PINN-EM: Physics-Guided Disease Progression Model of Geographic Atrophy

To construct a personalizable spatio-temporal disease progression model of patients with a late dry form of Age-Related Macular Degeneration (AMD), known as Geographic Atrophy (GA).

From a series of retinal optical coherence tomography (OCT) scans, we infer the coefficients for the parametrized partial differential equation (PDE), such that the parametrized PDE best describes the observed imaging data. Acting as a soft constraint, the recovered PDE helps to extrapolate an implicit neural representation (INR) of the GA segmentation map progression. To enable efficient training, we propose an iterative method - PINN-EM, designed to recover coefficients of non-linear PDEs. At each iteration, the method decouples the problem into PDE coefficients fitting and data fitting steps, resembling Expectation Maximization algorithm.

We extensively tested the proposed method in large-scale experiments using the open-source PDEBench benchmark to validate its performance. Furthermore, we applied the method to the challenging problem of GA progression modeling, where patients exhibit a high variance in GA growth patterns and speed. The proposed spatio-temporal disease progression model outperformed the baselines, even outperforming posterior knowledge models in Dice score for newly affected growth areas.

We demonstrated that the proposed spatio-temporal disease progression model fitted with introduced PINN-EM outperforms existing baselines in synthetic and real clinical applications, highlighting the extrapolation capabilities of the INR models.

The proposed spatio-temporal disease progression model and PINN-EM fitting procedure can be applied across diverse domains facing the challenge of fitting parametrized PDE to the empirical datasets.