278
Electromagnetic Fields in Biological Systems
Within each element, vector expansion functions are used that are tangential to all
element surfaces of which the edge is part and normal to all other surfaces. The edgeelement technique is also much better suited to nonhomogeneous problems, since no
internal boundary conditions between elements with different electromagnetic properties need to be enforced. Furthermore, in contrast to the conventional, node-based finite
element technique, the edge-element technique possesses a direct way of controlling
discretization errors in the solution by looking at the behavior of the normal components of the field between elements.
The finite element mesh gives, in principle, a very high flexibility for discretizing
almost any arbitrary geometry. However, the generation of meshes in 3D is still a formidable task. While there are reasonably good techniques for the discretization of technical structures, the difficulty of generating finite element models for the typically very
nonhomogeneous problems in dosimetry currently prevents wider use.
Nowadays, FEM is used extensively in commercially available software to resolve submillimeter induced currents, electric and magnetic fields, and SAR at lower frequencies.
The use of FEM to study the interaction of a cellular phone with the human head is
reported in Rakotomalala (2007), while in Forgy et al. (1997), FEM is applied to study
the performance of a special antenna for portable handsets.
5.2.3.2.5 Hybrid Techniques
Currently, none of the commercially available codes seem to be completely satisfactory for all cases of interest. A large deficiency is seen in the capability to perform reliable uncertainty assessments. Existing methods should be combined into new hybrid
approaches, keeping all the advantages and eliminating the disadvantages of component methods. For example, FDTD has become the most widely acceptable numerical
technique in the area of EM dosimetry. However, when exposure in an urban environment has to be modeled, the calculation burden of FDTD is prohibitive. In order to
discretize the huge dimensions of the region to be studied, huge memory and CPU time
are required.
On the other hand, field propagation in large environments can be efficiently studied
by using Kirchhoff’s integral (KI) or ray-tracing (RT) techniques. KI is a time-domain
near-field to near-field transformation that can be derived starting from Green’s theorem and Maxwell’s equations. RT is a frequency-domain technique based on geometrical
optics and the uniform theory of diffraction (UTD), and is able to study field propagation both in free space and in the presence of reflecting surfaces and diffracting edges.
Both KI and RT can easily evaluate field distribution produced by sources radiating in
free space but are unsuitable to predict field distribution in the presence of scatterers of
arbitrary shape.
A way to overcome the problems and drawbacks specific to each method is to use
hybrid techniques. The FDTD method can be used for the evaluation of the field in
confined volumes containing the antenna and/or scattering objects as well as for the
calculation of the SAR. The KI or RT methods can be used for the modeling of field
propagation in the empty space between these volumes. Following this approach,
the hybrid multiple-region/FDTD (MR/FDTD) (Bernardi et al. 2002a; Johnson and
Rahmat-Samii 1997) and ray-tracing/FDTD (RT/FDTD) (Bernardi et al. 2000a, 2002a,
Electromagnetic Fields in Biological Systems
Within each element, vector expansion functions are used that are tangential to all
element surfaces of which the edge is part and normal to all other surfaces. The edgeelement technique is also much better suited to nonhomogeneous problems, since no
internal boundary conditions between elements with different electromagnetic properties need to be enforced. Furthermore, in contrast to the conventional, node-based finite
element technique, the edge-element technique possesses a direct way of controlling
discretization errors in the solution by looking at the behavior of the normal components of the field between elements.
The finite element mesh gives, in principle, a very high flexibility for discretizing
almost any arbitrary geometry. However, the generation of meshes in 3D is still a formidable task. While there are reasonably good techniques for the discretization of technical structures, the difficulty of generating finite element models for the typically very
nonhomogeneous problems in dosimetry currently prevents wider use.
Nowadays, FEM is used extensively in commercially available software to resolve submillimeter induced currents, electric and magnetic fields, and SAR at lower frequencies.
The use of FEM to study the interaction of a cellular phone with the human head is
reported in Rakotomalala (2007), while in Forgy et al. (1997), FEM is applied to study
the performance of a special antenna for portable handsets.
5.2.3.2.5 Hybrid Techniques
Currently, none of the commercially available codes seem to be completely satisfactory for all cases of interest. A large deficiency is seen in the capability to perform reliable uncertainty assessments. Existing methods should be combined into new hybrid
approaches, keeping all the advantages and eliminating the disadvantages of component methods. For example, FDTD has become the most widely acceptable numerical
technique in the area of EM dosimetry. However, when exposure in an urban environment has to be modeled, the calculation burden of FDTD is prohibitive. In order to
discretize the huge dimensions of the region to be studied, huge memory and CPU time
are required.
On the other hand, field propagation in large environments can be efficiently studied
by using Kirchhoff’s integral (KI) or ray-tracing (RT) techniques. KI is a time-domain
near-field to near-field transformation that can be derived starting from Green’s theorem and Maxwell’s equations. RT is a frequency-domain technique based on geometrical
optics and the uniform theory of diffraction (UTD), and is able to study field propagation both in free space and in the presence of reflecting surfaces and diffracting edges.
Both KI and RT can easily evaluate field distribution produced by sources radiating in
free space but are unsuitable to predict field distribution in the presence of scatterers of
arbitrary shape.
A way to overcome the problems and drawbacks specific to each method is to use
hybrid techniques. The FDTD method can be used for the evaluation of the field in
confined volumes containing the antenna and/or scattering objects as well as for the
calculation of the SAR. The KI or RT methods can be used for the modeling of field
propagation in the empty space between these volumes. Following this approach,
the hybrid multiple-region/FDTD (MR/FDTD) (Bernardi et al. 2002a; Johnson and
Rahmat-Samii 1997) and ray-tracing/FDTD (RT/FDTD) (Bernardi et al. 2000a, 2002a,