## 3 Materials and Methods
### Determination of Kinetic Solubility
#### 3.1.5 In Vitro Diffusion Studies--Static Franz Diffusion Cell Method  
Accepted models for testing drugs and their formulations for onychomycosis treatments include penetration tests through cadaver nails [41], nail clippings, bovine hood slices, or keratin films [42] made from human keratin source. The non-uniformity of natural membranes causes huge inhomogeneity in the results [43; 44; 45], which makes the comparison of different formulations impossible. The aim of our study was to examine the diffusion properties of applied drugs in complex colloidal systems; therefore, in our opinion, the similarity in hydrophilicity and surface charge between the nail plate or nail bed and artificial membranes was of the highest importance for testing and comparison of the formulations. The nail plate acts as a negatively charged aqueous hydrogel, as it is described in the literature [46], and it has properties similar to that of the agar gel [47]. Based on the literature data obtained from independent researches, we compared the diffusion coefficient and flux of well-studied antibiotic chloramphenicol (5 mg/mL in phosphate-buffered saline) with different membranes, namely agar gel [48], bovine hood slice, and cadaver nail plate [49]. We found that the diffusion coefficients and flux values were very similar for agar gel and bovine hood slice membranes. Flux for bovine hood was 4.07 \(\pm\) 1.18\(\cdot\)10\({}^{-6}\) mg/cm\({}^{2}\)-s, for agar gel 1.96 \(\pm\) 0.47 10\({}^{-6}\) mg/cm\({}^{2}\)-s, and 8.21 \(\pm\) 2.11 10\({}^{-7}\) mg/cm\({}^{2}\)-s for the cadaver nail plate. The flux values for agar gel were closer to the value for the cadaver nail plate, which might suggest that agar gel is a good model membrane for water-based formulations. The agar gel membrane was used to model the nail plate. The composite membrane, consisting of the agar gel layer on top of the cellulose acetate membrane, was used to simulate the complex structure of nail plate and nail bed since nail bed has similar properties as skin [50; 51], and the cellulose membrane has been commonly used as a model for skin permeability [52]. The main aim of the study on two types of membranes was to examine whether the examined formulations could deliver the applied lipophilic drugs through agar gel as a model for nail plate, and the composite membrane was used to examine if the formulation could retain the drugs on the main site of the infection, namely nail bed. The amount of the drug transported through the membrane was calculated based on the amount introduced to the membrane. In the case of agar membrane, the goal was to prepare the drug delivery system that could deliver the highest drug amount through that membrane. The composite membrane was used to test the on-site retention of drugs in different formulations. The amount of retained drug was calculated as a difference between the drug amount passed through the agar gel membrane and the amount passed through the composite membrane  
For in vitro testing, the 2.1 mm thick 6 \(m\)/\(m\)% agar gel membrane (Agar powder, purity \(>\)95%, VWR Chemicals Ltd., Debrecen, Hungary) and the same agar gel membrane combined with 0.8 mm thick cellulose acetate with effective penetration area of 2.54 cm\({}^{2}\) (Membranfilter Porafil, Macherey-Nagel GmbH&Co. KG, Duren, Germany, pore size 0.2 \(\upmu\)m) were used. Before each measurement, the agar gel was always freshly prepared. The agar powder was dispersed in demineralized water, and the mixture was boiled in a closed vial for 3 min until all agar was completely dissolved. Exactly 10 mL of agar gel was poured into a plastic vessel (i.d. 70.8 mm), then left to cool (25 \({}^{\circ}\)C) and gelate. After the gelation, the agar gel was soaked in PBS buffer for 12 h. Finally, the agar membrane was cut out with a sharp home-made tool and placed on the Franz cell. The cellulose acetate membranes were also freshly soaked in PBS buffer before the experiments.