study of the influence of the magnetic field orientation ......the results shown in this...

Forum for Electromagnetic Research Methods and Application Technologies (FERMAT)

Study of the influence of the magnetic field

orientation using Polynomial Chaos

decomposition applied to the pregnant woman

exposure at 50 Hz By

I.Liorni1,2, M. Parazzini1, S. Fiocchi1 & P. Ravazzani1

1CNR Consiglio Nazionale delle Ricerche–Istituto di Elettronica e di Ingegneria

dell’Informazione e delle Telecomunicazioni IEIIT, Milano Italy, email:

[email protected] 2Dipartimento Elettronica, Informazione e Bioingegneria DEIB, Politecnico di Milano,

Milano Italy

Abstract: The modelling of human exposure in realistic exposure scenarios is complex, because

several parameters (e.g., the source design, the frequency band, the orientation of incident fields,

the morphology and posture of subjects) vary and influence the dose. Deterministic dosimetry, so

far used to quantify human exposure to electromagnetic fields (EMF), is highly time consuming if

the variations of those parameters are considered. Stochastic dosimetry is an alternative approach to

assess EMF exposure and consists in building analytical approximations of the exposure at a

parsimonious computational cost. In this study, it was used to assess the influence of magnetic flux

density (B) orientation on fetal exposure at 50 Hz using the polynomial chaos (PC) theory. A PC

expansion of induced electric field (E) in each fetal tissue at 7 months of gestational age (GA) was

built as a function of B orientation. Maximum E in each fetal tissue was estimated for different

exposure configurations and compared with the limits of the International Commission of Non-

Ionising Radiation Protection (ICNIRP) Guidelines 2010. PC theory resulted in an efficient method

to build accurate approximations of E in each fetal tissue. B orientation influenced E with a

variability across tissues in the range from 10% to 25% with respect to the mean value. However,

varying B orientation, maximum E in each fetal tissue was below the limits of ICNIRP 2010.

Keywords: fetus; ELF-MF exposure; stochastic dosimetry; polynomial chaos

Acknowledgements: The results shown in this presentation are based on the published paper:

Liorni I, Parazzini M, Fiocchi S, Ravazzani P, “Study of the Influence of the Orientation of a 50 Hz

Magnetic Field on Fetal Exposure using Polynomial Chaos Decomposition”, Int. J. Environ. Res.

Public Health 2015, 12(6): 5934-5953; doi:10.3390/ijerph120605934

References:

Blatman, G.; Sudret, B. Adaptive sparse polynomial chaos expansion based on least angle

regression. J. Comput. Phy. 2011, 230, 2345–2367.

Efron, B.; Hastie, T.; Johnstone, I.; Tibshirani, R. Least angle regression. Ann. Statist. 2004, 32,

407–499.

ICNIRP. Guidelines for limiting exposure to time-varying electric and magnetic fields (1 Hz to 100

kHz). Health Phys. 2010, 99, 818–836.

Liorni, I.; Parazzini, M.; Fiocchi, S.; Douglas, M.; Capstick, M.; Gosselin, M.C.; Kuster, N.;

Ravazzani, P. Dosimetric study of fetal exposure to uniform magnetic fields at 50 Hz.

Bioelectromagnetics 2014, 35, 580–597.

SEMCAD X v. 14.8.4. Available online: http://www.speag.com (accessed on 13 May 2015).

Soize, C.; Ghanem, R. Physical systems with random uncertainties: Chaos representations with

arbitrary probability measure. SIAM J. Sci. Comput. 2004, 26, 395–410.

Wiener, N. The homogeneous chaos. Amer. J. Math. 1938, 60, 897–936.

Xiu, D.; Karniadakis, G.E. The Wiener-Askey polynomial chaos for stochastic differential

equations. SIAM J. Sci. Comput. 2002, 24, 619–644.

Author’s Biodata:

Ilaria Liorni received the Master degree in Biomedical Engineering at the “Sapienza” University of

Rome (2011). From 2011 to 2013 she collaborated with the Milan Unit of the Institute of

Biomedical Engineering (ISIB), Italian National Research Council (CNR) and since November

2012 she is also a PhD student in Bioengineering at Politecnico

di Milano, Dipartimento di Elettronica, Informazione e

Bioingegneria (DEIB), Milan Italy. Since 2013 Ilaria Liorni

joined the Institute of Electronics, Computer and

Telecommunication Engineering (IEIIT-CNR) as Research

Associate.

Her research activity is focused on “Electromagnetic fields

(EMF) and Health”. The objective of this activity is the study of

the interactions between external electromagnetic fields and

biological tissues by applying computational electromagnetic

techniques and advanced stochastic tools.

In detail, her scientific interests are focused on: Numerical

dosimetry of electromagnetic fields; EMF interaction

mechanisms with biological systems; EMF effects on biological

systems; Stochastic methods applied to EMF exposure

assessment (Polynomial Chaos); Personal EMF Exposure Measurements; EMF characterization of

health support systems (Electroporation systems); EMF safety and medical applications.

*This use of this work is restricted solely for academic purposes. The author of this work owns the copyright and no

reproduction in any form is permitted without written permission by the author. *

CNR IEIIT – Engineering for Health and Well-Being Group

I. Liorni1,2, M. Parazzini1, S. Fiocchi1 & P. Ravazzani1

1CNR Consiglio Nazionale delle Ricerche–Istituto di Elettronica e di Ingegneria dell’Informazione e delle TelecomunicazioniIEIIT, Milano Italy, email: [email protected] Elettronica, Informazione e Bioingegneria DEIB, Politecnico di Milano, Milano Italy

Study of the influence of the magnetic field orientation usingPolynomial Chaos decomposition applied to the pregnant

woman exposure at 50 Hz

AcknoledgementsThe results shown in this presentation are based on the published paper:Liorni I, Parazzini M, Fiocchi S, Ravazzani P, “Study of the Influence of the Orientation of a 50 Hz MagneticField on Fetal Exposure using Polynomial Chaos Decomposition”, Int. J. Environ. Res. Public Health 2015,12(6): 5934-5953; doi:10.3390/ijerph120605934


INTRODUCTION: VARIABILITY OF HUMAN EXPOSURE TO EMF

In the evaluation of the human exposure to EMF it is necessary to take intoaccount several parameters, that vary in a real exposure scenario:

Source (location, design, frequency)

Orientation of the incident field

Environment

Morphology

Dielectric properties

Posture


INTRODUCTION: STUDY OF EMF EXPOSURE

HIGHLY TIME CONSUMING!

Input parameters

XFDTD,

FEM

Output

Y

• Orientation

Morphology

Posture


• Induced electric fields

Electric current density

SAR

Polynomial Chaos (PC) decomposition: approximation of Y on a suitable basis of orthogonal polynomials (Wiener 1938; Xiu et al., 2002)

DETERMINISTIC DOSIMETRY STOCHASTIC DOSIMETRY

EMF EXPOSURE

Input parameters

X

Model Function

M

Model

response

Y=M(X)

• Induced electric fields

Electric current density

SAR

• Orientation

Morphology

Posture



INTRODUCTION: POLYNOMIAL CHAOS (PC) PRINCIPLE (1)

deterministic coefficient

polynomial

X= vector of K indipendent input parameters each characterized by probability density function (PDF) fXi

Hp: E[Y2]<+∞

Soize and Ghanem, 2004

Construction of the polynomial basis Ψ(X)

polynomial

αj = maximum degree of

polynomial degree: |α|=α1+…+αK ≤ p

Ψ(X) size: P= (K+p)!/ K!p!

= family of polynomials orthogonal respect to each fXi



Experimental DesignX={x(1),x(2),…,x(N)}

Estimation of aj

pMSE< τ?

YES

Y=Y’

NO

Deterministic dosimetry

Observationsy={y(1),y(2),…,y(N)}

Experimental DesignX={x(1),x(2),…,x(N),…,x(N+δ)}

Observationsy={y(1),y(2),…,y(N),…y(N+δ)}

Validation set yval



Least Angle Regression algorithm (LAR, Efhronet al., 2004) adapted by Blatman et al., 2011 tothe PC theory

1. LAR generates a collection of PC expansions (the first expansion includes a single polynomial ψj, the second two polynomials (ψj, ψk), until m=min(P,N-1))

2. LAR chooses the best PC expansion by Leave-one-out cross-validation.

LAR

Estimation of coefficients of PC expansions and collection of PC

expansions

Selection of the best PC expansion


OBJECTIVES

Estimation of induced E field in each fetal tissue exposed to ELF-MF at 50 Hzchanging the B-field orientation by means of PC decomposition:

1. Build a PC expansion of E in each fetal tissue;

2. Statistical analysis of fetal exposure;

3. Identification of the worst-case exposure scenario with respect to theICNIRP Guidelines 2010.


MATERIAL AND METHODS: PC APPLIED TO ELF-MF PROBLEM

• Y= 99th percentile of induced E in each fetal tissue

• X input random vector:

• Ψ(X) polynomial basis: Legendre polynomials

θ uniform distribution [0,180°]

ϕ uniform distribution [-180°,180°]

Xiu et al., 2002


MATERIAL AND METHODS: EXPERIMENTAL DESIGN

• Pregnant woman model at 7 months GA (provided by IT’IS Foundation)

• Low Frequency Solver SEMCAD X

• Exposure: 200 μT uniform MF at 50 Hz

• Simulation setting adopted in Liorni et al., 2014

Experimental Design: generation of N couples (θ; ϕ) by Quasi-Monte Carlomethod based on Sobol’s function depending on joint PDF fX:

Observations: estimation of N induced E in each fetal tissue on theexperimental design.


MATERIAL AND METHODS: VALIDATION OF THE PC EXPANSION

PROCEDURE OF VALIDATION

1. S couples of θ and ϕ different from the experimental design X

2. Estimation of E on S by deterministic dosimetry (yvalD)

3. Estimation of E on S by PC expansion (yvalPC)

4. Calculation of the percentage mean square error (pMSE) between yvalD

and yvalPC


RESULTS: CHOICE OF PC EXPANSION

Example: Trend of pMSE increasing the number of observations to build a PC expansion of E induced in the fetus whole-body.

The validation has been performed for each fetal tissue at 7 mGA. N=300observations is suitable to build all PC expansions with pMSE not higherthan 0.17%.


RESULTS: STATISTICAL ANALYSIS OF FETAL EXPOSURE

Estimation of mean and standard deviation from PC coefficients (Blatman et al., 2011)

• Fetal skin, fat, liver, SAT present the highest mean E (up to 5.09 mV/m);

• Mean E induced in bone tissue up to 3.08 mV/m;

• Variation of E higher than 10% and up to 25.3% in gallbladder.


RESULTS: WORST-CASE SCENARIO RESPECT TO ICNIRP 2010

Ews is the max E among the 10000 random generated in each tissue

Elim ICNIRP 2010 Basic Restriction for the General Public at 50 Hz

• CNS of the head (limit of 0.02 V/m): 23% of the limit

• All the other tissues of head and body (limit of 0.4 V/m):

• Max E always under the limit,with WS% lower than 2%;

• Highest max E found in the fetaltissues with also the highestmean E.


CONCLUSIONS

• Polynomial Chaos decomposition results an efficient method to study the variation of humanexposure to EMF;

• Study of the variation of B-field orientation at 50 Hz on fetal exposure:

The highest mean and maximum exposure found in fetal skin, fat, SAT, liver at 7 monthsgestational age;

All the fetal tissues always result under the limit of the ICNIRP 2010 for the GeneralPublic at 50 Hz;

E distribution in some tissues is significantly influenced (up to 25%) by B variation.


References

Blatman, G.; Sudret, B. Adaptive sparse polynomial chaos expansion based on least angle regression. J.Comput. Phy. 2011, 230, 2345–2367.

Efron, B.; Hastie, T.; Johnstone, I.; Tibshirani, R. Least angle regression. Ann. Statist. 2004, 32, 407–499.

ICNIRP. Guidelines for limiting exposure to time-varying electric and magnetic fields (1 Hz to 100 kHz).Health Phys. 2010, 99, 818–836.

Liorni, I.; Parazzini, M.; Fiocchi, S.; Douglas, M.; Capstick, M.; Gosselin, M.C.; Kuster, N.; Ravazzani, P.Dosimetric study of fetal exposure to uniform magnetic fields at 50 Hz. Bioelectromagnetics 2014, 35, 580–597.

SEMCAD X v. 14.8.4. Available online: http://www.speag.com (accessed on 13 May 2015).

Soize, C.; Ghanem, R. Physical systems with random uncertainties: Chaos representations with arbitraryprobability measure. SIAM J. Sci. Comput. 2004, 26, 395–410.

Wiener, N. The homogeneous chaos. Amer. J. Math. 1938, 60, 897–936.

Xiu, D.; Karniadakis, G.E. The Wiener-Askey polynomial chaos for stochastic differential equations. SIAM J.Sci. Comput. 2002, 24, 619–644.

study of the influence of the magnetic field orientation ......the results shown in this...

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