Modeling and parameter identification for real-time temperature controlled retinal laser therapies

Abstract

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.

State and parameter estimation for model-based retinal laser treatment

“…We model heat diffusion inside the tissue by a linear parabolic partial differential equation (PDE) and present a parametric model order reduction (pMOR). For a more detailed explanation we refer to (Kleyman et al, 2020).…”

“…In the next step, we perform a spatial discretization via finite differences with n f ∈ N discretization points, cf. (Kleyman et al, 2020), and obtain the finite dimensional state space model…”

“…Peaktemperature control based on the approximate conversion from peak to volume temperature has been demonstrated in open-loop and closed-loop experiments in (Baade et al, 2017) and (Herzog et al, 2018). With the overall goal of increasing the safety, accuracy, and reliability of peak temperature control, a method for real-time estimation of the absorption coefficient based on a discrete, reducedorder model of the heat diffusion equation was developed in (Kleyman et al, 2020). To this end, the authors generalized the parametric model order reduction (pMOR) proposed in (Baur et al, 2011).…”

“…To this end, the authors generalized the parametric model order reduction (pMOR) proposed in (Baur et al, 2011). In the previous work (Kleyman et al, 2020), the parameter estimation was concluded via measurements of the peak temperature, which can, in general, be hard to obtain. A particular novelty of the present work is that we use a volume temperature for state and parameter estimation, which is more accessible in terms of our application.…”

“…Henceforth, one can express the peak temperature as a function of estimated states and the parameter, i.e., as another output of the system. In particular, we begin with an extension of the model and pMOR presented in (Kleyman et al, 2020). To this end, we employ the modeling of the optoacoustically determined volume temperature as proposed in (Brinkmann et al, 2012) for pMOR with polynomial parameter dependencies in the input and output operator.…”