Department of Electronics, University of Split, Croatia & Wessex Institute of Technology Southampton, UK Human Body Response to Extremely Low Frequency

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



CONTENTS

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


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.



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.



The Human Body Models

Cylindrical body model

•Body of revolution representation of the human being

• Realistic body model



The Human Body Models (cont’d)

• Cylindrical body model L=1.75m, a=0.14m, =0.5 S/m




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



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





a) Geometry definition b) Meshed model c) Internal organs taken into account

Mesh and postprocessing information of the human body are shown.




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



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



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)



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 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.




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 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).



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)



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)



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



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)



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.




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.





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.



3D mesh: Linear Triangular Elements Scaled potential lines in air

BEM with domain decomposition and triangular elements (40 000) is used.




Front and side view of equipotential lines in air are presented.


Scaled Equipotential lines in air



Induced axial current density


The presence of peaksin current density values again corresponds to the position of the ankle and the neck.




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.




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.



Induced current density for the various body models


Comparison between the following body modelsis presented:

• No arms • Arms up (60° from horizontal plane)• Cylinder




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



E [kV/m] Jz[mA/m2]

1 2

5 10

10 19

Peak values of the Jz versus E


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



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



… 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.



… 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)



Thank you very much for your attention.

This is the end of the talk.

Documents

Department of Electronics, University of Split, Croatia & Wessex Institute of Technology Southampton, UK Human Body Response to Extremely Low Frequency