Various skin impedance models based on physiological stratification

Abstract

Transdermal drug delivery is a non-invasive method of drug administration. However, to achieve this, the drug has to pass through the complicated structure of the skin. The complex structure of skin can be modelled by an electrical equivalent circuit to calculate its impedance. In this work, the transfer function of three electrical models of the human skin (Montague, Tregear and Lykken Model) based on physiological stratification are analysed. Sensitivity analysis of these models is carried out to consider the extent to which changes in system parameters (different types of R and C as described by different models) affect the behaviour of the model. Techniques like normal of derivative and Hausdorff Distance is also used to study and understand the different curves. Comparison is also made with CPE based model. As Montague Model is the most widely used model, Tregear and Lykken Model are compared with it. It can be commented that out of the above observations Tregear Model at Level 3 can be used for establishing the electrical equivalent of human skin due to its simplicity. However, fractional ordered CPE models provide a good approximation. Future prospect lies in developing a model that characterize both biological properties and physiological stratification.

Fig. 1

Structure of the dermis and epidermis. Figure adapted from Goldsmith [13]

Fig. 2

Penetration pathways in skin. Figure adapted from Alexander and Ajazuddin [24]

Fig. 3

Montague electrical model for skin impedance

Fig. 4

Skin impedance model provided by Tregear [36]

Fig. 5

Skin impedance model provided by Lykken [37]

Fig. 6

Three‐element model for skin impedance

Fig. 7

Sensitivity analysis of Montague model

Fig. 8

Sensitivity analysis of Tregear model

Fig. 9

Combined impedance plot of impedance spectra as obtained from the literature

Fig. 10

Combined impedance plot of impedance spectra and Montague circuit parameters

Fig. 11

Impedance plot of Montague model for varying values of $C_{SC}$

Fig. 12

Impedance plot of Montague model for varying values of $R_{SC}$

Fig. 13

Impedance plot of Montague model for varying values of $R_S$

Fig. 14

Impedance plot of Tregear model for different levels

Fig. 15

Normal of derivative of Tregear model for different levels

Fig. 16

Hausdorff distance between different levels of Tregear model

Fig. 17

Impedance plot of Lykken model for varying numbers of sections and parallel paths

Fig. 18

Normal of derivative between different impedance plots of Lykken model

Fig. 19

Hausdorff distance between different impedance plots of Lykken model

Fig. 20

Impedance plot of three‐element model for varying values of $\alpha$

Fig. 21

Normal of derivative between different impedance plots of varying $\alpha$ value

Fig. 22

Hausdorff distance between different impedance plots of varying $\alpha$ value

Fig. 23

Comparative impedance plot of Montague model and Tregear model

Fig. 24

Comparative impedance plot of Montague model and Lykken model

Fig. 25

Normal of derivative of Tregear and Lykken model impedance plot from Montague model

Fig. 26

Hausdorff distance calculator of Tregear and Lykken model impedance plot from Montague model

Fig. 27

Comparative impedance plot of Montague model and three‐element model

Fig. 28

Normal of derivative of three‐element model impedance plot from Montague model

Fig. 29

Hausdorff distance calculator of three‐element model impedance plot from Montague model