29
Coupling of Electromagnetic Fields into Biological Systems
where υ represents the speed of wave propagation in vacuum. Similarly, to ensure that
the solution is correct an accuracy condition must be satisfied:
max ( Δx, Δy, Δz) << λ min
(1.49)
where λ min is the minimum wavelength in a tissue medium with the highest dielectric
permittivity. Finally, to limit the computational domain for finite resources, absorbing
boundary conditions (ABCs) are employed. Several ABCs have been proposed over the
years (e.g., Mur’s ABC, Higdon ABC, and retarded time). At present, the ABCs most
often used are those proposed by Berenger (1994), known as perfectly matched layer
(PML). For more details, the reader is referred to recent books on the subject like the
ones by Kunz and Luebbers (1993) and Taflove (1995).
Several three-dimensional (3-D) models of the human body have been developed
and utilized for SAR computations. These have proved very useful since they offer
more realistic representations of the human anatomy. The most frequently used highresolution human model is from the “Visible Human” (VH) project of the National
Library of Medicine (Ackerman 1998). The VH is a 3-D digital image library representing an adult human male and female. The for both the male and female include
photographic images obtained through cryosectioning of human cadavers and digital images obtained through computed tomography (CT) and magnetic resonance
imaging (MRI) of the same cadavers. The male data set, the first to be constructed,
consists of 1871 digital axial images obtained at 1.0-mm intervals with a pixel resolution of 1 mm, whereas the female data set contains 5189 digital axial images obtained
with a finer spatial grid of 0.33 mm. The male images have been segmented at the Air
Force Research Laboratory, Brooks Air Force Base, Texas (Mason et al. 2000). The final
segmented model, made freely available to the scientific community (ftp://starview.
brooks.af.mil), consists of 586 × 340 × 1878 voxels with a resolution of 1 × 1 × 1 mm 3 .
The model is segmented into about 40 different tissue types with frequency-specific tissue permittivity, such as those given in Table 1.3, which are used to represent each tissue type in the inhomogeneous model of the human body. The model is widely used to
study head exposure to RF fields from cell phones (Bernardi et al. 2001a,b; Gjonaj et al.
2002; Wang et al. 2004; Pisa et al. 2005) and for other dosimetric calculations (Lin and
Wang 2010; Wang et al. 2007, 2008). In fact, the model is now included in many commercially available electromagnetic simulation tools with capabilities for d osimetric
calculations.
Cell phones can be modeled simply as half-wavelength dipoles or as quarterwavelength monopoles over a box; but more complex and realistic phone geometries
also have been considered. The half-wavelength dipole is used as a first approximation
(Dimbylow 1993; Chen and Wang 1994; Martens et al. 1995; Bernardi, Cavagnaro, and
Pisa 1996). A better model is a quarter-wavelength monopole over a box (Toftgard,
Hornsleth, and Andersen 1993; Jensen and Rahmat-Samii 1995; Nikita et al. 2000).
These antenna configurations can be regarded as rough models of the retractable
antenna, which was used in nearly all of the early cell phone handsets. Helical antennas for more compact terminals require the use of graded mesh in numerical models to
Coupling of Electromagnetic Fields into Biological Systems
where υ represents the speed of wave propagation in vacuum. Similarly, to ensure that
the solution is correct an accuracy condition must be satisfied:
max ( Δx, Δy, Δz) << λ min
(1.49)
where λ min is the minimum wavelength in a tissue medium with the highest dielectric
permittivity. Finally, to limit the computational domain for finite resources, absorbing
boundary conditions (ABCs) are employed. Several ABCs have been proposed over the
years (e.g., Mur’s ABC, Higdon ABC, and retarded time). At present, the ABCs most
often used are those proposed by Berenger (1994), known as perfectly matched layer
(PML). For more details, the reader is referred to recent books on the subject like the
ones by Kunz and Luebbers (1993) and Taflove (1995).
Several three-dimensional (3-D) models of the human body have been developed
and utilized for SAR computations. These have proved very useful since they offer
more realistic representations of the human anatomy. The most frequently used highresolution human model is from the “Visible Human” (VH) project of the National
Library of Medicine (Ackerman 1998). The VH is a 3-D digital image library representing an adult human male and female. The for both the male and female include
photographic images obtained through cryosectioning of human cadavers and digital images obtained through computed tomography (CT) and magnetic resonance
imaging (MRI) of the same cadavers. The male data set, the first to be constructed,
consists of 1871 digital axial images obtained at 1.0-mm intervals with a pixel resolution of 1 mm, whereas the female data set contains 5189 digital axial images obtained
with a finer spatial grid of 0.33 mm. The male images have been segmented at the Air
Force Research Laboratory, Brooks Air Force Base, Texas (Mason et al. 2000). The final
segmented model, made freely available to the scientific community (ftp://starview.
brooks.af.mil), consists of 586 × 340 × 1878 voxels with a resolution of 1 × 1 × 1 mm 3 .
The model is segmented into about 40 different tissue types with frequency-specific tissue permittivity, such as those given in Table 1.3, which are used to represent each tissue type in the inhomogeneous model of the human body. The model is widely used to
study head exposure to RF fields from cell phones (Bernardi et al. 2001a,b; Gjonaj et al.
2002; Wang et al. 2004; Pisa et al. 2005) and for other dosimetric calculations (Lin and
Wang 2010; Wang et al. 2007, 2008). In fact, the model is now included in many commercially available electromagnetic simulation tools with capabilities for d osimetric
calculations.
Cell phones can be modeled simply as half-wavelength dipoles or as quarterwavelength monopoles over a box; but more complex and realistic phone geometries
also have been considered. The half-wavelength dipole is used as a first approximation
(Dimbylow 1993; Chen and Wang 1994; Martens et al. 1995; Bernardi, Cavagnaro, and
Pisa 1996). A better model is a quarter-wavelength monopole over a box (Toftgard,
Hornsleth, and Andersen 1993; Jensen and Rahmat-Samii 1995; Nikita et al. 2000).
These antenna configurations can be regarded as rough models of the retractable
antenna, which was used in nearly all of the early cell phone handsets. Helical antennas for more compact terminals require the use of graded mesh in numerical models to