Electrochemical Impedance Simulation for Single Cell Analysis using

a Microelectrode

Masataka Shiozawa and Shigeyasu Uno

Graduate School of Science and Engineering, Ritsumeikan University,

1-1-1 Noji-Higashi, Kusatsu, Shiga, 525-8577, Japan

Keywords: Electrochemical Impedance, Simulation, Single Cell Analysis, Microelectrode.

Abstract: Electrochemical impedance spectroscopy (EIS) is one of the ways to monitor living cells in terms of

morphology and cell-substrate adhesion. In conventional cell analysis, averaged values from many cells on a

large area electrode are acquired. Meanwhile, single cell characteristics are obtained by using a microelectrode

which is smaller than single cell size. In this study, we investigated the impact of electrode size on single cell

EIS analysis by using a computer simulation. The electrode smaller than the cell size would enable

independent measurement of the cytoplasm electrical conductivity and the cell-substrate gap resistance. In

addition, changes in morphology such as cell height and radius should be monitored at the same time in

different frequency range. Thus, our simulation indicates that EIS measurement with microscale electrode

may be used in monitoring various physiological changes in cells such as immune response.

1 INTRODUCTION

Nowadays, the living cell monitoring is used in

disease diagnosis (Cheng et al., 2007) and drug

discovery (Weigl et al., 2003). In drug discovery, the

side effect on tissue culture is evaluated by

monitoring cells. This method is used in regenerative

medicine as well as in disease diagnosis and drug

discovery. In regenerative medicine, one of the basic

ways of treatment is to transplant the stem cell

induced differentiation to the affected area. During

inducing differentiation process, we need to monitor

the morphological change of the stem cell to detect

the progress of differentiation (Santelli et al., 2018).

As mentions above, the living cell monitoring is

needed in various areas.

The fluorescent labeling such as fluorescence

microscope (Hopt & Neher, 2001) and flow

cytometry (Nolan et al., 2018) has long been used as

the way of monitoring living cells. These methods

can selectively monitor any proteins and antigens due

to staining. In addition, these methods can provide the

quantitative information by estimating the fluorescent

reflection signal from cells irradiated with excitation

light (Hopt & Neher, 2001; Nolan et al., 2018).

However, the fluorescent labeling may alter original

characteristics of cells. In addition, the fluorescent

labeling eventually induces the cell death. Thus, it is

not appropriate to monitor the cells in long term, and

therefore, the label-free monitoring methods have

been explored.

There are some researches about the ways of

monitoring living cells without labeling, such as

Raman spectroscopy (Moura et al., 2016) and surface

plasmon microscopy (Toma et al., 2014). The

electrochemical impedance spectroscopy (EIS) is one

of the applicable ways which require no labeling.

Contrary to the fluorescent labeling, the EIS

measurement is suitable to monitor in long term. In

EIS measurement, the AC voltage of several mV is

applied to the electrode. Then the electric current is

measured, and impedance is calculated from the ratio

of current to voltage to analyze the object. Previous

studies have proven that the EIS measurement for cell

analysis can supply various information such as the

apoptosis, the movement of cancer cells through the

tight junction of endothelial cells (Anchan et al.,

2019), the wound healing (Gamal et al., 2019), the

cell proliferation (Cui et al., 2017; Iwakura et al.,

2019) and the cell migration (Cui et al., 2017;

Iwakura et al., 2019) by sweeping frequency. The EIS

measurement does not need any optical equipment.

Therefore, the EIS measurement should be used in

point of care (Hedayatipour et al., 2019; Ahmed et al.,

2014) by downsizing the whole measurement system

114

Shiozawa, M. and Uno, S.

Electrochemical Impedance Simulation for Single Cell Analysis using a Microelectrode.

DOI: 10.5220/0010266401140120

In Proceedings of the 14th International Joint Conference on Biomedical Engineering Systems and Technologies (BIOSTEC 2021) - Volume 1: BIODEVICES, pages 114-120

ISBN: 978-989-758-490-9

with CMOS technology (Hedayatipour et al., 2019;

Manickam et al., 2010).

In conventional cell analysis, cell characteristics

are obtained from average values of many cells on a

large electrode. However, recent study shows that

cells may have the difference of gene. Hence, the

individual cell difference such as the cell shape is

caused (Moura et al., 2016). Such analysis ignores

these individual cell differences (Zhou et al., 2010).

On the other hand, single cell monitoring is a useful

method because the individual cell differences can be

observed (Zhou et al., 2010). In EIS measurement,

various electrode structures have been used to

measure; the interdigitated electrodes have long been

used by many experimentalists as the electrochemical

sensor (Ibrahim et al., 2013; Radke & Alocilja, 2005).

Meanwhile, EIS using a microelectrode can provide

more capability of label-free and single cell analysis

than any other electrode structures. In fact,

experimental demonstration of impedance mapping

with microelectrode for tissues is reported (Vijay et

al., 2016; Miccoli et al., 2019). Such microscale

electrodes are proposed to be used in high sensitivity

measurement and detailed analysis in single cell

monitoring. Nevertheless, it is difficult to associate

experimental EIS data with underlying changes in cell

morphology. Such relation can be made clear by

computer simulation.

In this work, we demonstrate computer simulation

of EIS with microelectrode for single cell analysis.

Our computer simulation reveals relationship

between EIS data and cell morphology parameters.

Our findings will benefit experimentalists in analysis

of experimental data and optimization of sensor

microelectrode design.

2 THEORY

The equivalent circuit is used to analyse in EIS

measurement. Fig. 1(a) shows the equivalent circuit

model of conventional parallel facing electrode

(Tanaka et al., 2020), where the 𝐶



indicates the

electrochemical double layer capacitance and the 𝑍



indicates the impedance between cell and substrate

(Giaever & Keese, 1991). In addition, the 𝑅



indicates the solution resistance and the R

gap

indicates

the intercellular solution resistance. The electrical

components of cells were described as cell membrane

capacitance



𝐶





and cytoplasm resistance (R

cyto

Fig. 1(b) shows the schematic illustration of

impedance magnitude-frequency characteristics from

the equivalent circuit shown in Fig. 1(a). Note that, in

bode plot, the slope of capacitance and resistance are

Figure 1: (a) The equivalent circuit model of parallel facing

electrode for EIS measurement of cell. The WE and CE

indicate working electrode and counter electrode,

respectively. (b) Schematic illustration of impedance

magnitude-frequency characteristics. The 𝑅



||𝑅





indicates the combined resistance of R

gap

and R

cyto

parallel.

−1 and 0, respectively. On the other hand, the slope

of 𝑍



is −1 or more, but less than 0 because the 𝑍



expressed by the distributed model (Giaever & Keese,

1991). It should be noted that in this study, a

microelectrode was used as working electrode (WE),

and hence this equivalent circuit (Fig. 1(b)) is not

exactly applicable to the analysis for this study.

However, when we analyze the result of simulation

for single cell on a microelectrode, we should obtain

valuable information by comparing to this equivalent

circuit.

3 IMPEDANCE

CHARACTERISTICS FOR DISC

ELECTRODE

The simulation model of single cell monitoring on a

microelectrode is shown in Fig. 2(a). Constant bias

was set to Zero and a sinusoidal voltage with

Electrochemical Impedance Simulation for Single Cell Analysis using a Microelectrode

115

amplitude 5.0 mV was applied to WE while CE was

set to ground. The cell was modeled as hemisphere

(Ren & Chui, 2018) and the cell radius was set to 5μm.

The distance between the WE and single cell was set

to 100 nm (Ren & Chui, 2018). The mirror boundary

condition was imposed on the side face of solution.

Theoretical calculation with the following Eq. (1) is

used to calculate the solution resistance in Fig. 2(a)

(Denhoff, 2006).

2πr

arctan 

 , (1)

where 𝑟



is the WE radius, 𝜎 is the conductivity of

solution and b is the distance between WE and CE.

The simulated spreading resistance becomes

analogous to the spreading resistance calculated by

Eq. (1) under the condition that satisfies 𝑟



≪𝑏 and

𝑟



≪𝑟



, where 𝑟



is CE radius. Therefore, the

distance between WE and CE was 100 times or more

as long as WE radius. Likewise, CE radius was 100

times or more as long as WE radius. Actual

simulation is done in axisymmetric 2D (cylindrical

coordinate) as shown in Fig. 2(b) due to rotational

symmetry. Table. 1 shows the parameters used in

Figure 2: (a) Sensor structure, (b) simulation model in

cylindrical coordinate.

swept from 10



Hz to 10



Hz. Note that the WE radius

was changed from 2μm to 4.5μm stepped by 0.5μm.

These WE radius were based on the literature of

Miccoli et al (2019). We used COMSOL

Multiphysics

5.3a for numerical simulation. Note

that the differentail forms of Maxwell’s equations are

solved in this software.

Table. 1: Parameter used in simulation (Ermolina et al.,

2001).

3.1 Result

Fig. 3 shows the Bode plot of simulated impedance

from Fig. 2(b). In Fig. 3, the electrical double layer

capacitance (𝐶



) is dominant around 10

Hz. From

Hz to 10

Hz, most of potential drops across

solution between cell and sensor substrate, thus the

cell-substrate impedance (𝑍



) is dominant. Around

Hz, the impedance depends on the spreading

resistance (𝑅



) (Denhoff, 2006), and the capacitance

of solution is significant at 10

Hz. In Fig. 3, at 10

Hz, the slope of

𝑍

becomes closer to 0 as 𝑟



decreases. This behaviour is attributed to the fact that

the equivalent circuit model of 𝑍



changes from

distributed (Fig. 4(a)) (Giaever & Keese, 1991) to

lumped-constant (Fig. 4(b)) model. This result

indicates that the cell-substrate resistance could be

detected directly, enabling to detect the change of

conductivity between cell and sensor substrate. In

higher frequency range around 10

Hz, the slope of

𝑍

is almost 0. The impedance of cell membrane

capacitance can be ignored here, and the impedance

only depends on spreading resistance 𝑅



(Denhoff,

2006). Fig. 5 represents impedance characteristics for

disk microelectrode around 50 MHz. Note that in Fig.

5, the theoretical curve is calculated using the 𝑅



formula with cytoplasm and solution conductivity. In

Fig. 5, as 𝑟



decreases, the simulated impedance

becomes closer to the theoretical curve calculated by

cytoplasm conductivity. This is attributed to the

�

Cell

Solution

(

)

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116

Figure 3: Bode plot of simulated impedance from Fig. 2.

Legends indicate working electrode radius.

Figure 4: Schematic illustration of the equivalent circuit

model of the impedance 𝑍



between cell and sensor

substrate. (a) WE radius is close to cell radius and (b) WE

radius is much smaller than cell radius.

potential drop localization around WE due to the

decrease in 𝑟



. Consequently, most of 𝑅



becomes

the spreading resistance within the cell. Hence, for

smaller 𝑟



, the impedance around 10

Hz reflects the

cytoplasm conductivity. This indicates that a

microelectrode could reveal the conductivity inside

the cell.

4 CELL ADHESION

The cell adhesion is an important behaviour in the

healing process and immune response of tissues

(Wegener et al., 2000). Hence, we simulated the cell

adhesion process by using a microelectrode. Fig. 6(a)

represents the simulation model of cell adhesion. In

Fig. 6(a), the 𝑟



was swept parametrically while the

cell volume is fixed. Obviously, in Fig. 6(a), the

radius and the height of cell change simultaneously.

Therefore, another simulation as shown in Fig. 6(b)

Figure 5: Electrode radius-impedance characteristics at 56

MHz and schematic illustration of electric potential and

current flow. Electric potential drops from red to blue.

Figure 6: (a) Constant cell volume, (b) constant cell radius.

was done in order to identify which change has an

impact on impedance by sweeping only 𝑟



. In Fig.

6(b), the 𝑟



is fixed to 5μm and the 𝑟



is the same as

used in Fig. 6(a). Note that the WE radius was set to

1μm because from the result in Fig. 5, we predicted

that the smaller electrode should provide more

sensitive detection of the cell height change in

adherent process. The other parameters are the same

as Table. 1.

4.1 Result

Figs. 7(a) and 7(b) represent the Bode plot of

simulated impedance from Fig. 6(a) and Fig. 6(b),

respectively. Fig. 7(c) represents the impedance

sensitivity calculated based on Fig. 6(a). The

sensitivity is written as

(

)

(

)

�

�=5µm

100nm

� =1µm

�

�= 10µm

� =1µm

�

�=5µm

� =1µm

�

�=5µm

100nm

� =1µm

�

Electrochemical Impedance Simulation for Single Cell Analysis using a Microelectrode

117

Figure 7: (a) Bode plot of simulated impedance from Fig.6(a). (b) Bode plot of simulated impedance from Fig.6(b). (c)

Sensitivity calculated based on cell radius 5μm from (a), and (d) sensitivity calculated based on cell height 5μm from (b).

Legends of (a), (c) indicate the cell radius and legends of (b), (d) indicate the cell height.

Sensitivity [%]=





5μm



5μm



×100 ,





where 𝑍



 is the impedance magnitude when the

cell radius is 5μm and

𝑍



is the impedance

magnitude of each cell radius except for 5μm．

Likewise, Fig. 7(d) represents the impedance

sensitivity from Fig. 7(b). Note that the peak

sensitivity was achieved around 10

Hz in Fig. 7(c).

This is attributed to the increase in cell-substrate

resistance due to the increase in cell radius, which

should not appear in Fig. 7(d) as expected. In other

words, it is possible to measure independently the cell

radius and cell height from the impedance for each

frequency range.

5 DISCUSSION

In this study, we showed the benefit of using

microelectrodes smaller than single cell size by

computer simulation. The first point to be discussed

is the impact of electrode size. In Fig. 3, around 10

Hz, smaller electrode size leads to more distinct

detection of cell-substrate resistance. There is a report

showing impedance change of aspirin-treated cell

around 10

Hz (Yin et al., 2007), where the cells

treated with 1mM aspirin showed the difference from

the cells without treatment in the methyl tetrazolium

(MTT) assay. On the other hand, in EIS measurement

using electrode larger than single cell, there was no

difference between the treated cell and the control cell.

The microelectrode could provide the difference of

impedance magnitude between the cells treated with

BIODEVICES 2021 - 14th International Conference on Biomedical Electronics and Devices

118

1mM aspirin and the cells without treatment around

Hz. In Fig. 5, around 10

Hz, as the electrode size

decreases, the simulated impedance becomes closer

to the theoretical curve calculated using the 𝑅



formula with cytoplasm conductivity. This result

indicates that the theoretical value can provide the

cytoplasm electrical conductivity. Previous study

shows the measurement of cytoplasm impedance

changes under the different concentrations of drug

introduced into cells (Stolwijk et al., 2011). The

concentration of drug could be surmised from

cytoplasm electrical conductivity by using a

microelectrode. The second concerns the change in

morphology such as cell height and radius. Figs. 7(c)

and 7(d) show that the electrode smaller than single

cell size can provide the significant sensitivity to

detect the morphological change of single cell. A

recent study showed that the impedance change was

caused by the morphological change derived from

cellular differentiation (Hildebrandt et al., 2010).

However, the difference of impedance magnitude

between control and necrotic spheroids was 6% at

most (Hildebrandt et al., 2010). It is quite possible

that using microscale electrode instead of the

electrode having a diameter of 1mm affords the

significant difference of impedance magnitude in the

same experiment.

6 CONCLUSIONS

The simulation was performed to study the

characteristics of a microelectrode smaller than single

cell. First, a microelectrode shows the feasibility to

measure the resistance between cell and substrate at

low frequency. Second, microelectrode smaller than

a cell shows better performance in detection the

conductivity inside the cell at high frequency. The

simulation of the cell adhesion process showed that a

microelectrode exhibits sufficient sensitivity to

measure the radius and the height of cell

independently in different frequency range.

ACKNOWLEDGEMENTS

This work was supported by JSPS KAKENHI

19K04539.

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