LNODE: Uncovering the Latent Dynamics of A β in Alzheimer's Disease

$\text{A}\beta$ Positron Emission Tomography (PET) is often used to manage Alzheimer's disease (AD). To better understand $\text{A}\beta$ progression, we introduce and evaluate a mathematical model that couples $\text{A}\beta$ at parcellated gray matter regions. We term this model LNODE for "latent network ordinary differential equations". At each region, we track normal $\text{A}\beta$ , abnormal $\text{A}\beta$ , and $m$ latent states that intend to capture unobservable mechanisms coupled to $\text{A}\beta$ progression. LNODE is parameterized by subject-specific parameters and cohort parameters. We jointly invert for these parameters by fitting the model to $\text{A}\beta$ -PET data from 585 subjects from the ADNI dataset. Although underparameterized, our model achieves population $R^2\ge 98\%$ compared to $R^2\le 60\%$ when fitting without latent states. Furthermore, these preliminary results suggest the existence of different subtypes of $\text{A}\beta$ progression.