DESIGN AND EVALUATION OF A 2-D PLANAR THERAPEUTIC
ULTRASOUND PHASED ARRAY
by
Danish Suleiman Khatri
Submitted to the Department of Electrical Engineering and Computer Science in Partial
Fulfillment of the Requirements for the Degree of Master of Engineering in Electrical
Engineering and Computer Science at the Massachusetts Institute of Technology
-October 14, 2005
C Massachusetts Institute of Technology. All rights reserved
Signature of
Author
/
'
Danish S. Khatri
Department of Electrical Engineering and Computer Science
October 14, 2005
Certified
by
C eer
1
Kullervo Hynynen, PhD
Professor of Radiology, Harvard Medical School, Brigham and Women's Hospital
Thesis Advisor
-,
by
,Roger
G. Mark, MD, PhD
Distinguished Professor in Health Sci & Technology,
Harvard-MIT Division of Health Sciences & Technology
Pro.....
fssor of Electricaal"Engineering and Computer Science
M.I.T. Thesis Advisor
Accepted
by.
,
y krthur C. Smith, PhD
Chairman, Committee on Graduate Students
Department of Electrical Engineering and Computer Science
MASSACHUSM'r I06 lJE,
OF TECHNOLOGY
AUG 14 2006
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1
Design and Evaluation of a 2-D Planar Therapeutic Ultrasound Phased
Array
by
Danish Suleiman Khatri
Submitted to the Department of Electrical Engineering and Computer Science in Partial
Fulfillment of the Requirements for the Degree of Master of Engineering in Electrical
Engineering and Computer Science at the Massachusetts Institute of Technology
ABSTRACT
Focused ultrasound continues to be investigated as an exciting technique for several
medical therapy applications including tissue ablation. Phased array transducers serve as
important devices for delivering the high intensity focused ultrasound to the targeted
tissue. These arrays often produce undesired secondary foci called grating lobes that can
result in heating of non-targeted healthy tissue. Grating lobes can be eliminated by
setting the element-spacing between adjacent elements to V/2 or less.
The aim of this research is to construct and evaluate a 2-D planar phased array with close
to X/2 element-spacing. A 7x7 element array with element-spacing of 0.762mm was
constructed using 1,3-piezocomposite material. Acoustic field measurements of the array
focused at three different locations were taken to demonstrate its ability to scan the focus
in a volume. In addition, a maximum average intensity of 5.54W/cm 2 was measured for
the unfocused array using radiation force measurements.
Thesis Advisor: Kullervo Hynynen, PhD
Title: Professor of Radiology, Harvard Medical School, Brigham and Women's Hospital
ACKNOWLEDGEMENTS
I would like to thank my advisor, Professor Kullervo Hynynen, for the
opportunity to work in such an exciting research field and for his guidance, mentorship
and availability throughout my time at the Focused Ultrasound Laboratory.
His
achievements and immense contributions to the therapeutic ultrasound field are inspiring
and I am deeply honored to have been one of his students.
In addition, I also thank Professor Roger Mark for his role as my on-campus
advisor. I am grateful for the friendship, advice and mentorship of everyone at the FUL.
I would like to thank Jose Juste for his advice, mentorship and lessons on the ins-and-outs
of the VUDS system, Phillip Jason White and (Professor) Greg Clement for their advice
in matters of ultrasound and experiment setups. It was a great joy discussing circuits with
Sai-Chun Tang, a passionate and friendly circuits engineer and enthusiast. I thank XiangTao Yin for his comprehensive Matlab software to simulate the acoustic fields from
phased arrays and Russell Erich Caulfield for his advice and motivating discussions. I
am grateful to Susan (Sue) Agabian for teaching me to use the mill and sharing her
tremendous knowledge in machining and adhesives. I thank Keiko Fujiwara for her help
with all the formalities of being a graduate student. I also thank Thomas Gauthier, Sonali
Palchaudri, Anne Yu, Lisa (LT) Treat, Manabu Kinoshita, Anthony (Mr. T) Ross, Janne
Heikkila, Hao-Li Liu, Nickolai Sheikov, Vince Colucci, Nathan McDannold, Yong-Zhi
Zhang, Karen Tam and Natalia Vykhodtseva for making the lab enjoyable to work in.
They have all been as good friends as they have been research colleagues.
Finally, I would like to thank my family: my sister Sameera, my brother Fayaz,
Nizam, Lindsey and my adorable nephews Naheel, Saajid and niece Nailah.
Most
importantly, I am deeply grateful to my parents, Munira and Suleiman Khatri, for their
tremendous support and guidance without which I would never have made it to M.I.T.
This thesis is dedicated to them.
TABLE OF CONTENTS
LIST OF FIGURES ....................................................................................................
6
LIST OF TABLES ......................................................................................................
9
1
INTRODUCTION...................................................................................................
10
1.1
M OTIVATION ...................................................... .... ................. 10
1.2
ARRAY THEORY/ BACKGROUND ......................................
2
...
.......................
1.2.1
History.....................
1.2.2
GratingLobes.................................................................
1.2.3
1,3-Piezocomposites............................
1.2.4
Focusing of a PhasedArray ......................... .......................................
12
....................
...............................
........................................
12
.......... 13
.................... 15
.... ................. 16
2-D ARRAY DESIGN ........................................................................................
19
2 .1
INTRO DUCTION........................................................................................................................... 19
2.2
ELEMENT IMPEDANCE..................................................
2.3
AMPLIFIER SPECIFICATIONS
2.4
CIRCUIT MODELS ...........................................................
2.5
POWER TRANSFER AND CABLE SELECTION.............................
.................... 19
......................................
...............
21
21
....
.............. 26
3
2-D ARRAY CONSTRUCTION ......................................
............... 39
4
2-D ARRAY EVALUATION ..........................................................................
44
4.1
IMPEDANCE MEASUREMENTS......................................
...................... 44
4.2
ACOUSTIC FIELD MEASUREMENTS............................
.......................
4.2.1
Focus at (2.7, 2.7, -4.9) mm : .............................................. .. ............. 47
4.2.2
Focus at (4, 4, -9) mm: .............................................
4.2.3 Focus at (4, 4, -2)mm ...................................................................................................
4.3
45
RADIATION FORCE MEASUREMENTS ......................................
50
.............. 52
.................... 56
4.4
5
6
4.3.1
Maximum Power Out:........................
............
................... 57
4.3.2
Array Efficiency .............................
.........
.........................................................
D ISCUSSION ............................................................
......... 58
59
CONCLUSIONS AND RECOMMENDATIONS FOR FUTURE WORK....... 61
5.1
CON CLU SIONS .............................................................................
............... 6 1
5.2
RECOMMENDATIONS FOR FUTURE WORK ............................................... 62
REFERENCES........................................................................................................
63
LIST OF FIGURES
Figure 1.1: (a) annular array, (b) sector-vortex array, (c) spherically curved array with
square elements, and (d) linear array. Figures adopted from respective papers...... 12
Figure 1.2: Simulated acoustic field pressure-squared plot from a 15x 15 element array
............ 14
with diagonal inter-element spacing of .......................................
Figure 1.3: Structure of a 1,3-piezocomposite: piezoelectric rods distributed in a polymer
matrix ............................................................................
....................................... 15
Figure 1.4: Generating a focus at 11 from the element E1 ......................................
17
Figure 1.5: Software to generate phases for each element in an arbitrarily-sized planar
18
...............................................
array .... ......................................................
Figure 2.1: Impedance magnitude versus frequency for four randomly selected array
elem ents ........................................................... ..................... ............................. 20
Figure 2.2: Phase versus frequency for four randomly selected array elements ........... 20
Figure 2.3: Lumped electrical model for a coax cable.................................
.......
22
Figure 2.4: Simple model of transducer element used in circuit simulations............... 23
Figure 2.5: Circuit model of 0.30m coax cable terminated with an array element at
1.2M H z ..............................................................................
..............................
23
Figure 2.6: (a) Plot of the simulated and measured impedances of one of the three
elements whose impedances matched well and (b) of one of the two elements whose
impedances were slightly shifted in frequency ............................................... 24
Figure 2.7: Circuit model of cable terminated with an array element at 1.2MHz with
.........
parameters derived from Z, and Z, measurements...........................
25
Figure 2.8: Plot comparing the measured impedances and impedances simulated using
cable model parameters derived from Z, and Z, measurements. ........................... 26
Figure 2.9: Amount of power delivered to an array element connected to (a) 4 different
lengths of coax cable (b) 4 different diameters of 0.91m coax cable .................... 28
Figure 2.10: Model for a non-ideal inductor................................
30
Figure 2.11: Schematic showing matching network added between amplifier and cable
input ....................
.............. .......... .....................
31
Figure 2.12: Matching network derived from a Smith chart. (a) Impedances plotted on
the chart and (b) Schematic of matching circuit ...............................................
34
Figure 2.13: (a) Power transferred to the array element and (b) total power output from
the amplifier versus amplifier peak output voltage using the two matching networks
......................................................................
..................................... . . . ......
36
Figure 2.14: (a) Power transferred to 4 different array elements and (b) total output from
corresponding amplifiers versus peak output voltage using the same matching
n etw ork ............................................................. ........ ................. .. ........................ 3 6
Figure 2.15: (a) Power transfer to the element and (b) total power output from the
amplifier versus peak output voltage for a matching network with component values
at the nominal values, 5% larger and 5% smaller than the nominal values .............. 37
Figure 3.1: Photograph of 1,3-piezocomposite transducer showing dimensions of the
elem ents .............................................................................................
...................... 39
Figure 3.2: Images showing method to connect coax cables to array elements. (a)
Schematic showing layered method and dimensions. (b) Photograph showing brass
pins inserted into the PCB. (c) Photograph of milled acrylic housing................... 41
Figure 3.3: (a) Photograph of the complete 2-D array including the matching networks.
(b) photograph of the array face with the 1,3-piezocomposite and ground wire
v isib le ......................................................................
........................
43
Figure 4.1 : Impedance plots for elements 1,7 and 43 over a frequency range of 500kHz2M H z .........................................................
...........................................................
45
Figure 4.2: Apparatus for measuring acoustic field generated by the 2D-Array........... 46
Figure 4.3: Focus positions relative to 2D-array. Elements 1, 7 and 8 are numbered in the
left plot ...................................................
47
Figure 4.4: XY (a) and YZ (b) acoustic field scans with the focus at (2.7, 2.7, -4.9)mm.48
Figure 4.5: XY (a) and YZ (b) acoustic field scans after amplitude correction for a focus
at (2.7, 2.7, -4.9)mm. ................................................................................................ 49
Figure 4.6: XY (a) and YZ (b) acoustic field scans with no correction for a focus at (4, 4,
-9)m m........................................ ........ .................. .. .................................. 50
Figure 4.7: XY (a) and YZ (b) acoustic field scans with amplitude correction for a focus
at (4, 4, -9)m m . ............................
.... .......... .....................
51
Figure 4.8: XY (a) and XZ (b) acoustic field scans with no correction for a focus at (4, 4,
-2)m m ..........................
..............
.... .........
.................... . 52
Figure 4.9: XY (a) and XZ (b) acoustic field scans with amplitude and phase correction
for a focus at (4, 4, -2)mm ........................................... ....................................... 54
Figure 4.10: XY (a) and XZ (b) acoustic field scans with amplitude correction at the
focus and phase correction for a focus at (4, 4, -2)mm.................................
55
Figure 4.11: (a) XY and (b) XZ plane scans for the matched 2-D array focused at (2.7,
2.7, -4 .9)m m ........................................................................................................... 56
Figure 4.12: Radiation force measurements setup ..................................................... 57
Figure 4.13: Plot of total power output versus amplifier output peak-to-peak amplitude.
The series marked with the dots were measurements taken after the maximum power
output was observed. For each point five measurements were taken and averaged;
only two measurements could be taken for the maximum (circled) ...................... 58
Figure 4.14: Plot of measured acoustic power versus estimated electrical power. The
circled point indicates the efficiency for which the maximum acoustic power output
w as recorded. ............................................................................................................ 59
LIST OF TABLES
Table 2.1: Comparison of currents in a cable-element pair using 50n and 752 coax
cab les ....................................... .....................
.... ........ .......
.... ................... 2 9
1
INTRODUCTION
1.1
Motivation
Focused ultrasound has been investigated as a tool for numerous medical therapy
applications. These include tumor ablation (Adams et al. 1996, Fry et. al 1970, Fry et. al
1986, Stewart et. al 2003), drug delivery (Unger et. al 1998, Yuh et. al 2005), gene
therapy (Greenleaf et. al 1998, Huber & Pfisterer 2000, Silcox et. al 2005) and opening of
the blood brain barrier (Hynynen et al 2001, Vykhodtseva, Hynynen & Damianou 1994).
Therapeutic ultrasound proves to be suitable for all these applications for a number of
reasons. First, at frequencies of 500kHz-10MHz, commonly used in therapeutic
applications, significant penetration depth in soft tissue (10cm at IMHz) is possible
(Hynynen & Lulu 1990). Next, its ability to be focused to a small spot size on the order
of its wavelength (1.5mm at 1MHz) makes it suitable for targeting specific tissue regions.
Third, ultrasound can produce two known effects in tissue: localized heating and
cavitation which involves the formation, oscillation and possible collapse of bubbles
(Apfel 1981, Eller & Flynn 1969, Hynynen 1991, Lele 1977, Fry et. al 1970). Phased
arrays have been an important tool in delivering the ultrasound for some of these
therapeutic applications and hence a significant amount of research has been dedicated to
advancing the devices.
Some of this research is highlighted later in this introduction.
Phased arrays enable precise deposition of the acoustic energy onto targeted regions by
electrically steering the focal beam produced by the array. This thesis focuses on the
development and evaluation of a planar 2-D phased array for therapeutic purposes with
an unprecedented inter-element spacing of the order of X/2 i.e. half the ultrasound
wavelength. An element-spacing of W2 eliminates grating lobes in the array's acoustic
field resulting in an unambiguous focus.
This is significant in the therapeutic
applications because grating lobes can result in undesirable heating of healthy tissue.
Furthermore, planar 2-D arrays are predicted to have important applications such as the
trans-esophageal ablation of cardiac tissue responsible for arrhythmias.
Focused ultrasound has been investigated as a feasible method for inducing
necrosis in cardiac tissue (Zimmer et. al 1995, Hynynen et. al 1997). It has thus been
identified as a potential modality for the treatment of cardiac arrhythmias which occur in
tissues that have irregular electric conduction resulting in abnormal contraction rhythms.
Arrhythmias can be eliminated by irreversibly ablating or damaging the responsible
cardiac tissue regions. Currently, catheter-based ablation systems are widely used to
target abnormally-conducting tissue regions (Haines & Nath 1995, Calkins 2001). In the
catheter-based ablation systems, RF energy (350 kHz-700 kHz) is delivered through the
tip of a catheter which may be guided to the targeted tissue by fluoroscopy. However,
these systems suffer from several problems.
development when delivering RF energy.
It is difficult to monitor the lesion
Visualization of lesion development is
important because catheter-based ablation results in inflammation of healthy tissue
peripheral to the target and this could progress to necrosis. Next, as RF energy causes
lesion formation, coagulum and desiccated tissue form an insulating barrier to further
delivery of RF energy. Furthermore, catheter placement and manipulation may result in
damage to valvular apparatus. Finally, patients are exposed to harmful radiation when
fluoroscopy is used to guide the catheter to the target tissue.
The motivation for this research into planar 2-D phased arrays comes in part from
wanting to investigate the use of focused ultrasound, delivered via a high-power
intracavitary ultrasound array, as an alternative to catheter-based ablation systems. By
delivering the energy for ablation via a source placed away from the heart, we will avoid
the catheter placement and guidance complications that may arise in catheter-based
ablation systems. Lesion development from the focused ultrasound can be accurately
guided and monitored by magnetic resonance imaging (MRI) thermometry which has
been investigated extensively for focused ultrasound surgery (McDannold et. al 1998,
McDannold et. al 2002). The ultrasound array can deliver acoustic energy to the cardiac
tissue from within the esophagus which provides a convenient acoustic window to the
heart. The 2-D phased-array transducer will be capable of producing a focus that can be
freely moved in all three dimensions in front of the array with the array stationary in
place. Initial simulations of this application have been carried out by Yin, Epstein &
Hynynen where a 2280-element 2-D array arranged in a 114x20 configuration was used
to generate multiple lesions in the cardiac tissue (Yin, Epstein & Hynynen 2004).
1.2
Array Theory/ Background
1.2.1 History
Several types of phased arrays for therapeutic applications have been investigated.
One of the earliest implementations of a therapeutic phased array was the annular array
by Do-Huu and Hartemann for the purpose of deep localized hyperthermia (Do-Huu &
Hartemann 1981). They created an array of 14 concentric annular elements and were
able to move the focus along the central axis normal to the array by varying the phase and
magnitude of each element (figure 1.1 a).
>
=Amplifier and phase shifter
sin(wot)
Figure 1.1: (a) annular array, (b) sector-vortex array, (c) spherically curved array with
square elements, and (d) linear array. Figures adopted from respective papers.
Cain and Umemura proposed using the annular ring phased array to generate annular foci
that can be scanned in diameter and focal length. The annular ring arrays produced a
significant secondary focus along the central axis and they further proposed a sectorvortex configuration to remedy the secondary focus problem (Cain & Umemura 1986).
The sector-vortex array, illustrated in figure 1.1b, consisted of a transducer disc divided
into sectors of equal size. Umemura and Cain soon after combined the sector-vortex and
annular configurations into a single phased array (Umemura & Cain 1989).
Research into the combination of the two configurations was further carried out
by Fjield and Hynynen who constructed a 13-ring, 4-sector array to demonstrate the
ability to vary the focus size and scan the focus along the central axis (Fjield & Hynynen
1997). Research has also been carried out on spherically curved phased arrays with
square elements in which parameters such as the number of elements and multiple focispacing were varied to investigate the largest necrosed tissue volumes possible with these
arrays (Fan & Hynynen 1996). An illustration of this type of array is shown in figure
1.1c.
Such an array with 256 6.5x6.5mm elements was later constructed out of 1,3-
piezocomposite transducer material (Daum & Hynynen 1999).
More recently a 500-
element hemispherical array was developed for trans-skull ultrasound surgery. The array
was also constructed of 1,3-piezocomposite material (Clement et. al 2005). Linear (I-D)
phased arrays for intracavitary use have also been researched extensively. The focus
from a linear phased array can be electrically scanned both radially and axially. Linear
phased arrays for transrectal prostatic ablation have been investigated (Sokka & Hynynen
2000, Hutchinson, Buchanan & Hynynen 1996). Sokka's array used an ultrasonic motor
to rotate the linear array to allow focusing in all three-dimensions.
1.2.2
Grating Lobes
A common problem with phased arrays is the generation of grating lobes. Grating
lobes are secondary foci generated when the spacing between adjacent elements in the
array is greater than V/2.
Such element-spacing results in spatial aliasing and the
subsequent generation of multiple foci. Figure 1.2 shows the simulated pressure-squared
contour plot of the acoustic field from a 15x 15 element array with diagonal inter-element
spacing of X focused off-center at the edge of the array. The grating lobe is indicated on
the plot. In therapeutic ultrasound applications, grating lobes are highly undesirable since
they could result in heating of healthy tissue that surrounds the targeted tissue.
_40+
30
E
E
20
N
10
0
-20
-10
0
10
20
30
40
50
y (mm)
Figure 1.2: Simulated acoustic field pressure-squared plot from a 15x15 element array
with diagonal inter-element spacing of X.
A variety of methods have been employed to reduce the grating lobe levels. For
example, using optimized random distribution of elements of two different widths in
linear arrays resulted in 30-45% smaller grating lobes than from using uniform width
elements (Hutchinson, Buchanan & Hynynen 1996).
In ultrasound imaging where
grating lobes are generated when the field is undersampled by an array with elementspacing greater than k/2, sparse arrays of randomly distributed elements of width V/2
have been used to reduce the grating lobe levels (Turnbull & Lum 1991). Grating lobes
are eliminated when the element-spacing is reduced to V/2 or less.
Therapeutic
ultrasound phased arrays with such small element spacing have not been constructed in
the past for a number of reasons. First, at frequencies used in therapeutic applications
(-0.5-10OMHz), the array elements' widths would be very small (-0.075-1.5mm).
To
treat tissue at large depths, arrays with large apertures and hundreds to thousands of
elements will be required. Next, constructing such arrays would have been extremely
challenging using monolithic blocks of piezoelectric material such as lead zirconate
titanate (PZT). Finally, economically-viable driving systems with hundreds to thousands
of amplifiers to drive these arrays were not available.
1.2.3
1,3-Piezocomposites
The limitations of constructing an array with such a large number of elements
have been overcome by using novel composite transducer material. One such composite
is the 1,3-piezocomposite that was developed at Penn State University (Gururaja et al.
1980, Gururaja et al. 1984, Gururaja et al. 1985a, Gururaja et al. 1985b, Gururaja et al.
1985c, Shrout, Bowen, & Schulze 1980). The 1,3-piezocomposite is a network of tiny
piezoelectric rods aligned parallel to each other and distributed in a polymer matrix. The
composite structure is illustrated in figure 1.3.
£bctrvde
P*"
pe..0cchic rod
Figure 1.3: Structure of a 1,3-piezocomposite: piezoelectric rods distributed in a
polymer matrix
These
composites
offer
several
advantages
over monolithic
blocks
of
piezoelectric material. First, only the electrode surface of the 1,3-piezocomposite needs
to be etched out in order to create an array. In contrast, to construct an array out of a PZT
block, the block would have to be diced up and then glued together with an adhesive that
is also an acoustic and electric insulator. Thus a lower cost in terms of time, labor and
machinery is incurred in producing an array using the 1,3-piezocomposite. Next, for
high-density arrays in which the element widths approach the thickness of the transducer,
the 1,3-piezocomposite material offers better efficiency than a block of PZT. In a high
density array with homogeneous cuboid elements the applied electrical energy goes into
exciting both the longitudinal and lateral modes thereby decreasing the efficiency of the
longitudinal excitation (Desilets, Fraser, & Kino 1978). Since the piezoelectric material
in the composites takes the form of thin "one-dimensional" rods, the longitudinal mode is
always dominant even when the element widths approach the thickness of the transducer.
The 1,3-piezocomposites can also be manufactured with good electrical properties (low
impedance and low loss) as well as good mechanical properties (low loss and acoustic
impedance) (Smith 1992). Low acoustic impedances that match water or tissue help in
the transfer of acoustic energy from the transducer to the coupled medium. Finally, the
1,3-piezocomposites can be molded into custom shapes and sizes by gentle heating.
The absence of cost-effective large-scale amplifier systems also hampered the
development of phased arrays with large number of elements. However, recently our lab
developed a system capable of driving thousands of elements independently (Sokka &
Hynynen 2003). The system called the Versatile Ultrasound Driving System (VUDS) is
capable of delivering -1.1W per element. Such a system makes driving high-density
phased arrays with V2 spacing feasible.
The benefits of 2-D phased arrays over the linear phased arrays are
straightforward. As mentioned earlier, the focus from a 2-D phased array can be scanned
in all 3-dimensions making it possible to generate lesions that span whole volumes of
tissue without having to move the array.
Linear arrays would have to be rotated to
generate the same effect. In addition, 2-D arrays are capable of generating a larger
variety of focal patterns thus enabling better targeting of tissue. High-density 2-D arrays
are also capable of high focal scanning resolution. Finally high-density arrays would
enable multiple foci generation to speed up treatment time for large volume of target
tissue.
1.2.4 Focusingof a PhasedArray
The ultrasound beam focus, or region of maximum acoustic power deposition,
occurs at the point where waves emitted by each element undergo constructive
interference. The location of the focus can thus be varied by altering the phase of the
electrical signal to each element of the phased array. As an example, consider a linear
array with two elements E, and Ez (Figure 1.4). E emits a wave
4
= sin(kz) and E2
emits A = sin(kz+ 0) . To generate a focus at a distance 11 normal to El, the two waves
must constructively interfere at the focus. The phase 0 can thus be obtained as follows:
4() =4 (12 )=1
kl + 0 =
2
2
A
2
2
where 12=
2 +d2
E2
T
d
~.
12
......
F
El
Foc us.....................
11
,*1
Figure 1.4: Generating a focus at 11 from the element EF
This can be extended to a larger number of elements and to 2 dimensions. A
stand-alone Matlab application was written to generate the phases for every element in an
arbitrarily-sized planar array. This application was integrated into the existing VUDS
software. The user-interface is shown in figure 1.5. The main software application to
control VUDS was developed by our lab and written in Visual Basic.
Figure 1.5: Software to generate phases for each element in an arbitrarily-sized planar
array.
2
2-D ARRAY DESIGN
2.1
Introduction
In designing a focused ultrasound therapeutic array, several criteria must be
considered. To begin, there are three basic requirements that an ultrasound array must
satisfy. First, the array as a whole must be capable of delivering sufficient amount of
acoustic power to ablate the targeted tissue. Next, the array must be MRI-compatible if
MRI is used to monitor the thermal effects of the ultrasound. Third, the array must be
water-proof. For 2-D arrays with V2 spacing between elements, the element dimensions
move into the sub-millimeter range and finding suitable methods to connect electrical
cables to these becomes a challenge. In addition, there are tradeoffs to selecting different
types of cables and these tradeoffs should be understood. Circuit models for the cables
provide good insight into these tradeoffs. For a given transducer, it is also worthwhile to
examine its impedance spectrum to determine the driving frequency which will result in
most efficient electrical power to acoustic power transformation.
Impedance matching
circuits may also be required to increase the amount of electrical power delivered to the
array elements. It may not be practical to use bulky hand-wound inductors for arrays in
which the power per element is not large.
Finally, the specifications such as the
maximum current output of the system driving the array must be considered.
2.2
Element Impedance
The electrical characteristics of the elements provide good insight into the design
of the array. The impedance spectra of the elements show the optimum frequency at
which the elements can be driven. Impedance measurements are also used in simulations
that help optimize the electrical power transferred to the array elements.
Impedance measurements of four randomly-selected elements of the 2-D array
were taken using an impedance analyzer (Hewlett-Packard HP4195A). The impedance
was measured with the ground side of the array dipped in water. Figure 2.1 is a plot of
the impedance magnitude of the four elements versus frequency while figure 2.2 is a plot
of the phase of the same elements versus frequency.
Al 4
0
1
2
5
3
4
Frequency
(Hz)
7
6
x1o6
Figure 2.1: Impedance magnitude versus frequency for four randomly selected array
elements
U)
a)
a)
(D)
-C
a.-
0
1
2
3
Frequency
(Hz)
4
5
6
7
x 10
Figure 2.2: Phase versus frequency for four randomly selected array elements
The two plots show clearly the resonance frequency of about 1.2MHz.
As
discussed earlier, because of the composite structure of the transducer (thin piezoelectric
rods distributed within an acoustically non-conductive polymer), only one resonance
frequency is observed corresponding to the longitudinal excitation mode of the
piezoelectric rods. The peaks in the phase plots at approximately 3.7MHz and 6MHz
represent the third and fifth harmonic frequencies respectively. The resonance frequency
is the most efficient frequency to drive the array elements. At this frequency, the forward
stress wave and wave reflected off the air-backed side of the array element are in phase
and a larger effective stress wave is generated at the face of the element (Hynynen 1990).
The relatively high impedance of the order of 104f
is expected since the
capacitance of the array element, C decreases as its electrode area becomes smaller. Thus
its impedance, which is inversely proportional to C, increases. The array element can be
modeled as a parallel plate capacitor.
eA
t
where 6 is the permittivity of the composite material, A is the area of the electrode
surface and t is the thickness of the composite.
2.3
Amplifier Specifications
A multi-channel broadband amplifier system was developed at our lab to drive
transducer arrays (Sokka 2003). Each channel is capable of sourcing up to 150mA RMS
of current at a peak voltage of 11V. The maximum power deliverable per channel, Pmax,
is thus:
mx =
2.4
asPk = 1.17W
Circuit Models
Transducers used in conjunction with MRI are usually connected to the amplifier
system via coax cables of several meters in length. The lengthy coax cables allow the
amplifier system to be placed in a separate room from the magnet for MRI guided
applications.
The electrical characteristics of such transducers are significantly affected by the
electrical properties of the coax cables. Therefore, to properly analyze the power transfer
to the array elements, the transmission line effects of the coax cable must be included in
the circuit analysis. The coaxial cable can be represented by a lumped or distributed
model. A distributed model includes both spatial dimensions and time. The lumped
model, in which variables only depend on time, is sufficient for frequencies small enough
such that the length of the cable is much shorter than the wavelength of the AC signal
(Clayton 1994). At a frequency of 1MHz, the wavelength of the AC signal is 300m,
much longer than typical coax cable lengths of 3-4m.
R
L
Figure 2.3: Lumped electrical model for a coax cable
In the lumped model (figure 2.3), R is the DC resistance plus the resistance due to
the skin effect while G is the shunt resistance. L is the inductance and C the capacitance
of the coaxial cable respectively; L and C depend on the radii of the outer and inner
conductors and the properties of the dielectric insulator between the two conductors
(Alexander et. al 2000).
In order to carry out circuit simulations of the power transfer to the array
elements, an element was represented by a simple equivalent model of a resistor and
capacitor in parallel (figure 2.4). While this simple model does not give any information
about the efficiency of the element (amount of electrical power converted to acoustic
power), it does help optimize the amount of electrical power delivered to the array
elements. Other researchers have described elaborate electrical models for transducers
that take into account mechanical and electrical losses (Prokic 2004). However, it is
easier to determine the power efficiency of the 2-D array experimentally via radiation
force measurements (Stewart 1982).
Figure 2.4: Simple model of transducer element used in circuit simulations
The R, L, C and G parameters for the coax cable model can usually be obtained
from the manufacturer. To check on the accuracy of the model, measured and simulated
impedances of 0.30m-long 34AWG coax cables (Precision Interconnect, OR) connected
to five different array elements were compared. Figure 2.5 shows the model of the cable
terminated with one of the array elements. The values of the cable parameters shown are
for a frequency of 1.2MHz. Zce is the impedance looking into the cable
R (0.5792)
1
L (114.7nH)
•
2
CT (0.427pF)
IGI (0.158uS)
C (30pF
(7
RT (32 7k)
82
Zce = 572.8 - 428 = 4320e- .3)
Figure 2.5: Circuit model of 0.30m coax cable terminated with an array element at
1.2MHz
The simulated and measured impedances for three of the five elements matched
well.
Figure 2.6a is a plot of the impedances for one of the three elements.
The
simulated and measured impedances for the other two elements were slightly shifted in
frequency. Figure 6b is a plot of the impedances of one of these two elements.
5000,
;:: :
4000
tiement I
3000
'
1.05
1
S1.1
1.15
1.2
1.25
1.3
1.35
1.4
100
1.5
i
1.45
x6
Frequency (Hz)
x
10
(a)
-80
-90
rA
1
1.05
1.1
1.15
1.2
1.25
1.3
Frequency (Hz)
1.35
1.4
1.45
-100
1.5
x106
Figure 2.6: (a) Plot of the simulated and measured impedances of one of the three
elements whose impedances matched well and (b) of one of the two elements whose
impedances were slightly shifted in frequency.
When the cable parameters are not readily available from the manufacturer,
parameters can be estimated from impedance measurements of a known length of the
cable.
While it is not possible to measure the parameters individually, they can be
derived from two cable impedances: the impedances of the cable with its ends shorted
(Zs) and open (Zo) respectively (Cheng 1989, Griffith et. al 2000).
Z c = ZYZ 0
Y=
tanh-'
IR
Z c is the cable characteristic impedance
zo
y is the propagation constant; 1 is the length of the cable
ZcZc--- R+ jcoL ~ (0 is the frequency in rad/sec
7
ZC=GC
G+ jcoC
To test the cable model using R, L, C and G parameters derived from the equations
above, Zs and Zo were measured for the 0.30m 34AWG coax cable and the parameters
calculated over the 1MHz-1.5MHz frequency range. Figure 2.7 shows the model for a
frequency of 1.2MHz.
The capacitance, C, obtained is about 20pF higher than that
quoted by the manufacturer.
R (0.6141)
L (178.3nH)
T (0.427pF)
Zce = 212 - 2568i
Figure 2.7: Circuit model of cable terminated with an array element at 1.2MHz with
parameters derived from Zs and Zo measurements
Figure 2.8 shows a plot of the measured impedances and impedances simulated using the
derived parameters for one of the elements over a frequency range of IMHz-1.5MHz.
The simulated impedance does not match the measured value as well and has a lower
magnitude because of the higher derived cable capacitance.
Frequency (Hz)
x
Figure 2.8: Plot comparing the measured impedances and impedances simulated using
cable model parameters derived from Zs and Zo measurements.
2.5
Power Transfer and Cable Selection
The maximum amount of power delivered to an array element connected to 0.30m
of the 34AWG coax cable can be determined simply from the impedance of the cable and
element (Zce). The power, Pout output from the amplifier is given by:
PO =V I cos(4 )
Given Z, = 4030e'(Po,, =
11
11
,2 40302
842o,
cos(-84.20 )
Pout =1.51mW
The power delivered to the array element is less than Pout since some of the power
delivered by the amplifier is dissipated in the cable resistance R. R increases as the
length of the cable increases and as the diameter of the inner-conductor decreases;
therefore, as R increases the fraction of power delivered from the amplifier to the array
element decreases.
Figure 2.9a shows the results of a simulation to determine the
maximum amount of power delivered to an array element connected to increasing lengths
(0.30m, 0.91m, 1.52m and 3.04m) of 34AWG coax cable. Figure 2.9b shows a similar
simulation using 0.91m of coax cable with decreasing inner-conductor diameters
(34AWG, 38AWG, 40AWG and 42AWG) (Precision Interconnect, OR).
4 001
A
E
3
a,
a,
-E- Power to Element
80 $
-e- Power from Amplifier
0
-+- % to Array Element
E
(D
a-
a.
60
2
0
kA*
C-
40)
0.30m
0.91m
1.52m
Length of coax cable
(a)
3.04m
40
1.0
I .O
"
"-E
a0
Power to Element
-8-
E
-e- Power from Amplifier
-+- % to Array Element
1.7
95o
-o
E,
E
0)
n-
903o
1.6
1.
0
ci
C.,
O
1.5
34AWG
I
O]
I
O
I+
38AWG
40AWG
Coax cable size
42AWG
(b)
Figure 2.9: Amount of power delivered to an array element connected to (a) 4
different lengths of coax cable (b) 4 different diameters of 0.91 m coax cable
It is estimated that each element can handle approximately 19mW of electrical
power. However, in all the above cases, the maximum amount of power delivered to the
array element is only about 1.5mW. This is very small and not sufficient for therapeutic
applications.
Only a small amount of power is delivered to the element because the
impedance of the cable-element pair is large and very capacitive. This in turn is because
the array element impedance is much higher than that of the cable capacitance that
appears in parallel to the element. Thus, most of the current from the amplifier is shunted
through the cable capacitance instead of the array element.
For the 0.91m cable at
1.2MHz, the impedance magnitude of the cable capacitance is 14739
impedance magnitude of the element is 30.92kM.
while the
Thus, only about 5% of the current
from the amplifier is delivered to the element.
The current delivered to the array element can be increased by using a lower
capacitance cable and by increasing the total output current from the amplifier. If a lower
capacitance cable is used, a larger portion of the total current flows to the element. Since
the lower capacitance results in a higher impedance (Zce) seen at the input of the cable,
the total current sourced from the amplifier must also be increased to increase the total
current delivered to the array element. Table 2.1 compares the current in a cable-element
pair using 0.91m of 50n and 7592 42AWG coax cables.
The cable capacitances are
90.6pF and 49.5pF respectively. If the 502 and 75K2 cable-element pairs were driven
with the same total current, we would expect to have a larger amount of power delivered
to the element with the 75n2 cable attached.
Table 2.1: Comparison of currents in a cable-element pair using 50•2 and 75K2 coax
cables
To increase the total current output by the amplifier, the impedance seen by the
amplifier output must be decreased by adding an impedance matching network of
inductors and capacitors between the amplifier output and cable.
Traditionally, the
matching inductors have been constructed by winding a length of wire around a toroid
core. These inductors offer several benefits. Precise inductance values can be achieved
by varying the number of turns and the turn-spacing. Furthermore, these inductors have
low resistive loss and are able to handle large currents, making them suitable for highpower applications.
However, winding each inductor manually proves to be a time-
consuming and arduous task. In addition, the inductors tend to be very bulky. A fourchannel matching card for our older amplifier system containing four of the inductors
measures approximately 6.5" x 4.5" x 1"; the matching cards require almost the same
amount of rack-space as the amplifiers' analog and digital hardware. These drawbacks
make the inductors unsuitable for matching 2-D phased arrays which will have hundreds
to thousands of elements.
As an alternative, we propose using surface-mount chip
inductors for matching of the phased array. The biggest benefits of using these inductors
are smaller matching networks and faster matching time. A 100uH chip inductor is
available in a package as small as 2.5mmx3.2mm (Murata LQH32M). The properties of
these chip-inductors are less ideal than the toroid inductors. The chip inductors suffer
from a lower Q, which is the ratio of the power stored to energy dissipated in an inductor.
The Q-value depends on the inductance, frequency and resistance of the inductor.
Q=
co L
, R, is the series resistance
The Q-value of an inductor is usually quoted at a particular frequency hence the
equivalent series resistance, Rs at a particular frequency is proportional to the inductance
and inversely proportional to the Q-value. In addition, the chip-inductors have low selfresonance frequencies (SRF).
Beyond the self-resonance frequency, inductor devices
behave more like capacitors and their reactance drops with increasing frequency. Finally,
chip inductors have a lower current rating. As an example, at 0.796MHz the Q-value for
the 100uH chip inductor is 40. Thus its series resistance, Rs , 12.51.
The SRF for this
inductor is about 8MHz and its current rating is 80mA. The lower current rating for the
chip inductors is acceptable since the power delivered to each element in a high density
array is small.
To take these non-ideal characteristics into account in simulations, the inductor
can be modeled with three ideal elements (figure 2.10).
C
L
1 yV-
R
2
Figure 2.10: Model for a non-ideal inductor.
By using the chip-inductors in the matching networks, we trade off increased
power dissipation in the inductors for smaller size and faster matching time.
Several different configurations of matching networks can be employed to reduce
the impedance between the amplifier and the cable-element pair. Two configurations to
match elements connected to 0.91m of 34AWG cable are described here. The first,
schematized in figure 2.11, uses an inductor, Lmi, to cancel the large negative reactance
from the cable capacitance.
Figure 2.11: Schematic showing matching network added between amplifier and cable
input
31
L,= imag{Zce}
0)
The resistive loss in the inductor Lm, is given by:
, QLm, is the inductor Q
RLml =
QLml
An impedance transformer (L,, 2 , Cm) is then used to step up the resistance Rcez to a larger
value Rin (Lee 2003). The derivation of the values for Lm2 and Cm proceeds as follows:
R, = Rce2
LM2
LmLm
2O
Q=
2+1)
(1), where Rc2 = real{Zc,+ RLml and Q is the imp. transformer Q
(2)
+ 0Lm2
substituting (2) in (1):
R = Rce +
2
+1
Rearranging gives us a quadratic function of Lm2
(~
22
___
0+2
2
QLm2
LP= (
co21I
CnO2LP
Lm 2
2
( 2RceO R,, .oLm( + R
Qm2
QLm2
2
:
_,RnRe) =0
Ln2) , where Lp is the equivalent inductance parallel to C,,
The calculations above ignore the parasitic capacitance in the inductors due to
their finite SRF. In figure 2.11, RLml, C6, RLm2 and C5 are calculated assuming inductor
LmI has a Q of 65 and a SRF of 7MHz while Lm2 has a Q of 50 and a SRF of 12MHz.
Matching networks can also be derived from the Smith chart.
To obtain a
matching network, the two impedances Zce and Ri, are normalized and plotted on the
Smith chart. A path is then traced between the two normalized impedances. The path
consists of arcs, each one of which results from adding a reactive element to the matching
network.
In the second network, matching was achieved using three reactive
components. The smith chart with the paths traced out is shown in figure 2.12a* while
the corresponding circuit is shown in figure 2.12b. The impedance transformation from
Zce to Z2 is achieved by adding the series inductor Lml. Lm2 is then added in parallel to
obtain Z 3 and finally the capacitor Cm is placed in series to cancel the positive reactance
in Z3 .
* Plot using Microsoft Excel tool from RF Cafr:
http://www.rfcafe.com/business/software/smith_chartfor
excel/smithchart for excel.htm
(b)
Figure 2.12: Matching network derived from a Smith chart. (a) Impedances plotted on
the chart and (b) Schematic of matching circuit
34
In both matching configurations, the impedances Rin, Re, Z2, and Z3 are labeled as
the ideal values i.e. obtained if ideal reactive components were used to match the
impedances. In practice, these values will depart from the ideal due to the finite SRF and
resistive losses in the inductors. In simulating the above two matching configurations, Rin
of 59492 and 755M are obtained respectively. Also, the Ri,'s are not real and have phases
of 25.30 and 6.70 respectively.
The resulting matching inductor and capacitor values can be varied slightly so that
they correspond to readily-available standard values. Using standard inductor values
(27uH, 180uH in the first matching network and 47uH, 120uH in the second network) and
capacitor values (680pF for the first and 150pF for the second matching network), Rin of
482.7L2 and 51792 result respectively. In addition, the Rin have phases of 210 and -18.720
respectively. Figure 2.13 is a plot of the simulated power delivered to the array element
versus the input voltage swept from 0 to 1lV-peak for both of the matching
configurations using these standard-valued matching components.
Also shown is the
total power output from the amplifier.
Since the elements' impedances differ and the same matching network is applied
to every element, the power delivered to each element is expected to differ as is the total
power output from each corresponding amplifier.
Power transfer simulations were
carried out for 4 different elements with the same matching configuration applied to each
one. The results are shown in figure 2.14.
a
E
a)
0~
Amplifier Peak Output V (V)
(a)
Amplifier Peak Output V (V)
(b)
Figure 2.13: (a) Power transferred to the array element and (b) total power output from
the amplifier versus amplifier peak output voltage using the two matching networks
Amplifier Peak Output V (V)
(a)
Amplifier Peak Output V (V)
(b)
Figure 2.14: (a) Power transferred to 4 different array elements and (b) total output
from corresponding amplifiers versus peak output voltage using the same matching
network
In practice, the inductor and capacitor values with a quoted nominal value may
depart from this value by up to a quoted tolerance. Therefore, the power delivered to an
element can also vary because of this variation in matching components' values. To
investigate the effect of the variation in inductor and capacitor values from their nominal
values, a power transfer simulation was carried out using component values at their
nominal values, 5% larger and 5% smaller than the nominal. The results are shown in
figure 2.15. The variation in component values results in a larger variation in power
transfer and thus using components with the lowest tolerances is important.
nr~n
2OU
240
220
200
180
160
140
120
100
80
60
40
20
0
E
E
a)
i:ii
0
a)
0
CL
Amplifier Peak Output V (V)
(a)
Amplifier Peak Output V (V)
(b)
Figure 2.15: (a) Power transfer to the element and (b) total power output from the
amplifier versus peak output voltage for a matching network with component values at
the nominal values, 5% larger and 5% smaller than the nominal values.
From the simulations, it is evident that the amount of power delivered to the
elements will differ from one element to another due to the differences in element
impedances and the deviation in matching component values from their nominal values.
Thus, we expect the acoustic power delivered by each element will differ even when the
elements are driven by the same signal. The effects of the varying element impedances
and matching component values can be mitigated by calibrating the array in a scan tank
so that all the elements deliver the same acoustic power. The calibrating procedure
involves using a needle hydrophone to measure the acoustic pressure emitted by each
element and bringing the pressures to uniformity by correcting the corresponding
amplifier's output amplitude and phase. The calibrating procedure is explored further in
chapter 4.
3
2-D ARRAY CONSTRUCTION
A prototype 7x7 element array was constructed to demonstrate the capabilities of
2-D phased arrays.
One side of a 20.4mm x 20.4mm x 1.57mm 1,3-piezocomposite
transducer piece was etched into a 25x25 element grid. A K&S 780 dicing saw (Kulicke
& Soffa, Willow Grove, PA) fitted with a 3 mils (0.0762mm) diamond blade
(Thermocarbon Inc, Casselberry, FL) was used to etch the transducer in-house.
The
center-to-center spacing between adjacent elements is 30mils (0.762mm) while the kerf
size is 3mils (0.0762mm).
V/2 at 1MHz is approximately 0.75mm.
Figure 3.1, a
photograph of a small region of the etched transducer, shows these dimensions.
Figure 3.1: Photograph of 1,3-piezocomposite transducer showing dimensions of the
elements
A significant part of the design effort required finding a suitable method to
connect coax cables to the sub-millimeter elements. Soldering the cables to the elements
proved to be futile since the high temperatures required for the solder peeled off the gold
electrode and damaged the composite material. It also proved difficult to apply solder
uniformly without shorting out elements. An approach using layers of printed circuit
boards (PCB) and small pins was devised to connect 0.91m lengths of 34AWG coax
cables to 49 of the array elements. The layered approach allowed soldering of the coax
cables to a PCB first without exposing the array to the high solder temperature.
A
schematic of this design is shown in figure 3.2a. Small gold-plated brass pins (Mill-Max,
Oyster Bay, NY) were inserted into another PCB (PCBI) and aligned over the array. Pins
were used to make the electrical contact area on the elements as small as possible and to
ensure that the elements have some air-backing. Small contact area is assured since the
cylindrical stem of each pin is 12mils (0.3048mm) in diameter and the pin tip is rounded.
Each pin is 50mils (1.27mm) long while the PCB is 31mils (0.787mm) thick.
A
photograph of a magnified region of the PCB with the pins inserted is shown in figure
3.2b. Next, the two PCB layers were aligned and held together in an acrylic housing
(figure 3.2c) milled in-house. To ensure good electrical contact between the pins and
array elements, globules of an electrically conductive silver-epoxy adhesive (Mereco,
West Warwick, RI) were placed on the pin tips before connecting these to the array
elements. The adhesive was also applied onto the pin-heads to establish good electrical
contact between the pin heads and PCB 2. The adhesive was cured over 24 hours at roomtemperature. Finally, the coax cables' ground shields were soldered onto a ground-plane
PCB; copper tape was used to connect the array ground electrode to the ground-plane
PCB.
34AWG
To Amplifiers
-
coax
ass pin
I
PCB2PCBI"
,----
•2mils
I--------------
gnd
PCB
I
. .... ... a=0.203mm
{d
b = 0.787mm
C= l.L2mm
I
0.57mm
d = 057mm
yiiu tIdLcLIouU
gnd wire
_-2ml
etched electrode
e -28mm
(a)
(b)
Figure 3.2: Images showing method to connect coax cables to array elements. (a)
Schematic showing layered method and dimensions. (b) Photograph showing brass pins
inserted into the PCB. (c) Photograph of milled acrylic housing.
The thickness of the first two PCB layers, pins and array is only -3.6mm.
The
34AWG coax center conductor was just narrow enough to fit through the ground PCB
vias.
The ground PCB could not be moved closer than approximately 25.4mm from
PCB 2 because the center conductors could not be squeezed through the vias without
snapping off of PCB 2. With narrower coax cables, the overall thickness of the layered
design can be decreased from the current thickness of 28.7mm to about 5mm.
To make the array water-proof, the transducer was affixed onto the acrylic
housing using VI-SIL V-1022 silicone adhesive (Rhodia, Cedex, France). The 0.91m
coax cables were housed in silicone rubber tubing (Ipotec, Exeter, NH) and the tubing
was sealed onto the acrylic housing using an adhesive-lined heat-shrink tubing (3M,
Austin, TX), VI-SIL adhesive and RTV silicone sealant (GE Silicones, Wilton, CT).
Finally, a rubber tube with 1.5mm I.D. was positioned in the acrylic housing in order to
circulate air in the transducer via an external aquarium pump. The air pump helps push
any moisture out of the transducer. If left to build-up in the transducer, the moisture may
condense when the transducer is placed in cold water resulting in electrical shorts.
Acoustic field scans were taken with the complete 2-D array before the matching network
was added.
The matching network used readily available through-hole inductors with nominal
values of 180p.H (7MHz SRF and Q of 65) and 2 7 p.H (12MHz SRF and Q of 50) (J.W.
Miller Magnetics, Gardena, CA). The matching capacitors were ceramic and 680pF
nominal value. The inductors and capacitors had a tolerance of 5%. All the matching
components for the 49 elements were soldered onto a generic prototype board of size
3.5"x3".
A photograph of the complete phased array system with the matching network is
shown in figure 3.3a. Figure 3.3b shows the array face in more detail with the 1,3piezocomposite, PCB, and grounding wire visible.
(b)
Figure 3.3: (a) Photograph of the complete 2-D array including the matching networks.
(b) photograph of the array face with the 1,3-piezocomposite and ground wire visible
4
2-D ARRAY EVALUATION
Several measurements were made on the completed 2-D array to characterize it
and demonstrate its focusing and 3-D beam-steering abilities. Impedance measurements
were taken for all the elements of the array to evaluate the integrity of the electrical
connections and determine the best frequency to drive the array. Next, acoustic field
measurements were taken in a scan tank to demonstrate the focusing ability of the array.
Finally, radiation-force measurements were taken with the matched 2-D array to
determine the power efficiency of the array and demonstrate the improvement in power
output from the array.
4.1
Impedance Measurements
Impedance measurements were taken for all the elements in the unmatched array.
The impedance measurements provided information about the presence of electrical
shorts between elements and the best frequency to drive the array for acoustic field
measurements. Electrical shorts between elements were indicated by impedances which
were a common fraction of the predicted impedance of one cable-element pair. Electrical
shorts were found for 3 pairs of elements (elements 23-24, 32-39 and 37-38). To avoid
shorting out the amplifiers connected to these elements, only one amplifier was
connected to each pair of the shorted elements. The impedance measurements over
frequency differed from those predicted in the simulations. The measured impedances
were more capacitive and hence had more negative phase. Figure 4.1 is a plot of the
measured impedances of array elements 1, 7 and 43. All elements had phase greater than
-870"
4000
I
-
Element
rd,
impedance
p1
hase
-88
2000
-90
0
0.5
0.75
1.25
1
1.5
1.75
-92
2
Y -L
4UUU
Element7
I
E
S2000
.I
v
IIe
-90
10
8
•SQ
0.5
0.75
1.25
1
1.5
1.75
2
-00
Element'43
A
2000
lr
'i
'W'
II
I
-90
I,
0
0.5
2.)
0.75
1
1.25
frequency
1.5
1.75
2
x 10e
Figure 4.1: Impedance plots for elements 1,7 and 43 over a frequency range of
500kHz-2MHz
From the impedance plots, the maximum phase occurred at about 1.1MHz. The
unmatched array was thus driven at this frequency to obtain the best acoustic output for
the acoustic field measurements.
4.2
Acoustic Field Measurements
Acoustic field measurements, carried out in a scan tank, are useful for evaluating
the 2-D array's ability to generate a focus at various positions in the sonicated volume in
front of the array. In the scan tank setup, depicted in figure 4.2, the array is locked in
position in a tank filled with degassed water. A 0.2mm needle hydrophone (Precision
Acoustics, Dorcet, UK) is used to measure the relative acoustic pressure at points in the
sonicated volume; the hydrophone generates an electrical signal whose amplitude is
proportional to the acoustic pressure.
The AC signal is amplified and read using an
oscilloscope (Tektronix TDS 3012, Beaverton, OR). The hydrophone is attached to a
positioning system (Velmex, Bloomfield, NY) and can be moved in all three dimensions
with a spatial resolution of 3 tm. A PC with software written in-lab is used to control the
positioning system via the serial port and capture data from the oscilloscope via the GPIB
port. Finally, the VUDS 100-channel amplifier system is used to drive each of the 2Darray elements independently.
The software, written in BASIC captures the time
waveform and amplitude data from the oscilloscope and stores these on the hard-disk. A
C program utilizing the GrWin* graphics library was written to interface with the original
BASIC software to generate contour plots of the acoustic field at the end of each scan.
With this apparatus, we are thus able to generate acoustic field scans in any plane
perpendicular or parallel to the 2D-array surface.
n 2mm Nea•nrla
hydrophone
system
1
Issed
ter
m
...
....
Ampliifier System
PC 2
aQp
,,.,iIuN
.FIJCu
Figure 4.2: Apparatus for measuring acoustic field generated by the 2D-Array
To demonstrate the ability to focus the 2-D array in all 3 dimensions, acoustic field scans
were taken at three focus positions: a) at the center of the array and displaced at -4.9mm
in the radial direction i.e. at (2.7, 2.7, -4.9)mm in the Cartesian coordinates, b) displaced
*http://spdg1.sci.shizuoka.ac.jp/grwinlib/english/
by 1.3mm from the center of the array and at 9mm in the radial direction i.e. at (4, 4, 9)mm, and c) displaced by 1.3mm from the center of the array and at 2mm in the radial
direction i.e. at (4, 4, -2)mm. These focus points are shown relative to the array in the
two plots in figure 4.3.
0
1
x (mm)
2
3
-0
-10
4
5
0
1
E
E
2
E
E
N
3
4
5
y
I n
Focusa
I
I
c,,,,,II.II,,
I
I
r
^
O
""~I
X
I IkI)
Focus c
Figure 4.3: Focus positions relative to 2D-array. Elements 1, 7 and 8 are numbered in
the left plot
For each focus, scans were taken for the three orthogonal planes centered at the
focus. The plots presented here are normalized pressure squared plots showing the field
in two of the planes.
4.2.1 Focus at (2.7,2.7, -4.9) mm:
Figure 4.4a shows the normalized pressure squared plots for the XY plane at the
focus while figure 4.4b shows the normalized pressure squared plots for the YZ plane at
the focus. 3-D and contour plots are shown for both planes. The scans were 10x10mm
with a step size of 0.5mm. In all the contour plots presented, contours represent 10%100% of the maximum intensity with increments of 10%.
,r
0o
6
6
4
2
x2 (mm) 4
0
0
-2
-2
x (mm)
(a)
-
-
-
-
-
-----
0.1.-
611
'
'
'
'
'
"
'
'
0 -1 -2 -3 -4 -5 -6 -7 -8 -9-10-11
z (mm)
(b)
Figure 4.4: XY (a) and YZ (b) acoustic field scans with the focus at (2.7, 2.7, -4.9)mm.
A slightly smaller focus was achieved when amplitude correction was carried out.
As discussed earlier, amplitude and phase correction may be necessary because of the
variation in power emitted by different elements due to the differences in the elements'
impedances and variations in the matching components values in the case of the matched
array. To perform amplitude correction, the hydrophone was placed at the focus and each
of the 49 elements was driven with the others turned off with a constant amplitude signal.
48
The amplitude of the AC signal from the hydrophone was recorded for each of the
elements. The resulting amplitudes were inverted and normalized to 1. Each element
was then driven with its corresponding corrected amplitude. Figures 4.5a and 4.5b show
the XY and YZ plane scans after amplitude correction was carried out.
,1'
I
I..
(;;~)
0
·
2
·
·
--; -;------;--··-·--·-:
r
~C3~
4
x (mm)
·
·
·
·
·
:--
"
__I
'·- ;-_:p~..~......
; ;·;;
- · -;'-- ----
;;·
0l
·
·
·
·
·
·
·
·
·
·
0 -1 -2 -3 -4 -5 -6 -7 -8 -9-10-11
z (mm)
(b)
Figure 4.5: XY (a) and YZ (b) acoustic field scans after amplitude correction for a
focus at (2.7, 2.7, -4.9)mm.
4.2.2
Focus at (4, 4, -9) mm:
Figures 4.6a and 4.6b show the normalized pressure squared plots for the XY and
YZ planes with no amplitude or phase correction applied. As expected, the focus appears
larger and longer because it occurs further away from the 2-D array. Also, the focal
beam appears tilted.
-
,c~
I
\
II
2
2
00
4
4
x(mm)
6
6
8
8
x (mm)
k
1d1
-
0 -1 -2 -3 -4 -5 -6 -7 -8 -9-10-11
z (mm)
Figure 4.6: XY (a) and YZ (b) acoustic field scans with no correction for a focus at (4,
4, -9)mm.
Amplitude correction was then applied. The array elements were driven with the same
corrected amplitudes derived at the previous focus location. The XY and XZ acoustic
field scans are shown in figures 4.7a and 4.7b respectively.
-- I
(D
CD
C.
cj)
CO
C,
a)
z
0
.y'
\,"I,,,
x IIIIril)
2
2
4
4
x(mm)
6
6
8
x (mm)
.. . . . . . . .
0.1
I
o -1 -2 -3 -4 -5 -6 -7 -8 -9-10-11
z (mm)
(b)
Figure 4.7: XY (a) and YZ (b) acoustic field scans with amplitude correction for a
focus at (4, 4, -9)mm.
4.2.3 Focus at (4, 4, -2)mm
Figures 4.8a and 4.8b show the normalized pressure squared plots for the XY and
YX planes with no amplitude or phase correction applied. The focus is smallest here
because its is closest to the array surface.
--
I
--I
-
I
n
I
I
I
I
0
2
4
6
8
6
8
x (mm)
(a)
=
'II
-I
-1ti
0
z
0
2
4
x (mm)
Figure 4.8: XY (a) and XZ (b) acoustic field scans with no correction for a focus at (4,
4, -2)mm
Scans with amplitude correction applied looked similar to those with no
correction. To determine whether better foci were possible, scans were taken with both
amplitude and phase correction applied. Phase correction was carried out in a similar
manner to amplitude correction. The hydrophone was placed at the focus and its AC
signal response was read with only one of the 49 elements turned on at a time. The
difference in phase between the hydrophone response for each element and the first
element which served as a reference was recorded. This difference was then added or
subtracted to each element's driving signal so that the all the elements were in-phase at
the focus. The XY and YZ acoustic field scans taken after employing amplitude and
phase correction are shown in figures 4.9a and 4.9b respectively. A large secondary peak
(-30% of the focal peak) is observed in the XY scan.
--
.,
I
I
I
•8
6
CU
C,
C)
4
0'
U)
2
0
0
0
2
4
x (mm)
(a)
6
8
Co
CO
E
a.
N
N
0
z
-1-
0
2
4
x (mm)
6
8
(b)
Figure 4.9: XY (a) and XZ (b) acoustic field scans with amplitude and phase
correction for a focus at (4, 4, -2)mm
Amplitude correction was also attempted at this focus location.
Because the
amplitude correction was carried out very close to the array surface, there was a concern
that the hydrophone would not detect the acoustic signal from the furthest elements
because of the small angle between those elements and the hydrophone. A 0.5mm
hydrophone was used instead for this purpose.
The 0.5mm hydrophone has a larger
sensor area and provides a stronger response than the 0.2mm hydrophone. XY and XZ
scans with the phase correction and amplitude correction performed at (4, 4, 2)mm were
also performed. The results, presented in figures 4.10a and 4.10b, appeared similar to
those in figure 4.9 except that a smaller secondary peak (-10% of focal peak) was
recorded.
I
I
8
-0
6
C,
0.5
C,
4 E6
E
E
2
0
o
z
0
0
2
4
x (mm)
6
8
(a)
(a)
CO
"3
Cu
C/)
CO)
N
N
a
CO
z
Z
-2
0
2
4
6
mm11
A\IIIIII1
vI.---
(b)
Figure 4.10: XY (a) and XZ (b) acoustic field scans with amplitude correction at the
focus and phase correction for a focus at (4, 4, -2)mm.
Finally, the matching networks were added and the array was focused at the
center and 4.9mm away from the array plane, with amplitude and phase re-corrected.
The array was driven at 1.2MHz since the matching networks were tuned at this
frequency. The acoustic field scans for the matched 2-D array focused at (2.7, 2.7, 4.9)mm are shown in figures 4.1 la and 4.11lb. A step size of 0.4mm was used.
--
x (mm)
1
0.8
0.6
0.4
0.2
C
-11
-2
0
2
4
6
x (mm)
(b)
Figure 4.11: (a) XY and (b) XZ plane scans for the matched 2-D array focused at (2.7,
2.7, -4.9)mm.
4.3
Radiation Force Measurements
Radiation force measurements (Stewart 1982) were carried out to determine the
total power output from the 2-D array. The setup includes an ultrasound-absorbing target
that is hung down from a microbalance. The matched 2D-array was placed 5mm above
and facing the target. The setup is illustrated in figure 4.12. The force generated by the
array on the target is recorded by the microbalance, and is proportional to the power
output from the array.
F=mg=
DP
where P is the acoustic power, v is the velocity of sound in water and D=1I for the
absorbing target used in the setup.
crobalance
2-D Array
degassed
- water
.. Target
Figure 4.12: Radiation force measurements setup
To measure the force generated by the array, the microbalance output was
recorded before the array was powered and again as soon as the output reached a steady
state after powering the array.
The difference in outputs was calculated and the
measurement was repeated 5-6 times and an average obtained.
4.3.1 Maximum Power Out:
To determine the maximum power output from the array, 41 of the 49 elements
were each driven at 1.2MHz and 0-phase with increasing peak-to-peak voltages.
A
maximum power output of 1.32W was recorded with a peak-to-peak voltage of 18.5V.
Measurements repeated with similar increasing peak-to-peak voltages resulted in lower
power outputs indicating that the 2-D array was likely deformed when the maximum
power was recorded. Figure 4.13 is a graph of the power output with increasing amplifier
amplitudes and repeated measurements after the maximum power output was recorded.
0
1.2
x
0
0.8
a.
0.6
o
0.4
x
x
0.2
x
o
First Run
Repeated Measurements
Irll
0
2
4
6
8 10 12 14 16 18
peak-to-peak amplitude (V)
20
22
Figure 4.13: Plot of total power output versus amplifier output peak-to-peak amplitude.
The series marked with the dots were measurements taken after the maximum power
output was observed. For each point five measurements were taken and averaged; only
two measurements could be taken for the maximum (circled)
The maximum average intensity, Imax, for the unfocused array is thus calculated
as:
P_
Im -, where A is the area of the array
1.32W
=-41xIa=
0.285cm 2
5.5 Wcm2
49
4.3.2 Array Efficiency:
It was not possible to measure the actual electrical power delivered to each of the
array elements. The electrical power can be estimated from the known amplifier output
amplitude and the impedances of the matched array at the driving frequency.
The
matched array impedances were measured from 500 kHz-2 MHz using the HP4195A
impedance analyzer. If Zce is the impedance of a matched array element at 1.2MHz
driven with an amplifier output peak-voltage of Vout, the power output from the amplifier,
Pout, is simply given by:
-
V
2
cos(4Ze)
o 21Zoutelc
S
Figure 4.14 shows the acoustic power measured versus the estimated electrical
power for first run and repeated measurements. At the maximum acoustic power output
(1.32W), the amplifier output power estimated was 5.71W. Thus the estimated efficiency
was 23.1%.
1.2
0.8
1-
-1
0.6
1-
0.4
|-
x
.
I
0
i
1
First
Run
Repeated Measurements
2
3
4
5
6
Electrical Power from Amplifier (W)
7
8
Figure 4.14: Plot of measured acoustic power versus estimated electrical power. The
circled point indicates the efficiency for which the maximum acoustic power output
was recorded.
4.4
Discussion
In the power measurements section, the acoustic power versus amplifier peak-to-
peak amplitude plot did not have the expected quadratic relationship (Poc V2 ).
It is
uncertain why the quadratic relationship was not observed. We speculate that the voltage
across the array elements may not have been increasing monotonically with the amplifier
output voltage resulting in smaller acoustic power output than expected.
From the acoustic field scans, good focusing of the field was demonstrated.
Amplitude and phase correction were found to be necessary to obtain correct focusing at
(4, 4, -2)mm. It is worthwhile to note that the amplitude and phase correction need only
be done once. In the evaluation, the amplitude correction was done at (2.7, 2.7, -4.9)mm
and later at (4, 4, -2)mm. However, the hydrophone could be positioned at a fixed
distance normal to an element and the response of driving only that element recorded.
This would then be repeated for every element; the amplitude and phase correction
factors for every element can then be obtained from the recorded responses. The same
amplitude and phase correction factors can then be applied to every focus position.
5
CONCLUSIONS
AND
RECOMMENDATIONS
FOR
FUTURE
WORK
5.1
Conclusions
As demonstrated, the use of 1,3-piezcocomposite materials combined with the
development of cost-effective large-scale amplifier systems make the development and
use of these arrays feasible.
A 7x7 element prototype 2-D planar phased array was
constructed from a 1,3-piezocomposite transducer. Although the element-spacing was
zX/2 for a 1MHz driving signal, the unmatched array was driven at 1.1MHz to maximize
the power to the array elements to allow for acoustic field measurements. Scans of the
acoustic fields with foci at three different locations were taken. Amplitude and phase
correction were needed to generate a clearer off-center focus close to the array.
To increase the amount of power to the elements, the array was matched using
readily-available fixed chip inductors and capacitors. The fixed chip inductors are less
bulky and only have to be soldered in place. 49 of the matching networks occupied a
smaller volume than 4 of the traditional hand-wound inductor networks would have
occupied. The fixed inductors were deemed acceptable for the phased array application
despite their non-idealities because the power delivered to each element was small. Good
focusing was demonstrated with the matched array in water. Finally, radiation-force
measurements were taken.
The maximum average intensity from the array was
5.5W/cm 2 . In Yin's simulation study, acoustic power of between 20 and 86W with a 20s
sonication duration was required to generate lesions at 75 different locations in the
cardiac tissue using a 6cm 2 (60x10mm) array (Yin, Epstein & Hynynen 2004). With a
larger array of 6cm 2, we expect acoustic powers of approximately 30W and hence expect
to be able to generate lesions in cardiac tissue.
The benefits of high density 2-D phased arrays with element-spacing _5 /2 for
therapeutic ultrasound applications are compelling. The high density 2-D arrays allow
scanning of the focus with a high spatial resolution in all three dimensions without the
need for moving the array. Since the grating lobes are eliminated an unambiguous focus
is generated allowing precise lesions to be created without the side-effects of significant
heating of healthy tissue.
5.2
Recommendations for Future Work
There are several improvements that can be made to the current 2-D phased array
design. In constructing the array, development time may be decreased by using a ball
grid array (BGA) to connect the elements to the cables. The vias or pads for the cables
could be spread apart by distributing these to several PCBs that plug into the BGA board.
This would make soldering of the cables much easier and faster. For more flexible
designs, flex circuits could be used to link the stacked PCBs and the BGA board. Next,
thinner 40AWG 752 cables should be used in place of the 34AWG cables used in the
current design.
The 7592 cables offer lower capacitance per unit length thereby
increasing the percent of current shunted through the transducer element and hence the
power to the element.
Getting rid of the matching networks altogether would be the most significant step
in improving the design. The change in impedance and correspondingly the change in
power transferred to the array elements were most dependent on the tolerances of the
matching components. In order to rid the array of matching networks, the impedance of
the elements would have to be decreased significantly. In other words, the capacitances
of the elements would have to be increased substantially.
Researchers have used a
layered approach in imaging arrays to increase the element capacitances (Saitoh et. al
1989, Goldberg et. al 1992, Goldberg & Smith 1994). In these multi-layer arrays, the
layers are connected acoustically in series but electrically in parallel. For an N layer
array, the total capacitance of an element can be found from the equation for the
capacitance of a parallel plate capacitor:
Cl = N c A =N2
mN
6
d
N2C
where Cmi is the capacitance of the multilayer element and C is the capacitance of the
equivalent single layer element. The capacitance thus increases by a factor of N2 .
6
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