Mathematical model for controlled diffusional release of dispersed solute drugs from monolithic implants

Area of Science:

• Pharmacokinetics and Mathematical Modeling
• Materials Science and Drug Delivery

Background:

• Drug release from matrices often involves complex diffusion dynamics.
• High initial drug loading (c0 > solubility limit, cs) presents unique challenges in predicting release profiles.
• Understanding these dynamics is crucial for developing effective controlled-release drug formulations.

Purpose of the Study:

• To develop mathematical models for solute diffusion from multi-layered matrices with high initial drug loading.
• To provide analytical solutions for predicting cumulative mass release over time.
• To establish a computational tool for designing implantable drug delivery systems.

Main Methods:

• Formulation of new mathematical models incorporating a Stefan problem with moving boundaries.
• Analytical solutions derived for both non-erodible and biodegradable matrices.
• Identification of an inward moving diffusional front separating undissolved drug regions from extracted regions.

Main Results:

• The cumulative mass released is accurately determined as a function of time.
• Models account for the presence of undissolved drug and moving boundaries.
• The study provides a framework for analyzing diffusional release under supersaturation conditions.

Conclusions:

• The developed models and solutions offer a reliable design tool for specialized implantable drug delivery systems.
• This approach enables the fabrication of devices delivering prespecified and reproducible dosages.
• The mathematical framework can predict suitable dosages for new drugs, potentially reducing animal testing.