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ORIGINAL PAPER
Fractal Model of Transdermal Drug Delivery
1
University of Zielona Góra, Faculty of Mechanical Engineering, ul. Szafrana 4, 65-516, Zielona Góra, Poland
2
University Hospital of Zielona Góra, Oncology Department, ul. Zyty 26, 65-046, Zielona Góra, Poland
Online publication date: 2018-11-21
Publication date: 2018-11-01
International Journal of Applied Mechanics and Engineering 2018;23(4):989-1004
KEYWORDS
ABSTRACT
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.
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