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

Manuel Schaller, Mitsuru Wilson, Viktoria Kleyman, Mario Mordmüller, Ralf Brinkmann, Matthias A. Müller, Karl Worthmann

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.
Original languageEnglish
Article number128
JournalControl Engineering Practice
Volume128
Issue number128
Pages (from-to)105320
ISSN0967-0661
DOIs
Publication statusPublished - 16.08.2022

DFG Research Classification Scheme

  • 308-01 Optics, Quantum Optics, Atoms, Molecules, Plasmas

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