Biomedical Engineering Reference
grids, are excessively long. In contrast, the approaches outlined in
previous sections require only two samples per wavelength, and
sufficient computer memory is only needed for at most one or two
planes of pressure field values sampled at this lower rate. Thus, to
satisfy these time, error, and memory requirements, certain com-
promises are required. Most patient treatment planning calcula-
tions use homogeneous or layered tissue models for pressure field
simulations, although some newer approaches model more com-
plicated geometries. These homogeneous or layered tissue models
often provide a useful starting point for thermal therapy planning.
Two different blood perfusion models are evaluated in Roemer
et al. (1984), where one is uniformly perfused and the other is
highly perfused in the periphery, moderately perfused in an
intermediate region, and necrotic with no blood flow in the core.
The parameters in these simulations include tumor location and
size, scanning pattern radius, power deposition, transducer fre-
quency, and the transducer f/#. The simulated temperatures are
compared according to an algorithm that defines minimum and
maximum tumor temperatures as well as maximum normal tis-
sue temperatures. The results show that a mechanically scanned
transducer operating at 500 kHz with an f/# of 0.8 satisfies the
treatment objectives when the minimum tumor and maximum
tumor temperatures are defined as 42°C and 60°C, respectively.
In another simulation model, the temperature fluctuations
(Moros et al. 1988) produced by mechanically scanned ultra-
sound hyperthermia applicators are evaluated. The focal plane
temperature fluctuations are simulated with a 3D transient bio-
heat transfer model, where the input parameters are the f/#, the
blood perfusion, the scan time, and the scan diameter for single
circular scans and multiple concentric scans. The largest fluc-
tuations occur in the focal plane, and the magnitude of these
fluctuations increases linearly as a function of the scan time.
Acceptably small temperature fluctuations are demonstrated
with scan times of 10 seconds or less for a mechanically scanned
transducer with an f/# of 2.6. Larger temperature fluctuations
are also observed with smaller f/# transducers, and these require
even smaller scan times to achieve comparable temperature fluc-
tuations. Multiple concentric scan paths yield relatively uniform
temperature distributions when the difference in the diameter of
adjacent scans is equal to the focal spot diameter.
In a similar parametric study, pre-focal plane heating produced
by mechanically scanned ultrasound hyperthermia applicators is
characterized with a steady state bioheat transfer model (Moros
et al. 1990). The frequency, the f/#, the focal depth, the blood per-
fusion, and the scan pattern diameter are the input parameters,
and the resulting temperature distributions are evaluated for
single and multiple transducer configurations. The results dem-
onstrate that single and multiple circular scans produced exces-
sive temperatures between the applicator and the tumor target.
Although the peak power depositions are generated in the focal
plane, the overlapping power depositions along the central axis
cause the intervening tissue heating. Simulations of a mechani-
cally scanned configuration consisting of four tilted transducers
with overlapping foci also encounter the same problem unless the
transducer closest to the central axis is turned off during the scan
(Figure 6.7). This eliminates the excessive pre-focal plane heat-
ing by increasing the size of the effective acoustic aperture, which
effectively spreads the incident energy across a wider area.
Related simulations are evaluated for the scanning ultra-
sound reflector linear array system, or SURLAS (Moros et al.
1997). This device, which facilitates concurrent delivery of
ultrasound hyperthermia and radiation therapy, features two
fixed-phase linear ultrasound arrays combined with a reflec-
tor that is scanned along a linear path to achieve variable depth
control over the power deposition. The numerical model for the
18.104.22.168 Ultrasound Hyperthermia
with Fixed-phase applicators
Several numerical models have been developed for fixed-phase
ultrasound hyperthermia applicators (Strohbehn and Roemer 1984).
One such model computes the SAR and the temperature response
for a stationary spherically focused transducer (Swindell et al. 1982).
The pressure calculations for this model evaluate the Rayleigh-
Sommerfeld integral by superposing the contributions from thin
annular strips. This approach converts the 2D Rayleigh-Sommerfeld
integral into an equivalent 1D integral. For a fixed transducer, SAR
values and temperature maps are simulated for excitation frequen-
cies of 500 kHz and 2 MHz. The simulation results demonstrate
that the isothermal contours move closer to the transducer surface
at 2 MHz due to increased attenuation. Simulated temperature
maps also show that approximately spherical isothermal regions are
produced with a single circular scan and with multiple concentric
scans. In this model, the mechanically scanned ultrasound trans-
ducer rapidly traverses each concentric ring, uniformly depositing
power along the scan trajectory. The time-averaged power is then
computed, and the approximate temperature map is calculated
with the steady-state bioheat transfer equation.
Another numerical model computes the impulse response for a
scanned focused ultrasound transducer, approximates the inten-
sity and the effect of attenuation with separate plane wave mod-
els, and then calculates the cylindrically symmetric intensity of
the scanned pattern with a Hankel transform (Dickinson 1984).
The intensities are then converted into a specific absorption rate
(SAR), which equals the power deposition Q divided by the den-
sity ρ according to SAR = Q /ρ. This result provides the input to a
cylindrically symmetric 2D bioheat transfer model consisting of
planar layers of skin, fat, and muscle. The bioheat transfer model
also includes a cylindrical tumor that consists of a well-perfused
outer layer and a poorly perfused core. The temperature output
of the bioheat transfer model is then converted into thermal dose
specified in terms of equivalent minutes at 43°C.
A related model considers the effect of normal tissue and
tumor blood perfusion on the selection of mechanically scanned
transducer parameters (Roemer et al. 1984). The pressures are
once again computed by superposing the contributions from thin
curved strips on the transducer surface, and the mechanically
scanned intensity pattern is obtained from a circularly symmetric
convolution. Temperatures are then computed for a cylindrically
symmetric layered tissue model combined with a cylindrically
symmetric tumor model containing three concentric regions.