TY - JOUR

T1 - Parameter estimation and model reduction for model predictive control in retinal laser treatment

AU - Schaller, Manuel

AU - Wilson, Mitsuru

AU - Kleyman, Viktoria

AU - Mordmüller, Mario

AU - Brinkmann, Ralf

AU - Müller, Matthias A.

AU - Worthmann, Karl

N1 - Funding Information: The collaborative project “Temperature controlled retinal laser treatment” is funded by the German Research Foundation (DFG) under the project number 430154635 ( MU 3929/3-1 , WO 2056/7-1 , BR 1349/6-1 ). MS was also funded by the DFG, Germany (grant WO 2056/2-1 , project number 289034702 ). KW gratefully acknowledges funding by the German Research Foundation (DFG; grant WO 2056/6-1 , project number 406141926 ).

PY - 2022/11

Y1 - 2022/11

N2 - 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.

AB - 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.

KW - Model predictive control

KW - Parameter identification

KW - Parametric model order reduction

KW - Retinal laser treatment

UR - http://www.scopus.com/inward/record.url?scp=85138240176&partnerID=8YFLogxK

U2 - 10.1016/j.conengprac.2022.105320

DO - 10.1016/j.conengprac.2022.105320

M3 - Article

AN - SCOPUS:85138240176

VL - 128

JO - Control engineering practice

JF - Control engineering practice

SN - 0967-0661

M1 - 105320

ER -