J. Biomedical Science and Engineering, 2010, 3, 367-374 JBiSE
doi:10.4236/jbise.2010.34051 Published Online April 2010 (http://www.SciRP.org/journal/jbise/).
Published Online April 2010 in SciRes. http://www.scirp.org/journal/jbise
Transdermal drug delivery models
Grantham K. H. Pang, Da-Peng Qiao
Department of Electrical and Electronic Engineering, University of Hong Kong, Hong Kong, China.
Received 12 January 2010; revised 25 January 2010; accepted 9 February 2010.
ABSTRACT
In this paper, a preliminary study based on the different
models of the skin impedance is carried out. The
purpose is to examine the drug delivery method
through iontophoresis, which relies on active trans-
portation of the charged medication agent within an
electric field. It is a kind of transdermal drug delivery
method, and hence the method has to handle the
variability in skin characteristics of a patient. This
paper carries out a simulation study based on three
different skin impedance models.
Keywords: Target Drug Delivery; Biomedical Engineering;
Skin Impedance; Iontophoresis
1. INTRODUCTION
Nowadays, as opposed to the traditional oral intake and
hypodermal injection, drug delivery to a patient can be
carried out in many different ways. Transdermal drug
delivery releases the medicament into the patient’s body
via the skin. There are various methods for transdermal
drug delivery and they have been developed based on
various principles. The developed methods could be
based on diffusion, absorption, thermal energy, radio
frequency energy, ultrasound, electrostatic force (elec-
trophoresis) or electric field (iontophoresis). These are
non-invasive methods, and recent developments also
include transdermal skin patch that is placed on the skin
to deliver a specific dose of medication through the skin,
and then into the blood stream of the patient. The main
advantage of a transdermal drug delivery is that it provides
a controlled release of the medicament without serious
pain to the patient.
However, all transdermal drug delivery methods have
to deal with the complicated properties of the patient’
skin, which is a very effective barrier, and its character-
istics can vary a lot from one person to another. It is a
natural barrier to foreign chemicals and biological agents.
Methods that are based on the use of microneedles [1-3]
have also been developed. These microneedles would
physically puncture the skin but for less than 1 mm and
deliver the drug without piercing blood vessels or dam-
aging nerves, that are typically around 1 mm under the
skin surface. The mechanical stability and the punc-
ture behaviour of microneedles have been investigated
experimentally [3]. In this paper, several electrical models
for skin impedance are investigated and simulations
have been carried out for a comparative study of the
parameters for drug delivery through iontophoresis [4,5].
2. METHOD AND ANALYSIS
2.1. Introduction
Research has found that skin impedance can be modeled
by typical RC (resistor-capacitor) circuits, without the
need of any inductive component [6-9]. Hence, it is gen-
erally agreed that the skin impedance is made up of
some amount of resistance and some form of capacitance.
Different models of RC circuits can be developed to
simulate current responses in actual skin.
2.2. Model A
An early skin impedance model is given in [7] and it is
shown in Figure 1. The model is made up of a capacitor
C in parallel with the resistance R1. R1 is modeling the
resistance of the stratum corneum, which is the top layer
of the epidermis. C represents the capacitance of the skin.
The C-R1 parallel combination is in series with another
resistance R2 which represents the resistance of the
deeper tissues within the epidermis. Example of value
for R1 would range from around 100 Ω to 5000 kΩ cm2,
while R2 would range from around 0.1 Ω to 1.0 kΩ cm2.
Figure 1. Skin impedance Model A.

G. K. H. Pang et al. / J. Biomedical Science and Engineering 3 (2010) 367-374 368
This model is simple and can serve as an initial repre-
sentation to the skin characteristics. However, a more
complete representation is given in the next subsection.
2.3. Model B
Another model can also be found in [8] by Tregear
which is consisted of multiple parallel RC circuits in
series. This is designed to model the varying capacitance
and resistance of the epidermal skin layers at different
depths of the skin. This model is shown in Figure 2 be-
low. As mentioned in [5], this model represents the de-
creasing values of capacitance and resistance as individ-
ual layers of the stratum corneum are removed in ex-
periments. The experimental result was important as it
allows for the development of a more precise model of
the skin impedance. Also, it has shown that the stratum
corneum accounts for the major portion of the skin im-
pedance in the skin.
2.4. Model C
Lykken [9] has proposed another model of skin imped-
ance as shown in Figure 3. The model consists of sev-
eral parallel paths, and each path is made up of several
RC circuits, with each circuit representing a different
layer of the skin. Figure 3 provides a more distributed
nature when modeling the skin impedance, and can po-
tentially provide a more accurate model.
Figure 2. Skin impedance Model B.
Figure 3. Skin impedance Model C.
3. RESULTS AND SIMULATION
In this section, simulations based on the three skin
impedance models discussed in the previous section
are presented. In these simulations, a voltage is ap-
plied at time 0.1 second and it varies linearly to 5 V at
time 0.5 second.
3.1. Simulation Based on Model A
Several simulations have been carried out to examine the
characteristics of the responses that may be obtained
based on different parameter values. For the purpose of
simulation, R1 and R2 have been assigned a value of
100 kΩ cm2 and three different values of the capacitor
have been used. Below are the results from the simulation:
It can be seen from the simulation that as the voltage
is increased from 0.1 second to 0.5 second, the current
passes through the capacitor C of Model A. At 0.5 second,
the applied voltage has already reached the final value,
and the current passes through R1 and R2.
For all the three simulations, the final steady-state
current depends on the value of the two resistors. As
shown in Figures 4 to 6, the value of the capacitor can
have considerable effect on the shape of the response.
3.2. Simulation Based on Model B
In the first simulation of Model B, we will examine the re-
sponse from Level 1. The capacitance value is 0.1 μF cm2.
Figure 8 gives the current for Model B having only
three sections (Level 1). This would model after three
epidermal skin layers at different depths of the skin.

G. K. H. Pang et al. / J. Biomedical Science and Engineering 3 (2010) 367-374 369
Figure 9 gives the current for Model B having six
sections (Level 2). More sections (or skin layers) can be
included for further study, but in this paper, we show the
simulations of only Level 1 and 2. As shown in Figures
8 and 10, the current can have very different response at
different point of the circuit model. In both cases, the
current would settle down to its steady-state level very
quickly after the voltage has been steady at 0.5 second.
Figure 4. Model A with capacitor value 1 μF cm2.
Figure 5. Model A with capacitor value 10 μF cm2.

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Figure 6. Model A with capacitor value 100 μF cm2.
Figure 7. Level 1 of Model B.
Figure 8. Model B level 1 with capacitor value 0.1 μF cm2.

G. K. H. Pang et al. / J. Biomedical Science and Engineering 3 (2010) 367-374 371
Figure 9. Level 2 of Model B.
Figure 10. Model B level 2 with capacitor value 0.1 μF cm2.
3.3. Simulation Based on Model C
In Figure 11, Model C with three parallel paths is shown.
Each path is consisted of three sub-sections.
Figures 12 and 15 are similar in shape but differ in its
vertical scale. Hence, although these two results are
based on different circuit models (3 sub-section and 6
sub-section model), similar response shapes are obtained
with the use of different capacitor values. The vertical
scales can be aligned with a careful choice of the resistor
values.
4. CONCLUSIONS
The three-element circuit of Model A is a very simple
model of the skin impedance. Considering the different
characteristics to the different layer of the epidermis, the
model seems not too accurate in its representation. The
Model B by Tregear captures the effects of capacitance
for the different layers of the epidermis. However, it is
not clear how many stages should best represent the skin
Figure 11. Model C with three parallel paths, each with three
sub-sections.

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Figure 12. Simulation result of Model C with three parallel paths, each with three sub-sections, with ca-
pacitor value 100 μF cm2, R1 = 1000 Ω cm2, R2 = 100 Ω cm2.
Figure 13. Model C with three parallel paths, each with six sub-sections.

G. K. H. Pang et al. / J. Biomedical Science and Engineering 3 (2010) 367-374 373
Figure 14. Simulation result of Model C with three parallel paths, each with six sub-sections, with
capacitor value 10 μF cm2, R1 = 1000 Ω cm2, R2 = 100 Ω cm2.
Figure 15. Simulation result of Model C with three parallel paths, each with six sub-sections, with
capacitor value 100 μF cm2, R1 = 1000 Ω cm2, R2 = 100 Ω cm2.
impedance for a certain depth of the epidermis. The
Model C by Lykken has added another resistance in
between the different stage, which is used to represent
deep tissue resistance. This would provide a more
complete model to the skin impedance. Yet, the great
variability of the parameters in the model exists and
experimentally study is needed for a more complete
understanding of the impedance characteristics of the

G. K. H. Pang et al. / J. Biomedical Science and Engineering 3 (2010) 367-374 374
skin.
5. ACKNOWLEDGEMENTS
This research is supported by a Small Project Funding grant (10400021)
by the Committee on Research and Conference Grants of The University
of Hong Kong.
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