Temperature-controlled laser therapy of the retina via robust adaptive H∞{\mathcal{H}_{\infty }}-control

Abstract

Recent studies demonstrate therapeutic benefits in retinal laser therapy even for non-visible effects of the irradiation. However, in practice, ophthalmologists often rely on the visual inspection of irradiation sites to manually set the laser power for subsequent ones. Since absorption properties vary strongly between sites, this procedure can lead to under- or over-treatment. To achieve safe automatic retinal laser therapy, this article proposes a robust control scheme based on photoacoustic feedback of the retinal temperature increase. The control scheme is further extended to adapt to real-time parameter estimates and associated bounds on the uncertainty of each irradiation site. Both approaches are successfully validated in ex vivo experiments on pigs’ eyes, achieving consistent irradiation durations of 55 ms despite the uncertainty in absorption properties.

State and parameter estimation for model-based retinal laser treatment

“…Schematic sketch of the experimental setup. Herzog et al, 2018)) two lasers, a cw laser for heating and a pulsed laser for temperature probing, have been collinearly superimposed. We further developed the setup to one pulsed laser which can be used for both, heating and measuring.…”

“…To this end, in (Baade et al, 2013), an approximation of the underlying heat diffusion is calculated and employed for control. 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).…”

Model predictive control for retinal laser treatment at 1 kHz

“…In these works, a constant relation between the absorption coefficients is assumed to allow for an offline approximation of a direct conversion between the measured volume temperature and the corresponding control target, i.e., the peak temperature. Based on this conversion between both temperatures an open-loop control was designed in [1] and a closed-loop control in [11]. However, we found in our work [22], that the assumption of a constant relation between both absorption coefficient does not hold in general.…”

“…As this peak temperature is not measurable by means of non-invasive methods, we propose a model-based approach using Model Predictive Control (MPC; [8,21]) in order to control this peak temperature to ensure a safe and effective treatment. This approach is different to previous control strategies in [1,11]. In these works, a constant relation between the absorption coefficients is assumed to allow for an offline approximation of a direct conversion between the measured volume temperature and the corresponding control target, i.e., the peak temperature.…”

State and parameter estimation for retinal laser treatment

“…To this end, constant laser powers and a constant ratio between the absorption coefficients within the tissue were assumed. Based on the approximation of the peak temperature, an open-loop control strategy was developed in [7] and first closed-loop (robust PID) schemes were presented in [5] and [6]. However, the approximated conversion to the peak temperature is only valid under certain assumptions, e.g., a constant laser power that does not hold in closed-loop.…”