Int. J. Computational Biology and Drug Design, Vol. 3, No. 3, 2010
Fast algorithm in estimating high intensity focused
ultrasound induced lesions
Yufeng Zhou
Division of Engineering Mechanics,
School of Mechanical and Aerospace Engineering,
Nanyang Technological University,
639798, Singapore
and
Laboratory of Modern Acoustics
of Ministry of Education,
Nanjing University,
Nanjing 210093, China
Fax: 65-6792-4062
E-mail: yfzhou@ntu.edu.sg
Abstract: High Intensity Focused Ultrasound (HIFU) has been emerging as a
new and effective modality in non-invasive thermal ablation for cancers and
solid tumours. Although a theoretical model is available for calculating
thermal field and the consequent lesion production, its computation is too
time-consuming (~1 day) for HIFU treatment planning on the site. In this study,
several approximations were made on the BioHeat equation to estimate
HIFU-induced lesions. Experimental results, estimation and theoretical
calculation were compared with each other in a good agreement. However, the
computation time for 25 treatment spots was only 1 min. Altogether,
the developed fast algorithm provides an accurate outcome in a timely fashion
and can push the wide acceptance of HIFU technology in clinics.
Keywords: HIFU; high intensity focused ultrasound; BioHeat equation;
temperature elevation; approximation.
Reference to this paper should be made as follows: Zhou, Y. (2010)
‘Fast algorithm in estimating high intensity focused ultrasound induced
lesions’, Int. J. Computational Biology and Drug Design, Vol. 3, No. 3,
pp.215–225.
Biographical notes: Yufeng Zhou is an Assistant Professor at Nanyang
Technological University in Singapore and an Adjunct Professor at the
Laboratory of Modern Acoustics at Nanjing University in China. He received
his PhD in Bioacoustics from Duke University (2003). His research interests
include bubble dynamics, therapeutic ultrasound technology (shock wave
lithotripsy for stone treatment, high-intensity focused ultrasound for solid
tumour/cancer ablation, ultrasound-enhanced drug delivery, shock wave
therapy), non-destructive evaluation and acoustic wave propagation.
Copyright © 2010 Inderscience Enterprises Ltd.
215
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Y. Zhou
Introduction
High Intensity Focused Ultrasound (HIFU) is emerging as a new modality for solid
cancer/tumour treatment, such as prostate, kidney, liver, breast and pancreatic cancers
(Kenney, 2005). In Asia and Europe, more than 100,000 cases have already been
performed with great success. The principle of HIFU therapy is focusing a high-intensity
ultrasound beam into a tumour within the body for ablation. The acoustic intensity at the
focus is high enough to achieve temperatures reaching over 65°C within a few seconds to
coagulate the tissue. In comparison with traditional cancer therapies, such as surgery,
radiotherapy and chemotherapy, HIFU ablation has the advantage of being a completely
non-invasive therapy without exposing the patient to ionising radiation, resulting in
highly targeted therapy with fewer complications (Zhou, 2011).
Despite promising results, HIFU remains in its infancy stage with several technical
problems preventing it from becoming a widely adopted therapeutic procedure
(Zhou, 2011). For example, current HIFU systems, both clinical and experimental
models, have very limited capabilities of treatment planning. Under the guidance of either
sonography or Magnetic Resonance Imaging (MRI), the geometrical information
(i.e., contour and anatomical position) of to-be-treated cancers/solid tumours and vital
tissues (i.e., vessels and nerves) possible in the treatment region can be figured out, which
is critical in non-invasive therapy. Afterwards, most systems provide physician or
operator the HIFU treatment information (i.e., locations of the treatment spots and the
scanning pathway), but no information of the consequent ablation lesions is available.
Therefore, it becomes the physician’s responsibility to input the treatment parameters
(i.e., acoustic power, pulse parameters and interval spacing between the treatment spots),
which determine the lesion shape and size. Unfortunately, most physicians do not have a
sufficient background and understanding of physics underlying HIFU to set up those
parameters rationally. To improve the safety and efficacy of HIFU therapy, a more
effective method for treatment planning, which assists the user to determine the input
parameters and estimate the treatment outcome prior to beginning the therapy, is essential
and critical for the wide acceptance of HIFU technology.
The ablation mechanism of HIFU is the absorption and transfer of acoustic
energy into heat when an ultrasound wave propagates in tissue and the subsequent
high-temperature rise as high as 65°C within a few seconds at the focus of the therapy
transducer. At this temperature, the proteins are denatured and internal structure located
in the focal area can be precisely destroyed without any incision or injury to the
intervening tissue, as the suddenness and rapidity of this phenomenon prevent the
dissemination of heat around the focal point. It is, therefore, desirable to have complete
knowledge of the temperature distribution. In the fundamental studies of HIFU,
theoretical model has already been established to simulate the acoustic fields in the focal
region of any HIFU transducer. Briefly, the Khokhlov-Zabolotskaya-Kuznetsov (KZK)
non-linear evolution equation is first used to model numerically high-intensity acoustic
beams (Bakhvalov et al., 1987). Then, with knowledge of the acoustic fields, the Pennes
BioHeat equation is used to predict the temperature response and Thermal Dose (TD)
resulting from HIFU exposure in the tissue fairly accurately (Pennes, 1948), although
some limitations are included. The BioHeat equation can be solved with initial
and boundary conditions by numerical methods. These methods include the Finite
Element Method (FEM) (Das et al., 1999), the Finite Difference Time Domain (FDTD)
method (Curra et al., 2000) and solution by a semi-discrete scheme of Galerkian FEM
Fast algorithm in estimating high intensity
217
(Sohrab et al., 2006). These simulated results were found to be in a good agreement with
ex vivo and in vivo experimental observations (Chapelon et al., 1993). However, all of
these theoretical models are computationally intensive (several CPU hours). Therefore,
simulating the HIFU outcome just prior to the clinical treatment is not feasible using
current theoretical computation approaches.
In this study, the solution to the BioHeat equation was approximated to reduce the
computation time. A total of 25 treatment spots with different scanning pathways (raster,
spiral scanning from the outside to inside and spiral scanning from the inside to outside)
were evaluated. Calculation time of the fast algorithm was only about 1 min.
Approximation results were then compared with the produced lesion in the transparent
polyacrylamide tissue phantom embedded with Bovine Serum Albumin (BSA).
A quite good agreement was found between our estimation, theoretical calculation and
experimental outcome. Altogether, our approximation algorithm provides a fast HIFU
planning and evaluation option for physician and operators before clinical treatment.
2
Methods
2.1 BioHeat transfer equation
The mathematical model for temperature elevation in the tissue is based on the BioHeat
Transfer Equation (BHTE) (Pennes, 1948),
G
T − T0 Q(r ) F (t )
∂T
,
= k ∆T −
+
(1)
∂t
Cv
τ
where t is the time, τ is the perfusion time, T(r, t) is the tissue temperature, T0 is the
equilibrium temperature, k = K/Cv is the local tissue temperature conductivity, K is the
heat conductivity, Cv is the heat capacity of a unit volume, ¨ is the Laplacian operator,
G
F(t) is the temporal function indicating an HIFU pulse, and Q(r ) is the absorbed
ultrasound energy
G
G
Q(r ) = 2α I (r ),
(2)
G
where α is the ultrasonic absorption coefficient of the soft tissue and I (r ) is the acoustic
intensity. A solution to equation (1) for an infinite, homogeneous and isotropic medium
can be found using transform techniques (Davies, 1978; Carnes et al., 1991) as
1
G
T (r , t ) =
Cv
t
³³
0 V
G
G G
G
Q(r ′) F (ξ )G (r − r ′, t − ξ )dr ′ d ξ ,
G G 2
ª
r − r′ º
exp « − t − ξ −
»
4k (t − ξ ) ¼»
G G
¬« τ
,
G (r − r ′, t − ξ ) =
[4π k (t − ξ )]3/ 2
(3)
(4)
G
where G(*) is the appropriate Green’s function (Stakgold, 1979), r ′ is the source
variable coordinate and ξ is the temporal variable of the heat source. The corresponding
TD to HIFU pulses was calculated using
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Y. Zhou
t
TD 43°C (t ) = ³ R 43−T (t ') dt ′
0
(5)
with R = 0.25 if T(t) < 43°C and 0.5 otherwise (Sapareto and Dewey, 1984). The value
required to create a thermally irreversible damage in tissues is equivalent to the TD of a
240-minute exposure at 43°C (Lele, 1967; Damaniou and Hynynen, 1994).
2.2 Approximation
The lateral distributions of the acoustic intensity are assumed in Gaussian function
−
G
I (r ) = I 0 e
G G
( r − r0 ) 2
2σ 2
,
(6)
where I0 is the spatial-peak pulse-average acoustic intensity at the focus and calculated
from the pressure waveforms measured using a Fibre Optic Probe Hydrophone (FOPH)
(Zhou et al., 2006), r0 is the location of the treatment spot and σ is the variance and
determined by
σ=
(HPBW/2) 2
ln 2
(7)
where HPBW is 3 dB or half-power beam width. Although the pressure distribution could
be described more closely using a transverse beam profile 2 J1 (ar )/ar , where J1(*) is the
first-order Bessel function and a is the radius of HIFU transducer, the contribution of
side-lobes in the thermal ablation is usually neglected and Gaussian function is much
easier in calculation. Since the delivery of HIFU energy is in the format of pulse,
G
the equivalent absorbed ultrasound energy by the tissue, Qe (r ), can be approximated as
G
G
Qe (r )U (t ) = Q(r ) ⋅ dc% ⋅ F (t ),
(8)
where dc is the duty cycle of HIFU pulses and U(t) is the unit step function. Afterwards,
larger time step (0.5 s) can be used in the calculation of temperature field to save the
computation time without a reduction in its accuracy.
Two-dimensional thermal field was calculated first and then extended to 3D space
under the assumption that the ratio of the length of the generated lesion to its diameter is
same as the ratio of the measured −6 dB beam size in the axial direction to its lateral
direction.
2.3 Experimental set-up
The HIFU system used in this study (FEP-BY02, Yuande Bio-Engineering Ltd., Beijing,
China) consists of 251 individual PZT elements, driven all in phase and arranged in
a concave spherical holder. The HIFU transducer has a centre frequency of ~1 MHz,
an outer diameter of 33.5 cm and an inner diameter of 12 cm with integrated ultrasound
imaging probe (S3, Logiq 5, GE, Seongnam, Korea) mounted in the central hole co-axial
to the HIFU beam. An optically transparent gel phantom (L × W × H = 5.5 × 5.5
× 5 cm3), composed of polyacrylamide hydrogel and BSA that becomes optically opaque
when denatured by heat (Lafon et al., 2005), was surrounded by a tissue phantom that
contains 6.5% Alginate (Jeltrate, Dentsply International, York, PA). The centre of the
Fast algorithm in estimating high intensity
219
transparent gel phantom was aligned with the HIFU focus under the guidance of B-mode
ultrasound imaging. A LabVIEW (National Instruments, Austin, TX) program was
written and run on a PC to control the motion of the treatment table and delivery of HIFU
pulses (see Figure 1). After the treatment, the HIFU phantom was taken out and the
lesions were recorded photographically for comparison.
Figure 1
Experiment set-up of generating thermal lesions inside tissue phantom using
extracorporeal High-Intensity Focused Ultrasound system (see online version
for colours)
Three scanning pathways were used in this study: a conventional raster scan, spiral
scanning from the centre to the outside and spiral scanning from the outside to the centre
(see Figure 2) (Zhou et al., 2007). There were total 25 treatment spots arranged in the
shape of a diamond with a grid size of 4 mm. The treatment parameters are same
for each spot: the HIFU on time is 150 ms, the HIFU off time is 150 ms, there are
60 pulses per spot, interval time between the treatment spots is 6 s (including the
mechanical movement time) and the absorbed acoustic energy at the target is 1000 J.
The electrical output power of the HIFU transducer was calculated using our proposed
method (Hwang et al., 2009).
Figure 2
3
Motion pathway used in HIFU treatment in: (a) raster scanning; (b) spiral scanning
from the centre to the outside and (c) spiral scanning from the outside to the centre
for a total of 25 spots with 4 mm grid space (see online version for colours)
Results
Approximation of the effective heat source as in equation (8) was validated and shown in
Figure 3. HIFU exposure consists of 60 pulses with pulse duration of 300 ms and duty
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Y. Zhou
cycle of 50%. In each pulse, the temperature will increase when HIFU energy is delivered
and decrease at the HIFU-off stage, respectively, seeming as saw-teeth. Using the
effective heat source approximation and much longer temporal step size (500 ms),
the temperature profile fits well with the exact solution although without saw-teeth.
Because of the low-temperature elevation induced by each HIFU pulse (low amplitude of
each saw-tooth), its contribution to the overall TD can be ignored.
Figure 3
Approximation of the effective heat source in the temperature elevation calculation.
Blue line: HIFU pulses (150 ms on, 150 ms off, 60 pulses) with calculation time step
of 30 ms; red line: continuous HIFU exposure with effective heat source approximation
and calculation time step of 500 ms (see online version for colours)
The lesions generated in the gel phantom were found to have similar pattern and
characteristics as predicted by the theoretical simulations (see Figure 4) as well as using
the fast algorithm proposed in this study. By using the raster scanning method, the first
visual lesion was the third treatment spot and with the progress of the HIFU treatment the
lesion size became larger because of the thermal diffusion from nearby spots. Merging of
lesions occurred towards the end of the treatment. When using the spiral scanning
outwards pathway, only the first lesion was not visible. However, the other lesions were
smaller in comparison with those generated in the raster scanning pathway, and no
merging of lesions was observed. The lesion pattern using the spiral scanning inwards
had different characteristics with all treatment spots along the outside boundary (first 12
spots) not being visible. Since thermal energy is concentrated towards the centre of the
treatment area, the last a few lesions merged to form a large lesion. The patterns of lesion
production and their characteristics can also be assessed by observing the lesions from
the lateral direction (see Figures 5 and 6). The great differences lie in the computation
time. It took more than 24 h in computation using the accurate FTFD code running in a
workstation (Hewlett-Packard, Palo Alto, CA, USA) (Zhou et al., 2007). However, the
computation time reduced to about 1 min with the fast algorithm in a PC with 2.0 GHZ
CPU and 1GB memory run in Matlab (Mathworks, Natick, MA, USA). The maximum
lesion lengths in the gel phantom using these scanning pathways were 10.1, 6.9 and
12.2 mm, respectively. In comparison, the corresponding values using the fast algorithm
were 10.1, 5.2 and 9.5 mm, respectively, whose errors are within an acceptable range.
Fast algorithm in estimating high intensity
221
Figure 4
Thermal field calculation results using finite-time finite-difference method in (left)
raster, (middle) spiral scanning outwards and (right) spiral scanning inwards
Figure 5
Representative photos of lesions generated inside the gel phantom from: (a) top view,
lateral view in (b) X direction and (c) Y direction using pathway in (left) raster,
(middle) spiral scanning outwards and (right) spiral scanning inwards
Furthermore, Matlab environment provides several useful features for end-users.
For example, the predicted lesions can be viewed in 3D space from an arbitrary angle
(see Figure 7(a)), which provides direct impression on the clinical HIFU outcome if
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Y. Zhou
combined with the reconstructed anatomies from sonographs and MRI sections.
The temperature profile at any position is also available (see Figure 7(b)) to examine the
potential for the occurrence of boiling phenomenon (T > 100°C). The boiling bubbles are
of orders larger than those HIFU pulses-induced ones, blocking the propagation of the
following HIFU pulses, and subsequently distorting the lesions from a symmetric
cigar shape to an asymmetric tadpole shape (Watkin et al., 1996), which makes the
HIFU-induced lesions not expectable as in the stage of treatment planning and estimated
by theoretical model.
Figure 6
Simulated lesions generated with the fast algorithm from: (a) top view, lateral view in
(b) X direction and (c) Y direction using pathway in (left) raster, (middle) spiral
scanning outwards and (right) spiral scanning inwards (see online version for colours)
Figure 7
Features of simulation package in Matlab environment: (a) 3D view of generated
lesions in a raster scanning and (b) the temperature profile of the 23rd spot in spiral
scanning inwards way (see online version for colours)
(a)
(b)
Fast algorithm in estimating high intensity
4
223
Discussion and conclusion
HIFU is a new and effective modality in solid tumour/cancer treatment. Because of its
inherent advantages of non-invasiveness and non-ionisation, its application is increasing
rapidly. However, the high dependency of the clinical outcomes on input parameters,
which is difficult for most physicians because of their absence in understanding of HIFU
physics, limits the adoption. Although the theoretical model is available in calculating
thermal field and subsequent lesion size, it takes too much time (in the order of a day)
in the computation to be applied on the site. A fast algorithm was developed in this study
based on BioHeat equation and its solution using Green’s function. Comparison between
experimental, theoretical and estimated results was carried out. It is shown that the fast
algorithm produces a rather satisfactory outcome, but in a much shorter time
(in the order of a minute).
Several approximations were made in calculating the solution of BioHeat equation.
Despite that, the systematical error is within a satisfactory range because the purpose of
this algorithm is to provide an estimation of the sizes and shapes of HIFU-induced lesions
for physician/operator in a timely fashion. One of the limitations of this approach is the
need of calculating heat source from measured pressure waveform. Numerical method is
available to solve the KZK equation for finite-amplitude acoustic wave propagation
through multiple tissue layers (i.e., the abdominal layer of humans) both economically
and computationally (Soneson, 2008). Coupling this module with tissue information
obtained from either ultrasound or MRI images for the guidance of HIFU therapy, in vivo
acoustic pressure, distribution, and the consequent heat source could be available with
higher accuracy than those derrated using free field measurement and attenuation
coefficients of the tissue in the propagation path that was usually summarised from
ex vivo experiments.
Because the detectable tumour size (centimetres) is much larger than the HIFU focal
size (millimetres), the HIFU focus needs to be scanned throughout the entire target
volume. The common scanning pathway is a raster mode and HIFU parameters for each
spot are kept the same. Both gel phantom and theoretical studies have illustrated that
the energy delivered at the beginning of the HIFU ablation is insufficient to generate
visual lesions; however, with the HIFU ablation progress the lesion size will increase
due to the thermal diffusion effect and treatment spots later in the treatment may be
over-treated (see Figures 4 and 5). From the viewpoint of the physician, there are three
basic requirements for the ideal HIFU ablation:
•
ability to generate a predictable lesion for every treatment spot
•
all generated lesions need to be uniform
•
complete coverage of the entire treated volume.
Therefore, the delivered energy should be adjusted dynamically with the use of different
scanning pathways (Zhou et al., 2008).
The fast algorithm proposed in this study can be developed into an HIFU treatment
planning software that runs prior to the therapy when the patient lying at the table in
ready status. HIFU planning software may include the functionalities of having
a user-friendly interface and an intuitive operation that requires minimal training,
assisting the HIFU operator to evaluate the treatment protocols, determining the HIFU
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Y. Zhou
parameters without influencing the other steps (tumour diagnosis, HIFU ablation and
post-treatment observation) and reviewing the estimated lesions in 3D space. As a result,
it will make HIFU operation more easy and reduce the outcome variation due to operator
dependency. The most advantage of this fast algorithm is its universe application for all
commercial or experimental HIFU systems (different centre frequency, transducer
geometries and treatment parameters) and tissue targets (different tumour types and
anatomic structures on the HIFU propagation pathway). Furthermore, other relevant
information (i.e., instantaneous temperature, pressure and acoustic intensity distribution)
will also be available in considering the safety of HIFU therapy.
There are at least 11 major HIFU manufacturers in the market (5 in China, 2 in USA,
1 in Korea and 3 in Europe) and also several smaller ones worldwide. Since the HIFU
technology is still in its infancy stage and a large amount of clinical trials
have been performed with promising results, more manufacturers may penetrate this
cutting-edge medical device market. Although the healthcare fee related with HIFU
treatment is unknown, it is believed that with more acceptance of this novel technology
this number will increase significantly in the near future. According to our knowledge,
there is no capability of the HIFU treatment planning in currently available HIFU
systems, neither clinical nor experimental type. Therefore, our proposed fast algorithm
targets this niche market and may be able to push the wide acceptance of HIFU
technology, to enhance its efficiency and safety, and to facilitate the FDA clearance of
HIFU device for solid tumour treatment.
There are other FDA-approved ablation devices that utilise energy sources of
Radiofrequency (RF), laser and microwave to create thermal injury to tissue in
conjunction with a percutaneous approach. While thermal ablative techniques are rapidly
gaining acceptance in the treatment of inoperable tumours, incomplete treatments are
found common because of the thermal diffusion effect as in HIFU (Goldberg et al.,
1998). Although the energy sources are different, the principle of thermal lesion
production is same as HIFU. Therefore, the fast algorithm proposed here can also be
applied to the other thermal ablation methods.
In summary, the proposed fast algorithm is able to produce satisfactory accurate
results as the theoretical model but with reasonable computation time, which is feasible
for onsite evaluation of the treatment protocols and allows the development of HIFU
planning software for commercial system.
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