Erwan Filoux

Modeling of piezoelectric transducers with combined pseudospectral and finite-difference methods.

A new hybrid finite-difference (FD) and pseudospectral (PS) method adapted to the modeling of piezoelectric transducers (PZTs) is presented. The time-dependent equations of propagation are solved using the PS method while the electric field induced in the piezoelectric material is determined through a FD representation. The purpose of this combination is to keep the advantages of both methods in one model: the adaptability of FD representation to model piezoelectric elements with various geometries and materials, and the low number of nodes per wavelength required by the PS method. This approach is implemented to obtain an accurate algorithm to simulate the propagation of acoustic waves over large distances, directly coupled to the calculation of the electric field created inside the piezoelectric material, which is difficult with classical algorithms. These operations are computed using variables located on spatially and temporally staggered grids, which attenuate Gibbs phenomenon and increase the algorithms accuracy. The two-dimensional modeling of a PZT plate excited by a 50 MHz sinusoidal electrical signal is performed. The results are successfully compared to those obtained using the finite-element (FE) algorithm of ATILA software with configurations spatially and temporally adapted to the FE requirements. The cost efficiency of the FD-PS time-domain method is quantified and verified.

Characterization of the spatial resolution of different high-frequency imaging systems using a novel anechoic-sphere phantom

The spatial resolution of high-frequency ultrasound (HFU, >;20 MHz) imaging systems is usually determined using wires perpendicular to the beam. Recently, two tissue-mimicking phantoms (TMPs) were developed to estimate three-dimensional (3-D) resolution. Each TMP consists of nine 1-cm-wide slabs of tissue-mimicking material containing randomly distributed anechoic spheres. All anechoic spheres in one slab have the same dimensions, and their diameter is increased from 0.1 mm in the first slab to 1.09 mm in the last. The scattering background for one set of slabs was fabricated using 3.5-μm glass beads; the second set used 6.4-μm glass beads. The ability of a HFU system to detect these spheres against a speckle background provides a realistic estimation of its 3-D spatial resolution. In the present study, these TMPs were used with HFU systems using single-element transducers, linear arrays, and annular arrays. The TMPs were immersed in water and each slab was scanned using two commercial imaging systems and a custom HFU system based on a 5-element annular array. The annular array had a nominal center frequency of 40 MHz, a focal length of 12 mm, and a total aperture of 6 mm. A synthetic-focusing algorithm was used to form images with an increased depth-of-field. The penetration depth was increased by using a linear-chirp signal spanning 15 to 65 MHz over 4 μs. Results obtained with the custom system were compared with those of the commercial systems (40-MHz probes) in terms of sphere detection, i.e., 3-D spatial resolution, and contrast-to-noise ratio (CNR). Resulting B-mode images indicated that only the linear-array transducer failed to clearly resolve the 0.2-mm spheres, which showed that the 3-D spatial resolution of the single-element and annulararray transducers was superior to that of the linear array. The single-element transducer could only detect these spheres over a narrow 1.5 mm depth-of-field, whereas the annular array was able to detect them to depths of at least 7 mm. For any size of the anechoic spheres, the annular array excited by a chirp-coded signal provided images of the highest contrast, with a maximum CNR of 1.8 at the focus, compared with 1.3 when using impulse excitation and 1.6 with the single-element transducer and linear array. This imaging configuration also provided CNRs above 1.2 over a wide depth range of 8 mm, whereas CNRs would quickly drop below 1 outside the focal zone of the other configurations.The spatial resolution of high-frequency ultrasound (HFU, >;20 MHz) imaging systems is usually determined using wires perpendicular to the beam. Recently, two tissue-mimicking phantoms (TMPs) were developed to estimate three-dimensional (3-D) resolution. Each TMP consists of nine 1-cm-wide slabs of tissue-mimicking material containing randomly distributed anechoic spheres. All anechoic spheres in one slab have the same dimensions, and their diameter is increased from 0.1 mm in the first slab to 1.09 mm in the last. The scattering background for one set of slabs was fabricated using 3.5-μm glass beads; the second set used 6.4-μm glass beads. The ability of a HFU system to detect these spheres against a speckle background provides a realistic estimation of its 3-D spatial resolution. In the present study, these TMPs were used with HFU systems using single-element transducers, linear arrays, and annular arrays. The TMPs were immersed in water and each slab was scanned using two commercial imaging systems and a custom HFU system based on a 5-element annular array. The annular array had a nominal center frequency of 40 MHz, a focal length of 12 mm, and a total aperture of 6 mm. A synthetic-focusing algorithm was used to form images with an increased depth-of-field. The penetration depth was increased by using a linear-chirp signal spanning 15 to 65 MHz over 4 μs. Results obtained with the custom system were compared with those of the commercial systems (40-MHz probes) in terms of sphere detection, i.e., 3-D spatial resolution, and contrast-to-noise ratio (CNR). Resulting B-mode images indicated that only the linear-array transducer failed to clearly resolve the 0.2-mm spheres, which showed that the 3-D spatial resolution of the single-element and annulararray transducers was superior to that of the linear array. The single-element transducer could only detect these spheres over a narrow 1.5 mm depth-of-field, whereas the annular array was able to detect them to depths of at least 7 mm. For any size of the anechoic spheres, the annular array excited by a chirp-coded signal provided images of the highest contrast, with a maximum CNR of 1.8 at the focus, compared with 1.3 when using impulse excitation and 1.6 with the single-element transducer and linear array. This imaging configuration also provided CNRs above 1.2 over a wide depth range of 8 mm, whereas CNRs would quickly drop below 1 outside the focal zone of the other configurations.

Pulse-Encoded Ultrasound Imaging of the Vitreous With an Annular Array

The vitreous body is nearly transparent both optically and ultrasonically. Conventional 10- to 12-MHz diagnostic ultrasound can detect vitreous inhomogeneities at high gain settings, but has limited resolution and sensitivity, especially outside the fixed focal zone near the retina. To improve visualization of faint intravitreal fluid/gel interfaces, the authors fabricated a spherically curved 20-MHz five-element annular array ultrasound transducer, implemented a synthetic-focusing algorithm to extend the depth-of-field, and used a pulse-encoding strategy to increase sensitivity. The authors evaluated a human subject with a recent posterior vitreous detachment and compared the annular array with conventional 10-MHz ultrasound and spectral-domain optical coherence tomography. With synthetic focusing and chirp pulse-encoding, the array allowed visualization of the formed and fluid components of the vitreous with improved sensitivity and resolution compared with the conventional B-scan. Although optical coherence tomography allowed assessment of the posterior vitreoretinal interface, the ultrasound array allowed evaluation of the entire vitreous body.

Single-element ultrasonic transducer modeling using a hybrid FD-PSTD method.

In a recent publication [E. Filoux, S. Callé, D. Certon, M. Lethiecq, F. Levassort, Modeling of piezoelectric transducers with combined pseudospectral and finite-difference methods, J. Acoust. Soc. Am. 123 (6) (2008) 4165-4173], a new finite-difference/pseudospectral time-domain (FD-PSTD) algorithm was presented and used to model the generation of acoustic waves by a piezoelectric resonator and their propagation in the structure and the surrounding water. In this paper, the model has been extended to simulate the two-dimensional behaviour of a complete single-element transducer, composed of the resonator, a backing and a front matching layer. This further version of the model takes into account the mechanical loss in materials, and enables the calculation of electrical impedance, which is a characteristic of high interest to optimize the performance of ultrasonic transducers. The impedance curves of a PZT [URL: http://www.ferroperm-piezo.com (last viewed 04/2008); B. Jaffe, R.S. Roth, S. Marzullo, Piezoelectric properties of lead zirconate-lead titanate solid-solution ceramics, J. Appl. Phys. 25 (1954) 809-810] plate-based high-frequency transducer, with a 50 MHz thickness resonant frequency, were compared to those of a KLM model [R. Krimholtz, D.A. Leedom, G.L. Matthei, New equivalent circuit for elementary piezoelectric transducers, Electron. Lett. 6 (1970) 398-399] in the one-dimensional case. The acoustical properties were also found to be in good agreement with those obtained using the finite element (FE) method of ATILA software in two-dimensional configuration.

P3Q-3 Curved Piezoelectric Thick Films for High Resolution Medical Imaging

A fabrication process is described to fabricate an integrated structure involving a curved piezoelectric thick film. The development of this multilayer structure is performed to minimize the fabrication steps of the corresponding high frequency single element transducer. On the basis of previous work carried out in order to choose the material of each layer and in particular a porous PZT substrate directly used as the backing, a pad-printing process has been developed and used to deposit several layers of PZT paste to obtain a curved PZT thick film. The effective thickness coupling factor has a value of 47% and resonant frequency can easily reach 50 MHz. Two high frequency transducers have been successfully fabricated and characterized for medical imaging with center frequencies at 20 and 30 MHz. Very good axial resolution is obtained (41 mum at a center frequency of 20 MHz) while keeping satisfactory sensitivity. Images of human skin in vivo and of phantoms confirm the good properties delivered by the transducers using these integrated structures

High-frequency annular array with coaxial illumination for dual-modality ultrasonic and photoacoustic imaging

This paper presents a combined ultrasound and photoacoustic (PA) imaging (PAI) system used to obtain high-quality, co-registered images of mouse-embryo anatomy and vasculature. High-frequency ultrasound (HFU, >20 MHz) is utilized to obtain high-resolution anatomical images of small animals while PAI provides high-contrast images of the vascular network. The imaging system is based on a 40 MHz, 5-element, 6 mm aperture annular-array transducer with a 800 μm diameter hole through its central element. The transducer was integrated in a cage-plate assembly allowing for a collimated laser beam to pass through the hole so that the optical and acoustic beams were collinear. The assembly was mounted on a two-axis, motorized stage to enable the simultaneous acquisition of co-registered HFU and PA volumetric data. Data were collected from all five elements in receive and a synthetic-focusing algorithm was applied in post-processing to beamform the data and increase the spatial resolution and depth-of-field (DOF) of the HFU and PA images. Phantom measurements showed that the system could achieve high-resolution images (down to 90 μm for HFU and 150 μm for PAI) and a large DOF of >8 mm. Volume renderings of a mouse embryo showed that the scanner allowed for visualizing morphologically precise anatomy of the entire embryo along with corresponding co-registered vasculature. Major head vessels, such as the superior sagittal sinus or rostral vein, were clearly identified as well as limb bud vasculature.

Non-planar pad-printed thick-film focused high-frequency ultrasonic transducers for imaging and therapeutic applications

Pad-printed thick-film transducers have been shown to be an interesting alternative to lapped bulk piezoceramics, because the film is deposited with the required thickness, size, and geometry, thus avoiding any subsequent machining to achieve geometrical focusing. Their electromechanical properties are close to those of bulk ceramics with similar composition despite having a higher porosity. In this paper, pad-printed high-frequency transducers based on a low-loss piezoceramic composition are designed and fabricated. High-porosity ceramic cylinders with a spherical top surface are used as the backing substrate. The transducers are characterized in view of imaging applications and their imaging capabilities are evaluated with phantoms containing spherical inclusions and in different biological tissues. In addition, the transducers are evaluated for their capability to produce high-acoustic intensities at frequencies around 20 MHz. High-intensity measurements, obtained with a calibrated hydrophone, show that transducer performance is promising for applications that would require the same device to be used for imaging and for therapy. Nevertheless, the transducer design can be improved, and simulation studies are performed to find a better compromise between low-power and high-power performance. The size, geometry, and constitutive materials of optimized configurations are proposed and their feasibility is discussed.

3-D numerical modeling for axisymmetrical piezoelectric structures: application to high-frequency ultrasonic transducers

The transient analysis of piezoelectric transducers is often performed using finite-element or finite-difference time-domain methods, which efficiently calculate the vibration of the structure but whose numerical dispersion prevents the modeling of waves propagating over large distances. A second analytical or numerical simulation is therefore often required to calculate the pressure field in the propagating medium (typically water) to deduce many important characteristics of the transducer, such as spatial resolutions and side lobe levels. This is why a hybrid algorithm was developed, combining finite- difference and pseudo-spectral methods in the case of 2-D configurations to simulate accurately both the generation of acoustic waves by the piezoelectric transducer and their propagation in the surrounding media using a single model. The algorithm was redefined in this study to take all three dimensions into account and to model single-element transducers, which usually present axisymmetrical geometry. This method was validated through comparison of its results with those of finite-element software, and was used to simulate the behavior of planar and lens-focused transducers. A high-frequency (30 MHz) transducer based on a screen-printed piezoelectric thick film was fabricated and characterized. The numerical results of the hybrid algorithm were found to be in good agreement with the experimental measurements of displacements at the surface of the transducer and of pressure radiated in water in front of the transducer.

Synthetic-focusing strategies for real-time annular-array imaging

Annular arrays provide a means to achieve enhanced image quality with a limited number of elements. Synthetic-focusing (SF) strategies that rely on beamforming data from individual transmit-to-receive (TR) element pairs provide a means to improve image quality without specialized TR delay electronics. Here, SF strategies are examined in the context of high-frequency ultrasound (>15 MHz) annular arrays composed of five elements, operating at 18 and 38 MHz. Acoustic field simulations are compared with experimental data acquired from wire and anechoic-sphere phantoms, and the values of lateral beamwidth, SNR, contrast-to-noise ratio (CNR), and depth of field (DOF) are compared as a function of depth. In each case, data were acquired for all TR combinations (25 in total) and processed with SF using all 25 TR pairs and SF with the outer receive channels removed one by one. The results show that removing the outer receive channels led to an overall degradation of lateral resolution, an overall decrease in SNR, and did not reduce the DOF, although the DOF profile decreased in amplitude. The CNR was >1 and remained fairly constant as a function of depth, with a slight decrease in CNR for the case with just the central element receiving. The relative changes between the calculated and measured quantities were nearly identical for the 18- and 38-MHz arrays. B-mode images of the anechoic phantom and an in vivo mouse embryo using full SF with 25 TR pairs or reduced TR-pair approaches showed minimal qualitative difference.

Coherence-Weighted Synthetic Focusing Applied to Photoacoustic Imaging Using a High-Frequency Annular-Array Transducer.

This paper presents an adaptive synthetic-focusing scheme that, when applied to photoacoustic (PA) data acquired using an annular array, improves focusing across a greater imaging depth and enhances spatial resolution. The imaging system was based on a 40-MHz, 5-element, annular-array transducer with a focal length of 12 mm and an 800-µm diameter hole through its central element to facilitate coaxial delivery of 532-nm laser. The transducer was raster-scanned to facilitate 3D acquisition of co-registered ultrasound and PA image data. Three synthetic-focusing schemes were compared for obtaining PA A-lines for each scan location: delay-and-sum (DAS), DAS weighted with a coherence factor (DAS + CF), and DAS weighted with a sign-coherence factor (DAS + SCF). Bench-top experiments that used an 80-µm hair were performed to assess the enhancement provided by the two coherence-based schemes. Both coherence-based schemes increased the signal-to-noise ratio by approximately 10 dB. When processed using the DAS-only scheme, the lateral dimension of the hair in a PA image with 20 dB dynamic range was between 300 µm and 1 mm for imaging depth ranging from 8 to 20 mm. In comparison, the DAS + CF scheme resulted in a lateral dimension of 200 to 450 µm over the same range. The DAS + SCF synthetic focusing further improved the smallest-resolvable dimension, which was between 150 and 400 µm over the same range of imaging depth. When used on PA data obtained from a 12-day-old mouse embryo, the DAS + SCF processing improved visualization of neurovasculature.