Statistical learning of spatiotemporal patterns from longitudinal manifold-valued networks

International audienceWe introduce a mixed-effects model to learn spatiotempo-ral patterns on a network by considering longitudinal measures distributed on a fixed graph. The data come from repeated observations of subjects at different time points which take the form of measurement maps distributed on a graph such as an image or a mesh. The model learns a typical group-average trajectory characterizing the propagation of measurement changes across the graph nodes. The subject-specific trajectories are defined via spatial and temporal transformations of the group-average scenario, thus estimating the variability of spatiotemporal patterns within the group. To estimate population and individual model parameters, we adapted a stochastic version of the Expectation-Maximization algorithm, the MCMC-SAEM. The model is used to describe the propagation of cortical atrophy during the course of Alzheimer's Disease. Model parameters show the variability of this average pattern of atrophy in terms of trajectories across brain regions, age at disease onset and pace of propagation. We show that the personaliza-tion of this model yields accurate prediction of maps of cortical thickness in patients

Learning distributions of shape trajectories from longitudinal datasets: a hierarchical model on a manifold of diffeomorphisms

We propose a method to learn a distribution of shape trajectories from longitudinal data, i.e. the collection of individual objects repeatedly observed at multiple time-points. The method allows to compute an average spatiotemporal trajectory of shape changes at the group level, and the individual variations of this trajectory both in terms of geometry and time dynamics. First, we formulate a non-linear mixed-effects statistical model as the combination of a generic statistical model for manifold-valued longitudinal data, a deformation model defining shape trajectories via the action of a finite-dimensional set of diffeomorphisms with a manifold structure, and an efficient numerical scheme to compute parallel transport on this manifold. Second, we introduce a MCMC-SAEM algorithm with a specific approach to shape sampling, an adaptive scheme for proposal variances, and a log-likelihood tempering strategy to estimate our model. Third, we validate our algorithm on 2D simulated data, and then estimate a scenario of alteration of the shape of the hippocampus 3D brain structure during the course of Alzheimer's disease. The method shows for instance that hippocampal atrophy progresses more quickly in female subjects, and occurs earlier in APOE4 mutation carriers. We finally illustrate the potential of our method for classifying pathological trajectories versus normal ageing

Learning Riemannian geometry for mixed-effect models using deep generative networks.

We take up on recent work on the Riemannian geometry of generative networks to propose a new approach for learning both a manifold structure and a Riemannian metric from data. It allows the derivation of statistical analysis on manifolds without the need for the user to design new Riemannian structure for each specific problem. In high-dimensional data, it can learn non diagonal metrics, whereas manual design is often limited to the diagonal case. We illustrate how the method allows the construction of a meaningful low-dimensional representation of data and exhibit the geometry of the space of brain images during Alzheimer's progression

Méthodes numériques et statistiques pour l'analyse de trajectoire dans un cadre de geométrie Riemannienne.

This PhD proposes new Riemannian geometry tools for the analysis of longitudinal observations of neuro-degenerative subjects. First, we propose a numerical scheme to compute the parallel transport along geodesics. This scheme is efficient as long as the co-metric can be computed efficiently. Then, we tackle the issue of Riemannian manifold learning. We provide some minimal theoretical sanity checks to illustrate that the procedure of Riemannian metric estimation can be relevant. Then, we propose to learn a Riemannian manifold so as to model subject's progressions as geodesics on this manifold. This allows fast inference, extrapolation and classification of the subjects.Cette thèse porte sur l'élaboration d'outils de géométrie riemannienne et de leur application en vue de la modélisation longitudinale de sujets atteints de maladies neuro-dégénératives. Dans une première partie, nous prouvons la convergence d'un schéma numérique pour le transport parallèle. Ce schéma reste efficace tant que l'inverse de la métrique peut être calculé rapidement. Dans une deuxième partie, nous proposons l'apprentissage une variété et une métrique riemannienne. Après quelques résultats théoriques encourageants, nous proposons d'optimiser la modélisation de progression de sujets comme des géodésiques sur cette variété

Learning distributions of shape trajectories from longitudinal datasets: a hierarchical model on a manifold of diffeomorphisms

International audienceWe propose a method to learn a distribution of shape tra-jectories from longitudinal data, i.e. the collection of individual objects repeatedly observed at multiple time-points. The method allows to compute an average spatiotemporal trajectory of shape changes at the group level, and the individual variations of this trajectory both in terms of geometry and time dynamics. First, we formulate a non-linear mixed-effects statistical model as the combination of a generic statistical model for manifold-valued longitudinal data, a deformation model defining shape trajectories via the action of a finite-dimensional set of diffeomorphisms with a man-ifold structure, and an efficient numerical scheme to compute parallel transport on this manifold. Second, we introduce a MCMC-SAEM algorithm with a specific approach to shape sampling, an adaptive scheme for proposal variances , and a log-likelihood tempering strategy to estimate our model. Third, we validate our algorithm on 2D simulated data, and then estimate a scenario of alteration of the shape of the hippocampus 3D brain structure during the course of Alzheimer's disease. The method shows for instance that hippocampal atrophy progresses more quickly in female subjects, and occurs earlier in APOE4 mutation carriers. We finally illustrate the potential of our method for classifying pathological trajectories versus normal ageing

Riemannian metric learning for progression modeling of longitudinal datasets

International audienceExplicit descriptions of the progression of biomarkers across time usually involve priors on the shapes of the trajectories. To circumvent this limitation, we propose a geometric framework to learn a manifold representation of longitudinal data. Namely, we introduce a family of Riemannian metrics that span a set of curves defined as parallel variations around a main geodesic, and apply that framework to disease progression modeling with a mixed-effects model, where the main geodesic represents the average progression of biomarkers and parallel curves describe the individual trajectories. Learning the metric from the data allows to fit the model to longitudinal datasets and provides few interpretable parameters that characterize both the group-average trajectory and individual progression profiles. Our method outperforms the 56 methods benchmarked in the TADPOLE challenge for cognitive scores prediction

A precision medicine initiative for Alzheimer's disease: the road ahead to biomarker-guided integrative disease modeling

After intense scientific exploration and more than a decade of failed trials, Alzheimer’s disease (AD) remains a fatal global epidemic. A traditional research and drug development paradigm continues to target heterogeneous late-stage clinically phenotyped patients with single 'magic bullet' drugs. Here, we propose that it is time for a paradigm shift towards the implementation of precision medicine (PM) for enhanced risk screening, detection, treatment, and prevention of AD. The overarching structure of how PM for AD can be achieved will be provided through the convergence of breakthrough technological advances, including big data science, systems biology, genomic sequencing, blood-based biomarkers, integrated disease modeling and P4 medicine. It is hypothesized that deconstructing AD into multiple genetic and biological subsets existing within this heterogeneous target population will provide an effective PM strategy for treating individual patients with the specific agent(s) that are likely to work best based on the specific individual biological make-up. The Alzheimer’s Precision Medicine Initiative (APMI) is an international collaboration of leading interdisciplinary clinicians and scientists devoted towards the implementation of PM in Neurology, Psychiatry and Neuroscience. It is hypothesized that successful realization of PM in AD and other neurodegenerative diseases will result in breakthrough therapies, such as in oncology, with optimized safety profiles, better responder rates and treatment responses, particularly through biomarker-guided early preclinical disease-stage clinical trials

Progression models for imaging data with Longitudinal Variational Auto Encoders

International audienceDisease progression models are crucial to understanding degenerative diseases. Mixed-effects models have been consistently used to model clinical assessments or biomarkers extracted from medical images, allowing missing data imputation and prediction at any timepoint. However, such progression models have seldom been used for entire medical images. In this work, a Variational Auto Encoder is coupled with a temporal linear mixed-effect model to learn a latent representation of the data such that individual trajectories follow straight lines over time and are characterised by a few interpretable parameters. A Monte Carlo estimator is devised to iteratively optimize the networks and the statistical model. We apply this method on a synthetic data set to illustrate the disentanglement between time dependant changes and inter-subjects variability, as well as the predictive capabilities of the method. We then apply it to 3D MRI and FDG-PET data from the Alzheimer's Disease Neuroimaging Initiative (ADNI) to recover well documented patterns of structural and metabolic alterations of the brain