Biomedical Engineering Reference
In-Depth Information
ultrasound, this generally includes linear or nonlinear pres-
sure field calculations along with some combination of bioheat
transfer modeling, thermal dose calculations, applicator path
and orientation optimization, phased array beamforming, and
visualization. Most treatment planning simulations predict
the pressure and temperature fields generated during a treat-
ment, and more detailed evaluations also optimize various
treatment parameters.
at 43°C. A commonly accepted objective for hyperthermia treat-
ments is 60 minutes at 43°C, although much smaller values for
the thermal dose are often achieved with clinical hyperther-
mia applicators. The thermal dose of 240 equivalent minutes is
a standard threshold for tissue coagulation (McDannold et al.
1998), where tissues reaching or exceeding this value define the
expected size of the ablated volume. For both hyperthermia and
thermal ablation, Equation 6.34 calculates the thermal dose for
prospective treatment evaluation and optimization.
6.3.1 Bioheat transfer Model
The bioheat transfer equation (BHTE) (Pennes 1948) is a sim-
plified model for heat transfer in biological systems (Strohbehn
and Roemer 1984) that provides a comparative basis for ther-
mal treatment evaluation (Roemer 1990). The transient bioheat
transfer equation,
6.3.3 thermal therapy planning
Patient treatment planning attempts to determine treatment
parameters that maximize treatment efficacy while minimiz-
ing normal tissue toxicity. To achieve these objectives, treat-
ment planning for therapeutic ultrasound combines pressure
and temperature simulations with optimization and visualiza-
tion in an effort to conform therapeutic temperatures or thermal
doses to the tumor volume. Simultaneously, treatment planning
attempts to identify and avoid sources of patient pain and nor-
mal tissue damage. These problems are caused by bone heat-
ing (Fessenden et al. 1984), reflections at tissue/bone interfaces
(Hynynen and DeYoung 1988), reflections at tissue/air interfaces
(Hynynen 1990b), “hot spots” or excessive thermal doses caused
by surface heating or intervening tissue heating (Damianou and
Hynynen 1993, Moros et al. 1990, Wang et al. 1994), and cavita-
tion in normal healthy tissues (Hynynen 1990a, Hynynen and
Lulu 1990). These sources of normal tissue toxicity can be treat-
ment limiting, so most treatment plans evaluate pressures and
temperatures in both diseased and normal tissues.
For patient treatment planning, pressure and temperature dis-
tributions are ideally computed and evaluated in a detailed patient-
specific model. However, the capabilities of most simulation
models of therapeutic ultrasound are limited by the computation
time, numerical error, and computer memory. Therapeutic ultra-
sound simulations are typically completed in seconds, minutes, or
hours, where the numerical errors achieved in models of homoge-
neous tissue are preferably less than or equal to 1%. The available
computer memory determines the size of the problem that can be
simulated, and the number of points in a 3D computational grid
defined for patient treatment planning is very large due to the rela-
tively small wavelength of therapeutic ultrasound in tissue (about
1.5 mm at 1 MHz). These large grids, which routinely extend hun-
dreds of wavelengths in each direction, are presently incompat-
ible with 3D finite element and finite difference methods when
evaluated on a fully equipped desktop computer. Although some
finite element and finite difference models sample the pressure
field 10 times per wavelength, much smaller numerical errors are
obtained with these methods at 40 samples per wavelength, espe-
cially when complicated tumor and organ geometries, each with
different tissue parameters, are incorporated into the simulation
model. Unfortunately, maintaining such a large grid of pressure
values is beyond the memory capacity of most modern desktop
computers, and the computation times associated with finite ele-
ment and finite difference methods, when applied to very large
κ− −+−ρ
∂
∂
T
t
·(
TWCT TQC
)
(
)
=
0
(6.32)
b
a
describes the time-dependent tissue temperature
T
in °C pro-
duced by the power distribution
Q
. In Equation 6.32,
T
a
is the
arterial temperature,
W
b
represents the blood perfusion rate,
C
b
indicates the specific heat of blood, κ represents the thermal
conductivity of tissue, ρ is the density of tissue, and the specific
heat of tissue is indicated by
C
. The transient bioheat transfer
equation in Equation 6.32 calculates changes in the tissue tem-
perature in response to time-dependent variations in the blood
perfusion or power deposition.
The steady-state bioheat transfer equation, evaluated for a
constant thermal conductivity κ, is given by
2
(6.33)
QWCT T
−
(
−
)
+κ
T
=
0.
bb
a
Equation 6.33 calculates the tissue temperature
T
for fixed values
of the blood perfusion and the power deposition. Equation 6.33
also calculates temperatures for equivalent steady-state power
depositions when the ultrasound applicator switches between
field patterns much more rapidly than the thermal time constant
of the medium (Moros et al. 1988).
6.3.2 thermal Dose Calculations
The transient and steady-state temperatures computed with the
bioheat transfer equations in Equation 6.32 and Equation 6.33,
respectively, also provide the input for thermal dose calculations.
The thermal dose is computed as (Sapareto and Dewey 1984)
N
∑
(
T
−°
3C)
t
=
t R
·
,
(6.34)
n
43 C
°
n
=
1
where
T
n
is the average temperature during the time interval
n
,
N
is the number of temperature samples collected, and Δ
t
is the
duration of each time interval. The parameter
R
is equal to 2 for
temperatures less than 43°C, and
R
is equal to 4 for temperatures
greater than or equal to 43°C. The thermal dose
t
43 °
represents
the equivalent time at which the tissue temperature is maintained
