Transcript Slide 1

Department of Electronics, University of Split, Croatia
&
Wessex Institute of Technology
Southampton, UK
Human Body Response
to Extremely Low Frequency
Electric Fields
Dragan Poljak1, Andres Perrata2, Cristina Gonzales2
1Department
of Electronics
University of Split
R.Boskovica bb,
HR-21000 Split, Croatia
2Wessex
Institute of Technology
Ashurst Lodge, Ashurst,
Southampton SO40 7AA
England, UK
Department of Electronics, University of Split, Croatia
&
Wessex Institute of Technology
Southampton, UK
CONTENTS
• Introduction
• The Human Body Models
• The Formulation
• The Boundary Element Method
• Computational Examples
• Concluding Remarks
Department of Electronics, University of Split, Croatia
&
Wessex Institute of Technology
Southampton, UK
Introduction
MOTIVATION: Human being can be exposed to two kinds of fields generated
by low frequency (LF) power systems:
1) low voltage/high intensity systems (The principal radiated
field is the magnetic one, while the induced currents form close loops
in the body);
2) high voltage/low intensity systems (The principal radiated
field is the electric one while the induced currents have the axial character).
OBJECTIVE:This paper deals with human exposure assessment to high
voltage ELF fields.
Basically, human exposure to high voltage ELF electric fields results in
induced fields and currents in all organs. These induced currents and fields
may give rise to thermal and nonthermal effects.
Department of Electronics, University of Split, Croatia
&
Wessex Institute of Technology
Southampton, UK
Introduction (cont’d)
NUMERICAL METHOD: The Boundary Element Method (BEM) with domain
decomposition is applied to the modeling of the human body.
Main advantage: A volume meshing is avoided.
Main drawback: The method requires the calculation of singular integrals.
FORMULATION:The quasi-static approximation of the ELF E- field and the
related continuity equation of the Laplace type are used.
HUMAN BODY MODELS: Three models are implemented:
• cylindrical body model
• multidomain body of revolution
• realistic, anatomically based body model
RESULTS: Solving the laplace equation and solving the scalar potential along the
body, one can calculate the induced current density inside the body.
Department of Electronics, University of Split, Croatia
&
Wessex Institute of Technology
Southampton, UK
The Human Body Models
Cylindrical body model
•Body of revolution
representation of the human being
• Realistic body model
Department of Electronics, University of Split, Croatia
&
Wessex Institute of Technology
Southampton, UK
The Human Body Models (cont’d)
• Cylindrical body model
L=1.75m, a=0.14m, =0.5 S/m
Department of Electronics, University of Split, Croatia
&
Wessex Institute of Technology
Southampton, UK
The Human Body Models (cont’d)
The body of revolution representation of human being
The body of revolution representation of human being consists of 9 portions.
Body
portion
Region
Conductivity
 [S/m]
Head
I , II
0.12
Neck
III
0.6
Shoulders
IV
0.04
Thorax
V
0.11
Pelvis
and crotch
VI
0.11
Knee
VII
0.52
Ankle
VIII
0.04
Foot
IX
0.11
I
II
III
IV
V
VI
VII
VIII
IX
Multidomain model of the body and conductivities at ELF frequencies
Department of Electronics, University of Split, Croatia
&
Wessex Institute of Technology
Southampton, UK
The Human Body Models (cont’d)
The upper plate electrode is assumed to be at a given potential of a high
voltage power line.
The human body is located between the parallel plate electrodes, in the middle
of the lower one.
  U0

0
n

0
n
 0
Calculation domain with the prescribed boundary conditions
Department of Electronics, University of Split, Croatia
&
Wessex Institute of Technology
Southampton, UK
The Human Body Models (cont’d)
Mesh and postprocessing information of the human body are shown.
a) Geometry definition b) Meshed model c) Internal organs taken into account
Department of Electronics, University of Split, Croatia
&
Wessex Institute of Technology
Southampton, UK
The Human Body Models (cont’d)
Realistic human body models
The effect of arms and their relative
positions with respect to the vertical
are studied separately.
The prescribed boundary conditions
are identical to the ones used in
the case of body of revolution model.
Department of Electronics, University of Split, Croatia
&
Wessex Institute of Technology
Southampton, UK
The Formulation
The equation of continuity
The continuity equation is usually given in the form:

J 
0
t
where is the current density and  represents the volume charge density.
The induced current density can be expressed in terms of the scalar
electric potential using the constitutive equation (Ohm’s Law):
J  
Department of Electronics, University of Split, Croatia
&
Wessex Institute of Technology
Southampton, UK
The Formulation (cont’d)
The charge density and scalar potential are related through the equation:
     
The equation of continuity becomes:
   

( )  0
t
For the time-harmonic ELF exposures it follows:
   j     0
where =2f is the operating frequency.
Department of Electronics, University of Split, Croatia
&
Wessex Institute of Technology
Southampton, UK
The Formulation (cont’d)
In the ELF range all organs behave as good conductors and the continuity
equation simplifies into Laplace equation:
( )  0
The air is a lossless dielectric medium and the governing equation is:
( )  2  0
the induced current density can be obtained from Ohm’s Law.
Department of Electronics, University of Split, Croatia
&
Wessex Institute of Technology
Southampton, UK
The Formulation (cont’d)
The air-body interface conditions
The tangential component of the E-field near the interface is given by:


n  Eb  Ea  0
Expressing the electric field in terms of scalar potential, it follows:
n   b  a   0
The induced current density near the body-air surface is given by:
n  J   js
where s denotes the surface charge density.
Department of Electronics, University of Split, Croatia
&
Wessex Institute of Technology
Southampton, UK
The Formulation (cont’d)
Expressing the current density in terms of scalar potential:
 b nb   j s
where σb is the tissue conductivity and φb is the potential at the body surface.
The boundary condition for the electric flux density at the air-body surface is:
n  D  s
or, expressing the electric flux density in terms of scalar potential it follows:
 0 n  a   s
where φa and denotes the potential in the air in the proximity of the body.
Department of Electronics, University of Split, Croatia
&
Wessex Institute of Technology
Southampton, UK
The Boundary Element Method
The problem consists of finding the solution of the Laplace equation in a nonhomogenous media with prescribed boundary conditions
    0
 
on Ω
on Γ1


nj 
x j
n j
on Γ2
The integration domain is considered piecewise homogeneous, so it can be
decomposed into an assembly of N homogeneous subdomains Ωk (k = 1, m).
Department of Electronics, University of Split, Croatia
&
Wessex Institute of Technology
Southampton, UK
The Boundary Element Method (cont’d)
Green’s theorem yields the following integral representation for a subdomain:
 *
 *
c         
d  
 d
n
n
k
k
*
where  is the 3D fundamental solution of Laplace equation,  * n
is the derivative in normal direction to the boundary.
Discretization to Nk elements leads to an integral relation:
Nk
 *
 *
cii    
d   
 d
n
j 1 k , j
j 1 k , j n
Nk
Potential and its normal derivative can be written by means of the interpolation
functions ψa
6
  ξ    a  ξ a
a 1
and
  ξ 
n
6
  a  ξ  a
a 1
Department of Electronics, University of Split, Croatia
&
Wessex Institute of Technology
Southampton, UK
The Boundary Element Method (cont’d)
The system of equations for each subdomain can be written as:
φ
Hφ  G
0
n
where H and G are matrices defined by:
*




a
H  hij    a 
 d
 n  j
k , j
G  gija 
*


 a d
k , j
The matching between two subdomains can be established through their shared
nodes:


j A  j B
and


   
 
  A
   A





n j 

 n j  B
A
Department of Electronics, University of Split, Croatia
&
Wessex Institute of Technology
Southampton, UK
Computational Examples
The multidomain body of revolution model
The well-grounded body model of 175cm height exposed to the10kV/m/60Hz
power line E-field. The height of the power line is 10m above ground.
Power
line
plane
plane
Human body
Ground
plane
The boundary element mesh
Department of Electronics, University of Split, Croatia
&
Wessex Institute of Technology
Southampton, UK
Computational Examples (cont’d)
The current density values increase at narrow sections such as ankle and neck.
0,02
Current Density [A/m2]
0,018
0,016
0,014
0,012
0,01
0,008
0,006
0,004
0,002
0
0
0,2
0,4
0,6
0,8
1
Height [m]
1,2
1,4
1,6
1,8
The current density distribution inside the human body
Department of Electronics, University of Split, Croatia
&
Wessex Institute of Technology
Southampton, UK
Computational Examples (cont’d)
Comparison between the BEM, FEM and experimental results for the current
density at various body portions, expressed in [mA/m2]
Part of the
body
BEM
FEM
Experimental
Neck
4.52
4.62
4.66
Pelvis
2.32
2.27
2.25
Ankle
18.91
19.16
18.66
The calculated results via BEM agree well with FEM and experimental results.
Department of Electronics, University of Split, Croatia
&
Wessex Institute of Technology
Southampton, UK
Computational Examples (cont’d)
The main difference is in the area of ankles and neck. The peak values of J in
those parts maintain the continuity of the axial current throughout the body.
Comparison with the basic restrictions
Exposure scenario
The comparison with the cyilindrical model
Current
density
J[mA/m2]
ICNIRP guidelines for
occupational exposure
10
ICNIRP guidelines for general
public exposure
2
Jzmax (cylinder on earth)
3
Jzmax (body of revolution model)
19
Department of Electronics, University of Split, Croatia
&
Wessex Institute of Technology
Southampton, UK
Computational Examples (cont’d)
The realistic models of the human body
The electric field in the air begins to “sense” the presence of the grounded body
at around 5m above ground level.
A plan view of the
integration domain
Electric field in the air near the body
Department of Electronics, University of Split, Croatia
&
Wessex Institute of Technology
Southampton, UK
Computational Examples (cont’d)
BEM with domain decomposition and triangular elements (40 000) is used.
3D mesh: Linear Triangular Elements
Scaled potential lines in air
Department of Electronics, University of Split, Croatia
&
Wessex Institute of Technology
Southampton, UK
Computational Examples (cont’d)
Front and side view of equipotential lines in air are presented.
Scaled Equipotential lines in air
Department of Electronics, University of Split, Croatia
&
Wessex Institute of Technology
Southampton, UK
Computational Examples (cont’d)
The presence of peaks
in current density values again
corresponds to the position
of the ankle and the neck.
Induced axial current density
Department of Electronics, University of Split, Croatia
&
Wessex Institute of Technology
Southampton, UK
Computational Examples (cont’d)
An oversimplified cylindrical
representation of the
human body is unable
to capture the current density
peaks in the regions with
narrow cross section.
Distribution of the internal current density
Department of Electronics, University of Split, Croatia
&
Wessex Institute of Technology
Southampton, UK
Computational Examples (cont’d)
The mesh and scalar potential for the body model with arms up is presented.
3D mesh: the realistic model of
the body with arms up
Scalar potential distribution
in the vicinity of the human body
Department of Electronics, University of Split, Croatia
&
Wessex Institute of Technology
Southampton, UK
Computational Examples (cont’d)
Comparison between the
following body models
is presented:
• No arms
• Arms up
(60° from horizontal plane)
• Cylinder
Induced current density for the various body models
Department of Electronics, University of Split, Croatia
&
Wessex Institute of Technology
Southampton, UK
Computational Examples (cont’d)
Comparison between the
following body models
is presented:
• No arms
• Arms up
(60° from horizontal plane)
• Open arms
Induced current density for the various body models
Department of Electronics, University of Split, Croatia
&
Wessex Institute of Technology
Southampton, UK
Computational Examples (cont’d)
Peak values of the current density in the ankle for some typical values of
electric field near ground under power lines are presented in the table.
Peak values of the Jz versus E
E [kV/m]
Jz[mA/m2]
1
2
5
10
10
19
Exposure limits for Jz
ICNIRP
Safety Standards
J[mA/m2]
Occupational exposure
10
General public exposure
2
Department of Electronics, University of Split, Croatia
&
Wessex Institute of Technology
Southampton, UK
Concluding Remarks
Human exposure to high voltage ELF electric fields is analysed via BEM
with domain decomposition.
Two 3D body models have been implemented:
• the cylindrical body model
• the body of revolution representation
• realistic body model
The internal current density distribution is obtained by solving the
Laplace equation via BEM.
This efficient BEM procedure is considered to be more accurate than
FDTD and computationally less expensive than FEM.
Numerical results obtained by the BEM are also in a good agreement
with FEM and experimental results.
Department of Electronics, University of Split, Croatia
&
Wessex Institute of Technology
Southampton, UK
… more concluding remarks
Analyzing the obtained numerical results the following conclusions
can be drawn:
• Wherever a reduction of the cross section of the human body
exists, there is a significant increase of the current density, i.e. the
peaks occur in neck and ankles.
• The arms extended upwards cause a screening of the electric
field from the top, thus reducing the peak of current density in the
neck.
• Oversimplified cylindrical representation of the human body
suffers from inability to capture the effect of high current density
values in regions of reduced cross section.
Department of Electronics, University of Split, Croatia
&
Wessex Institute of Technology
Southampton, UK
… and future work
• Analysis of the human body model in substation scenarios
• Sensibility analysis in order to measure the fluctuation of
the peak values with different geometrical changes
• Extension of the method to higher frequencies (Although
from the theoretical point of view, this step would appear to
involve radical changes, from a computational point of
view, it will only require to replace the associated Green
Function)
Department of Electronics, University of Split, Croatia
&
Wessex Institute of Technology
Southampton, UK
This is
the end
of the
talk.
Thank you
very much
for your
attention.