The human body is a complex system, and the human eye is no exception. Despite significant advancements in medical research, many questions regarding ocular pathologies remain unanswered.

The use of mathematical and computational models has revealed intricate mechanisms underlying human physiology. Due to its special connection with the brain, the eye is considered a window into the brain, providing non-invasive access to a range of biological markers that can aid in diagnosing neurodegenerative diseases. Therefore, understanding the eye’s behavior, the diseases that affect it, and the potential treatments is crucial.

This work focuses on the mathematical modeling and numerical simulation of ocular fluid dynamics within the human eye, particularly on heat transfer and aqueous humor flow. These methods must undergo validation with clinical data to ensure their reliability. Bio-physical models involve numerous parameters that may be patient-specific or influenced by external conditions. The objective of this sensitivity analysis is to understand how these parameters affect the eye’s behavior and how they can be used for disease diagnosis, potentially assisting clinicians in selecting the best treatment.

Such a study requires numerous simulations, which can be computationally expensive for the complex models used in this thesis. To reduce this computational cost, we have developed model reduction methods that decrease the number of equations to solve while maintaining result accuracy.