Modeling Bioimpedance Chapterbook

S.C. Mukhopadhyay et al. (Eds.): New Developments and Appl. in Sen. Tech., LNEE 83, pp. 169–189. springerlink.com © Springer-Verlag Berlin Heidelberg 2011

Physical and Electrical Modeling of Interdigitated Electrode Arrays for Bioimpedance

Spectroscopy

M. Ibrahim1, J. Claudel1, D. Kourtiche1, B. Assouar2, and M. Nadi1

1 Electronic Instrumentation Laboratory of Nancy, Nancy University, France

2 Institute Jean Lamour, Nancy University, France

Abstract. This paper concerns a theoretical and electrical modelling of interdigital sensor in a wide band frequency. A theoretical approach is proposed to optimize the use of the sensor for bioimpedance spectroscopy. CoventorWare® software was used to modelize in three dimensions the interdigital sensor system for measuring electrical impedance of biological medium. Complete system simulation by Finite element method (FEM) was used for sensor sensitivity optimization. The influence of geometric parameters (number of fingers, width of the electrodes, …), on the impedance spectroscopy of biological medium was studied.

A high level description of the sensor and the biological medium was also developed under VHDL-AMS with SystemVision® software from mentor graphics. The simulation results are compared with measurements obtained with a true interdigitated sensor illustrating a good correlation. This shows that even the theoretical model is simple, it remains very effective.

1 Introduction

Electrical impedance measurement has been demonstrated as a potential useful approach in biomedical applications. This method allows to determine the physiological status of ex vivo or living tissues as well as their electromagnetic characterization [1]. The changes induced by some pathologies could be associated with variations of essential tissue parameters such as the physical structure or the ionic composition that can be reflected as changes in the passive electrical properties. The range of applications derived from this technique is quite wide [2, rigaud et morucci].

Planar interdigitated electrode arrays have become more prominent as a sensor device due to the ongoing miniaturization of electrodes and the low cost of those systems [3]. An important advantage of these sensor devices is the simple and inexpensive mass-fabrication process and the ability to use these devices over a wide range of applications without significant changes in the sensor design [4-5]. Typically these sensors have been used for the detection of capacitance, dielectric constant and bulk conductivity in biological medium [6-7]. Basically, the structure consists on two

170 M. Ibrahim et al.

parallel coplanar electrodes whose design (width, gap between electrodes, length) is repeated periodically [8].

This paper, based on previous work [9], presents a new approach of physical and electrical modelling system of a biological sensor. The electrical and physical modelling of the Interdigital sensor and the medium was developped by using COVENTORWARE® and Systemvision (MENTORGRAPHICS®) sofware respectively.

Section two describes the correlation between design parameters and frequency behavior in coplanar impedance sensors. By developing total impedance equations and modeling equivalent circuits we propose a theoretical optimization of the geometrical parameters of the sensor. One objective was to get the optimal ratio between the width of the electrodes and the gap. The third section gives a description of the sensor and medium model with the finite element method FEM using CoventorWare® software. We studied the influence of the medium’s physical properties on the frequency sensor response. We simulated the influence of electrodes number and we found the number 16 as optimized for a cross section 1mm*1mm.

In the fourth section, we give a description of electrical model for IDT sensor with VHDL-AMS (SystemVision software®). This software provides an electrical approach that can be readily used in current electronic design flow to include distributed physics effects. VHDL-AMS language permits to simulate the sensor and medium. It allows fast simulations to validate a simplified model and to serve as a reference to power conditioning.

The sensor manufacturing is described in the fifth section. A test bench based on a measurement system composed by RCL meter connected with computer was built to test the sensor. Preliminary bioimpedance measurements were done on calibrated ionic solution of NaCl.

Section six concludes on the validity of models and presents the perspectives.

2 Theoretical Aspect

2.1 Description of Interdigital Sensors

Interdigital sensor is equivalent to a parallel plate capacitor (Figure 1) [10-11]. An electric field is created between the positive and negative electrodes (instantaneous polarity) shown on figure 1 (a) and (b) respectively. When a medium is placed on the sensor, the electric field across the medium under test is also shown on figure 1 (c). The dielectric properties of the material as well as the geometry of the material under test affect the capacitance and conductance between the two electrodes. The variation of the electric field can be used to determine the properties of the material depending on the application.

To use them in bioimpedance domain, a potential difference is applied between two electrodes and the electrical impedance between the electrodes is measured.

The electrodes of the interdigital sensor are coplanar, so the measured impedance will have a very low signal-to-noise ratio.

Physical and Electrical Modeling of Interdigitated Electrode Arrays 171

Fig. 1. Funtion principle of an Interdigital sensor.

The main dimensional characteristics parameters of such a pair of electrodes are (figure 2):

1. The number of digits N. 2. The length of digit L. 3. The digit width W. 4. The distance between a digits S.

Fig. 2. Interdigitated sensor structure and dimensional parameters

2.2 Equivalent Circuit Model

Figure 3.a gives the configuration of the planar structure when switched as an interdigitated impedance cell. When such a cell is immersed in an electrolyte, the simplified equivalent electrical circuit is represented by figure 3.b.

Fig. 3. (a) Configuration of interdigitated impedance cell and (b) its equivalent circuit


The electrical elements in the equivalent circuit modelize the physical phenomena that determine the total electrical impedance (Z) detected in the measurement cell (figure 3.a). Thus, the equivalent model elements could be expressed in terms of physical quantities.

The resistance RSol of the resistance is the sensing element and is related to the electrolyte conductivity σSol by the cell constant KCell [12]:

Sol

CellSol

σK

R = (1)

The cell constant KCell is equal to [13] :

( )( )

( )k²-1K

kK.

L1-N

2 KCell =

with ( ) ( )( ) dt 1

0 k²t²-1t²-1

1 kK ∫= and ⎟

⎠⎞

⎜⎝⎛

+=

WS

W.

2

πcos k

(2)

Where N is the number of fingers, S the finger spacing, W the finger width and L the finger length.

The function K(k) is the incomplete elliptic integral of the first kind [14]. So, the cell constant depends entirely on the geometry of the sensor.

The lead resistance RLead is the result of the series resistances of the connecting wires.

Direct capacitive coupling between the two electrodes is represented by the cell capacitance CCell given by:

Cell

Solr, 0.Cell

K

C

εε= (3)

with εr,sol ≈ εr,water = 80. One model element which is not drawn in figure 1.b is a capacitor representing the

direct capacitive coupling between the connecting wires. This capacitor comes in parallel with CCell and will therefore virtually increase the observed cell capacitance.

The impedances that explain the interface phenomena occurring at the electrode-electrolyte interfaces, are simplified to the double layer capacitances CDL. These are depending on the electrode material and the electrolyte solution but, for horizontal electrode surfaces, they can be approximated by:

SurfaceDL,SurfaceDL, DL C0.5.W.L.N. C0.5.A. C == (4)

where A is the electrode surface and CDL,Surface the characteristic of the double layer capacitance of the electrode-electrolyte system. One must notice that the factor 0.5 is the result of CDL determined by only half of the electrode surface A. The characteristic of the double layer capacitance CDL, Surface is supposed to be equal to the characteristic capacitance of the Stern layer for electrolytes having a quite high ionic strength. This characteristic capacitance of the Stern layer is approximated by CStern,

Surface = 10-20 μF/cm2 [15, 16].


Based on the equivalent circuit of figure 1.b, the total observed impedance can be expressed as

( )1 ZC.j.ω

Z 2R jωZ

1 Cell.

1Lead

++= (5)

Where

DLSol1

C.j.ω

2 R Z +=

2.3 Theoretical Optimization of the Sensor

Figure 4 shows a schematic graph of total impedance of equivalent circuit (Figure 3.b). There are three zones in the impedance spectrum, which correspond to the three kind of elements in equivalent circuit. The frequency dependent property of these zones can be analysed using the equivalent circuit mentioned above.

As shown in Figure 3.b, there are two parallel branches (CCell and CDL). When the frequency is not adequatly higher than fHi, the current cannot cross the middle of the dielectric capacitor. That is, the capacitor is inactive, and just acts as an open circuit. Then , the total impedance corresponds to the double layer capacitance and solution resistance in series. Although both CDL and RSol provide to the total impedance below fHi, each of them dominates at different frequencies.

Frequency, Hertz

Impe

danc

e, O

hm

Cdl CcellRsol

Fig. 4. Schematic diagram of total impedance–frequency plots

The CDL becomes essentially resistive at the frequency lower than fLow, and it contributes mainly to the total impedance value:

DL

SolDL

.C j.ω

.R.C jω 2 Z

+≈ (6)


and

DLSol

Lo

C R π.

1 f ≈ (7)

The impedance increases with the decrease in the frequency (double layer region). However, above fLow, double layer capacitance offers no impedance. This is

explained by the fact that only the resistance of the solution contributes to the impedance while below fHi the influence of CCell is not yet indicative, the total impedance is independent of the frequency (resistance of the solution zone). This results into a frequency band, restricted by fLo and fHi, in which the results (e.g. the conductivity) can be deduced from the observed impedance using:

( ) SolLead R 2R jωZ += (8)

To optimize the impedance cell leads to maximize the plateau width in the curve of figure 4.

When the frequency is higher than fHi, the current cross the middle of the dielectric capacitor instead of crossing the electrolyte solution resistance.

That is, the branch (CDL + RSol + CDL) is inactive, and the branch (CCell) is active. In this zone, the dielectric capacitance of the medium governs the total impedance, and the double layer capacitance and medium resistance could be neglected. Thus, the total impedance value is inversely proportional to the frequency:

1 .R.C j.ω

R Z

SolCell

Sol

+≈ (9)

and

l.C.R π2.

1 f

CelSolHi ≈ (10)

Or in terms of conductivity parameters:

CellSurfaceDL,

SolLo

K . C N. L. .W. 0.5.π f

σ≈ (11)

and

Solr,0

SolHi

. .2. f

σεεπ

≈ (12)

Note that the higher boundary frequency, fHi, is not dependent on the geometry, according to the theory, when the wiring capacitance is not present.

Obviously, maximising the width of the plateau can only be done by decreasing the lower boundary frequency. In order to make the lower boundary frequency (11) as low as possible, the geometrical term


W. L. N. KCell (N, L, S, W) (13)

should be maximised. When using a square structure of L*L, one variable can be eliminated since

L*L : L = N. (W+S) - S

With L in mm and S in microns

L + S ≈ L

Finaly

L = N. (W+S) (14)

However, it is more illustrative to introduce a factor a = S/W. Using the substitutions:

( )1 a

1.

N

L W

+= and ( )1 a

a.

N

L S

+= (15)

Which are based on equation (15) together with the ratio a, expression (13) becomes:

( ) ( )( )

( )k² - 1K

kK .

1 a

1 .

1 - N

2.L

+ = X (N, L) * Y(a) (16)

Where

( ) ( )1 - N

2.LL N,X = and ( ) ( )

( )( )k² - 1K

kK .

1 a

1 aY

+=

The function K has the same meaning as it had in equation (2). This optimisation expression, which has to be maximised in order to minimise flo,

can be split into two parts. The first is the factor X (N, L), showing that the cell size L*L must be as large as possible while the number of fingers must be reduced. Since there is no maximum in the desired cell size, with respect to the optimisation of flo,

the value L can be chosen arbitrarily. A cell size of about 1*1 mm² will be used in the modeling. The optimal number of fingers N has a minimum for N = 2 since this is the lowest possible number of fingers. On the other side, the sensitivity of the impedance measurement depends on the number of fingers. Then, the modelling allows us to study the influence of the number of fingers on the impedance measurement. The highest the number of fingers, the highest the sensitivity.

The factor X (N, L) is related to the sum W+S according to equation (14), the second factor in expression (16) has only the ratio W/S = a as a parameter. In figure 5 this factor is plotted as a function of a, a varying from 0 to 10.

For a = 1, the finger width is equal to the gap between them. It can be seen that this is not the optimal ratio, for a = 0.66 the optimisation function has a maximum which means that the finger width should be approximately 1.5 the gap width W = 3S/2. This maximum for the function denoted in the figure as f (a) is equal to 0.66.


Therefore, when designing a square structure, the design rule, based on the maximum frequency range criterion becomes according to equation (14): L = (2.5N-1).S. When the minimum number of fingers, N = 2, is also taken into account, the design rule becomes : L = 5S.

0 1 2 3 4 5 6 7 8 9 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

X: 0.66Y: 0.51

a

Y(a

)

Y(a)

Fig. 5. Optimisation of the S/W ratio.

3 COVENTORWARE® Modeling

3.1 Model Description

In this section, the model of the sensor loaded by the blood medium is described. This model was developed for simulation with the finite element method FEM using CoventorWare® software.

We used the module MEMS electro quasistatic harmonic response proposed by the software.

3.1.1 Sensor Modeling The structure of the impedance sensor used in this simulation is at micron scale. It is composed by layers of glass and platinum and is showed in figure 6.

A glass layer of length 1 000 µm and width of 1 000 μm has been defined as a substrate thickness of 1 000 μm to carry the system (gray layer on figure 6). The glass is a good electrical insulator (10-17S.m-1) with a relative permittivity around 5-7.

As the glass has a very small permittivity, we do not need to put an insulating layer between the substrate and the electrodes.

Next, we define a mask of platinum electrodes (thickness 1 μm) known as a good conductor 9.66*106 S·m-1, using the graphical editor of CoventorWare. This is deposited on the glass (red layer on figure 5). The effective region of electrodes forms a square 1 000 μm*1 000 μm.


Fig. 6. 3D view of a planar interdigitated electrode arrays.

The characteristic parameters of the electrodes, the length of digit L, the number of digits N, the digit width W and the distance between a digits S, were selected according to formulas of optimization given in section 2:

L is fixed at 1000 μm,

2

3.S W = μm, ( )15.N/2

L S

−= μm

and N is a variable. For example, N = 4 electrodes, S = 1000/(5.4/2-1) = 111 μm and W = 3.111/2 =

167 μm.

3.1.2 Modeling the Medium The medium modeled is composed by two layers:

The two layers DL, that describe the interface phenomena occurring at the electrode-electrolyte interfaces, are simplified to a single equivalent layer. This is the first layer shown on figure 7 (green layer). The second layer is the blood (blue layer).

The double layer can be formed from interface phenomena platinum electrode-middle blood, with a thickness about 50 A° [17]. The relative permittivity of the layer DL (thickness 50 A°) for medium blood is about 97 [18]. The 50 A° thickness creates problems for the mesh system, then they were shifted to a thickness of 10 µm (equal to 50 A°*2*1000) and a relative permittivity 194 000 (equal to 97 *2*1000) in order to not change the capacity of this layer. One can notice that DL layer is almost insulating.

We tested the blood as a biological medium with 0.7 S/m as conductivity and 80 at a frequency of 1 Ghz as relative permittivity [19]. The layer of the blood was equal to 500µm of thickness.


Fig. 7. 3D view of a planar interdigitated electrode arrays and the blood medium.

3.2 Results and Discussion

A 1 volt sinusoïdal signal between terminals of interdigitated electrodes and a frequency range from 100 Hz to 1000 GHz was applied.

The biological impedance was measured for different cases of electrode configuration. For the first three models, we arbitrarily chose N equal 16 electrodes.

Figure 8 shows the influence of the double layer DL on biological impedance of the blood medium. Simulation results are obtained with and without interface double layer DL. One can notice that the impedance is constant in the second case (without DL) and does not take into account the cut off frequencies fLo and fHi. The impedance consists of only resistance in parallel with capacitance (negligible).

Figure 9 shows the influence of the conductivity of the blood medium. Simulation results are obtained for two different conductivity : 0.7 and 9 m/s. When the conductivity increases, the RSol decreases and the plateau shifts to a lower

impedance. In addition, a change in the height of the plateau implies a change in the boundary frequencies fLo and fHi, (equations 11 and 12 of section 2).

Figure 10 gives the influence of medium permittivity on biological impedance and the boundary frequencies fLo and fHi. By comparing simulation results for two different permittivities, one can observe that the permittivity does not affect the impedance for small frequencies (less than 107 Hertz). For high frequencies when the permittivity increases, the impedance decreases and the fHi takes a smaller value which is similar to the equations (12) of the second paragraph.

Figure 11 gives simulation for N fingers. Six different structures were used with respect to the conditions of optimization explained above in the paragraph sensor modeling.

The case N equal 2 is taken as reference since this is the lowest possible number of fingers. In this case we can see that the impedance shows an unpredicted resonance at high frequencies.


For N equals 8 a resonance is not observed but an unstable plateau occurs for high frequencies.

Where N equals 12, there is not resonance or instability, but the distinction of fHi is not clear.

The two curves of 16 and 20 electrodes are almost together, and we can distinguish three regions of frequencies between fLow and fHi. For N equal 30, the impedance curve shows a resonance at high frequency.

102

104

106

108

1010

1012

100

101

102

103

104

105

106

107

Frequency, Hertz

Impe

danc

e, O

hm

16 electrodes, with interface double layer DL16 electrodes, out interface double layer DL

flow fhigh

Fig. 8. Simulated impedance of a blood medium deposited on the structure of the sensor number of fingers 16 electrodes, with and without interface double layer DL.

102

104

106

108

1010

1012

100

101

102

103

104

105

106

107

108

Frequency, Hertz

Impe

danc

e, O

hm

16 electrodes, conductivity = 0.7 s/m16 electrodes, conductivity = 9 s/m

flow flow fhigh fhigh

Fig. 9. Impedance-frequency characteristics for t conductivities of 0.7 S / m and 9 S/m


102

104

106

108

1010

1012

100

101

102

103

104

105

106

107

Frequency, Hertz

Impe

danc

e, O

hm

16 electrodes, permittivity = 8016 electrodes, permittivity = 5200

Fig. 10. Influence of the blood permittivity on the impedance.

102

104

106

108

1010

1012

100

101

102

103

104

105

106

107

Frequency, Hertz

Impe

danc

e, O

hm

2 electrodes8 electrodes12 electrodes16 elctrodes20 electrodes30 electrodes

Fig. 11. Biological impedance of the medium at various the number of digits N.


4 VHDL-AMS Modeling

4.1 Model Description

In this section, we describe the model of the sensor and the medium that we developed and simulated using the high-level behavioral language VHDL-AMS using SystemVision software.

The systems libraries was used to describe the model as an electrical circuit.

4.1.1 Electrical Modeling for Sensor and Medium In VHDL-AMS, the sensor and medium are described as an electrical circuit. In this circuit, the impedance of medium depends on the geometry of the sensor; therefore one must model the sensor loaded by the medium. The general model, in figure 12, is obtained by symmetry from the simple model between two classical plane electrodes; that represents the impedance between two fingers.

Fig. 12. General electrical model for an interdigitated sensor with medium

CDL, e represents the double layer capacity per finger, ZMed, e and CCell, e the impedance of medium and the cell capacitance between two fingers. These components are governed by the same equations (1), (3) and (4), but with a different cell constant, which does not contain the term N and (N-1) : the electrodes form factor Ke (equation 17).

( )( ) ( )1-NK

k²-1K

kK.

L

2 K Cell.e == and ( ) Cell .be

e Med,Med K)(jZ

1-N

Z Z ω== (17)

This model can be easily be simulated in VHDL-AMS, but its remains very difficult to write its equations. It is necessary to simplify it in order to allow a simple use. To do this, one supposes that the effect of the double layer can be divided into two equal parts. We divide the interface capacity into two equal parts to obtain a parallel circuit between the electrodes (figure 13). This new model can be simplified in a simple circuit with 4 components : 2 double layer capacitors CDL, the cell capacitor CCell and the medium impedance ZMed. This is the circuit presented in the


theoretical part in figure 3.b. This simplified model proves that one can find the conductivity and permittivity of medium by using cell constant.

Fig. 13. Steps to simplify the model.

4.1.2 VHDL-AMS Description The sensor loaded by a blood sample is described, using VHDL-AMS, like a dipole consisting on simple passives components. Their values are calculated, from the geometric characteristics of the sensor and the medium. For example, the electrode constant is calculated with the Euler method in a loop (figure 14). The final circuit is realized by placing basic components with a loop; it is the “Port Map” function (figure 15).

Fig. 14. Example of calculation of constants (here: the electrodes form factor and CCell).

constant nu : real := W/(W+G); constant ki : real :=sin(nu*MATH_PI/2.0); constant kip : real :=sqrt(1.0-ki**2);

pure function K(x:real) return real is variable y,nbr,pas,t,result: real; begin result:=0.0; pas:= 1.0/100000.0;

for nbr in 1 to 99999 loop t:=real(nbr)/100000.0; y:= result + pas*(1.0/sqrt((1.0-t**2.0)*(1.0-(x**2.0)*(t**2.0))));

result:=y; end loop; return y; end K; constant Fac:real:= L*K(ki)/(2.0*K(kiP));

--------------------------------------------------------------------------------------- constant ccel: real:=PHYS_EPS0*(epssub+epsech)*Fac;


Fig. 15. Placement of components by Port Map for an electrolytic medium.

4.2 Results and Discussion

4.2.1 Ionic Solution Sample An ionic solution is characterized by its conductivity σSol. So, the medium impedance ZMed,e is a resistance. This model has been simulated in VHDL-AMs using SystemVisionTM with the same parameters used in ConventorWare® model. We choose N=16, L=1mm, W=38µm, S=26µm and σSol=0.7 S/m.

The frequency analysis simulation is made by connecting an alternative current source to the sensor. An AC current of 1A was applied at a frequency varying from 100Hz to 1GHz. Figure 15 gives the simulation result of the impedance variation. The central plateau is the resistance of the solution.

102

10 3 10 4 105

106

107

108

109

102

103

104

Frequency (Hz)

Impedance (Ohm)

- simulation for 16 electrodes, conductivity=0,7 S/m

Fig. 16. Simulated impedance of a sensor with 16 electrodes, for an electrolytic medium with a conductivity of 0.7 S/m.

begin proc1 :for i in 1 to (N/2) generate c1:entity WORK.capa(ideal) generic map (cap => cdl)

port map ( P1 => P1, P2 => NM(2*i-1));

c2:entity WORK.capa(ideal) generic map (cap => cdl) port map ( P1 => P2, P2 => NM(2*i)); end generate proc1; proc2 :for i in 1 to (N-1) generate c1:entity WORK.res(ideal) generic map ( re => rsol) port map ( P1 => NM(i), P2 => NM(i+1)); c2:entity WORK.capa(ideal) generic map ( cap => ccel)


4.2.2 Blood Sample The electric and dielectric behavior of blood sample present more properties than a simple ionic solution. It is constituted by free cells in an electrolyte : the blood plasma. The cells are composed by an electrolyte which is contained in an insulating membrane. The classical modeling is a resistance for the electrolyte, and a résistance in series with a capacitor is given by Fricke’s model (figure 17). We take for ZMed,e the equation of figure 17 with the electrodes form factor. For this simulation, we keep the same geometric parameters than the previous simulation for ionic solution. The values for blood’s parameters are σP=1.5 S/m, σC=1 S/m, Cm=1.75 µF/cm² and Ø=55%. The surface capacity of membrane is high but less than the capacity of double layer. Its effect appears at higher frequency. The results of the simulation are given in figure 18 and figure 19.

Fig. 17. Fricke’s Model for blood and its equivalent impedance in [Ohm.m]. With rP, rC, Cm, a and Ø the resistivity of plasma in [Ohm.m], the intern resistivity of blood cells in [Ohm.m], the membrane surface capacity in [F/m], the radius of blood cells in [m] and the volume in percentage of blood cells.

10 2 10 3 10 4 105

106

107

108

10 9

10 2

10 3

10 4

Frequency (Hz)

Impedance (Ohm)

- Simulation for 16 electrodes; blood model

Fig. 18. Simulated impedance of a sensor with 16 electrodes, for a blood medium.


102

10 3 10 4 105

106

107

108

10 9 10 -12

10 -10

10 -8

10 -6

10 -4

10 -2

Frequency (Hz)

Conductivity (S)

Capacity (F)

y p y

Fig. 19. Conductance and capacity of a sensor with 16 electrodes for blood medium.

The figures 18 represents the impedance; one can see two plateaux which correspond respectively to the plasma resistance and plasma resistance in parallel with blood cell resistance. The value of capacitance is difficult to evaluate in this type of curve, but it is easily find in the figure 19.

Figure 19 gives the conductance and the capacity versus the frequency. For the conductivity, each plateau represents respectively the plasma resistance and the plasma resistance in parallel with the blood cell resistance. In capacity, each plateau represents respectively the double layer capacity, the blood cells capacity and CCell.

5 Experimental Validation

5.1 Sensor Manufacturing

The sensor was provided by our colleague from the IJL team (Institut Jean Lamour, Henri Poincaré-Nancy 1 University). It was obtained by a deposit of 500 nm platinum on an insulating glass substrate in a 5 steps process:

• Sensor cleaning with acetone and isopropanol. • Deposition of a platinum by ion-beam sputtering. • UV lithography: deposit resin, mask application, insolation and development. • Ion beam etching. • Removal resin with acetone and isopropanol.

Its geometrical parameters are N=100, W=4µm, S=8µm and L=1000µm. This is a first prototype sensor for which we recycled a mask designed for SAW interdigitated sensor previously developped at IJL. A printed circuit board (PCB) was designed and built to connect the sensor with an appropriat measuring instrument. The connections between the sensor and the PCB were realized using a gold wires bonding figure 20.


Fig. 20. Sensor and PCB connection and its gold wires bonding and partial microscopic view of the fingers

5.2 Measurements

The measurement system is composed of an LCR meter HP4284A controlled by

VEE© software with a GPIB interface. It allows a fast and automatic measurements

between 20Hz and 1 MHz. A photography of this system is given in the figure 20a. The measurements were performed with a calibrated drop of ionic solution. This solution contains 0.9% of NaCl, and has an approximate conductivity of 0.72 S/m. We placed a drop directly on the sensor, as shown on figure 21.b. The sensor connections (bonding) were not isolated, and can cause some errors of measurements. These first measurements were done just to validate the model . Figure 22 shows the measurement results compared to VHDL-AMS simulation results.

(a)

Fig. 21. (a): Measurement system using the HP4284A PRECISION LCR METER. (b): Deposit of a drop of calibrated solution on the sensor.


(b)

Fig. 21. (continued)

10 2 10 3 104

105

106

10 7

102

103

104

105

Frequency (Hz)

Impedance (Ohm)

Measured impedance for a NaClcalibrated solution: conductivity = 0.72 S/m

Simulated impedance for anionic solution: conductivity = 0,72 S/m

Fig. 22. Comparison between measurements and the two simulations

Simulation of complex system by the finite element method with CoventorWare®, takes lot of memory for computation. For N equal 100 electrodes, our simulation equipment was not able to model and simulate the whole system.

The preliminary experimental measurements agree with the simulation. One can see a plateau at higher frequency, at a level close to that of simulation, but the instrument frequency limitation do not allow to check the precise level. The slope of the curve is slightly lower in measurement, because the real system response is not exactly the same those classical passive electronic components.


6 Conclusion

This paper presents a comparative approach for simulation of biological sensor modeling in physical and electrical domains using two softwares. CoventorWare® software for three dimensional interdigilal sensor simulation techniques to analyse the influence of the physical properties of the medium and the impedance response was used. The simulation results are in agreement with the theoretical equations of optimization.

This optimization method used for bioimpedance spectroscopy sensor is obtained from theoretical equations, by developing total impedance equations and modeling equivalent circuits. The equations given relate the cutoff frequencies to the geometric parameters of the sensor and physical properties of the measured medium. A geometric structure of the sensor was proposed. The use of a square cross section permit to eliminate one of the geometric parameters of the sensor, that simplifies the optimization and the analysis of the sensor.

Electrical modeling of the interdigital sensor and the medium is carried out with VHDL-AMS software from MENTOR GRAPHICS®. The use of VHDL-AMS language shows the advantage to combine multiphysical domains. The approach can be readily used in current electronic design flow to include distributed physics effects into modelling and simulation process with VHDL-AMS. Simulations results give similar results as physical simulation. However, all the physical properties are not represented, especially at high frequency. The useful properties are correctly simulated.

The use of behavioural models in simulation simplify physics and explore interactions between different domains in a reasonable amount of time compared to physics modelling with CoventorWare® software.

The simulation results of the impedance obtained with VHDL AMS don’t show any resonance because all the geometric parameters, such as thickness of the medium and the interactions between ions were not include in the model.

The experimental results obtained with a sensor, designed by the IJL (Institut Jean Lamour, Nancy University) team, are in agreement with those obtained by simulation.

The future goal is to design a specific sensor by optimizing its dimensions for blood measure samples. It will be necessary to design a tank on the active area of the sensor, to avoid measurement errors, and do measurement at higher frequency.

The simulation and measured curves present many similarities; the preliminary experiment measures are satisfactory. The next goal is to realise our own sensor by optimizing dimensions to measure blood samples. It will be necessary to design a tank limited to the active area of the sensor, to reduce measurement errors, and allows measurement at higher frequency.

References

[1] Faes, T.J., Meij, H.A., de Munck, J.C., Heethaar, R.M.: The electric resistivity of human tissues (100 Hz-10 MHz): a meta-analysis of review studies. Physiol. Meas. 1999 20, R1-10 (1999)

[2] Katz, E., Willner, I.: Electroanalysis 15(11), 913–947 (2003) [3] Mukhopadhyay, S.C.: Sensing and Instrumentation for a Low Cost Intelligent Sensing

System. In: SICE-ICASE International Joint Conference, pp. 1075–1080 (October 2006)


[4] Mukhopadhyay, S.C., Gooneratne, C.P., Demidenko, S., Sen Gupta, G.: Low cost sensing system for dairy products quality monitoring. In: Proceedings of 2005 International Instrumentation and Measurement Technology Conference, IEEE Catalog Number 05CH37627C, pp. 244–249 (2005) ISBN 0-7803-8880-1

[5] Van Gerwen, P., Laureyn, W., Laureys, W., Huyberechts, G., Op De Beeck, M., Baert, K., Suls, J., Sansen, W., Jacobs, P., Hermans, L., Mertens, R.: Nanoscaled interdigitated electrode arrays for biochemical sensors. Sens. Actuators, B 49, 73–80 (1999)

[6] Timms, S., Colquhoun, K.O., Fricker, C.R.: J. Microbiol. Meth. 26, 125 (1996) [7] Geng, P., Zhang, X., Meng, W., Wang, Q., Jin, L., Feng, Z., Wu, Z.: Electrochim.

Acta 53, 4663 (2008) [8] Igreja, R., Dias, C.J.: Sensors and Actuators A 112, 291–301 (2004) [9] Borkholder, D.: Based biosensors using microelectrodes. Ph.D. dissertation, Stanford

University, Palo Alto (1998) [10] Mamishev, A., Sundara-Rajan, K., Yang, F., Du, Y., Zahn, M.: Interdigital sensors and

transducers. Proceedings of the IEEE 92, 808–845 (2004) [11] Sundara-Rajan, K., Byrd II, L., Mamishev, A.V.: Moisture content estimation in paper

pulp using fringing field impedance spectroscopy. IEEE Sensors Journal 4, 378–383 (2003)

[12] Olthuis, W., Streekstra, W., Bergveld, P.: Sensors and Actuators B 24-25, 252–256 (1995) [13] Jacobs, P., Varlan, A., Sansen, W.: Design optimisation of planar electrolytic

conductivity sensors. Medical & Biological Enfineering & Computing, 802–810 (November 1995)

[14] Abramowittz, M., Stegun, I.: Handbook of mathematical functions. Dover Publications Inc., New York (1965)

[15] Dahmen, E.A.M.F.: Electroanalysis Theory and applications in aqueous and non aqueous media and in automated chemical control. Elsevier, Amesterdam (1986)

[16] Bard, A.J., Faulkner, L.R.: Electrochemical methods, fundamentals and applications. John Wiley and Sons, New York (1980)

[17] Kovacs, G.T.A.: Introduction to the theory, design, and modeling of thin-film microelectrodes for neural interfaces. In: Stenger, D.A., McKenna, T.M. (eds.) Enabling Technologies for Cultured Neural Networks, pp. 121–165. Academic, London (1994)

[18] Bard, A.J., Faulkner, L.R.: Electrochemical Methods. Willey, New York (2001) [19] Jaspard, F., Nadi, M., Rouane, A.: Dielectric properties of blood: an invetigation of

haematocrit dependance. Physiological Measurement 24, 134–147 (2003)

Documents

Modeling Bioimpedance Chapterbook