Parameter estimation and model reduction for model predictive control in retinal laser treatment

• Published in: Control engineering practice 2022-11, Vol.128, p.105320, Article 105320
• Main Authors: Schaller, Manuel, Wilson, Mitsuru, Kleyman, Viktoria, Mordmüller, Mario, Brinkmann, Ralf, Müller, Matthias A., Worthmann, Karl
• Format: Article
• Language: English
• Subjects: Model predictive control; Parameter identification; Parametric model order reduction; Retinal laser treatment
• ISSN: 0967-0661; 1873-6939
• DOI: 10.1016/j.conengprac.2022.105320

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. •Parametric model reduction for model-based control in retinal laser treatment.•Model predictive control in 1 kHz using reduced order models.•Case study and sensitivity analysis w.r.t. spot-dependent absorption coefficients.•Thorough evaluation and comparison of two parametric model reduction methods.