1

8. Supplementary materials

8.1. The simulation conditions of each prediction

TableV: Simulationconditions

Figure number for simulation / Drug concentration / Formulation / pH / Reference
2 / 10mM / 0.208% PC / 25µl solution / Multiple / Ahmed and Patton 1984 (26)
3-A-B / 10mM / 0.208% PC / 25µl solution / Multiple / Ahmed and Patton 1984 (26)
4-A / 10mM / 0.27% PC-nitrate / 25µl solution / 6.24 / Lee and Robinson 1979 (11)
4-B / 10mM / 0.208% PC / 25µl solution / 6.24 / Sieg and Robinson 1976 (24)
4-C / 10mM / 0.208% PC / 25µl solution / 6.24 / Makoid and Robinson 1979 (12)
Himmelstein et al 1978 (10)
4-D / 10mM / 0.208% PC / 25µl solution / 7.38 / Chrai and Robinson 1974 (19)
5 / 40µM / 15µg/ml FML / 50µl solution / - / Sieg and Robinson 1981 a
6-A / 40µM / 15µg/ml FML / 50µl solution / - / Sieg and Robinson 1981 a
6-A / Saturated FML / 50µl solution / - / Sieg and Robinson 1975b
6-B / 0.1% FML / 50µl suspension, 2.5µm particles / - / Sieg and Robinson 1975 b
6-C / 0.1% FML / 50µl suspension, 10.4µm particles / - / Hui and Robinson 1986 (13)
6-D / 0.4% FML / 50µl suspension, 6µm particles / - / Hui and Robinson 1986 (13)

aSieg JW, Robinson JR. Mechanistic Studies On Trans-Corneal Permeation Of Fluorometholone. Journal of Pharmaceutical Sciences. 1981;70(9):1026-1029.

bSieg JW, Robinson JR. Vehicle Effects On Ocular Drug Bioavailability I: Evaluation Of Fluorometholone. Journal of Pharmaceutical Sciences. 1975;64(6):931-936.

8.2. Derivation of equation 8

The release of the drug from spherical particles can be described via the decrease of particle diameter. As the volume of a single sphere is and the mass of the single sphere is, the dissolution of multiple spherical particles with the total mass of m becomes

(S1)

whered denotes diameter, ρ density and N the number of particles. In the current model, the particles are treated as a single mass, therefore the number of particles (N) can be substituted with

(S2)

According to Hixson-Crowellc and Carstensend, the diameter of a dissolving spherical particle decreases over time in the following way:

(S3)

wherek denotes the dissolution rate constant, s the solubility of investigated drug, C the concentration of the drug in medium. When the change of the diameter is substituted into equation S2, the rate of dissolution is obtained as:

(S4)

For the purposes of the simulation, the number of particles (N) and concentration of the drug (C) are considered to be in a pseudo steady-state. Equation S4 is then used in the current model to describe the drug release from solid particles

cHixson W, Crowell JH. Dependence of Reaction Velocity upon surface and Agitation. Industrial & Engineering Chemistry. 1931;23(8):923-931.

dCarstensen JT. Pharmaceutics Of Solids And Solid Dosage Forms. New York: John Wiley & Sons; 1977.

8.3. Conversion of absorption rate constant into permeability coefficient

The fluorometholone absorption rate constant was converted into permeability coefficient using equation S5, which expresses the extent of absorption in two different ways.

(S5)

where P is permeability coefficient, A the surface area of cornea, Ctear drug concentration in tears, k absorption rate constant, mtear the mass of the drug in tears and Vtear-average the average volume of the tear during the drainage of the drug. When the rate constant is known, the permeability coefficient can be calculated by re-arranging the first part of equation and assuming that the average volume on the eye is 32.5µl when 50µl drop is instilled ( ), as shown in equation S6

(S6)

8.4. Pilocarpine permeability values from literature

Table VI: Pilocarpine permeability values from literature

Reference / Model / pH / pH independent intrinsic permeability, µm/min
Mitra and Mikkelson 1988 (36) / In vitro rabbit cornea / Multiple / Ionized: 2.9. Non-ionized: 5.8
Suhonen et al 1998 (35) / In vitro rabbit cornea / Multiple / Ionized: 1.15. Non-ionized: 6.14
Scholz et al 2002 (33) / In vitro rabbit cornea / 6.4 / 3.8
Aktas et al 2003 e / In vitro rabbit cornea / 7.0 / 14.7

eAktas Y, Unlu N, Orhan M, Irkec M, Hincal AA. Influence of hydroxypropyl beta-cyclodextrin on the corneal permeation of pilocarpine. Drug Development and Industrial Pharmacy. 2003;29(2):223-230.

Table VII: Pilocarpine permeability values used in modelling

Reference / Permeability / pH / pH independent intrinsic permeability, µm/min
Miller et al 1981 (15) / CL = 0.545 µl/min / 7.2 / 3.6 µm/min
Makoid and Robinson 1979 (12) / Kabs = 0.0062 /min / 6.24 / 2.9 µm/minf
Lee and Robinson 1979 (11) / CL = 0.13 µl/min / 6.24 / 3.0 µm/min
f Conversion of absorption rate constant to permeability coefficient described insupplementary materials 8.3.

8.5. Drainage rate values when the effect of viscosity on pilocarpine bioavailability was simulated

Table VIII: Tear fluid drainage rate adjusted according to experimental viscosity of methylcellulose vehicle(19)

Viscosity (cps) / Drainage rate (min-1)
1.0 / 0.55
1.8 / 0.46
4.2 / 0.36
12.5 / 0.18
100 / 0.05

8.6. Downloadable Stella model

The downloadable model can be improved, altered and redistributed without any constrictions. If the user desires only to operate the model, the only requirement is to download Isee Player software ( The Isee Player is free of charge, but requires Isee Systems account, which can be obtained for free. Once the Isee Player is installed, open the software and select the downloaded Stella model to start simulations