Learning Mechanistic Subtypes of Neurodegeneration with a Physics-Informed Variational Autoencoder Mixture Model

Modelling the underlying mechanisms of neurodegenerative diseases demands methods that capture heterogeneous and spatially varying dynamics from sparse, high-dimensional neuroimaging data. Integrating partial differential equation (PDE) based physics knowledge with machine learning provides enhanced interpretability and utility over classic numerical methods. However, current physics-integrated machine learning methods are limited to considering a single PDE, severely limiting their application to diseases where multiple mechanisms are responsible for different groups (i.e., subtypes) and aggravating problems with model misspecification and degeneracy. Here, we present a deep generative model for learning mixtures of latent dynamic models governed by physics-based PDEs, going beyond traditional approaches that assume a single PDE structure. Our method integrates reaction-diffusion PDEs within a variational autoencoder (VAE) mixture model framework, supporting inference of subtypes of interpretable latent variables (e.g. diffusivity and reaction rates) from neuroimaging data. We evaluate our method on synthetic benchmarks and demonstrate its potential for uncovering mechanistic subtypes of Alzheimer's disease progression from positron emission tomography (PET) data.

Investigating the Role of Bilateral Symmetry for Inpainting Brain MRI

Inpainting has recently emerged as a valuable and interesting technology to employ in the analysis of medical imaging data, in particular brain MRI. A wide variety of methodologies for inpainting MRI have been proposed and demonstrated on tasks including anomaly detection. In this work we investigate the statistical relationship between inpainted brain structures and the amount of subject-specific conditioning information, i.e. the other areas of the image that are masked. In particular, we analyse the distribution of inpainting results when masking additional regions of the image, specifically the contra-lateral structure. This allows us to elucidate where in the brain the model is drawing information from, and in particular, what is the importance of hemispherical symmetry? Our experiments interrogate a diffusion inpainting model through analysing the inpainting of subcortical brain structures based on intensity and estimated area change. We demonstrate that some structures show a strong influence of symmetry in the conditioning of the inpainting process.