Spatiotemporal modeling of distribution-valued data applied to DTI tract evolution in infant neurodevelopment

pre-printThis paper proposes a novel method that extends spatiotemporal growth modeling to distribution-valued data. The method relaxes assumptions on the underlying noise models by considering the data to be represented by the complete probability distributions rather than a representative, single-valued summary statistics like the mean. When summarizing by the latter method, information on the underlying variability of data is lost early in the process and is not available at later stages of statistical analysis. The concept of 'distance' between distributions and an 'average' of distributions is employed. The framework quantifies growth trajectories for individuals and populations in terms of the complete data variability estimated along time and space. Concept is demonstrated in the context of our driving application which is modeling of age-related changes along white matter tracts in early neurodevelopment. Results are shown for a single subject with Krabbe's disease in comparison with a normative trend estimated from 15 healthy controls

Parametric regression scheme for distributions: analysis of DTI fiber tract diffusion changes in early Brain Development

pre-printTemporal modeling frameworks often operate on scalar variables by summarizing data at initial stages as statistical summaries of the underlying distributions. For instance, DTI analysis often employs summary statistics, like mean, for regions of interest and properties along fiber tracts for population studies and hypothesis testing. This reduction via discarding of variability information may introduce significant errors which propagate through the procedures. We propose a novel framework which uses distribution-valued variables to retain and utilize the local variability information. Classic linear regression is adapted to employ these variables for model estimation. The increased stability and reliability of our proposed method when compared with regression using single-valued statistical summaries, is demonstrated in a validation experiment with synthetic data. Our driving application is the modeling of age-related changes along DTI white matter tracts. Results are shown for the spatiotemporal population trajectory of genu tract estimated from 45 healthy infants and compared with a Krabbe's patient

Doctor of Philosophy

dissertationMagnetic Resonance (MR) is a relatively risk-free and flexible imaging modality that is widely used for studying the brain. Biophysical and chemical properties of brain tissue are captured by intensity measurements in T1W (T1-Weighted) and T2W (T2-Weighted) MR scans. Rapid maturational processes taking place in the infant brain manifest as changes in co{\tiny }ntrast between white matter and gray matter tissue classes in these scans. However, studies based on MR image appearance face severe limitations due to the uncalibrated nature of MR intensity and its variability with respect to changing conditions of scan. In this work, we develop a method for studying the intensity variations between brain white matter and gray matter that are observed during infant brain development. This method is referred to by the acronym WIVID (White-gray Intensity Variation in Infant Development). WIVID is computed by measuring the Hellinger Distance of separation between intensity distributions of WM (White Matter) and GM (Gray Matter) tissue classes. The WIVID measure is shown to be relatively stable to interscan variations compared with raw signal intensity and does not require intensity normalization. In addition to quantification of tissue appearance changes using the WIVID measure, we test and implement a statistical framework for modeling temporal changes in this measure. WIVID contrast values are extracted from MR scans belonging to large-scale, longitudinal, infant brain imaging studies and modeled using the NLME (Nonlinear Mixed Effects) method. This framework generates a normative model of WIVID contrast changes with time, which captures brain appearance changes during neurodevelopment. Parameters from the estimated trajectories of WIVID contrast change are analyzed across brain lobes and image modalities. Parameters associated with the normative model of WIVID contrast change reflect established patterns of region-specific and modality-specific maturational sequences. We also detect differences in WIVID contrast change trajectories between distinct population groups. These groups are categorized based on sex and risk/diagnosis for ASD (Autism Spectrum Disorder). As a result of this work, the usage of the proposed WIVID contrast measure as a novel neuroimaging biomarker for characterizing tissue appearance is validated, and the clinical potential of the developed framework is demonstrated

Doctor of Philosophy

dissertationStatistical analysis of time dependent imaging data is crucial for understanding normal anatomical development as well as disease progression. The most promising studies are of longitudinal design, where repeated observations are obtained from the same subjects. Analysis in this case is challenging due to the difficulty in modeling longitudinal changes, such as growth, and comparing changes across different populations. In any case, the study of anatomical change over time has the potential to further our understanding of many dynamic processes. What is needed are accurate computational models to capture, describe, and quantify anatomical change over time. Anatomical shape is encoded in a variety of representations, such as medical imaging data and derived geometric information extracted as points, curves, and/or surfaces. By considering various shape representations embedded into the same ambient space as a shape complex, either in 2D or 3D, we obtain a more comprehensive description of the anatomy than provided by an single isolated shape. In this dissertation, we develop spatiotemporal models of anatomical change designed to leverage multiple shape representations simultaneously. Rather than study directly the geometric changes to a shape itself, we instead consider how the ambient space deforms, which allows all embedded shapes to be included simultaneously in model estimation. Around this idea, we develop two complementary spatiotemporal models: a flexible nonparametric model designed to capture complex anatomical trajectories, and a generative model designed as a compact statistical representation of anatomical change. We present several ways spatiotemporal models can support the statistical analysis of scalar measurements, such as volume, extracted from shape. Finally, we cover the statistical analysis of higher dimensional shape features to take better advantage of the rich morphometric information provided by shape, as well as the trajectory of change captured by spatiotemporal models

Statistical Analysis of Symmetric Positive-definite Matrices

This dissertation is motivated by addressing the statistical analysis of symmetric positive definite (SPD) matrix valued data, which arise in many applications. Due to the nonlinear structure of such data, it is challenging to apply well-established statistical methods to them. Our goal is to develop statistical models and perform statistical inferences on the Riemannian manifold of the space of SPD matrices. This dissertation has three major parts. In the first part, we develop a local polynomial regression model for the analysis of data with SPD matrix responses on the Riemannian manifold. The independent variable of this model is from Euclidean space. We examine two commonly used metrics including the affine invariant metric and the Log-Euclidean metric on the space of SPD matrices. Under each metric, we develop an associated cross-validation bandwidth selection method, and derive the asymptotic bias, variance, and normality of the intrinsic local constant and local linear estimators and compare their asymptotic mean square errors. Simulation studies are further used to compare the estimators under the two metrics and examine their finite sample performance. In the second part, we develop a functional data analysis framework to model diffusion tensors along fiber bundles as functional responses with a set of covariates of interest, such as age, diagnostic status and gender, in real applications. We propose a statistical model with varying coefficient functions to characterize the dynamic association between functional SPD matrix-valued responses and covariates. We calculate a weighted least squares estimation of the varying coefficient functions under the Log-Euclidean metric in the space of SPD matrices. We also develop a global test statistic to test specific hypotheses about these coefficient functions and construct their simultaneous confidence bands. Simulated data are further used to examine the finite sample performance of the estimated varying coefficient functions. The third part is to develop a varying coefficient model framework under the affine invariant metric. This framework is very similar to that in the second part. However, this metric is more complex than the Log-Euclidean metric, which makes the subsequent estimation of the varying coefficient functions and the theoretical derivations very challenging. Since there is no explicit form formula for the estimators, we developed an optimization method for calculating it. We also derive the asymptotic properties for the estimated coefficient functions, which are important for constructing the simultaneous confidence band and the global test statistic. Moreover, comparisons of the statistical powers of the varying coefficient models under the affine invariant and Log-Euclidean metrics are made by using simulated data.Doctor of Philosoph

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

Early and Late Stage Mechanisms for Vocalization Processing in the Human Auditory System

The human auditory system is able to rapidly process incoming acoustic information, actively filtering, categorizing, or suppressing different elements of the incoming acoustic stream. Vocalizations produced by other humans (conspecifics) likely represent the most ethologically-relevant sounds encountered by hearing individuals. Subtle acoustic characteristics of these vocalizations aid in determining the identity, emotional state, health, intent, etc. of the producer. The ability to assess vocalizations is likely subserved by a specialized network of structures and functional connections that are optimized for this stimulus class. Early elements of this network would show sensitivity to the most basic acoustic features of these sounds; later elements may show categorically-selective response patterns that represent high-level semantic organization of different classes of vocalizations. A combination of functional magnetic resonance imaging and electrophysiological studies were performed to investigate and describe some of the earlier and later stage mechanisms of conspecific vocalization processing in human auditory cortices. Using fMRI, cortical representations of harmonic signal content were found along the middle superior temporal gyri between primary auditory cortices along Heschl\u27s gyri and the superior temporal sulci, higher-order auditory regions. Additionally, electrophysiological findings also demonstrated a parametric response profile to harmonic signal content. Utilizing a novel class of vocalizations, human-mimicked versions of animal vocalizations, we demonstrated the presence of a left-lateralized cortical vocalization processing hierarchy to conspecific vocalizations, contrary to previous findings describing similar bilateral networks. This hierarchy originated near primary auditory cortices and was further supported by auditory evoked potential data that suggests differential temporal processing dynamics of conspecific human vocalizations versus those produced by other species. Taken together, these results suggest that there are auditory cortical networks that are highly optimized for processing utterances produced by the human vocal tract. Understanding the function and structure of these networks will be critical for advancing the development of novel communicative therapies and the design of future assistive hearing devices

Activation of the pro-resolving receptor Fpr2 attenuates inflammatory microglial activation

Poster number: P-T099 Theme: Neurodegenerative disorders & ageing Activation of the pro-resolving receptor Fpr2 reverses inflammatory microglial activation Authors: Edward S Wickstead - Life Science & Technology University of Westminster/Queen Mary University of London Inflammation is a major contributor to many neurodegenerative disease (Heneka et al. 2015). Microglia, as the resident immune cells of the brain and spinal cord, provide the first line of immunological defence, but can become deleterious when chronically activated, triggering extensive neuronal damage (Cunningham, 2013). Dampening or even reversing this activation may provide neuronal protection against chronic inflammatory damage. The aim of this study was to determine whether lipopolysaccharide (LPS)-induced inflammation could be abrogated through activation of the receptor Fpr2, known to play an important role in peripheral inflammatory resolution. Immortalised murine microglia (BV2 cell line) were stimulated with LPS (50ng/ml) for 1 hour prior to the treatment with one of two Fpr2 ligands, either Cpd43 or Quin-C1 (both 100nM), and production of nitric oxide (NO), tumour necrosis factor alpha (TNFα) and interleukin-10 (IL-10) were monitored after 24h and 48h. Treatment with either Fpr2 ligand significantly suppressed LPS-induced production of NO or TNFα after both 24h and 48h exposure, moreover Fpr2 ligand treatment significantly enhanced production of IL-10 48h post-LPS treatment. As we have previously shown Fpr2 to be coupled to a number of intracellular signaling pathways (Cooray et al. 2013), we investigated potential signaling responses. Western blot analysis revealed no activation of ERK1/2, but identified a rapid and potent activation of p38 MAP kinase in BV2 microglia following stimulation with Fpr2 ligands. Together, these data indicate the possibility of exploiting immunomodulatory strategies for the treatment of neurological diseases, and highlight in particular the important potential of resolution mechanisms as novel therapeutic targets in neuroinflammation. References Cooray SN et al. (2013). Proc Natl Acad Sci U S A 110: 18232-7. Cunningham C (2013). Glia 61: 71-90. Heneka MT et al. (2015). Lancet Neurol 14: 388-40