Department of Electronics, University of Split, Croatia

1
Department of Electronics, University of Split,
Croatia Wessex Institute of Technology Southamp
ton, UK
Human Body Response to Extremely Low Frequency
Electric Fields
Dragan Poljak1, Andres Perrata2, Cristina
Gonzales2 1Department of Electronics
2Wessex Institute of Technology University
of Split Ashurst
Lodge, Ashurst, R.Boskovica bb,
Southampton SO40 7AA HR-21000 Split,
Croatia England, UK
2
Department of Electronics, University of Split,
Croatia Wessex Institute of Technology Southamp
ton, UK

• CONTENTS
• Introduction
• The Human Body Models
• The Formulation
• The Boundary Element Method
• Computational Examples
• Concluding Remarks

3
Department of Electronics, University of Split,
Croatia Wessex Institute of Technology Southamp
ton, 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). OBJECTIVEThis 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.
4
Department of Electronics, University of Split,
Croatia Wessex Institute of Technology Southamp
ton, UK

• Introduction (contd)
• 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.
• FORMULATIONThe 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.

5
Department of Electronics, University of Split,
Croatia Wessex Institute of Technology Southamp
ton, UK

• The Human Body Models
• Cylindrical body model
• Body of revolution
• representation of the human being
• Realistic body model

6
Department of Electronics, University of Split,
Croatia Wessex Institute of Technology Southamp
ton, UK

• The Human Body Models (contd)
• Cylindrical body model
• L1.75m, a0.14m, ?0.5 S/m

7
Department of Electronics, University of Split,
Croatia Wessex Institute of Technology Southamp
ton, UK
The Human Body Models (contd) 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
Multidomain model of the body and conductivities
at ELF frequencies
8
Department of Electronics, University of Split,
Croatia Wessex Institute of Technology Southamp
ton, UK
The Human Body Models (contd)
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.
Calculation domain with the prescribed boundary
conditions
9
Department of Electronics, University of Split,
Croatia Wessex Institute of Technology Southamp
ton, UK
The Human Body Models (contd)
Mesh and postprocessing information of the human
body are shown.
a) Geometry definition b) Meshed model c)
Internal organs taken into account
10
Department of Electronics, University of Split,
Croatia Wessex Institute of Technology Southamp
ton, UK
The Human Body Models (contd)
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.
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Department of Electronics, University of Split,
Croatia Wessex Institute of Technology Southamp
ton, UK
The Formulation
The equation of continuity The continuity
equation is usually given in the form
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 (Ohms Law)
12
Department of Electronics, University of Split,
Croatia Wessex Institute of Technology Southamp
ton, UK
The Formulation (contd)
The charge density and scalar potential are
related through the equation
The equation of continuity becomes
For the time-harmonic ELF exposures it follows
where ?2?f is the operating frequency.
13
Department of Electronics, University of Split,
Croatia Wessex Institute of Technology Southamp
ton, UK
The Formulation (contd)
In the ELF range all organs behave as good
conductors and the continuity equation
simplifies into Laplace equation
The air is a lossless dielectric medium and the
governing equation is
the induced current density can be obtained from
Ohms Law.
BEM/MRM 27, Orlando, Florida, USA, March 2005
14
Department of Electronics, University of Split,
Croatia Wessex Institute of Technology Southamp
ton, UK
The Formulation (contd)
The air-body interface conditions The tangential
component of the E-field near the interface is
given by
Expressing the electric field in terms of scalar
potential, it follows
The induced current density near the body-air
surface is given by
where ?s denotes the surface charge density.
15
Department of Electronics, University of Split,
Croatia Wessex Institute of Technology Southamp
ton, UK
The Formulation (contd)
Expressing the current density in terms of scalar
potential
where sb is the tissue conductivity and fb is the
potential at the body surface. The boundary
condition for the electric flux density at the
air-body surface is
or, expressing the electric flux density in terms
of scalar potential it follows
where fa and denotes the potential in the air in
the proximity of the body.
16
Department of Electronics, University of Split,
Croatia Wessex Institute of Technology Southamp
ton, UK
The Boundary Element Method The problem
consists of finding the solution of the Laplace
equation in a non-homogenous media with
prescribed boundary conditions
on ?
on G1
on G2
The integration domain is considered piecewise
homogeneous, so it can be decomposed into an
assembly of N homogeneous subdomains ?k (k 1,
m).
17
Department of Electronics, University of Split,
Croatia Wessex Institute of Technology Southamp
ton, UK
The Boundary Element Method (contd)
Greens theorem yields the following integral
representation for a subdomain
where
is the 3D fundamental solution of Laplace
equation,
is the derivative in normal direction to the
boundary.
Discretization to Nk elements leads to an
integral relation
Potential and its normal derivative can be
written by means of the interpolation functions ?a
and
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Department of Electronics, University of Split,
Croatia Wessex Institute of Technology Southamp
ton, UK
The Boundary Element Method (contd)
The system of equations for each subdomain can
be written as
where H and G are matrices defined by
The matching between two subdomains can be
established through their shared nodes
and
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Department of Electronics, University of Split,
Croatia Wessex Institute of Technology Southamp
ton, 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
20
Department of Electronics, University of Split,
Croatia Wessex Institute of Technology Southamp
ton, UK
Computational Examples (contd)
The current density values increase at narrow
sections such as ankle and neck.
The current density distribution inside the
human body
21
Department of Electronics, University of Split,
Croatia Wessex Institute of Technology Southamp
ton, UK
Computational Examples (contd)
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.
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Department of Electronics, University of Split,
Croatia Wessex Institute of Technology Southamp
ton, UK
Computational Examples (contd)
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 Current density JmA/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
The comparison with the cyilindrical model
23
Department of Electronics, University of Split,
Croatia Wessex Institute of Technology Southamp
ton, UK
Computational Examples (contd)
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
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Department of Electronics, University of Split,
Croatia Wessex Institute of Technology Southamp
ton, UK
Computational Examples (contd)
BEM with domain decomposition and triangular
elements (40 000) is used.
3D mesh Linear Triangular Elements
Scaled potential lines in air
25
Department of Electronics, University of Split,
Croatia Wessex Institute of Technology Southamp
ton, UK
Computational Examples (contd)
Front and side view of equipotential lines in air
are presented.
Scaled Equipotential lines in air
26
Department of Electronics, University of Split,
Croatia Wessex Institute of Technology Southamp
ton, UK
Computational Examples (contd)
The presence of peaks in current density values
again corresponds to the position of the ankle
and the neck.
Induced axial current density
27
Department of Electronics, University of Split,
Croatia Wessex Institute of Technology Southamp
ton, UK
Computational Examples (contd)
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
28
Department of Electronics, University of Split,
Croatia Wessex Institute of Technology Southamp
ton, UK
Computational Examples (contd)
The mesh and scalar potential for the body model
with arms up is presented.
Scalar potential distribution in the vicinity
of the human body
3D mesh the realistic model of the body with
arms up
29
Department of Electronics, University of Split,
Croatia Wessex Institute of Technology Southamp
ton, UK
Computational Examples (contd)

• 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
30
Department of Electronics, University of Split,
Croatia Wessex Institute of Technology Southamp
ton, UK
Computational Examples (contd)

• 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
31
Department of Electronics, University of Split,
Croatia Wessex Institute of Technology Southamp
ton, UK
Computational Examples (contd)
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
Exposure limits for Jz
E kV/m JzmA/m2
1 2
5 10
10 19
ICNIRP Safety Standards JmA/m2
Occupational exposure 10
General public exposure 2
32
Department of Electronics, University of Split,
Croatia Wessex Institute of Technology Southamp
ton, 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.

33
Department of Electronics, University of Split,
Croatia Wessex Institute of Technology Southamp
ton, 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.

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Department of Electronics, University of Split,
Croatia Wessex Institute of Technology Southamp
ton, 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)

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Department of Electronics, University of Split,
Croatia Wessex Institute of Technology Southamp
ton, UK
This is the end of the talk.
Thank you very much for your attention.