Parameter estimation and model reduction for retinal laser treatment

TL;DR

This paper develops a reduced-order model for retinal laser treatment that enables real-time model predictive control by efficiently approximating temperature distribution with parametric dependencies, and estimates key absorption parameters in pig eyes.

Contribution

It introduces a combined global-basis and empirical interpolation approach tailored for laser photocoagulation, improving computational efficiency and parameter estimation accuracy.

Findings

The proposed method outperforms Taylor-series approximation in computation time.

Sensitivity analysis shows higher impact of RPE absorption coefficient on temperature increase.

Case study successfully estimates absorption parameter ranges in porcine eyes.

Abstract

Laser photocoagulation is one of the most frequently used treatment approaches for retinal diseases such as diabetic retinopathy and macular edema. The use of model-based control, such as Model Predictive Control (MPC), enhances a safe and effective treatment by guaranteeing temperature bounds. In general, real-time requirements for model-based control designs are not met since the temperature distribution in the eye fundus is governed by a heat equation with a nonlinear parameter dependency. This issue is circumvented by representing the model by a lower-dimensional system which well-approximates the original model, including the parametric dependency. We combine a global-basis approach with the discrete empirical interpolation method, tailor its hyperparameters to laser photocoagulation, and show its superiority in comparison to a recently proposed method based on Taylor-series approximation. Its effectiveness is measured in computation time for MPC. We further present a case study to estimate the range of absorption parameters in porcine eyes, and by means of a theoretical and numerical sensitivity analysis we show that the sensitivity of the temperature increase is higher with respect to the absorption coefficient of the retinal pigment epithelium (RPE) than of the choroid's.