Two-stage empirical likelihood for longitudinal neuroimaging data

Longitudinal imaging studies are essential to understanding the neural development of neuropsychiatric disorders, substance use disorders, and the normal brain. The main objective of this paper is to develop a two-stage adjusted exponentially tilted empirical likelihood (TETEL) for the spatial analysis of neuroimaging data from longitudinal studies. The TETEL method as a frequentist approach allows us to efficiently analyze longitudinal data without modeling temporal correlation and to classify different time-dependent covariate types. To account for spatial dependence, the TETEL method developed here specifically combines all the data in the closest neighborhood of each voxel (or pixel) on a 3-dimensional (3D) volume (or 2D surface) with appropriate weights to calculate adaptive parameter estimates and adaptive test statistics. Simulation studies are used to examine the finite sample performance of the adjusted exponential tilted likelihood ratio statistic and TETEL. We demonstrate the application of our statistical methods to the detection of the difference in the morphological changes of the hippocampus across time between schizophrenia patients and healthy subjects in a longitudinal schizophrenia study.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS480 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Shape analysis based on depth-ordering

In this paper we propose a new method for shape analysis based on the ordering of shapes using band-depth. We use this band-depth to non-parametrically define a global depth for a shape with respect to a reference population, typically consisting of normal control subjects. This allows us to globally quantify differences with respect to “normality”. Using the depth-ordering of shapes also allows the detection of localized shape differences by using α-central values of shapes. We propose permutation tests to statistically assess global and local shape differences. We further determine the directionality of shape differences (local inflation versus deflation). The method is evaluated on a synthetically generated striatum dataset, and applied to detect shape differences in the hippocampus between subjects with first-episode schizophrenia and normal controls

An Investigation into the Behaviour of the Magnetic Field from 1 Ga to Present Day

The magnetic field of Earth and its behaviour over time is linked to its origin within Earth’s liquid outer core. Complex internal processes that operate within the outer core are not only responsible for the creation of the geomagnetic field, but also the magnetic field’s strength, stability, and position on Earth. The magnetic field acts as a critical barrier of protection, shielding Earth from harmful solar radiation from the sun and confining Earth’s atmosphere beneath the exosphere. As Earth’s core evolves and cools over time, it releases heat at the core-mantle boundary (CMB), the magnetic field reflects this evolution by weakening, strengthening, and reversing in polarity over time. It is important to study and form a better understanding of the behaviour of the magnetic field and its intensity over time, as its ability to weaken may give rise to biological and technological damage to Earth and its inhabitants. Variation in magnetic field behaviour over time is preserved in the geologic record, but data is scarce and poorly constrained, thus, numerical modelling solutions remain an essential aspect of paleo-geomagnetic field analysis. In this study, we analyse model-predicted core-mantle boundary heat flux as a proxy indicator of the dynamic evolution of the magnetic field, from 1 Ga to present for four model cases. We do this in aim of including periods known to exhibit the weakening of the magnetic field (superchrons, hyperactive periods and periods of biological extinction), and also investigate the spherical harmonics and Pearson correlation between these data and the current paleo-geomagnetic reversal rate data of two previous studies (Hounslow et al. 2018), Olson et al. 2013). Results conclude that CMB heat flux correlates weakly with the geomagnetic reversal rates, with equatorial CMB heat flux variability (q* equatorial) correlating the greatest of all quantities investigated. Spherical 3 harmonics analysis reveals a 200 Myr cycle in magnetic field intensity that may correlate with Earth’s 200 Myr deep mantle convection cycle

Effects of Aerial LiDAR Data Density on the Accuracy of Building Reconstruction

Previous work has identified a positive relationship between the density of aerial LiDAR input for building reconstruction and the accuracy of the resulting reconstructed models. We hypothesize a point of diminished returns at which higher data density no longer contributes meaningfully to higher accuracy in the end product. We investigate this relationship by subsampling a high-density dataset from the City of Surrey, BC to different densities and inputting each subsampled dataset to reconstruction using two different reconstruction methods. We then determine the accuracy of reconstruction based on manually created reference data, in terms of both 2D footprint accuracy and 3D model accuracy. We find that there is no quantitative evidence for meaningfully improved output accuracy from densities higher than 4 p/m2 for either method, although aesthetic improvements at higher point cloud densities are noted for one method

Longitudinal changes in subcortical morphology in Huntington Disease and the relationship with clinical, motor and neurocognitive outcomes

Huntington disease (HD) is a devastating inherited neurodegenerative disease which causes progressive motor, psychiatric and cognitive disturbances as well as neurodegeneration. Mapping the spatiotemporal progression of neuroanatomical change in HD is fundamental to developing biomeasures suitable for prognostication and to aid in development and testing of potential treatments. The neostriatum is central to HD and is known to start to degenerate more than a decade before observable motor onset. It is central to a number of frontostriatal re-entrant circuits which regulate motor control and other forms of behaviour. Changes in striatal morphology can consequently be correlated with observable clinical, motor and cognitive outcomes. However, the neostriatum is merely one part of the "hubs and spokes" of neural circuitry and neurodegeneration in HD also occurs in other areas of the brain. The hippocampus has been less fully studied in HD and has implications for neural plasticity, particularly given neurogenesis continues into adulthood in this region. Furthermore, thickness of the corpus callosum may be used as a proxy for cortical changes that are known to occur later in HD. This thesis uses data from the IMAGE-HD study to characterise neuroanatomical changes in HD, with the aim to improve knowledge of HD-associated neurodegenerative pathways and to provide further insight to relate quantitative measures of morphology to function. A number of analytical techniques are used to investigate changes in size and shape of neuroanatomical structures and to correlate these with clinical, motor and neurocognitive outcomes. This thesis demonstrates that shape changes in the neostriatum in HD and pre-symptomatic HD correlate with functional measures subserved by corticostriatal circuits, and identifies significant longitudinal differences in putaminal and caudate shape. Only the putamen has a significant group by time interaction, suggesting that it is a better marker for longitudinal change in pre-symptomatic HD and HD. While HD has its most marked effects on the neostriatum, it also has more subtle effects on other subcortical areas. This thesis shows surface contraction occurring in HD in the hippocampus compared to controls, although without correlations to functional measures or significant longitudinal change. Unlike these "hubs", this thesis finds that the large "spoke" of the corpus callosum is not impacted early in the HD process but becomes affected after symptom onset, highlighting the spread of neurodegeneration in other structures. This is the first time that such robust statistical analysis of longitudinal shape change in HD has been able to be performed and shows the neostriatum, particularly the putamen, as a potentially useful structural basis for the characterisation of an endophenotype of HD. This thesis provides a more comprehensive picture of neuroanatomical change in HD by using a "hubs and spokes" approach to analyse key areas, increasing knowledge about neurodegenerative pathways and functional outcomes

Image and Shape Analysis for Spatiotemporal Data

In analyzing brain development or identifying disease it is important to understand anatomical age-related changes and shape differences. Data for these studies is frequently spatiotemporal and collected from normal and/or abnormal subjects. However, images and shapes over time often have complex structures and are best treated as elements of non-Euclidean spaces. This dissertation tackles problems of uncovering time-varying changes and statistical group differences in image or shape time-series. There are three major contributions: 1) a framework of parametric regression models on manifolds to capture time-varying changes. These include a metamorphic geodesic regression approach for image time-series and standard geodesic regression, time-warped geodesic regression, and cubic spline regression on the Grassmann manifold; 2) a spatiotemporal statistical atlas approach, which augments a commonly used atlas such as the median with measures of data variance via a weighted functional boxplot; 3) hypothesis testing for shape analysis to detect group differences between populations. The proposed method for cross-sectional data uses shape ordering and hence does not require dense shape correspondences or strong distributional assumptions on the data. For longitudinal data, hypothesis testing is performed on shape trajectories which are estimated from individual subjects. Applications of these methods include 1) capturing brain development and degeneration; 2) revealing growth patterns in pediatric upper airways and the scoring of airway abnormalities; 3) detecting group differences in longitudinal corpus callosum shapes of subjects with dementia versus normal controls.Doctor of Philosoph

IEEE TRANSACTIONS ON MEDICAL IMAGING 1 Tensor-based Cortical Surface Morphometry via Weighted Spherical Harmonic Representation

Abstract — We present a new tensor-based morphometric framework that quantifies cortical shape variations using a local area element. The local area element is computed from the Riemannian metric tensors, which are obtained from the smooth functional parametrization of a cortical mesh. For the smooth parametrization, we have developed a novel weighted spherical harmonic (SPHARM) representation, which generalizes the traditional SPHARM as a special case. For a specific choice of weights, the weighted-SPHARM is shown to be the least squares approximation to the solution of an isotropic heat diffusion on a unit sphere. The main aims of this paper are to present the weighted-SPHARM and to show how it can be used in the tensorbased morphometry. As an illustration, the methodology has been applied in the problem of detecting abnormal cortical regions in the group of high functioning autistic subjects. Index Terms — Spherical harmonics, tensor-based morphometry, SPHARM, cortical surfac

Proceedings of the Third International Workshop on Mathematical Foundations of Computational Anatomy - Geometrical and Statistical Methods for Modelling Biological Shape Variability

International audienceComputational anatomy is an emerging discipline at the interface of geometry, statistics and image analysis which aims at modeling and analyzing the biological shape of tissues and organs. The goal is to estimate representative organ anatomies across diseases, populations, species or ages, to model the organ development across time (growth or aging), to establish their variability, and to correlate this variability information with other functional, genetic or structural information. The Mathematical Foundations of Computational Anatomy (MFCA) workshop aims at fostering the interactions between the mathematical community around shapes and the MICCAI community in view of computational anatomy applications. It targets more particularly researchers investigating the combination of statistical and geometrical aspects in the modeling of the variability of biological shapes. The workshop is a forum for the exchange of the theoretical ideas and aims at being a source of inspiration for new methodological developments in computational anatomy. A special emphasis is put on theoretical developments, applications and results being welcomed as illustrations. Following the successful rst edition of this workshop in 20061 and second edition in New-York in 20082, the third edition was held in Toronto on September 22 20113. Contributions were solicited in Riemannian and group theoretical methods, geometric measurements of the anatomy, advanced statistics on deformations and shapes, metrics for computational anatomy, statistics of surfaces, modeling of growth and longitudinal shape changes. 22 submissions were reviewed by three members of the program committee. To guaranty a high level program, 11 papers only were selected for oral presentation in 4 sessions. Two of these sessions regroups classical themes of the workshop: statistics on manifolds and diff eomorphisms for surface or longitudinal registration. One session gathers papers exploring new mathematical structures beyond Riemannian geometry while the last oral session deals with the emerging theme of statistics on graphs and trees. Finally, a poster session of 5 papers addresses more application oriented works on computational anatomy