal data spanning the entire disease timeline.

The effect of rare variants in TREM2 and PLD3 on longitudinal cognitive function in the Wisconsin Registry for Alzheimer's Prevention.

Recent studies have found an association between functional variants in TREM2 and PLD3 and Alzheimer's disease (AD), but their effect on cognitive function is unknown. We examined the effect of these variants on cognitive function in 1449 participants from the Wisconsin Registry for Alzheimer's Prevention, a longitudinal study of initially asymptomatic adults, aged 36-73 years at baseline, enriched for a parental history of AD. A comprehensive cognitive test battery was performed at up to 5 visits. A factor analysis resulted in 6 cognitive factors that were standardized into z scores (∼N [0, 1]); the mean of these z scores was also calculated. In linear mixed models adjusted for age, gender, practice effects, and self-reported race/ethnicity, PLD3 V232M carriers had significantly lower mean z scores (p = 0.02) and lower z scores for story recall (p = 0.04), visual learning and memory (p = 0.049), and speed and flexibility (p = 0.02) than noncarriers. TREM2 R47H carriers had marginally lower z scores for speed and flexibility (p = 0.06). In conclusion, a functional variant in PLD3 was associated with significantly lower cognitive function in individuals carrying the variant than in noncarriers.

Intensity inhomogeneity correction of SD-OCT data using macular flatspace.

Images of the retina acquired using optical coherence tomography (OCT) often suffer from intensity inhomogeneity problems that degrade both the quality of the images and the performance of automated algorithms utilized to measure structural changes. This intensity variation has many causes, including off-axis acquisition, signal attenuation, multi-frame averaging, and vignetting, making it difficult to correct the data in a fundamental way. This paper presents a method for inhomogeneity correction by acting to reduce the variability of intensities within each layer. In particular, the N3 algorithm, which is popular in neuroimage analysis, is adapted to work for OCT data. N3 works by sharpening the intensity histogram, which reduces the variation of intensities within different classes. To apply it here, the data are first converted to a standardized space called macular flat space (MFS). MFS allows the intensities within each layer to be more easily normalized by removing the natural curvature of the retina. N3 is then run on the MFS data using a modified smoothing model, which improves the efficiency of the original algorithm. We show that our method more accurately corrects gain fields on synthetic OCT data when compared to running N3 on non-flattened data. It also reduces the overall variability of the intensities within each layer, without sacrificing contrast between layers, and improves the performance of registration between OCT images.

Temporal Order of Alzheimer's Disease-Related Cognitive Marker Changes in BLSA and WRAP Longitudinal Studies.

Investigation of the temporal trajectories of currently used neuropsychological tests is critical to identifying earliest changing measures on the path to dementia due to Alzheimer's disease (AD). We used the Progression Score (PS) method to characterize the temporal trajectories of measures of verbal memory, executive function, attention, processing speed, language, and mental status using data spanning normal cognition, mild cognitive impairment, and AD from 1,661 participants with a total of 7,839 visits (age at last visit 77.6 SD 9.2) in the Baltimore Longitudinal Study of Aging (BLSA) and 1510 participants with a total of 3,473 visits (age at last visit 59.5 SD 7.4) in the Wisconsin Registry for Alzheimer's Prevention (WRAP). This method aligns individuals in time based on the similarity of their longitudinal measurements to reveal temporal trajectories. As a validation of our methodology, we explored the associations between the individualized cognitive progression scores (Cog-PS) computed by our method and clinical diagnosis. Digit span tests were the first to show declines in both data sets, and were detected mainly among cognitively normal individuals. These were followed by tests of verbal memory, which were in turn followed by Trail Making Tests, Boston Naming Test, and Mini-Mental State Examination. Differences in Cog-PS across the clinical diagnosis and APOEɛ4 groups were statistically significant, highlighting the potential use of Cog-PS as individualized indicators of disease progression. Identifying cognitive measures that are changing in preclinical AD can lead to the development of novel cognitive tests that are finely tuned to detecting earliest changes.

Structural cerebellar correlates of cognitive and motor dysfunctions in cerebellar degeneration.

See King et al. (doi:10.1093/aww348) for a scientific commentary on this article.Detailed mapping of clinical dysfunctions to the cerebellar lobules in disease populations is necessary to establish the functional significance of lobules implicated in cognitive and motor functions in normal subjects. This study constitutes the first quantitative examination of the lobular correlates of a broad range of cognitive and motor phenomena in cerebellar disease. We analysed cross-sectional data from 72 cases with cerebellar disease and 36 controls without cerebellar disease. Cerebellar lobule volumes were derived from a graph-cut based segmentation algorithm. Sparse partial least squares, a variable selection approach, was used to identify lobules associated with motor function, language, executive function, memory, verbal learning, perceptual organization and visuomotor coordination. Motor dysfunctions were chiefly associated with the anterior lobe and posterior lobule HVI. Confrontation naming, noun fluency, recognition, and perceptual organization did not have cerebellar associations. Verb and phonemic fluency, working memory, cognitive flexibility, immediate and delayed recall, verbal learning, and visuomotor coordination were variably associated with HVI, Crus I, Crus II, HVII B and/or HIX. Immediate and delayed recall also showed associations with the anterior lobe. These findings provide preliminary anatomical evidence for a functional topography of the cerebellum first defined in task-based functional magnetic resonance imaging studies of normal subjects and support the hypotheses that (i) cerebellar efferents target frontal lobe neurons involved in forming action representations and new search strategies; (ii) there is greater involvement of the cerebellum when immediate recall tasks involve more complex verbal stimuli (e.g. longer words versus digits); and (iii) it is involved in spontaneous retrieval of long-term memory. More generally, they provide an anatomical background for studies that seek the mechanisms by which cognitive and motor dysfunctions arise from cerebellar degeneration. Beyond replicating these findings, future research should employ experimental tasks to probe the integrity of specific functions in cerebellar disease, and new imaging methods to quantitatively map atrophy across the cerebellum.

Towards Topological Correct Segmentation of Macular OCT from Cascaded FCNs.

Optical coherence tomography (OCT) is used to produce high resolution depth images of the retina and is now the standard of care for in-vivo ophthalmological assessment. In particular, OCT is used to study the changes in layer thickness across various pathologies. The automated image analysis of these OCT images has primarily been performed with graph based methods. Despite the preeminence of graph based methods, deep learning based approaches have begun to appear within the literature. Unfortunately, they cannot currently guarantee the strict biological tissue order found in human retinas. We propose a cascaded fully convolutional network (FCN) framework to segment eight retina layers and preserve the topological relationships between the layers. The first FCN serves as a segmentation network which takes retina images as input and outputs the segmentation probability maps of the layers. We next perform a topology check on the segmentation and those patches that do not satisfy the topology criterion are passed to a second FCN for topology correction. The FCNs have been trained on Heidelberg Spectralis images and validated on both Heidelberg Spectralis and Zeiss Cirrus images.

INTENSITY INHOMOGENEITY CORRECTION OF MACULAR OCT USING N3 AND RETINAL FLATSPACE.

As optical coherence tomography (OCT) has increasingly become a standard modality for imaging the retina, automated algorithms for processing OCT data have become necessary to do large scale studies looking for changes in specific layers. To provide accurate results, many of these algorithms rely on the consistency of layer intensities within a scan. Unfortunately, OCT data often exhibits inhomogeneity in a given layer's intensities, both within and between images. This problem negatively affects the performance of segmentation algorithms and little prior work has been done to correct this data. In this work, we adapt the N3 framework for intensity inhomogeneity correction, which was originally developed to correct MRI data, to work for macular OCT data. We first transform the data to a flattened macular space to create a template intensity profile for each layer giving us an accurate initial estimate of the gain field. N3 will then produce a smoothly varying field to correct the data. We show that our method is able to both accurately recover synthetically generated gain fields and improves the stability of the layer intensities.

Landmark Based Shape Analysis for Cerebellar Ataxia Classification and Cerebellar Atrophy Pattern Visualization.

Cerebellar dysfunction can lead to a wide range of movement disorders. Studying the cerebellar atrophy pattern associated with different cerebellar disease types can potentially help in diagnosis, prognosis, and treatment planning. In this paper, we present a landmark based shape analysis pipeline to classify healthy control and different ataxia types and to visualize the characteristic cerebellar atrophy patterns associated with different types. A highly informative feature representation of the cerebellar structure is constructed by extracting dense homologous landmarks on the boundary surfaces of cerebellar sub-structures. A diagnosis group classifier based on this representation is built using partial least square dimension reduction and regularized linear discriminant analysis. The characteristic atrophy pattern for an ataxia type is visualized by sampling along the discriminant direction between healthy controls and the ataxia type. Experimental results show that the proposed method can successfully classify healthy controls and different ataxia types. The visualized cerebellar atrophy patterns were consistent with the regional volume decreases observed in previous studies, but the proposed method provides intuitive and detailed understanding about changes of overall size and shape of the cerebellum, as well as that of individual lobules.

Voxel Based Morphometry in Optical Coherence Tomography: Validation & Core Findings.

Optical coherence tomography (OCT) of the human retina is now becoming established as an important modality for the detection and tracking of various ocular diseases. Voxel based morphometry (VBM) is a long standing neuroimaging analysis technique that allows for the exploration of the regional differences in the brain. There has been limited work done in developing registration based methods for OCT, which has hampered the advancement of VBM analyses in OCT based population studies. Following on from our recent development of an OCT registration method, we explore the potential benefits of VBM analysis in cohorts of healthy controls (HCs) and multiple sclerosis (MS) patients. Specifically, we validate the stability of VBM analysis in two pools of HCs showing no significant difference between the two populations. Additionally, we also present a retrospective study of age and sex matched HCs and relapsing remitting MS patients, demonstrating results consistent with the reported literature while providing insight into the retinal changes associated with this MS subtype.

A multivariate nonlinear mixed effects model for longitudinal image analysis: Application to amyloid imaging.

It is important to characterize the temporal trajectories of disease-related biomarkers in order to monitor progression and identify potential points of intervention. These are especially important for neurodegenerative diseases, as therapeutic intervention is most likely to be effective in the preclinical disease stages prior to significant neuronal damage. Neuroimaging allows for the measurement of structural, functional, and metabolic integrity of the brain at the level of voxels, whose volumes are on the order of mm(3). These voxelwise measurements provide a rich collection of disease indicators. Longitudinal neuroimaging studies enable the analysis of changes in these voxelwise measures. However, commonly used longitudinal analysis approaches, such as linear mixed effects models, do not account for the fact that individuals enter a study at various disease stages and progress at different rates, and generally consider each voxelwise measure independently. We propose a multivariate nonlinear mixed effects model for estimating the trajectories of voxelwise neuroimaging biomarkers from longitudinal data that accounts for such differences across individuals. The method involves the prediction of a progression score for each visit based on a collective analysis of voxelwise biomarker data within an expectation-maximization framework that efficiently handles large amounts of measurements and variable number of visits per individual, and accounts for spatial correlations among voxels. This score allows individuals with similar progressions to be aligned and analyzed together, which enables the construction of a trajectory of brain changes as a function of an underlying progression or disease stage. We apply our method to studying cortical ß-amyloid deposition, a hallmark of preclinical Alzheimer's disease, as measured using positron emission tomography. Results on 104 individuals with a total of 300 visits suggest that precuneus is the earliest cortical region to accumulate amyloid, closely followed by the cingulate and frontal cortices, then by the lateral parietal cortex. The extracted progression scores reveal a pattern similar to mean cortical distribution volume ratio (DVR), an index of global brain amyloid levels. The proposed method can be applied to other types of longitudinal imaging data, including metabolism, blood flow, tau, and structural imaging-derived measures, to extract individualized summary scores indicating disease progression and to provide voxelwise trajectories that can be compared between brain regions.

Automated cerebellar lobule segmentation with application to cerebellar structural analysis in cerebellar disease.

The cerebellum plays an important role in both motor control and cognitive function. Cerebellar function is topographically organized and diseases that affect specific parts of the cerebellum are associated with specific patterns of symptoms. Accordingly, delineation and quantification of cerebellar sub-regions from magnetic resonance images are important in the study of cerebellar atrophy and associated functional losses. This paper describes an automated cerebellar lobule segmentation method based on a graph cut segmentation framework. Results from multi-atlas labeling and tissue classification contribute to the region terms in the graph cut energy function and boundary classification contributes to the boundary term in the energy function. A cerebellar parcellation is achieved by minimizing the energy function using the α-expansion technique. The proposed method was evaluated using a leave-one-out cross-validation on 15 subjects including both healthy controls and patients with cerebellar diseases. Based on reported Dice coefficients, the proposed method outperforms two state-of-the-art methods. The proposed method was then applied to 77 subjects to study the region-specific cerebellar structural differences in three spinocerebellar ataxia (SCA) genetic subtypes. Quantitative analysis of the lobule volumes shows distinct patterns of volume changes associated with different SCA subtypes consistent with known patterns of atrophy in these genetic subtypes.

A toolbox to visually explore cerebellar shape changes in cerebellar disease and dysfunction.

The cerebellum plays an important role in motor control and is also involved in cognitive processes. Cerebellar function is specialized by location, although the exact topographic functional relationship is not fully understood. The spinocerebellar ataxias are a group of neurodegenerative diseases that cause regional atrophy in the cerebellum, yielding distinct motor and cognitive problems. The ability to study the region-specific atrophy patterns can provide insight into the problem of relating cerebellar function to location. In an effort to study these structural change patterns, we developed a toolbox in MATLAB to provide researchers a unique way to visually explore the correlation between cerebellar lobule shape changes and function loss, with a rich set of visualization and analysis modules. In this paper, we outline the functions and highlight the utility of the toolbox. The toolbox takes as input landmark shape representations of subjects' cerebellar substructures. A principal component analysis is used for dimension reduction. Following this, a linear discriminant analysis and a regression analysis can be performed to find the discriminant direction associated with a specific disease type, or the regression line of a specific functional measure can be generated. The characteristic structural change pattern of a disease type or of a functional score is visualized by sampling points on the discriminant or regression line. The sampled points are used to reconstruct synthetic cerebellar lobule shapes. We showed a few case studies highlighting the utility of the toolbox and we compare the analysis results with the literature.

A computational method for computing an Alzheimer's disease progression score; experiments and validation with the ADNI data set.

Understanding the time-dependent changes of biomarkers related to Alzheimer's disease (AD) is a key to assessing disease progression and measuring the outcomes of disease-modifying therapies. In this article, we validate an AD progression score model which uses multiple biomarkers to quantify the AD progression of subjects following 3 assumptions: (1) there is a unique disease progression for all subjects; (2) each subject has a different age of onset and rate of progression; and (3) each biomarker is sigmoidal as a function of disease progression. Fitting the parameters of this model is a challenging problem which we approach using an alternating least squares optimization algorithm. To validate this optimization scheme under realistic conditions, we use the Alzheimer's Disease Neuroimaging Initiative cohort. With the help of Monte Carlo simulations, we show that most of the global parameters of the model are tightly estimated, thus enabling an ordering of the biomarkers that fit the model well, ordered as: the Rey auditory verbal learning test with 30 minutes delay, the sum of the 2 lateral hippocampal volumes divided by the intracranial volume, followed (by the clinical dementia rating sum of boxes score and the mini-mental state examination score) in no particular order and at last the AD assessment scale-cognitive subscale.