Uncertainty propagation and sensitivity analysis: results from the Ocular Mathematical Virtual Simulator

Model order reduction and sensitivity analysis for complex heat transfer simulations inside the human eyeball

Heat transfer in the human eyeball, a complex organ, is significantly influenced by various pathophysiological and external parameters. Particularly, heat transfer critically affects fluid behavior within the eye and ocular drug delivery processes. Overcoming the challenges of experimental analysis, this study introduces a comprehensive three-dimensional mathematical and computational model to simulate the heat transfer in a realistic geometry. Our work includes an extensive sensitivity analysis to address uncertainties and delineate the impact of different variables on heat distribution in ocular tissues. To manage the model's complexity, we employed a very fast model reduction technique with certified sharp error bounds, ensuring computational efficiency without compromising accuracy. Our results demonstrate remarkable consistency with experimental observations and align closely with existing numerical findings in the literature. Crucially, our findings underscore the significant role of blood flow and environmental conditions, particularly in the eye's internal tissues. Clinically, this model offers a promising tool for examining the temperature-related effects of various therapeutic interventions on the eye. Such insights are invaluable for optimizing treatment strategies in ophthalmology.

The ocular mathematical virtual simulator: A validated multiscale model for hemodynamics and biomechanics in the human eye

We present our continuous efforts from a modeling and numerical viewpoint to develop a powerful and flexible mathematical and computational framework called Ocular Mathematical Virtual Simulator (OMVS). The OMVS aims to solve problems arising in biomechanics and hemodynamics within the human eye. We discuss our contribution towards improving the reliability and reproducibility of computational studies by performing a thorough validation of the numerical predictions against experimental data. The OMVS proved capable of simulating complex multiphysics and multiscale scenarios motivated by the study of glaucoma. Furthermore, its modular design allows the continuous integration of new models and methods as the research moves forward, and supports the utilization of the OMVS as a promising non-invasive clinical investigation tool for personalized research in ophthalmology.