# Pharmacokinetics of Pullulan-Dexamethasone Conjugates in Retinal Drug Delivery
## 3 Results
### Pharmacokine Simulations  
A kinetic model (Figure 2) was used to simulate the concentrations of pullulan-DEX in the vitreous and aqueous humor. The simulated results matched the experimental results from rat and rabbit vitreous, when the model assumes that all elimination takes place anteriorly (Figure 6A,B). For rabbit eye, the simulated concentrations in the aqueous humor were remarkably close to experimental values, supporting the dominant role of anterior route for nanoparticle elimination from the vitreous. The experimental values for aqueous humor could not be measured accurately with fluorophotometry in the rat eyes. In order to scale the kinetics of the formulation from preclinical animals to human, the vitreal kinetics of pullulan conjugate were simulated in humans (Figure 6C). It is evident that the retention of pullulan conjugates is longer in the human eyes than in the rabbit eyes. Retention in the rabbit eyes is much longer than in the rat eyes (Figure 6A,B). \begin{table}
\begin{tabular}{l l l l l l} \hline \hline
**Material** & **Dose (\(\upmu\)g)** & **Species** & **C\({}_{0}\)** & **t\({}_{1/2}\)** & **V\({}_{d}\)** & **CL** \\  & **(\(\upmu\)g/mL)** & **(\(\upmu\)g/mL)** & **(\(\upmu\)h)** & **(\(\upmu\)L)** & **(\(\upmu\)L/h)** \\ \hline BDP-pullulan & 15 & rats & 386.4 \(\pm\) 110.2 & 17.4 \(\pm\) 3.9 & 42 \(\pm\) 12 & 1.8 \(\pm\) 0.7 \\ BDP-pullulan-DEX & 30 & rats & 393.7 \(\pm\) 134.1 & 16.7 \(\pm\) 0.8 & 84 \(\pm\) 30 & 3.5 \(\pm\) 1.2 \\ BDP-pullulan-DEX* & 500 & rabbits & 539.3 \(\pm\) 43.1 & 60.3 \(\pm\) 4.9 & 932 \(\pm\) 72 & 11 \(\pm\) 0.4 \\ \hline \hline \end{tabular}
* The elimination half-life in rabbit aqueous humor was 87.5 \(\pm\) 73 h.  
\end{table} 
Table 2: Kinetic parameters of intraviterally injected fluorescently labelled: BDP-pullulan (\(n\) = 6 rat eyes) and BDP-pullulan-DEX (\(n\) = 5 rat eyes; \(n\) = 6 rabbit eyes) derived from fluorophotometric measurements. Figure 5: Concentrations of fluorescently labelled BDP-pullulan-DEX in the vitreous and aqueous humor of six rabbit eyes. Each line was fitted for the experimental data of one eye at different time points. One compartment model with first-order elimination rate constant was used for curve fitting. The route of BDP labelled pullulan dexamethasone conjugate elimination in the rabbit eyes was further explored with Maurice plot that shows the relationship between \(\mathrm{C_{a}/C_{v}}\) and vitreal half-life (Figure 7) [49]. Location of pullulan conjugate in this plot, next to the straight line of compounds with anterior elimination route, supports the notion that the conjugate is mainly eliminated via anterior route. The plot is based on the equation \(\mathrm{C_{a}/C_{v}}=\mathrm{V_{v}}\ \mathrm{k_{v}/nf}\), where \(\mathrm{C_{a}}\) is the concentration in the aqueous humor, \(\mathrm{C_{v}}\) is the concentration in the vitreous humor, \(\mathrm{V_{v}}\) is the volume of distribution in the vitreal compartment (unit: uL), \(\mathrm{k_{v}}\) is the first order elimination rate constant (i.e., \(\mathrm{k_{v}}=\mathrm{ln2/t_{1/2}}\)) (unit: h\({}^{-1}\)), \(f\) is the outflow rate of aqueous humor (unit: uL/min) and \(n\) is the coefficient that indicates the  
Figure 6: Simulated and experimental concentrations of BDP-pullulan-DEX in (**A**) rat, (**B**) rabbit and (**C**) human. The blue and red line shows the simulated concentration in vitreous and aqueous humor, respectively. The experimental concentrations in the vitreous and aqueous humor are indicated in the graphs. fraction of anterior drug elimination after intravitreal injection. The average experimental C\({}_{\text{a}}\)/C\({}_{\text{v}}\) ratio is 0.072 \(\pm\) 0.021. Using a literature value of f (3 uL/min) and experimental values for V\({}_{\text{v}}\) (932 uL) and t\({}_{1/2}\) (60.3 h), we obtained \(n\) value of 0.827 or 82.7% elimination via anterior route. At average rabbit V\({}_{\text{v}}\) from the literature (1150 uL) [50], we obtained \(n\) value of 1.02 suggesting complete (\(\approx\)100%) anterior elimination.