Aligning personalized biomarker trajectories onto a common time axis: a connectome-based ODE model for Tau–Amyloid beta dynamics

Abstract

Abnormal tau and amyloid beta are two primary imaging biomarkers used to assist in the diagnosis of Alzheimer’s disease (AD). Recent efforts have focused on developing mechanism-based biophysical models to explain the spatiotemporal dynamics of these biomarkers. In this study, we adopt a connectome-based ODE model to capture the dynamics of tau and amyloid beta ($\text{A}\beta$), aiming to predict personalized future values of these biomarkers. The ODE model includes diffusion, reaction, and clearance terms, and accounts for tau–$\text{A}\beta$ interactions. Additionally, it assumes a sparse initial condition (IC) of abnormalities, based on the assumption of localized initiation. Besides tau and $\text{A}\beta$, brain atrophy is used as a marker of neurodegeneration. We discuss the mathematical model of atrophy integrated into the tau–$\text{A}\beta$ model. A common limitation in popular models is the use of chronological age as the time axis, which prevents the unification of subject trajectories onto a common time scale and hinders comprehensive cohort analysis. To address this issue, we use a normalized disease age that relates chronological age to biomarker values. In the ODE model, we use the disease age to track time and the biomarker dynamics. Furthermore, our analysis of region-of-interest-wise tau–$\text{A}\beta$ temporal correlation reveals that different regions of interest (ROIs) play distinct roles across various disease stages.