Journal of Robotics, Networking and Artificial Life, Vol. 4, No. 4 (March 2018) 330-333___________________________________________________________________________________________________________Simulation of Cell Dielectric Properties Based on COMSOL
Shudong Li 1, Xiaoyan Chen 1*, Fengze Han 1
1

College of Electronic Information and Automation,Tianjin University of Science and Technology, China;
E-mail: * cxywxr@tust.edu.cn
www.tust.edu.cn

Abstract
The dielectric properties of cells can be observed by injecting a low amplitude current at different frequencies(1MHz~100MHz). The simulation research is taken on the software platform named COMSOL Multiphysics. Theelectric field and the cell model is created with prior information. By simulation, it’s verified that at low frequencies,
the region of interest (ROI) behaves the conductivity characteristic while the electrical signal cannot pass throughthe cell membrane due to its capacitor properties. With the excitation frequency increasing, the ROI behaves more
permittivity characteristic that the current flowing through the cell membrane becomes more and the current density
increases. The research of the cell dielectric properties provides an auxiliary method to diagnose the status of thecell.
Keywords: dielectric properties, cell model, excitation frequency, finite element method (FEM), auxiliary method

1. Introduction
The cell membranes are composed of insulating bilayer
phospholipid and proteins. The membranes separate theintracellular and extracellular fluid. However, water andsome micro-molecular proteins can exchange between
intracellular and extracellular fluid, due to the permeable
selective characteristic and the structure of themembranes.

1.1 Cell structure
From the biological point, cells are the smallest units that
constitute the biological tissues. Most biological cells
consist of cell fluid and membrane. The cell fluid can bedivided into intracellular fluid and extracellular fluid asshown in Fig.1. Intracellular fluid can be regard as saline
solution which consists of water mainly, inorganic salt
and other metabolites. Extracellular fluid provides theliving environment for cells with appropriate PH value
and saline concentration. Both intracellular andextracellular fluid have good electrical conductivity [1].

1.2 Cell dielectric properties
The specified structure of a cell determines its special
electrical characteristics. When a direct current or a lowfrequency alternating current is injected into the cell, alittle or even none current can flow into the cell becauseof the insulated membrane. This behavior is called
low-frequency dielectric property. When the excitation
frequency gradually increasing, the membrane becomes
electrically invisible and the current can inject into thecell by passing through the membrane. This performanceis called high-frequency dielectric property[2]. The current
lines flow as shown in Fig.2.

Membrane

Extracellular
Fluid

Intracellular
Fluid

Fig.1. Simplified single cell structure model

Copyright © 2018, the Authors. Published by Atlantis Press.
This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
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Journal of Robotics, Networking and Artificial Life, Vol. 4, No. 4 (March 2018) 330-333___________________________________________________________________________________________________________

1.3 Finite element method

IThe finite element method (FEM) was defined andpublished by Clough in 1960. With the development ofcomputer, the numerical solution of differential equations
has been developed and applied a lot. The main idea ofFEM is to approach an entire continuous domain by finite
discrete domains. The unknown function on the entire
domain is represented by functions on each discrete
domain approximately[4]. A commercial software named
COMSOL Multiphysics is a powerful solution engine.
2. Method

Low-frequency ACThis section uses the software COMSOL Multiphysics tobuild the model of single cell. The geometric shape ofmodel and the value of dielectric properties of cell are
selected referring to blood cells[5].

High-frequency ACFig.2. Current flows through the cell

According to the theory of cell dielectric properties,
cell membrane has the characteristic of capacitance andthe two cell fluids has the characteristic of resistance[3].
The electrical characteristics of single cell can be equaled
to an electrical circuit as shown in Fig.3(a), where theparameters represent different parts of the cell.
𝑅𝑚 : equivalent resistance of membrane
𝐶𝑚 : equivalent capacitance of membrane
𝑅𝑖 : equivalent resistance of intracellular fluid
𝐶𝑖 : equivalent capacitance of intracellular fluid
𝑅𝑒 :equivalent resistance of extracellular fluid
𝐶𝑒 : equivalent capacitance of extracellular fluid
While 𝑅𝑚 , 𝐶𝑖 and 𝐶𝑒 are much larger than 𝐶𝑚 , 𝑅𝑖
and 𝑅𝑒 , less current would go through them, so these canbe neglected to achieve a simplified equivalent electricalmodel as shown in Fig.3(b).

RmCi

2.1.1 Modeling and parameter settings
The parameters of the single cell model is shown in Fig.4.
The meaning of the parameters is as follows:εe: permittivity of extracellular fluid
σe: conductivity of extracellular fluid
εi: permittivity of intracellular fluid
σi: conductivity of intracellular fluid
εm: permittivity of membrane
σm: conductivity of membrane
R: radius of single cell
Tm: thickness of membrane
εe=80
σe=1 S/mεi=80
σi=1 S/m

Cm

Cm

ReRi

2.1. Single cell modelReCe

R=5um

width||
18.0umεm=5σm=10-5 S/m

Ri

Tm=2umlength=20.0um

(a)

(b)

Fig.4. Geometric and electrical parameters of single cell model

Fig.3(a). A equivalent circuit model of single cell(b). Simplified equivalent circuit model of single cell331

Journal of Robotics, Networking and Artificial Life, Vol. 4, No. 4 (March 2018) 330-333___________________________________________________________________________________________________________As shown in Fig.4, the excitation current with current
density of 1A/m2 enters the region of interest (ROI) fromthe left boundary and flows out from the right boundary.
The above and bottom boundaries are electricalinsulation.
2.1.2 Meshing grid
Meshing is the process by which the active geometricalspace (domain) of a model is sub-divided into acollection of sufficiently smaller spaces so that linear or
higher order polynomial approximations can be used as areasonable analog of the functional physical behavior
being modeled, which is the core of finite element
method.
The software COMSOL is used to generate the grid. If
using coarse mesh size (CMS) to structure the grid, theaccuracy of calculation results is not enough because of
the less grids. But too refined meshing grid takes a lot ofmemory which leads to long time calculation. All things
considered, this paper used normal mesh size (NMS) thatthe number of generated elements is between coarse meshsize (CMS) and fine mesh size (FMS) to create themeshing grid as shown in Fig.5 and Fig.7.

(a)(b)
Fig.6(a). Geometric model of multi-cell(b) Meshing grid of multi-cell model (2962 elements)And three simulation works were implemented towatch the influence on cells that caused by the changes
on the membrane electrical parameters. Table.1 shows
the parameters setting of three groups of experiments.
The parameters are set as the single cell model in Fig.4.
Table.1. Membrane electrical parameters of multi-cell modelGroup Aεm
1235Group B

σmεm（S/m）
10-2
10-5
10-8

357Group C

σmεm（S/m）
10-5357σm（S/m）
10-8
10-510-2

3. Simulation result
3.1. Single cell simulation result
The current density distribution at three typical different
frequencies (1MHz, 50MHz and 100MHz separately) as
shown in Fig.8. It can be observed that there is no current
flowing through the cell model at 1MHz. It is because themembrane works as capacitance in parallel with a large
resistance. The membrane has high insulation and low
conductivity at low frequency. With the frequency
gradually increasing, a part of current starts to passthrough the membrane at frequency 50MHz. It's apparent
that the cell membrane becomes electrically invisible
when the frequency reaches 100MHz.The current density
in the whole domain is homogeneous.

Fig.5. Meshing grid of single cell model(3014 elements)

2.2. Multi-cell model
Because of the special electrical properties of cell
membranes, cells show different characteristics in theelectric field with different frequencies and the changesof cell membrane’s electrical properties lead to changes
on physiological state of cells.
In order to observe the dielectric properties of cells
under different physiological states, this paper establisheda multi-cell model based on the single cell model insection 2.1 as shown in Fig.6(a) and the meshing gridusing SMM is shown in Fig.6(b).

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Journal of Robotics, Networking and Artificial Life, Vol. 4, No. 4 (March 2018) 330-333___________________________________________________________________________________________________________1MHz

50MHz

100MHzbiological cell with finite element method. In view ofphysiology, most diseases are originated from cell lesion,and the dielectricity of cell is changed earlier than thestructural lesion. If the cell dielectricity can be detectedby current signal at routine check-up, it’s worthwhile fordiseases precaution.
The search results of this paper indicate that thedifferent physiology status cells can show up different
dielectrical characteristics when is stimulated withdifferent frequencies.

Fig.8.Current density distribution of single cell at different
frequency

3.2. Multi-cell simulation result
Table.2. Multi-cell model simulation resultsGroupA(changes onσm)

1Mhz

50MHz

5. Acknowledgements

100MHzThis research work is supported by the National
Natural Science Foundation of China (Grant
No.61301246) and the Science and Technology Project ofTianjin (12JCYBJC19300).

GroupB(changeson εm)

References
1Mhz

50MHz

100MHz

1Mhz

50MHz

100MHz

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GroupC(changeson εm andσm )Table 2 shows the three sets of simulation results, in thesame current field,the three cells with different membrane
have respective frequency response. This because themembrane works as a capacitance in parallel with a largeresistance, when setting different electrical parameters(permittivity ε and conductivity σ) to the membrane, thevalue of the capacitance and the resistance changed. The
simulation results proves that the change of cell’s
physiological status can affect its dielectric properties on
account of changes on membrane.
4. Discussion
The finite element method has been widely used inmechanics of biological tissue[6]. But at the cell level,
there are few papers that introduce the electromagnetic
characteristics[7].
This paper preliminarily build a single-cell model anda multi-cell model from microcosmic view and conduct atentative research at the dielectric properties of the333