26
Electromagnetic Fields in Biological Systems
quantities such as SAR can be derived by a simple conversion formula. For example,
from an induced electric field E in volts per meter one can calculate SAR:
SAR = σE 2 /ρ m
(1.46)
where σ is the bulk electrical conductivity and ρ m is the mass density (kilogram per cubic
meter) of tissue, respectively. At present, the smallest isotropic implantable electric field
probe available with sufficient sensitivity for practical use is about 1 mm in diameter and
is quite expensive. Consequently, a common practice in experimental dosimetry relies on
the temperature elevation produced under a short-duration (<30 seconds) high-intensity
exposure condition. (The short duration is insufficient for significant convective or conductive heat contribution to temperature rises in tissues.) The intensity is sufficient to
produce a measurable temperature elevation. In this case, the time rate of initial rises
in temperature (slope) can be related to SAR through a secondary procedure, such that
SAR = cΔT/Δt
(1.47)
where ΔT is the temperature increment (in degree Celsius), c is the specific heat capacity of tissue (joules per kilogram degree Celsius), and Δt is the time duration over which
ΔT is measured. It is important to distinguish the use of SAR and its derivation from
temperature-based measurements. The quantity of SAR is merely a metric for energy
deposition or absorption and it should not be construed to imply any mechanism of
interaction, thermal or otherwise. However, it is a quantity that pertains to a macroscopic
phenomenon by virtue of the use of bulk electrical conductivity and mass density in its
derivation in Equation 1.46 and the use of specific heat capacity of tissue in Equation 1.47.
It is important to note the use of bulk electrical conductivity, specific heat capacity,
and mass density (kilogram per cubic meter) of tissue in the derivation of SAR from electric field strength and temperature elevation. The use of these factors in the derivation
of SAR implies that a volume of tissue mass must be selected over which SAR is determined. In common usage, 1 or 10 g of tissue in the form of a cubic volume are specified.
It is obvious that the numerical value of SAR would be the same regardless of what mass
or volume is chosen if the induced field and power deposition are uniform. A variance
arises when the absorption is nonuniform or when tissues with differing properties are
included within the same volume of averaging mass. In principle, a 10-g averaging mass
can underestimate SARs of nonuniform fields by up to a factor of 10 compared with a
1-g averaging mass. It is emphasized here that recent advances suggest spatial resolutions comparable to 0.01 g or less are routinely obtained using available computational
algorithms and resources to provide higher spatial precision in SAR determination.
1.11.1 Coupling from Handheld Mobile Phones
A topic of considerable current interest is the coupling of RF energy from handheld
cellular mobile telephones and other personal communication systems into the human
head or body. Cell phones are designed to operate in close proximity with the user
and are typically located next to the user’s head. Aside from the intended purpose of
Electromagnetic Fields in Biological Systems
quantities such as SAR can be derived by a simple conversion formula. For example,
from an induced electric field E in volts per meter one can calculate SAR:
SAR = σE 2 /ρ m
(1.46)
where σ is the bulk electrical conductivity and ρ m is the mass density (kilogram per cubic
meter) of tissue, respectively. At present, the smallest isotropic implantable electric field
probe available with sufficient sensitivity for practical use is about 1 mm in diameter and
is quite expensive. Consequently, a common practice in experimental dosimetry relies on
the temperature elevation produced under a short-duration (<30 seconds) high-intensity
exposure condition. (The short duration is insufficient for significant convective or conductive heat contribution to temperature rises in tissues.) The intensity is sufficient to
produce a measurable temperature elevation. In this case, the time rate of initial rises
in temperature (slope) can be related to SAR through a secondary procedure, such that
SAR = cΔT/Δt
(1.47)
where ΔT is the temperature increment (in degree Celsius), c is the specific heat capacity of tissue (joules per kilogram degree Celsius), and Δt is the time duration over which
ΔT is measured. It is important to distinguish the use of SAR and its derivation from
temperature-based measurements. The quantity of SAR is merely a metric for energy
deposition or absorption and it should not be construed to imply any mechanism of
interaction, thermal or otherwise. However, it is a quantity that pertains to a macroscopic
phenomenon by virtue of the use of bulk electrical conductivity and mass density in its
derivation in Equation 1.46 and the use of specific heat capacity of tissue in Equation 1.47.
It is important to note the use of bulk electrical conductivity, specific heat capacity,
and mass density (kilogram per cubic meter) of tissue in the derivation of SAR from electric field strength and temperature elevation. The use of these factors in the derivation
of SAR implies that a volume of tissue mass must be selected over which SAR is determined. In common usage, 1 or 10 g of tissue in the form of a cubic volume are specified.
It is obvious that the numerical value of SAR would be the same regardless of what mass
or volume is chosen if the induced field and power deposition are uniform. A variance
arises when the absorption is nonuniform or when tissues with differing properties are
included within the same volume of averaging mass. In principle, a 10-g averaging mass
can underestimate SARs of nonuniform fields by up to a factor of 10 compared with a
1-g averaging mass. It is emphasized here that recent advances suggest spatial resolutions comparable to 0.01 g or less are routinely obtained using available computational
algorithms and resources to provide higher spatial precision in SAR determination.
1.11.1 Coupling from Handheld Mobile Phones
A topic of considerable current interest is the coupling of RF energy from handheld
cellular mobile telephones and other personal communication systems into the human
head or body. Cell phones are designed to operate in close proximity with the user
and are typically located next to the user’s head. Aside from the intended purpose of