Institute of Physics and Engineering in Medicine Phys. Med. Biol. 60 (2015) 2195–2215

Physics in Medicine & Biology doi:10.1088/0031-9155/60/6/2195

A novel, flat, electronically-steered phased array transducer for tissue ablation: preliminary results Nicholas P K Ellens1,2, Benjamin B C Lucht1, Samuel T Gunaseelan1, John M Hudson1,2 and Kullervo H Hynynen1,2,3 1

  Sunnybrook Research Institute, 2075 Bayview Avenue, Toronto, ON M4N 3M5, Canada 2   Department of Medical Biophysics, University of Toronto, 27 King’s College Circle, Toronto, ON M5S, Canada 3   Institute of Biomaterials and Biomedical Engineering, University of Toronto, 27 King’s College Circle, Toronto, ON M5S, Canada E-mail: [email protected] Received 15 August 2014, revised 22 October 2014 Accepted for publication 13 January 2015 Published 16 February 2015 Abstract

Flat, λ/2-spaced phased arrays for therapeutic ultrasound were examined in silico and in vitro. All arrays were made by combining modules made of 64 square elements with 1.5 mm inter-element spacing along both major axes. The arrays were designed to accommodate integrated, co-aligned diagnostic transducers for targeting and monitoring. Six arrays of 1024 elements (16 modules) and four arrays of 6144 elements (96 modules) were modelled and compared according to metrics such as peak pressure amplitude, focal size, ability to be electronically-steered far off-axis and grating lobe amplitude. Two 1024 element prototypes were built and measured in vitro, producing over 100 W of acoustic power. In both cases, the simulation model of the pressure amplitude field was in good agreement with values measured by hydrophone. Using one of the arrays, it was shown that the peak pressure amplitude dropped by only 24% and 25% of the on-axis peak pressure amplitude when steered to the edge of the array (40  mm) at depths of 30  mm and 50  mm. For the 6144 element arrays studied in in silico only, similarly high steerability was found: even when steered 100 mm off-axis, the pressure amplitude decrease at the focus was less than 20%, while the maximum pressure grating lobe was only 20%. Thermal simulations indicate that the modules produce more than enough acoustic power to perform rapid ablations at physiologically relevant depths and steering angles. Arrays such as proposed and tested in this study 0031-9155/15/062195+21$33.00  © 2015 Institute of Physics and Engineering in Medicine  Printed in the UK

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have enormous potential: their high electronic steerability suggests that they will be able to perform ablations of large volumes without the need for any mechanical translation. Keywords: focused ultrasound, uterine fibroid ablation, phased arrays, high-intensity focused ultrasound, image-guided surgery (Some figures may appear in colour only in the online journal) 1. Introduction High-intensity focused ultrasound (HIFU) thermal coagulation is emerging rapidly as a desirable, non-invasive or minimally-invasive alternative to some conventional surgeries. With this technique, ultrasound (US) is focused deep in tissue to cause localized heating and tissue coagulation at the focus while leaving the intervening tissue unscathed. Clinically, this technique has been used to treat prostate (Rebillard et al 2005, Blana et al 2008, Warmuth et al 2010, Chopra et al 2012), breast (Hynynen et al 2001, Wu et al 2002, Wu et al 2003, Zippel and Papa 2005), liver (Wu et al 2004), kidney (Köhrmann et al 2002), pancreatic (Wu et al 2005) and thyroid cancers (Kovatcheva et al 2010, Esnault et al 2011), bone metastases (Wu et al 2002, Catane et al 2007, Liberman et al 2008) and to ablate regions of the brain trans-cranially to treat essential tremor and Parkinson’s disease (Elias et al 2013, Lipsman et al 2013). One of the most developed applications of HIFU is for the treatment of uterine fibroids. Fibroids are highly prevalent, benign pelvic tumors that require intervention for one in four women of reproductive age (Stewart 2001, Fennessy and Tempany 2006). Through the use of magnetic resonance (MR) or diagnostic US guidance, fibroids can be treated without any incision. Currently, three systems have received some clinical approval: the Insightec ExAblate (Tempany et al 2003), the Philips Sonalleve (Kohler et al 2009) and the Chongqing Haifu JC (Zhang et al 2010). Recent results of MR-guided HIFU have been very good: 91% of those treated experienced significant improvement and only 28% required subsequent intervention within 1 year of the procedure (Fennessy et al 2007, Hesley et al 2008). HIFU is comparably effective to uterine arterial embolization (UAE), a minimally-invasive procedure after which 20–24% of recipients require subsequent fibroid treatment (Gabriel-Cox et al 2007, Volkers et al 2007, Park et al 2008). HIFU excels, conversely, in regard to quality of life: patients typically return to normal activity within 1–2 d, compared to 13.1 d with UAE (Stewart et al 2006, LeBlang et al 2010). Preliminary data suggest that MR-guided HIFU is a cost-effective treatment if one considers factors such as loss of productivity and compares it to alternative procedures (Zowall et al 2008, O'Sullivan et al 2009). Nevertheless, the cost of the procedure and lack of insurance reimbursement remain significant challenges to clinical adoption (Schlesinger et al 2013). The cost of the procedure is driven in part by the high cost of MR time. Efforts have been made to reduce treatment time and, with it, cost (Pulkkinen and Hynynen 2010, Coon et al 2011, Voogt et al 2011a, 2011b, Coon et al 2012, Jeong 2013, Park et al 2013). One strategy to accelerate treatment time and reduce cost is to use a lower frequency which heats the near-field in front of the fibroid less (Lele 1980), thereby reducing the inter-sonication cooling time. Typical HIFU devices for fibroid ablation consist of a spherically-curved shell containing several hundred independently-controlled transducer elements arranged in annular rings (Do-Huu and Hartemann 1981) or aperiodically sparsely-distributed (Goss et al 1996). For both of these arrangements, small-scale steering of the focus (typically less than 10% of the 2196

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focal depth) is accomplished electronically by varying the driving phase of each element. Large-scale steering beyond these distances is accomplished by mechanical translation. Such designs achieve very high pressure at and near the focus for much lower pressure on the transducer surface which is advantageous for extracorporeal therapy. Far from the geometric focus, however, such arrays do not focus well. Sparse arrays, chosen for their suppression of grating lobes, also deposit energy incoherently in the near-field (Payne et al 2011) which is disadvantageous as this energy leads to extended wait times between sonications. In contrast, we previously proposed the use of a flat phased-array operating at 500 kHz with elements spacing of half of the wavelength λ / 2 (Ellens et al 2011). Flat phased arrays with λ / 2 element spacing can be steered anywhere in a half-space without generating grating lobes (Stone 1902). Exploiting this versatility, we proposed leaving the transducer fixed in one location and accomplishing all steering electronically. The use of a 500 kHz frequency versus commonly used frequencies of 1.0–1.5 MHz both reduces near-field heating per unit energy delivered and increases the US wavelength, relaxing the element density required for λ / 2 spacing. These benefits are realized at the expense of a lower cavitation threshold, lower spatial resolution and the increased possibility of heating beyond the focus, as will be discussed in section 4. Nevertheless, based on previously published results (Ellens and Hynynen 2014), we believe that a low frequency approach is worth pursuing, despite these trade-offs. For this approach to be effective, however, several technical drawbacks must be overcome. First, the design and construction of an array with thousands of small, tightly-spaced elements is an enormous technological and engineering challenge. Second, such an array must be able to focus effectively, even when steered far off-axis. Third, the use of a lower frequency results in decreased attenuation and thus more power is needed to effectively ablate tissue. Although 2D arrays with λ / 2 element spacing have been developed for US imaging (Turnbull and Foster 1992) the requirement of high sustained output power has been an obstacle that has not been solved for therapy arrays. This study aims to quantify the performance of a 1024 element prototype transducer with λ / 2 element spacing. It will compare in vitro and simulation results. With further simulations, it will extrapolate to larger, 6144 element arrays and comment on expected capabilities. 2. Methods 2.1.  Transducer arrays

All of the arrays tested and simulated in this study used some configuration of small, 64 element modules, developed and built in-house. Each module consisted of 64 square elements (8 × 8) with a center-to-center spacing of 1.5 mm, λ / 2 at the driving frequency of 516 kHz in soft tissue (c = 1540 m s−1). Each element, 1.35 × 1.35 mm2 in size, was constructed of lead zirconate titanate and driven in its lateral vibration mode so as to reduce its electrical impedance and negate the need for electrical matching circuits, as described by Song et al (2012). Each element was driven by one channel of an in-house constructed multi-channel driving system and could be individually controlled for both phase and amplitude (Sokka et al 2003). Each module, as constructed, was surrounded by a 0.5 mm wall and, on two sides, a 0.5 mm mounting ridge which produced an overall module footprint of 13 × 14 mm2. When driven at maximum power, each module produced 6–10 W of acoustic power, as measured by the acoustic radiation force applied to an acoustic absorber (Aptflex F28P, Precision Acoustics, Ltd., Dorset, UK) resting on an electronic balance (MS304S, Mettler Toledo, Greifensee, Switzerland). Modules were assembled into larger arrays by affixing them to custom designed frames. 2197

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2.2.  1024 element arrays

As proofs-of-concept, six arrays were examined in silico with different arrangements of 16 modules, for a total of 1024 individual elements. These arrays are shown in figure 1, labelled 16-a through 16-f. The designs were chosen so as to pack the modules together closely (as per the lessons learned previously (Ellens and Hynynen 2014)) but subject to the module size constraints. Each array was designed to accommodate a central diagnostic transducer for guidance and target selection and treatment monitoring: an Ultrasonix L14-5/38 (Analogic, Richmond, Canada) for design 16-a and an Ultrasonix PA7-4/12 (Analogic, Richmond, Canada) for designs 16-b through 16-f. Two of these designs, 16-a and 16-c were built and tested in vitro. The fill fractions of each array, obtained by dividing the radiating area by the area of the smallest circle or rectangle that could contain each array, were 0.49, 0.32, 0.34, 0.35, 0.31 and 0.28 for arrays 16-a through 16-f, respectively. The mean distances from the centre to each radiating element were 29.4 mm, 33.1 mm, 31.2 mm, 30.4 mm, 31.8 mm and 33.2 mm. 2.3.  6144 element arrays

Four designs were proposed for the ablation of uterine fibroids. As uterine fibroids can be located in many locations in and around the uterus, an effective and versatile fibroid ablation transducer must be able to focus at targets at least 100 mm deep, though deeper could be required for larger patients (Ellens and Hynynen 2014). Fortunately, the abdomen affords a large acoustic window which allows for large aperture transducers to be employed, though consideration must be given to the intervening near-field tissue such as bowel which could introduce air into the acoustic near-field. Several design constraints were employed: each array consisted of 96 64-element modules and each had a central vacancy that was sufficiently large so as to accommodate an Ultrasonix C7-3 probe (Analogic, Richmond, Canada). Though there remain engineering challenges such as connecting and driving so many elements, the modular design scales with relative ease. Each of these proposed arrays could be built with the modules described. These arrays are shown in figure 2. The fill fractions for each array, obtained by dividing the radiating area by the area of a circle or an irregular octagon containing all of the modules, were 0.30, 0.35, 0.47 and 0.50 for arrays 96-a through 96-e, respectively. The mean distance from the centre to each transducer element was 79.7 mm, 75.4 mm, 62.6 mm and 60.4 mm. The overall apertures ranged from just over 200 mm to 150 mm. 2.4.  Ultrasound simulation model

Simulated ultrasound pressure maps, p (r), were generated by solving the Rayleigh integral over the surface of all of the transducer elements, S: (Sun and Hynynen 1998) ikcρc p (r) = 2π

∫ S

e−jkcR u ds, R

(1)

where kc = k − iα is the complex wavenumber, ρ is the density, c is the speed of sound and R is the Cartesian distance between each surface element and the target point in question. Attenuation, α, is frequency-dependant according to a power law: α = α0fy where y is about 1.1 for muscle. This equation was solved numerically using in-house developed code and a discretization of λ / 12 on the transducer surface. The discretization of the target region was λ / 30 for 1D simulations and λ / 6 for the 2D field plots and 3D simulations used to simulate heating. The generation of grating lobes was explored in 2D over a large area with a discretization 2198

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Figure 1. Six arrangements of 16 modules: 16-a was designed to accommodate a centrally-located Ultrasonix L14-5/38 probe, while 16-b through 16-f were designed to accommodate an Ultrasonix PA7-4/12 imaging probe.

of λ / 3. With the exception of these 2D simulations, the discretizations used were greater or equal to λ / 6 which commonly regarded as sufficient for such simulations (Marburg 2002). Target sizes varied based on the size of the focus at that location. Thermal deposition was simulated by propagating forward from water into tissue. Velocity u of sources surface S was integrated to give u′ on a surface some distance away according to (Liu et al 2005) ik c u  ′(r) = 2π

−i k c R

∫ ue R S

⎛ 1 ⎞ ⎜1 − i ⎟ T cos (θ ) ds, ⎝ kc R ⎠

(2)

where kc = k − iα is the complex wave number of the medium and α the attenuation coefficient. R is the Cartesian distance between the target and a source surface element of velocity u and area ds. θ is the angle between the vector R and a vector normal to the surface at r. T is the transmission coefficient, given by T  =

2ρc cos θ′ . ρ′c′ cos θ + ρc cos θ′

(3)

Reflections were neglected. The pressure in the volume between media interfaces was determined according to equation  (1). Acoustic parameters used in simulations are given in table  1. The simulation domain consisted of the transducer, a 10  mm layer of water, a 200 mm × 200 mm flat water/tissue boundary parallel to the transducer and a volume of tissue that was 50 mm × 50 mm with a depth ranging from 65 mm (50 mm sonications) to 130 mm (100 mm sonications). 2199

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Figure 2.  Four arrangements of 96 modules, identified as 96-a to 96-d, all designed to accommodate an Ultrasonix C7-3 imaging probe. Table 1.  Acoustic and thermal parameters (Spells 1960, Lassen 1964, Goss et al 1978, Goss et al 1979, Goss et al 1980, Dumas and Barozzi 1984, Hinghofer-Szalkay and Greenleaf 1987, Duck 1990).

Medium

ρ (kg m−3) c (m s−1) α0 (Np m−1 MHz−1) C (J kg−1·°C) κ (W m−1·°C) w (s−1)

Water (tank scans) Water (thermal simulation) Muscle Blood

1000

1466

2.88 × 10−4

N/A

N/A

N/A

1000

1500

2.88 × 10−4

4180

0.615

N/A

1138 1050

1569 N/A

4 N/A

3565 3850

0.498 0.506

7.94 × 10−4 N/A

2.5.  Thermal simulation model

From the pressure calculated for a voxel, the absorbed power density, Q, was determined according to (Nyborg 1981) 2200

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Q  =α

∣p∣2 . ρc

(4)

Using the Pennes' bioheat equation (Pennes 1948), ρC

∂T (r, t ) = ∇· [κ ∇ T (r, t ) ] − wρb Cb [T (r, t ) − Tb ] + Q, ∂t

(5)

the temperature evolution was simulated in muscle tissue over time. Here, T is temperature, t is time, C and κ are the specific heat capacity and thermal conductivity of the tissue, respectively, while ρb, Cb, w are the density, specific heat capacity and perfusion rate of the blood. For in vivo simulations, Tb, the temperature of the blood, was held at 37 °C though the local perfusion was set to drop to 0 when a given voxel of tissue accrued a thermal dose causing coagulation (Lenard et al 2008). Computationally, equation (5) was solved using an in-house built finite-difference time-domain solver (Pulkkinen et al 2011), adapted to run with the Compute Unified Device Architecture (CUDA) graphics processing unit (GPU) platform. Thermal dose, D, was calculated according to Sapareto and Dewey’s thermal dose equation throughout heating and cooling stages (Sapareto and Dewey 1984): tfinal

D(r)= ∑ R 43 − T (r , t )· Δt , t=0

where: ⎧ 0.25 (T (r , t ) ⩽ 43°C ) . R =⎨ ⎩ 0.5 (T (r , t ) > 43°C )

(6)

Thermal dose was used to quantify the volume of tissue ablated and is measured in equivalent minutes at 43 °C, henceforth EM43. Thermal parameters used are given in table 1. The thermal domain was padded 20–25 mm in ± x, ± y and +z compared to the US simulation domain such that very little heat reached the boundary during the course of simulation and a fixed boundary condition was applied. A 10 mm diameter cell consisting of one central focus and eight foci arranged around it at a radius of 5 mm was sonicated in a time of 30 s (divided between the nine foci) (Ellens and Hynynen 2014), followed by a cooling period of 180 s where dose could continue to accrue while the thermal energy dissipated and was removed by perfusion. 2.6.  Hydrophone measurements

Two 16 module arrays were constructed: 16-a and 16-c. Each was mounted such that its face was submerged in a large tank of degassed water lined with absorbing rubber. The acoustic axis was defined as the +z axis, while the transducer face lay on the xy-plane. The array was electronically focused at various target locations and driven with 4.8 Vpp, about 7% of maximum power, in 2 ms bursts with a 50 Hz pulse-repetition frequency. A fibre-optic hydrophone (Precision Acoustics Ltd., Dorset, UK) captured 20 µs samples of the signal (10–11 cycles) at and near the focus. The data were recorded in a custom LABVIEW (National Instruments, Austin, USA) program and analysed offline using MATLAB (Mathworks, Natick, USA). The sonication parameters were chosen empirically: 7% power and the 10% duty cycle allowed the transducer to sonicate for long durations (>1 hr) with negligible heating while still yielding a good signal (5% standard deviation in peak magnitude across the sample). For 1D measurements along the x- and y-axis, a span of 40 mm was scanned with a discretization of 0.1 mm. Along the z-axis, 50 mm was scanned at a discretization of 0.2 mm. For 2D measurements, xy-planes were scanned over spans of 10–30 mm with 0.5 mm discretization in both directions. 2201

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b

Beam width (mm)

8

4 x 4 (a): x 4 x 4 (a): y 4 + 12 (b) 5 + 11 (c) 6 + 10 (d) 7 + 9 (e) 8 + 8 (f)

6 4 2 0

Beam depth of field (mm)

a

20

40

60

80

40

4 x 4 (a) 4 + 12 (b) 5 + 11 (c) 6 + 10 (d) 7 + 9 (e) 8 + 8 (f)

30 20 10 0

20

40

60

80

Depth (mm)

Depth (mm)

Peak pressure amplitude (normalised)

c 1.0

4 x 4 (a) 4 + 12 (b) 5 + 11 (c) 6 + 10 (d) 7 + 9 (e) 8 + 8 (f)

0.9 0.8 0.7 0.6 0.5 20

40

60

80

Depth (mm)

Figure 3.  Beam width (a) and depth of field (b) of the simulated in vitro pressure amplitude profiles of each 1024 element array. Due to its lateral asymmetry, the x and y beam widths of array a are shown separately. (c) Normalized, peak acoustic pressure as a function of focal depth.

For both the xz and yz-planes, 20–30 mm was used though the discretization in the z direction was increased to 0.75. Under some steering conditions, the scan range was increased so as to accommodate larger ultrasound foci. 3. Results 3.1.  1024 element array simulations

The round arrays (16-b through 16-f) all produced foci that were nearly totally symmetric, while the rectangular array (16-a) focused more tightly along the x-axis, parallel to the imaging array. The tightness of focus is shown in figures 3(a) and (b). The round arrays produced foci that were narrower but longer than the rectangular array. Each array was electronically steered to varying depths and off-axis to ascertain the volume of tissue the array could target effectively. Increasing the depth of focus from 30 mm to 70 mm decreased the peak pressure by about a third, shown in figure 3(c). Peak pressure decreased as aperture increased with the smaller arrays producing higher peak pressure amplitudes. This effect was less pronounced at greater depths as would be expected geometrically based on mean distance between each transducer and the focus. Plots of the pressure profiles of the different arrays at a depth of 50 mm are shown in figure 4. The profile of the pressure field is shown in figures  5(a) and (b). Though the pressure dropped off with steering angle, the peak pressure at the arrays' periphery (40  mm) was still only modestly reduced to 70–80% of the peak pressure at the centre. This is shown in figures 5(c) and (d). 2202

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0.8

4 x 4 (a) 4 + 12 (b) 5 + 11 (c) 6 + 10 (d) 7 + 9 (e) 8 + 8 (f)

a

0.6 0.4 0.2 0 -20

-10

0 x (mm)

10

Pressure amplitude (normalized)

1

20

4 x 4 (a) 4 + 12 (b) 5 + 11 (c) 6 + 10 (d) 7 + 9 (e) 8 + 8 (f)

c 0.8 0.6

1 Pressure amplitude (normalized)

Pressure amplitude (normalized)

1

0.8

4 x 4 (a) 4 + 12 (b) 5 + 11 (c) 6 + 10 (d) 7 + 9 (e) 8 + 8 (f)

b

0.6 0.4 0.2 0 -20

-10

0 y (mm)

10

20

d

0.4 0.2 0 20

30

40

50 z (mm)

60

70

80

Figure 4.  Simulated pressure amplitude profiles in (a)–(c) for each array along the x, y,

and z-axis respectively. In (d), the 50% isocontour of the normalized pressure amplitude field produced by array 16-c is shown. In all cases, the arrays were focused at (x, y, z) = (0, 0, 50) mm.

3.2.  1024 element array in vitro

Array 16-a was built and subjected to preliminary hydrophone tests, while array 16-c was studied under a wider array of steering conditions. Both arrays showed good agreement between simulations and in vitro measurements. As shown in simulations, array 16-a had very large sidelobes along the y-axis. A sample of the in vitro results using this array is shown in figure 6. Based on simulation comparisons of arrays 16-b through 16-c, 16-c was built and underwent more extensive in vitro testing. A sample of the results is shown in figure  7. Pressure as a function of steering was well-predicted by the simulation model, as shown in figures 5(e) and (f). 3.3.  6144 element array simulations

The four 6144 array prototypes clearly fall into two categories: one based on concentric rings, the other more rectilinear. The beam profiles and performance specifications reflect this distinction. The beam width and depth of field of the different arrays as functions of focus depth are shown in figures  8(a) and (b). The round arrays slightly out-performed the rectilinear arrays in this regard and focused more narrowly at all depths and with a shorter depth of field 2203

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60

50

50

40

40

z (mm)

z (mm)

Pressure amplitude (normalized)

70

60

30

30

20

20

10

10

0 -10

c

b

70

0

10

20 30 x (mm)

40

0 -10

50

d 1.0 0.8 0.6

0.4 0.2 0.0

0

10

20

30

40

50

Pressure amplitude (normalized)

a

0

10

0.6

0.4 0.2 0.0

0

10

0.8 0.6 0.4 0.2 20

30

40

50

Pressure amplitude (normalized)

Pressure amplitude (normalized)

f

10

20

30

40

50

40

50

Steering in x (mm)

1.0

0

50

0.8

4 x 4 (a) 4 + 12 (b) 5 + 11 (c)

0.0

40

1.0

Steering in x (mm)

e

20 30 x (mm)

6 + 10 (d) 7 + 9 (e) 8 + 8 (f)

1.0 0.8 0.6 0.4 0.2 0.0

0

10

Steering in x (mm)

20

30

Steering in x (mm) in vitro

in silico

Figure 5. (a, b): Simulated 50% contours of array 16-a (a) and 16-c (b) focused at

depths of 30 and 50 mm and radially from the centre at distances of 0 to 40 mm in 10 mm increments. The central axis is shown as a dotted red line while the approximate extent of the array is marked with a thick grey line along the horizontal axis. (c, d): In silico peak pressure amplitude as a function of steering along the x-axis at focal depths of 30 mm (c) and 50 mm (d). Both (c) and (d) are normalized to the peak pressure amplitude generated by the 16-a array at the specified depth. (e, f): In vitro normalized pressure amplitude produced by array 16-c as a function of steering in the x direction at a depth of 30 mm (e) and 50 mm (f) compared to calculated in silico results. Errorbars are approximated by measuring the maximum standard deviation of the peaks of 10 successive cycles near the focus for a representative set of points.

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Figure 6.  A comparison of simulations (left-hand column) with in vitro measurements (centre column) and overlaid 50% contours (right-hand column) of the pressure amplitude distributions produced by array 16-a. Three orthogonal planes are shown: from top to bottom xy, xz, and yz. The array was focused at (x, y, z) = (0, 0, 35) mm.

at most locations. The beam profiles at a depth of 100 mm are shown in figure 9. The rectilinear arrays produced higher peak pressure amplitudes than the ring arrays and were only slightly less tightly focused. In terms of steering, the peak pressure of the rectilinear arrays dropped off more quickly when steered far off-axis than the larger-aperture ring arrays but, in absolute terms, produced higher peak pressures than the ring arrays until steered about 100  mm off-axis where all of the arrays produced comparable peak pressures (figures 8(c) and (d)). Though the intramodule element spacing was λ / 2, the inter-module spaces were periodic and the mean centreto-centre spacing of the elements was greater than λ / 2, making these arrays susceptible to grating lobes. Scans of large, xz-planes revealed the emergence of small grating lobes near to the transducer surface on the non-sonicated half-space. These increased with steering, though remained quite low (

A novel, flat, electronically-steered phased array transducer for tissue ablation: preliminary results.

Flat, λ/2-spaced phased arrays for therapeutic ultrasound were examined in silico and in vitro. All arrays were made by combining modules made of 64 s...
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