**Background:** Age-related macular degeneration (AMD) is a leading cause of vision loss in industrialized countries, affecting 10% of those over 65 and 25% over 75. The standard treatment for wet AMD involves repeated intravitreal injections of anti-VEGF drugs, which are risky, unpopular, and ineffective for some patients. Current dosing regimens (monthly, bimonthly, pro-re-nata, treat-and-extend) are not fully personalized. This study aims to develop a computational model (Virtual Eye) to simulate drug distribution in the vitreous and optimize injection parameters, reducing reliance on costly and ethically constrained experiments.
**Methods:** The authors constructed a patient-specific 3D geometry of the vitreous body using a modified Limacon formula fitted to ultrasound data from 12 patients (164 data points each, maximum deviation 0.34 mm). The mathematical model couples a steady-state Darcy equation for aqueous humor flow (with a Poiseuille inflow profile at the hyaloid membrane and Robin-type outflow at the retina) with a time-dependent convection-diffusion equation for drug concentration. Anisotropic diffusion due to collagen fibers and gravity (via an additional transport term) are included. The model was solved using the Finite Element method in deal.ii (over 6000 lines of code): first the Darcy equation with mixed finite elements (Raviart-Thomas for velocity, discontinuous piecewise constant for pressure) using the Schur complement and CG method, then the convection-diffusion equation with trilinear Lagrange elements using the Rothe method and GMRES with ILU preconditioning. The fractional step theta scheme (strong A-stable) was used for time-stepping over 30 days (one injection cycle). Output functionals quantified drug remaining in the vitreous (JΩ), drug at the macula (JM, radius 2 mm), total drug available over time (JM,Ω), and drug lost through the retina (JR). Simulations tested gravity (5 head positions), injection position (4 sites), injection angle (ψxy = 25°, 50°, 75°; ψz = 90°, 115°, 140°), and diffusion coefficient (D = 2×10⁻¹¹, 4×10⁻¹¹, 8×10⁻¹¹ m²/s; D = 4×10⁻¹¹ corresponds to bevacizumab).
**Key Results:** Gravity had negligible effect: maximum difference in drug concentration at the macula was less than 1% across all head positions (best: lying on right side, 38.4% of drug reached macula, peak concentration 0.287 kg/m³ at 6 days; worst: lying on left side, 37.6%, peak 0.281 kg/m³). For injection position, the standard injection (3.5 mm from limbus) resulted in the lowest macula concentration. Injection into the central vitreous (10 mm from limbus, needle depth ~10 mm) provided the longest drug presence at the macula (best for longer-acting drugs like aflibercept). Injection closer to the macula (fourth position, needle depth ~18 mm) gave 10× higher concentration initially but declined faster (best for intensified initial treatment). For injection angle, ψxy = 25° and 50° yielded similar results (~40% of drug reached macula, 60% lost through retina), while ψxy = 75° resulted in only ~30% reaching macula and 70% lost. For ψz, increasing angle reduced macula drug: ψz = 90° gave 40% at macula, ψz = 115° gave 10% less, ψz = 140° gave 38% less (75% lost through retina). Peak concentration occurred at ~6 days for all angles (0.291 kg/m³ at 25°, 0.282 kg/m³ at 50°, 0.214 kg/m³ at 75°). For diffusion coefficient, smaller D (heavier molecules) was beneficial: D = 2×10⁻¹¹ m²/s resulted in ~50% drug lost through retina, ~40% at macula, 10% remaining in vitreous after 30 days; D = 8×10⁻¹¹ m²/s gave ~80% lost, 20% at macula, none remaining. Peak concentration was highest for larger D (2.9 kg/m³ at D = 8×10⁻¹¹ vs. 2.7 kg/m³ at D = 2×10⁻¹¹), but duration of therapeutic concentration was longer for smaller D (22 days vs. 10 days).
**Clinical Implications:** The study demonstrates that computational modeling can identify optimal injection parameters to improve anti-VEGF therapy for AMD. Key recommendations include: (1) inject centrally into the vitreous for longer-acting drugs; (2) inject closer to the macula for intensified initial treatment; (3) orient the needle toward the macula (ψxy 25-50°, ψz 90°) to avoid up to 38% drug loss; (4) use heavier drug molecules (smaller diffusion coefficient) to prolong drug presence at the macula. The model can be personalized using patient ultrasound data and may reduce the need for animal and clinical experiments. Limitations include the assumption of a healthy homogeneous vitreous and the need for experimental validation. Future extensions include viscoelastic vitreous models, fluid-structure interaction, and pharmacology of drug-VEGF binding.