1. 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 1 Department of Electronics 2 Wessex 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 Southampton, 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 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.

4. 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.

5. 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

6. 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

7. 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 RegionConductivity  [S/m] HeadI, II0.12 NeckIII0.6 ShouldersIV0.04 ThoraxV0.11 Pelvis and crotch VI0.11 KneeVII0.52 AnkleVIII0.04 FootIX0.11 I II III IV V VI VII VIII IX Multidomain model of the body and conductivities at ELF frequencies

8. Department of Electronics, University of Split, Croatia & Wessex Institute of Technology Southampton, 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. Calculation domain with the prescribed boundary conditions The Human Body Models (cont’d)

9. Department of Electronics, University of Split, Croatia & Wessex Institute of Technology Southampton, 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.

10. Department of Electronics, University of Split, Croatia & Wessex Institute of Technology Southampton, UK The Human Body Models (cont’d) 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. Realistic human body models

11. Department of Electronics, University of Split, Croatia & Wessex Institute of Technology Southampton, UK 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): The Formulation

12. Department of Electronics, University of Split, Croatia & Wessex Institute of Technology Southampton, UK 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. The Formulation (cont’d)

13. Department of Electronics, University of Split, Croatia & Wessex Institute of Technology Southampton, UK BEM/MRM 27, Orlando, Florida, USA, March 2005 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. The Formulation (cont’d)

14. Department of Electronics, University of Split, Croatia & Wessex Institute of Technology Southampton, UK 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. The Formulation (cont’d)

15. Department of Electronics, University of Split, Croatia & Wessex Institute of Technology Southampton, UK Expressing the current density in terms of scalar potential: where σ b is the tissue conductivity and φ b 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 φ a and denotes the potential in the air in the proximity of the body. The Formulation (cont’d)

16. 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 Γ 1 on Γ 2 The integration domain is considered piecewise homogeneous, so it can be decomposed into an assembly of N homogeneous subdomains Ω k (k = 1, m).

17. Department of Electronics, University of Split, Croatia & Wessex Institute of Technology Southampton, UK 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 N k elements leads to an integral relation: Potential and its normal derivative can be written by means of the interpolation functions ψ a and The Boundary Element Method (cont’d)

18. Department of Electronics, University of Split, Croatia & Wessex Institute of Technology Southampton, UK 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 The Boundary Element Method (cont’d)

19. Department of Electronics, University of Split, Croatia & Wessex Institute of Technology Southampton, 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

20. Department of Electronics, University of Split, Croatia & Wessex Institute of Technology Southampton, UK The current density values increase at narrow sections such as ankle and neck. The current density distribution inside the human body Computational Examples (cont’d)

21. Department of Electronics, University of Split, Croatia & Wessex Institute of Technology Southampton, UK Comparison between the BEM, FEM and experimental results for the current density at various body portions, expressed in [mA/m 2 ] Part of the body BEMFEMExperimental Neck 4.52 4.62 4.66 Pelvis 2.32 2.27 2.25 Ankle18.9119.1618.66 The calculated results via BEM agree well with FEM and experimental results. Computational Examples (cont’d)

22. Department of Electronics, University of Split, Croatia & Wessex Institute of Technology Southampton, UK The comparison with the cyilindrical model Comparison with the basic restrictions Exposure scenario Current density J[mA/m 2 ] ICNIRP guidelines for occupational exposure 10 ICNIRP guidelines for general public exposure 2 J zmax (cylinder on earth)3 J zmax (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)

23. Department of Electronics, University of Split, Croatia & Wessex Institute of Technology Southampton, 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.

24. Department of Electronics, University of Split, Croatia & Wessex Institute of Technology Southampton, UK 3D mesh: Linear Triangular ElementsScaled potential lines in air BEM with domain decomposition and triangular elements (40 000) is used. Computational Examples (cont’d)

25. Department of Electronics, University of Split, Croatia & Wessex Institute of Technology Southampton, UK Front and side view of equipotential lines in air are presented. Computational Examples (cont’d) Scaled Equipotential lines in air

26. Department of Electronics, University of Split, Croatia & Wessex Institute of Technology Southampton, UK Induced axial current density Computational Examples (cont’d) The presence of peaks in current density values again corresponds to the position of the ankle and the neck.

27. Department of Electronics, University of Split, Croatia & Wessex Institute of Technology Southampton, 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.

28. Department of Electronics, University of Split, Croatia & Wessex Institute of Technology Southampton, 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.

29. Department of Electronics, University of Split, Croatia & Wessex Institute of Technology Southampton, UK Induced current density for the various body models Computational Examples (cont’d) Comparison between the following body models is presented: No arms Arms up (60° from horizontal plane) Cylinder

30. 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

31. Department of Electronics, University of Split, Croatia & Wessex Institute of Technology Southampton, UK E [kV/m]J z [mA/m 2 ] 12 510 19 Peak values of the J z 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/m 2 ] Occupational exposure10 General public exposure2 Exposure limits for J z

32. Department of Electronics, University of Split, Croatia & Wessex Institute of Technology Southampton, 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

33. 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.

34. 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)

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