An Inverse Problem Solution Scheme for Solving the Optimization Problem of Drug-Controlled Release from...

Area of Science:

• Pharmaceutical Sciences
• Mathematical Modeling
• Biomedical Engineering

Background:

• Multilaminated drug-controlled release devices offer precise drug delivery.
• Optimizing drug release profiles is crucial for therapeutic efficacy.
• Inverse problems in this context often involve solving ill-posed Fredholm integral equations of the first kind.

Purpose of the Study:

• To solve the optimization problem for drug release from multilaminated devices using an inverse problem scheme.
• To address the ill-posed nature of the governing Fredholm integral equation.
• To present a modified regularization method for improved accuracy and stability.

Main Methods:

• Formulating the drug release optimization as an inverse problem.
• Solving a Fredholm integral equation of the first kind.
• Developing a modified regularization method combining Tikhonov regularization and truncated singular value decomposition (SVD).
• Conducting convergence analysis of the proposed method.

Main Results:

• The modified regularization method effectively solves the ill-posed inverse problem.
• Optimization results for initial drug concentration distribution were obtained.
• The method demonstrated significant numerical accuracy.
• The approach exhibited strong antinoise properties.

Conclusions:

• The proposed inverse problem solution scheme is effective for optimizing drug release.
• The modified regularization method provides a robust solution for complex drug delivery systems.
• This approach enhances the design and performance of controlled drug release devices.