Jñānābha‎, Vol. 51 (1) (2021), (219-231)



Archana Sharma¹ and V. P. Saxena²

¹Department of Mathematics, Government Nehru Postgraduate College Ashoknagar-473338, Madhya Pradesh, India

²Former Vice-Chancellor, Jiwaji University, Gwalior-474009, Madhya Pradesh, India

Email:archanaaryaman80@ gmail.com, dr.archanasharma@mp.gov.in; vinodpsaxena@ gmail.com

(Received : January 13, 2021; Revised : February 06, 2021; In final form : June 29, 2021)


Background: Transderrnal drug delivery is the platform of delivering a remedial substance to the body via skin. With the help of this delivery the patient obtain the required dose in a convenient way that does not disturb his or her normal activities. The distribution of drug through membrane from the reservoir to the objected site is multi directional phenomena. Therefore the study of drug diffusion in the skin in two dimensions is an important issue to address.

Aim: The present paper is an attempt to set up a mathematical model for the distribution of drugs in two dimensional steady state cases. It is assumed that the drug is administered internally through reservoir. Dermal region under consideration is alienated into three parts i.e. outermost layers that are epidermis, middle layers dermis and innermost layers subcutaneous tissues for the study.

Methods: The finite element method with triangular element has been used with appropriate boundary conditions. The solution of governing partial differential equation for two-dimensional steady state case is obtained through this technique.

Conclusion: The effect of various parameters on concentration profile can be found in this study. It can be found that increasing the diffusivity increases the drug concentration and increasing the absorption coefficient decreases the drug concentration. These changes can be seen with the help of the graphs which were drawn by using MATLAB software.

2010 Mathematics Subject Classifications: 65N22, 65N30.

Keywords and phrases: Diffusion in two dimensional region, drug delivery through skin, finite element method and mathematical model.

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