Page 81 - Biomedical Engineering and Design Handbook Volume 1, Fundamentals

58 BIOMECHANICS OF THE HUMAN BODY

Determination of SAR. Several methods are used to determine the SAR distribution induced by
various heating applicators. The SAR distribution can be directly derived from the Maxwell equa-
tion of the electromagnetic field (Camart et al., 2000; Gentili et al., 1995; Ling et al., 1999; Stauffer
et al., 1998; Strohbehn, 1984). The electrical field E and magnetic field B are first determined
analytically or numerically from the Maxwell equation. The SAR (W/kg) is then calculated by
the following equation (Sapozink et al., 1988)
⎛ σ ⎞ 2
SAR = ⎜ ⎟ E (2.24)
⎝ ρ2 ⎠
where ρ and σ represent the density and conductivity of the media, respectively. This method is fea-
sible when the derivation of the electromagnetic field is not very difficult. It generally requires a
rather large computational resource and a long calculation time, though it is flexible for modeling
the applicators and the surrounding media.
Other methods in clinical and engineering applications are experimental determination of the
SAR distribution based on the heat conduction equation. The experiment is generally performed on
a tissue-equivalent phantom gel. The applicability of the SAR distribution measured in the phantom
gel to that in tissue depends on the electrical properties of the phantom gel. For energy absorption of
ultrasound in tissue, the gel mimics tissue in terms of ultrasonic speed and attenuation/absorption
properties. For heat pattern induced by microwave or radio frequency, the applicability requires that
the phantom gel mimic the dielectric constant and electrical conductivity of the tissue. The electrical
properties of various tissues at different wave frequencies have been studied by Stoy et al. (1982). It
has been shown that in addition to the electromagnetic wave frequency, water content of the tissue
is the most important factor in determining the electrical properties. Thermal properties such as heat
capacity and thermal conductivity of the gel are not required if no thermal study is conducted. The
ingredients of the gel can be selected to achieve the same electrical characteristics of the tissue for a
specific electromagnetic wavelength. As shown in Zhu and Xu (1999), the basic ingredients of the
gel used for an RF heating applicator were water, formaldehyde solution, gelatin, and sodium chloride
(NaCl). Water was used to achieve a similar water content as the tissue. Formaldehyde and gelatin
were the solidification agents. NaCl was added to obtain the desired electrical conductivity of tissue
at that frequency. The resulted phantom gel was a semitransparent material that permits easy and pre-
cise positioning of the temperature sensors during the experimental study.
The simplest experimental approach to determining the SAR distribution is from the temperature
transient at the instant of power on (Wong et al., 1993; Zhu et al., 1996b). In this approach, temper-
ature sensors are placed at different spatial locations within the gel. Before the experiment, the gel
is allowed to establish a uniform temperature distribution within the gel. As soon as the initial heating
power level is applied, the gel temperature is elevated and the temperatures at all sensor locations are
measured and recorded by a computer. The transient temperature field in the gel can be described by
the heat conduction equation as follows:

∂ T 2
ρC =∇ T + SAR(, ,
x y z)
k
t ∂ (2.25)
t = 0 T = T env
Within a very short period after the heating power is on, heat conduction can be negligible if the
phantom gel is allowed to reach equilibration with the environment before the heating. Thus, the
SAR can be determined by the slope of the initial temperature rise, i.e.,
∂T
SAR = ρC (2.26)
∂t = t 0
Since the SAR at each spatial location is a constant during the heating, the temperature rise at each
location is expected to increase linearly if heat conduction is negligible. Figure 2.9 gives the measured
temperature rise at different radial locations from an injection site of the nanofluid. Note that the