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Fractal model of transdermal drug delivery

Walicka A., Iwanowska-Chomiak B.

International Journal of Applied Mechanics and Engineering

2018

Vol. 23, no. 4

989--1004

Skin, separating the vital organs of a human body, is a desirable route for drug delivery. However, the intact skin is normally permeable only for drug molecules with a low molecular weight. The stratum corneum (SC), being the outermost layer of the skin and the epidermis being the second – more permeable – layer of the skin, play an essential function in transdermal drug delivery. Physical and chemical methods of skin poration are used to enhance transdermal drug delivery. Each poration leads to an irregular system of pores which are connected with a system of micro-capillaries passing through the epidermis. Both the systems by their irregularity form a fractal porous matrix. Drugs administrated by this matrix can be either suspensions and solutions or creams and gels, therefore they have to be modelled as non-Newtonian fluids. To analyse the fluid flow through the porous matrix the model of the epidermis is assumed as gobbet-andmortar with the tortuous mortar of variable thickness and after transition from the mortar to the tube one considered classical and fractal capillary flows of selected non-Newtonian fluids. Fractal expressions for the flow rate, velocity and permeability of fluids flow in a porous matrix are derived based on the fractal properties of the epidermis and capillary model. Each parameter in the proposed expressions does not contain any empirical constant and has a clear physical meaning and the proposed fractal models relate the flow properties of considered fluids with the structural parameters of the epidermis as a porous medium. The presented analytical expressions will help understand some of the physical principles of transdermal drug delivery.

Estimation of epidermis and dermis thicknesses on the basis of skin surface temperature

Majchrzak E., Jasiński M.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

2006

Vol. 5, nr 1

124-133

Heat transfer in the skin tissue is treated as a multi-layer domain in which one can distinguish the epidermis, dermis and subcutaneous region is described by the system of Pennes equations and adequate boundary, initial and geometrical conditions. Many of the parameters used in the mathematical model are difficult to measure, e.g. epidermis or dermis thickness. In the paper the numerical algorithm of these geometrical parameters identification is presented in which the knowledge of skin surface temperature is assumed.