An Explainable Framework for the Relationship between Dementia and Metabolism Patterns

High-dimensional neuroimaging data poses a challenge for the clinical assessment of neurodegenerative diseases, as it involves complex non-linear relationships that are difficult to disentangle using traditional methods. Variational Autoencoders (VAEs) provide a powerful framework for encoding neuroimaging scans into lower-dimensional latent spaces that capture meaningful disease-related features. In this work, we propose a semi-supervised VAE framework that incorporates a flexible similarity regularization term designed to align selected latent variables with clinical or biomarker measures related to dementia progression. This approach allows adapting the similarity metric and the supervised variables according to specific goals or available data. We demonstrate the framework using Positron Emission Tomography (PET) scans from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database, guiding the model to capture neurodegenerative patterns associated with Alzheimer's Disease (AD) by maximizing the similarity between the first latent dimension with a clinical cognitive score, and the second dimension with age. Leveraging the first supervised latent variable, we generate average reconstructions corresponding to different levels of cognitive impairment. A voxel-wise General Linear Model (GLM) confirms reduced metabolism in key brain regions, predominantly in the hippocampus, and within major Resting State Network (RSN)s, particularly the Default Mode Network (DMN) and the Central Executive Network (CEN). Further examination of the remaining latent variables show that they encode affine transformations-rotation, translation, and scaling-as well as intensity variations, capturing common confounding factors such as inter-subject variability and site-related noise. Our findings indicate that the framework effectively disentangles this neuroimaging biomarker ( $z_0$ ) from confounding factors and age, providing an interpretable and adaptable tool to model and visualize neurodegenerative progression.