5th International Workshop on Biological Effects of Electromagnetic Fields. September 28th - October 2nd 2008, Città del Mare, Terrasini, Palermo

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5th Internatonal Workshop on Bologcal Effects of Electromagnetc

Palermo COMPLIANCE WITH EU BASIC RESTRICTIONS NEAR INDUCTION

ANALYSIS USING THE SCALAR POTENTIAL FINITE DIFFERENCE (SPFD)

Danele Andreuccett IFAC-CNR Insttute of Appled Physcs Nello Carrara

Sesto Forentno (FI), Italy n.zoppett@fac.cnr.t d.andreuccett@fac.

1 5th Internatonal Workshop on Bologcal Effects of Electromagnetc Felds September 28th - October 2nd 2008, Cttà del Mare, Terrasn, Palermo COMPLIANCE WITH EU BASIC RESTRICTIONS NEAR INDUCTION FURNACES USED IN PRECIOUS METAL INDUSTRY: A 3D NUMERICAL DOSIMETRIC ANALYSIS USING THE SCALAR POTENTIAL FINITE DIFFERENCE (SPFD) TECHNIQUE AND A POSTURABLE DIGITAL BODY MODEL Ncola Zoppett and Danele Andreuccett IFAC-CNR Insttute of Appled Physcs Nello Carrara of the Italan Natonal Research Councl va Madonna del Pano 10, Sesto Forentno (FI), Italy n.zoppett@fac.cnr.t d.andreuccett@fac.cnr.t Complance wth eu basc restrctons near nducton furnaces N.Zoppett D.Andreuccett IFAC-CNR

2 Complance wth eu basc restrctons near nducton furnaces N.Zoppett D.Andreuccett IFAC-CNR Summary Verfyng the complance of exposure lmt values for current denstes mples dfferent sequental steps. The example of a man workng near an nducton furnace used n gold ndustry s presented here: 1. Buldng the exposure scenaro 2. Modellng the exposed subject (posture) 3. Modelng the source 4. Calculatng the current densty 5. Post-processng (surface averagng, lmtaton to CNS tssues) 6. Result analyss

3 Complance wth eu basc restrctons near nducton furnaces N.Zoppett D.Andreuccett IFAC-CNR Exposure scenaro Used n the gold ndustry Magnetc feld only F = 3450 Hz I = 400 A Monophase source Cx=0,3m Cy=0,75m Cz=0,75m Radus= 0,09m The edge of the fngers are less then 10 cm dstant from the conductors

Reference voxel phantom: VHP body model Model nx ny nz n_cells Model memory occupaton [Mb] Head 1mm 178 235 211 8826130 8.42 Man 3mm 196 114 626 13987344 13.34 Man 2mm 293 170 939 46771590 44.

4 Reference voxel phantom: VHP body model Model nx ny nz n_cells Model memory occupaton [Mb] Head 1mm Man 3mm Man 2mm Man 1mm The reference voxel phantom s the VHP model of the entre body at 3mm resoluton. Wth that choce the dosmetrc problems can be solved wth standard PC. Wth hgher resolutons, problems may arse regardng both calculaton tme and memory resources demand. Complance wth eu basc restrctons near nducton furnaces N.Zoppett D.Andreuccett IFAC-CNR

Artculaton algorthm: subdvson n portons Vhp models represent

for dosmetrc evaluatons n dfferent postures, as requred by

An artculaton algorthm s presented that s partcularly suted

Model at rest Subdvson n portons Artculaton of the sngle

5 Artculaton algorthm: subdvson n portons Vhp models represent the human body n standng posture and cannot be drectly used for dosmetrc evaluatons n dfferent postures, as requred by occupatonal exposure studes. An artculaton algorthm s presented that s partcularly suted for use n conjuncton wth fnte dfference calculaton technques. Model at rest Subdvson n portons Artculaton of the sngle portons Complance wth eu basc restrctons near nducton furnaces N.Zoppett D.Andreuccett IFAC-CNR

Complance wth eu basc restrctons near nducton

wth the others (translated and/or rotated) to

6 Complance wth eu basc restrctons near nducton furnaces N.Zoppett D.Andreuccett IFAC-CNR Artculated voxel phantoms The artculated portons are re-assembled together wth the others (translated and/or rotated) to compose the artculated voxel phantom Models used n the examples showed n ths presentaton

The artculaton process deforms the voxels close to the jonts, so that the artculated body model has to be resampled over a

7 Elastc model An elastc model s bult whch separates voxels that undergo rgd translatons and rotatons (bones for example) and voxels that go through elastc deformatons (fleshy parts). The artculaton process deforms the voxels close to the jonts, so that the artculated body model has to be resampled over a regular grd before t can be used as a base for fnte dfference calculatons. Resamplng n two steps Complance wth eu basc restrctons near nducton furnaces N.Zoppett D.Andreuccett IFAC-CNR

8 Complance wth eu basc restrctons near nducton furnaces N.Zoppett D.Andreuccett IFAC-CNR Tssue contnuty Mass conservaton Checks on artculated models blood vessels, nerves crtcal n conjuncton wth the resamplng step (+0,4 kg n the presented case)

9 Complance wth eu basc restrctons near nducton furnaces N.Zoppett D.Andreuccett IFAC-CNR Modelng the source Based on the numercal ntegraton of Laplace law Solenod dmensons (dameter, length) are taken from manufacturer s specfcatons Col current s n agreement wth manufacturer s electrcal data (voltage, power) Current x turn product and col exact poston n the apparatus are adjusted to ft expermental data Here I s the col current, Q s the pont where felds are computed, Γ s the col path and P s a generc pont along t B Q = I 0 4 P dp Q P Q P 3 A Q = 0 I 4 P dp Q P

10 Complance wth eu basc restrctons near nducton furnaces N.Zoppett D.Andreuccett IFAC-CNR Modelng the source (cont.) Measurement setup and results

11 Complance wth eu basc restrctons near nducton furnaces N.Zoppett D.Andreuccett IFAC-CNR Layout of the numercal analyss SPFD n m 6 1 m n 1 j l A c m J peak Feld dstrbuton n the body model volume A Col model

are consdered not the empty space n the box contanng the model) Valdated wth expermental data and

12 Numercal method and applcaton Based on the Scalar Potental Fnte Dfference method (SPFD) scalar method also n 3D problems no addtonal boundary condtons solvng the magnetc problem only the conductve cells are consdered not the empty space n the box contanng the model) Valdated wth expermental data and analytcal models Complance wth eu basc restrctons near nducton furnaces N.Zoppett D.Andreuccett IFAC-CNR

Medan sagttal secton (x=0,3 m) The maxmum

13 Medan sagttal secton (x=0,3 m) The maxmum value (close to the hands ant to the cols) s over 2,5 mt B feld The major part of the body volume s over the acton value 30,7 mt Complance wth eu basc restrctons near nducton furnaces N.Zoppett D.Andreuccett IFAC-CNR

Coronal secton (y=0,15 m) dstrbuton of J

14 Coronal secton (y=0,15 m) dstrbuton of J (peak) Axal secton (z=0,85 m) Sagttal secton (x=0,30 m) 3450 Hz = 0,0345 A/m 2 Sagttal secton (x=0,10 m) Complance wth eu basc restrctons near nducton furnaces N.Zoppett D.Andreuccett IFAC-CNR

15 Complance wth eu basc restrctons near nducton furnaces N.Zoppett D.Andreuccett IFAC-CNR J (peak) Exposure lmt 3450 Hz : 34,5 ma/m 2

16 Complance wth eu basc restrctons near nducton furnaces N.Zoppett D.Andreuccett IFAC-CNR Layout of the numercal analyss SPFD n m 6 1 m n 1 j l A c m J peak Feld dstrbuton n the body model volume A Col model Surface averagng Lmtaton to CNS The complance analyss ends wth the comparson of the current densty surface average (1cm 2 ) lmted to CNS wth the exposure lmt value at the source frequency

17 Post-processng Once the local peak current densty dstrbuton has been calculated two other steps has to be done : Surface average of the current densty [...] over a crosssecton of 1 cm 2 perpendcular to the current drecton (Note 3 of Table 1 of the 2004/40 Drectve ) Lmtaton to central nervous system tssues snce The exposure lmt values on the current densty are ntended to protect aganst acute exposure effects on central nervous system tssues n the head and trunk of the body (Note 2 of Table 1 of the 2004/40 Drectve ) Complance wth eu basc restrctons near nducton furnaces N.Zoppett D.Andreuccett IFAC-CNR

Surface average: smplfed algorthm Dawson et al. [*] ntroduced a smplfed algorthm for current densty averagng.

squares wth 1 cm edges centered on the voxel and parallel to the three prncpal Cartesan planes.

The smplfed algorthm ntroduces two man approxmatons: t uses square cross-sectons that ntersect dfferent portons of surroundng voxels, dependng on ther orentatons.

18 Surface average: smplfed algorthm Dawson et al. [*] ntroduced a smplfed algorthm for current densty averagng. Accordng to t: "the components of the current densty average assocated wth a gven voxel are computed by averagng the perpendcular components of current densty over squares wth 1 cm edges centered on the voxel and parallel to the three prncpal Cartesan planes. The resultng vector feld s treated smlar to the current densty tself n dosmetry computatons". The smplfed algorthm ntroduces two man approxmatons: t uses square cross-sectons that ntersect dfferent portons of surroundng voxels, dependng on ther orentatons. the cross-sectons used to average the current densty are not necessarly perpendcular to the current drecton, as requred by the Drectve. [*] T.W.Dawson, K.Caputa and M.Stuchly. Magnetc feld exposures for UK lvelne workers. Physcs n Medcne and Bology, Vol.47 (2002), pp Complance wth eu basc restrctons near nducton furnaces N.Zoppett D.Andreuccett IFAC-CNR

The crcular 1 cm 2 cross-secton that les on the averagng plane and has center n the applcaton pont s consdered.

19 Complance wth eu basc restrctons near nducton furnaces N.Zoppett D.Andreuccett IFAC-CNR Surface average: exact algorthm A plane ( averagng plane ) s chosen that s perpendcular to the current densty n the consdered voxel (the applcaton pont of the average). The crcular 1 cm 2 cross-secton that les on the averagng plane and has center n the applcaton pont s consdered. The ntersectng secton S of every voxel wth the crcular cross-secton of the prevous step s determned. Snce, n general, the averagng plane s not necessarly perpendcular to a voxel face, ths ntersectng secton can assume the form of a generc polygon wth 3,4,5 or 6 edges. The cross-secton average of the current densty s calculated n every voxel accordng to the followng expresson: J S N 1 S N 1 J S V

20 Complance wth eu basc restrctons near nducton furnaces N.Zoppett D.Andreuccett IFAC-CNR exact algorthm vs smpl. algorthm Dfferences between the two averagng algorthm can be above 3 db (wth both sgns)

21 Complance n the Central Nervous System (CNS) Complance wth eu basc restrctons near nducton furnaces N.Zoppett D.Andreuccett IFAC-CNR Also mportant, the target tssues for ths averagng are the tssues of the central nervous system (CNS), as Note 2 of the same table specfes that The exposure lmt values on the current densty are ntended to protect aganst acute exposure effects on central nervous system tssues n the head and trunk of the body. There s a problem: When the applcaton pont of the averagng cross-secton s close to a surface separatng an organ of the CNS from a dfferent tssue, the averagng cross-secton wll possbly ntersect voxels that do not belong to the CNS. How to proceed n such cases?

22 Complance wth eu basc restrctons near nducton furnaces N.Zoppett D.Andreuccett IFAC-CNR Complance n the Central Nervous System (CNS) full averagng In ths work, the averagng applcaton pont s always taken n a voxel that belongs to the central nervous system, but the contrbutes of all other voxels (even not belongng to the CNS) that ntersect the averagng plane are also fully consdered (FULL AVERAGING). Ths choce s nspred by Note 3 of Table 1 of the Drectve, that ntroduces the current densty averagng because of the electrcal nhomogenety of the body. If the am of the averagng s to take nto account the electrcal nhomogenety, t seems a nonsense to exclude some voxels once the averagng crosssecton has been defned.

Results wth full averagng Exposure lmt value @ 3450 Hz : 34,5 ma/m 2 Usng the full averagng algorthm the maxmum surface average n some tssues s hgher than the local

23 Results wth full averagng Exposure lmt 3450 Hz : 34,5 ma/m 2 Usng the full averagng algorthm the maxmum surface average n some tssues s hgher than the local peak. Ths can happen when the consdered tssue s surrounded by more conductve dstrcts. Complance wth eu basc restrctons near nducton furnaces N.Zoppett D.Andreuccett IFAC-CNR

24 Complance wth eu basc restrctons near nducton furnaces N.Zoppett D.Andreuccett IFAC-CNR Alternatve aproaches to the lmtaton to CNS J S N 1 ZERO WEIGHTING: the averagng applcaton pont s always taken n a voxel that belongs to the central nervous system, and the contrbutes of all the voxels not belongng to the CNS that ntersect the averagng plane are zero weghted on numerator (the averagng surface s effectvely 1 cm 2 ). PARTIAL AVERAGE: the averagng applcaton pont s always taken n a voxel that belongs to the central nervous system, and the contrbutes of all the voxels not belongng to the CNS that ntersect the averagng plane are not consdered at all (zero weghted on both numerator and denomnator; the averagng surface could be less than 1 cm 2 ). S N 1 J S V

25 Results: s the presented case complant wth EU Drectve? Complance wth eu basc restrctons near nducton furnaces N.Zoppett D.Andreuccett IFAC-CNR Usng the geometrcal algorthm the exposure lmt value s exceeded n the perpheral nerves of the pelvs regon. Usng the smplfed algorthm the exposure lmt value s exceeded n the cerebro-spnal flud.

26 Fnal remarks Whle the calculus of the local peak dstrbuton of the current densty s straghtforward, n the post processng steps there are some key questons that are not completely specfed both n drectve and n the lterature: Lmtaton to the Central Nervous System: Whatever s the group of tssues consdered part of CNS, dfferent algorthms are possble to do the surface average of current densty close to the nterfaces between CNS and not-cns tssues. Surface averagng method: Adoptng two dfferent algorthms leads n ths case to dfferences of more than 3 db The concept of cross-secton perpendcular to a vector wth ellptc or crcular polarzaton s not well defned and the choce of the cross-secton orentaton s arbtrary Complance wth eu basc restrctons near nducton furnaces N.Zoppett D.Andreuccett IFAC-CNR

Numerical dosimetry and 2004/40 European Directive

Numerical dosimetry and 2004/40 European Directive Occupational exposure to quasi-static electromagnetic fields and the EU 2004/40 Directive: assessment of induced current densities in realistic scenarios using a 3D dosimetric approach based on the scalar