Riemannian metric learning for progression modeling of longitudinal datasets

By Benoît Sauty, Stanley Durrleman

Keywords: Disease Progression Modelling Alzheimer's disease Forecast of cognitive decline

In this work we propose new progression models for biomarkers across Alzheimer’s disease. For any biomarker, brain volumes or cognitive scores for instance, we learn the shape of the average trajectory of decline, as well individual progression profiles that describe each individual patient’s trajectory. Most importantly, we know if each patients starts declining earlier or later than average, and declines faster or slower than average.

This allows to both predict future evolution of patients with higher certainty than former methods, and also describe the severity of the decline compared to an average scenario that is truly representative of the underlying biological processes. This method is applied to biomarkers for Alzheimer’s Disease patients.

Published in International Symposium on Biomedical Imaging (ISBI) 2022 the 28/03/2022

Normative scenario predicted by our model for 3 biomarkers : main logistic (plain) and parallels (dotted). One parrallel curve is highlighted with crosses.

Full title Riemannian metric learning for progression modeling of longitudinal datasets

Article abstract:

Explicit 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 frame- work 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.