Page 36 - Computational Modeling in Biomedical Engineering and Medical Physics

22 Computational Modeling in Biomedical Engineering and Medical Physics

the body by thermal conduction; thermal conductivity is thus an important physical prop-
erty to quantify the process. Dielectric properties of tissues do influence both the penetra-
tion depth and the distribution of the absorbed energy, while the thermal properties
govern the evolution of the heat distributionintissues.Animportant role in theregula-
tion of temperature distribution is played by the cooling effect of the blood flow; the
energy absorbed through metabolic intake could be considered too in the completion of
the energy balance (Chapter 7: Magnetic Stimulation).
Literature presents several studies on the electrical characteristics of tissues and true col-
lections of values associated to the electrical conductivity and permittivity of most significant
tissues involved in the description of anatomical models for various frequency ranges were
offered by Stuchly and Stuchly (1980) or Durney et al. (1986), according to the growth of
computational resources, in the context of the increasing interest for numerical modeling.
However, a systematic study dedicated to the dielectric tissues properties was not properly
conducted until the 1990s, when the group led by Camelia Gabriel presented its compre-
hensive database, including tens of tissues, both human and animal, investigated over consid-
erably large frequency ranges, from very low (10 Hz) to microwaves (20 GHz). They have
also the merit to discuss their results, compare them with previous literature and show details
on the measurement methods and on the mathematical approach for finding proper
parametric expressions of continuous functions, useful to cover all needed frequencies, as
shown by Gabriel et al. (1996a,b,c) and Gabriel and Gabriel (1996). The database founded
by Gabriel’s team is maintained and continuously enriched at the Institute of Applied
Physics, Italian Research Council of Florence, as an internet public resource presented by
Andreuccetti et al. (1997), available online for the benefit of researchers all over the world.
Since most applications operate in, or could be reduced to time-harmonic working
conditions, the complex form of EMF equations represents a significant computational
facility, adopted by a large section of software packages for the numerical analysis of
AC and RF EMFs. In that context, the dielectric properties are included in one single
theoretical quantity—the complex conductivity σ 5 σ 1 jωε, or its correspondent—the
σ σ
complex permittivity ε 5 jω 5 ε 2 j , where σ S=m is the true electrical conductivity,
ω
p
ffiffiffiffiffiffiffiffi
ε F=m is the true dielectric permittivity j 5 2 1.
Biological materials (tissues) are generally nonmagnetic materials for the whole
Hertzian frequency range, and the magnetic permeability is commonly considered identi-
cal with the permittivity in free space μ 5 4π 3 10 27 H=m. The presence of magnetic
0
materials inclusions in biological tissues—like magnetite associated with injected chemicals
used in magnetic drug targeting procedures, or the excess of ferrous oxides absorbed in
various tissues due to pollution or other causes—might be considered by the increase of
the magnetic permeability, according to the proper concentration.
When exposed to low frequency EMF human tissues behave as conductive materi-
als, with specific electrical conductivity for different tissues. The blood has a major
influence in the variability of the electrical conductivity (Chapter 5: Bioimpedance