Transcript Electromagnetic dosimetry

International Workshop
ELECTROMAGNETIC FIELDS
AT THE WORKPLACES
SESSION 2. INSTRUMENTATION AND
TECHNIQUES FOR EXPOSURE ASSESSMENT
Warszawa, Poland – 5 September 2005
Principles of Quasi-static Electromagnetic Dosimetry
Summary 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
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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
Industrial
RF heater
must stay within levels
well below
the
thresholds of known(dielectric
effects. loss)
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What is the electromagnetic
dosimetry?
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.
2
J
SAR 

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J   Ei
• EM fields induce currents inside
biological tissues
• Currents produce power (Joule
effect)
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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Who needs or uses the
electromagnetic dosimetry?
• 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.
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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!
In vivo measurements on
humans pose ethical
problems!
Results of measurements
on animals can’t be easily
extended to humans.
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
J   Ei
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2
J
SAR 

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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Phantom measurement of SAR by
means of temperature probes
• Implantable thermometers
– Thermocouple-based
– Thermistor-based
• IR thermocamera
• Thermochromic liquid crystal
sheets
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T
SAR  c
t
(LTI phase, i.e. at
the beginning of the
exposure)
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 MHz
Measurement range from 1 to 1000 mA
HI-3702 clamp-on current
meter (current transformer)
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HI-3701 stand-on current meter
Not just the current density, but even
the current induced by the magnetic
field…
Industrial
induction heater
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…cannot be
measured noninvasively!
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 DOSIMETRY
The quasi-static approach
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The quasi-static approach
The 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.
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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.
The quasi-static approach
2. The size of the
exposed object is
comparable to or
smaller than the
magnetic skin depth.
3. In the exposed
object, conduction
currents prevail
over displacement
currents.
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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.
The quasi-static approach
condition n.2
Penetration depth [m]
1000
100
10
1
0,1
1
10
100
1000
10000
Frequency [kHz]
Blood
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Muscle
Fat
Bone (cortical)
Nerve
Skin (dry)
The quasi-static approach
condition n.3
1000
Loss tangent
100
10
1
0,1
0,01
1
10
100
1000
10000
Frequency [kHz]
Blood
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Muscle
Fat
Bone (cortical)
Nerve
Skin (dry)
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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Results of basic analytical models
J E  k E fE0
J B  kB fB0
Dosimetric coefficient kE depends on the body
district only. It’s value for the thorax region is kE
= 3x10-9 (A/m2)/Hz/(V/m)
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
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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 freespace or on a perfectly conductive plane which
represents the ground surface.
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Advanced analytical models
• 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).
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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 dosimetry:
an overview of main steps
• 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).
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Numerical dosimetry:
an overview of main steps
• 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.
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Numerical dosimetry:
an overview of main steps
• 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).
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Numerical dosimetry:
resource demand comparison
• 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.
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Numerical dosimetry
general 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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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).