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Electromagnetic Fields in Biological Systems
5.2.3.1 Analytical Methods
Analytical techniques are so-called because, in contrast to numerical techniques, they
consist of some solution to Maxwell’s equation that is not based on a direct numerical
solution and does not require the inversion of large matrices.
Much work to approach the problem of interaction of EM radiation with parts of
the human body in an analytical way has been done in early dosimetric calculations
(Cerri, De Leo, and Rosellini 1997; Durney, Massoudi, and Iskander 1986; Forgy et al.
1997; Lu et al. 1996; Meier et al. 1997; Sullivan, Borup, and Gandhi 1987; Zhou and van
Oosterom 1992). The main restriction consists in adopting a simplified model of the
whole body or parts of it. The choice of these highly simplified geometries is essential
due to the necessity of characterizing a structure resembling the human body and/or
parts of it and having at the same time a closed form of the wave equation.
Regarding the field source, most of the papers adopt a plane wave as incident field,
while some others consider an elementary dipole. For example, the problem of interaction of a homogeneous sphere with a simple waveform (e.g., plane wave, short dipole) has
been treated in Lin (1976) using analytical methods. In Zhou and van Oosterom (1992),
the effort was focused on the evaluation of potential distribution inside spherical or
spheroid volumes; these studies were related to a theoretical approach of electroencephalography (EEG) and evoked potential for the localization of brain activity. A quasistatic
approximation was used because of the low frequency range of interest but the method
was applied to layered anisotropic media.
Finally, most of the papers deal with the evaluation of the EM field, and therefore of
the SAR, inside the simplified body model at RF or for a pulsed excitation. In the formulation of the problem, the EM field is usually described in terms of spherical wave vector
eigenfunctions consisting of a combination of Legendre and spherical Bessel functions.
The expansion coefficients are determined by the boundary conditions after applying
the mode orthogonality and accounting for the external fields.
Although the analytical solutions do not provide detailed dosimetry information for
actual human bodies, they contribute to qualitative analyses. They are particularly useful to test numerical codes, identify the structure resonant frequencies that represent
conditions of maximum power deposition inside the human body, evaluate the effect of
dielectric and geometric parameters spread, commonly inferred from the literature, and
select the parameters of greater influence on SAR distribution.
5.2.3.2 Numerical Methods
From the end of the 1970s, numerical calculation methods for dosimetric studies have
attracted great attention due to their advantage in modeling the anatomy of a human
body. The constant evolution of computer systems (e.g., parallel systems) offers new possibilities for the execution of numerical codes with high computing requirements, thus
facilitating more realistic and accurate modeling.
5.2.3.2.1 Method of Moments
The Method of Moments (MoM) was introduced by Harrington in 1967 in a very general formulation (Harrington 1967). It was mainly used in the 1980s for numerical
Electromagnetic Fields in Biological Systems
5.2.3.1 Analytical Methods
Analytical techniques are so-called because, in contrast to numerical techniques, they
consist of some solution to Maxwell’s equation that is not based on a direct numerical
solution and does not require the inversion of large matrices.
Much work to approach the problem of interaction of EM radiation with parts of
the human body in an analytical way has been done in early dosimetric calculations
(Cerri, De Leo, and Rosellini 1997; Durney, Massoudi, and Iskander 1986; Forgy et al.
1997; Lu et al. 1996; Meier et al. 1997; Sullivan, Borup, and Gandhi 1987; Zhou and van
Oosterom 1992). The main restriction consists in adopting a simplified model of the
whole body or parts of it. The choice of these highly simplified geometries is essential
due to the necessity of characterizing a structure resembling the human body and/or
parts of it and having at the same time a closed form of the wave equation.
Regarding the field source, most of the papers adopt a plane wave as incident field,
while some others consider an elementary dipole. For example, the problem of interaction of a homogeneous sphere with a simple waveform (e.g., plane wave, short dipole) has
been treated in Lin (1976) using analytical methods. In Zhou and van Oosterom (1992),
the effort was focused on the evaluation of potential distribution inside spherical or
spheroid volumes; these studies were related to a theoretical approach of electroencephalography (EEG) and evoked potential for the localization of brain activity. A quasistatic
approximation was used because of the low frequency range of interest but the method
was applied to layered anisotropic media.
Finally, most of the papers deal with the evaluation of the EM field, and therefore of
the SAR, inside the simplified body model at RF or for a pulsed excitation. In the formulation of the problem, the EM field is usually described in terms of spherical wave vector
eigenfunctions consisting of a combination of Legendre and spherical Bessel functions.
The expansion coefficients are determined by the boundary conditions after applying
the mode orthogonality and accounting for the external fields.
Although the analytical solutions do not provide detailed dosimetry information for
actual human bodies, they contribute to qualitative analyses. They are particularly useful to test numerical codes, identify the structure resonant frequencies that represent
conditions of maximum power deposition inside the human body, evaluate the effect of
dielectric and geometric parameters spread, commonly inferred from the literature, and
select the parameters of greater influence on SAR distribution.
5.2.3.2 Numerical Methods
From the end of the 1970s, numerical calculation methods for dosimetric studies have
attracted great attention due to their advantage in modeling the anatomy of a human
body. The constant evolution of computer systems (e.g., parallel systems) offers new possibilities for the execution of numerical codes with high computing requirements, thus
facilitating more realistic and accurate modeling.
5.2.3.2.1 Method of Moments
The Method of Moments (MoM) was introduced by Harrington in 1967 in a very general formulation (Harrington 1967). It was mainly used in the 1980s for numerical