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A unified mathematical model for diffusion from drug-polymer composite tablets

J C Fu, C Hagemeir, D L Moyer

    Journal of Biomedical Materials Research
    |September 1, 1976
    PubMed
    Summary

    A new mathematical model estimates drug release rates from composite tablets. This unified, three-dimensional approach accurately predicts drug diffusion across various tablet shapes for sustained release applications.

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    Area of Science:

    • Pharmacokinetics and Drug Delivery
    • Materials Science and Engineering
    • Mathematical Modeling and Simulation

    Background:

    • Accurate estimation of drug release rates is crucial for designing effective sustained-release drug delivery systems.
    • Existing models may not adequately capture the complex diffusion dynamics in variously shaped drug-polymer composites.
    • Homogeneous distribution of drugs within polymer matrices presents unique challenges for predictive modeling.

    Purpose of the Study:

    • To derive and experimentally validate a unified mathematical model for drug release rate estimation.
    • To develop a comprehensive method applicable to a range of drug-polymer composite tablet geometries.
    • To compare model predictions with experimental drug diffusion data for specific drug-polymer systems.

    Main Methods:

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    • Utilized cylindrical coordinates to solve the diffusion equation in a three-dimensional system.
    • Developed a general solution for the fraction of drug released over time.
    • Applied the model to drug-polymer composite tablets with geometries varying from disks to rods.
    • Experimentally verified the model using pyrimethamine and hydrocortisone diffusion studies.

    Main Results:

    • The derived mathematical model accurately estimates drug release rates from composite tablets.
    • The model demonstrates applicability across a spectrum of tablet shapes, from disks to cylinders.
    • Calculated drug diffusion rates closely matched experimental data for pyrimethamine and hydrocortisone composites.
    • The three-dimensional approach provides a robust method for sustained-release tablet analysis.

    Conclusions:

    • The unified mathematical model offers a comprehensive tool for predicting drug release from composite tablets.
    • Cylindrical coordinates provide an effective framework for modeling three-dimensional diffusion in diverse tablet geometries.
    • Experimental validation confirms the model's reliability for sustained drug delivery applications.
    • This approach enhances the design and optimization of drug-polymer composite formulations.