Thin-film sparse boundary array design for passive ... - IEEE Xplore

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IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control ,

vol. 59, no. 10,

October

2012

Thin-Film Sparse Boundary Array Design for Passive Acoustic Mapping During Ultrasound Therapy Christian M. Coviello, Member, IEEE, Richard J. Kozick, Member, IEEE, Andrew Hurrell, Penny Probert Smith, Member, IEEE, and Constantin-C. Coussios Abstract—A new 2-D hydrophone array for ultrasound therapy monitoring is presented, along with a novel algorithm for passive acoustic mapping using a sparse weighted aperture. The array is constructed using existing polyvinylidene fluoride (PVDF) ultrasound sensor technology, and is utilized for its broadband characteristics and its high receive sensitivity. For most 2-D arrays, high-resolution imagery is desired, which requires a large aperture at the cost of a large number of elements. The proposed array’s geometry is sparse, with elements only on the boundary of the rectangular aperture. The missing information from the interior is filled in using linear imaging techniques. After receiving acoustic emissions during ultrasound therapy, this algorithm applies an apodization to the sparse aperture to limit side lobes and then reconstructs acoustic activity with high spatiotemporal resolution. Experiments show verification of the theoretical point spread function, and cavitation maps in agar phantoms correspond closely to predicted areas, showing the validity of the array and methodology.

I. Introduction

R

eal-time treatment monitoring of therapeutic ultrasound, i.e., the determination of both the spatial extent and dose of the therapy, is a key issue for widespread clinical adoption, whether the application is high-intensity focused ultrasound (HIFU) ablation of cancerous tissue [1], [2] or ultrasound-enhanced targeted drug delivery [3]. In fact, one of the key limitations of HIFU surgery is the lack of an affordable and effective real-time monitoring strategy [1]. Several different affordable ultrasound (US)based monitoring methods have been suggested, including interleaving B-mode imaging and therapy pulses [4] and harmonic motion detection [5]. Neither of these methods specifically monitors acoustic cavitation, which has been shown to enhance both HIFU surgery and drug delivery. Further, interleaving B-mode and HIFU is not truly real time, and harmonic motion detection applies only to thermal-based therapies. Instead, recent work has shown that passive spatial mapping of the acoustic emissions using di-

Manuscript received April 8, 2012; accepted June 26, 2012. This work was funded by the Wellcome Trust and Engineering and Physical Sciences Research Council (EPSRC) under grant number WT 088877/Z/09/Z. C. M. Coviello, P. Probert Smith, and C.-C. Coussios are with the Institute of Biomedical Engineering, Department of Engineering Science, University of Oxford, Oxford, UK (e-mail: [email protected]. uk). R. J. Kozick is with Bucknell University, Lewisburg, PA. A. Hurrell is with Precision Acoustics Ltd., Higher Bockhampton, UK. DOI http://dx.doi.org/10.1109/TUFFC.2012.2457 0885–3010/$25.00

agnostic linear-array probes has tremendous promise both for focus localization and real-time treatment monitoring [1], [6] and the method applies to both HIFU surgery and drug delivery. However, linear arrays are only able to map emissions in one plane, whereas a 2-D array can provide full 3-D spatial coverage, providing more information regarding the extent of treatment. When designing 2-D sensor arrays for passive imaging, two key characteristics are the aperture size and the layout geometry, because these dictate the resolution of the targeted activity. Thus, to be able to image in the transverse, elevation, and axial directions with suitable resolution requires a large 2-D aperture. The financial cost and complexity, however, associated with large, fully-filled and regularly-spaced 2-D arrays increases dramatically with the size of the aperture to be used. This is especially true when the added per-channel cost of amplification, filtering, and digitization of each array element is considered. Further, the cost of manufacturing an array from traditional piezoceramics can be expensive and time-consuming because of the manufacturing process. The high acoustic impedance of piezoceramics, relative to that of water or tissue, necessitates the use of acoustic impedance matching layers. Finally, piezoceramics are intrinsically resonant devices and although damping is commonly applied to such materials, they remain bandlimited devices. This study presents a novel 2-D monitoring array that overcomes the shortcomings of traditional ultrasound array design to achieve passive acoustic mapping using an array with a small number of elements and that can be produced relatively inexpensively using thin-film hydrophone technology. In this study, we use the concept of the coarray [7], [8] to synthesize a fully-filled 2-D weighted aperture. This provides the performance of an array with much higher element count but with much reduced complexity and cost at the expense of additional signal processing. Other examples of arrays for passive acoustic mapping of broadband emissions related to ultrasound therapy have been reported [9], [10], but these studies used random arrays or did not exploit the coarray to improve performance. Random arrays (with sensor positions chosen according to a probability distribution) are one approach to producing a large aperture with few sensor elements. The point spread function (PSF) of a random array is itself a random function, but on average, the PSF is characterized by a main lobe with a fairly uniform side lobe level

© 2012 IEEE

coviello et al.: thin-film sparse boundary array design for passive acoustic mapping

[11]. Arrays that are deterministically thinned by omitting elements at locations along a regular grid typically have PSFs with large side lobes in certain directions (grating lobes). In this paper, we use a particular thinned 2-D array with elements on the boundary of a rectangle, and signal processing to achieve imaging performance that is comparable to a filled rectangular array. The key property is that the boundary and filled arrays share the same coarray, so the boundary array is capable of producing the same images through additional data collection and signal processing. Recordings of acoustic emissions from therapeutic ultrasound show both harmonic and broadband components, implying the possible presence of both stable and inertial cavitation, as well as scattering of nonlinear components of the incident wave by tissue. Diagnostic ultrasound probes in previous passive acoustic mapping studies [1], [6] are made from traditional piezoceramic materials. Because of the relatively narrowband behavior of the piezomaterials used, these probes are typically designed with a relatively small bandwidth because the goal is to optimize active imaging at a particular frequency. This can mean that much of the broadband component of the acoustic emissions is lost. Although recent temporal sparse reconstruction techniques that attempt to recover out-ofband frequencies to improve the quality of acoustic maps have shown promise [12], a further advantage of using thin film technology is the opportunity for wideband detection and high sensitivity on receive. Thin-film materials such as polyvinylidene fluoride (PVDF) and PVDF copolymers such as P(VDF-TrFE) have long been used in a variety of ultrasound sensors for exactly these reasons [13]–[15]. In this study, a PVDF array made from multiple-layer printed circuit board (PCB) was used because of the advantageous acoustic sensing properties as well as the low cost of construction and easily configurable array design. The rest of the paper is organized as follows: Section II describes passive acoustic mapping for ultrasound therapy, including the general problem formulation and model. Section III provides the details of using boundary arrays for passive imaging as well as the algorithm used to compute the weights. In Section IV, the construction of the array is outlined and its properties for passive acoustic mapping of ultrasound therapy are enumerated. Section V recounts the experimental setup used for collection of passive acoustic maps for ultrasound-based therapy, and Section VI details the results. Finally, Section VII contains concluding remarks. II. Passive Acoustic Mapping During Ultrasound Therapy Ultrasound therapies are emerging as competitive options in the treatment of various cancer types because of their ability to tightly focus energy deep into the body completely noninvasively with few adverse side effects [1], [16]. One of several key phenomena that can be exploited

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and monitored during ultrasound therapy is that of acoustic cavitation, or the nucleation and oscillation of microscopic bubbles caused by acoustic waves traveling in the body. Cavitation has the potential to enhance the local heating rate during HIFU ablation [17] and can also augment desired mechanical bioeffects of ultrasound [16]. This is useful in applications such as the dissolution of blood clots (thrombolysis), tissue homogenization (histotripsy), and aiding in cell permeability for drug transport [16]. Of the two general regimes of cavitation, inertial cavitation, which is the rapid expansion and collapse of a bubble, is of primary concern in the context of monitoring therapy. The bubble collapse, being an impulse-like event in the time domain, generates broadband acoustic emissions which, in addition to their helpful bioeffects [16], [17], can also be used to monitor the spatial extent of the therapy. Assume that we have a sensor array located at positions defined in a coordinate system by xj = (xj, yj, zj)T for j = 1, 2, …, 4(N − 1) sensors. Let A = {xj : j = 1, 2, …, 4(N − 1)} be the set of sensor array element locations. Proceeding as in [2], the source strength measured by the array of sensors at a position x is given as

q(x, t) =

4π 4(N − 1)α

4(N −1)

∑ d j(x)s j(t − d j(x)/c), (1) j =1

where sj(t) is the signal recorded on channel j, α is a conversion factor from pressure to voltage, and the distance from sensor element to source field position is

d j(x) =

(x j − x )2 + (y j − y)2 + (z j − z )2. (2)

The source power can then be found by time-averaging the source strength

Ψ(x) =

1 4πρocT

∫t

t 0 +T

2

q(x, t) dt , (3)

0

where ρo is the density of the medium and c is the speed of propagation. Although in conventional passive acoustic mapping, such as in [6], [10], [18], apodization or weighting functions have not been applied to the power estimates, weights can be applied to shape the receive beam to reduce the effect of noise and unwanted reflections [14]. Weighting based on optimal beamforming criteria has, however, been demonstrated previously [19], [20]. Our approach to applying weights follows the passive imaging formulation in [7]. First, the source strength in (1) is computed two times with the array, with different weights w1,j and w2,j applied to each array element: 4(N −1)

q k(x, t) = β

∑ w k,j d j(x)s j(t + d j(x)/c), (4) j =1

for k = 1, 2, and where β = (4π )/(4(N − 1)α). Strictly speaking, in near-field imaging, the weight vector, wk,j, will have a range dependence, although this is omitted

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from (4). The source power estimate, then, in (3) is generalized with weighting as

ΨW (x) =

1 4πρocT

∫t

t 0 +T 0

q 1(x, t)q 2(x, t)∗ dt, (5)

where ∗ denotes the complex conjugate. In the next section, we will show that by utilizing the concept of the coarray, weights may be chosen over a sparse aperture that “fills in the data from the interior of the aperture” [8], allowing higher quality passive imaging compared with a sparse array and conventional passive acoustic mapping. III. Boundary Arrays For Passive Imaging Consider a rectangular boundary array with five elements per side (N = 5) as shown in Fig. 1, which has a total of 4(N − 1) = 16 elements. For any array, the coarray, specifically the difference coarray when describing passive imaging, is defined as the “set of all vector differences between points in the aperture” [7] or

C d = { y | y = x i − x j,

∀ x i, x j ∈ A } . (6)

The difference coarray for the N = 5 boundary array is shown in Fig. 1, with the multiplicity of each point in the coarray shown. The coarray is also the support of the inverse Fourier transform of the PSF and the morphological autocorrelation of the array [7]. If array weights w1,j and w2,j are used as in (4) and (5), then the inverse transform of the resulting PSF can be written as the cross-correlation of the weights applied to the receive elements [7], [8],

γ(y) =

∑

* w 1,i w 2, j,

y ∈ C d, (7)

{i, j : y = x i − x j }

which is called the coarray weighting function. It should also be noted that the array can be separated into separate coplanar apertures and different weightings applied to each [8].

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The fundamental point to consider is that the difference coarray of a fully-filled rectangular array and that of a sparse rectangular boundary array are equivalent, meaning that the sparse array should be able to achieve imaging performance comparable to the fully-filled array. It is only left to determine the weighting to be applied to the array so as to limit the effect of side lobes. A boundary array having fewer elements than a fully-filled array should be limited in the weightings that could be applied. Linear imaging, however, allows any sets of weights to be applied to the sparse array elements, through construction of multiple intermediate images which are then coherently combined to yield the final image [21]. Given a desired weighting function, it is necessary to synthesize these individual subimage weights to be applied. First, a 2-D weighting function, γ(y), is chosen over Cd, which is represented by a matrix C of size (2N − 1) × (2N − 1). The goal of the weight synthesis algorithm is to decompose C into a sum of outer products of weight vectors, each of size 4(N − 1) × 1, with each outer product making an intermediate image. To do so, we need a mapping from the coarray weighting function represented by C, to a 4(N − 1) × 4(N − 1) matrix Cw of element-pair weights, shown in Fig. 2. Each element in Cd is formed from a pair of array elements, and the array weighting function represented by C is sampled over Cd. Thus, by taking the value of C at each point in Cd normalized by the multiplicity and mapping it to the row and column of Cw that contributed to it, we get the mapping from difference coarray to array element space. Now, with Cw in hand, we then decompose it using the singular value decomposition (SVD) 4(N −1)

C w = USV

H

=

∑ u σ v H , (8) =1

where H denotes conjugate-transpose. Let be the index over subimages, and w 1(), w 2() be the 4(N − 1) × 1 weight vectors used to form q 1(x, t; ) and q 2(x, t; ) using (4). Then assign w 1() = u σ 1/2 and w 2() =

Fig. 1. (a) An N = 5 rectangular boundary array and (b) its difference coarray with multiplicity of each coarray point.


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Fig. 2. Diagram showing an example of the transform from coarray weighting function, C, to weight matrix, Cw. The coarray weighting function for a particular 2-D weight function is shown overlaid on the sample grid of the difference coarray. In this particular example, the difference coarray point is created from element 5 and 13 as labeled in Fig. 1(a), and the difference coarray is thus at the top-left most extreme in Fig. 1(b). This point in the difference coarray has only a single multiplicity, and thus the value goes directly into row 5, column 13. 

v σ 1/2 for = 1, …, 4(N − 1), so we have the weight vector pairs for each subimage, which are computed using (5):

Ψ (x) =

1 4πρocT

∫t

t 0 +T 0

q 1(x, t; )q 2(x, t; )*dt. (9)

Finally, all of the subimages are summed together to form the output image:

Ψ TOTAL(x) =

∑Ψ (x). (10)

The complete algorithm description is shown in Algorithm 1 (see Appendix). An immediate question is how many intermediate images to use, with the maximum being 4(N − 1). In practice, only a few singular values are significant, so the image addition in (10) may be truncated with negligible effect on image quality. For efficiency, the weights can be pre-computed for all ranges once the sensor array is fixed. For a rectangular boundary array, this would require storage of a (N × N × 2) matrix of weights per pixel position. Depending on the processing system to be used, this gives a trade-off of memory size and access versus computation speed. It can also be noted that Algorithm 1 is very parallelizable for potential implementation on graphical processing units (GPUs) or other multiprocessor systems. A means of assessing the potential performance of an imaging array is that of the PSF, which allows the determination of the possible imaging resolution. For a 2-D sparse array and a point source at position xs = (xs, ys, zs)T, let us start by assuming that the array is situated in the XY-plane (zj = 0, ∀j); then, the PSF as a function of frequency and position can be written as [2], [22] 4(N −1)

P(x, f ) =

∑ w j exp { j φ(x j )}

2

, (11)

j =1

φ(x j ) = k ( (x − x j )2 + (y − y j )2 + z 2 −

(x s − x j )2 + (y s − y j )2 + z s2 ),

(12)

where wj is the weighting on array element j, and k = (2πf )/c is the wavenumber. Note that this PSF is formulated for the case in which the same weights w1,j = w2,j = wj are used to compute q1(x, t) and q2(x, t) in (4). This equation can be simplified to find the spatial resolution for both the transverse and axial imaging planes by assuming w to be a smooth function. This allows us to write the PSF as

P(x, f ) =

∞

2

∫−∞

w(l ) exp { j φ(x j)} dl . (13)

For the transverse plane, z = zs and letting δx = x − xs and δy = y − ys, the PSF can be shown to be

P(x, f ) =

∞

{

∫−∞

w(l ) exp jk

2

}

(δx + δy) dl , (14) zs

which is the Fourier transform of the aperture weighting function with scaled frequency (k(δx + δy))/zs. For uniform weighting, and ignoring grating lobes, this would simply be the square of the sinc function, or 2

 Lk δx 2 + δy 2   , (15) P(δx, δy, f ) = sinc    2πz s

where L = L2x + L2y is the aperture size. Similarly, to find the axial resolution, assume a smooth, uniform weighting function and axisymmetry (an approximation for noncircular arrays), the Fresnel integral allows us to represent the PSF as [2]

P(δz, f ) =

F

(

k δz 4π(z sL)2 k δz 4π(z sL)2

)

2

, (16)

where F(·) is the Fresnel integral. Plotting both the axial and transverse PSF versus depth (zs) allows the determination of the resolutions in both planes from the full-

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width, and is on a center-to-center pitch of 3 mm. This arrangement yields a sparse rectangular boundary array with a final aperture size of 24.2 × 24.2 mm and active elements that are 0.2 × 0.2 mm. The electrode connections from each edge of the array are led out to a connection tab on the FPC that is designed for insertion into an industry-standard zero insertion force (ZIF) connector. A construction diagram showing the side and top view of the array is shown in Fig. 4. V. Experimental Setup

Fig. 3. The transverse and axial resolutions versus depth from the face of the array at an assumed center frequency of 3.75 MHz and a propagation speed of 1500 m/s.

width at half-maximum value (FWHM) of the PSF peak. Fig. 3 shows the resolutions of the array versus depth for an array with a center frequency of f = 3.75 MHz and a speed of propagation of 1500 m/s. IV. PVDF Array Description PVDF and its copolymers have been used in many applications involving acoustic sensors because of their low acoustic impedance, large receive bandwidth, and the material flexibility that facilitates custom nonrigid sensors [13]–[15]. In fact, many of the widely reported uses for PVDF and P(VDF-TrFE) are in hydrophones, both single-element (needles and membranes) and arrays [13]. Because the acoustic emissions in ultrasound therapy tend to have both harmonic and broadband components, a material with a large bandwidth and high receive efficiency is highly desired. Further, the relative cost in construction of an array made from prepoled PVDF film can be much less than conventional piezoceramic materials, such as PZT, because of the high manufacturing cost in dicing, wirebonding, and associated backing and matching layers. In this section, the design of the 2-D PVDF array created by Precision Acoustics (Dorchester, UK) is described. Prepoled 52-μm PVDF film is layered between two custom flexible printed circuits (FPCs). Low-viscosity epoxy is used to bond the layers of the laminate together. Each FPC comprises a base layer of polyimide, adhesivelessly bonded copper electrodes and a final outer, oxidization resistant gold layer. Sensor elements are formed at the overlap region between electrodes on the two FPCs. One FPC acts solely as ground electrode and has a single electrode strip (0.2 mm wide) that runs around the rectangular periphery of the array. The other FPC has 32 electrodes arranged to intersect the ground electrode perpendicularly such that the element count on any one side is N = 9. Each of these signal-side electrodes is also of 0.2 mm

Two separate experiments were run to test the imaging quality of the sparse boundary array. First, a scattering experiment was run to determine the experimental PSF and compare it to the theoretical resolutions obtained previously. Second, the array was tested using a tissue-mimicking material (TMM) loaded with cavitation-nucleating particles to determine the passive acoustic mapping performance versus predictions. In the scattering experiment, the tip of a 75-μm Precision Acoustics needle hydrophone is used as a scattering point source, placed in the focus of an Olympus Panametrics (Waltham, MA) non-destructive testing (NDT) transducer [0.5 in (12.7 mm) diameter, fo = 15 MHz]. The NDT transducer has a focus of 75 mm, and the needle hydrophone is arranged so that just the tip enters into the sound field. The (N = 9) 32-element sparse rectangular boundary array is arranged at 90° to the NDT transducer and centered directly above the needle, as shown in Fig. 5(a). The source applied to the NDT transducer was a broadband pulse from a DPR300 pulser-receiver (JSR Ultrasonics, Pittsford, NY). The distance from the needle to the sparse array was determined experimentally to be approximately 25 mm so that all elements were seeing the (weak) scattered signal from the needle tip. The signals collected by the array were first sent to custom filters and preamplifier units designed by Det Norske Veritas (Port-

Fig. 4. The N = 9, 32-element sparse boundary array construction details from (left) the top and (right) the side. Note that the dashed line on the top view indicates that the ground lead is hidden because it is on flexible printed circuit (FPC) 2. The polyvinylidene fluoride (PVDF) thickness is 52 μm, whereas the overall sensor is approximately 140 μm thick. 


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Fig. 5. Experimental setup for (a) determination of the point spread function by scattering and (b) cavitation mapping in a phantom. 

land, UK). The high-pass filters have a cutoff of 1.5 MHz, and the preamplifiers are fixed gain of 37×. In the case of scattering, the array data was collected using a 44XI digital oscilloscope (LeCroy Corp., Chestnut Ridge, NY) averaging over 1000 pulses at fs = 250 MHz and transferred to PC for use with Matlab (The MathWorks Inc., Natick, MA). In all experiments, a 2-D raised cosine was used as the coarray weighting function, and the number of subimages was chosen based on a threshold of 95% of the total energy of the singular values. For mapping cavitation, a homogeneous 3% aqueous agar gel as a TMM was prepared using deionized water. The agar is mixed with talc, a rough hydrophobic particle, which is used to provide consistent and repeatable cavitation results. For the mixture, 4.34 g of particles were added per 275 mL of 3% agar solution as suggested by Arora [23], and the mixture was degassed at −50 kPa before pouring in a poly(methyl methacrylate) (PMMA) holder with removable sides. Although the viscoelasticity of the TMM will make its cavitation behavior similar to that of tissue, its attenuation and speed of propagation will be quite similar to water. The setup for this experiment is shown in Fig. 5(b). A 500-kHz HIFU transducer (H107-013, Sonic Concepts, Bothell, WA), confocally aligned axially with an Olympus Panametrics NDT transducer [0.5 in (12.7 mm) diameter, fo = 5 MHz, dfocus = 75 mm], was used to initiate cavitation in the TMM. The NDT transducer is used as a passive cavitation detector (PCD) to ensure the presence of cavitation and is connected first to a 2-MHz passive filter (Allen Avionics, Mineola, NY), a 10× pre-amplifier (Stanford Research Systems, Sunnyvale, CA), and the digital oscilloscope. The HIFU transducer is driven with a function generator (33250A, Agilent Technologies Inc., Santa Clara, CA) connected to a 55-dB power amplifier (Model A300, Electronic Navigation Industries, Rochester, NY) sending out a single 10-cycle sine wave at 500 kHz. It should be noted that the resulting cavitation maps were generated using only one 10-cycle pulse per map. As was done in the previous setup, the sparse rectangular boundary array is aligned at 90° to the agar phantom, centered on the HIFU transducer focus. Finally, the signals from the array are sent through the custom filters and preamplifiers and then sampled by a National Instruments (Austin, TX) PXI Express (PXIe)-

based data collection system. The system, which is eminently scalable and capable of on-board processing, consists of a field-programmable gate array (FPGA) card (NI PXIe-7962R) and adapter module (NI PXIe-5752) housed in a PXIe crate (NI PXIe-1082). A total of thirty-two 12bit channels can be simultaneously sampled at 50 MHz. The data files are written directly to a PC for processing with custom software written in Matlab. VI. Results To determine the experimental PSF, the sparse rectangular boundary array recorded the scattered signals from the needle hydrophone with record length of 35 μs. The received bandwidth of the pulse at the array is approximately 3.75 MHz, as shown in Fig. 6. Thus, using the plot in Fig. 3, the expected resolution should be 0.28 mm transverse and 1.31 mm axially at 25 mm. The data were processed into passive acoustic maps using a conventional technique, time exposure acoustics (TEA) [2], as well as the sparse aperture weighted algorithm (here called SWTEA) in Algorithm 1. The 1-D slices through the peaks are shown in Figs. 7(a) and 7(b). The resolution in either plane will be represented by the FWHM value or the

Fig. 6. Frequency spectrum of the signal recorded on Element 4 during scattering experiments showing the bandwidth of the received signal to be approximately 4.2 MHz with a center frequency of around 3.75 MHz.

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Fig. 7. Experimentally collected transverse and axial point spread function (PSF) peak slices showing the (a) transverse and (b) axial resolution. For time exposure acoustics (TEA), the resolutions are 0.44 mm transverse and 2.95 mm axial. For the sparse aperture weighted algorithm (SW-TEA), the resolutions are 0.34 mm transverse and 2.2 mm axial.

width of the peaks at the −6-dB points. For the transverse resolution, the TEA algorithm has a FWHM of 0.44 mm, and SW-TEA achieves a resolution of 0.34 mm. Similarly for the axial plane, the TEA algorithm has a resolution of 2.95 mm, and SW-TEA is again lower at 2.2 mm. In both cases, neither algorithm achieves exactly the theoretical resolution, but SW-TEA comes closest. That the theoretical resolution is not exactly achieved is not surprising: the SNR is very low because the point source is so small and is thus a weak scatterer. It is also not surprising that the SW-TEA performs better than standard TEA because the weighting function tends to reduce noise coming in through the side lobes. The double-peak in the axial plane can be explained by movement of the needle hydrophone resulting from acoustic pulse, thus giving two scattering points in the axial dimension in range. This also potentially explains why the transverse resolution is not exactly achieved, also because of needle movement. One difficulty in assessing the accuracy of passive acoustic maps is the lack of alternative validated experimental techniques that enable accurate sizing of regions of inertial cavitation activity. It is possible, however, to predict the size of the region using knowledge of the cavitation threshold for the material and the transducer calibration. The cavitation threshold of this type of TMM was studied by Faragher [10] and found to be 1.42 MPa. Using an accurate calibration of the HIFU transducer, the predicted cavitation region should coincide with the size of the HIFU beam above the cavitation threshold at a particular insonating amplitude, as shown in Fig. 8 [10]. After data was collected using the setup in Fig. 5(b), the SW-TEA algorithm was used to generate cavitation maps. In Fig. 9, the resulting maps are shown for increasing peak negative focal pressures (PPNFP) of 2.23, 2.62, and 3.35 MPa in the transverse-axial plane. In these images, the HIFU is traveling from top to bottom, thus the axial dimension is away from the HIFU transducer. The maps are also overlaid with black ellipses that represent the predicted inertial

cavitation region for that insonating amplitude. From the images, it can be noted that the predicted inertial cavitation region correlates strongly with the experimental passive acoustic maps. As passive acoustic mapping has been previously shown to be able to discern discrete regions of cavitation activity [1], [18], the double maxima in the 2.62 MPa exposure, while not an artifact of the algorithm, could be a result of uneven distribution of talc particles in the TMM, although too much should not be read into this. The main point is that the extent of activity corresponds closely to predicted size. It should also be noted that with TEA alone, maps showing cavitation regions were uninterpretable because of low SNR (mainly because of the small element sizes on the PVDF array) and side lobe noise. Thus, the use of the sparse array coupled with the ability to generate an array weighting by using the

Fig. 8. “The size of the cavitation region indicates the area where the acoustic amplitude exceeds the inertial cavitation threshold. For a lower insonating amplitude (shown in green), the region where the pressure exceeds the cavitation threshold is smaller.” Figure reprinted and caption quoted with permission from [10].


Fig. 9. The sparse aperture weighted algorithm (SW-TEA) mapping of the cavitation region in the tissue phantom with increasing (from left to right) peak negative pressure at the focus. The black ellipses show the expected cavitation shapes and sizes for the high-intensity focused ultrasound (HIFU) focus at the peak negative pressures PPNFP = 2.23, 2.62, and 3.35 MPa. 

difference coarray with image addition also allows for improved passive acoustic mapping. VII. Concluding Remarks In this paper, a prototype array for monitoring of ultrasound therapy using the concept of sparse rectangular boundary arrays was presented, as well as an algorithm for sparse-aperture weighted passive beamforming to create the passive acoustic maps. It was shown that the imaging performance, as measured by the PSF, was verified by both theoretical and experimental methods with reasonable agreement. In the experimental determination of the PSF, the sparse-aperture weighted beamforming algorithm achieved better performance than conventional passive acoustic mapping using TEA. Because the main interest in the array and methods is related to mapping inertial cavitation regions for monitoring ultrasound therapy, the performance of the methods compared with predicted regions of cavitation activity is crucial. The developed methods were shown to have good agreement in the passive maps compared with theory whereas for the same trials the conventional passive acoustic mapping using TEA was unable to achieve adequate performance. Future work in this area will be focused on a larger aperture array with larger element size for more clinically relevant applications in ultrasound therapy as well as algorithms that can deal with partial occlusions caused by ribs. Appendix Algorithm 1 Sparse Aperture Weighted Passive Beamforming.

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Given: i indexes the pixels, j index sensor positions, x = (x, y, z)T, sj(t) is received sensor data for sensor j. for i = 1 → M pixels do Compute delay: { τ ij = d ij /c : ∀j } Presteer data: for j = 1 : 4(N − 1) do s j(t) ← s j(t + τ ij ) end for Shift weight mask: C = γ(y) ← γ(y + x i ) Map Weights: C w ← Transform{C} Compute SVD: USV H ← SVD(C w) Threshold: N subimage ← threshold(S) for = 1 : N subimage do Form Weights: w 1() ← u σ l1/2 w 2() ← v σ l1/2 Apply weights: 4(N −1) q 1(t; ) ← β ∑j =1 w 1, j()d ijs j(t) 4(N −1)

q 2(t; ) ← β ∑j =1 w 2, j()d ijs j(t) Compute pixel values: t 0 +T 1 Ψ ,i ← q 1,i(t; )q 2,i(t; )∗ dt ∫ t 4πρocT 0 end for Sum subimages: Ψ TOTAL,i ← Ψ ,i end for

∑

Acknowledgments The present work was supported by the Oxford Centre of Excellence in Personalized Healthcare funded by the Wellcome Trust and the EPSRC under award number WT088877/Z/09/Z. The authors are grateful for the support of P. Doust and M. Tanner in the Acoustic Resonance Technology Centre of Det Norske Veritas, Portland, UK, for design and construction of the custom multichannel filter and preamplifier system. Additionally, the authors acknowledge the generous support of J. Hottenroth and R. McFadyen at National Instruments, and their help in with the PXI-based data collection system. From the Biomedical Ultrasonics, Biotherapy and Biopharmaceuticals Laboratory (BUBBL) at the University of Oxford, the authors thank J. Fisk and D. Salisbury for phantom holder construction, and J. Collin, S. Faragher, and C. Jensen for their technical expertise. References [1] M. Gyöngy and C.-C. Coussios, “Passive spatial mapping of inertial cavitation during HIFU exposure,” IEEE Trans. Biomed. Eng., vol. 57, no. 1, pp. 48–56, Jan. 2010. [2] M. Gyöngy, “Passive cavitation mapping for monitoring ultrasound therapy,” Ph.D. dissertation, Dept. of Eng. Sci., University of Oxford, Oxford, UK, 2011. [3] I. Rivens, A. Shaw, J. Civale, and H. Morris, “Treatment monitoring and thermometry for therapeutic focused ultrasound,” Int. J. Hyperthermia, vol. 23, no. 2, pp. 121–139, Mar. 2007. [4] T. Yu and C. Xu, “Hyperecho as the indicator of tissue necrosis during microbubble-assisted high intensity focused ultrasound: Sensitivity, specificity and predictive value,” Ultrasound Med. Biol., vol. 34, no. 8, pp. 1343–1347, 2008.

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[5] G. Hou, J. Lou, F. Marquet, C. Maleke, J. Vappou, and E. Konofagou, “Performance assessment of HIFU lesion detection by harmonic motion imaging for focused ultrasound (HMIFU): A 3-D finite-element framework with experimental validation,” Ultrasound Med. Biol., vol. 37, no. 12, pp. 2013–2027, 2011. [6] C. Jensen, R. Ritchie, M. Gyöngy, J. Collin, T. Leslie, and C.-C. Coussios, “Spatiotemporal monitoring of high-intensity focused ultrasound therapy passive acoustic mapping,” Radiology, vol. 262, no. 1, pp. 252–261, Jan. 2012. [7] R. Hoctor and S. Kassam, “The unifying role of the coarray in aperture synthesis for coherent and the unifying role of the coarray in aperture synthesis for coherent and incoherent imaging,” Proc. IEEE, vol. 78, no. 4, pp. 735–752, Apr. 1990. [8] R. Kozick and S. Kassam, “Linear imaging with sensor arrays on convex polygonal boundaries,” IEEE Trans. Syst. Man Cybern., vol. 21, no. 5, pp. 1155–1166, Sep./Oct. 1991. [9] J. Collin, R. Ritchie, M. Gyongy, D. Cranston, F. Wu, T. Leslie, and C.-C. Coussios, “Integration of an acoustically transparent passive cavitation detection array with a clinical high intensity focused ultrasound device,” presented at 11th Int. Symp. Therapeutic Ultrasound, New York, NY, 2011. [10] S. Faragher, “Cavitational methods for characterising and testing clinical high-intensity focused ultrasound systems,” Ph.D. dissertation, Dept. of Eng. Sci., University of Oxford, Oxford, UK, 2011. [11] B. Steinberg, Principles of Aperture and Array System Design: Including Random and Adaptive Arrays. New York, NY: Wiley, 1976. [12] M. Gyöngy and C. Coviello, “Passive cavitation mapping with temporal sparsity constraint,” J. Acoust. Soc. Am., vol. 130, no. 5, pp. 3489–3497, 2011. [13] A. Hurrell and F. Duck, “A two-dimensional hydrophone array using piezo-electric PVDF,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 47, no. 6, pp. 1345–1353, Nov. 2000. [14] T. Szabo, Diagnostic Ultrasound Imaging: Inside Out. Burlington, MA: Elsevier Academic Press, 2004. [15] L. Brown, “Design considerations for piezoelectric polymer ultrasound transducers,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 47, no. 6, pp. 1377–1396, Nov. 2000. [16] C.-C. Coussios and R. Roy, “Applications of acoustics and cavitation to noninvasive therapy and drug delivery,” Annu. Rev. Fluid Mech., vol. 40, pp. 395–420, 2008. [17] C.-C. Coussios, C. Farny, G. ter Haar, and R. Roy, “Role of acoustic cavitation in the delivery and monitoring of cancer treatment by high-intensity focused ultrasound HIFU,” Int. J. Hyperthermia, vol. 23, no. 2, pp. 105–120, 2007. [18] M. Gyöngy and C.-C. Coussios, “Passive cavitation mapping for localization and tracking of bubble dynamics,” J. Acoust. Soc. Am., vol. 128, no. 4, pp. EL175–EL180, 2010. [19] C. Coviello, “Robust Capon beamforming for passive cavitation mapping during HIFU therapy,” presented at 160th Meeting of Acoustical Society of America, 2010. [20] C. Chiffot, “Real-time passive mapping of acoustic cavitation during ultrasound therapy using parallel computing architectures,” M.Sc. thesis, Dept. of Eng. Sci., University of Oxford, Oxford, UK, Aug. 2011. [21] R. Kozick and S. Kassam, “Synthetic aperture pulse-echo imaging with rectangular boundary arrays,” IEEE Trans. Image Process., vol. 2, no. 1, pp. 68–79, Jan. 1993. [22] T. Mast, “Fresnel approximations for acoustic fields of rectangularly symmetric sources,” J. Acoust. Soc. Am., vol. 121, no. 6, pp. 3311–3322, Jun. 2007. [23] M. Arora, C. Arvanitis, and C.-C. Coussios, “Microparticle-based cavitation nucleation for enhancement of ultrasound therapy,” Ultrasonics, 2012, to be published. Christian Coviello received the B.S. degree in electrical engineering with honors from Bucknell University and, in August 2005, received the Ph.D. degree in electrical engineering from The Pennsylvania State University. From 2000 to 2005, he was a graduate research assistant under Dr. Leon Sibul at the Applied Research Laboratory at The Pennsylvania State University. From 2005 to 2009, he was employed as a senior scientist with SAIC in the Advanced Systems and Technology Division in Arlington, VA, where he remains as a consultant. In 2009, he

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joined the Biomedical Ultrasonics, Biotherapy and Biopharmaceuticals Laboratory (BUBBL) in the Institute of Biomedical Engineering at the University of Oxford. His research interests are in therapeutic ultrasound system design and targeted drug delivery.

Richard J. Kozick received the B.S. degree from Bucknell University in 1986, the M.S. degree from Stanford University in 1988, and the Ph.D. degree from the University of Pennsylvania in 1992, all in electrical engineering. From 1986 to 1989 and from 1992 to 1993, he was a Member of Technical Staff at AT&T Bell Laboratories. Since 1993, he has been with the Electrical Engineering Department at Bucknell University, where he is currently a Professor. His research interests are in the areas of statistical signal processing and com-

munications. Dr. Kozick received a 2006 Best Paper Award from the IEEE Signal Processing Society and the Presidential Award for Teaching Excellence from Bucknell University in 1999. He serves on the editorial boards of the Journal of the Franklin Institute and the EURASIP Journal on Wireless Communications and Networking.

Andrew M. Hurrell was born in Ashford, Kent, England, on January 12, 1972. He received a B.Sc. (Hons) degree in physics and modern acoustics from the University of Surrey in 1994 and a Ph.D. degree in underwater acoustics from the University of Bath in 2002. From 1994 to 1996, he was a member of the Acoustic Materials Team at the Defence Research Agency (Holton Heath). In 1996, he joined Precision Acoustics Ltd., Dorchester, where he is now a Senior Research Physicist. His current interests include design and construction of transducers, hydrophones, and piezoelectric arrays; development of novel sensor systems; and the use of finite-difference techniques to model acoustic phenomena. Dr. Hurrell has more than 35 publications and textbook chapters to his name, has won two prizes for the development of ultrasonic devices, and also serves as one of the UK members of IEC Technical Committee TC87 (Ultrasonics), and the British Standards Committee EPL/87 that shadows it.

Penny Probert Smith is a Reader of Engineering Science at the University of Oxford and has worked for the last twenty years in data fusion and imaging. In the last seven years, her interests have moved into medical imaging and image formation, in particular, using electromagnetic and ultrasound signals.

Constantin-C. Coussios was born in Athens, Greece, in 1977. He received B.A., M.Eng., M.A., and Ph.D. degrees in engineering from the University of Cambridge in the UK in 1997, 1998, 2000, and 2002, respectively, and was the recipient of the F. V. Hunt postdoctoral fellowship of the Acoustical Society of America in 2002–2003. He is currently the Professor of Biomedical Engineering at the University of Oxford, where he heads the Biomedical Ultrasonics, Biotherapy, and Biopharmaceuticals Laboratory in the Oxford Institute of Biomedical Engineering. He was a Board Member and Secretary of the International Society for Therapeutic Ultrasound between 2006 and 2010, was elected a Fellow of the Acoustical Society of America in 2009, and was chosen as the recipient of the Society’s Bruce Lindsay Award in 2012.