Mathematical modeling of diffusion-mediated release from bulk degrading matrices

Area of Science:

• Biomaterials Science
• Chemical Engineering
• Pharmacokinetics

Background:

• Drug delivery systems often utilize bulk degrading matrices to control active agent release.
• Understanding the release kinetics is crucial for optimizing therapeutic efficacy.
• Existing models may not fully capture the complexity of release from degrading matrices with multiple active agent pools.

Purpose of the Study:

• To develop a linear reaction-diffusion model for active agent release from bulk degrading matrices.
• To differentiate the contributions of mobile and immobilized active agent pools to the overall release profile.
• To analyze the impact of matrix degradation kinetics and boundary conditions on release dynamics.

Main Methods:

• Formulation of a linear reaction-diffusion problem considering two active agent pools (mobile and immobilized).
• Analytical solution derived for first-order degradation kinetics and perfect sink boundary conditions.
• Numerical solution using the finite element method (FEM) for mass transfer boundary conditions.

Main Results:

• The model successfully explains the characteristic bi-phasic release profiles observed in hydrolytically degradable matrices.
• A closed-form analytical solution was obtained for perfect sink conditions, applicable to systems like the PerioChip.
• Numerical analysis confirmed that diffusion layers are typically not rate-limiting under standard mixing conditions.

Conclusions:

• The proposed linear reaction-diffusion model provides a robust framework for predicting active agent release from degrading matrices.
• The model's ability to explain biphasic release highlights the importance of considering distinct active agent pools.
• The findings suggest that analytical solutions under perfect sink conditions offer accurate approximations for many practical scenarios.