Download Establishing an Electrical Equivalent Circuit of the Human Skin

1st International Conference on Advancements of Medicine and Health Care through Technology, MediTech2007,
27-29th September, 2007, Cluj-Napoca, ROMANIA
Establishing an Electrical Equivalent Circuit of the
Human Skin Using Virtual Instrumentation
Rodica Holonec, Marius Nicolae Birlea, Florin Dragan, Sinziana Iulia Birlea
Abstract — Human skin has electrical properties. We studied the electrical properties of human skin by injecting a pulsing current
and measuring the resulted voltage. The form of the voltage obtained so has been compared to the form of an electric circuit that we
supposes equivalent to that of human skin. We could determine so the values of the main components of human skin (Rs, Rp, C). The
current source and the electrodes used were made in laboratory and the measurements were done with the help of Lab VIEW and of
the data acquisition board PCI – 6023E.
Keywords: Human skin, Electrical components, Simulation, Data acquisition, LabVIEW,
Typical values of the relative conductivity and
permittivity of human skin are given in Table 1. Only a
limited number of studies were done for frequencies
under 100 kHz and there are considerable discrepancies
between the values reported by different investigators [2]
[9]. These factors are an indicator of the difficulty in
realizing the measurements of the electrical properties invivo.
1. INTRODUCTION
Electrical stimulation of human skin is a non-invasive
procedure, with minimum risks and side effects. Its
clinical applications are multiple: muscular stimulation,
pain treatment, introduction of medicines under skin,
bioelectric analysis of impedance and others.
Electrical properties of biological tissues are a field of
interests for researchers since many years ago. Galvani’s
experiment in 17th century is considered to be also the
moment of the first observation of a bioelectric
phenomenon [6]. Two different metals in contact with the
muscle of a frog leg provoke the stimulation of that
muscle due to the electric current generated. Since this
first discovery, the origin of bioelectric potentials and the
electrical properties of the biologic tissues were
investigated in detail by many researchers [8].
Human body may be considered as a volume conductor
composed by tissues with different electrical properties,
which are distributed inside this volume. In contrast to
the metallic conductors, the conduction inside biological
tissues is due to the movement of ions and not of
electrons [7]. In the presence of an electric field a
conduction current Ic appears due to the movement of the
mobile ions in that biological background. This current is
related to the content of ions and their mobility inside the
tissue, fact expressed by the conductivity of that tissue σ.
The pair tasks linked (electric dipoles) inside the tissue
give birth to some dielectric complex properties, so the
displacement current Id appears and it contributes to the
description of the variation in time of the electric
behavior of the tissue [1].
Table 1. Typical values of the relative conductivity and
permittivity of human skin
Tissue
Skin conductivity
Skin –
relative
permittivity
1kHz
7·10
-4
4·104
10kHz
4·10
-3
3·104
Frequencies
100kHz
1MHz
6·10
-2
2·104
10MHz
-1
4·10-1
2·103
2·102
3·10
When measurements of the electrical properties of the
tissues are done, it is important that the tissues respect a
linear characteristic in relation to an intensity of the
applied field. Pething [10] sustained that most of the
dielectrics have a linear behavior up to the intensity of the
applied field of 105 Vm-1. Although the intensity of the
field along the membrane of biologic cells may surpass
107 Vm-1 and there are proofs that the membrane of the
neurons has a nonlinear behavior. The supposal of the
linear behavior of the tissues is although maybe correct
because the insignificant non-linearity occurs at
frequencies over 1MHz [1][9].
Until now it is proved the existence of a resistive
component and a capacitive one in the case of human
skin, the question arising is which is the value of each of
those components.
The purpose of the present work is to determine the value
of the components of the electric circuit equivalent of
human skin using techniques of virtual instrumentation.
Rodica Holonec is with the Technical University of Cluj-Napoca,
Romania, Electrical Measurements Department, phone: +40-264-599896; e-mail: [email protected].
Marius Nicolae Birlea is with the Thechnical University of ClujNapoca, Romania, Physics Department, phone: +40-264-401-260; email: [email protected]
Florin Dragan is with the Technical University of Cluj-Napoca ,
Romania, Electrical Measurement Department, phone: +40-264-599896, e-mail: [email protected]
Sinziana Iulia Birlea is with the Thechnical University of ClujNapoca,
Romania,
Medical
Engineering;
e-mail:
[email protected]
197
1st International Conference on Advancements of Medicine and Health Care through Technology, MediTech2007,
27-29th September, 2007, Cluj-Napoca, ROMANIA
t ∈ [0 ,T − 20 ÷ 200 μs ]
⎧0 mA,
Is = ⎨
⎩0.1 ÷ 10 mA, t ∈ [T − 20 ÷ 200 μs ,T ]
2. THE EQUIVALENT ELECTRICAL CIRCUIT OF HUMAN
SKIN
(1)
T = 10 ÷ 20 ms + 20 ÷ 200 μs
Figure 1. Equivalent electric circuit of human skin
Figure 4. Signal generated by the source of pulsing current
We supposed that human skin has as equivalent electric
circuit the circuit in figure 1. The three essential
components of the equivalent electric circuit of human
skin are: the serial resistance Rs, the parallel resistance
Rp, and the capacitor C. With the help of the current
source Is we inject a pulsing current then we measure the
voltage U on the skin surface. Depending on the voltage
values obtained we were able to determine the value of
the three components.
The acquisition board PCI-6023E allows the signal to be
taken over and processed by means of graphic
programming language Lab VIEW.
4. ACKNOWLEDGMENTS RESULTS AND DISCUSSIONS
Consequently to the measurements done we obtained the
form of voltage that occurs on the surface of human skin
in the moment of injecting the current Is. This form of
voltage was then compared to that obtained consequently
to the simulation of an equivalent electric circuit.
In order to be able to simulate the equivalent electric
circuit of human skin (Figure 1) we had to calculate
previously from a physical point of view the equation of
voltage that results at the ends of this circuit. We present
bellow this calculation.
Starting from the fact that the voltages on the resistance
Rp and on the capacitor C are equal (Kirchhoff’s 2nd law)
and the current Is equals the sum of the currents Ip and Ic
(Kirchhoff’s 1st law) the followings may be written:
⎧
I ⋅ dt
⎧⎪U p = U c
⎪I p ⋅ R p = ∫ c
⇔⎨
(2)
⎨
C
⎪⎩ I s = I p + I c
⎪I = I − I
s
c
⎩ p
From the system results:
(I s − I c ) ⋅ R p = 1 ⋅ ∫ I c ⋅ dt
(3)
C
Or:
3. EXPERIMENTAL METHOD OF TESTING THE
EQUIVALENT ELECTRIC CIRCUIT OF THE HUMAN SKIN
Figure 2. Experimental method of testing the equivalent
electric circuit
As shown in Figure 2, the experimental method used
implied an adjustable source of pulsing current; the
current generated by it was then injected in the skin by
means of electrodes and from those electrodes the voltage
information was collected by the acquisition board PCI6023E, then the information was processed using Lab
VIEW environment.
The source of pulsing current and the electrodes (Figure
3) are realized in laboratory. The signal generated by the
source is represented in Figure 4., its amplitude and
frequency can be controlled by means of some
potentiometers.
∫
R p ⋅ C ⋅ I s − R p ⋅ C ⋅ I c = I c ⋅ dt
(4)
By taking into account that the electric charge on the
capacitor is q = ∫ I c ⋅ dt , we have:
Rp ⋅ C ⋅ I s − Rp ⋅ C ⋅
dq
=q
dt
(5)
Or:
dq
− Rp ⋅ C ⋅ Is = 0
(6)
dt
This relation can be rewritten by taking into account the
time constant τ = R p ⋅ C :
q + Rp ⋅ C ⋅
Figure 3. Source of pulsing current together with the
electrodes put on human skin
τ⋅
198
dq
= τ ⋅ Is − q
dt
(7)
1st International Conference on Advancements of Medicine and Health Care through Technology, MediTech2007,
27-29th September, 2007, Cluj-Napoca, ROMANIA
By separating the variables we have:
τ ⋅ dq
= dt
τ ⋅ Is − q
Rearranging:
dq
dt
=
τ ⋅ Is − q τ
dt
dq
=
τ τ ⋅ Is − q
By integrating:
t
τ
t'
3. At the moment when the current
drop on the serial resistance becomes zero and it remains
only the last maximum value of the voltage on the
capacitor
4. The capacitor starts to discharge according to the
equation
(8)
(9)
U disch arg e = U c . max .ch arg e ⋅ e
(10)
= − ln(τ ⋅ I s − q ) 0
q'
I s is zero the voltage
−
t
τ
(22)
The form of the voltage that appears on the surface of the
human skin at the moment of injecting the current Is is
represented in Figure 5.
(11)
0
= ln(τ ⋅ I s ) − ln(τ ⋅ I s − q' ) = − ln
t'
τ
τ ⋅ I s − q'
τ ⋅ Is
(12)
If q0 = τ ⋅ I s we have:
q0 − q
q0
By integrating:
−
e
−
t
τ
= ln
t
τ
= 1−
(13)
t
t
⎛
−
−
q
q
⇒
= 1 − e τ ⇒ q = q0 ⎜ 1 − e τ
⎜
q0
q0
⎝
⎞
⎟
⎟
⎠
(14)
Figure 5. The shape of voltage obtained on the equivalent
electrical circuit of the human skin
The potential of the capacitor is defined as the current
through the capacitor:
q
Uc =
(15)
C
The current through the capacitor is
t
t
−
dq q0 −τ
(16)
Ic =
=
⋅e = Is ⋅e τ
τ
dt
We find the current through the resistor Rp as being
t
⎛
− ⎞
I p = I s − I c = I s ⋅ ⎜1 − e τ ⎟
(17)
⎜
⎟
⎝
⎠
The voltage on the surface of the skin is the sum of the
voltages on the resistances Rs and Rp:
t
⎛
− ⎞
U ch arg ing (t ) = I s ⋅ Rs + I s ⋅ R p ⋅ ⎜ 1 − e τ ⎟
(18)
⎜
⎟
⎝
⎠
When interrupting the current on the surface of the skins
remains only the voltage on the capacitor that discharges
on the resistance R p following the law:
U disch arg ing (t ) = U c . max .ch arg ing ⋅ e
−
t
τ
By using the previous equations we created a virtual
instrument using the programming environment
LabVIEW which simulates the equivalent electrical
circuit of the human skin. The shape of the voltage curve
can be observed on the front panel of the virtual
instrument (Figure 6).
(19)
Consequently to the calculus done we reach to the
conclusion that the chronological line of events from the
electric point of view at current injection is the following:
1. At the moment of starting the injection of current Is,
the first voltage drop occurs:
U = I s ⋅ Rs ,
(20)
2. Starts the gradually charging of the capacitor and so to
the initial voltage is added the voltage on the capacitor in
continuous growing, phenomenon described by the
equation 21:
t
⎛
− ⎞
(21)
U ch arg hing = I s ⋅ Rs + I s ⋅ R p ⋅ ⎜ 1 − e τ ⎟ ,
⎜
⎟
⎝
⎠
Figure 6. The front panel of the virtual instrument, which
simulates the equivalent circuit of the human skin, the shape
of the voltage obtained
Modifying within this virtual instrument the values of the
resistances Rs and Rp and of the capacitor C, in the
moment when the form of the resulted voltage respected
the same rules of increasing and decreasing as the form of
voltage measured directly on the human skin, at the same
injected current, we may state that we found the
approximate values of those parameters. The obtained
values are below (23).
199
1st International Conference on Advancements of Medicine and Health Care through Technology, MediTech2007,
27-29th September, 2007, Cluj-Napoca, ROMANIA
R s = 1kΩ = 1000 Ω
R p = 30 kΩ = 30000 Ω
6. REFERENCES
(23)
[1] Brown B.H., Tissue Impedance Methods, Guildford: Surrey,
University Press, 1983
[2] Gabriel C., Gabriel. S., Courthout E. The Dielectric
Properties of Biological Tissues: I. Literature Survey Phis.
Med. Biol 41, 1996
[3] Gabriel. S., Lau R. W., Gabriel C. The Dielectric Properties
of Biological Tissues: II. Measurements in the Frequency Range
10Hz to 20GHz, Phis. Med. Biol 4, 1996
[4] Hutte, Manualul inginerului, Editura Tehnica, Bucuresti,
1989
[5] Metherall P., Three Dimensional Electrical Impedance
Tomography of the Human Thorax, Department of Medical
Phisics and Clinical Engineering, Univarsity of Sheffield,
United Kingdom, 1998
[6] Offner F.F., Bioelectric potentials – Their Source,
Recording and Significance, IEEE transactions on biomedical
engineering, vol 31, no 12, pag 863-868, 1985
[7] Plonsey R., Bioelectric Phenomena, McGraw-Hill, New
York, 1969
[8] Gedees L.A. and Baker L.E., The Specific Resistance of
Biological Material – A compendium of Data for the
Biomedical Engineer and Physiologist, Medical and Biological
Engineering and Computing, Volume 5, Number 3 / May, pp
271–293, 1967
[9] Barber D C and Brown B H Applied potential tomography
J. Phys. E: Sci. Instrum. 17 No 9 pp 723-733, 1984
[10] Pething R., Dielectric and electronic properties of
biological materials- John Wiley & Sons, Chichester, 1979
C = 200 nF = 0.0000002 F
In figure 7 are presented in comparison the two voltages,
that of the equivalent electric circuit and that measured
directly on the human skin.
Figure 7. Comparative view of the shape of the voltage on
the equivalent circuit and on the human skin
The block diagram of the virtual instrument by means of
which the voltage was measured directly on the human
skin is displayed in Figure 8
Figure 8. The block diagram of the virtual instrument used
to measure the voltage on the human skin
5. CONCLUSIONS
In this paper we established the three major electrical
components of the equivalent electrical circuit of the
human skin. We put then the question „What is the use of
the equivalent electrical circuit of the human skin and its
components?” The answer is simple. Already there are
multiple devices, which perform measurements on the
human skin or inject current through it for different
purposes. All of these devices are influenced by the
electrical behavior of the human skin, and in their turn
they influence the electrical behavior of the skin. By
knowing the electrical behavior of the human skin,
measurements performed on it can become more and
more accurate, and electrical stimulation applied to ore
through the skin can be controlled a lot better, in the aim
of avoiding injury to the tissue and obtaining better
results. Some of the most commonly known applications
which could use the data we have obtained are tissue
classification, tissue monitoring, electrical impedance
monitoring etc.
200