Biomedical Engineering Reference
In-Depth Information
4
Physics of Electromagnetic
Energy Sources
4.1 Introduction ...............................................................................................................................57
4.2 Static Electric and Magnetic Fields .........................................................................................57
4.3 Time-Varying Electric and Magnetic Fields..........................................................................58
4.4 Interaction of Electric and Magnetic Fields with Tissues ...................................................59
4.5 Propagation of Electromagnetic Fields in Tissues ............................................................... 60
4.6 Principles of Electromagnetic Heating Techniques ............................................................ 64
4.7 Invasive Heating Techniques ...................................................................................................65
RF Interstitial Hyperthermia ∙ RF Ablation (RFA) ∙ Invasive Microwave Techniques
4.8 External Heating Techniques ..................................................................................................67
Capacitive and Inductive Techniques ∙ Aperture Sources ∙ Arrays of Applicators
References ...............................................................................................................................................72
Jeffrey W. Hand
King's College London
4.1 Introduction
small compared to the distance between them,
r
, and which are
remote from other dielectric media is
The use of electromagnetic energy to cause heating and/or abla-
tion of biological tissue is widespread as evidenced in other
chapters in this topic. To understand and optimize the use of
such energy sources it is necessary to consider some fundamen-
tal aspects of the electromagnetic spectrum (see Figure 4.1).
We shall be interested in nonionizing electromagnetic fields
for which the photon energy, given by the product of the fre-
quency and Planck's constant (= 6.626 × 10
−34
Js), is insufficient
to cause ionization. In particular we shall discuss aspects of
interactions between the body and electromagnetic fields such
as microwaves (MW) and radiofrequency (RF) fields. The term
RF is often used in the biological effects and medical applica-
tions literature to cover the ranges from 3 kHz to 300 GHz,
respectively. The frequency range from 300 MHz to 300 GHz is
also referred to as the “microwave range.” The consensus of sci-
entific opinion is that interactions between such fields and the
human body are thermal, and although there have been claims
for other mechanisms of interaction, the plausibility of the vari-
ous nonthermal mechanisms that have been proposed is very
low (ICNIRP, 2009).
1
4πε
qq
r
F
e
=
12
2
r
(4 .1)
where
q
1
and
q
2
are the charges and ε is the permittivity of the
medium in which they are located. In free space ε = ε
0
= 8.854 ×
10
−12
F m
−1
.
Bold
typeface indicates a vector quantity. When the
charge
q
2
is distributed over a region of space the force exerted
on
q
1
is the vector sum of the forces due to all the elemental
charges
dq
n
that make up
q
2
and so
1
4
qdq
r
∑
F
=
1
n
r
(4.2)
e
n
2
πε
n
n
where
r
n
is the distance between
q
1
and
dq
n
and
r
n
is the unit vec-
tor along the line joining them. From Equation 4.2, the force per
unit charge at the location of
q
1
is
F
e
1
dq
r
∑
E
==
πε
n
r
.
(4.3)
q
4
2
n
1
n
n
E
is known as the electric field. If the charge distribution can be
expressed in terms of charge density ρ(
r
) within a volume
V
then
4.2 Static Electric and Magnetic Fields
1
ρ
()
rr
∫
E
=
dV
(4.4)
4
πε
r
2
Electric and magnetic fields are produced by electric charges and
their motion. Electric charge may be positive or negative. The
force
F
e
between two charged spherical bodies whose radii are
V
where
dV
is an elemental volume located at position
r
.
57
