Evaluation of Specific Absorption Rate as a Dosimetric
Quantity for Electromagnetic Fields Bioeffects
Dimitris J. Panagopoulos
*, Olle Johansson
, George L. Carlo
1Department of Biology, University of Athens, Athens, Greece, 2Radiation and Environmental Biophysics Research Centre, Athens, Greece, 3Experimental Dermatology
Unit, Department of Neuroscience, Karolinska Institute, Stockholm, Sweden, 4The Science and Public Policy Institute, Institute for Healthful Adaptation, Washington, D.C.,
United States of America
To evaluate SAR as a dosimetric quantity for EMF bioeffects, and identify ways for increasing the precision in EMF
dosimetry and bioactivity assessment.
We discuss the interaction of man-made electromagnetic waves with biological matter and calculate the energy
transferred to a single free ion within a cell. We analyze the physics and biology of SAR and evaluate the methods of its
estimation. We discuss the experimentally observed non-linearity between electromagnetic exposure and biological effect.
We find that: a) The energy absorbed by living matter during exposure to environmentally accounted EMFs is
normally well below the thermal level. b) All existing methods for SAR estimation, especially those based upon tissue
conductivity and internal electric field, have serious deficiencies. c) The only method to estimate SAR without large error is
by measuring temperature increases within biological tissue, which normally are negligible for environmental EMF
intensities, and thus cannot be measured.
SAR actually refers to thermal effects, while the vast majority of the recorded biological effects from man-made
non-ionizing environmental radiation are non-thermal. Even if SAR could be accurately estimated for a whole tissue, organ,
or body, the biological/health effect is determined by tiny amounts of energy/power absorbed by specific biomolecules,
which cannot be calculated. Moreover, it depends upon field parameters not taken into account in SAR calculation. Thus,
SAR should not be used as the primary dosimetric quantity, but used only as a complementary measure, always reporting
the estimating method and the corresponding error. Radiation/field intensity along with additional physical parameters
(such as frequency, modulation etc) which can be directly and in any case more accurately measured on the surface of
biological tissues, should constitute the primary measure for EMF exposures, in spite of similar uncertainty to predict the
biological effect due to non-linearity.
Citation: Panagopoulos DJ, Johansson O, Carlo GL (2013) Evaluation of Specific Absorption Rate as a Dosimetric Quantity for Electromagnetic Fields
Bioeffects. PLoS ONE 8(6): e62663. doi:10.1371/journal.pone.0062663
Editor: Nils Cordes, Dresden University of Technology, Germany
Received November 21, 2012; Accepted March 22, 2013; Published June 4, 2013
Copyright: ß2013 Panagopoulos et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits
unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Funding: The authors have no support or funding to report.
Competing Interests: The authors have declared that no competing interests exist.
* E-mail: email@example.com
Specific Absorption Rate (SAR) is defined as the amount of
absorbed non-ionizing radiation power (or rate of absorbed
energy) by unit mass of biological tissue.
The reason for the introduction of SAR as a non-ionizing
radiation – Radio Frequency (RF) Electromagnetic Field (EMF)
dosimetric quantity, was – as with the rate of absorbed dose in the
ionizing case – to describe the amount of absorbed energy and the
rate by which it is absorbed within an exposed tissue and not just
the radiation/field intensity on its surface. This derives from the
fact that when radiation exposes matter, most usually, it does not
interact completely with it and in such a case only a part of its
energy gets absorbed. The remainder just passes through without
affecting the medium.
The amount of absorbed energy by a certain amount of matter
(within a certain time interval) will determine the degree of
interaction. But in the case of biological matter this is not as
simple. Biological tissue is a much more complicated and
organized form of matter compared to inanimate. The degree of
interaction does not necessarily determine the biological effect
because that depends on which specific bio-molecule – or set of
bio-molecules – from a whole tissue or organ will interact with the
radiation. Some bio-molecules may get damaged while others may
not by the same amount of radiation energy absorbed within the
Interaction between man-made electromagnetic
radiation and living matter
Man-made electromagnetic waves are produced by electromag-
netic oscillation circuits (‘‘Thomson’’ circuits), not by atomic
events (as in the case of natural electromagnetic radiation –
infrared, visible, ultraviolet, x-rays, c), and for this they are
polarized in contrast to natural electromagnetic radiation that is
not. The plane of polarization is determined by the geometry of
PLOS ONE | www.plosone.org 1 June 2013 | Volume 8 | Issue 6 | e62663
the circuit. Polarized electromagnetic waves (in contrast to non-
polarized) can produce interference effects and induce coherent
forced-vibrations on charged/polar molecules within a medium.
When a polarized, non-ionizing electromagnetic oscillation –
wave – passes through a mass of polar and charged molecules,
such as those composing biological tissue induces a forced-
oscillation on each of these particles that it meets and transfers to
each of them a tiny part of its energy. This induced oscillation will
be most intense on the free particles which carry a net electric
charge such as the free (mobile) ions that exist in large
concentrations in all types of cells or extracellular biological tissue
determining practically all cellular/biological functions [1,2]. The
induced oscillation will be much weaker or even totally negligible
on the polar biological macromolecules and the water molecules
that do not have a net charge and additionally are usually bound
chemically to other molecules.
After each such event of interaction between the wave and a
charged or polar particle, the remaining wave continues on its way
through the tissue possibly scattered by a tiny angle and reduced
by a tiny amount in its amplitude/intensity. After large numbers of
such events, depending on the tissue’s mass, density, and the
number of polar/charged molecules, the remaining wave, if any,
leaves the tissue as a scattered wave of reduced amplitude/
When the amplitude/intensity Eof the oscillating field or wave
is decreasing after interaction with the charged/polar molecules of
a medium, its energy density decreases as well, according to the
equation for the energy density of a plane, harmonic electromag-
netic wave (as those usually produced by ‘‘Thomson’’ circuits):
is the total energy per unit volume of the electromagnetic
wave, and Ethe intensity of the electric component of the wave
within a medium with relative permittivity e.
is the vacuum permittivity.
That means that a part of its energy per unit volume is
transferred to the charged/polar molecules of the medium.
The amount of energy absorbed by a single free ion within
biological tissue will manifest itself as kinetic energy of the forced-
oscillation induced on that particle. The maximum kinetic energy
of the forced-oscillation is given by:
is the ion mass which in the case of a Na
ion, is m
is the particle’s maximum velocity of the
forced-oscillation assumed to be equal to >0.25 m/s,which is the
drift velocity of Na
ions along an open trans-membrane sodium
channel, as calculated by patch-clamp ionic current measurements
through open channels [3–5]. This maximum velocity (and kinetic
energy) of the free ion is independent of the frequency of the
external field [5,6].
From Eq. (2) we get that the energy absorbed by a single ion due
to the interaction with the electromagnetic wave, is: [i
Considering that the concentration of free ions within cells is on
the order of 1 ion per nm
 and a typical cell volume up to
, a single cell contains about 10
free ions and thus it will
absorb about 10
J. A human body of average
size consisting of ,10
cells, will absorb about
J. For waves emitted by a supposed
unidirectional antenna operating with 1 W ( = 1 J/sec) output
power, (thereby transmitting energy 1 J per sec) it takes about 10
human bodies in sequence in order to be totally absorbed,
according to the above mechanism, which seems a reasonable
But as mentioned already, except of the energy absorbed by
mobile ions within biological tissue there will be additional energy
absorption by the water dipoles and the charged or polar
macromolecules like proteins, lipids, or nucleic acids, which will
also be forced to oscillate by the applied field. While we can have
an estimation as shown above for the energy absorbed by mobile
ions, we are unable to estimate much smaller amounts of energy
absorbed by charged or polar biological molecules. These smaller
amounts of energy may be of decisive importance for the
Even if we could accurately estimate macroscopically the
amount of absorbed energy by a whole organ (e.g. by measuring
an increase in temperature if any), again the biological effect
depends basically on which specific bio-molecule(s) will absorb a
certain amount of energy during a certain time-interval and this is
impossible to discern. For example, when radiation is absorbed by
lipids the damage will most likely be less than when the same
amount of energy is absorbed within the same time-interval by
enzymes and potentially even smaller than when absorbed by
nucleic acids – especially DNA. Moreover, the situation becomes
even more complicated in case that the biological effects are
indirect. For example, a damage in the DNA may be due not to
the energy absorbed directly by the DNA molecule but due to a
conformational change in a membrane protein leading to irregular
alteration of intracellular ionic concentrations [5,6] and this in
turn giving a signal for a cascade of intracellular events causing
irregular release of free radicals or DNases which finally damage
DNA (indirect effect).
Thus, even if we were able to determine the total amount of
energy absorbed by an organ, tissue, or even a single cell during a
certain time-interval, we still are not able to know the biological
effect because this depends on the amounts absorbed by a variety
of different biomolecules presenting widely varying interactive
sensitivities to the radiation. In regard to ionizing radiation, this is
well established. More specifically, it is well known that the
biological effects of ionizing radiation depend a) on the type of
ionizing radiation; it is known that equal doses (absorbed energy
per unit mass of biological tissue, in Gy = J/kg) of different
radiation types (e.g. alpha, beta, gamma, x, etc) absorbed during
the same time-interval, result to different biological effects on the
same type of biomolecule/tissue, b) on the type of biomolecule/
tissue that absorbs a certain dose at a certain rate; a certain dose of
a specific type of radiation – absorbed within a certain time-
interval – will induce different effects on different biomolecules/
tissue-types depending on their sensitivity and size [7,8,9]. We may
then reasonably speculate that respectively, different types of non-
ionizing radiation of the same SAR (differing between them in
modulation, frequency, polarization, wave shape, etc) will induce
different effects on a given type of biomolecule/tissue and
moreover, that sensitivity of different biological molecules plays
a crucial role in regard to the possibility of damage by a specific
type of non-ionizing radiation at a certain SAR as well. These
important issues are not addressed by SAR dosimetry.
Thereby, it follows that in the case of biological matter, the
amount of absorbed energy as well as the rate of its absorption
(SAR) does not determine the biological effect.
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The absorbed energy is normally well below the thermal
While we are unable, as explained, to calculate accurately
(microscopically) the absorbed energy at cellular level, we can
estimate macroscopically with some satisfactory accuracy the
energy absorbed by a whole body, or organ or tissue. But as we
shall show (in the next section of the present study), only when the
absorbed energy is large enough to cause measurable temperature
increases. This naturally occurs when the absorbed radiation has a
frequency above the lower limit of infrared which is about
Hz . Man-made microwave radiation used in modern
telecommunications and other applications with frequencies 10
Hz cannot directly cause temperature increases in biological
tissue unless it is of large enough power density (well above 1 mW/
). Radiation of even lower frequency would need to be of even
larger power/intensity to produce thermal effects. Usual micro-
wave intensities in modern human environment (mainly due to
mobile telephony handsets and base station antennas, Wi-Fi, and
radio-television station antennas) range between 0.01 mW/cm
and 100 mW/cm
. Man-made radiation that has neither the
frequency nor the intensity to cause thermal effects, it can still be
absorbed – as explained above – in much smaller quantities by
inducing forced-oscillations on polar molecules and free charges
such as the free ions within all living cells. These forced-oscillations
are superimposed on the thermal vibration of the same particles,
increasing their thermal energy. But as we shall demonstrate, the
energy of the oscillations induced by external EMFs at environ-
mental exposure levels (intensities) is normally millions of times
smaller than the average thermal energy kT of the molecules
within a biological tissue, and thus does not produce measurable
temperature increases. Although these induced oscillations (with
kinetic energy usually millions of times lower than the average
thermal energy) normally do not add to tissue temperature, they
can still cause severe biological alterations (such as DNA damage)
without heating the tissue . These are called ‘‘non-thermal
effects’’ and if not properly equilibrated by the organism’s immune
and other compensatory systems, they may very well result in
health effects [11–14].
The maximum velocity of the ion’s induced vibration is
assumed to be, u
>0.25 m/s as explained, and the corresponding
maximum kinetic energycalculated by Eq (2), is: [i<10
This ion possesses also an additional average velocity u
, due to
its thermal energy. The average kinetic energy of a single-atom
molecule/free ion due to thermal motion , is:
where T= 310
K (the temperature of the human body 37
the Boltzmann’s constant, and m
kg for Na
From Eq (3), (4) we get:[kT >6.4610
Comparing the values of the above two different velocities/
energies we find that, the maximum velocity acquired by a free ion
within a cell due to an environmental EMF is normally about
) times smaller than its average thermal velocity
and its corresponding maximum kinetic energy [i=1
induced by the environmental EMF is about 5.3610
smaller than the average thermal energy 3
2kT of such a particle.
The average values of the environmental EMF-induced velocity
and kinetic energy are even smaller than the above average
Thereby, we have shown that oscillations induced on biological
molecules by environmental EMFs do not usually contribute to the
tissue temperature, except if these fields were millions of times
more powerful, like for example the fields within a microwave
oven operating at about 1000 W and focusing all of its radiating
power within its cavity, in contrast to e.g. a GSM (Global System
for Mobile telecommunications) mobile phone (,0.1–1 W) or
even a mobile telephony base station antenna (,10–100 W)
radiating (and distributing their energy) in all directions within
Except of the tissue heating by high-power microwave
radiation, the induction of small temperature increases on the
order of 0.15–0.3uC has been reported after exposure of biological
samples (C. elegans) to continuous wave 1 W, 1 GHz microwave
radiation within a Transverse Electro-Magnetic (TEM) cell .
Nevertheless, in real exposure conditions as e.g. in the case of a
GSM mobile phone during normal ‘‘talk’’ operation the average
power density even in contact with the antenna hardly exceeds
and does not induce temperature increases at a
0.05uC level as shown by use of a sensitive Hg thermometer with
0.05uC accuracy [17,18]. Similar findings are also presented by
other experimenters [19,20]. Human exposure from base station
antennas at a distance of a few meters is normally of even lower
Thus, environmental man-made EMFs are indeed unlikely to
induce temperature increases in biological tissue, not even at the
level of 0.05uC. Even the well-established thermal effect of
‘‘microwave hearing’’ attributed to thermo-elastic waves induced
within the human/animal head by pulsed microwave radiation is
calculated to correspond to temperature increases at a threshold of
uC . Moreover, in the present paper it is shown
theoretically that the energy absorbed by moving particles (free
ions) within biological tissue due to environmental EMFs is
millions of times smaller than the average thermal energy of such
particles. Therefore if any temperature increases occur within
biological tissue during exposure to environmentally accounted
EMFs, they will normally be several orders of magnitude below
1uC and thus are not detectable.
The fact that the energy absorbed by living organisms due to the
action of environmentally accounted man-made EMFs is indeed
millions of times smaller than the average bio-molecular thermal
energy, is the main reason why initially it was believed by scientists
and authorities that environmental EMFs could not induce any
biological effect . That was based on the arbitrary hypothesis
that an external EMF can only affect a living organism by
increasing its temperature. Therefore, any non-thermal biological
effect due to environmental man-made EMFs should be either not
real, or attributed to hypothetical mechanisms such as the
‘‘stochastic resonance’’ by which biological matter can allegedly
amplify small bits of information in a ‘‘sea’’ of white (thermal)
noise by using the energy of the noise . Such speculations –
although they cannot be excluded – are not anymore necessary,
since it is now known that due to forced-oscillation, the coherent
motion (in the same direction) of several charged particles (free
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ions) within a cell in phase with a polarized external field can exert
a larger resultant force on certain sensors (such as e.g. the voltage-
sensors of electro-sensitive ion channels on cell membranes) than
the mutually extinguishing forces on the same sensors due to their
random thermal motions in all possible different directions [5,6].
Even though some scientists still express skepticism regarding
the existence of non-thermal effects , there is already a large
and constantly increasing number of studies indicating that
environmental man-made EMFs can produce severe biological
alterations such as DNA damage without heating the biological
tissue [10,11,17–20,25–32]. This can take place through non-
thermal mechanisms that involve direct changes in intracellular
ionic concentrations or changes in enzymatic activity [5,6,33–35].
DNA damage may lead to cancer, neurodegenerative deceases,
reproductive declines, or even heritable mutations. Brain tumors,
decrease in reproductive capacity, or symptoms reported as
‘‘microwave syndrome’’ (headaches, memory loss, fatigue, etc), are
observed among people exposed to mobile telephony radiation
during recent years [30,36–45]. Recently the International Agency
for Research on Cancer (IARC) has classified RF/microwave
EMFs as ‘‘possibly carcinogenic to humans’’ .
The physics and biology of SAR
Usually, SAR values are reported in papers regarding exposure
of biological material to RF EMFs, without any information about
their calculation and without reporting the corresponding error.
As already mentioned, SAR is defined as the ratio of the
absorbed power P, per unit mass of tissue, (in W/kg). To be more
accurate, since electric power is not equally absorbed by different
parts of biological matter, SAR is defined as the incremental power
dP absorbed by an incremental mass of the tissue dm contained in a
volume element dV of a given density r:
where dm =rdV,(rin kg/m
Using Ohm’s law:
where jis the electric current density (in A/m
) within the tissue
due to the internal electric field Egenerated within the tissue, and
sthe specific conductivity of the tissue (in S/m), relation (5) after
operations (see Appendix S1), becomes:
From the derivation of the last relation for SAR (Appendix S1) it is
obvious that the quantities: j(generated current density), E
(generated internal electric field), r(tissue density), s(tissue
conductivity) are assumed to be constant within an organ (e.g. eye)
or a group of organs (e.g. head) of a living body where we want to
calculate SAR. This, of course, is an oversimplification since every
organ or group of organs consists of many different types of
biological tissue and all the above quantities vary significantly
between different biological tissues and even within a single type of
tissue and within a single cell.
More specifically, conductivity varies for different tissues and
different field frequencies. For example at a frequency of 1 GHz,
conductivity in different tissues of the human body can vary from
about 0.04 S/m (bone marrow) to about 2.45 (cerebro-spinal
fluid). Moreover the conductivity of a given tissue type increases
considerably and non-linearly with frequency (up to a hundred
times for a frequency range between 10
Hz) . Even
within a single cell, conductivity can have large variations from
S/m (cell membrane) to 0.5–1 S/m (cytoplasm, extracellular
aqueous solution) [49,50].
In addition, the available data on tissue conductivity are
collected from measurements on dead animals and include large
variations in relation to both tissue type and frequency range
[48,51]. These variations become even larger at in vivo conditions
in alive animals. Higher conductivity values up to ,300% than
those previously reported, were recently measured in porcine
organs of just sacrificed animals. The differences were attributed to
the fact that the organs were still alive and filled with blood during
the measurements in contrast to the previous studies which were
performed on dead organs . Moreover, the electrical
properties of tissues – especially of the head – in all animals
change with age. The relative permittivity of an adult human brain
is calculated to be around 40 while the corresponding value for a
young child’s brain is between 60 and 80 resulting in almost
double the radiation absorption and SAR [53,54].
Moreover, human tissue density varies from about 900 kg/m
(fat) to about1200 kg/m
(tumor) between different soft tissue
types and reaches a value of about 1800 kg/m
for bones .
From this analysis it follows that Eq. (7) provides a poor
definition of SAR due to the large variations of the related
quantities, regardless of the estimating method. Thus, any
estimating method for SAR based on Eq. (7) (see next section)
includes a very large uncertainty.
For an homogeneous medium (thus neglecting again the local
density variations) with specific heat c, [in J/(kg?K)] (thus
neglecting also the local variations in the specific heat) and by
use of a form of the calorimetry law:
equation (5), becomes:
dt is the wave power, transformed into an incremental
amount of heat dQ, within the tissue of mass m, producing an
incremental temperature increase dT during the incremental time
For a measurable time interval dtand a corresponding
measurable temperature increase dT, Eq. (9) can be written as:
Since variations in specific heat within biological matter are
usually much smaller than corresponding variations in conductiv-
ity [48,51,55] resulting in a much more uniform temperature than
electric field distribution, Eqs. (9), (10) provide a better way for
SAR estimation and, consequently, definition.
In addition, while differences in internal electric field intensity
are retained during the whole exposure period since they depend
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on tissue permittivity which has large variations even within a
single cell, differences in temperature between different locations
of a tissue or organ are extinguished short time after the beginning
of a constant exposure and temperature gets evenly distributed
within a whole organ or even body. Moreover, while tissue
conductivity and permittivity/internal electric field change signif-
icantly with different frequencies of the external field/radiation,
specific heat is independent from the external field and depends
only on tissue properties. In case of exposure to microwave
radiation which includes more than one different frequencies
(carrier, pulse, modulation frequencies), conductivity and internal
field intensity depend on different simultaneous frequencies and
their accurate estimation becomes, in any case, extremely
Even if we consider only one frequency and additionally neglect
internal electric field intensity and density differences, conductivity
variations alone result in a considerably larger variability of SAR as
calculated by Eq (7) than by Eq. (10). For example, most organs/
parts of the human/animal body contain both muscle and fat
tissues. While at 1 GHz muscle conductivity (,1.006 S/m) is
about 1760% higher than fat conductivity (,0.054 S/m), muscle
specific heat (,3.5 kJ/kg?K) is only 56% higher than fat specific
heat (,2.3 vkJ/kg?K). This would result to a ,1700% larger
variability in the SAR of this specific organ or part of the animal
body when estimated by Eq (7) than when estimated by Eq. (10).
At smaller frequencies conductivity variations increase consider-
ably resulting in an even larger variability in the SAR calculation
while specific heat has the same value. For example, at 10 MHz
the above difference in SAR variability (,1700%) between Eqs (7)
and (10) becomes,2125% (or 21.25 times larger variability in SAR
value according to Eq (7) than according to Eq (10)) [56,57]. If we
add variations in internal electric field intensity and tissue density
we may have hundreds of times larger variability in SAR values
according to Eq (7) than according to Eq (10). Thus, while
variation in SAR calculation according to Eq (10) is restricted to
measurement errors and the assumption that chas the same value
throughout the tissue, which somehow can be tolerated, corre-
sponding variation in SAR according to Eq (7) includes similar
errors plus tenths or even hundreds of times larger variability. This
shows exactly that the only way to estimate SAR with some
satisfactory accuracy is by measuring macroscopically the corre-
sponding temperature increases – if any – within biological matter.
Therefore, it follows that SAR actually applies only to thermal
effects and it actually expresses the rate by which electromagnetic
energy from an external electromagnetic wave/field is converted
into heat within biological matter. But as we have shown already,
man-made electromagnetic fields at environmental levels do not
normally cause thermal effects (measurable temperature increases
within exposed biological matter) and this is in agreement both
with experimental studies [10,11,17–20,28,31,32,58] and plausible
proposed mechanisms for the action of EMFs on cells [5,6,33–35].
Thereby, it follows that, SAR is not a proper measure to describe
the biological activity of man-made electromagnetic fields at
The estimation of SAR
SAR is estimated by one of the following ways, : 1) Insertion
of micro-antennas or probes into the tissue, which detect the
internal electric field. If the conductivity and the density of the
tissue are known (assuming they have constant values) and
neglecting local variations in internal field value, the SAR can be
computed from Eq. (7). 2) Insertion of miniature thermal probes
into the tissue. If a change dT in the temperature of the tissue is
recorded, caused by the radiation/field during a time interval dt,
and the tissue is supposedly homogeneous with known specific
heat, then SAR can be computed by Eq. (10). 3) Numerical
modeling, like the Finite Difference Time Domain, (FDTD)
method, simulating the spatial distribution of the radiation energy
within an object with the dimensions of the human body and
computing SAR by Eq. (7). All the above ways/methods include
The first way does not take into account the local variations of
conductivity, density and internal electric field within the tissue as
explained already. Therefore this approach to SAR assessment is
highly simplified compared to the complexity of real biological
The second way provides a better approximation since
temperature is much more evenly distributed within biological
tissue than conductivity or electric field. But this assumes that there
are detectable temperature increases (dT) – thus assuming solely
thermal effects – while usually there are not as already shown, and
additionally, the insertion of needles (thermal probes) disturbs any
living tissue/organ and distorts its physical properties in unpre-
The third way, like the FDTD method, considered the best,
simulates numerically the tissue by use of computers, dividing its
volume into little pieces (voxels). Each voxel is assigned to certain
values of conductivity, permittivity and density. Then SAR is again
computed according to Eq. (7). Since within each voxel
conductivity, permittivity, and density are assumed to be constant,
this way also (alike the first way) represents an approximation and
simplification. This is why earlier SAR estimations, defining the
current criteria for whole body average SAR , are questioned
by more recent and more accurate FDTD calculations [61–63]. In
any case, all methods of simulation, no matter how much
improved, are and will always be, highly simplified compared to
living tissue, since they can never take into account the countless
variations in the physical parameters of living matter especially at
It follows that all the existing methods for SAR estimation, and
especially those based on Eq (7), have serious deficiencies.
In addition, it becomes evident that all methods for SAR
estimation are highly sophisticated, complicated, and time-
consuming, so that SAR cannot be readily measured/calculated
by use of the equipment of an ordinary radiation/biological
The non-linearity between electromagnetic exposure
and biological effect
Dosimetry in science is necessary in order to find a quantitative
relationship between cause and effect. The more well defined this
relationship, the more useful the dosimetry. By knowing the
relationship between cause and effect, we can predict the effect for
different values of the magnitude of the cause for which we might
have no experimental data. The most accurate prediction is when
the cause-effect diagram is a straight line, e.g., where doubling the
cause doubles the effect. In such a case we say that the cause-effect
relationship is linear.
The biological/health effects from man-made EMFs/non-
ionizing radiation, do not follow a linear dose-response (or
cause-effect) relationship according to the experimental evidence.
Experiments have shown that, the absorption of a larger amount
of energy by the same mass of a given tissue and within the same
time-interval, does not necessarily induce a larger biological effect.
In other words, a more intense field or larger SAR does not
necessarily relate to a larger biological response or consequent
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The non-linearity of biological effects of man-made EMFs, and
especially RF/microwave fields modulated by Extremely Low
Frequency (ELF) signals (0–300 Hz), where the largest effects do
not correspond to the largest SAR or intensity values,has been
reported in several experiments since the mid-seventies [64–67].
Since then, it has been repeatedly verified by numerous studies
[18,31,68]. For example, in one of the studies regarding effect of
GSM radiation on the permeability of the blood-brain barrier in
rats, and although other studies found no effect on the blood-brain
barrier , it was reported that the strongest effect was produced
by the lowest SAR values which corresponded to the weakest
radiation intensity .
Moreover, in several studies, regions of increased bioactivity
called ‘‘windows’’ were recorded, where the biological effects
reach a maximum compared to the effects at smaller or larger
values of a physical parameter like the intensity (and thus SAR)or
frequency of the radiation. The ‘‘windows’’ represent an as yet
unexplained phenomenon of the biological effects of EMFs, where
increased bioactivity appears within certain values of a physical
parameter of the field/radiation, but not for lower or higher values
of this parameter [18,31,67,70,71]. Recently an intensity window
on the biological effects of mobile telephony radiation was
discovered where the effect on DNA damage was more intense
around the value of 10 mW/cm
in terms of the microwave –
carrier – radiation intensity, than for intensities larger than
. More specifically, the borders of this ‘‘window’’
were found to be located between 8 and 28 mW/cm
In such a case of non-linearity, the inaccuracy between cause
and predicted effect can be large. We should not make it even
larger by using a dosimetric quantity that is further inaccurately
estimated such as the SAR. Instead, we should at least use a
measure that can be known more precisely.
Such a more precise quantity is the radiation/field intensity on
the surface of the biological object as measured by any qualified
and calibrated radiation/field meter (plus the additional physical
parameters of the field/radiation which can also be accurately
known, such as pulse and/or carrier frequency, waveform,
Any inaccuracy in the intensity measurement, as for example it
may occur within an antenna’s reactive near field, would be
further increased in a corresponding SAR estimation. More
specifically, if the electric field intensity Evaries significantly
within an antenna’s near field, the corresponding SAR value
depending on E
(according to Eq. 9) will include this variation
plus the variation in the conductivity and density of the biological
The reason for the non-linearity between electromagnetic
exposure and biological effect may well be exactly the fact that
the amount of absorbed energy or the rate of its absorption (SAR,
field intensity) does not determine the biological effect as we
explained. Indeed, the amount of absorbed energy during a
certain time-interval (in other words the rate of energy absorption)
increases with increasing intensity or SAR. If the corresponding
biological effect increased proportionally, there would be no
‘‘windows’’ or other non-linear effects in regards to intensity or
SAR. Nevertheless such effects exist and they are repeatedly
recorded since the mid-seventies.
Finally, the non-linearity of several types of biological effects has
been reported regardless of exposure to EMFs, and in response to
a variety of external factors such as ionizing radiation, physiolog-
ical, pharmacological, or chemical agents, environmental contam-
inants, etc [73–78], indicating that a non-linear response to
environmental factors is intimately associated with living matter.
Discussion and Conclusions
As explained, the only way that SAR can be calculated more
accurately is through Eq. (10) by measuring temperature increases
within the exposed biological tissues. But as shown in the present
study, man-made EMFs at environmental levels do not normally
cause measurable temperature increases except if they were
millions of times more powerful. Thus, SAR – although not
formally introduced specifically as a thermal term – actually refers
only to thermal effects while the vast majority of the reported
effects from environmental EMFs are non-thermal.
Moreover, as we explained, even if SAR for a whole body,
organ, tissue, or even a single cell could be accurately estimated for
exposures to environmentally accounted man-made EMFs, the
biological effect depends on which specific biomolecule(s) absorb
certain amount of energy within a certain time-interval, and this is
impossible to discern.
Further, SAR offers no information at all with respect to
frequency, waveform, or modulation of the EMF/radiation
although these parameters are directly related in the literature to
biological (and consequent health) effects. More specifically, it is
repeatedly reported that amplitude-modulated or pulsed fields are
more bioactive than non-modulated or continuous fields of the
same carrier frequency, and the same average intensity (and thus
the same SAR) [31,64–67,79–87]. Moreover, it is reported that
signals of the same SAR but with different modulation types
produce different effects in the same biological sample [79,81,84].
Real voice-modulated electromagnetic waves are considered to be
more bioactive than simulated/periodically-modulated waves of
similar other parameters and of the same SAR [10,28,31,58]. In
some cases it is also reported that microwave radiation modulated
in amplitude by an ELF field, produced similar effects with the
specific ELF field alone .
A plausible explanation for the reported increased bioactivity of
the ELF components of a microwave field can be given by the ‘‘ion
forced-oscillation theory’’ [5,6], according to which the bioactivity
of oscillating EMFs is inversely proportional to the frequency of
the field and directly proportional to the amplitude of the forced-
oscillation induced on free ions in the vicinity of cell membrane
electrosensitive channels within the exposed biological tissue.
Moreover, according to the same theory, pulsed fields are twice as
much bioactive than the corresponding continuous wave (CW)
fields with identical other parameters [5,6] and this explains the
results of several studies reporting that pulsed fields are more
bioactive than the corresponding CW ones [80,82,85,86].
A significant effect of carrier and modulation/pulse repetition
frequency in microwave radiation is also indicated by several
studies which have reported that fields of the same SAR but of
different carrier or modulation frequencies produced different
biological effects on the same biological sample [71,88–90].
The above evidence regarding the importance of modulation
and frequency of EMFs in regard to their biological activity is in
total contradiction with any SAR approach, since it becomes
evident that SAR alone – even if accurately estimated – is
inadequate for predicting the biological effect, and the type of
modulation as well as the frequency (modulation/pulse, carrier)
have to be considered.
Thus, not only the biological effect depends upon undetermined
tiny amounts of energy/power absorption by specific biomolecules
exhibiting different sensitivities to the specific external field/
radiation, but, moreover, it depends upon characteristics of the
field/radiation, not taken into account in SAR calculation, such as
modulation and frequency. Moreover, as explained, SAR estima-
Evaluation of SAR as a Dosimetric Quantity
PLOS ONE | www.plosone.org 6 June 2013 | Volume 8 | Issue 6 | e62663
tion encounters significant error, especially in the case of
environmentally accounted man-made EMFs.
In contrast to SAR, the characteristics of the external field,
(intensity, frequency, etc.), can at the very least be measured much
more accurately in any case. In case that the biological object is
exposed within the reactive near field of an antenna where large
variations of the intensity occur, SAR would be even more
For taking into account possible field distortion by the exposed
biological object due to possible resonance phenomena and
localized regions of enhanced radiation absorption, although such
phenomena are not expected to alter significantly the field,
radiation/field intensity measurements must be carried out both in
the presence and in absence of the biological object and in
different locations corresponding to different parts of its surface. In
case that the measured values in presence and in absence of the
object are significantly different between them, both sets of
measured values must be reported.
Certainly, because of the usually accounted non-linearity in the
response of living matter to different external/environmental
agents and especially to EMFs, neither SAR, neither radiation/
field intensity are expected to be precise predictors of the induced
biological effects. But at the very least, radiation/field intensity can
be readily and more accurately measured than SAR can ever be
estimated, especially for environmentally accounted man-made
We conclude that SAR should not be considered as a proper
dosimetric quantity to describe non-thermal effects which consti-
tute the vast majority of the effects produced by man-made EMFs
in our everyday environment. SAR should only be used
complementarily to intensity measurements and the methods of
its calculation along with the corresponding error should always be
reported so that the reader can have information about the
variability of the stated SAR values. For the same reason the
radiation/field meter type and model used to measure the
exposing field should always be reported in papers plus the
variability (e.g. standard deviation) of the measured intensity
As increasing evidence is being accumulated for intense
biological activity of man-made EMFs with consequent adverse
effects on the human health and the natural environment, the
need for fast and reliable measurement/dosimetry of such fields is
becoming demanding. Thus, the measurement/dosimetry of
EMFs should be easily performed by biological/radiation labora-
tories around the world by proper use of accurate field/radiation
meters which are readily available in the market and easy to be
used by qualified scientists/technicians, and not be based on
complicated, time-consuming, and largely inaccurate methods of
SAR estimation that cannot be readily performed.
This study was supported by the University of Athens, Greece, the Swedish
Allergy, Cancer and Diabetes Foundation, and the Karolinska Institute,
Stockholm, Sweden. The contribution of Prof. A. R. Liboff with remarks
and suggestions on the manuscript is gratefully acknowledged. The Irish
Doctors Environmental Association, the Alliance for Irish Radiation
Protection, Daryl Vernon, and Brian Stein, are gratefully acknowledged for
their general support.
Analyzed the data: DJP OJ GLC. Wrote the paper: DJP OJ GLC.
Conceived and designed the study: DJP. Performed calculations: DJP.
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