Mathematical Modeling of Drug Release From Polymeric Devices- An Overview of Widely Used Models - Theory, Implementation and Rationale

Ritu Mehra Gilhotra, Vishv Priya Bhardwaj, Neeraj Gilhotra, D N Mishra

Abstract: Describing mode or mechanism of drug release from developed polymeric system, meant to delivery drug conventionally or in controlled manner, is executed by applying various mathematical models nowadays. The major advantages of these models are: (i) the elucidation of the underlying mass transport mechanisms; and (ii) the possibility to predict the effect of the device design parameters (e.g., shape, size and composition) on the resulting drug release rate. Various Simple empirical or semi-empirical models such as the classical Higuchi equation and the so-called power law, as well as more complex mechanistic theories that consider diffusion, swelling and dissolution processes simultaneously are applied in dosage form research to understand the mechanism and actual behavior drug polymer matrix in dissolution testing. In the present work, some frequently used models of drug release from polymeric devices are discussed.
Experimentation with new polymers and compositions of many polymers to make carrier matrices of polymers to sustain or prolong the drug release is highly practiced in dosage form research. One way of achieving this is by the incorporation of the drugs into polymers. Drug-polymer systems can not only prolong the release of a pharmacologic agent, but can also modulate the rate of release of the drug to be dependent on the vehicle itself rather than on the environmental conditions. High reproducibility of the release profiles can also be achieved by using a drug-polymer system. The advantages of a controlled delivery device can be appreciated further by comparing the idealized drug levels achieved by conventional drug formulations (tablets and injections) and those achieved from a polymeric controlled drug delivery system. The goal of a controlled release device is to maintain the concentration of the drug between these two levels for a prolonged period of time from a single dosage form. This would alleviate the need for repeated doses and cause fewer side effects. Controlled release drug delivery systems enhance the safety, efficacy, and reliability of drug administration. An ideal controlled drug delivery system (DDS) is the one which delivers the drug at a predetermined rate locally or systematically for a specified period of time.
An Overview of Drug Release Mechanisms and Patterns
The overall drug release mechanism may be affected by many factors such as polymer
Swelling, polymer erosion, drug dissolution / diffusion characteristics, drug distribution
In matrix, drug polymer ratio & system geometry (cylinder sphere so on) the following Phenomena are involved -

  1. At the beginning of process ; firstly water comes in the contact to the polymer & imbibed in to the matrix .To describe this process this process adequately ,it is imp. to consider :

    • The exact geometry of the device

    • In case of cylinders both axial and radial direction of the mass transport &

    • The significant dependence of the water diffusion coefficient on the matrix swelling ratio

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