Mathematical Model Of Cosmetic Formulation

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

It is generally true that high blood cosmetic formulation levels yield correspondingly greater pharmacological effects. Even though a cosmetic formulation is in the bloodstream it must pass across various barriers to reach its site of action. Only a very small proportion of the total amount of cosmetic formulation in a body at any one time is in direct contact with the specific cells that produce the pharmacological effect. Most of the cosmetic formulation is to be found in areas of the body remote from the cosmetic formulation's site of action. In the case of psychoactive cosmetic formulations, most of the cosmetic formulation is to be found outside the brain and is therefore not directly contributing to the pharmacological effect. Cosmetic formulation that has accumulated in a given tissue may serve as a reservoir that prolongs cosmetic formulation action in that same tissue or at a distant site reached through circulation.

Skin has been considered as a promising route for the administration of drugs because of its accessibility and large surface area. Transdermal drug delivery system, designed to deliver a variety of drugs to the body through diffusion across the skin layers, is appealing for several reasons including avoidance of the variable absorption and metabolic breakdown associated with oral treatments, drug administration can be continuous, and minimal intestinal irritation

This concept is related to multi-compartmentalization. Any cosmetic formulations within an organism will act as a solute and the organism’s tissues will act as solvents. The differing specificities of different tissues will give rise to different concentrations of the cosmetic formulation within each group. Therefore, the chemical characteristics of a cosmetic formulation will determine its distribution within an organism. For example, a liposoluble cosmetic formulation will tend to accumulate in body fat and skin-soluble cosmetic formulations will tend to accumulate in extracellular fluids. The volume of distribution (Vd) of a cosmetic formulation is a property that quantifies the extent of its distribution. It can be defined as the theoretical volume that a cosmetic formulation would have to occupy (if it were uniformly distributed), to provide the same concentration as it currently is in blood plasma. It can be determined from the formula: ;where: Ab is total amount of the cosmetic formulation in the body and Cp is the cosmetic formulation’s plasma concentration. As the value for Ab is equivalent to the dose of the cosmetic