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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 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

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 themagnetic 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

II

III

IV

V

VI

VII

VIII

IX

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.

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.

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 armsand their relative positionswith respect tothe 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:

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):

Department of Electronics, University of Split, Croatia

&

Wessex Institute of Technology

Southampton, UK

The Formulation (cont’d)

The charge density and scalar potentialare related through the equation:

The equation of continuity becomes:

For the time-harmonic ELF exposures it follows:

where =2fis 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:

The air is a lossless dielectric medium and the governing equation is:

the induced current density can be obtained from Ohm’s Law.

BEM/MRM 27, Orlando, Florida, USA, March 2005

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:

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.

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:

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:

or, expressing the electric flux density in terms of scalar potential it follows:

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 non-homogenous media with prescribed boundary conditions

on Ω

on Γ1

on Γ2

The integration domain is considered piecewise homogeneous, so it can be decomposed into an assembly of Nhomogeneous 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:

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 derivativecan be written by means of the interpolation functions ψa

and

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:

where H and G are matrices defined by:

The matching between two subdomains can be established through their shared nodes:

and

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.

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]

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

The comparison with the cyilindrical model

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.

Scalar potential distribution

in the vicinity of the human body

3D mesh: the realistic model of

the body with arms up

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 anklefor some typical values of

electric field near ground under power lines are presented in the table.

Peak values of the Jzversus E

Exposure limits for Jz

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.

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