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Electromagnetic Fields in Biological Systems
body model in the discretized space is of major importance. Finally, the presence of
reflecting objects (metallic or dielectric walls) nearby the emitting antenna has been
shown to affect the source and radically change the dosimetric quantities (Bernardi,
Cavagnaro, and Pisa 1996). In some papers, extensions of the treatments developed in
order to describe more accurately real situations have been mentioned.
The accuracy of the numerical results produced is mainly checked with the following
methods:
1. Convergence tests to check the convergence and stability of the numerical technique (Lazzi and Gandhi 1997; Massoudi et al. 1979; Meier et al. 1997; Zhou and
Oosterom van 1992). Sufficient number of iterations ensures that the system has
reached its steady-state.
2. Further analysis of the obtained results, by considering the specific implementation details of the numerical method. For example, FDTD even when applied for
the analysis of well-defined canonical cases may lead to significant differences,
depending on the specific implementation details (discretization in space and
time, details of building the body model and the source in the Yee grid, details
of the procedure for SAR averaging, distance between scatterers and absorbing
boundaries, and simulation time). Boundary conditions that require truncating
the region used for FDTD calculations is also a source of uncertainty although
reported significance of this effect (PML boundaries) on the whole-body SAR has
not been consistent among related studies (Findlay and Dimbylow 2006; Laakso,
Ilvonen, and Uusitupa 2007; Wang et al. 2006).
3. Comparisons with measurements (Hombach et al. 1996; Karimullah, Chen, and
Nyquist 1980; Meier et al. 1997; Toftgard, Hornsleth, and Andersen 1993). In
order to allow easy comparison with experimental results, numerical canonical
problems have been defined in complete agreement with experimental canonical
problems.
4. Comparisons with analytical or semianalytical methods. For example, in the
studies of Koulouridis and Nikita (2004), Cerri, De Leo, and Rosellini (1997), and
Lazzi and Gandhi (1997), the accuracy of the numerical results is checked against
the results obtained for spherical canonical problems by using a semianalytical
method, based on Green’s functions theory.
5. Comparisons with other numerical methods (Dimbylow and Mann 1994;
Gandhi, Lazzi, and Furse 1996; Meier et al. 1997; Nikita et al. 2000a). It is highly
recommended to validate the dosimetry by comparing with the results obtained
with other methods. Canonical problems are still used as a reference to validate
numerical results (Anderson 2003).
6. Interlaboratory comparisons. Some standard organizations have undertaken
interlaboratory comparison for evaluating the uncertainty of SAR calculations.
A recent study reported that a standard deviation of 30% was found in 12 separate
SAR calculations of head models exposed to the near field of a cellular phone with
the same anatomically based models and exposure conditions (Beard et al. 2006).
An interlaboratory comparison of whole-body SAR calculations and the uncertainty of the calculations are given in Dimbylow, Hirata, and Nagaoka (2008).
Electromagnetic Fields in Biological Systems
body model in the discretized space is of major importance. Finally, the presence of
reflecting objects (metallic or dielectric walls) nearby the emitting antenna has been
shown to affect the source and radically change the dosimetric quantities (Bernardi,
Cavagnaro, and Pisa 1996). In some papers, extensions of the treatments developed in
order to describe more accurately real situations have been mentioned.
The accuracy of the numerical results produced is mainly checked with the following
methods:
1. Convergence tests to check the convergence and stability of the numerical technique (Lazzi and Gandhi 1997; Massoudi et al. 1979; Meier et al. 1997; Zhou and
Oosterom van 1992). Sufficient number of iterations ensures that the system has
reached its steady-state.
2. Further analysis of the obtained results, by considering the specific implementation details of the numerical method. For example, FDTD even when applied for
the analysis of well-defined canonical cases may lead to significant differences,
depending on the specific implementation details (discretization in space and
time, details of building the body model and the source in the Yee grid, details
of the procedure for SAR averaging, distance between scatterers and absorbing
boundaries, and simulation time). Boundary conditions that require truncating
the region used for FDTD calculations is also a source of uncertainty although
reported significance of this effect (PML boundaries) on the whole-body SAR has
not been consistent among related studies (Findlay and Dimbylow 2006; Laakso,
Ilvonen, and Uusitupa 2007; Wang et al. 2006).
3. Comparisons with measurements (Hombach et al. 1996; Karimullah, Chen, and
Nyquist 1980; Meier et al. 1997; Toftgard, Hornsleth, and Andersen 1993). In
order to allow easy comparison with experimental results, numerical canonical
problems have been defined in complete agreement with experimental canonical
problems.
4. Comparisons with analytical or semianalytical methods. For example, in the
studies of Koulouridis and Nikita (2004), Cerri, De Leo, and Rosellini (1997), and
Lazzi and Gandhi (1997), the accuracy of the numerical results is checked against
the results obtained for spherical canonical problems by using a semianalytical
method, based on Green’s functions theory.
5. Comparisons with other numerical methods (Dimbylow and Mann 1994;
Gandhi, Lazzi, and Furse 1996; Meier et al. 1997; Nikita et al. 2000a). It is highly
recommended to validate the dosimetry by comparing with the results obtained
with other methods. Canonical problems are still used as a reference to validate
numerical results (Anderson 2003).
6. Interlaboratory comparisons. Some standard organizations have undertaken
interlaboratory comparison for evaluating the uncertainty of SAR calculations.
A recent study reported that a standard deviation of 30% was found in 12 separate
SAR calculations of head models exposed to the near field of a cellular phone with
the same anatomically based models and exposure conditions (Beard et al. 2006).
An interlaboratory comparison of whole-body SAR calculations and the uncertainty of the calculations are given in Dimbylow, Hirata, and Nagaoka (2008).