279
Mobile Communication Fields in Biological Systems
2003) techniques have been developed. Another typical hybrid technique is the combination of the MoM and the FDTD method (Mangoud, Abd-Alhameed, and Excell 2000;
Mochizuki et al. 2004). Such an approach is commonly used in the SAR calculation of
a helical antenna next to a human head because the FDTD method has difficulties in
modeling a curved wire.
5.2.4 Uncertainty Assessment
Error evaluation and its a posteriori prediction are important issues in all numerical simulations. Although we may have the wishful thinking that codes can be treated as a “black
box,” the reality is that erroneous results can be obtained due to geometrical or numerical modeling difficulties. In EM, considerations relating to numerical error have only
appeared sporadically, but will continue to become of greater concern as we rely more
heavily on numerical simulations for designs and other purposes. For risk assessment,
it is important to investigate the uncertainty associated with dosimetry. Uncertainty is
defined as the amount by which the estimated value may depart from the correct value.
Many different uncertainty components must be considered, which can be grouped
into three main categories: the simulation uncertainty, the body model uncertainty,
and the source uncertainty. The simulation uncertainty is related to the uncertainty in
assessing a parameter of interest (e.g., the spatial peak SAR value), assuming that the
source modeling and position as well as the body modeling are error free. For example,
in evaluating the spatial peak SAR value, different tasks are involved, such as the evaluation of the electric field distribution, the calculation of the SAR distribution, spatial integration procedures, and search routines to localize the peak SAR value averaged over 1 g
or 10 g. The simulation uncertainty corresponds to errors generated from the discretization in space and time, such as numerical artifacts or errors generated in the treatment
of material boundaries. Due to the lossy media encountered, some other FDTD errors
(e.g., phase velocity changes in the grid or errors from boundary modeling) are expected
to have almost no impact on the total uncertainty in FDTD dosimetry.
The body modeling uncertainty describes the uncertainty in the simulated parameters
of interest produced by the deviation of the numerical representation of the body model
with respect to the theoretical definition, as described in the test case. This uncertainty
in the simulated parameters of interest related to the exact way in which the body model
is built in the Yee grid represents a very critical component in the total uncertainty
assessment. For example, simple models have long been considered as typical worst-case
models and some reports of comparison of various realistic voxel models have been
published (Kainz et al. 2005). It is however noted that simpler models may provide considerably higher doses (SAR or induced current density) or artificial phenomena such
as the appearance of maximum local SAR in the deep region of the model (Lin 2002).
Since in numerical methods the device must be replaced by a numerical model, a
significant error can be produced. Source uncertainty describes the uncertainty in
the results obtained, caused by deviations from the defined device geometry, settings
(output power, etc.), and position. The crucial parameters to model are the accurate locations, magnitudes, and distributions of the highest surface currents on the device and
the antenna. Furthermore, the accurate definition of the antenna position against the
Mobile Communication Fields in Biological Systems
2003) techniques have been developed. Another typical hybrid technique is the combination of the MoM and the FDTD method (Mangoud, Abd-Alhameed, and Excell 2000;
Mochizuki et al. 2004). Such an approach is commonly used in the SAR calculation of
a helical antenna next to a human head because the FDTD method has difficulties in
modeling a curved wire.
5.2.4 Uncertainty Assessment
Error evaluation and its a posteriori prediction are important issues in all numerical simulations. Although we may have the wishful thinking that codes can be treated as a “black
box,” the reality is that erroneous results can be obtained due to geometrical or numerical modeling difficulties. In EM, considerations relating to numerical error have only
appeared sporadically, but will continue to become of greater concern as we rely more
heavily on numerical simulations for designs and other purposes. For risk assessment,
it is important to investigate the uncertainty associated with dosimetry. Uncertainty is
defined as the amount by which the estimated value may depart from the correct value.
Many different uncertainty components must be considered, which can be grouped
into three main categories: the simulation uncertainty, the body model uncertainty,
and the source uncertainty. The simulation uncertainty is related to the uncertainty in
assessing a parameter of interest (e.g., the spatial peak SAR value), assuming that the
source modeling and position as well as the body modeling are error free. For example,
in evaluating the spatial peak SAR value, different tasks are involved, such as the evaluation of the electric field distribution, the calculation of the SAR distribution, spatial integration procedures, and search routines to localize the peak SAR value averaged over 1 g
or 10 g. The simulation uncertainty corresponds to errors generated from the discretization in space and time, such as numerical artifacts or errors generated in the treatment
of material boundaries. Due to the lossy media encountered, some other FDTD errors
(e.g., phase velocity changes in the grid or errors from boundary modeling) are expected
to have almost no impact on the total uncertainty in FDTD dosimetry.
The body modeling uncertainty describes the uncertainty in the simulated parameters
of interest produced by the deviation of the numerical representation of the body model
with respect to the theoretical definition, as described in the test case. This uncertainty
in the simulated parameters of interest related to the exact way in which the body model
is built in the Yee grid represents a very critical component in the total uncertainty
assessment. For example, simple models have long been considered as typical worst-case
models and some reports of comparison of various realistic voxel models have been
published (Kainz et al. 2005). It is however noted that simpler models may provide considerably higher doses (SAR or induced current density) or artificial phenomena such
as the appearance of maximum local SAR in the deep region of the model (Lin 2002).
Since in numerical methods the device must be replaced by a numerical model, a
significant error can be produced. Source uncertainty describes the uncertainty in
the results obtained, caused by deviations from the defined device geometry, settings
(output power, etc.), and position. The crucial parameters to model are the accurate locations, magnitudes, and distributions of the highest surface currents on the device and
the antenna. Furthermore, the accurate definition of the antenna position against the