RF/Microwave Delivery Systems for Therapeutic Applications - RF/Microwave Interaction with Biological Tissues - page 257

where k is the wave number , with k = 2p/l. Also,

E = 0 and H = H = 0

(6.14)

ø r q

The static field varies inversely with r 3 , the induction field varies inversely with
r 2 , and the radiation field varies inversely with r . At a distance r

= l/2p
the radiation field becomes the leading term, and at a larger distance, the static
and the induction fields are negligible relative to the radiation field. However,
it is only at distances much greater than r

> 1/ k

= l/2p that one can neglect the static

and induction fields.
The dipole impedance consists of a resistive component and a reactive com-
ponent in which the resistive component corresponds to the power delivered
by the dipole. The power delivered to the dipole in turn divides into the ohmic
losses in the conductors and the radiated power. In an ideal case (no ohmic
loss), the resistive component of the impedance is its radiation resistance. The
reactive component corresponds to energy stored in the antenna near-field
region.
If P is the average power radiated per unit time and R r is the radiation
resistance ,

2

= 1

PI (6.15)

0 r

The radiation resistance is given as

12

kl m

e

22

Ê
Ë

ˆ
¯

R = (6.16)

r

6p

If we assume the dipole length to be a small fraction of l, R r in turn will be
small, and this resistance will produce a low efficiency radiation . This is why
an effective antenna length should be an appreciable fraction of a wavelength.
In summary, Figure 6.4 shows an elementary length l of wire carrying a
current I that is assumed to be of the same amplitude and phase through the
element. The most commonly used assumption is to consider the source of
radiation to be an isotropic point source, modified in directivity by a gain
factor, from which emanates an ever-increasing spherical wavefront that can
be considered to be an equiphase plane wave in the far-field region. In the
case of an interstitial antenna, intended to heat only the most proximal tissue,
these assumptions are not valid. The much more complicated near-field and
intermediate-field regions must be considered.
The near-field region , where a different set of simplifying assumptions can
be used, is considered to be within radial distances of less than 0.01l; the inter-
mediate field , where simplifying assumptions are not used, extends from the
near-field limit to approximately 5l. A further complication is that the wave-
length l is a function of the square root of the dielectric constant of the
medium in which the antenna is immersed. The effective dielectric constant of
water and muscle tissue modified by the plastic of the catheter will be on the