Towards a digital twin of the eye: mathematical modeling, simulation and order reduction

Understanding the behavior of the human eye is challenging due to the complex interactions between various physical phenomena, such as heat transfer, fluid dynamics, and tissue deformation. Although medical data can offer valuable insights into ocular physiopathology, the available information can be scarce and noisy. Moreover, in experimental studies, multiple factors come into play and it is difficult to isolate the contributions of individual mechanisms. Therefore, developing a robust and accurate digital twin for ocular applications can enhance our understanding of this complex system, by integrating governing mechanisms and data variability. 

This talk presents our ongoing efforts in this direction, focusing on the thermo-fluid dynamics governing aqueous humor flow in the anterior and posterior chambers and its coupling with heat transfer throughout the eyeball. Our methodology involves developing a comprehensive mathematical and computational model based on the finite element method, rigorously validated against experimental data and numerical studies. To facilitate real-time feedback, we derived a reliable reduced-order model using the certified reduced basis method. We performed forward uncertainty quantification studies with the reduced model, utilizing experimental based stochastic inputs, and conducted global sensitivity analysis to address variability and noise. We will illustrate these developments, discuss their applications, and address the remaining challenges, including inverse problems and parameter identification.

The presentation is based on a joint work with Thomas Saigre (Inria, Strasbourg), Vincent Chabannes (Cemosis, Univ. de Strasbourg) and Christophe Prud'homme (Cemosis, Univ. de Strasbourg).