  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.
