Table 3.
Parameter Values Used in the Mathematical Models (See Equations 2–13), Given to a Maximum of Three Significant Figures
| Parameter | Description | Value | Source |
|---|---|---|---|
| τloss | Time for tear volume to return | 5.00 × 10−2 h | 39–43 |
| to normal (human)/zero (porcine) | 5.00 × 10−2 h | This study and 39–43 | |
| V Drop | Volume of eye drop | 4.50 × 10−2 mL | This study |
| Volume of normal tear film | 6.35 × 10−3 mL | 44, 45 | |
| N/A | — | ||
| Volume of tear reservoir | 3.00 × 10−2 mL | 40, 42, 46, 47 | |
| N/A | — | ||
| V Aq | Volume of aqueous | 0.160 mL | 48 |
| 0.310 mL | 49, 50 | ||
| V Vit | Volume of vitreous | 4.50 mL | 17, 49, 51, 52 |
| 3.10 mL | 49, 50, 53, 54 | ||
| A Tear-Aq | Area of the tear-aqueous interface | 1.30 cm2 | Calculated from data in 55, 56 |
| 1.51 cm2 | Calculated from data in this study and 57 | ||
| A Aq-Vit | Area of the aqueous-vitreous interface | 0.349 cm2 | Calculated from data in 58 |
| 0.301 cm2 | Calculated from data in 55, 57, 59–64 | ||
| A Vit-Ret | Area of the vitreo-retinal interface | 10.9 cm2 | Calculated from data in 65 |
| N/A | — | ||
| k + | Binding rate of R to VR (to form RVR) | 0.576 pmol−1 mL h−1 | 66 |
| k − | Unbinding rate of VR (to form V + R) | 2.63 × 10−2 h−1 | 66 |
| δi, j | Rate of molecular degradation | 0 h−1 | Simplifying assumption |
| (i ∈ {Aq, Vit} and j ∈ {v, r, u, w}) | |||
| βTear-Aq,r | Permeability of the tear-aqueous | 1.10 × 10−6 cm h−1 | Inferred from porcine value using |
| interface to R with CPP | data in 24, 55, 59, 64 | ||
| 5.93 × 10−7 cm h−1 | Model fit | ||
| βAq-Vit,v | Permeability of the aqueous-vitreous | 0.985 cm h−1 | Inferred from βAq-Vit,r using |
| interface to V | data in 17, 67, 68 | ||
| βAq-Vit,r | Permeability of the aqueous-vitreous | 0.929 cm h−1 | Model fit |
| interface to R | |||
| βAq-Vit,u | Permeability of the aqueous-vitreous | 0.755 cm h−1 | Inferred from βAq-Vit,r using |
| interface to VR | data in 17, 67, 68 | ||
| βAq-Vit,w | Permeability of the aqueous-vitreous | 0.653 cm h−1 | Inferred from βAq-Vit,r using |
| interface to RVR | data in 17, 67, 68 | ||
| βVit-Ret,r | Permeability of the vitreo-retinal | 6.80 × 10−4 cm h−1 | 19 |
| interface to R | 0 cm h−1 | — | |
| βVit-Ret,u | Permeability of the vitreo-retinal | 6.44 × 10−4 cm h−1 | 19 |
| interface to VR | 0 cm h−1 | — | |
| βVit-Ret,w | Permeability of the vitreo-retinal | 6.23 × 10−4 cm h−1 | 19 |
| interface to RVR | 0 cm h−1 | — | |
| ϕVit,v | Rate at which retina contributes V | 2.34 × 10−4 pmol h−1 | Mean value from 17 |
| to vitreous | 0 pmol h−1 | — | |
| ψTear | Rate of inflow/outflow to/from tear film | 7.20 × 10−2 mL h−1 | 44 |
| 0 mL h−1 | — | ||
| ψAq | Rate of inflow/outflow to/from aqueous | 0.150 mL h−1 | 17, 24, 69, 70 |
| 0 mL h−1 | — | ||
| Initial V concentration in aqueous | 1.56 × 10−3 pmol mL−1 | Model steady-state without R | |
| 0 pmol mL−1 | Simplifying assumption/this study | ||
| Initial V concentration in vitreous | 2.24 × 10−3 pmol mL−1 | Model steady-state without R | |
| 0 pmol mL−1 | Simplifying assumption/this study | ||
| r Dose | R dose concentration | 2.07 × 104 pmol mL−1 | This study and 17, 67 |
| Initial R concentration in tear | 1.81 × 104 pmol mL−1 | Calculated | |
| 2.07 × 104 pmol mL−1 | Calculated | ||
| Initial R concentration in vitreous | 2.07 × 102 pmol mL−1 | Calculated | |
| 4.29 pmol mL−1 | This study |
Parameters are fixed quantities that do not change during a simulation.
Where a single value is given, this holds for both human and porcine eyes. Where two values are given, the first is for human eyes and the second is for porcine eyes. See Appendix A: Parameter Justification for a description of how each parameter value was determined.