department of electronics , university of split, croatia & wessex institute of technology
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Department of Electronics , University of Split, Croatia & Wessex Institute of Technology Southampton, UK. Human Body Response to Extremely Low Frequency Electric Fields. Dragan Poljak 1 , Andres Perrata 2 , Cristina Gonzales 2 - PowerPoint PPT PresentationTRANSCRIPT
Department of Electronics, University of Split, Croatia &
Wessex Institute of TechnologySouthampton, 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 7AAHR-21000 Split, Croatia England, UK
Department of Electronics, University of Split, Croatia &
Wessex Institute of TechnologySouthampton, 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 TechnologySouthampton, UKIntroduction
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 TechnologySouthampton, 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 TechnologySouthampton, 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 TechnologySouthampton, 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 TechnologySouthampton, 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 TechnologySouthampton, UK
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.
0n
0
n
0U
0 Calculation domain with the prescribed boundary conditions
The Human Body Models (cont’d)
Department of Electronics, University of Split, Croatia &
Wessex Institute of TechnologySouthampton, UK
The Human Body Models (cont’d)
a) Geometry definition b) Meshed model c) Internal organs taken into account
Mesh and postprocessing information of the human body are shown.
Department of Electronics, University of Split, Croatia &
Wessex Institute of TechnologySouthampton, UK
The Human Body Models (cont’d)
The effect of arms and their relative positions with respect to the verticalare studied separately.
The prescribed boundary conditionsare identical to the ones used in the case of body of revolution model.
Realistic human body models
Department of Electronics, University of Split, Croatia &
Wessex Institute of TechnologySouthampton, UK
The equation of continuity
The continuity equation is usually given in the form:
0Jt
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
The Formulation
Department of Electronics, University of Split, Croatia &
Wessex Institute of TechnologySouthampton, UK
The charge density and scalar potential are related through the equation:
The equation of continuity becomes:
( ) 0t
For the time-harmonic ELF exposures it follows:
0j
where =2f is the operating frequency.
The Formulation (cont’d)
Department of Electronics, University of Split, Croatia &
Wessex Institute of TechnologySouthampton, UK
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.
The Formulation (cont’d)
Department of Electronics, University of Split, Croatia &
Wessex Institute of TechnologySouthampton, UK
The air-body interface conditions
The tangential component of the E-field near the interface is given by:
0b an E E
Expressing the electric field in terms of scalar potential, it follows:
0b an
The induced current density near the body-air surface is given by:
sn J j
where s denotes the surface charge density.
The Formulation (cont’d)
Department of Electronics, University of Split, Croatia &
Wessex Institute of TechnologySouthampton, UK
Expressing the current density in terms of scalar potential:
b b sn j
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: sn D
or, expressing the electric flux density in terms of scalar potential it follows:
0 a sn
where φa and denotes the potential in the air in the proximity of the body.
The Formulation (cont’d)
Department of Electronics, University of Split, Croatia &
Wessex Institute of TechnologySouthampton, 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
0
on Ω
on Γ1
jj j
nx n
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 TechnologySouthampton, UK
Green’s theorem yields the following integral representation for a subdomain:
*
*
k k
c d dn n
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:
, ,
**
1 1
k k
k j k j
N N
i ij j
c d dn n
Potential and its normal derivative can be written by means of the interpolation functions ψa
6
1a a
a
ξ ξ and 6
1a a
an
ξ
ξ
The Boundary Element Method (cont’d)
Department of Electronics, University of Split, Croatia &
Wessex Institute of TechnologySouthampton, UK
The system of equations for each subdomain can be written as:
0
φ
Hφ Gn
where H and G are matrices defined by:
,
*
k j
aij a
j
H h dn
,
* k j
aij aG g d
The matching between two subdomains can be established through their shared nodes:
j A j B and A A
j jA Bn n
The Boundary Element Method (cont’d)
Department of Electronics, University of Split, Croatia &
Wessex Institute of TechnologySouthampton, UK
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.
Human body
Ground plane
Power line plane plane
The boundary element mesh
Computational Examples
Department of Electronics, University of Split, Croatia &
Wessex Institute of TechnologySouthampton, UK
The current density values increase at narrow sections such as ankle and neck.
0
0,002
0,004
0,006
0,008
0,01
0,012
0,014
0,016
0,018
0,02
0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6 1,8Height [m]
Cu
rren
t D
en
sit
y [
A/m
2]
The current density distribution inside the human body
Computational Examples (cont’d)
Department of Electronics, University of Split, Croatia &
Wessex Institute of TechnologySouthampton, UK
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.
Computational Examples (cont’d)
Department of Electronics, University of Split, Croatia &
Wessex Institute of TechnologySouthampton, UK
The comparison with the cyilindrical model
Comparison with the basic restrictions
Exposure scenarioCurrent densityJ[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
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.
Computational Examples (cont’d)
Department of Electronics, University of Split, Croatia &
Wessex Institute of TechnologySouthampton, UK
Computational Examples (cont’d)
The realistic models of the human body
A plan view of the integration domain
Electric field in the air near the body
The electric field in the air begins to “sense” the presence of the grounded body at around 5m above ground level.
Department of Electronics, University of Split, Croatia &
Wessex Institute of TechnologySouthampton, UK
3D mesh: Linear Triangular Elements Scaled potential lines in air
BEM with domain decomposition and triangular elements (40 000) is used.
Computational Examples (cont’d)
Department of Electronics, University of Split, Croatia &
Wessex Institute of TechnologySouthampton, UK
Front and side view of equipotential lines in air are presented.
Computational Examples (cont’d)
Scaled Equipotential lines in air
Department of Electronics, University of Split, Croatia &
Wessex Institute of TechnologySouthampton, UK
Induced axial current density
Computational Examples (cont’d)
The presence of peaksin current density values again corresponds to the position of the ankle and the neck.
Department of Electronics, University of Split, Croatia &
Wessex Institute of TechnologySouthampton, UK
Computational Examples (cont’d)
Distribution of the internal current density
An oversimplified cylindrical representation of the human body is unable to capture the current density peaks in the regions with narrow cross section.
Department of Electronics, University of Split, Croatia &
Wessex Institute of TechnologySouthampton, UK
Computational Examples (cont’d)
3D mesh: the realistic model of the body with arms up
Scalar potential distribution in the vicinity of the human body
The mesh and scalar potential for the body model with arms up is presented.
Department of Electronics, University of Split, Croatia &
Wessex Institute of TechnologySouthampton, UK
Induced current density for the various body models
Computational Examples (cont’d)
Comparison between the following body modelsis presented:
• No arms • Arms up (60° from horizontal plane)• Cylinder
Department of Electronics, University of Split, Croatia &
Wessex Institute of TechnologySouthampton, UK
Computational Examples (cont’d)
Comparison between the following body modelsis 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 TechnologySouthampton, UK
E [kV/m] Jz[mA/m2]
1 2
5 10
10 19
Peak values of the Jz versus E
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.
ICNIRP Safety Standards
J[mA/m2]
Occupational exposure 10
General public exposure 2
Exposure limits for Jz
Department of Electronics, University of Split, Croatia &
Wessex Institute of TechnologySouthampton, UK
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.
Concluding Remarks
Department of Electronics, University of Split, Croatia &
Wessex Institute of TechnologySouthampton, 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 TechnologySouthampton, UK
… and future work
• Analysis of the human body model in substation scenarios
• Sensibility analysis in order to measure the fluctuation ofthe peak values with different geometrical changes
• Extension of the method to higher frequencies (Althoughfrom the theoretical point of view, this step would appear toinvolve radical changes, from a computational point ofview, it will only require to replace the associated GreenFunction)
Department of Electronics, University of Split, Croatia &
Wessex Institute of TechnologySouthampton, UK
Thank you very much for your attention.
This is the end of the talk.