Laser photocoagulation is a widely used treatment for a variety of retinal diseases. Temperature-controlled irradiation is a promising approach to enable uniform heating, reduce the risks of over- or undertreatment, and unburden the ophthalmologists from a time consuming manual power titration. In this paper, an approach is proposed for the development of models with different levels of detail, which serve as a basis for improved, more accurate observer and control designs. To this end, we employ a heat diffusion model and propose a suitable discretization and subsequent model reduction procedures. Since the absorption of the laser light can vary strongly at each irradiation site, a method for identifying the absorption coefficient is presented. To identify a parameter in a reduced order model, an optimal interpolatory projection method for parametric systems is used. In order to provide an online identification of the absorption coefficient, we prove and exploit monotonicity of the parameter influence.

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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.

Laser photocoagulation is one of the most frequently used treatment approaches in ophthalmology for a variety of retinal diseases. Depending on indication, treatment intensity varies from application of specific micro injuries down to gentle temperature increases without inducing cell damage. Especially for the latter, proper energy dosing is still a challenging issue, which mostly relies on the physician’s experience. Pulsed laser photoacoustic temperature measurement has already proven its ability for automated irradiation control during laser treatment but suffers from a comparatively high instrumental effort due to combination with a conventional continuous wave treatment laser. In this paper, a simplified setup with a single pulsed laser at 10 kHz repetition rate is presented. The setup combines the instrumentation for treatment as well as temperature measurement and control in a single device. In order to compare the solely pulsed heating with continuous wave (cw) tissue heating, pulse energies of 4 µJ were applied with a repetition rate of 1 kHz to probe the temperature rise, respectively. With the same average laser power of 60 mW an almost identical temporal temperature course was retrieved in both irradiation modes as expected. The ability to reach and maintain a chosen aim temperature of 41 °C is demonstrated by means of model predictive control (MPC) and extended Kalman filtering at a the measurement rate of 250 Hz with an accuracy of less than ±0.1 °C. A major advantage of optimization-based control techniques like MPC is their capability of rigorously ensuring constraints, e.g., temperature limits, and thus, realizing a more reliable and secure temperature control during retinal laser irradiation.

Laser photocoagulation is a technique applied in the treatment of retinal diseases. While this is often done manually or using simple control schemes, we pursue an optimization-based approach, namely Model Predictive Control (MPC), to enforce bounds on the peak temperature and, thus, safety during the medical treatment procedure -despite the spot-dependent absorption of the tissue. To this end, a repetition rate of 1 kHz is desirable rendering the real-time requirements a major challenge. We present a tailored MPC scheme using parametric model reduction, an extended Kalman filter for the parameter and state estimation, and suitably constructed stage costs and verify its applicability both in simulation and experiments with porcine eyes. Moreover, we give some insight on the implementation specifically tailored for fast numerical computations.