Biomedical Engineering Reference
In-Depth Information
A few software programs have been developed for ultrasound
imaging simulations. The most popular of these is Field II (Jensen
1996), which is a freely downloadable program (http://server
.oersted.dtu.dk/personal/jaj/field/) that runs within MATLAB
®
.
Field II consists of a well-developed and well-documented set
of routines and user interfaces that were primarily designed for
diagnostic ultrasound simulations. Field II is also sometimes
used for thermal therapy simulations that require calculations
of time-harmonic pressure fields. Other freely available soft-
ware for diagnostic imaging simulations includes the DREAM
toolbox (http://www.signal.uu.se/Toolbox/dream/) and the
Ultrasim package (http://folk.uio.no/ultrasim/). Although
DREAM and Ultrasim generate useful results for other ultra-
sound applications, these programs are infrequently applied to
simulations of thermal therapy.
FOCUS is a software package that is presently under develop-
ment for both therapeutic and diagnostic ultrasound simulations.
FOCUS (http://www.egr.msu.edu/~fultras-web) is a “fast object-
oriented C++ ultrasound simulator” that quickly performs lin-
ear simulations of time-harmonic and transient pressure fields.
Time-harmonic pressures are computed with the fast near-field
method and the angular spectrum approach (Zeng and McGough
2009), and transient pressures are computed with the fast near-
field method and time-space decomposition (Kelly and McGough
2006). In FOCUS, these time-harmonic and transient pressure
calculations are implemented for circular, rectangular, and spher-
ically focused transducers. The main routines in FOCUS com-
pute pressure fields much faster than the Rayleigh-Sommerfeld
integral, the rectangular radiator method, Field II, DREAM,
and Ultrasim for both time-harmonic and transient excitations,
where the greatest advantage is achieved in the near-field region.
FOCUS also provides routines for the Rayleigh-Sommerfeld inte-
gral to facilitate comparisons and to provide references as needed.
New features, including nonlinear propagation, are also under
development.
HIFU Simulator is a software package that simulates nonlin-
ear propagation of ultrasound (Soneson 2009). This software,
which presently models axisymmetric 2D pressure distribu-
tions, simulates nonlinear ultrasound propagation for time-
harmonic inputs with the KZK equation and the resulting
temperature response with the Pennes bioheat transfer equation
(BHTE). Support for layered tissue models is also included in
HIFU Simulator. Routines that calculate nonlinear 3D pressure
fields are presently under development.
In Equation 6.29, the intensity at a point in space is represented
by
I
(
x ,y,z
), the absolute value of the peak pressure is |
p
(
x ,y,z
)|,
the density is ρ
0
, and the speed of sound is
c
. The units for the
intensity
I
(
x ,y,z
) are watts per square meter (W/m
2
). he pres-
sure in Equation 6.29 is typically evaluated in a lossy medium,
which is modeled for a time-harmonic excitation by the complex
wave number
ω
k
=−
ja
.
(6.30)
c
Equation 6.30 describes the wave number
k
for an outward prop-
agating (or left to right propagating) wave where the positive
time convention indicated by
e
j
ω
t
represents the time-harmonic
component of the pressure. In Equation 6.30, ω is the radian
frequency of the time-harmonic excitation, and
a
is the attenu-
ation in nepers per meter (Np/m). For pressure calculations in
lossy media, the complex wavenumber
k
is inserted into any
of the integral expressions given in previous sections, and the
integral is evaluated using the same approaches described previ-
ously without any other changes. Pressure calculations with the
angular spectrum approach also modify the propagation term to
represent the loss (Zeng and McGough 2008).
The power deposition
Q
is twice the product of the intensity
and the absorption coefficient (Nyborg 1981)
Q
= 2α
I
,
(6 . 31)
where α represents the absorption in Np/m and the units of
the power deposition
Q
a re W/m
3
. The absorption coefficient
α describes the component of the attenuated ultrasound wave-
form that is converted into heat, whereas the remaining attenu-
ation components are scattering, reflection, and refraction
(Cobbold 2007). In some soft tissue models, the attenuation
coefficient
a
and the absorption coefficient α are equal (Nyborg
and Steele 1983), and in others, the ratio α/
a
is less than 1/2
(Goss et al. 1979).
6.3 thermal Modeling and
treatment planning
Patient treatment planning determines an optimal combi-
nation of treatment parameters that maximize the effec-
tiveness of a treatment while minimizing undesirable side
effects. For ultrasound-based thermal therapies, treatment
planning attempts to optimize conformal delivery of hyper-
thermic temperatures or ablative thermal doses while mini-
mizing thermal or mechanical damage to healthy tissues. For
mechanically scanned ultrasound systems, treatment plan-
ning involves calculations of applied powers and applica-
tor locations/orientations, and for ultrasound phased arrays,
treatment planning optimizes the phase and amplitude of the
driving signal for each array element. Treatment planning is
often a computationally intensive process, and for therapeutic
6.2.7 Intensity and power Calculations
Temperature simulations require intermediate calculations of
the power deposition values, which in turn depend on the inten-
sity. Thermal therapy simulations typically utilize the plane
wave approximation for the intensity, which is given by
2
|(,,)|
2
px yz
c
(6.29)
Ixyz
(, ,)
=
.
ρ
0
