A Stage-Aware Mixture of Experts Framework for Neurodegenerative Disease Progression Modelling

The long-term progression of neurodegenerative diseases is commonly conceptualized as a spatiotemporal diffusion process that consists of a graph diffusion process across the structural brain connectome and a localized reaction process within brain regions. However, modeling this progression remains challenging due to 1) the scarcity of longitudinal data obtained through irregular and infrequent subject visits and 2) the complex interplay of pathological mechanisms across brain regions and disease stages, where traditional models assume fixed mechanisms throughout disease progression. To address these limitations, we propose a novel stage-aware Mixture of Experts (MoE) framework that explicitly models how different contributing mechanisms dominate at different disease stages through time-dependent expert weighting.Data-wise, we utilize an iterative dual optimization method to properly estimate the temporal position of individual observations, constructing a co hort-level progression trajectory from irregular snapshots. Model-wise, we enhance the spatial component with an inhomogeneous graph neural diffusion model (IGND) that allows diffusivity to vary based on node states and time, providing more flexible representations of brain networks. We also introduce a localized neural reaction module to capture complex dynamics beyond standard processes.The resulting IGND-MoE model dynamically integrates these components across temporal states, offering a principled way to understand how stage-specific pathological mechanisms contribute to progression. The stage-wise weights yield novel clinical insights that align with literature, suggesting that graph-related processes are more influential at early stages, while other unknown physical processes become dominant later on.

Rician likelihood loss for quantitative MRI using self-supervised deep learning

Purpose: Previous quantitative MR imaging studies using self-supervised deep learning have reported biased parameter estimates at low SNR. Such systematic errors arise from the choice of Mean Squared Error (MSE) loss function for network training, which is incompatible with Rician-distributed MR magnitude signals. To address this issue, we introduce the negative log Rician likelihood (NLR) loss. Methods: A numerically stable and accurate implementation of the NLR loss was developed to estimate quantitative parameters of the apparent diffusion coefficient (ADC) model and intra-voxel incoherent motion (IVIM) model. Parameter estimation accuracy, precision and overall error were evaluated in terms of bias, variance and root mean squared error and compared against the MSE loss over a range of SNRs (5 - 30). Results: Networks trained with NLR loss show higher estimation accuracy than MSE for the ADC and IVIM diffusion coefficients as SNR decreases, with minimal loss of precision or total error. At high effective SNR (high SNR and small diffusion coefficients), both losses show comparable accuracy and precision for all parameters of both models. Conclusion: The proposed NLR loss is numerically stable and accurate across the full range of tested SNRs and improves parameter estimation accuracy of diffusion coefficients using self-supervised deep learning. We expect the development to benefit quantitative MR imaging techniques broadly, enabling more accurate parameter estimation from noisy data.