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Theoretical Evaluation of Moderately Focused Spherical Transd-ucers and Mult i-focus Acoust ic
Lens/Transducer Combinations for High Intensity Focused Ultrasound Thermal Therapy
Xia Wu
A thesis submitted in conformity with the requirements
for the degree of Master of Science
Graduate department of Medical Biophysics
The University of Toronto
@ Copyright Xia Wu 2001
A uisitions and Acquisitions et ~ 8 b g m p h i c Seivices senrices Wbîtographiquro
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Theoretical Evaluation of Moderately Focused
Spherical Transducers and Multi-focus Acoustic
Lens/Transducer Combinations for High Intensity
Focused Ultrasound Thermal Therapy
Xia Wu, B.A.Sc. Department of Medical Biophysics
The University of Toronto, 2001
Impractically long treatment tinies are required for highly focased spherical trans-
ducers [HF] to destroy tumours because thermal lesions generated by tliese trans-
ducers are srnall and a large number of such lesions are required. Moderately focused
spherical transducers [MF] and multi-focus acoustic lens/transducer combinations
[LTC] can generate larger lesions compared to those produced by highly focused
spherical t ransducers, and t herefore shorter treatment times are expected. The
degree of improvement in total treatment time by the use of MFs and LTCs was
quantified in this study. A 3-D ultrasound thermal mode1 and a target mode1 were
developed to calculate treatment times required for various ultrasound transducers,
under identical treatment conditions. A LTC design method was developed to de-
termine the thickness of lens elements for production of specified multi-focus fields.
The simulation results show for the treatment of a 2 x 2 x 2cm3 tumour, a HF, MF and LTC require 150, 42 and 30 min respectively.
Acknowledgment s
1 would like to thank the following people My supervisor, Dr. Michael Sherar, for his scientific inspiration, encourage-
ment and continuous support during this project, My cornmittee members, Dr. John Hunt and Dr. Brian Wilson, for their
advice and helpful discussions, Dr. Michael Kolios, for his scientific insight and experience, Dr. Mark Gertner for his invaluable guidance on writing and his great pa-
t ience, Car1 Kumaradas for his advice and help in science, computers and many other
things Mihaela Pop, Lee Chin, Peter Bevan, Arthur Worthington and Sean Davidson
for sharing their knowleclge and for their assistance. Mum and Dad for their unending support and al1 their sacrifices, Jack, for his loving encouragement.
iii
Contents
Abstract
Acknowledgment s
List of Figures
Nomenclature
iii
viii
Chapter 1 Introduction 1
. . . . . . . . . . . . . . . . . 1.1 Thermal Therapy in Cancer Tkeatment 1
1.1.1 Biological Rationale and Clinical Experience . . . . . . . . . . 1
. . . . . . . . . . . . . . . . . . . . . . . . . 1.1.2 Thermal Delivery 4
1.2 High Intensity Focused Ultrasound Thermal Therapj . . . . . . . . . 7 . . . . . . . . . . . . . . . . . . . . . . . . 1.2.1 Clinical Experience 7
1.2.2 Focused UI trasound Transducer Designs . . . . . . . . . . . . 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Objective 17
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 ThesisOutiine 17
Chapter 2 Theoretical Evaluation of Moderately Focused Spherical lkansducers for High Intensity Focused Ultrasound Thermal Ther-
aPY 19 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Abstract 19
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Introduction 20
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Methods 23 . . . . . . . . . . . . . . . . . . . 2.3.1 Ultrasound-Thermal Mode1 23
. . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.2 Tumour Mode1 25
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Results 28
. . . . . . 2.4.1 Verification of Ultrasound-Thermal Mode1 Accuracy 28
2.4.2 Comparison of Highly and Moderately Focused Spherical Trans- . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ducers 32
2.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6 Conclusions 41
Chapter 3 Theoretical Evaluation of Multi-focus Acoustic Lens/Tkansducer Combinations for High Intensity Focused Ultrasound Thermal Ther-
aPY 43 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Abstract 43
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Introduction 44 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Methods 47
. . . . . . 3.3.1 LTC Ultrasound Intensity Distribution Calcuiations 47 . . . . . . . . . . . . . . . . . . . . . . . 3.3.2 LTC Design Method 48
. . . . . . . . . . . 3.3.3 Methods for Determining aeatment Times 52 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Results 52
. . . . . . . . . . . . . 3.4.1 Comparison of LTCs and phased arrays 53 . . . . . . . . . . . . . . . . . . . . . . 3.4.2 Effect of Focus Spacing 58
. . . . . . . . . . . . . . . . . . . . . 3.4.3 Effect of Number of Foci 61
. . . . . . . . . 3.4.4 Multiple Exposure Tkeatments of the Tumour 64 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Discussion 65
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6 Conclusions 69
Chapter 4 Summary and F'uture Work 71 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Summary 71
. . . . . . . . . . . 4.1.1 Moderately Focused Spherical lkansducers 71
. . . . . 4.1.2 Multi-focus Acoustic Lens/Transducer Combinations 72 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Future Work 73
. . . . . . . . . . . . . . . . . . 4.2.1 Ultrasound-Thermal Modeling 73 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.2 LTCs 77
References 81
List of Figures
Surviving fraction as a function of heating time . . . . . . . . . . . . 2
Schemat ic representation of using high intensity focused ultrasound
to treat tissue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Schematic representation of the therapeutic ultrasound applicator . . . 9
. . . . . . . . . . . . . . . . . . Focused splierical transducer designs 10
. . . . . . . . . . . . . . Schernatic of the reflector focusing applicator 13
. . . . . . . . . . . . . . . . . . . . Schematic of the 2-D acoustic lens 16
During the transducer movement from left to right to form lesions side
by side. some normal tissues in the nearfield remain in the pathway
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . of the beam 21
Block diagram of numerical model to simulate ultrasound-thermal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . effects in tissue 2 3
. . . . . . . . . . . . . . . . . nimour geometry employed in this work 26
Thermal computation domain and mesh spacing dx. dy and dz . . . . 26
. . . . . . . . . . . . . Thermal Dose threshotds of the tumour mode1 28
Comparison of measiired lesion diameters with the results predicted
. . . . . . . . . . . . . . . . . . . . . . . . . by our theoretical mode1 31
Thermal dose distributions calculated using our theoretical model . . 31
Lesion lengt h and diameter and transducer 6dB beamlengt h and
beamwidth versus radius of curvature of focused spherical transducers . 33
Ultrasound intensity distributions and thermal dose distributions pro-
. . . . . . . . . . . . . . . . . . . . . . . . . . duced by SPI and SP2 34
. . . . . . . . . . . . . . . . . . . . . . . . . 2.10 Transducer step patterns 35
. . . . . . . 2.1 1 Temperatures reached in the tissue as a function of time 37
2.12 Thermal dose profiles for treatments of the tumour using SPI and SP2 38
2.13 Thermal dose distributions for treatments of the tumour using SPI
Coordinates and parameten used in the calculation of LTC field dis-
tributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
Coordinates and parameters used in the pseudoinverse method . . . . 49
Geometry of the turnour mode1 in Cartesian coordinates . . . . . . . 53
9 focus pattern with 2 mm focus spacing . . . . . . . . . . . . . . . . 54
The intensity distributions generated by LTCl and PA . . . . . . . . 55 The lens surface profile of LTCl . . . . . . . . . . . . . . . . . . . . . 56
Thermal dose distributions generated by LTCl and PA . . . . . . . . 57 The iiltrasound intensity distributions generated by LTCl and LTC2 59
Thermal dose distributions generated by LTCl and LTC2 . . . . . . . 60
2 mm spaced. 16-focus pattern . . . . . . . . . . . . . . . . . . . . . . 61
Ultrasound intensity distributions generated by LTCl and LTC3 . . . 62 3.12 Thermal dose distributions generated by LTCl and LTC3 . . . . . . . 63
3.13 Lateral step pattern for LTCl . . . . . . . . . . . . . . . . . . . . . . . 64
3.14 Thermal dose distributions generated by LTC1. SP2 and SPI at the
end of the treatment . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
3.15 Thermal dose isosurface distributions generated by LTC1. SP2 and
SPI at the end of the treatrnent . . . . . . . . . . . . . . . . . . . . . 67
. . . . . . . . . 4.1 Diagam of a beam traversing t hrough layered tissues 75
4.2 Schematic of the rotation of a 9 focus LTC with 2 mm focus spacing . 79
4.3 Thermal dose distributions generated by LTCl with and lwithout the
pseudo-rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
Nomenclature
S ymbols
a, Distance between the surface of the transducer and the lens
element n [cm]
6, Thickness of the lens element n [cm]
c Speed of sound [cm S-'1
cb Heat capaci ty of blood [J g-' 0" C-'1
ci,. Speed of sound in the lens [cm s-'1
q Heat capacity cf tissue [J g-' - O C-'1
c,.t,, Speed of sound in water [cm S-'1 p p p p p p p p - - - - - - - -
d Distance [cm]
d, Distance between the lens element n and the field point (x,y,z) [cm]
dS Surface area of the source element [cm2]
D 'Ikansducer diameter [cm]
f F'requency [MHz]
G Intensity gain
H Matrix describing the propagation of the ultrasound wave
I Intensity [W cm-*]
jd=-l
6 Thermal conductivity of tissue [W **cm-' 9 " C-'1
k, Wave number [cm-']
M Number of field points intended to be foci
N Total number of lens elements
P Pressure [Pa]
P Complex field pressure [Pa]
R Radius of curvature [cm]
s Axial distance between the skin surface and the field [cm]
S Surface area of a lens element [cm2]
SAR Specific Absorption Rate [W
t Time [s]
Total lleatment Time [s]
T Temperature [OC]
Ta Temperature of arterial blood ['Cl
TD Thermal Dose [EMd3 ]
TDd3,, Thermal dose where attenuation coefficient starts to change [E& ]
TD43i Thermal dose where attenuation coefficient reaches a plateau [EMd3 ]
un Amplitude of the complex particle velocity of the lens element n [cm a * s - ' 1
U Particle velocity [cm *-s-']
Û Complex particle velocity [cm *es-1]
wb Volumetric perfusion rate [g s-l cm-3]
wm Initial blood perfusion [g s-' cm-3]
a Amplitude absorption coefficient [Np cm-' MHZ-'1
p Amplitude attenuation coefficient [Np cm-' MHZ-'1
po Initial amplitude attenuation coefficient [Np cm-' MHz-']
pl Plateau amplitude a t tenuation coefficient [ J g-l OC-']
p Density of the medium [g cm-3]
pt Density of tissue [g cm-3]
0, Phase of the complex particle velocity of the Iens eleinent n
Abbreviat ions
BHTE Bioheat Dansfer Equation
EMd3 equivalent minutes a t 43 OC
HIFU High Intensity Focused Ultrasound
LTC Lens/Transducer Combination
LTCl LTC designed to produce a 2mm spaced, 9 focus field
LTC2 LTC designed to produce a 2.5rnm spaced, 9 focus field
LTC3 LTC designed to produce a 2mm spaced, 16 focus field
MNS Minimum Norm Solution
MW Microwave
PA Phased array designed to produce a 2mm spaced, 9 focus field
RF Radiofrequency
SPI Highly focused spherical transducer
SP2 Moderately focused spherical transducer
Chapter 1
Introduction
1.1 Thermal Therapy in Cancer Treatment
Thermal therapy refers to the clinical use of heat. Hippocrates recorded the use of
red-hot irons to treat small, non-ulcerating cancers in 400 B.C. Modern interest in
thermal therapy began with Coley [9], who used bacterial pyrogens to deliberately
induce fevers in cancer patients. In 1906, Clowes [8] demonstrated that murine carci-
noma cells heated to 45OC failed to produce tumours on subsequent inoculation into
rnice. In 1921, it was shown that diathermy (hyperthermia) and ionizing radiation
had a synergistic anti-cancer effect [58]. Although pursued with great enthusiasm,
much of the early clinical work provided only anecdotal evidence that elevated tem-
peratures have any clinical benefits. Over the past 30 years, a better understanding
of the behaviour of tissues a t elevated temperatures has developed. Effort has also
been focused on development of heating technology, to improve heat localisation
and energy penetration in tissues.
1.1.1 Biological Rationale and Clinical Experience
Heat damages cells directly, causing membrane disruption and cellular protein de-
naturation. Survival curves of chinese hamster ovary cells, as shown in figure 1.1,
demonstrate that the percentage of cells killed is an exponential function of heat-
ing time for temperatures above 43°C. This relationship is valid for most cells
in vitroand tissues in vivo (3, 16,281. Based on this relationship, Sapareto and
THERMAL
Figure 1.1: Surviving fraction as a function of heating time for Chinese hamster ovary cells at various temperatures. The figure was modified from [29].
Dewey [60] developed the concept of thermal dose, a formalism to quantify ther-
mal treatments. The thermal dose, descri bed by equation 1.1, converts different
heating protocols incorporating various heating times at different temperatures into
equivalent heating durations a t a reference temperature of 43°C.
where
T = temperature [OC]
TD = thermal dose [EMe (equivalent minutes a t 43"C)I
ttotai = total treatment time [s]
The thermal dose equation indicates that for each I0C increase above 43°C the
heating time can be halved to achieve the same biological effect.
Based on the thermal dose equation, two general treatment strategies can
be adopted to achieve the same biological endpoint. The first strategy, known as
hyperthermia, is to expose tumour tissues to mild temperatures (43OC-45OC) for long
1.1. THERMAL THERAPYINCANCER TREATMENT
periods of time (from 30 minutes to several hours). This is usually combined with
radiotherapy or chemotherapy as an adjuvant. In the second strategy, known as high
temperature thermal therapy, the minimum target temperature is approximately
50°C such that tissue coagulation is achieved in seconds to a few minutes. This can
be given as a stand-alone treatment.
Hypert her mia
No ciinical studies have been able to validate the efficacy of hyperthermia as an
independent therapeutic agent. Difficulties in raising the temperature of the entire
tumour volume to the target range using current heating applicator technology have
been reported 1721. Studies on combining hyperthermia with other treatment modalities including
radiotherapy and chemotherapy have produced more favourable results. In vivo and
in vitro studies have demonstrated that hyperthermia is especially effective against
hypoxic cells, which are radioresistant, in the centre of tumours, while radiation
eliminates the cells in the peripheral, well-vascularized regions of the tumours which
are difficult to heat but sensitive to radiation (541. A study of 70 patients with
recurrent melanomas, performed by the European Society of Hyper theniu Oncology,
reported complete response of 62% for patients treated with thermoradiotherapy,
compared to 35% of patients treated by radiotherapy alone 1551. A collaborative
study between Dutch Hyperthennia Group, the Medical Research Council (England),
the Evropean Society ojHyperthennHa Oncology and the Princess Margaret Hospital
(Canada) of patients with advanced primary or recurrent breast cancer reported
complete response in 59% of patients treated with thermoradiot herapy, compared
to 41% for patients treated by radiotherapy alone 1761. In addition, the cytotoxicity
of many chemotherapy drugs are enhanced by moderately elevated temperatures
[27,51].
High Temperature Thermal Therapy
Poor temperature distributions achieved in tumours dunng hypert hermia treatments
are caused by inadequate heat ing technologies, tissue inhomogenei ties, and heat
transfer due to conduction and blood flow [5,37]. Consequently, several groups
1 . l , THERMAL THERAPY IN CANCER TREATMENT
suggested the use of high temperature short exposure thermal treatmeuts. In such
treatments, the high temperatures (> 50°C) attained would rapidly coagulate tu- mour tissues, allowing the tumour response rate to be less dependent on the local
tissue physiology such as blood flow and tissue thermal conduction [2,30]. In the
past 10 years, interest in high temperature thermal therapy has been propelled by
advances in medical imaging that have allowed the near real-t ime monitoring of ther-
mal treatments. Temperature distribut ions and coagulated regions of heated tissues
have been measured non-invasively using Magnetic Resonance Imaging [33,50,64,78]
and ultrasound imaging [l, 621.
Clinical trials to evaluate high temperature thermal therapy are ongoing.
Phase 1/11 trials have been aimed at establishing treatment feasibility and safety
[59,77]. Because of relatively mal1 tissue volumes that can be heated to high
temperatures effectively by currently heating techniques, target sites have been focal
cancers such as liver metastases 167,771, prostate cancer [74,77] and renal tumours
[77]. A considerable portion of work in this field is now focusing on the development
of heating applicators that can treat larger, deep-seated tumour volumes.
1.1.2 Thermal Delivery
There are many ways to heat a tumoiir and the choice of a particular delivery
modality depends on several factors, including the location, shape and size of the
tumour and the proximity of critical normal tissues. Temperature rise in tissue is
induced by the deposition of energy, which can be delivered to the region of the
tumour by using a laser, an ultrasound transducer, a radiofrequency or microwave
applicat or.
Thermal therapy applicators are generally classified as i) external, (applied
from outside the body), ii) intracavitary, (applied from within a body cavity such as the rectum) and iii) interstitial, (embedded directly into the tumour tissue). The
goal of thermal therapy treatments is to coagulate the entire tumour volume while
sparing overlying and surrounding normal tissues. Therefore, the ability of an appli-
cator to deliver energy that will be localised in the target volume and, if necessary,
penetrate deeply into the body is of primary importance. Intracavitary and inter-
stitial applicators are effective in achieving these goals. However, treatment sites
1.1. THERMAL THERAPY IN CANCER TREATMENT 5
accessible to intracavitary applicators are limited. Intentitial applicaton are in-
vasive and are not well suited to heating large irregular tissue volumes. External
heating devices are non-invasive, and have the flexibility to access many more treat-
ment sites than is possible with intracavitary applicators. The three most common
energy sources used in externd heating devices are radiofrequency, microwave and
ultrasound.
Radiofkequency Heating
Radiofrequency [RF] heating involves the use of electromagnetic waves in the range
of 0.1-27MHz. In capacitive RF heating, the tissue volume to be heated is sand-
wiched between two electrodes, forming a circuit element similar to a parallel plate
capacitor. The energy dissipated in the tissue volume is determined by the current
between the two electrodes and the tissue resistivity. Capacitive RF heating is the
only form of thermal therapy in which the energy absorption does not decreiise expo-
nentially with increasing deptb in tissue. However, maximum energy deposition for
capacitive RF heating occurs in tissues with high electrical resistivity, such as fat,
where excess heating can limit power deposition. Inductive RF heating is produced
by using a coil which is either placed near the body of the patient or completely
surrounds the body. The electric field induced in the body by the magnetic flux
from the coil produces an electric current within the tissues, leading to tissue heat-
ing. Maximum energy deposition for inductive heating occurs in tissues with low
resistivity, such as muscle.
The drawback of RF heating is that, because of the long electromagnetic
wavelength in tissue, it is very difficult to localise heating at depth to a specific
target volume. Selective heating of tumour tissue can only rely on the fact that
tumours often have reduced blood flow compared to normal tissues [65].
Microwave Heating
Microwave [MW] applicators produce electromagaetic waves which carry energy
into tissue. Due to international agreements, only the frequencies of 433, 915 and
2450 MHz can be used in thermal therapy treatments in electrically un-shielded facil-
ities. Energy delivered by microwaves is attenuated exponentially in tissue. Hence,
1.1. THERMAL THERAPY IN CANCER TREATMENT 6
increasing heating at depth has to be achieved through surface cooling. Because
of the large values of MW attenuation coefficient at high frequencies, the energy
penetration in tissue is poor. For example, the penetration depthl of a plane MW field is 1.2 cm in muscle tissue a t 915 MHz. Considerable irnprovement in energy
penetration occurs for sources with frequencies lower than 500 MHz. However, be-
cause of the longer wavelengths for frequencies of less than 500 MHz, constraint of
the waves into an applicator of practical size is difficult.
Single MW waveguide radiators have been developed for use in surface heat-
ing. Their power deposition patterns are often uneven and cannot be corrected
for variations in tissue cooling. Recently, special boluses have been developed [63]
employing different concentrations of saline solution, which are capable of both cre-
ating a more uniform power deposition during the treatment and increasing the
penetration depth.
Ultrasound Heating
Ultrasound devices produce mechanical waves in tissue which cause heating. Ultra-
sound applicators for therapeutic use operate in a frequency range from 0.5 MHz
to 5MHz. The energy transported by an ultrasound wave is attenuated exponen-
tially as it propagates through tissue. The greatest advantage of ultrasound heat-
ing over MW and RF heating is that ultrasound beams can be focused, because
the ultrasound wavelengths (0.3-3 mm) a t frequencies in the therapeutic range are
much shorter than the diameter of the applicator. Focused ultrasound waves can be
generated by either a geornetrically focused applicator or an electronically phased
multi-element applicator. Focused ultrasound in particular is well suited to the lo-
calised heating of deep-seated tumours. However, typical single-focus ultrasound
applicators produce a beam only a few millimetres wide at the focus, and therefore
can only heat small volumes.
Because of large changes in acoustic impedance, ultrasound is strongly re-
flected a t tissue-bone and tissue-gas interfaces. These reflections can cause intense
heating at tissues immediately ahead of these interfaces and prevent heating be-
'Penetration depth refers to the depth at which the intensity reduces to 50% of the surface value.
1.2. HIGH INTENSITY FOCUSED ULTRASOUND THERIMAL THERAPY 7
yond the interfaces. Hence, external ultrasound heating is only useful for regions
with "acoustic windows", i. e. regions in the body where ultrasound is not blocked
by bone or gas.
1.2 High Intensity Focused Ultrasound Thermal
Therapy
The schernatic in figure 1.2 illustrates the principle of external High Intensity Fo-
cused Ultrasound [HIFU] thermal therapy. Water is used between the transducer
1 Waier Tank 1
Figure 1.2: Schematic representation of using high intensity focused ultrasound to treat tissue.
and the body for efficient coupling of ultrasound into the body. Ultrasound pen-
etrates intervening tissues focusing on the target. Thus, sufficient heat can be
generated in the focal zone in a short period of time, while the intervening tissues
are spared.
1.2.1 Clinical Experience
HIFU heating for cancer treatment was first proposed by Burvo [6], who had in-
vestigated the effect of HIFU on Brown-Pierce tumours in rabbits and reported a
cure rate of 60%-80%. Since the 19606, many studies have been devoted to HIFU thermal therapy. Complete tumour destruction was noted in the range in 744%
of animal tumours treated with HIFU [82]. The lack of tumour response in some
animals may be attributed to the HIFU beam missing a portion of the tumour be-
1 .P. HIGH INTENSITY FOCUSED ULTRASOUAD THERMAL THERAPY 8
cause of animal movement, under-assessrnent of tumour size, insufficient coverage
of surroundiiig tissue or blood flow cooling.
Clinical trials of HIFU thermal therapy have produced encouraging results.
Katsumi [36] and Tsuchidate [69] reported a clinical study of 35 patients. Different
types of advanced tumours were treated. Malignant tissue was destroyed, tumours
decreased in size and there was no increase in metastasis. A phase 1 study conducted
by Vallancien et al. [73] reported that 11 patients with superficial bladder tumours of
4-20 mm diameter were treated. No specific side-effects were encountered, although
al1 patients developed transient haematuria Iasting 1-2 days. In an update on this
series, 50% of (87) patients treated by HIFU remained tumour-free, similar to that of
patients treated with conventional surgery. A more recent phase 1 trial, conducted
by ter Haar and CO-worken (771, demonstrated that HIFU treatment of tumours
of the liver, kidriey and prostate could be performed in fully conscious patients.
Regions of tumours situated up to 12cm below the skin surface were heated, while
al1 normal tissue lying in the beam path was spared.
No phase II or phase III trials have been conducted, probably because of
inadequate HIFU applicator technology for treatment of the entire tumour volume.
In the phase 1 study conducted by Vallancian et al. [73], it was found that a mean of
395 heating exposures was required to treat a target volume with a mean diarneter
of 1.4 cm, resulting in relatively long treatment times of 45 min to 68 min. The
phase 1 trial conducted by Visioli et al. [77] also reported similar problems. The
treatment of a 1.3cm3 turnour volume lasted for approximately 35min. Because
of the impractically long treatrnent time, complete tumour coagulation was not
performed.
HiFU, as a non-invasive technique, is suited to many oncological and uro-
logical applications. Prostatic carcinoma, bladder carcinoma, renal carcinoma, Iiver
metastasis and benign prostatic hyperplasia are suitable targets due to good trans-
abdominal access. Several of the above clinical studies, however, reported long
treatment times for the entire tumour volume using current HIFU applicator tech-
nology. This establishes the need for investigation into HIFU applicator designs to
reduce treatment times.
1.2. HIGH INTENSITY FOCUSED ULTRASOUMI THERMAL THERAPY 9
1.2.2 Focused Ultrasound Transducer Designs
Ultrasound transducers employ piezoelectric materials, whose dimensions change
in the presence of an electric field. When an oscillating electric voltage is applied
across a piezoelectric transducer, the material expands and contracts. Electric en-
ergy is converted into mechanical energy which rnanifests itself as a traveling ultra-
sound wave. To ensure al1 mechanical energy is emitted via the front surface of the
transducer, the acoustical impedance mismatching between the transducer and the
backing should be maximized. Air backing has proven to be almost ideal for the
high intensity therapy applications. Figure 1.3 illustrates a schematic of a thera-
peutic ultrasound applicator. Early therapy transducers employed cross-cut quartz
Figure 1.3: Schematic representation of the therapeutic ultrasound applicator.
crystals. Most therapy transducers a t present adopt piezoelectric ceramics such as PZT4 made of lead zirconate titanate. The advantages of ceramics over quartz are
the low cost and the possibility to manufacture transducers in many shapes. How- ever, mechanical and electrical losses are greater in ceramics. Also, the properties of
ceramics change with temperature and age. In contrast, quartz crystals are stable
at high power output and during prolonged use.
Focused ultrasound applicators have been constructed using many different
designs, the most common which is the focused spherical transducer. More complex
applicator designs include phased arrays and acoustic lens/transducer combinations.
1.2. HIGH INTENSITY FOCUSED ULTRASOUND THERMAL TIIERAPY 10
Highly Focused Spherical lkansducer Design
The cornmonest way to produce a focused ultrasound field is to form a transducer
into a spherically-shaped radiator or to couple a spherically-shaped acoustic lens
with a planar transducer, as shown in figure 1.4. The major advantages of these
Figure 1.4: (a) Focused spherical transducer. (b) Planoconcave acoustic lens combined with a planar transducer. Because the speed of sound in most acoustic lens materials is greater than the speed of sound in water, focusing acoustic lenses are concave in shape.
two configurations, both referred to here as spherical transducer designs, are t heir
simplicity and low cost. However, spherical transducers can only produce single
focus ultrasound fields. The focal zone dimension of a spherical transducer is deter-
mined by physical parameters of the transducer [31], including the diameter, radius
of curvature and operat ing frequency (equation 1.2).
R c GdB beamwidth î! 1.41-9
of where
6dB beamwidth = full width at 25% of intensity maximum in the focal plane
of the transducer [cm]
R = radius of curvature [cm]
D = diameter or aperture [cm]
c = speed of sound [cm d] f = operating frequency [MHz]
1.2. HIGH INTENSITY FOCUSED ULTRASOUND THERMAL THERAPY 11
The focused spherical ultrasound transducers employed in thermal therapy
usually have an aperture being larger than 5cm so that sufficient acoustic power
deposition as well as sufficient focusing can be achieved a t depths in the body. If
such a focused spherical transducer has a 6dB beamwidth of less than 2mm or
a 6dB beamlength2 of less than 10 mm, it is categorized here as a highly focused
transducer. Because of their small focal zones, highly focused spherical transducers
have been widely used in neurosurgical and opthalmological HIFU treatments, where
the treatment goal is to destroy small, precisely located tissue volumes. A study of
the use of HIFU in neurosurgery conducted by Lele 1461 demonstrated that a highly
focused spherical t ransducer successfull y generated "t rackless" thermal lesions at
preselected regions in cat brain. The diameter and length of these thermal lesions
were only 0.1 mm and 1 mm respectively.
When highly focused spherical transducers were applied to thermal treat-
ments of large target volumes, these transducers proved to be problematic. A study
of HIFU thermal treatment of rat liver tissue reported that 1000 exposures were re-
quired for a highly focused transducer to destroy a tissue volume of 1 x 1 x l cm3 [81].
Each of these exposures lasted for 4s followed by a 10s off-time to cool the inter-
vening tissue, resulting in a total treatment time of 4 hours. A theoretical study
conducted by Fan and Hynynen 1241 reported the same problem (10 houn for a
treatment of a 3 x 3 x 3 cm3 tissue volume).
The size of thermal lesions can be controlled by varying the exposure duration
or intensity in a certain range. Increasing exposure duration allows lesion broadening
through thermal conduction. However, these exposures should still be sufficiently
brief to avoid blood flow cooling effects, which can become significant after tens
of seconds. Since perfusion in tissue is difficult to measure accurately and can
be altered by temperature increase during heating, blood flow cooling introduces
uncertainties into the dimension of thermal lesions [39].
Increasing the ultrasound exposure intensity can also lead to enlargement of
thermal lesions. However, exposure intensity should be lower than a certain thresh-
old to avoid non-linear ultrasound beam propagation, which can lead to uncontrolled
mechanical tissue destruction (321. Moreover, in order to precisely control the for-
*6dB beamlength refers to the fuil length (dong the applicator axis) at 25% of intensity maxi- mum of the transducer focal zone.
1.2. H M INTENSITY FOCUSED ULTRASOUND THERMAL THERAPY 12
mation of thermal lesions, tissue temperatures close to lOO0C should be avoided
because cavitation and the formation of vapor in tissue distort the deposition pat-
tern of ultrasound energy and modify tissue acoustic properties, making the control
of Iesion format ion difficul t (321.
Moderately Focused Spherical Transducer Design
Compared to highly focused spherical transducers, moderately focused spherical
transducers have a larger f-number or a lower operating frequency. Due to the weak
focusing, energy is less localised in the field of moderately focused transducers. If a
spherical transducer has a beamwidth geater than 2 mm and a beamlength geater
than 10 mm, it is categorized here as a moderately focused transducer.
Among al1 the reported HIFU heating systems, only the one developed by ter
Haar and CO-workers employs a moderately focused spherical transducer [77]. In an
investigation into the feasibility of HIFU treatments of kidney in pig, this moder-
ately focused spherical transducer was used to generate thermal Iesions of 2.5 mm
in diameter and 17mm in length. Applying this heating system to a phase 1 clin-
ical study, Visioli et al. [77] reported encouraging results in that the treatment of
a 1.3 cm3 volume of tumour tissue in kidney required approximately 30-35 thermal
exposures, each of which lasted for 1 s followed by a 1 min cooling period. The total
treatment time was therefore approximately 30-35 min. This result appears to be a
significant improvement on the treatment time required with highly focused spher-
ical transducers. However, the conclusion should be drawn with caution as many
treatment parameters, including the shape and location of the target volume and
the criterion for determining cooling periods are different between these treatments
and those using highly focused spherical transducers. To allow a useful cornparison
and to quantitatively evaluate the improvement of the use of moderately focused
spherical transducers, a study is needed to estimate treatment times required for
highly and moderately focused spherical transducers to treat an identical target un-
der identical treatment conditions. This question forms the fint part of this thesis.
1.2. HIGH INTENSiTY FOCUSED ULTRASOUND THERMAL THERAPY 13
Other Single-focus lkansducer Design
In addition to the focused spberical transducer designs, other transducer designs
can produce single focus ultrasound fields. Fry [25] described the use of four plane
transducers, each with a planoconcave spherical lens. The four focused beams were
brought to a coincident focus and were individually phased to maximize the intensity
output at the focal spot. This niulti-transducer single focus design was also adopted
in the HIFU heating system build by Vallancian et al. [73]. Because of the small focal
zones, these two heating systems can be categorized as highly focused transducer
designs. Fky [25] applied their HIFU heating system to the treatment of Parkinson's
disease. Following craniotomy, which was necessary due to the problem of ultrasound
transmission through the skull, the target tissues were exposed to HIFU. Syrnptorns
of Parkinsonism were claimed to be eliminated. Vallancian et al. [73] applied their
heating system to the treatment of benign prostatic hypertrophy and superficial
bladder tumours, the results of which were discussed in section 1.2.1.
Fry [25] also reported the use of a reflector transducer design, as shown in
figure 1.5, in HIFU neurosurgical treatments. This applicator design is equivalent
to a conical transducer design. Because the focal zone is small, this design is also
categorized as the highly focused transducer design. The major drawback of the
reflector design is its large aperture, which limits its use in clinical applications due
the size of acoustic "windows" available in the body surface.
Figure 1.5: Schematic of the reflector focusing applicator used by Fky [25].
1.2. HIGH INTENSITY FOCUSED ULTRASOUND THERMAL THERAPY 14
Phased Array Design
Since the size of individual thermal lesions generated by single-focus transducers is
small compared to the size of tumours, several groups have suggested the use of
multi-focus transducer designs that would produce large thermal lesions [19,23,45].
The simplest way to produce a multi-focus ultrasound field is to place several single-
focus transducers adjacent to each other. Since the size of the applicator aperture is
limited by the size of available acoustic "windows" at the body surface, individual
transducen must have a small aperture. However, the small aperture reduces the
transducer focusing, which may lead to damage to the surrounding tissue during the
treat ment.
A phased array applicator uses many small transducer elements to create indi-
vidual foci. These small transducer elements are individually electronically phased
such that waves generated by the elenients interfere constructively at the focus.
Since the transducer elements that contribute to the constructive interference are
distributed over the entire aperture, sufficient focusing can be achieved.
Phased array applicators were introduced to the field of ultrasound thermal
therapy in the early 1980s. Several different designs have been proposed and inves-
tigated including annular or concentric-ring arrays [li', 521, sec tor-vortex arrays (711,
spherically sectioned phased 1-D arrays [47,48], cylindrically and spherically sec-
tioned phased 2-D arrays [14,19,23]. Annular phased arrays, consisting of CO-planar
concentric ring elements, generate annular foci. Annular foci can be used to heat
the periphery of the tumour, where the cooling is expected to be highest, with the
interior of the field being heated over time by conduction. A major drawback of
annular arrays is that unwanted, intense secondary foci can be produced on axis be-
yond the annular focus [35]. These secondary foci can damage normal tissues during
treatment. The second drawback of annular array is that if strong localised cooling
occurs inside the annulus, for example near a large blood vessel, the interior region
may not reach a therapeutic temperature [35]. A modified annular array design, i.e.
sector-vortex array design [71], and other array designs have been proposed to elim-
inate these drawbacks. The sector-vortex phased array is geometrically focused and
consists of concentric rings, each of which further consists of sector elements. Like
annular arrays, the sector-vortex phased array also produces annular foci. However,
1.2. HIGH INTENSITY FOCUSED ULTRASOUND THERMAL T K E W Y 15
secondary foci on the axis are eliminated by controlling the phases of individual
sector elements,
Phased 2-D arrays, consisting of a 2-D grid of square shaped elements, can
produce multiple focus fields of various shapes and sizes, allowing greater flexibility
to control thermal lesion formation than sector-vortex arrays. Another advantage of
2-D arrays is that the foci of these arrays can be scanned electronically, eliminating
the need for mechanically moving the applicator. The general drawback of phased
2-D array designs is they require a large aperture and small element spacing to
produce good focusing without the production of gating lobes [70]. This results in
a large number of array elements, and consequently great cost and complexity. The
use of geometrically focused 2-D arrays, such as cylindrically or spherically sectioned
arrays. reduces the requirement for small element spacing. However, larger array
elements then limit the range over which foci may be created to the vicinity of the
geometric focus of the array. Due to the complexity and cost, the most sophisticated
phased 2-D array built for thermal therapy applications is a 256 element spherically
sectioned array [14]. Although this array offered much better focusing than its
predecessor, it still suffered from significant secondary foci when phased to generate
cornplex focus patterns (the number of foci was more than 8). When synthesizing 9
focus or 16 focus fields to heat large tissue volumes, this 256 element phased array
had to switch ternporally betwcen a series of multiple focus patterns each with
<8 foci, appearing a t various positions. Thermal lesion volumes of approximately - 5.4 cm3 were successfully produced in pig muscle tissue by using this 256 element
phased array in a single exposure.
Multi-focus Acoustic Lens/'liansducer Combination Design
Due to the great cost and complexity of phased 2-D array applicators, multi-focus
acoustic lens/transducer combinations [LTC] have been developed to mimic their
focusing ability for mild heating ultrasound applications 1451. Figure 1.6 shows a
schematic of an LTC. Unlike the smooth surfaces of single focus converging lenses,
surfaces of the multiple focus lenses are machined into a 2-D grid of small elements
of different thicknesses. The differences in thickness between lens elements results in
phase shifts, similar to those introduced electronically in the case of phased arrays.
1.2. HIGH INTENSITY FOCUSED ULTRASOUND THERMAL THERAPY 16
rA S a t h A-A
Figure 1.6: Schematic of the 2-D acoustic lens.
The primary advantage of LTCs over phased arrays is that LTCs consisting of
a large number of small elements are simple to build and inexpensive. The greater
number of elements rnay allow more comylex multiple focus patterns. For example,
LTCs of 2000 elements have been constructed, which were ahln to produce cornplex
focus patterns such as a 2 plane 18 focus field (451. Although LTCs are less flexible
than phased arrays in that an LTC can only produce a single multi-focus pattern,
many different lenses may be coupled to a single transducer, and lenses may be
designed for individual patients.
Whereas elements of a phased 2-D array can generate waves of both different
amplitudes and phases, elements of an LTC produce waves of identical amplitude,
because the LTC elements are activated by a single ultrasound source. The lack of amplitude modulation in the case of LTCs may result in some degradation of
the focus pattern relative to that created by a phased array using both modulated
amplitude and phase. However, a theoretical study, by Lalonde et al. [45], com-
paring focal plane intensity distributions of the 8 focus fields generated by a 2000
element phased array using only phase modulation or using both phase and ampli-
tude modulation reported only srnaIl differences. There was up to 10% reduction on
intensity gain3 at the foci in the case of "phase only modulation" compared to phase
and amplitude modulation. This difference was found to have only a small effect
on the simulated as well as measured temperature distributions in hypertherrnia
treatments [45].
31ntensity gain at foci is defined as the ratio of the sum of intensities at al1 focus points to the sum of intensities at the applicator surface.
1.3. OBJECTIVE 17
To date, LTCs have only been investigated for mild heating ultrasound treat-
ments [44,45]. The ability of LTCs to mimic the focusing of phased arrays and
generate large thermal lesions for high temperature thermal t herapy applications
has not yet been explored. The effect of "phase only modulation" of LTCs on the
shape and size of high temperature thermal lesions remains to be investigated. These
questions form the second part of this thesis.
1.3 Objective
HIFU thermal therapy is a promising treatment modality for oncology applications.
However , thermal lesions produced by highly focused transducers are too small to
treat the entire tumour volume in a clinically practical t h e period. The use of
moderately focused spherical transducers may be able to rediice the treatment time.
The first objective of this study is to theoretically evaluate the difference between
the total times required by a highly and a moderately focused spherical transducer
to treat the same target under identical treatment conditions.
LTCs can mimic phased 2-D arrays to produce multi-focus fields, but with
substantially lower cost and complexity. Multi-focus fields allow the production of
large thermal lesions. It has been demonstrated that the use of ptiased 2-D arrays
can reduce the treatment times for large tissue vdumes compared to the use of
highly focused spherical transducers. However, LTCs have only been investigated
for mild heating applications. The second objective of this study is to demonstrate
theoretically that an LTC requires significantly shorter time for the treatment of a
large tissue volume than either a highly or a moderately focused spherical transducer.
1.4 Thesis Outline
In Chapter 2, a 3-D ultrasound-thermal model is developed for the calculation of
thermal dose distributions in tissue caused by ultrasound heating. The accuracy of
the model is verified by comparing the results with published experimental thermal
lesion data. A theoretical tumour model is developed which provides a standard
target to compare different transducer designs under identical treatment conditions.
1.4. THESIS OUTLINE 18
Thermal dose profiles generated by a highly and a moderately focused spherical
transducer and total times required for them to treat the turnour are compared.
The moderately focused transducer is constrained to have the same aperture and
frequency as the highly focused transducer, while the focal length of this transducer
is selected such that the number of lesions required to ''filln the tumour is a minimum.
In Chapter 3, a design method of LTCs to produce multi-focus fields is de-
veloped. The method then is used to design LTCs in order to examine the effects
of LTC focus spacing and number of foci on the shape and size of thermal lesion.
The effect of "phase only modulation" of LTCs on the shape and size of thermal
lesions is also exarnined. Thermal dose profiles generated by an LTC design and the
time required for it to treat a 2 x 2 x 2 cm3 tumour are determined and compared
to those for the highly and moderately focused spherical transducers investigated
in Chapter 2. The ultrasound-thermal model and the tumour rnodei developed in
Chapter 2 are also adopted in this study.
In the final chapter, the results of the thesis are summarized and future work
is outlined. Future direct ions in ultrasound-t hermal modeling include extending
the ultrasound-thermal model to layered tissue geometries, taking into account the
change in tissue properties with temperature and time and incorporating the effect
of large blood vessels. Future directions in development of 2-D LTC designs include
validating beam profiles and thermal lesion predictions and investigating the effect
of layered tissue geornetries on complex focus patterns of LTCs. Furthermore, pre-
liminary work on rotating LTCs during heating to irnprove the shape of thermal
lesions for tumour treatmeots is presented.
Chapter 2
Theoret ical Evaluat ion of
Moderately Focused Spherical
Transducers for High Intensity
Focused Ultrasound Thermal Therapy
Abstract
High intensity focused ultrasound thermal therapy can be used to destroy deep
seated tumours non-invasively. Due to the strong focusing and simplicity, highly
focused spherical transducers have been widely adopted for HIFU applications.
However, highly focused spherical transducers are not optimal because the ther-
mal lesions they generate are very small, leading to impractically long treatment
times. Moderately focused spherical transducen can produce larger thermal lesions
compared to highly focused transducers. However, due to the weak focusing, more
heat may be deposited in surrounding normal tissues. Although some encouraging
results have been reported, it is difficult to quantitatively evaluate the ability of mod-
erately focused spherical transducer to reduce the treatment times for large tissue
volumes. A theoretical study of comparing treatment times required for highly and
2.2. INTRODUCTION
moderately focused spherical transducers to treat the same target under identical
treatmeut conditions is presented here. A 3-D ultrasound thermal model was de-
veloped to calculate thermal dose profiles generated by ultrasound applicators. The
accuracy of the model was verified by comparing the results to published in vivo
thermal lesion data. A tumour model was constructed with a 2 x 2 x 2cm3 tumour
volume located 5cm below the body surface. The treatment goal was to deliver
to the entire tumour volume a thermal dose higher than 240 EM& while sparing
the surrounding tissue by limiting the thermal dose level to less than 60EM43 in
regions more than 5 mm beyond the tumour edge. The highly and moderately fo-
cused spherical transducers studied here had an identical aperture and operating
frequency. The focal length of the moderately focused spherical transducer was cho-
sen so that the number of thermal lesions required for this transducer to treat the
tumour was minimized. It was demonstrated thet the moderately focused spherical
transducer required a total time of 40 min to treat the 2 x 2 x 2 cm3 tumour, while
the highly focused spherical transducer required 150 min. However, it was also found
that the moderately focused transducer produced more sub-lethal thermal dose in
the intervening tissue regions. For example, the 30EM13 thermal dose contour ex-
tended to approximately 1.5cm in front of the target, compared to lcm in the case
of the highly focused spherical transducer.
2.2 Introduction
High intensity focused ultrasound [HIFU] thermal therapy involves raising the tem-
perature of a pre-selected tissue volume to between 50°C and 90°C. The high tem-
perature causes rapid coagulation of the target tissue. Moreover, large thermal
gradients in the target region are desired so that the surrounding normal tissue is
spared. l k a t ment pro tocols adop t ing highly focused transducers' were successful
in achieving this goal. However, such protocols were problematic for the treatment
of large tissue volumes. Due to the small thermal lesion volume produced for each
individual exposure, a large number of ultrasound exposures was required for the
complete destruction of the target volume [81]. Moreover, when the t ransducer was
'See the definition in section 1.2.2.
moved to deliver the exposures, some normal tissue in the nearfield remaineci in the
overlapping beam pathways, as illustrated in figure 2.1. Although the temperature
rise in the nearfield after a single exposure was low compared to that in the focal
region, continua1 exposures of the same tissue region in the nearfield could result
in a large temperature rise and significant thermal damage [34]. Damianou and
Hynynen [IO] have demonstrated that a cooling period must be employed between
exposures to allow tissues in the nearfield to cool. Consequently, the treatment time
for large tissue volumes were impractically long 1231. For example, a study of HIFU
Figure 2.1: During the transducer movement from left to right to form lesions side by side, some normal tissues in the nearfield remain in the pathway of the beam.
thermal treatment by Yang et al. [81] found that 4 hours were required for a highly
focused transducer to destroy an 1 cm3 tissue volume in rabbit liver.
One approach to reducing the treatment time is to enlarge individual thermal
lesions so that their number can be reduced. This can be achieved by increasing
exposure duration and/or exposure intensity. However, blood Bow cooling effects as-
sociated with long exposures and non-linear ultrasound beam propagation associated
with high intensities may make the control of lesion formation difficult. Enlarging
thermal lesions can also be achieved by employing a transducer with a larger focal
zone such as the moderately focused spherical transducer*. However, the large fo-
cal zone associated with the weak focusing results in more heat being delivered to
tissues surrounding the target. Due to this safety issue, only one system arnong al1
the reported HIFU heating systems has employed a moderately focused spherical
transducer [77]. Applying this heating system to a phase 1 clinical study, Visioli
2See the definition in section 1.2.2.
2.2. INTRODUCTION 22
et al. [77] reported encouraging results that the treatment of a 1.3cm3 volume of
tumour tissue in kidney required approximately 30-35 min. This result appean to
be a significant improvement on the treatment times required with highly focused
spherical transducers. However, the conclusion should be drawn with caution as
many t reat ment parameten, including the shape and location of the target volume
and the criterion for determining cooling periods, are different between the exper-
imental studies using the highly focused transducer designs and those using the
moderately focused spherical transducer designs.
A second approach to increasing the volume of individual thermal lesions is
through the use of a phased array. Fan and Hynynen [23] have developed phased
2-D array ultrasound applicators to generate large thermal lesions, where the focal
zone volume was significantly enlarged compared to those of single-focus ultrasound
applicators. Daum et al. [14] reported that an approximately 3 cm3 volume of tissue
could be thermally destroyed in a single 20s exposure by a 256 element phased 2-D array using a 16 focus field. Compared to phased array designs, moderately fo-
cused spherical transducen are simple to construct, inexpensive and commercially
available. In addition, unlike the 256 element phased array which required long
exposures (20s) to ensure that tissue volumes were completely destroyed by multi-
ple foci, moderately focused spherical transducers, which generate single foci, can
adopt short exposures, making lesion formation less dependent on blood flow cooling
effects.
To quantitatively evaluate the use of moderately focused spherical transduc-
ers, a theoretical study is presented here to compare treatment times required for
a highly and a moderately focused spherical transducer to treat a 2 x 2 x 2cm3
turnour volume under identical treatment conditions. An ultrasound-thermal mode1
was developed and used to predict treatment times. Thermal dose profiles generated
by these two transducers were also compared to examine the effect of transducer
focusing on thermal damage produced in the surrounding tissues.
2.3. METHODS
2.3 Methods
2.3.1 Ultrasound-Thermal Mode1
A three dimensional mathematical model was developed to predict ultrasound in-
duced thermal damage in tissues. The model consists of three parts (see figure 2.2).
Figure 2.2: Block diagram of numerical model to simulate ultrasound-thermal effects in tissue
Ultrasound Intensity Distributions
The first modeling step was to calculate the ultrasound intensity distribution gen-
erated by a transducer in a non-attenuating medium. The transducer surface was assumed to be composed of an array of small element sources of ultrasound energy.
The contributions €rom these sources to the intensity a t each point in the field were
superimposed, according to the Rayleigh-Sommerfeld integral [53].
= intensity at the field point (x,y,z) [W cm-*]
= particle velocity amplitude a t the transducer surface [cm s-'1
= wave number [cm-']
= speed of sound in the medium [cm s-'1
= density of the medium [g - cmw3]
= distance [cm] between the source element (xo,yo,xo) and the field point
= surface area of the source element [cm2]
2.3. METHODS
Heat transfer in tissue
The temperature rise in tissue due to ultrasound exposures was predicted by the
Bioheat 'Pransfer Equation [BHTE] [57]
Wh Y, 2, t ) ~ t c t + wbca(T(x, y,z, t ) - Ta) = k V* T(x, Y, 2, t ) + SAR(x, y, z ) (2.2) dt
where
T
Pt
ct
Wb
Cb
T a k
SAR
= temperature [OC] at the field point (x,y,z) at time t [s]
= density of tissue [g -cm-3]
= heat capacity of tissue [J g-' C-'1
= volumetric perfusion rate [g -s-' - cm-3]
= heat capacity of arterial blood [J m g - ' e o C-'1 = temperature of arterial blood [OC]
= thermal conductivity of tissue [W -cni-' 0" Cs'] = Specific Absorption Rate [W - cm-3], which is the amount of
power absorbed by tissue per unit volume
In this equation, it was assumed that heat transfer between blood vessels and tis-
sues occurred rnainly across the rnicrovasculature. The blood in the capillary bed
would instantly thermally equilibrate to the temperature of the surrounding tissues.
Heat transfer by large vessels which create significant temperature gradients in their
vicinity was not taken into account in this model.
The SAR was celculated using equation 2.3. To sirnplify the calculations,
it was assumed that the attenuated energy can be calculated by integating the
attenuation coefficient over the axial distance traversed.
where
P = amplitude attenuation coefficient [Np **cm-' -.MHz-', 1NP x 8.686 = ldB]
s = axial distance [cm] between the skin surface and the field
point a = amplitude absorption coefficient [Np - cm-' - MHZ-'1
A finite difference algorithm was used to solve the BHTE in Cartesian coordi-
nates [41]. The temperature change was calculated at every node in a computation
domain, the size of which will be specified in section 2.3.2. Temperatures at the
boundaries of this computation domain were set to be constant at 37°C. The initial
temperature at each node was assurned to be 37°C. To simplify the calculations, al1
tissues wit hin the computation domain were assumed to possess identical acoustic
and thermal properties which remained constant during heating.
Thermal damage in tissue
Thermal dose to the tissue was quantified using the following equation [61].
where
TD
ttatd
t
= thermal dose [EMIS ] = total treatment time [s]
= time [SI
This formula has been verified for temperatures up to 57°C [3] and bas been suc-
cessfully used in predicting thermal lesion size in vivo [12].
In order to evaluate different transducer geometries in terms of treatment time under
identical treatment conditions, a tumour mode1 was developed which included the
tumour geometry, tissue properties, thermal dose targets for the tumour and thermal
dose limits for the protection of the normal tissue.
liimour Geometry
The tumour geometry employed in this work is illustrated in figure 2.3. The tumour
Figure 2.3: Tumour geometry employed in this work.
selected was in the shape of a cube (2 x 2 x 2cm3), with its centre located 5cm
below the skin surface. A cube shaped target was useful as a first approach in
this theoretical investigation because the volume can be easily filled by any array
of individual, identical lesions, as illustrated in figure 2.3. Given this tumour size,
the size of the thermal computation domain was chosen to be 4 x 4 x 9cm3, to
achieve reasonable computation times (figure 2.4). The mesh spacings dx, dy and
Figure 2.4: Thermal computation domain and mesh spacing dx, dy and dz.
dz were chosen to be 0.5, 0.5 and 1 mm (figure 2.4). The time step was chosen to be
O. 1 S. These were the smallest achievable values given a pract ical computation time.
Al1 the computations were performed on Sun Enterprise 450 Server (400 MHz Ultra
SPARC-IICPU), and they were usually completed in from 36 hours to 1 week.
Tissue Properties
The values of acoustic and thermal properties of human muscle tissue were used in
this study (table 2.1). Muscle tissue has a lower perfusion rate than most other tis-
Ampl. atten. coeff. [Np cm-' * MHz-'] Ampl. absor. coeff. [Np cm-' MHZ-'1 Speed of sound [cm s-'1 Tissue density [g Blood density [g cm-=] Tissue heat capacity [J - g-' -O C-'1 Blood heat capacity [J g-' C-'1 Tissue conductivity [W cm-' a' C-'1 Perfusion rate [g - sdl cm-3]
Table 2.1: The acoustic and thermal parameters used in this study. These values are taken from Duck [Ml. ' The value of the absorption coefficient is chosen to be the same as that of the attenuation coefficient, in order to simplib the model.
sues, and therefore represents a "worst case" scenario because the nearfield heating
would be large.
Thermal Dose Thresholds
A thermal lesion was defined as the volume bounded by the 240 EM43 thermal dose
isosurface. The thermal dose of 240 EMd3 was selected because it lead to complete
necrosis in a variety of tissues [15]. The cooling time was chosen such that the
60 Endd3 thermal dose contour just extended t o 5 mm beyond the tumour boundary
(figure 2.5). Therefore, the normal tissue 5 mm beyond the tumour boundary would
receive a thermal dose of less than 60 EM4. This was to spare the normal tissue. The
value of 60 EM43 was selected because a thermal dose of less than 60 EM43 would not
result in severe damage in most critical tissues and organs (151. The 5 mm normal
tissue zone (figure 2.5) allowed the 240 EM43 thermal dose isosurface to completely
encompass the tumour volume by sacrificing some normal tissue directly adjacent
to the tumour boundary.
Figure 2.5: Thermal doses to d l of the tumour tissue were intended ta be higher than 240EW3 and thermal doses to ail of the n o r d tissue 5 mm beyond the turnour boundary were intended to be lower than 60 EIbbJ.
Cooling periods were determined iteratively by simulating entire multi-exposure
treatments using the ultrasound-thermal model. After each simulation, the calcu-
lated 60 EMd3 thermal dose contour, based on an initially selected cooling time, was
compared with the specified 5mm limit. The cooling time was then adjusted and
the simulation repeated as required until the thermal dose limits shown in figure 2.5
were achieved. The cooling time in the first iteration was chosen such that tissues
everywhere could cool to 43OC before the next exposure was delivered.
2.4 Results
2.4.1 Verification of Ultrasound-Thermal Mode1 Accuracy
The accuracy of the mathematical model was determined by comparing predicted
transducer 6dB beamlengths3, beamwidthsJ and thermal lesion dimensions with
publis hed experimental data.
3See the definition in section 1.2.2. 4See the definition in section 1.2.2.
Applicator used by
Focal length (cm) Diameter (cm) Operating frequency (MHz) 6dB beamlength
Table 2.2: Measured and predicted 6dB beamlength and beamwidth of the applicators used by Sanghvi et al. [59], Chen et al. [7) and Watkin et al. [79]. The %difference between the measured and predicted values was caiculated as P " d i ~ ~ ~ ~ ~ ~ U r e ~ .
Sanghvi et al. i591 7.5 5.5
measured (mm) :predicted (mm) (% difference) 6dB beamwidth measured (mm) : predicted (mm) (% difference)
Verifying Intensity Distribution Predictions
4 7:6.6
Intensity distribution calculations for transducers in a non-attenuating medium were
Watkin et al. [791 15 10
(-5%)
0.65:0.75 (15%)
verified by comparing predicted beamlengths and beamwidths to the published ex-
Chen et al. 171 14 10
1.68 19:18.5
perimental data of three applicators (table 2.2). Two of these applicators, used
1.7 18:16.2
(-2%)
1.7:l.g (12%)
by Sanghvi et al. [59] and Watkin et al. [79], consisted of single spherical shaped
(-10%)
1.6:1.8 (12.5%)
transducers. The third applicator, used by Chen et al. [7], was a combination of
a planar transducer and a converging lens. The results indicate that the theoreti-
cal model overestimated the 6dB beamwidth for all three transducers. The largest
difference (15%) occurred for the highly focused transducer of Sanghvi et al. [59].
The difference reduced to 12% for the moderately focused transducer of Watkin
et al. (791. The model underestimated the 6dB beamlength by 5% for the highly fo-
cused transducer of Sanghvi et al. [59] and 2% for the moderately focused transducer
of Watkin et al. [79]. The large difference of 10% between the measured and pre-
dicted -6dB beamlengths for the lens/transducer combination was probably caused
by the spherical aberration of the lens.
2.4. RESULTS 30
Verifying Thermal Dose Predictions
Thermal dose calculations were tested by comparing the predicted lesion size with
experimentally measured data [7]. Cases with and without blood flow were tested.
In Chen et al. [7], thermal lesions were consistently formed 2 mm below the surface
of rat liver using the focused spherical applicator described above. During these
experiments, the rat liver was exposed so that the liver could be accessed directly
with the ultrasound beam without passing through intervening tissue layers. In the
theoretical predictions, tissue acoustic and thermal properties were chosen to match
the experimental conditions (table 2.3). The volume bounded by the thermal dose
isosurface of 30 EMd3 (as opposed to the 240 EMd3 used in subsequent investigations)
was defined here as the thermal lesion volume. The thermal dose of 30EMd3 was
found to induce heptocyte loss and fibrosis in dog liver t i s s ~ e [15].
Ampl. atten. coeff. [Np cm-' +
Ampl. absor. coeff. [Np cm-' MHz-'] Speed of sound [cm s-'1 Tissue density [g cm-3] Blood density [g cm-3] Tissue heat capacity[J g-1 -O C-'1 Blood heat capacity [J g-' e 0 C-'1 Tissue conductivity [W cm-' 6" C-'1 Perfusion rate [g s-' cm-3]
Table 2.3: Tissue acoustic and thermal properties used in prediction of lesion size in rat liver [18].
Figure 2.6 compares the measured and predicted lesion diameters. The the-
oretical values of lesion diameter were measured from the calculated thermal dose
profiles, as illustrated in figure 2.7.
In most cases, the predicted thermal lesion dimensions fell within the ex-
perimentai error range, and agreement was better for the non-perfused cases. For
the perfused cases, the mode1 overestimated Iesion diameters by approximately 12%
for short exposures of 3s and 6s and underestimated lesion diameters by 10% for
the long exposure of 20 S. A possible explanation of the overestimation for 3 s and
6 s exposure cases was that the perfusion rate used in the theoretical predictions
5 -
I 2 4 6 8 10 12 14 16 10 20 22
pulse durath: second
Figure 2.6: Cornparison of meavured lesion diameters [Cl with the results predicted by oiir theo- retical model.
Figure 2.7: Thermal dose distributions calculated using our t heoretical model. Treatment param- eters, tissue acoustic and thermal properties were chosen to match the experimentd conditions (table 2.3). The non-perfused, 12 s heating exposure case was shown here.
was lower than that in the experimental situation. For the case of 20s exposure,
micro-vasculature collapse is expected to occur during heating [go], which would
have reduced the perfusion cooling effect and allowed for a larger lesion volume. In
our model, however, the perfusion rate was assurned to be constant regardless of
heating.
2.4.2 Cornparison of Highly and Moderately Focused Spher-
ical Transducers
Physical parameters of the highly focused (denoted as SPI) and the moderately
focused (denoted as SP2) spherical transducen investigated in this study are given
in table 2.4. Exposures of 10 s were adopted for both designs, which are sufficiently
brief to limit the blood flow cooling effects in the case of low perfused tissues [Il], but
also long enough to allow relatively large thermal lesions to be produceci. SP2 had
Radius of curvature (cm) Aperture (cm)
Beamlength (mm) 1 10 1 23
Operating frequency(MH2) Beamwidth (mm)
Table 2.4: Physical parameters of two focused spherical transducers studied in this work.
SP1 8.5 10
the same aperture and operating frequency as SPI, but a larger radius of curvature.
The radius of curvature of SP2 was selected such that the thermal lesion generated by
it in a 10s exposure would be slightly larger in the axial direction than the tumour.
The determination of the radius of curvature of SP2 was based on figure 2.8, which
shows lesion length and diameter5 after a 10 s exposure venus radius of curvature of
focused spherical transducers. The thermal lesions were placed at the centre of the
tumour. Spatial peak intensities [I,,] were chosen such that the predicted maximuni
temperature in the tissue after the exposure [TpeaL] was approximately 85OC to avoid
tissue vaporization. The values of I,,used are aven in table 2.5.
SP2 13 10
1 1.9
51n this work, the length or the diameter of a thermd lesion refen to the maximum dimension of the lesion measured axially or laterdy.
1 3
- diameter of lesion .O 1 .-* -WB beamlength -.- -6dB beamwidth
l
# B
# 4
80 90 100 110 120 130 140 150 Radius of curvature: mm
Figure 2.8: Lesion length and diameter and transducer 6dB beadength and beamwidth versus radius of curvature of focused spherical transducers. The transducers were assumed to give a 10 s exposure to the tumour.
Table 2.5: Spatial peak intensities used in figure 2.8.
Focal length (cm) 8.5
Tpeak (OC) 85.1
ISP (W cm-2)
1003
Acoustic power output (W) 14.4
2.4. RESULTS 34
The relative intensity distributions of SPI and SP2 and thermal doses gen-
erated by these two transducers For a single 10 s exposure are plotted in figure 2.9.
Both these transducen produced single, ellipsoid-sbaped focal zones and similarly
Figure 2.9: Figures (a) and (b) show relative ultrasaund intensity distributions produced by SPI and SP2 respectively. The distributions are shown as contour plots relative to the peaii value in 10% intervais starting at 10%. The axial planes at y=Omrn are displayed. The focal plane is at z=50mm. Figures (c) and (d) show the thermal dose profiles generated by SPI and SP2 respectively. The thernial dose profiles are displayed as contour plots, showing contours representing 240, 60, 30 and 5 EMd3, progressing outwards from the lesion centre. Dashed lines represent the tumour boundary. The lesions were produced by placing the centre of the focal zone at the centre of the tumour and deiivering a 10 s e-xposure.
shaped thermal lesioos (the volume bounded by the 240 thermal dose con-
tour). Figure 2.9 (a) and (b) show that intensity gradients generated by SP2 are
smaller than those generated by SPI. Figure 2.9 (c) and (d) show that both SPI and SP2 produced sharp thermal dose gradients over a single exposure. The dis-
tance betwecn the 240 EMd3 and 5 EMs3 contours in the axial direction for SPI was
2.4. RES ULTS 35
slightly shorter than that for SP2.
Since the length of the thermal lesion generated by SPI was only 50% of the
tumour length (z direction), two lesions arrays at two different depths, separated by
10 mm, were required for the treatment. Only one lesion array was required for SP2
because the size of thermal lesions was equal to the size of the tumour along the z
direction. Moreover, more thermal lesions were required to cover al1 of the tumour
in the lateral direction for SPI because individual lesions were smaller in diameter
compared to those generated by SP2. Figure 2.10 illustrates transducer step patterns employed for SPI and SP2.
Axial movemcnt of SPI focus was chosen to step from the distal region of the tumour
towards the proximal region (figure 2.10(a)). This pattern was chosen to avoid
coagulated tissue being present in the pre-focal regions of subsequent exposures.
Coagulated tissue, which attenuates ultrasound more than uncoagulated tissue [13,
261, would prevent penetration of ultrasound fields to distal regions.
The lateral step patterns (figure 2.10 (b) and (c)) were suggested by Fan and
Hynynen (1996). The advantage of these patterns was that excessive heating was
avoided by delivering successive exposures to regions which were not adjacent to
each other. After determination of the transducer step patterns, treatments were
Figure 2.10: Tcansducer step patterns for SPI ((a) rutid and (b) lateral) and SP2 ( ( c ) lateral).
simulated to determine the cooling times required to spare the surrounding normal
tissue. Table 2.6 compares the number of exposures, exposure times, cooling times
and total treatment times required for SP1 and SP2 to treat the tumour. The
maximum tissue temperatures predicted are also given in table 2.6. They are higher
than the Tpeakin single exposures, because of the heat accumulation, but lower than
the vaporization temperature of 100°C. Temperatures reached in the tissue during
Number of exposures Exposure time [sj spatial peak intensity [W cm-*] Acoustic power output [W] Maximum temperature [ O C ] Cooling time [s] Total time [hour]
Table 2.6: Total treatment times, number of exposures, exposure times and intensities, and cool- ing times for SP1 and SP2 to treat the tumour. The acoustic power outputs over each exposure and the maximum temperatures occurred in the tissue during multiple exposures are aiso listed.
the entire treatment using SP2 were shown in figure 2.11. Figure 2.1 1 shows that
immediately after the first heating exposure, which was given to the center of the
tumour, the tissue temperature at (O, 0, 4 cm) reached the maximum value. The
temperature then dropped during the cooling period. As the transducer moved to
heat the peripheral region of the tumour, the peak temperatures at (O, 0, 4cm)
after individual exposures gradually decreased, because little amount of energy was
deposited at this location. The gradua1 increase in temperature at (O, 0, 3.5cm)
and (0, O, 1 cm) during the initial 15 exposures indicates that heat accumulates at
these locations. The highest tissue temperature ever reached during the treatment
at Icm below the skin surface was approximately 4 l 0 c .
Thermal dose profiles produced at the end of the treatments using SPI and
SP2 are displayed in figure 2.12. Figure 2.12 shows that in both treatments, some
small volumes of tumour tissue received a sub-lethal thermal dose of less than
240 EM13. This could have been avoided if more lesions had been formed. Compar-
ison of figure 2.12(a) and figure 2.12(c) indicates that, a t the end of the treatments,
the thermal dose delivered to the nearfield by SP2 was greater than for SPI. For cornparison, thermal dose profiles generated by SPI and SP2 with longer
cooling times are displayed in figure 2.13, where the cooling times were chosen such
that the 30 EM43 thermal dose contour extended approximately 5 mm beyond the
2.5. DISCUSSION
351 I l 1 I O 500 Io00 1500 2000 2500
Treatment time: second
Figure 2.11: Temperatures reached in the tissue as a function of tirne during the tumour treatment using SP2. Temperatures of the tissue that was located on the central axis (x=O mm, y=O mm) were plotted.
tumour boundary a t the end of the treatnient (as opposed to the 60 EMd3 threshold
used in figure 2.12). Given this criterion, the cooling periods chosen were 70s and
120 s for SPI and SP2 respectively. The resulting total treatment times were 2.8
houn and 0.9 houn for SPI and SP2 respectively. Cornparison of figure 2.12(c) and
figure 2. U(c) shows t hat the thermal dose delivered to the nearfield was significantly
reduced due to the longer cooling period.
2.5 Discussion
The results showed that for the treatment of a 2 x 2 x 2 cm3 tumour 5 cm deep in the
body, the moderately focused spherical transducer required 42 min, 28% of the time
required for the highly focused spherical t ransducer . This demonstrates a significant
improvement in total treatment time by the use of the moderately focused spherical
t ransducer.
Alt hough the cornparison was performed under identical treatment condi-
tions, this conclusion should still be drawn with caution. Firstly, if the criterion for
choosing cooling periods is changed, the difference between treatment times required
2.5. DISCUSSION
Figure 2.12: Therrnd dose profiles for tretttmcnts of the tumour using SPI (a, b) and SP? ( c d ) . The cooling time in the treatments was chosen such that the 60 EMdt3 thermai dose contour just extended to 5mni beyond the turnour boundary at the end of the treatments. Figures (a), (c) show the axial plane y=Omm, where the 5, 30 a d 60E& thermal dose cantours are ma.uimally c-xtended beyond the tumour boundary. Figures (b), (d) show the laterd planc z=50 mm. Thermal dose profiles are displayed as contour plots, representing 240, 60, 30 =and 5 Dashed lines represent the tumour boundary.
2.5. DISCUSSION
Figure 3.13: Tïcemd dose distributions for treatments of the tuniour using SPI (a, b) and SP2 (c. d). The cooling time in the treatments was chosen such that the 30 EMt3 thermai dose contour just extended to 5mm bcyond the tumour boundary at the end of the trcatments. Figures (a), ( c ) show the axial plane y=Omm, where the 5, 30 and 60E& thermal dose contours are maximally extended beyond the tumour boundary. Figures (b), (d) show the lrrtcrd plane z=50mni. Thermal dose profiles are displayed as contour plots, representing 240, 60, 30 and 5 E&. Dashed lines represent the turnour boundary.
2.5. DISCUSSION
by the highly and moderately focused spherical transducers may also change. For
example, when the 30 EM43 thermal dose contour extending no further than 5 mm beyond the tumour boundary was employed as the normal tissue thermal dose limit,
the moderately focused spherical transducer required 54 min to treat the same tu-
mour volume. This indicates that as the thermal sensitivity of the normal tissues
surrounding the target increases, the ability of moderately focused spherical trans-
ducen to reduce the treatnient time rnay be reduced, due to the increase in cooling
period required. Secondly, the ability of moderately focused spherical transducers
to reduce the treatment time also depends on the shape of the target. Figure 2.8 in-
dicates that thermal lesions generated by moderately focused spherical transducers
over single exposures are elongated. Thus, the use of moderately focused spherical
transducers enlarges thermal lesinns mainly in the axial direction compared to the
use of highly focused spherical transducers. Hence, for the treatment of tumour
volumes which are small in the axial direction, moderately focused spherical trans-
ducers will not offer any improvement in treatment time. On the other hand, the
use of moderately focused spherical transducers will be more effective in reducing
treatment time if the axial dimension of the tumour volume is larger than that
investigated here.
To simplify the calculations and reduce computation time, constant tissue ul-
trasound attenuation and constant perfusion were assumed in the ultrasound ther-
mal model. Tissue ultrasound at tenuation, however, has been demonstrated to
increase with temperature and time during heating [13,26]. In addition, perfusion
has beeii found to decrease with increasing temperature and time (41. The assump-
tion of constant perfusion rnay lead to an underestimation of the thermal lesion
volume (section 2.4.1). Since a relatively low perfusion rate was assumed in tbis
study, the assumption of constant perfusion was expected to have a small effect on
treatment time cornparison result. A preliminary study conducted by Kolios [38]
has demonstrated that the assumption of constant ultrasound at tenuation resulted
in an overestimation of the axid dimension of the thermal lesion volume and an
underestimation of the lateral dimension of the thermal lesion volume. However,
the efFect of the assumption of constant ultrasound attenuation on treatment time
calculation result is not known.
2.6. CONCL USIONS 41
This study also examined the effects of the weak focusing on treatrnent out-
cornes including thermal dose profiles and the selection of cooling periods. To limit
the thermal dose to the surrounding tissue below the threshold, the moderately
focused spherical transducer required a cooling period of 90 s between exposures,
as compared to 60s for the highly focused spherical transducer. Although the dif-
ference between thermal dose gradients generated by the highly and moderately
focused spherical transducers is small over single exposures, it increases over multi-
ple exposures in the nearfield region, due to heat accumulation. This indicates that
the use of a moderately focused transducer will lead to more (sub-lethal) thermal
dose deposited in the intervening tissue regions.
In order to furtlier reduce the number of thermal lesions to make treatments of
large tissue volumes more efficient, transducer designs capable of producing thermal
lesions larger in the lateral dimensior must be employed. Phased 2-D arrays [14]
and rnulti-focus acoustic lens/transducer combinations [45], which are capable of
generating multiple focus fields, are potential solutions. These transducer designs
will be investigated in Chapter 3.
2.6 Conclusions
A 3-D mathematical model was developed to predict ultrasound-induced thermal
damage in tissue. The accuracy of the model was verified by comparing the predicted
results with published in vivo lesion data. The predicted thermal lesion size agreed
with measured results [7] for the non-perfused cases. For the case of high perfusion
rates, the difference between measured and predicted lesion sizes was attributed
to a difference between the perfusion rate in the experimental conditions and the
value used in simulations and to changes in perfusion during heating that were not
modelled. By using the ultrasound-thermal model, treatments of a 2 x 2 x 2cm3
tumour volume using a highly and a moderately focused spherical transducer were
simulated, and the total treatment times were determined. It was demonstrated
that the moderately focused spherical transducer required a total time of 42 min to
treat the tumour, 28% of the time required by the highly focused spherical tram-
ducer. However, the use of the moderately focused spherical transducer resulted
2.6. CONCLUSIONS 42
in more (sub-let hal) thermal dose being delivered to the intervening tissue regions. The study suggests that transducer designs capable of generating larger thermal le-
sions should be employed to further reduce the total treatment time for large tissue
volumes.
Chapter 3
Theoret ical Evaluat ion of
Multi-focus Acoustic
Lens/Transducer Combinat ions
for High Intensity Focused
Ultrasound Thermal Therapy
3.1 Abstract
The diameters of thermal lesions generated by single-focus transducers are on the
order of a few millimetres, which are usuaiiy small compared to the diameter of
the tumour volume. The combination of a single transducer and an acoustic lens
incorporating a 2-D grid of "elements" can produce multiple foci. Thermal lesion
volumes generated by these multi-focus 1ensJtransducer combinations [LTC] may be greater than those generated by single-focus spherical transducers. Compared to
phased array designs, which can also generate multi-focus fields, LTCs are simple,
inexpensive, and may offer greater flexibility for producing complex focus patterns,
due to the greater number of elements. However, unlike phased arrays, whose ele-
ments can produce amplitude as well as phase modulation, LTCs can only use phase
modulation because al1 LTC elements are activated by a single source. A theoret-
3.2. INTRODUCTION
ical evaluation of the ability of LTC designs to generate large thermal lesions for
high temperature thermal treatments is presented. A design rnethod, based on the
pseudoinverse method, was developed to determine uniform amplitude activation
signals required for LTCs to generate specified multi-focus fields. We demonstrate
that LTC "phase only modulation" bas very small effects on thermal lesion shape
and size. To use LTCs for thermal lesion formation, longer exposure durations of
50s are suggested even though variable blood flow may produce large thermal does
changes in the field. The effect of focus spacing and number of foci produced by the
LTC on the shape and size of thermal lesions was investigated. Specifically, thermal
lesions volumes generated by 9 focus LTCs with 2 m m or 2.5 mm focus spacing and
by a 16 focus LTC with a 2 mm focus spacing were compared. The results indi-
cate that increasing focus spacing or number of foci lead to enlargement of thermal
lesion volumes in both the lateral and axial directions. I t was demonstrated that
a 9 focus LTC with 2mm focus spacing required a total tiine of 30 min to treat a
2 x 2 x 2 cm3 tumour, compared to approximately 40 min and 150 min required by
moderately and highly focused spherical transducers respectively.
3.2 Introduction
It was found in Chapter 2 that moderately focused spherical transducers offered
significantly shorter tirnes for the treatment of a 2 x 2 x 2 cm3 tissue volume than
highly focused spherical transducers. However, there is a limitation on reducing the
lesion number because thermal lesions generated by focused spherical transducers
are longer in the axial direction than in the lateral direction. Thus, even if the
lesion length is identical to the tumour length, the lesion diameter is far from being
sufficiently large to cover the tumour in the lateral direction over a few exposures.
One approach to enlarge the lesion diameter is to use transducer designs which can
generate multiple laterally adjacent foci. When the focus spacing is sufficiently small
or the exposure duration is sufficiently long, individual thermal lesions will coalesce
into one single large lesion, due to thermal conduction.
Three ways to create multi-focus fields are being considered in this chapter.
The first way is to use several focused spherical transducers placed adjacent to each
3.2. INTRODUCTION 45
other. Each transducer must have a small aperture because the size of available
acoustic "windows" a t the body surface is limited by bones or air cavities. However,
the small aperture reduces the transducer focusing which may lead to damage to
tissues surrounding the target. A second way is to use a phased 2-D array [14,23].
A phased 2-D array applicator consists of a 2-D grid of srnall piezoelectric elements,
each of which is an individually activated ultrasound source. By activating these
elements in a phase delay sequence, interference fields can be created which contain
multiple foci. Phased 2-D arrays can also be used to scan and switch between various
multiple focus fields electronically. To increase the focusing and to avoid grating
lobes [70], a large aperture and small element spacing are required, resulting in a
large number of array elements. However, the complexity and cost to build phased
array applicators increases dramatically with the number of array elements.
A third way to generate multi-focus fields is to use a combination of a single
transducer and a conjugate acoustic lens [45]. Such a lens is formed by cutting the
surface of a flat plastics into a 2-D grid of small elements of different thicknesses.
The different thicknesses create the phase shifts that are introdiiced electronically
in the case of phased arrays. Whereas elements of a phased array can generate
waves with modulated amplitude and phase, elements of a conjugate lens/transducer
combination [LTC] produce waves of identical amplitude because the LTC elements
are activated by a single ultrasound source. The lack of amplitude modulation may
result in some degradation of the focus patterns generated by LTCs. However, the
primary advantage of LTCs over phased arrays is that LTCs consisting of a large
number of small elernents are simple to build and inexpensive. A greater nuniber
of elements may allow more complex multi-focus patterns. Although LTCs are less
flexible than phased arrays in that an LTC can only produce a single multi-focus
pattern, many different lenses rnay be coupled to a single transducer, and Ienses
rnay be designed for individual patients.
A theoretical study conducted by Fan and Hynynen [24] has demonstrated
t hat phased 2-D arrays required significantl y shorter treatnient times for large tissue
volumes than highly focused spherical transducers. The phased 2-D arrays that Fan
et al. [23] investigated were spherically focused, to reduce the requirement for srna11
element size. However, the large element size of these arrays, which was 2 x 2 cm2,
limited the range over which foci may be created to the vicinity of the geometric
focus of the arrays. The smallest element size being reported for the phased 2-D
array design is 0.65 x 0.65 cm2 [14]. This axray, which consisted of 256 elements and
was geometrically focused to achieve strong focusing, could coagulate tissue volumes
of 0.7cm(x axis) x 0.7cm(y a i s ) x 1.2 cm(z axis) using a 9 focus field for a single
exposure of 20 S.
To date, LTCs have been investigated for mild heating ultrasound treatments
by Lalonde and Hunt [44,45]. The element size of 2 x 2 mm2 was chosen for the
LTC designs as a compromise between increase in grating lobe levels and surface
roughness [43]. Ultrasound scattering from the rough surfaces reduced the efficiency
of transmission of ultrasound through the lenses. LTCs of 1000 elements have been
constructed, which were able to uniformly heat a 1 x 1 x l cm3 tissue volume to the
hyperthermie temperature by using a 12 focus field [43]. Conjugate lenses can be
coupled to either focused or unfocused transd~icers. I t was found that by combining
conjugate lenses wit h focused t ransducers, the roughness of the lenses was reduced.
The intent of this chapter is to evaluate theoretically the ability of LTCs to
mimic the focusing of phased arrays and to generate large thermal lesions for high
temperature thermal treatments. A design method, based on the pseudoinverse
method, was developed to determine the uniform amplitude activation signals for
LTCs to produce specified multi-focus fields. The effect of LTCs being restricted to
"phase only modulation" on the shape of the t herrnal lesion volume were examined.
The effect of the LTC focus spacing and number of foci on the thermal lesion shape
and size was also examined. The time required for a 2 mm spaced, 9 focus LTC to treat a 2 x 2 x 2cm3 tumour volume was deterrnined, and compared with those
required for the highly and moderately focused spherical transducers investigated in
Chapter 2. The ultrasound thermal model and turnour model developed in Chapter
2 were also employed in this study.
3.3. METHODS
3.3 Methods
3.3.1 LTC Ult rasound Intensity Distribution Calculations
The ultrasound intensity distribution of an LTC was determined using equation 3.1.
This equation was modified from equation 2.1 to take account of the phase delays
created by different thicknesses of LTC elements. Note that al1 LTC elements must
share a single particle velocity amplitude value because they are activated by a single
source.
where
I = intensity at the field point (x,y,z) [W -cm-2]
P = complex pressure a t the field point (x,y,z) [Pa]
Un = amplitude of the complex particle velocity of the lens element n
(u, = [cm s-l]
0, = phase of the complex particle velocity of the lens element n
N = total number of lens elements
b a v e = wave number [cm-']
d, = distance [cm] between the lens element n and the field point (x,y,z)
(see figure 3.1)
S = surface area of a lens element [cm2]
j =J-i
The phase delay (-r < On < T ) was determined from the thickness of the LTC element n by equation 3.2.
where
f = operat ing frequency [MHz] an = distance [cm] between the surface of the transducer and the lens
4:
Figure 3.1: Coordinates and parameters used in the calculation of LTC field distributions.
element n (figure 3.1)
th = thickness [cm] of the lens element n
cm&, = speed of sound [cm s-*] in water
C~ens = speed of souiid [cm s-'1 in the lens
3.3.2 LTC Design Method
An LTC design method, based on the pseudoinverse method [19], was developed
here to determine the phase delay (O,, see equation 3.1) required for elements of an
LTC to produce a specified multi-focus field.
3.3.2.1 Pseudoinverse Method
The pseudoinverse method was developed by Ebbini et al. f19) to determine the
amplitude and phase (un and O,, see equation 3.1) required for phased array elements
to produce specified intensity values a t intended foci and minimum acoustic power
elsewhere (figure 3.2). The amplitude values (un, n = 1 N) determined by the
pseudoinverse method usually are not identicai, whereas in the case of the LTC the
amplitude values of al1 elements must be identical because the lens is coupled to
a single transducer . Hence, the pseudoinverse met hod canno t be directly applied
to LTC design. Because only small modifications to the pseudoinverse method was
made for the design of LTCs, the Following discussion det ails the pseudoinverse
method as applied to the phased array, and the LTC case is presented after.
cle
field point M
Figure 3.2: Coordinat es and parameters used in the pseudoinverse method.
To apply the pseudoinverse method, equation 3.1 is rewritten in the matrix
form:
P = HU
= vector representing complex field pressure, where p, and 4, represent the amplitude and phase of the complex pressure at the field point m
respectively
M = number of field points interested
H = M x N matrix describing the propagation of the ultrasound
wave from each element of the array to each field point
Û = vector representing complex particle velocity, where un and 0,
represent the amplitude and phase of the complex particle velocity of the phased array
element n respectively
N = number of phased array elements
d n ~ = distance between the field point rn and the phased array element n
(see figure 3.2)
S = surface area of the phased array element
Equation 3.3 is solved for u (If equation 3.3 had been solved for the design
of an LTC, there would be a constraint of un = un+l). To ensure that solutions
to equation 3.3 exist, the number of field points (M) in P must not be larger than
the number of elements (N) contained in a phased array. When M is less than N ,
and the positions of these M field points are such that al1 of the row vectors of H are linearly independent, equation 3.3 possesses an infinite number of solutions [66].
One of these solutions is called the minimum norm solution (equation 3.4 [49]),
because the norm of this solution (zSi l n2 ) is the minimum of al1 solutions.
where
H* = conjugate transpose of H (661
Because un2 is proportional to the intensity of the wave generated by the nth element,
the minimum norm solution [MNS] results in a total energy present a t the phased
array field that is minimized for a given P. Thus, with the MNS, the likelihood
is that the greatest constructive interference, and therefore the greatest pressure
amplitude, will occur at the field points specified in P, the intended foci. However,
any solution to equation 3.3. including the MNS, cannot guarantee that the intended
foci will be produced. It is possible that field points not specified in can possess
greater constructive interference than the field points specified in P. Because the
MNS is the most likely solution to produce an intended multi-focus pattern, it was
adopted in the design of phased arrays [19,21,23]. Thus, M can represent the
number of foci in the specified field, dm, is the distance between the focus rn and
the array element n, where p, and #m are the relative amplitude and phase of the
complex pressure at the focus m. Because H*(HH*)-l is called the pseudoinverse
matrix [66], the use of the MNS (equation 3.4) is also called the pseudoinverse
method.
Since the pseudoinverse method could not be directly applied to the design of
LTCs, a method based on the pseudoinverse method was developed for LTC design.
The first step in this method was to use the pseudoinverse method to determine the
amplitude and phase required for applicator elements to produce specified foci. The
second step was to calculate the thicknesses of LTC elements from the phase values
determined by the pseudoinverse rnethod using equation 3.2, where the amplitude
values determined by the pseudoinverse method was ignored.
3.3.2.2 Phase Optirniration
The values specified in f represent the complex pressures at the intended foci. Since
the intensity of the wave is a phase-independent quantity, changing the pressure
phase value of the acocistic waves a t the intended foci will not affect the intensity
values at these foci. By varying the relative pressure phase values at the intended
foci, it is possible to increase the constructive interference at these foci, and therefore
increase localization of energy in the field. This can be explained rnathernatically.
For eacli choice of P, there is an MNS. Given the nurnber, position and pressure am-
plitudes of foci, there exists one particular phase pattern of foci ([$1 * - * 4, * * - $bM])
which will produce an MNS of the lowest norm. Thus, this phase pattern of foci,
compared to other phase patterns of foci, results in the greatest likelihood that the
pressure amplitude values at each focus in P will be greater than that a t any other
field points. To obtain this particular phase pattern, the following equation was
derived [21]
where
G = intensity gain, a measure of energy concentration at the foci relative
to the entire field
The phase pattern of P which minimizes the norm of the MNS (CL, un2) maximises
G. Substit uting H*(HH*) P (equation 3.4) for Ûdnnorm, equation 3.5 is expressed
Based on this equation, the phase pattern of P which maximizes G can be found
iteratively (201. A direct solution, according to Ebbini and Cain [21j, is the phase
pattern of the eigenvector that corresponds to the smallest eigenvalue of matrix
( H H ) Although this solution results in a suboptimal value of G, it was employed
because of its simplicity.
3.3.2.3 Summary of LTC Design Procedure
The procedure for the design of an LTC to produce a multi-focus field is summarized
as follows
Step 1: A multi-focus pattern was specified, including the number and position of
foci and the pressure amplitudes at these foci. The specified pressure amplitude
values were normalized to the maximum of al1 foci. Parameters of the transducer
source were also specified, including the aperture, radius of curvature and operating
frequency.
Step 2: Optimization of the phase pattern of the intended foci was performed ac-
cording to the method discussed in section 3.3.2.2.
Step 3 The MNS was obtained using equation 3.4.
Step 4: The relative intensity distribution of this LTC was calculated using equation
3.1 where 0, were equal to the phases of the MNS.
3.3.3 Methods for Determining 'Ikeatment Times
The total time required for an LTC to treat a 2 x 2 x 2 cm3 tumour, illustrated in
both figure 2.3 and figure 3.3, was determined using the ukrasound-thermaI mode!
developed in Chapter 2.
3.4 Results
The LTCs investigated here employed identical spherically focused transducers as
the energy source, which had a 10 cm aperture, an 8.5 cm radius of curvature and was
operated at a frequency of I MHz. This transducer was highly focused so that when
multi-focus lenses, which were diverging lenses, were placed in front, sufficiently
Figure 3.3: Geometry of the tumour model in Cartesian coordinates. Dashed lines represent the tumour boundary. The body surface is located at the z=0 mm plane.
strong focusing could still be maintained in the field. Al1 the LTCs consisted of
2000 elements with each element being 2 x 2 mm2.
3.4.1 Comparison of LTCs and phased arrays
To evaluate if the shape and size of thermal lesions generated by LTCs are similar
to those produced by phased array, ultrasound intensity distributions and thermal
dose distributions produced by a 2-D phased array and an LTC were compared
where these two applicators possessed identical physical parameters, including the
diameter, radius of curvature, number of elements and operating frequency, and
were designed to produce identical multi-focus patterns. The pseudoinverse method
was used in the design of the phased array. The LTC was designed using the method
developed in this study. The thermal dose distributions were calculated using the
ultrasound-thermal model and tumour model developed in Chapter 2.
The ultrasound intensity distributions produced by an LTC (denoted as
LTC1) and a phased array (denoted as PA) that possessed identical physical pa-
rameters and were designed to produce an identical 9-focus pattern (figure 3.4) are
shown in figure 3.5. In order to compare the intensity distributions of multi-focus
applicators in a useful way, both 2-D contour plots of the applicator focal plane in-
tensity distribution and 6dB and lOdB isosurfacel plots of the entire applicator field
are shown. The 2-D contour plots show that, whereas the intensity values at the - - - -
'The 6dB and lOdB isosurfaces refer to the isosurfaces of25% and 10% of the intensity maximum respectively.
Figure 3.4: 9 focus pattern with 2 mm focus spacing. All foci were assigned to have the identical pressure amplitude values.
foci of PA are identical, intensity values at the foci of LTCl Vary considerably, but
these values were still in a symmetrical pattern. The 6dB isosurface plots indicate
considerable difference between the shapes of the focal zone volumes of LTCl and
PA. Whereas the individual focal zones of LTCl varied in length and diverged at
angles at the proximal and distal ends, the individual focal zones of PA were nearly
identical in length and al1 parallel to the applicator axis. The lOdB isosurface plots
show the similarity between the focal zone shapes of LTCl and PA. In both cases,
individual focal zones varied in length and diverged at angles at both the proximal
and distal ends. Figure 3.6 plots the lens surface profile of LTC1. The maximum
thickness of the elements is 5 mm. The minimum thickness is approximately 0.9 mm.
The thermal dose profiles generated by LTCl and PA for exposure durations
of 20 and 50 s are shown in figure 3.7. The exposures were delivered such that the
focal plane of the applicators was a t a depth of 5cm below the skin surface. The
values for IsPys (table3.1) were chosen such that the 60 E M 4 thermal dose contour
extended approximately 5 mm beyond the tumour boundary after the exposure. A sufficiently long cooling period (200 and 400 s for exposure durations of 20 and 50 s
respectively) was included to allow the tissue to cool to approximately 40°C. This
was necessary for calculating the thermal dose to surrounding tissues because a
considerable thermal dose was delivered to these tissues after the power was turned
off. The thermal lesion volumes (volumes enclosed by the 240EMd3 isosurface)
generated by both LTCl and PA were irregular in shape, with "wings" outside
the main lesion volumes. To avoid t hese "wings" damaging surrounding tissues,
Figure 3.5: The intensity distributions generated by LTCl (a, c, e), PA (b, d, f ) . Figures (a) and (b) display the contour plots at the focal plane (z=50 mm), wit h contours in 10% intervals of the peak value, beginning with the 10% contour. Figures (c) and (d) display the -6dB isosurfaces. Figures (e) and (f) display the -10dB isosurfaces.
50
Element number 50 Element number
Figure 3.6: The lens surface profile of LTC1. The element size is 2 x 2 mm2.
LTCl (figure 3.7 (c))
Table 3.1: Values of I,,used in the study.
LTCl (figure 3.7 (e)) LTCZ (figure 3.9 (b)) LTC2 (figure 3.9 (c)) LTC3 (figure 3.12 (b)) LTC3 (figure 3.12 (c))
PA (figure 3.7 (d)) PA (figure 3.7 (f))
(SI 20 50 50 50 50 50 20 50
(OC) 66.5
(W cm-*) 510
71.9 72.4 65.8 70.6 65.6 80.3 81
270 270 225 270 230 530 323
Figure 3.7: Thermal dose distributions generated by LTCl (a, c, e) and PA (b, d, f ) for 20s (a, b, c, d) and 50s (e, f) exposure duratious. Figures (a) and (b) display the thermal dose distributions at y=0 mm and z=50 mm. Figures (b), (c), (d) and (f) display 240 (opaque surface) and 60 Eh& (transparent surface) thermal dose isosurfaces. Dashed lines represent the t umour boundary.
sufficiently small 1,'s were required. However, this also resulted in thermal lesion
volumes that were not sufficiently large to cover the tumour volume along the axial
direction. Hence, the use of LTCl and PA to treat a target volume of 0.8 cm(x axis) x
0.8 cm(y axis) x 2 cm(z axis) for a 20s exposure would lead t o 19% and 18% of the
target volume being delivered with a thermal dose of less than 240 EMd3. In the case of 50s exposure durations, the thermal lesion shapes were less
irregular due to the thermal conduction effect. The lateral dimension of the lesion
volumes also increased. To treat a larger target volume of 1 x 1 x 2cm3 for a
50s exposure duration, the use of LTCl would lead to a thermal dose of less than
240EM43 delivered to 10% of the target volume, compared t o 19% for the use of
PA.
3.4.2 Effect of Focus Spacing
The effect of LTC focus spacing on the shape and size of thermal lesions was exam-
ined by comparing the thermal dose profiles generated by two LTCs that produced
an identical number of foci, but with different focus spacings.
The ultrasound intensity distri butions produced by LTCl (investigated in
section 3.4.1) and an LTC (denoted as LTCZ) which was designed to produce the
same 9 focus pattern (figure 3.4) but with a focus spacing of 2.5mm are shown in
figure 3.8. The 2-D contour plots show that the difference between the intensity
values a t foci was larger in the case of LTC2. The isosurface plots show that the
difference between the lengths of individual focal zones was larger in the case of
LTCZ. The focal zones of LTCZ also diverged at larger angles tlian those of LTC1. The thermal dose distributions generated by LTCl and LTC2 for an exposure
durations of 50 s are displayed in figure 3.9. The exposures were delivered such that
the focal plane of the applicators was at a depth of 5 cm below the skin surface. In
the cases of figure 3.9 (a) and (c), the values for I,(table 3.1) were chosen such that
the 60 EM43 thermal dose contour extended approximately 5 mm beyond the tumour
boundary after the exposure and a cooling period of 400s, which allowed the tissue
to cool to approximately 40°C. In the case of figure 3.9 (b), the 1,value (table 3.1)
was chosen to be the same as that used in the case of figures 3.9 (a). Figure 3.9
shows that, given identical exposure intensities and durations, LTC2 generated a
Figure 3.8: The ultrasound intensity distributions generated by LTCl (a, b) and LTC2 (c, d). Figures (a) and (c) display the contour plots at the focal plane (z=50 mm), with contours in 10% intervals of the peak value, beginning with the 10% contour. Figures (b) and (d) display the 6dB isosurfaces.
Figure 3.9: 240 Ebh3 (opaque surface) and 60Ebh3 (transparent surface) isosurface plots of thermal dose distributions generated by LTCl (a) and LTC2 (b and c) for a 50s exposure duration. Dashed lines represent the tumour boundary. In the case of figure (b), the Ispvalue was chosen to be the same as that used in the case of figure (a). In the case of figure (c), the values for i,,was chosen such that the 60 E1N3 thermal dose contour extended approximately 5 mm beyond the tumour boundary after the exposure and a cooling period of 400 S.
3.4. RESULTS 61
larger thermal lesion volume, in both the axial and lateral directions, than LTC1. If
the 60 EMd3 thermal dose contour a t 5 mm beyond the tumour boundary was used
as the criterion to choose the exposure intensity, the sizes of thermal lesion volumes
generated by LTCl and LTC2 were nearly identical. To treat a 1 x 1 x 2 cm3 target
volume for an exposure duration of 50s, the use of LTCZ would lead to a thermal
dose of less than 240 EMd3 in 7% of the target volume, compared to 10% for the use
of LTC 1.
3.4.3 Effect of Number of Foci
The effect of number of foci on the shape and size of thermal lesions was examined
by cornparing the thermal dose profiles generated by two LTCs with identical focus
spacings, but different numbers of foci.
The ultrasound intensity distributions produced by LTCl (investigated in
section 3.4.1) and an LTC (denoted as LTC3) which was designed to produce the
16 focus pattern (figure 3.10) are illustrated in figure 3.11. The 2-D contour plots
Figure 3.10: 2mm spaced, 16-focus pattern.Al1 foci were assigned to have the same pressure amplitudes. Foci are numbered as shown.
show that the difference between the intensity values at foci was larger in the case
of LTC3 than for LTC1. The isosurface plots indicate that the difference between
the lengths of individual focal zones was larger in the case of LTC3. The focal zones
of LTC3 also diverged a t larger angles than those of LTC1. The thermal dose distributions generated by LTCl and LTC3 after a 50 s
exposure duration are displayed in figure 3.12. The exposures were delivered such
3.4. RESULTS
5 - 4 -
3. 2 -
O v ii O 0 -1 .
-2. -3 - -4.
-5- -6 20 t m m -6- ' ' y: mm -6 -5 -4 -3 -2 -1 O 1 2 3 4 5 6
Figure 3.11: Ultrasound intensity distributions generated by LTCl (a, b) and LTC3 (c, d). Fig- ures (a) and (c) display the contour plots at the focal plane (z=50mm), with contours in 10% i n t e d s of the peak value, beginning with the 10% contour. Figures (b) and (d) display the 6dB isosurfaces.
3.4. RESULTS 63
that the focal plane of the applicators was at a depth of 5 cm below the skin surface.
In the cases of figure 3.12 (a) and (c), the values for I,,(table 3.1) were chosen such
that the 60 EMd3 thermal dose contour extended approximately 5 mm beyond the
tumour boundary after the exposure and a cooling period of 400 s, which allowed the
tissue to cool to approximately 40°C. In the case of figure 3.12 (b), the &,value (table
3.1) was chosen to be the same as that used in the case of figures 3.12 (a). Figure
Figure 3.12: 240 E h 3 (opaque surface) and 60EM43 (transparent surface) isosurface plots of thermal dose distributions generated by LTCl (a) and LTC3 (b and c) for a 50s exposure duration. Dashed Lines represent the tumour boundary. In the case of figure (b), the I,,value was chosen to be the same as that used in the case of figure (a). in the case of figure (c), the values for I,, was chosen such that the 60 EWs thermal dose contour extended approximately 5 mm beyond the tumour boundary after the exposure and a cooling period of 400 S.
3.12 shows t hat , given identical exposure intensities and durations, LTC3 generated
a larger thermal lesion volume, in both the axial and lateral directions, than LTC1.
If the 60 EMd3 thermal dose contour at 5 mm beyond the tumour boundary was used
as the criterion to choose the exposure intensity, the axial dimensions of thermal
lesion volumes generated by LTCl and LTC3 were nearly identical. The lateral
dimension of the thermal lesion volume generated by LTC3 was slightly larger than
that generated by LTC1. To treat a 1 x 1 x 2cm3 target volunie, the use of LTC3 would lead to a thermal dose less than 240EM43 in 14% of the target volume,
compared to 10% for the use of LTCl.
3.4.4 Multiple Exposure neatments of the nimour
Since the thermal lesion volumes generated over single exposures by the LTC designs
investigated here were not sufficiently large to cover a 2 x 2 x 2 cm3 tumour volume
in the lateral direction, multiple exposures treatments were required. Among al1
LTC designs investigated here, LTCl and LTC2 appeared to be preferable because
both LTCs can be used to achieve the destruction of 90% of the target volume over a
single exposure with the restriction on the thermal dose to the surrounding normal
tissue. Thermal lesion volumes generate by LTC2 had more "wings" than those
generated by LTC1. T h e "aings" might overlap when multiple adjacent exposures
were delivered to treat large tissue volumes, resulting in damage in surrounding
normal tissue regions. Therefore, LTCL was chosen to be the "optimal" design and
the total time required for LTCl to treat the 2 x 2 x 2cm3 tumour volume was
determined. Four exposures were required to treat this tissue volume with LTCl (figure 3.13). The cooling periods were chosen such that the tissue couid cool to
Figure 3.13: Lateral step pattern for LTC1.
approxiinately 40°C after each exposure. To avoid damage to surrounding tissues
due to overlaps between adjacent exposures, the exposure intensities used in the
3.5. DISCUSSrON 65
multi-exposure treatment were reduced from 270 W cm-* to 250 W cm-*. The
number of exposures, exposure intensity and duration, cooling period and total
time required for LTCl to treat the tumour volume are given in table 3.2. For
comparison, the corresponding values for the highly (SPI) and moderately (SP2)
focused spherical transducers investigated in Chapter 2 are also given. Figures 3.14
Table 3.2: Total treatment times, number of exposures, e.xposure durations and intensities, cool- ing times and tumour volume under 240E& for LTCl, SP2 and SPI to treat the tumour volume.
Number of exposures Exposure time (s) spatial peak intensity (W - cm-2) Cooling period (s) Total time (hour) Tumour volume under 240 EMr3
and 3.15 displays the thermal dose distributions generated by LTC1, SP2 and SPI
at the end of the treatment. Due to the gaps between thermal lesion volumes
and the irregularity of the thermal lesion shapes, approximately 21% of the tumour
volume received a thermal dose of less than 240 EMA3 in the case of LTC1, compared
to 26% and 6% for SP2 and SPI respectively. The axial plane thermal dose contour
plots indicate that thermal dose gradients generated by LTCl in the nearfield are
higher than those produced by SP2 and SPI.
' LTCl 4 50 250 400 0.5 21%
3.5 Discussion
The results demonstrated that the shape and size of thermal lesion volumes gen-
erated by LTCs were similar to those generated by the equivalent phased arrays,
which had the same physical parameten as the LTC including the number of ele-
ments, aperture, radius of curvature and operating frequency. Hence, the effect of
LTCs being restricted to "phase only modulation" had a very small efFect on the
shape and size of thermal lesion volumes. The LTC design method was evaluated
for designing LTCs to produce symmetrical focus patterns with uniform intensity
3.5. DISCUSSION
i -20 / O 10 M 30 4û 50 60 70 86 -% -16 0 .O 20
t m m 'I' mn
Figure 3.14: Thermd dose distributions generated by LTCl (a, b), SP2 (c, d) and SPI (e, f ) at the end of the treatment. Dashed lines represent the tuniour boundary. Figures (a). ( c ) and (e ) display the central axial plane y=Omm. Figures (b), (d) and (e) display the lateral plane z=50 mm.
3.5. DISCUSSION
Figure 3.15: 240 EW3 (opaque surface) and 60 EM43 (transparent surface) isosurface plots of thermal dose distributions generated by LTCl (a), SP2 (b) and SPI (c) at the end of the treat- ment. Dashed lines represent the tumour boundary.
a t foci. It was found that the resulting focus patterns were symmetrical, but with
reduced intensity values at the central foci. The effect of this "non-uniform focus
intensity" on the thermal lesion shape was small because the tissue located at the
central region of the focal zone could be heated through thermal conduction by the
foci a t the periphery. It can be predicted that the method may not be suitable for
designing LTCs to produce the focus fields which contain a large number of foci or
large focus spacings. This is because the degradation of intensity values at central
foci was already much greater for the 2.5 mm spaced, 9 focus LTC and the 2 mm
spaced, 16 focus LTC compared to that for the 2 mm spaced, 9 focus LTC. The results also demonstrated that both the lateral and axial dimension of
the thermal lesion volumes increased with LTC focus spacing or number of foci.
This finding was expected because an increase in focus spacing or number of foci
results in a decrease in applicator focusing, given that the aperture of the applicator
remains the same. The decrease in the applicator focusing leads to an enlargement
of the focal zone, and therefore the thermal lesion volumes, in both the lateral
and axial directions. Increasing the lateral dimension of the thermal lesion volume
while keeping the axial dimension unchanged is desirable because it can further
decrease the number of lesions required to treat the target volume. A prerequisite
for achieving this, by increasing the LTC focus spacing or number of foci, is a
corresponding increase in the focusing of the transducer source. Increasing the
focusing of an applicator can be achieved by increasing operating frequency, or
decreasing the f-number . For treatments of deep-seated tumour volumes, a sufficiently large radius
of curvature of the applicator is necessary. Tissue ultrasound attenuation increases
linearly with the applicator operating frequency. Therefore, increasing the operating
frequency essentially reduces the ability of the applicator to deliver sufficient energy
to deep seated tissue volumes. A larger aperture of the applicator is desirable for
increasing the focusing. However, in practice, the aperture size is limited by the
size of available acoustic "windows" at the body surface. Hence, given a target
volume, the minimal number of thermal lesions required for a multi-focus applicator
to treat this volume is limited by physical parameters including the depth of the
target, the ultrasound attenuation of the intervening tissues and the size of available
3.6, CONCL USIONS
acoustic "windows" . This minimum lesion number can be achieved by optimizing
the treatment parameters such as the physical parameters of the applicator, and
exposure duration.
The physical parameters of those LTC designs investigated here, including
the focus pattern, aperture, radius of curvature and operating frequency, and the
exposure durations investigated here were not optimized for the treatment of the
target volume. The intent of this study is to demonstrate the potential of LTCs for
the treatrnent of large tissue volumes. The results showed that a 2 mm spaced, 9
focus LTC required a total time of 30 min to treat a 2 x 2 x 2cm3 tissue volume,
70% and 20% of the time required by the moderately and highly focused spherical
transducers investigated in Chapter 2 respectively. Furthermore, compared to the
use of the highly and moderately focused spherical transducers the use of this LTC design resulted in the sharpest thermal dose gradients in the nearfieid region at the
end of the treatment, due to the significantly long cooling periods which minimized
the heat accumulation in the normal tissue regions. One drawback of the use of
LTCs is that long exposure durations of 50s must be adopted to allow the thermal
conduction to improve the shape of thermal lesions. When these longer exposure
durations, compared to those (10s) used for simple spherically focused transducers,
were adopted, the temperature distributions as well as the thermal dose distributions
achieved in the tissue would be more dependent on the perfusion. Since perfusion
is one of the most uncertain factors in actual treatments, the use of longer exposure
durations may lead to difficulties in the control and prediction of thermal lesion
formation.
3.6 Conclusions
A theoretical evaluation of the ability of multi-focus acoustic lensltransducer corn-
binations [LTC] to produce large thermal lesion volumes for high temperature focus
ultrasound thermal treatments was presented. LTCs were demonstrated to be able
to produce thermal lesions with shape and size similar to those generated by phased
arrays. Since thermal lesion volumes generated by LTCs were irregular in shape,
long exposure durations of 50 s were required for the LTCs to produce thermal lesion
3.6. CONCL USIONS 70
volumes of a useful shape. It was also found that, in order to enlarge thermal lesion
volume solely along the lateral direction, the LTC focusing needs to be increased.
The results dernonstrated that LTCs required significantly shorter treatment times
for large tissue volumes t han highly and moderatel y focused spherical tramducers.
Chapter 4
Summary and Future Work
4.1 Summary
The goal of this thesis was to theoretically evaluate novel HIFU applicator designs,
including the moderately focused spherical transducer design and the LTC design,
for enabling practical treatment times for large tissue volumes. A 3-D mathemati-
cal model was developed to simulate ultrasound-induced thermal damage in tissue.
The accuracy of the model was verified by comparing predicted transducer focal
zone sizes and thermal lesion sizes with published experimental data. A theoretical
tumour model was constructed to allow treatment times of different transducer de-
signs to be compared under identical treatment conditions. The following sections
summarize the conclusions of each chapter and their contribution to the literature.
4.1.1 Moderately Focused Spherical Tkansducers
In Chapter 2, treatments of a 2 x 2 x 2 cm3 tumour volume using a highly and a mod-
erately focused spherical transducer were simulated using the ultrasound-thermal
model. Physical parameten of the moderately focused spherical transducer were
chosen such that the number of thermal lesions required for it to treat the tumour
was minimized. The simulation results demonstrated that the total time required
for the moderately focused sphericai transducer to treat the tumour was approxi-
mately 40 min, compared to 2.5 hours for the highly focused spherical transducer.
However, due to the weak focusing, more sub-lethal thermal dose was delivered
4.1. SUMMARY 72
to the nearfield. Since the diameters of thermal lesion volumes generated by the
moderately focused spherical transducer were still small compared to the tumour
diameter, it was suggested that multiple focus transducer designs, which are able to
produce thermal lesions with a greater diameter, sbould be investigated to further
reduce the treatment time for tumoun of typical size.
This work was the first study to quantitatively examine the difference between
treatment times offered by highly and moderately focused spherical transducers for
coagulation of large tissue volumes. Since moderately focused spherical transducers
are simple, inexpensive and commercially available, treatment protocols adopting
these transducers may be preferable to those adopting more complex and expensive
transducer designs such as phased arrays. Examination of the thermal dose in
the nearfield generated by the highly and moderately focused spherical transducers
suggested that the moderately focused spherical transducer design should be adopted
with caution, because the use of this design resulted in more heat deposited in
the intervening tissue regions. Careful treatment planning including determining
sufficient cooling durations is therefore necessary when using the moderately focused
spherical transducer design to produce a safe and effective treatment .
4.1.2 Multi-focus Acoustic Lens/Transducer Combinations
In Chapter 3, the potential of LTCs to produce large thermal lesions for high temper-
ature thermal therapy applications was evaluated. A design method was developed
to determine the activation signals required for LTCs to produce speciîied multi-
focus fields. The results indicate that the shape and size of thermal lesion volumes
generated by LTCs and phased arrays are similar, although LTC elements only pro-
duce phase modulation. Heating exposures of 50s were found to be necessary for
LTCs to produce thermal lesions of sufficiently regular shape in order to cover most
of the tumour tissue and spare the surrounding normal tissue. The effects of LTC
focus spacing and number of foci on the shape and size of thermal lesions were also
investigated. As the LTC focus spacing or number of foci was increased, both the
lateral and axial dimensions of the thermal lesion volumes were increased. An in-
crease in LTC focusing was found to be necessary to increase the lateral dimension
of thermal lesion volume while keeping the axial dimension unchanged. The total
4.2. FUTURE WORK 73
time required for a 2mm spaced, 9-focus LTC to treat the 2 x 2 x 2cm3 tumour
was 30 min, compared to 40 min and 150 min required for the highly and moderately
focused spherical transducers investigated in Chapter 2 . Furthermore, the resulting
thermal dose gradients in the nearfield were largest in the case of the LTC. For ex-
ample, the thermal dose level of 5 EMd3 extended to approximately 1.7 cm in front
of the target volume, compared to 2cm and 2.9cm in the cases of the highly and
moderately focused spherical transducers.
The work presented in Chapter 3 is the fint investigation of the potential
of the use of LTCs in high temperature thermal therapy applications. The effect
of LTCs being restricted to "phase only modulation" was found to be srna11 on
the shape and size of thermal lesion volumes. Since long exposure durations of
50s are necessary for LTCs to produce thermal lesion volumes of a regular shape,
thermal treatments using LTCs may be liable to significant blood flow cooling effect.
Hence, treatment planing for LTCs in particular should take account of the blood
flow cooling effect. In summary, this study demonstrates that LTCs are prornising
applicator designs for high temperature thermal treatments of large tissue volumes,
and suggests that they should be further investigated for these applications.
4.2 Future Work
4.2.1 Ultrasound-Thermal Modeling
Ultrasound beams must penetrate intervening tissue layers, including skin, fat and
muscle tissue, to access the target in HIFU thermal treatments. These tissue layers
are known to possess varied acoustic and thermal property values, as indicated in ta-
ble 4.1. However, to simplify the calculations and reduce the computation tirnes, the
ultrasound-thermal model developed in this work assumed al1 these tissue layers to
possess identical acoustic and thermal properties. The model also assumed that val-
ues of al1 the tissue properties remained constant during heating. Changes in tissue
ultrasound attenuation and absorption coefficients as well as changes in perfusion
with temperature and time have been observed in experinental studies [4,13,26].
Comparing the results predicted by this rnodel with thermal Iesion sizes measured in
perfused liver tissues indicates t hat the assumption of constant perfusion resulted in
4.2. FUTURE WORK 74
tissue type ( Speed of Sound 1 Ampl. Atten 1 Density ( Perfusion
fat muscle kidney liver
skin
Table 4.1: Acoustic and thermal properties for normal human tissues [18]. - data are not d l - able.
an underestimation of lesion size for the case of long exposures. Kolios [40] developed
a non-linear thermal model to take into account the tissue ultrasound attenuation
changes during heating. The preliminary data indicates that thermal lesion volumes
predicted by the non-linear model were greater in diameter and smaller in length
compared to those predicted by the simplified model. Moreover, lesions "rnoved"
towards the transducer in the non-linear model. In addition, Fan and Hynynen [22]
demonstrated that a model which did not take into account the differences in speed
of sound between tissue layers underestimated the focal depth of a spherical trans-
ducer, and overestirnated the peak intensity value in tissues.
For the purpose of comparing thermal lesion volumes and thermal dose gradi-
ents generated by different transducer designs under identical treatment conditions,
the simplified rnodel developed in t his work is a reasonable approach, because al1 the
assumptions affect the results of different transducers in a similar manner. However,
to predict actuel t reatment resufts or to select treatrnent parameters (the exposure
intensity, cooling period and number of lesions) for a particular transducer design
to destroy a particular tumour volume and spare surrounding normal tissues, t his
model is not sufficient, and should be extended to simulate more realistic treatment
conditions.
Three improvements to this model are proposed. The first is to extend the
calculations of ultrasound intensity distributions to layered tissues, including skin,
fat, muscle, organ and tumour. The ultrasound intensity distributions in these
tissue layen can be calculated using a method developed by Fan and Hynynen (221.
This method takes account of beam reflection and refraction at tissue interfaces.
(m S-l) 1498
(NP cm-' MHZ-l)
0.4 (g
1.2 (g S-l cm-3)
0.0024
4.2. FUTURE: WORK 75
By determining the exact path of an ultrasound beam traversing through tissue
layers, this method can be used to accurately calculate the phase delay acquired
by the beam as it propagates through the tissue layers (figure 4.1). Thus, the
intensity distribution generated by the applicator in layered tissues can be accurately
predic t ed.
Figure 4.1: Diagram of a beam traversing through layered tissues. The phase delay this beam acquires from point source A to field point B ig cdculated as &($ A + $ +. :+ C. COS B. 1 7
where c, is speed of sound in tissue layer i.
The mode1 should also take account of changes in tissue ultrasound attenu-
ation and absorption coefficients and perfusion rate during heating. The method
described in Patankar [56] can be used to solve the nonlinear form of the bioheat
transfer equation. The decrease in perfusion rate due to heating can be modelled
by equation 4.1 based on the experimental data of Brown et al. 141.
where
4.2. FUTURE WORK
ww = initial blood perfusion [Np cm-' MHZ-'1
"Y = constant [s-'1
The data of Damianou et al. [13] c m be used to model the thermal dose dependency
of the ultrasound attenuation coefficient (equation 4.2).
where
Po = initial amplitude attenuation coefficient [Np cm-' MHZ-'1 PL = plateau amplitude attenuation coefficient [Np - cm-l MHZ-'1 TD430 = thermal dose where attenuation coefficient starts to increase [EM43 ] TD4% = thermal dose where attenuation coefficient reaches a plateau [EM43]
C = constant of fitting procedure [Np + cmm1]
The mode1 should also take into account large blood vesse1 effects. Kolios
et al. 1391 demonstrated that temperature gradients generated by the large vessels
of 0.3 mm or greater diameter dominated temperture distributions during high tem-
perature thermal treat ments. A 3-D thermal dose calculat ion model incorporating
the vasculature data (geometry and flow) of the target volume will be developed.
The thermal modelling method developed by van Leeuwen [75] will be adopted here.
In this method, heat transfer to large vessls is modelled by calculating the entire
volumetric temperature distribution using heat transfer coefficients derived from
analytical expressions [42], while heat transfer due to smaller vessels is modelled
by attaching local heatsinks at the terminal ends of the feeding vessels or by using
the bioheat transfer equation. 3-D vasculature data of the target volume will be
obtained by either Magnetic Resonance Angiography, Doppler Ultrasound or CT Angiography.
4.2. FUTURE: WORK
LTCs
4.2.2.1 Validation of Theoretical Predictions
A theoretical study of LTC designs for thermal therapy applications is presented in
Chapter 3. The next step is to experimentally validate these t heoretical predictions
by constructing a prototype LTC. The 3-D beam profiles of this LTC will be mea-
sured in a water tank. Thermal lesions will be formed in excised pig muscle tissues,
where the sizes and shapes of these lesions are measured. Of particular concern here
will be the ability of the LTC to deliver sufficient energy into the target zone to
form lesions. This concerns arises because the energy absorbed by the acoustic iens
increases in proportion to the energy delivered into the target zone. Since the lens
material possesses a low thermal conductivity, the energy absorbed by the lens may
result in melting.
4.2.2.2 Focusing in Inhomogeneous Tissues
Complex multi-focus patterns of LTCs were designed assuming that these patterns
were produced in homogeneous media. Tissue inhomogeneities are expected to in-
troduce phase shifts into the beams, and therefore might degrade the focus patterns.
Pliase errors in tissues can be divided into two parts: large, non-random erron due
to layered tissues discussed earlier and small, random errors [68]. Lalonde et al. [45]
added randorn phase errors from O to 0.2 n radians to the LTC element phases for an
8 focus LTC. No substantial changes in the positions of the foci were found. How-
ever, the intensities a t individual foci were reduced by up to 50%, due to increasing
phase incoherence. Random phase errors from O to 0.2 s radians were added to the
LTC element phases for the 2 mm spaced, 9-focus LTC (LTC1 in Chapter 3). No
changes in the sizes or shapes of the focal zone were found (data not shown). These
results suggest that multi-focus patterns of LTCs in real tissues may be insensitive
to random phase errors. Non-random phase errors, which could cause greater focus
degradation, ha?a not yet been investigated. Therefore, the next step is to deter-
mine the effect of layered tissues on the focal zone shape of LTCs and the shape of
thermal lesion volumes generated by these LTCs. The method described in section
4.2.1 will be employed for this study. Non-random phase errors can be corrected by
4.2. FUTURE WORK 78
incorporating tissue geometries into the calculation of the phase delays needed for
LTC elements. However, an LTC built with the phase-error correction is applicable
to a single tissue geometry. Moving the LTC to treat a large tissue volume may not
be successful when the variation in tissue geometry is large in the target region.
Rotation of LTCs
The results in Chapter 3 demonstrated that individual focal zones of LTCs varied
in length and diverged at angles at both the proximal and distal ends. As a result,
thermal lesion volumes generated by individual focal zones did not coalesce a t the
proximal and distal regions. To make these LTCs useful for tumour treatments,
long exposure durations were necessary to allow thermal lesion volumes generated by
individual focal zones to completely coalesce through thermal conduction. However,
due to the blood flow cooling effects, the use of long exposure durations may result
in difficulties in control and prediction of thermal lesion formation.
An alternative way to improve the shape of thermal lesion volumes generated
by LTCs is presented here. An examination of the focal zones of the LTCs investi-
gated in Chapter 3 revealed that the 4 individual focal zones located at the corners
of the focus pattern always had a greater length than other focal zones. If the LTC is
rotated upon its axis during heating (figure 4.2), the locations of the "corner" focal
zones in tissue will keep changing so that the energy deposited by these focal zones
in a certain tissue volume will be reduced. Some preliminary results are presented
here to demonstrate the efficacy of this method.
The 9 focus LTC with 2 mm focus spacing investigated in Chapter 3 (LTCl) was employed in this preliminary study. To simplify the computation, the case that
LTCl switched continuously between the orientations of 0,45, 90, 135, 180,225, 270
and 315" (figure 4.2) during heating was simulated. The LTC was assumed to stay
at each of the orientations for 0.5 S. The time spent between the orientations was
assumed to be zero. This continuous switching was used to mimic the rotation, and
is referred to here as pseudo-rotation. The thermal dose distributions generated by
this LTC with and without pseudo-rotation for a single exposure duration of 20s are
displayed in figure 4.3. The exposures were delivered such that the focal plane of
LTCl was at a depth of 5 cm below the skin surface. Spatial peak intensities were
4.2. FUTURE: WORK
Figure 4.2: Schematic of the rotation of the 9 focus LTC with 2mm focus spacing (LTC1 in Chapter 3). The orientations of 0, 45, 90, 135, 180, 225, 270 and 315' are as iiiustrated.
chosen such that the 60 EMd3 thermal dose contour extended approximately 5 mm
beyond the tumour boundary after the exposure and a cooling period which allowed
the tissue temperature to reduce to approximately 40°C. Comparison of the thermal
lesion shapes demonstrates the potential of the rotation method in that "wings"
nearly disappeared. To treat a target volume of 0.8 cm(x axis) x 0.8 cm(y axis) x
2 cm(z axis), the use of the LTC with the pseudo-rotation would lead to the thermal
dose of less than 240 EMd3 to be delivered to only 6% of the target volume, compared
to 19% for the use of the LTC wzthout the pseudo-rotation. The preliminary results
demonstrate that the rotation of LTCs during heating can significantly improve the
shape of the thermal lesion volume. As a result, short exposure durations (20s) as
compared to the 50s exposure durations can be adopted in treatments using LTCs,
and the treatment results will be less dependent on the blood flow cooling effect.
However, the rotation method may not be applicable to an LTC built with the
phase-error correction because the tissue geometry for which the LTC is corrected
is dependent on the LTC orientation.
4.2. FUTURE WORK
Figure 4.3: 240 EW3 (opaque surface) and 60EW3 (transparent surface) isosurface plots of thermal dose distributions generated by LTCI with (a) and without (b) the pseudo-rotation for a 20s exposure duration. Dashed lines represent the turnour boundary.
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