Page 35 - Computational Modeling in Biomedical Engineering and Medical Physics

Physical, mathematical, and numerical modeling 21

mechanical) is based on the response given by a substance to a certain form of stress.
The elemental such response is quantified through adequate materials properties. In
most biomedical applications, numerical modeling is performed at a macroscopic scale.
The numerical analysis is based on equations of classical physics, applied to compo-
nents of the human body up to the cellular level; characteristic dimensions might be as
small as the typical cells, that is, down to the micron range magnitudes and the move-
ment is very slow, that is, low speeds, like for Newton mechanics. The frequencies of
the electric and magnetic fields are within the nonionizing (Hertzian) range, that is,
lower than 300 GHz.
Specific macroscopic impact phenomena generated by the interactions of EMFs
and biological matter (tissues) could be classified in two large groups: stimulation of
excitable tissue, for low and medium frequency range, and heating, for medium and
high frequency domain.
Stimulation represents the electrical activation of excitable cells membranes (local
membrane depolarization, by the opening of transmembrane active channels for the
transfer of selected ion flows) (Chapter 4: Electrical Activity of the Heart). The stimu-
lus is an electrical signal (current), induced either by an applied external electric field
(electrical stimulation) or by a variable magnetic field through electromagnetic induc-
tion effect (magnetic stimulation). Biophysical effects of stimulation target the activa-
tion of nerves, muscles or sensitive tissue and it is macroscopically quantified by the
local distribution of the induced electric field or current density. Induced currents
could also produce interferences with natural electrophysiological phenomena and dis-
turbance of normal generation and transmission of biocurrents from various body
sources (heart, brain, peripheral nerves, sensor analyzers), which are commonly used in
medical diagnosis. Simulation of such phenomena requires specification of the tissue
dielectric properties: conductivity and permittivity that are highly dependent on the
electric field frequency. For the strengths of the electric field commonly associated to
nondestructive tissue applications (bioelectrical phenomena, medical procedures, or
environmental body exposure), the tissues show linear behavior to both dielectric
properties (Chapter 8: Hyperthermia and Ablation). Some tissues (like bone and mus-
cle) are anisotropic concerning dielectric properties in the low-medium frequency
spectrum, up to 100 kHz. The anisotropy is acknowledged in field equations by the
tensor representation of the dielectric property; however, in most applications an aver-
age value is considered as a constant dielectric property.
Heating occurs in conductive materials, which absorb the electromagnetic radiation
[Chapter 7: Magnetic Stimulation and Chapter 8: Hyperthermia and Ablation
(Thermotherapy Methods)]. This process is effective for high frequencies (radio waves and
microwaves); the energy transferred by the incident electromagnetic waves to the target
tissues is converted into heat. The higher the frequency, the lower is the penetration depth
of the radiation and the heating is more superficial, but heat is further transported inside