State and parameter estimation for model-based retinal laser treatment

TL;DR

This paper introduces a model-based approach for real-time state and parameter estimation in retinal laser treatment, using a heat diffusion model and advanced estimation techniques to improve safety and effectiveness.

Contribution

It develops a combined state and parameter estimation framework using heat diffusion modeling and model order reduction for retinal laser therapy.

Findings

Moving horizon estimation outperforms extended Kalman filter in convergence speed.

The approach accurately estimates temperature and absorption coefficient in simulated and experimental data.

Real-time applicability demonstrated through model order reduction.

Abstract

We present an approach for state and parameter estimation in retinal laser treatment by a novel setup where both measurement and heating is performed by a single laser. In this medical application, the temperature that is induced by the laser in the patient's eye is critical for a successful and safe treatment. To this end, we pursue a model-based approach using a model given by a heat diffusion equation on a cylindrical domain, where the source term is given by the absorbed laser power. The model is parametric in the sense that it involves an absorption coefficient, which depends on the treatment spot and plays a central role in the input-output behavior of the system. After discretization, we apply a particularly suited parametric model order reduction to ensure real-time tractability while retaining parameter dependence. We augment known state estimation techniques, i.e., extended Kalman filtering and moving horizon estimation, with parameter estimation to estimate the absorption coefficient and the current state of the system. Eventually, we show first results for simulated and experimental data from porcine eyes. We find that, regarding convergence speed, the moving horizon estimation slightly outperforms the extended Kalman filter on measurement data in terms of parameter and state estimation, however, on simulated data the results are very similar.