Experimental Studies and Modeling of Drug Release from a Tunable Affinity-Based Drug Delivery Platform

Abstract

An affinity-based drug delivery platform for controlling drug release is analyzed by a combination of experimental studies and mathematical modeling. This platform has the ability to form selective interactions between a therapeutic agent and host matrix that yields advantages over systems that employ nonselective methods. The incorporation of molecular interactions in drug delivery can increase the therapeutic lifetime of drug delivery implants and limit the need for multiple implants in treatment of chronic illnesses. To analyze this complex system for rational design of drug delivery implants, we developed a mechanistic mathematical model to quantify the molecular events and processes. With a β-cyclodextrin hydrogel host matrix, defined release rates were obtained using a fluorescent model drug. The key processes were the complexation between the drug and cyclodextrin and diffusion of the drug in the hydrogel. Optimal estimates of the model parameters were obtained by minimizing the difference between model simulation and experimentally measured drug release kinetics. Model simulations could predict the drug release dynamics under a wide range of experimental conditions.

Appendix

Method of Lines

We can discretize the derivatives with respect to z* starting with

$$ \Updelta = \frac{1}{N},\;z_{i}^{*} = i\Updelta \quad (i = 0,1,2, \ldots ,N) $$

Discretized first derivatives are either forward or backward differences; discretized second derivatives are central differences. The discretized governing equations are

$$ \frac{{dC_{{{\text{L}},i}}^{*} }}{d\tau } = P_{2} \frac{{C_{{{\text{L}},i + 1}}^{*} - 2C_{{{\text{L}},i}}^{*} + C_{{{\text{L}},i - 1}}^{*} }}{{\Updelta^{2} }} - R_{{{\text{b}},i}}^{*} \quad (i = 1,2, \ldots ,N - 1) $$

(6)

$$ \frac{{dC_{{{\text{L}} \cdot {\text{C}},i}}^{*} }}{d\tau } = R_{{{\text{b}},i}}^{*} \quad (i = 1,2, \ldots ,N - 1) $$

(7)

where $R_{{{\text{b}},i}}^{*} = P_{1} C_{{{\text{L}},i}}^{*} \left( {P_{3} - C_{{{\text{L}} \cdot {\text{C}},i}}^{*} } \right) - C_{{{\text{L}} \cdot {\text{C}},i}}^{*}$

$$ \frac{{dM_{\text{R}}^{*} }}{d\tau } = RR^{*} = - \frac{1}{2}P_{2} \frac{{C_{{{\text{L}},N}}^{*} - C_{{{\text{L}},N - 1}}^{*} }}{\Updelta } $$

(8)

The discretized initial conditions are

$$ \tau = 0{:}\;C_{\text{L}}^{*} = \frac{{C_{\text{L}}^{\text{eq}} }}{{C_{0} }};\;C_{{{\text{L}} \cdot {\text{C}}}}^{*} = \frac{{C_{{{\text{L}} \cdot {\text{C}}}}^{\text{eq}} }}{{C_{0} }};\;M_{\text{R}}^{*} = 0; $$

The discretized boundary conditions are

$$ i = 0{:}\;\frac{{\partial C_{{{\text{L}},0}}^{*} }}{{\partial z^{*} }} = 0 \Rightarrow \, C_{{{\text{L}},1}}^{*} = C_{{{\text{L}},0}}^{*} $$

$$ i = N{:}\;C_{{{\text{L}},N}}^{*} = 0 $$

These are incorporated into the equations for i = 1 and i = N − 1, respectively:

$$ \begin{aligned} i & = 1{:}\;\frac{{\partial C_{{{\text{L}},1}}^{*} }}{{\partial z^{*} }} = P_{2} \frac{{C_{{{\text{L}},2}}^{*} - C_{{{\text{L}},1}}^{*} }}{{\Updelta^{2} }} - R_{{{\text{b}},1}}^{*} \\ i & = N - 1{:}\;\frac{{\partial C_{{{\text{L,}}N - 1}}^{*} }}{{\partial z^{*} }} = P_{2} \frac{{ - 2C_{{{\text{L}},N - 1}}^{*} + C_{{{\text{L}},N - 2}}^{*} }}{{\Updelta^{2} }} - R_{{{\text{b}},N - 1}}^{*} \\ \end{aligned} $$