Report

Teaser, summary, work performed and final results

Periodic Reporting for period 2 - LEASP (Learning spatiotemporal patterns in longitudinal image data sets of the aging brain)

Teaser

Time-series of multimodal medical images offer a unique opportunity to track anatomical and functional alterations of the brain in aging individuals. A collection of such time series for several individuals forms a longitudinal data set, each data being a rich iconic-geometric...

Summary

Time-series of multimodal medical images offer a unique opportunity to track anatomical and functional alterations of the brain in aging individuals. A collection of such time series for several individuals forms a longitudinal data set, each data being a rich iconic-geometric representation of the brain anatomy and function. These data are already extraordinary complex and variable across individuals. Taking the temporal component into account further adds difficulty, in that each individual follows a different trajectory of changes, and at a different pace. Furthermore, a disease is here a progressive departure from an otherwise normal scenario of aging, so that one could not think of normal and pathologic brain aging as distinct categories, as in the standard case-control paradigm.

Bio-statisticians lack a suitable methodological framework to exhibit from these data the typical trajectories and dynamics of brain alterations, and the effects of a disease on these trajectories, thus limiting the investigation of essential clinical questions. To change this situation, we propose to construct digital dynamical models of brain aging by learning typical spatiotemporal patterns of alterations propagation from longitudinal iconic-geometric data sets.

By including concepts of the Riemannian geometry into Bayesian mixed effect models, the project will introduce general principles to average complex individual trajectories of iconic-geometric changes and align the pace at which these trajectories are followed. It will estimate a set of elementary spatiotemporal patterns, which combine to yield a personal aging scenario for each individual. Disease-specific patterns will be detected with an increasing likelihood.

This new generation of statistical and computational tools will unveil clusters of patients sharing similar lesion propagation profiles, paving the way to design more specific treatments, and care patients when treatments have the highest chance of success.

Work performed

We have implemented methods to continuously vary iconic and geometric data by deforming the geometrical support of the shape (i.e. a mesh) or varying the texture mapped on the geometry. Two approaches have been proposed: (i) geodesic shooting in which the iconic-geometric variations are seen as geodesic paths on a Riemannian manifold, and (ii) exp-parallelisation where the trajectory is seen as an extension of a parallel to a geodesic path on a Riemannian manifold. This latter method required the development of a specific numerical scheme for computing parallel transport on a manifold. We evaluated these approaches in various registration tasks, and in prediction of the future shape of an anatomical structure given few past observations of the structure.

We also extended the definition of Bayesian mixed-effects models for longitudinal data in order to better take into account missing modalities at some observation time-points. We also extended this model to a mixture model to allow unsupervised clustering in the spatiotemporal domain. We evaluated such Bayesian mixed-effects models on the data from the Alzheimer\'s Disease Neuroimaging Initiative (ADNI) to construct a model of cognitive decline (unstructured feature vector), cortical atrophy (varying texture on a fixed mesh) and hippocampal atrophy (varying geometry with no texture) from the prodromal to the clinical phase of the disease. The model can be visualized at www.digital-brain.org

Most of the methods developped have been implemented in the publicly available software Deformetrica (www.deformetrica.org) and the software LEASPy (not yet released).

Final results

The work carried so far allowed us to define the theoretical and computational foundations of a new generation of statistical learning techniques to infer long-term scenario of changes from multiple short-term observations covering various stages of the observed phenomenon. The use of the tools from Riemannian geometry allowed us to define a common framework for both unstructured and structured data such as meshes or texture maps on meshes. It yields personalized models of disease progression that for the first time could reproduce the effects of the Alzheimer\'s Disease on brain structure and cognition at both the individual and population level.

The project will continue by further refining our statistical and computational models for longitudinal data. In particular, we will try to overcome the need to prescribe a typical form of data variations (given by the Riemannian metric) by learning it from the data. We will also develop new methods to compare estimated trajectories of data changes from different population, e.g. healthy aging population and subjects developing a neurodegenerative disease, at both the population and individual level. Eventually, we will develop methods to predict the future brain and cognitive state of a subject using the personnalization of the models to unseen data.

Website & more info

More info: https://who.rocq.inria.fr/Stanley.Durrleman/leasp.html.