Variational finite element method to study the absorption rate of drug at various compartments through transdermal drug delivery system

Peer review under responsibility of Alexandria University Faculty of Medicine.

Available online 25 November 2014

Abstract

Background

The delivery of drugs through dermal layers known as transdermal drug delivery is one of the important contributions in medical practice. It represents an alternative to oral drug delivery and is poised to provide a substitute to hypodermic injections too. The diffusion of drug from the source to the target site is therefore an important issue to address.

Aim

This paper is an attempt to establish a mathematical model for the diffusion of drugs through the transdermal drug delivery system. The model identifies the pattern of drug diffusion in human body and its effective absorption rates at various compartments of skin and sub-cutaneous tissues.

Methods

The finite element method has been used to obtain the solution of the mass diffusion equation with appropriate boundary conditions. The tissue absorption rate of drug has been taken as the decreasing function of drug concentration from the skin surface towards the target site. The concentration at nodal points has been calculated which in turn determines the drug absorption at various layers.

Conclusion

The drug concentration at the nodal points of different dermal layers has been computed and the graphs were plotted between drug concentration and thickness of dermal layers using MATLAB software. It has been observed that due to dense network of connective tissues in dermal and sub-dermal parts, the drug absorption is maximum as compared to cutaneous tissues.

Keywords:

• Transdermal drug delivery
• Diffusion equation
• Finite element method

Acknowledgements

The authors wish to thank the DST, Govt. of India for providing financial support under DST- INSPIRE programme.

Notes

Peer review under responsibility of Alexandria University Faculty of Medicine.

Available online 25 November 2014

† A physical process in which ion flow diffusively in a medium driven by an applied electric field.

‡ Let $F(s)\text{and}G(s)$ be two polynomials in s where the degree of $F(s)$ is lower than that of $G(s)$ and if $G(s)$ has n distinct roots ${\alpha }_i(i=1\text{,}2\text{,}\dots \text{,}n)$, then${\mathcal{L}}^{-1}\left[\frac{F(s)}{G(s)}\text{;}t\right]={\displaystyle \sum _{i=1}^n}\frac{F({\alpha }_i)}{G^{\prime }({\alpha }_i)}{e}^{{\alpha }_{i}t}$