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Principles of Quasi-static Electromagnetic DosimetrySummary of methods for evaluating current density and

SAR induced in the tissues of an exposed subject for

frequencies up to a few megahertz

Daniele Andreuccetti, IFAC-CNR, Firenze

ELECTROMAGNETIC FIELDSAT THE WORKPLACES

SESSION 2. INSTRUMENTATION AND TECHNIQUES FOR EXPOSURE ASSESSMENT

Warszawa, Poland – 5 September 2005

International Workshop

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Industrial RF heater (dielectric loss)

What is the electromagnetic dosimetry?

When a biological object is immersed in an electromagnetic field, the field forces induce some physical quantities (charges, currents, power) in its tissues.

Physical quantities of interest are those responsible for biological effects: basic restrictions in RF exposure guidelines (exposure limit values) are expressed through these basic quantities, which must stay within levels well below the thresholds of known effects.

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• EM fields induce currents inside biological tissues

• Currents produce power (Joule effect)

At low frequencies (up to a few hundreds chilohertz), the basic quantity is the current density J induced in the tissues, at higher frequencies the Specific Absorption Rate (SAR) is also considered.

iJ E

2JSAR

What is the electromagnetic dosimetry?

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What is the electromagnetic dosimetry aimed at?

Electromagnetic dosimetry is aimed at determining the basic quantities as functions of the distribution of impressed electromagnetic field, of the characteristics of the exposed organism and those of the so-called exposure theatre. It makes use of:

instrumentation & measurement (experimental dosimetry);

direct theoretical solutions of Maxwell equations (analytical dosimetry);

computer techniques (numerical dosimetry).

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• Radiation standards utilize dosimetric results in conventional exposure conditions in order to develop reference levels (action values) from basic restrictions (exposure limit values).

• Experts directly apply dosimetric models and methods in actual exposure conditions in order to verify compliance with basic restrictions (exposure limit values) when reference levels (action values) are violated.

Who needs or uses the electromagnetic dosimetry?

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EXPERIMENTAL DOSIMETRY

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Measurement of induced current density and SAR

Induced current densities and SARs can be measured with invasive methods only!

Results of measurements on animals can’t be easily extended to humans.

In vivo measurements on humans pose ethical problems!

Phantom measurements are probably the preferred choice for experimental dosimetry.

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Phantom measurement of induced current density or SAR by means of

internal electric field probes

2

i

JJ E SAR

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Phantom measurement of induced current density or SAR by means of

internal electric field probes

• At low frequencies (below 10 kHz): AC coupled probes with bipolar sensors

• Problems: noise, CMRR, contact impedance• At higher frequencies: DC coupled (detected)

probes with bipolar sensors and diode detectors (thanks to square low, output is directly proportional to SAR!)

• Liquid or semi-liquid phantoms needed (they can’t be truly realistic!)

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• Implantable thermometers– Thermocouple-based– Thermistor-based

• IR thermocamera• Thermochromic liquid crystal

sheets

Phantom measurement of SAR by means of temperature probes

TSAR c

t

(LTI phase, i.e. at the beginning of the exposure)

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Phantom measurement of SAR by means of thermal probes

False-color IR thermocamera

Thermochromic liquid-crystal sheet

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Measurement of derived dosimetric quantities: limb current or total body current induced by the electric field

Industrial RF heater (dielectric loss)

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Frequency band from 3 kHz to 110 MHzMeasurement range from 1 to 1000 mA

HI-3701 stand-on current meter

HI-3702 clamp-on current meter (current transformer)

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Not just the current density, but even the current induced by the magnetic

field…

…cannot be measured non-invasively!

Industrial induction heater

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Experimental dosimetry: conclusions

• For ethical reasons, human in-vivo experimental dosimetry is limited to those measures which can be done non-invasively (derived quantities).

• Measurements on animals pose (perhaps) fewer ethical problems, but results can’t be easily extended to humans.

• Phantom measurements are probably the preferred choice for experimental dosimetry, but there are still some technical difficulties and severe phantom limitations (phantoms can’t be realistic).

• Although these limitations could be partially overcome with further research, it seems unlikely that experimental dosimetry will play a decisive role in future applications, apart from being used as a check for numerical methods.

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THEORETICAL DOSIMETRYThe quasi-static approach

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The quasi-static approachThe analysis of the interaction of biological objects and low-frequency electric or magnetic fields is greatly simplified if three conditions are satisfied.

1. The dimensions of the involved objects and their mutual distances should be small when compared to the free space wavelength.

Propagation effects are negligible: the electric and magnetic fields can be calculated by using the methods of electrostatics and magnetostatics.

W.T.Kaune, J.L.Guttman and R.Kavet: “Comparison of coupling of humans to electric and magnetic fields with frequencies between 100 Hz and 100 kHz”, Bioelectromagnetics vol.18, pp.67–76, 1997.

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The quasi-static approach

3. In the exposed object, conduction currents prevail over displacement currents.

2. The size of the exposed object is comparable to or smaller than the magnetic skin depth.

The applied magnetic field will be essentially unperturbed by the exposed body.

Charges move and rearrange in phase with fields. Body is equipotential. The calculation of the electric fields outside and inside the body is separated into two problems.

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The quasi-static approachcondition n.2

0,1

1

10

100

1000

1 10 100 1000 10000

Frequency [kHz]

Pe

ne

tra

tion

de

pth

[m]

Blood Muscle Fat Bone (cortical) Nerve Skin (dry)

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0,01

0,1

1

10

100

1000

1 10 100 1000 10000

Frequency [kHz]

Lo

ss ta

ng

en

t

Blood Muscle Fat Bone (cortical) Nerve Skin (dry)

The quasi-static approachcondition n.3

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The quasi-static approach

The quasi-static conditions are strictly verified up to just a few hundred chilohertz…

… however, the quasi-static approach is often applied up to the limit of the sub-resonance range.

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ANALYTICAL DOSIMETRY

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Analytical dosimetry

• Analytical dosimetry is aimed at finding the solution of the set of Maxwell equations which describes the coupling of the electromagnetic field with the exposed body, taking source characteristics and environment properties into account.

• This approach suffers from a major limitation: it cannot easily accommodate complex environments, particular postures and internal body structure.

• Nevertheless, analytical models are useful because they often provide an insight into the qualitative nature of the coupling mechanism and, once again, a good check for numerical techniques.

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Basic analytical models

• Basic analytical models, although simple and rough, are able to provide an overview of the general properties of the field-body interaction in quasi-static conditions.– Induced current densities are directly proportional to

both amplitude and frequency of the impressed fields.– Current densities induced by electric fields do not

depend on tissue conductivities.– Current densities induced by magnetic fields are

directly proportional to tissue conductivities.

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0E EJ k fEDosimetric coefficient kE depends on the body district only. It’s value for the thorax region is kE

= 3x10-9 (A/m2)/Hz/(V/m)

0B BJ k fB

Dosimetric coefficient kB depends on the body district and conductivity. It’s value for the thorax region (assumed filled with muscle) is kB = 0.12 (A/m2)/Hz/T

Results of basic analytical models

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Advanced analytical models

• Advanced analytical methods are based on an attempt to solve the field equations in the low frequency quasi-static approximation with reference to uniform fields and homogeneous objects of simple shapes.

• Geometries usually taken into consideration are the sphere, the cylinder, the spheroid and the ellipsoid, simulating a man standing in free-space or on a perfectly conductive plane which represents the ground surface.

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• In literature we found analytical solutions for (at least) the problems in which the exposed subject is represented with:– a sphere (Mie: scattering theory);– a cylinder (McLeod, Polk: Bessel’s equations and

functions);– a spheroid or an ellipsoid (Durney et al.: perturbation

theory (Stevenson’s method); expansion in in a power series of the free-space propagation constant).

Advanced analytical models

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NUMERICAL DOSIMETRY

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Numerical dosimetry

• Numerical dosimetry takes advantage of computational techniques in order to seek the solution of the interaction equations by the use of a digital computer.

• One has to abandon the “general” point of view typical of the analytical approach and concentrate on specific and particular problems.

• Quasi-static applications of numerical dosimetry usually adopt a multi-step approach.

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• Numerical modeling is the first step, in which a set of differential or integral equations (with proper boundary conditions) suitable to describe the problem being considered is developed.

• Segmentation is the process by which a mathematical model of the exposed object is built, subdividing it into “segments”, i.e. small homogeneous elements with regular geometry (e.g. square pixels in 2D problems, cubic voxels in 3D problems).

Numerical dosimetry:an overview of main steps

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• In the third step, each segment is assigned a pair of values for the dielectric properties (i.e. the conductivity and the relative permittivity) which depend on the frequency of the field. Usually, this is accomplished through preliminary assessment of the type of tissue which composes each segment. Very important, in this respect, is the thorough work of C.Gabriel and colleagues, who developed a parametric model able to represent the dielectric properties of biological tissues in the frequency range from 10 Hz to 100 GHz and have determined the values of the 14 model parameters for 45 different tissues.

Numerical dosimetry:an overview of main steps

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• At this point, a set of algebraic equations is usually derived from the previous steps and a standard computational algorithm is applied to numerically solve the linear system thus obtained.

• Among the most popular ones for quasi-static problems, we can cite the impedance method, the method of moments (particularly useful for low resolution problems modeled with integral equations) and the family of finite difference methods (more suited for high resolution 2D or 3D problems expressed by means of a system of linear differential equations).

Numerical dosimetry:an overview of main steps

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• In an N cell-problem, the method of moments requires computer storage proportional to N2 and computation time proportional to N3; this situation becomes prohibitive when dealing with high resolution heterogeneous models. Finite difference-like methods (including impedance methods), on the contrary, have storage and time requirements proportional to N.

• The number of cells N is substantially larger in the finite difference and impedance methods than in the moment method because of the overhead of free-space cells surrounding the body, often necessary to guarantee the proper boundary conditions.

Numerical dosimetry:resource demand comparison

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Numerical dosimetrygeneral remarks

• Numerical methods are rapidly becoming the preferred dosimetric techniques, as they benefit of the continuously growing speed and memory storage and decreasing costs of modern digital computers.

• Applications to more and more complex problems should be expected, involving multiple sources in realistic environments and a very detailed representation of exposed subjects.

• However, research work is still needed to produce accurate, high resolution digital models of the human body and to achieve a better knowledge of the dielectric properties of its tissues at lower frequencies.

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ELECTROMAGNETIC DOSIMETRY:

GENERAL RESULTS

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Electromagnetic dosimetry: general results

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Averaged SAR (normalized to 1 W/mq) versus frequency. Literature results (red line) – Conservative values adopted by international guidelines (blue line).

Electromagnetic dosimetry: general results