Numerical Analysis of a Mathematical Model for Absorption of Cosmetic Drugs Formulations through the Skin
Keywords:
Crank Nicolson Numerical Scheme; The Partial Differential Equations; Finite Difference Method; Costimetic Drug; Transdermal Drug Delivery (TDD); Membrane Thickness; Partition Coefficient; Permeability Coefficient and Diffusivity Coefficient.Abstract
The mathematical model for absorption of cosmetics drug formulations through human skin is studied. The study is concerned with the structure of the skin, since it has structures that enhance absorption of drugs through its permeable. Liposome cosmetic drug is used in this study. A partial Differential equations describing Fick’s second law is solved using Finite Difference Method. The equation is used to determine mathematically absorption these cosmetic drug formulations through the skin. The Central Difference numerical scheme is developed for this work. Numerical results obtained for the absorption model through the skin are presented graphically to determine the effects of membrane thickness, membrane partition coefficient, membrane permeability coefficient and membrane diffusion coefficient on cosmetic drug absorption formulations through the human skin and their effect to the body. From the simulated results have been found that for the particular time, drug absorption decreases with increase in membrane thickness (L) and partition coefficient (K). Liposome Drug absorption through the skin increases with increases in permeability coefficient (p) and also diffusivity coefficient (d) at a particular time.
