Mathematical modeling and simulation of coupled aqueous humor flow and temperature distribution in a realistic 3D human eye geometry

TL;DR

The paper presents a high-fidelity, three-dimensional model that couples aqueous humor flow in the eye with full-eye heat transfer, solved with a finite-element approach on a realistic CAD-based geometry. The authors implement a Newton-based solver with a field-split preconditioner and GAMG/Schur complement strategies to efficiently tackle the nonlinear, large-scale system, validating the results against prior 2D/3D studies and exploring posture- and ambient-temperature effects on flow and wall shear stress. Key contributions include full-eye thermo-fluid coupling, accurate WSS computation in both chambers, and a detailed HPC-enabled performance assessment across multiple postures, with results aligned to physiological expectations. The work paves the way for real-time or patient-specific simulations and informs ocular drug delivery and surgical design, while proposing future extensions such as model-order reduction and inclusion of AH production/drainage and pharmacokinetic transport.

Abstract

We present a comprehensive computational model to simulate the coupled dynamics of aqueous humor flow and heat transfer in the human eye. To manage the complexity of the model, we make significant efforts in meshing and efficient solution of the discrete problem using high-performance resources. The model accurately describes the dynamics of the aqueous humor in the anterior and posterior chambers and accounts for convective effects due to temperature variations. Results for fluid velocity, pressure, and temperature distribution are in good agreement with existing numerical results in the literature. Furthermore, the effects of postural changes and wall shear stress behavior are analyzed, providing new insights into the mechanical forces acting on ocular tissues. Overall, the present contribution provides a detailed three-dimensional simulation that enhances the understanding of ocular physiology and may contribute to further progress in clinical research and treatment optimization in ophthalmology.

Figures (10)

• Figure 1: Description of the human eyeball (left panel), zoom on the anterior and posterior chambers of the eye (right panel).
• Figure 2: Production and drainage of AH in the front part of the eye, adapted from ramakrishnan_aqueous_2013.
• Figure 3: Results of the mesh convergence study. For each curve, the point on the left corresponds to mesh Mr1, and the point on the right to mesh Mr5. The reference quantity use to compute the relative error as been obtained with the mesh Mr5 and the discretization $\mathbb{P}_2\text{--}\mathbb{P}_2\mathbb{P}_1$, and a higher order of accuracy required to the solver.
• Figure 4: Scalability results: time of execution to simulate coupled model (left panel), and corresponding speed-up, for an increasing number of parallel processes, and for the three subject positions (right panel).
• Figure 5: Absolute and relative computational time for the coupled heat-fluid test case in the standing position, performed on Gaya with the meshes Mr4 (left), Mr5 (middle), and Mr6 (right).

Theorems & Definitions (4)

• Remark 1
• Theorem 1: Existence and Uniqueness
• proof
• Remark 2