Optimal interdigitated electrode sensor design for biosensors using multi-objective particle-swarm optimization

International Journal of Electrical and Computer Engineering (IJECE)
Vol. 13, No. 3, June 2023, pp. 2608∼2617
ISSN: 2088-8708, DOI: 10.11591/ijece.v13i3.pp2608-2617 ❒ 2608
Optimal interdigitated electrode sensor design for
biosensors using multi-objective particle-swarm
optimization
Issa Sabiri1
, Hamid Bouyghf2
, Abdelhadi Raihani1
1EEIS Laboratory, ENSET Mohammedia, Hassan II University of Casablanca, Casablanca, Morocco
2LSIB Laboratory, Faculty of Sciences and Techniques, Hassan II University of Casablanca, Casablanca, Morocco
Article Info
Article history:
Received Jul 5, 2022
Revised Aug 22, 2022
Accepted Sep 2, 2022
Keywords:
Impedance spectroscopy
Interdigitated electrodes
Optimization
Particle swarm optimization
algorithm
Sensitivity
ABSTRACT
Interdigitated electrodes (IDEs) are commonly employed in biological cellular
characterization techniques such as electrical cell-substrate impedance sensing
(ECIS). Because of its simple production technique and low cost, interdigitated
electrode sensor design is critical for practical impedance spectroscopy in the
medical and pharmaceutical domains. The equivalent circuit of an IDE was
modeled in this paper, it consisted of three primary components: double layer
capacitance, Cdl, solution capacitance, CSol, and solution resistance, RSol. One
of the challenging optimization challenges is the geometric optimization of the
interdigital electrode structure of a sensor. We employ metaheuristic techniques
to identify the best answer to problems of this kind. multi-objective optimization
of the IDE using multi-objective particle swarm optimization (MOPSO) was
achieved to maximize the sensitivity of the electrode and minimize the Cut-off
frequency. The optimal geometrical parameters determined during optimization
are used to build the electrical equivalent circuit. The amplitude and phase of the
impedance versus frequency analysis were calculated using EC-LAB® software,
and the corresponding conductivity was determined.
This is an open access article under the CC BY-SA license.
Corresponding Author:
Issa Sabiri
EEIS Laboratory, ENSET Mohammedia, Hassan II University of Casablanca
Casablanca, Morocco
Email: issa.sabiri@etu.fstm.ac.ma
1. INTRODUCTION
Giaever and Keese created the key impedance-based technology known as electrical cell-substrate
impedance sensing (ECIS) in 1984 for the in-vitro, real-time evaluation of biological cellular activities [1].
Traditional round gold electrodes were employed to research cell adhesion, proliferation, migration, invasion,
and barrier activities in the early stages of biosensor development [2]–[6]. Non-ionizing radiation interactions
with biological matter are progressing in diagnostic and therapeutic issues. The electromagnetic properties
of the propagation medium must be determined in order to make progress [7]. Another application aspect
that requires the values of electrical characteristics such as conductivity and permittivity of biological tissues
is public health problems related to electromagnetic fields (dosimetry, biological impacts). These biological
tissue values at the frequencies of interest are unknown [8].
The electrode design has a significant impact on biosensor accuracy and sensitivity. Cell-based biosen-
sors offer a wide range of applications, including clinical diagnostics, drug discovery, and electrophysiology
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Int J Elec & Comp Eng ISSN: 2088-8708 ❒ 2609
[9]. Impedimetric and conductometric approaches can be used to measure morphological changes in cells,
which are impacted by the electrode geometry [10]–[11]. Microelectrodes have several advantages over con-
ventional macroscopic electrodes, including cost, high current densities during measurement, and the ability
to integrate them into other instrumental devices to create portable measurement systems, or even biochips or
lab-on-chips.
Microelectrodes, on the other hand, have a substantially larger resistance than macroelectrodes due
to contact phenomena. The interaction between ions and molecules at the border between the electrolyte’s
surface and the measuring electrodes causes an interface capacitance, or double layer, which manifests these
phenomena. This capacitance is inversely proportional to the surface area of the electrodes. As a result, the
double layer capacitance acts as a limitation, increasing measurement inaccuracy.
In all engineering fields, particularly in electronics used in biomedical circuits, reliable, efficient, and
robust optimization strategies are highly desired [12]. In this paper, we emphasize the application of a bio-
inspired technique, specifically particle swarm optimization. The optimization of IDEs or sensor shape is criti-
cal since it can enhance the bioimpedance measurement range, allowing for the most accurate cellular electrical
depiction. Several methods for optimizing interdigitated electrodes (IDEs) for bioimpedance spectroscopy have
already been investigated. Ibrahim et al. [13] used analytical modeling and simulation to investigate the re-
lationship between design factors and IDE frequency behavior in order to optimize configuration for a square
area cross section. Zhang et al. [14] used mathematical models to investigate the effect of electrode size on
ECIS sensitivity. Ngo et al. [15] used a modeling and experimental technique to optimize geometrical parame-
ters for biological media characterisation by reducing polarization impact and Mansor and Nordin [1] examine
the distribution of electric fields on various sensor geometries. Some research, such as the optimization of
IDEs for HS578T cancer cells [11], are more application specific. However, there hasn’t been much research
into employing metaheuristics algorithms to improve the IDE’s sensitivity and cut-off frequency (FLow). For
cellular research, the shape of the sensor can be changed to get more sensitive and accurate results.
This research shows the similar circuit model of IDEs that are optimized for blood abnormalities.The
ECIS technique is used to optimize the IDEs’ design to increase sensitivity to changes in blood cells. The ECIS
approach enables accurate electrical representation of a cell’s biological response. Using the multi-objective
optimization approach based on the particle swarm optimization (PSO) algorithm, the IDE’s shape will be
adjusted so that the IDE’s sensitivity is maximized and the cut-off frequency of the interfacial impedance
is minimized. The corresponding circuit model is analytically modeled in section 2. Section 3 looks into
multi-objective optimization using PSO and the methodology to introduce the objective function from two dif-
ferent perspectives: sensitivity and cut-off frequency. The optimization results and conclusion are presented in
section 4.
2. THEORETICAL BACKGROUND
2.1. Biosensors with interdigitated electrodes
Single-plane electrodes are used in biosensors with interdigitated electrodes, which are manufactured
via traditional metal deposition [16]. Sensors with interdigital electrodes have been designed to identify de-
oxyribonucleic acid (DNA) sequences using impedance spectroscopy and blood analysis, and have been im-
proved to improve the frequency band. An interdigital sensor, as illustrated in Figure 1, is made up of two
comb-shaped metal electrodes, each with a width W, a length L of electrodes, and a spacing S between two
consecutive electrodes.
An interdigital electrode sensor works on the same concept as a parallel plate capacitor. The sensor
is deposited on a substrate, and a voltage is used to create an electric field between the two electrodes. An
electromagnetic field is created and travels through the sensor when a biological component is placed on it
[10]. The geometry of the object under research and the biological fluid’s dielectric characteristics affect the
capacitance and conductance between the two electrodes. Depending on the use, the difference in the electric
fields is used to describe how the biological environment affects the organism. Based on the equivalent circuit,
the total impedance can be represented as (1).
Z = 2.Zdl + ZRsol//ZCsol =
2
jwCdl
+
RSol
(1 + jwCSol.RSol)
(1)
The impedance modulus Rsol or resistance of the electrolyte solution mimics the conductive effects of the
Optimal interdigitated electrode sensor design for biosensors using ... (Issa Sabiri)

2610 ❒ ISSN: 2088-8708
medium under the influence of an electric field. This is the measurement’s most delicate component. To
mathematically explain the effect of the IDE geometry on each component of the equivalent circuit model,
Olthuis et al. [17] created a new parameter called the cell constant, KCell. The proportionality factor between
the electrolyte’s resistivity/permittivity and the actual measurement is KCell, which only exists at the electrode-
electrolyte interface. It is fully dependent on the sensor’s geometry, as illustrated in (2)-(5).
Rsol =
KCell
σSol
(2)
With:
KCell =
2
(N − 1)L
∗
Γ(k)
Γ
√
1 − k)
(3)
Γ(K) =
Z 1
0
1
p
(1 − t)(1 − kt)
(4)
K = cos (
π
2
∗
W
W + S
) (5)
The dielectric component of the material under test is represented by Ccell. It depicts the two electrodes’ direct
capacitive interaction. The dielectric permittivity is proportional to the capacitance.
CCell =
ϵ0ϵrSol
KCell
(6)
The impedances that describe the interface effects produced at the electrode-electrolyte interfaces are made
possible by the double-layer capacitance Cdl. Both the electrolyte solution and the material used to form the
electrodes have an impact on the impedances. The simple capacitive coupling between the two electrodes is
what is meant by the capacitance that mimics the dielectric portion of the medium under test. The dielectric
permittivity and this capacitance are connected by (7).
Cdl = 0, 5 ∗ A ∗ C(dl,Surface) = 0, 5 ∗ W ∗ L ∗ N ∗ C(dl,Surface) (7)
The overall electrode surface area is A. When a factor of 0.5 is applied, a single capacitance Cdl is produced by
dividing in half the two interface capacitances produced by interface effects at the entire electrode surface. In
the case of interdigitated electrodes, this surface equals the electrode length times their width times the number
of electrodes. The characteristic double layer called Stern’s capacity, C0 = 0.047F/m2
, for electrolytes with a
very high ionic concentration is thought to be the same as the characteristic double layer capacity, Cdl, surface.
Figure 1. Similar circuit model of IDEs in a liquid environment
Int J Elec & Comp Eng, Vol. 13, No. 3, June 2023: 2608-2617

2.2. The IDE’s sensitivity
Bouyghf et al. [12] and Mansor et al. [1] have shown that two cut-off frequencies separate the
dominance of components, namely FLow and FHigh. The ZSol will be quite high at frequencies between FLow
and FHigh, and the CSol will behave practically as an open circuit, allowing current to flow through the Cdl
and RSol branches. Cdl prevails at lower frequencies below FLow, about a few kHz. FLow frequencies ranging
from 0 to hundreds of kHz are dominated by RSol.
With increasing frequency, the impedance reduces until it reaches FLow. The double-layer capacity,
however, does not intervene in the overall impedance above the cutoff frequency FLow. Because only the
resistance RSol (or modulus of total impedance) affects impedances less than FHigh, and because CCell is
not yet informative, this is the case. In this frequency band, which is limited by FLow and FHigh, the total
impedance is the same no matter what frequency it is.
The observed impedance is based on the total impedance fields and represents an accurate measure-
ment of the biological sample within this range (for example, the conductivity, which can be estimated from
the RSol value). We might draw the conclusion that the sensitivity of the frequency measurement needs to be
improved. The dominant impedance spectra of the RSol module’s need a wider frequency range. By reducing
the low cut-off frequency FLow as much as is practical, increasing the frequency range (also referred to as
the useful frequency range) prevents the interface phenomenon represented by the double layer capacitance.
In square structure of IDEs with an LxL dimension, (8) and (9) determine the sensitivity (Sen) and cut-off
frequency FLow respectively.
Sen =
∆Z
∆σ
=
(|Z2| − |Z1|)
(σ2 − σ1)
(8)
FLow =
σsol
πKCellCdl
(9)
3. METHOD
3.1. Multi-objective optimization
The following is a mathematical formulation of the general multi-objective optimization problem:
minimize
H(⃗
x) = [h1(⃗
x), h2(⃗
x), ...fk(⃗
x)]T
subject to: (
⃗
f(⃗
x) ≤ 0
⃗
g(⃗
x) = 0
⃗
x ∈ Rn
,⃗
h(⃗
x) ∈ Rk
, ⃗
f(⃗
x) ∈ Rm
and ⃗
g(⃗
x) ∈ Rq
.
X = ⃗
x | fm(⃗
x) ≤ 0 , m = 1, 2, 3...m, gq
⃗
(x) = 0, q = 1, 2, 3...q, S = H(⃗
x) | ⃗
x ∈ X
Here ⃗
x ∈ Rn
is the vector of design variables and n is the number of decision variables. k ≥ 2 is the number
of objective functions, and H(⃗
x) ∈ Rk
is their vector in which hi(⃗
x) : Rn
→ R1
. In addition, m and ⃗
f(⃗
x)
stand for the quantity and direction of inequality restrictions, respectively. The number of equality constraints
and their vector, respectively, are q and ⃗
g(⃗
x). The feasible decision and criteria spaces, respectively, are X and
S.
Machairas et al. [18] proposed one of the most prominent approaches for presenting multi-objective
solutions. If there is no other possible option that improves one goal without worsening at least one other,
it is called a Pareto or non-dominated solution. For solving multi-objective optimization problems, there are
two main types of decision-making techniques. The second searches simultaneously for all non-dominated
solutions, as opposed to the first, which solves a single objective problem for each Pareto-optimal solution
[19]–[21].
The most popular multi-criteria decision-making approach in decision theory is the weighted sum
method (WSM) [22]. By summing standardized objective functions scaled by their weighting coefficients, ki,
the weighted sum technique can reduce the multi-objective task of reducing a vector of criteria functions into
such a scalar problem. In [23] shows the formula for the weighted sum method as (10):

2612 ❒ ISSN: 2088-8708
Hws(x) =
k
X
i=1
λi
hi(x) − hi(x)min
hi(x)max − hi(x)min
(10)
where Hws(x) is the overall objective function, k is the number of objective functions hi(x) and λi ∈ [0, 1]
when
Pk
i=1 λi = 1. In addition, hi(x)min
and hi(x)max
are the minimum and maximum values of the
objective functions, respectively, as they are optimized independently.
3.2. Multi-objective particle swarm optimization (MOPSO)
The particle swarm optimization (PSO) algorithm was created in 1995 by Eberhart and Kennedy [24].
This stochastic optimization method is population-based. In order to determine the best solution, the PSO
method first generates a set of random particles. At the conclusion of each generation, the two best values
are applied to each particle. The first option has so far had the best results. Another is the highest value that
any population particle has ever attained. This is the world’s best value. The best value is a local best when
a particle uses the population as its topological neighbors. Once you know the two best values for a particle’s
speed and location, you can change them [25]. The position of xi(t) is calculated by adding its velocity, vi(t)
to the current position, i.e:
xi(t) = xi(t − 1) + vi(t). (11)
where the velocity vector is expressed as (12).
vi(t) = wvi(t − 1) + C1r1[Pbest − xi(t)] + C2r2[Gbest − xi(t)] (12)
The inertia weight w is used to influence the effect of the particle’s previous velocity on the current velocity.
C1 is the cognitive learning factor, which shows how interested a particle is in its own success. C2 is the social
learning factor, which shows how interested a particle is in the success of its neighbors. Positive constants,
C1 and C2, are commonly used [21]. Furthermore, r1 and r2 ∈ [0, 1] are two independent random number
sequences used to avoid entrapment on local minimums and to allow a tiny number of particles to diverge in
a more thorough search of the search space [26]; the personal and global best positions are Pbest and Gbest.
Figure 2 shows the particle swarm optimization algorithm’s velocity and position updates. To turn a PSO
algorithm into a MOPSO, it is common to create an external repository to store the non-dominated solutions
and use a leader selection method to pick a global leader for the particles from a group of equally good solutions
based on some criteria. When the external repository fills up, an archiving method is required to prune it and
keep it at a predetermined size, removing non-dominant solutions based on some criterion. Due to the large
number of non-dominated populations, this criterion has a big effect on the quality of the solutions found by
the search, especially when there are many goals.
Figure 2. The updating process of the particle velocity
3.3. Formalization
The optimization problem can be incisively described as following maximize the sensibility (Sen)
subject to minimize FLow where:

Smin ≤ S ≤ Smax
Wmin ≤ W ≤ Wmax
Nmin ≤ N ≤ Nmax
Sen is given by (8) and Smin,max, Wmin,max, Nmin,max is the minimum and maximum of each parameter
appropriate to the IDEs. This makes it easier for the algorithm to find the best design parameters for the best
performance.
To resolve multiobjective problems, we proposed the algorithm given in Figure 3. The parameter
settings have been fine-tuned to provide the best possible result. As mentioned already, our IDE is optimized
in order to improve the sensitivity, have reduced solution resistance, and have a low cut-off frequency. The
MOPSO algorithm was utilized in this method because of its good reputation when it comes to optimizing
multiple objective functions. The optimization was done considering the electrolytic medium with a change of
∆σ =+
− 0.110−6
S. Global parameters and data used are shown in Table 1.
Figure 3. Flowchart for the intended simulation-based method to optimization
Table 1. Parameters and technical data
Parameter Designation
nPop Population Size (=100)
nRep Repository Size (=10)
MaxIt Maximum Iterations (=1000)
alpha Grid Inflation Parameter (0.1)
nGrid Number of Grids per each Dimension (=100)
beta Leader Selection Pressure Parameter (=2)
gamma Repository Member Selection Pressure (=4)
∆σ Electrolytic medium change (=0.1 10−6 S)
Wlb- Wub Lower and Upper Bounds (1-100µm)
Slb − Sub Lower and Upper Bounds (1-100µm)
Nlb − Nub Lower and Upper Bounds (2-100)
L X L Square length of the IDE (6×6 mm)

2614 ❒ ISSN: 2088-8708
4. SIMULATION RESULTS
This section was focused on discussion of the multi-objective particle swarm optimization results for
the proposed application of our objective functions. We used MATLAB software to find the optimum result for
each parameter. The equivalent circuit model was implemented using EC-LAB® tools to validate the theory.
4.1. Optimization result
After fixing each parameter and technical data on the MATLAB software, the number of iterations
was set to 1,000 and the function tolerance was set to 10−4
. The best outcomes are depicted in Figure 4 and
summarized in Table 2. The best-picked selected solution responds to our goals and criteria, according to Preto
Front analysis. L must adhere to the linear equality that fellow: N.(W + S) ≈ 6 mm, with a maximum
sensitivity of 437.75 Ohm.m/S and a minimum cut-off frequency of 35.53 Khz.
Figure 4. Pareto front
Table 2. Parameters and technical data
Wopt(µm) Sopt(µm) Nopt N.(S + W)(mm) Sensitivity (Ohm.µm/S) FLow(Khz)
98.04 65.01 45.30 9 7.40 237.19 43.45
76.52 93.17 28.35 4.81 48.74 28.15
92.91 99.00 67.35 12.92 106.53 38.09
96.00 58.82 40.33 6.24 332.72 470.93
18.08 11.00 54.11 1.57 165.68 140.34
71.77 40.08 99.00 11.07 48.10 97.88
84.97 16.58 29.25 2.97 576 194.93
cyan99.13 78.32 33.48 5.94 437.75 35.53
75.63 11.86 64.47 5.64 116.34 312.06
4.2. Electrical simulation using equivalent circuit
The optimal geometrical parameters determined during optimization are used to build the electrical
equivalent circuit. The amplitude and phase of the impedance versus frequency analysis were calculated using
EC-LAB® software, and the corresponding conductivity was determined. The corresponding circuit compo-
nents are summarized in Table 3.
The total electrical impedance Zjw can be trigonometrically expressed as in (13).
Zjw = |Zjw|eiθ
(13)
The resistance Rsol will be presiding from the cut-off frequency FLow then the total impedance can be simpli-
fied as (14).
FLow =
RSol
(1 + jwCSolRSol)
(14)

The conductivity can be expressed as showing in (15).
σSol =
kCell
|Zjw|
cos(θ) (15)
Table 3. Equivalent circuit components
RSol (Ω) CSol (pF) Cdl (µF)
11.82 41.73 0.76
The characteristics of the designed biosensors is essential for the effective use of impedance spec-
troscopy in the medical and pharmaceutical fields. The technical features of the designed IDE at the acquisition
frequency Fmdl simulated under its equivalent circuit. As shown in Figure 5, Figure 6, and Table 4.
Figure 5. Impedance vs. frequency analysis using EC-LAB® software
Figure 6. Phase vs. frequency analysis using EC-LAB® software

2616 ❒ ISSN: 2088-8708
Table 4. Characteristics of the IDE
W(µm) S(µm) N L (mm) KCell(µm−1) Sen(Ω.µm/S) Fmidl(MHz) σmeasured(S/µm)
99.13 78.32 34 6 10.41 437.75 0.36 0.24 10−6
5. CONCLUSION
This study presents a physical model of an IDE that uses the MOPSO algorithm and Pareto Front
analysis to detect DNA sequences utilizing impedance spectroscopy and blood analysis. The simulation results
demonstrate the benefit of improving the sensor’s components. Finally, utilizing the best results, we built the
electrical equivalent circuit components and analyzed their impedance responses with the EC-LAB® program.
Theoretical and simulation results support the concept of having a maximum sensitivity and a low cut-off
frequency. However, factors such as electrical field distribution, fabrication process capabilities, working area
limitation, and relevance to the intended application limit the ideal configuration’s selection.
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BIOGRAPHIES OF AUTHORS
Issa Sabiri was born in Msemrir, Morocco on April 18, 1995. In 2016 he had got his
license degree in Bio Medical Instrumentation and Maintenance, at the Institute of Health Sciences
Settat-Morocco (ISSS) at the University Hassan I Settat-Morocco, then he had got a Master’s degree
in biomedical engineering from FST Settat in 2018. He is currently a Ph.D. student in Laboratory of
electrical engineering and intelligent systems (EEIS), ENSET Mohammedia, Hassan II University of
Casablanca, Morocco. His works studies and interests are focused on development, design and opti-
mization of electronic systems for biomedical engineering and health sciences. He can be contacted
at email: issa.sabiri@etu.fstm.ac.ma.
Hamid Bouyghf was born in Errachidia, Morocco in 1982. He received the B.S. and
M.S. degrees in electrical engineering and telecom from the University of Science and Technology,
Fez, Morocco, in 2007 and the Ph.D. degree in electrical engineering and telecom from Faculty of
Science and Technic - Mohammedia, Hassan II University of Casablanca, Morocco, in 2019. From
2015 to 2019, he was a Research Assistant with the Princeton Plasma Physics Laboratory. Since 2019,
he has been an Assistant Professor with the electrical Engineering Department, FST Mohammedia,
Hassan II University, Casablanca, Morocco. He is the author of more articles in optimization of
ICs area. His research interests include electronic applied to biomedical domain and analog ICs
design, electromagnetic field, low power design, and BLE applications. He can be contacted at
email: hamid.bouyghf@fstm.ac.ma.
Abdelhadi Raihani was appointed as a professor in Electronics Engineering at Hassan II
University of Casablanca, ENSET Institute, Mohammedia Morocco since 1991. He received the B.S.
degree in Applied Electronics in 1991 from the ENSET Institute. He has his DEA diploma in Infor-
mation Processing from Ben M’sik University of Casablanca in 1994. He received the Ph.D. in Par-
allel Architectures Application and Image Processing from the Ain Chock University of Casablanca
in 1998. His current research interests are in the medical image processing areas, electrical engineer-
ing fields, particularly in renewable energy, energy management systems, power and energy systems
control. He supervised several Ph.D. and Engineers students in these topics. He can be contacted at
email: raihani@enset-media.ac.ma.

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