Improved contrast to tissue ratio at higher harmonics

The challenge in ultrasound contrast imaging is a better discrimination between the perfused tissue and the contrast bubbles, which is usually expressed by contrast to tissue ratio (CTR). Imaging based on the second harmonic frequency showed a higher CTR than imaging at the fundamental frequency. However, because of nonlinear propagation of ultrasound waves, harmonic frequencies are generated. These harmonic frequencies will be linearly reflected by the tissue and therefore limit the CTR at the second harmonic frequency. In order to reduce the scattering of tissue at harmonic frequencies and by that increase the CTR, nonlinear distortion has to be reduced. We demonstrate in this study that the CTR increases with the harmonic number. The increase is substantial when transmitting at lower frequencies. To take advantage of the higher harmonics (third, fourth, fifth and the ultraharmonics and termed here super harmonics), we have developed a new phased array transducer with a wide frequency band. In-vitro measurements using the new probe show an increase of 40 dB of the CTR for super harmonic components over the conventional second harmonic system. The increase in CTR is in agreement with the calculations using existing models for the response of encapsulated bubbles and known theory of nonlinear propagation.     

Measurement of high intensity focused ultrasound fields by a fiber optic probe hydrophone

The acoustic fields of a high intensity focused ultrasound (HIFU) transducer operating either at its fundamental (1.1 MHz) or third harmonic (3.3 MHz) frequency were measured by a fiber optic probe hydrophone (FOPH). At 1.1 MHz when the electric power applied to the transducer was increased from 1.6 to 125 W, the peak positive/negative pressures at the focus were measured to be p(+) = 1.7-23.3 MPa and p(-) = -1.2(-) -10.0 MPa. The corresponding spatial-peak pulse-average (I(SPPA)) and spatial-average pulse-average (I(SAPA)) intensities were I(SPPA) =77-6000 W/cm2 and I(SAPA) = 35-4365 W/cm2. Nonlinear propagation with harmonics generation was dominant at high intensities, leading to a reduced -6 dB beam size (L x W) of the compressional wave (11.5 x 1.8-8.8 1.04 mm) but an increased beam size of the rarefactional wave (12.5 x 1.6-13.2 x 2.0 mm). Enhancement ratio of absorbed power density in water increased from 1.0 to 3.0. In comparison, the HIFU transducer working at 3.3 MHz produced higher peak pressures (p(+) = 3.0-35.1 MPa and p(-) = -2.5(-) - 13.8 MPa) with smaller beam size (0.5 x 4 mm). Overall, FOPH was found to be a convenient and reliable tool for HIFU exposimetry measurement.     

Transfer functions of US transducers for harmonic imaging and bubble responses

Current medical diagnostic echo systems are mostly using harmonic imaging. This means that a fundamental frequency (e.g., 2 MHz) is transmitted and the reflected and scattered higher harmonics (e.g., 4 and 6 MHz), produced by nonlinear propagation, are recorded. The signal level of these harmonics is usually low and a well-defined transfer function of the receiving transducer is required. Studying the acoustic response of a single contrast bubble, which has an amplitude in the order of a few Pascal, is another area where an optimal receive transfer function is important.

We have developed three methods to determine the absolute transfer function of a transducer. The first is based on a well-defined wave generated by a calibrated source in the far field. The receiving transducer receives the calibrated wave and from this the transfer functions can be calculated. The second and third methods are based on the reciprocity of the transducer. The second utilizes a calibrated hydrophone to measure the transmitted field. In the third method, a pulse is transmitted by the transducer, which impinges on a reflector and is received again by the same transducer. In both methods, the response combined with the transducer impedance and beam profiles enables the calculation of the transfer function.

The proposed methods are useful to select the optimal piezoelectric material (PZT, single crystal) for transducers used in reception only, such as in certain 3D scanning designs and superharmonic imaging, and for selected experiments like single bubble behavior.

We tested and compared these methods on two unfocused single element transducers, one commercially available (radius 6.35 mm, centre frequency 2.25 MHz) the other custom built (radius 0.75 mm, centre frequency 4.3 MHz). The methods were accurate to within 15%.     

Feasibility of 3D harmonic contrast imaging

Improved endocardial border delineation with the application of contrast agents should allow for less complex and faster tracing algorithms for left ventricular volume analysis. We developed a fast rotating phased array transducer for 3D imaging of the heart with harmonic capabilities making it suitable for contrast imaging. In this study the feasibility of 3D harmonic contrast imaging is evaluated in vitro. A commercially available tissue mimicking flow phantom was used in combination with Sonovue. Backscatter power spectra from a tissue and contrast region of interest were calculated from recorded radio frequency data. The spectra and the extracted contrast to tissue ratio from these spectra were used to optimize the excitation frequency, the pulse length and the receive filter settings of the transducer. Frequencies ranging from 1.66 to 2.35 MHz and pulse lengths of 1.5, 2 and 2.5 cycles were explored. An increase of more than 15 dB in the contrast to tissue ratio was found around the second harmonic compared with the fundamental level at an optimal excitation frequency of 1.74 MHz and a pulse length of 2.5 cycles. Using the optimal settings for 3D harmonic contrast recordings volume measurements of a left ventricular shaped agar phantom were performed. Without contrast the extracted volume data resulted in a volume error of 1.5%, with contrast an accuracy of 3.8% was achieved. The results show the feasibility of accurate volume measurements from 3D harmonic contrast images. Further investigations will include the clinical evaluation of the presented technique for improved assessment of the heart.     

面向水下应用的电容式微机械超声换能器*

电容式微机械超声换能器具有宽频带和易于制造二维阵列等优势,已经成为一种重要的新型超声换能器。该文针对图像声呐系统对新型超声换能器的迫切需求,提出了一种电容式微机械超声换能器结构和参数,并利用硅微加工技术制备出了该换能器,最后对其主要性能参数进行了测试和分析。测试结果表明该换能器具有发射和接收超声波的功能,中心工作频率为1.965 MHz,6 dB相对带宽达到109.4%,在1 MHz、2 MHz和3 MHz频率时的接收灵敏度分别为-218.29 d B、-219.39 dB和-218.11 dB。该文研制的电容式微机械超声换能器显示出了优秀的宽频带特性,且工作频率和接收灵敏度性能均基本满足了高频图像声呐系统的需求。     

High frequency shear horizontal plate acoustic wave devices

It has been shown recently that shear horizontal acoustic waves propagating in piezoelectric plates whose thickness h is much less than the acoustic wavelength λ possess a number of attractive properties for use in sensor and signal processing applications. In order to exploit the potential benefits of these waves, however, one needs to fabricate devices on very thin plates. We have developed a suitable fabrication method which can be used to realize devices on such thin plates. In this method, the device is first fabricated on a plate of normal thickness (approximately 500 μm) and the substrate is then lapped from the back side to reduce the thickness. The technique has been utilized to realize devices on plates of thickness less than 70 μm. A shear horizontal plate acoustic wave (SH-PAW) delay line of fundamental resonant frequency greater than 25 MHz and insertion loss less than 7 dB has been realized on a 60 μm thick Y – cut, X – propagation lithium niobate substrate. The device also shows strong response near the third harmonic frequency of 75 MHz.     

高频聚焦超声声场和温度场的仿真研究*

为探究临床常用的7 MHz高频聚焦超声在多层生物组织中的声传播以及毫秒级时间内的生物传热规律问题,基于Westervelt方程和Pennes传热方程,使用有限元方法建立高频聚焦超声辐照多层组织的非线性热黏性声传播及传热模型。首先分析了线性模型和非线性模型之间的差异,然后在非线性模型下探究换能器的参数对声场和温度场的影响。仿真结果显示：在7 MHz频率下,当换能器输出声功率超过5 W时,声波传播的非线性效应不可忽视(p <0.05);当声功率从5 W增大到15 W时,非线性模型与线性模型预测的温度偏差从20%增加到34.703%;高频聚焦超声波的非线性行为比低频更加显著,基频能量向高次谐波转移的程度增大,声功率为10 W和15 W时4次谐波与基波之比分别达到7.33%和12.12%;高频换能器参数的改变对组织中声场和温度场分布的影响较大,换能器焦距从12 mm减小到11.2 mm,焦点处最高温度增加了77%。结果表明,7 MHz聚焦超声的非线性声传播需要考虑到4次谐波的影响。该文提出的多层组织非线性仿真模型可为高频聚焦超声换能器参数优化及制定安全、有效的术前治疗方案提供理论参考。     

Multi-frequency harmonic arrays: initial experience with a novel transducer concept for nonlinear contrast imaging

Nonlinear contrast imaging modes such as second harmonic imaging (HI) and subharmonic imaging (SHI) are increasingly important for clinical applications. However, the performance of currently available transducers for HI and SHI is significantly constrained by their limited bandwidth. To bypass this constraint, a novel transducer concept termed multi-frequency harmonic transducer arrays (MFHA's) has been designed and a preliminary evaluation has been conducted. The MFHA may ultimately be used for broadband contrast enhanced HI and SHI with high dynamic range and consists of three multi-element piezo-composite sub-arrays (A-C) constructed so the center frequencies are 4f(A) = 2f(B) = f(C) (specifically 2.5/5.0/10.0 MHz and 1.75/3.5/7.0 MHz). In principle this enables SHI by transmitting on sub-array C receiving on B and, similarly, from B to A as well as HI by transmitting on A receiving on B and, likewise, from B to C. Initially transmit and receive pressure levels of the arrays were measured with the elements of each sub-array wired in parallel. Following contrast administration, preliminary in vitro HI and SHI signal-to-noise ratios of up to 40 dB were obtained. In conclusion, initial design and in vitro characterization of two MFHA's have been performed. They have an overall broad frequency bandwidth of at least two octaves. Due to the special design of the array assembly, the SNR for HI and SHI was comparable to that of regular B-mode and better than commercially available HI systems. However, further research on multi-element MFHA's is required before their potential for in vivo nonlinear contrast imaging can be assessed.     

Fabrication and evaluation of fully-sampled, two-dimensional transducer array for "Sonic Window" imaging system

A low-cost, fully-sampled, 3600 element 2D transducer array operating at 5 MHz and designed for use in a hand-held ultrasound system is described here. Four array configurations are presented - (1) array with both matching and pedestal backing layers, (2) array with a matching layer but no backing pedestal, (3) array with a backing pedestal but no matching layer, and (4) array with neither matching layer nor backing pedestal. Each array was characterized in terms of impedance measurements, pulse-echo response, and experimental beamprofile. Comparative finite element analysis simulations are also presented. Average estimated active element yield for the four arrays was 94%. The array with pedestal layer proved the most promising, providing a 26% bandwidth and a 1.7 dB improvement in sensitivity with respect to the array with neither pedestal nor matching layer. Although this bandwidth is acceptable for our specific application (C-scan imaging), reverberations within the substrate material remain a potential challenge. We are currently working to fabricate a custom PCB material to address this concern, and may also consider using a pre-compensated transmit waveform or matched digital filter approach to further reduce the effects of such reverberations.     

Acoustic microscopy system: design and preliminary results

An acoustic microscopy system was designed to perform 2D imaging in the C-plane with a single-element transducer. The ultrasound transducer was fabricated by polishing bulk lithium niobate (LiNbO(3)) to the required thickness (approximately 60 or 45 micro) for the desired operating frequency (55 or 75 MHz). The polished LiNbO(3) was attached to acoustic backing and matching layers. Finally, an epoxy lens was applied and the transducer mounted in a housing. The transducer was mounted in a 3D motorized positioning stage and operated by a high-frequency pulser/receiver. Received echoes were sampled with a 2 GHz ADC card and displayed on a PC using software developed in the Matlab environment. Transducer frequency and bandwidth were measured off a steel plate positioned at the focal length. A penny was scanned initially to confirm expected performance before acquiring data from liver (n=3) and spleen (n=3) specimens. For the first probe, the peak frequency was 54.05 MHz with a -6 dB bandwidth of 6.76 MHz. The axial and lateral resolutions were estimated to be 114 and 188 microm, respectively. For the second probe, the peak frequency was measured to 82 MHz with a -6 dB bandwidth of approximately 23 MHz. The axial and lateral resolutions were estimated to be around 33 and 81 microm, respectively. C-scans of the penny clearly showed detailed structures on front and back, while the capsule and the trabecular structures of the splenic tissues could easily be separated in different layers. In conclusion, an acoustic microscopy system operating at 55-75 MHz has been constructed and the feasibility of obtaining high-resolution images of tissue specimens demonstrated.     

Microwave frequency modulation in CW EPR at W-band using a loop-gap resonator

Loop-gap resonator (LGR) technology has been extended to W-band (94GHz). One output of a multiarm Q-band (35GHz) EPR bridge was translated to W-band for sample irradiation by mixing with 59 GHz; similarly, the EPR signal was translated back to Q-band for detection. A cavity resonant in the cylindrical TE011 mode suitable for use with 100 kHz field modulation has also been developed. Results using microwave frequency modulation (FM) at 50 kHz as an alternative to magnetic field modulation are described. FM was accomplished by modulating a varactor coupled to the 59 GHz oscillator. A spin-label study of sensitivity was performed under conditions of overmodulation and gamma2H1(2)T1T2<1. EPR spectra were obtained, both absorption and dispersion, by lock-in detection at the fundamental modulation frequency (50 kHz), and also at the second and third harmonics (100 and 150 kHz). Source noise was deleterious in first harmonic spectra, but was very low in second and third harmonic spectra. First harmonic microwave FM was transferred to microwave modulation at second and third harmonics by the spins, thus satisfying the "transfer of modulation" principle. The loaded Q-value of the LGR with sample was 90 (i.e., a bandwidth between 3 dB points of about 1 GHz), the resonator efficiency parameter was calculated to be 9.3 G at one W incident power, and the frequency deviation was 11.3 MHz p-p, which is equivalent to a field modulation amplitude of 4 G. W-band EPR using an LGR is a favorable configuration for microwave FM experiments.     

Third harmonic transmit phasing for SNR improvement in tissue harmonic imaging with Golay-encoded excitation

Background

Ultrasound tissue harmonic signal generally provides superior image quality as compared to the linear signal. However, since the generation of the tissue harmonic signal is based on finite amplitude distortion of the propagating waveform, the penetration and the sensitivity in tissue harmonic imaging are markedly limited because of the low signal-to-noise ratio (SNR).

Methods

The method of third harmonic (3f₀) transmit phasing can improve the tissue harmonic SNR by transmitting at both the fundamental (2.25 MHz) and the 3f₀ (6.75 MHz) frequencies to achieve mutual enhancement between the frequency-sum and the frequency-difference components of the second harmonic signal. To further increase the SNR without excessive transmit pressure, coded excitation can be incorporated in 3f₀ transmit phasing to boost the tissue harmonic generation.

Results

Our analyses indicate that the phase-encoded Golay excitation is suitable in 3f₀ transmit phasing due to its superior transmit bandwidth efficiency. The resultant frequency-sum and frequency-difference components of tissue harmonic signal can be simultaneously Golay-encoded for SNR improvement. The increase of the main-lobe signal with the Golay excitation in 3f₀ transmit phasing are consistent between the tissue harmonic measurements and the simulations. B-mode images of the speckle generating phantom also demonstrate the increases of tissue harmonic SNR for about 11 dB without noticeable compression artifacts.

Conclusion

For tissue harmonic imaging in combination with the 3f₀ transmit phasing method, the Golay excitation can provide further SNR improvement. Meanwhile, the axial resolution can be effectively restored by pulse compression while the lateral resolution remains unchanged.     

Localization and source level estimates of black drum (Pogonias cromis) calls

A four hydrophone linear array was used to localize calling black drum and estimate source levels and signal propagation. A total of 1025 source level estimates averaged 165 dB(RMS) relative (re:) 1 μPa (standard deviation (SD)=1.0). The authors suggest that the diverticulated morphology of the black drum swimbladder increase the bladder's surface area, thus contributing to sound amplitude. Call energy was greatest in the fundamental frequency (94 Hz) followed by the second (188 Hz) and third harmonics (282 Hz). A square root model best described propagation of the entire call, and separately the fundamental frequency and second harmonic. A logarithmic model best described propagation of the third harmonic which was the only component to satisfy the cut-off frequency equation. Peak auditory sensitivity was 300 Hz at a 94 dB re: 1 μPa threshold based on auditory evoked potential measurements of a single black drum. Based on mean RMS source level, signal propagation, background levels, and hearing sensitivity, the communication range of black drum was estimated at 33-108 m and was limited by background levels not auditory sensitivity. This estimate assumed the source and receiver were at approximately 0.5 m above the bottom. Consecutive calls of an individual fish localized over 59 min demonstrated a mean calling period of 3.6 s (SD=0.48), mean swimming speed of 0.5 body lengths/s, and a total distance swam of 1035 m.     

Flexible piezoelectric transducer for ultrasonic inspection of non-planar components

This paper presents the fabrication and characterisation of a flexible ultrasonic transducer using commercially available PZT-5A piezoelectric fibers which are lapped to form rectangular piezoelectric elements. The key feature in the device construction is the inclusion of gaps between the piezoelectric fibers to ensure good flexibility in the plane normal to the fiber direction. The spatial response of the transducer ultrasonic output was assessed using acoustographic imaging. The flexibility of the transducer and its applicability in pulse-echo mode on curved sections was demonstrated by testing on a 38 mm diameter steel rod. The transducer response was found to be broad band and highly non uniform but good pulse-echo performance was achieved at 5 MHz.     

Effect of dual-frequency clutter suppression in harmonic Doppler detection

Background

High-frequency Doppler imaging is highly potential for detection of blood flow in microcirculation. In a swept-scan system, however, the spectral broadening of tissue clutter limits the detectability of low-velocity flow signal. Conventionally, the scanning speed of transducer has to be reduced to alleviate the clutter interference but at the cost of imaging frame rate. For example, the blood velocity of 0.5 mm/s becomes detectable only with a scanning speed lower than 1 mm/s. In this study, an alternative method is examined by suppressing the clutter magnitude to reduce the interference to flow signal without sacrificing scanning speed.

Methods

The method of third harmonic (3f₀) transmit phasing can suppress the tissue harmonic clutter by transmitting at the fundamental and the additional 3f₀ frequencies to achieve mutual cancellation between the frequency-sum and the frequency-difference components of the second harmonic signal. With 3f₀ transmit phasing, the cut-off frequency of wall filtering can be reduced to preserve low-velocity flow without compromising the frame rate.

Results

Our results indicate that the 3f₀ transmit phasing effectively reduces the harmonic clutter magnitude and thus improves the flow signal-to-clutter ratio. Compared to the conventional counterpart, the clutter-suppressed color flow and power Doppler images show fewer clutter artifacts and is capable of detecting more low-velocity flow of microbubbles. The resultant color-pixel-density also improves with clutter suppression.

Conclusion

For the swept-scan high-frequency (>20 MHz) system, 3f₀ transmit phasing is capable of providing effective clutter suppression. With the same achievable scanning speed, the resultant Doppler image has higher sensitivity for low-velocity flow and is less susceptible to clutter artifacts.     

Lens-focused transducer modeling using an extended KLM model

The goal of this work was to develop an extended ultrasound transducer model that would optimize the trade-off between accuracy of the calculation and computational time. The derivations are presented for a generalized transducer model, that is center frequency, pulse duration and physical dimensions are all normalized. The paper presents a computationally efficient model for lens-focused, circular (axisymmetric) single element piezoelectric ultrasound transducer. Specifically, the goal of the model is to determine the lens effect on the electro-acoustic response, both on focusing and on matching acoustic properties. The effective focal distance depends on the lens geometry and refraction index, but also on the near field limit, i.e. wavelength and source radius, and on the spectrum bandwidth of the ultrasound source. The broadband (80%) source generated by the transducer was therefore considered in this work. A new model based on a longitudinal-wave assumption is presented and the error introduced by this assumption is discussed in terms of its maximum value (16%) and mean value (5.9%). The simplified model was based on an extension of the classical KLM model for transducer structures and on the related assumptions. The validity of the implemented extended KLM model was evaluated by comparison with finite element modeling, itself previously validated analytically for the one-dimensional planar geometry considered. The pressure field was then propagated using the adequate formulation of the Rayleigh integral for both the extended KLM and finite element results. The simplified approach based on the KLM model delivered the focused response with good accuracy, and hundred-fold lower calculation time in comparison with a mode comprehensive FEM method. The trade-off between precision and time thus becomes compatible with an iterative procedure, used here for the optimization of the acoustic impedance of the lens for the chosen configuration. An experimental comparison was performed and found to be in good agreement with such an extension of the KLM model. The experiments confirm the accuracy of such a model in a validity domain up to −12 dB on the pulse-echo voltage within a relative error of 9% between experiment and modeling. This extended KLM model can advantageously be used for other transducer geometries satisfying the assumption of a predominantly longitudinal vibration or in an optimization procedure involving an adequate criteria for a particular application.     

Theoretical analysis of a quartz-enhanced photoacoustic spectroscopy sensor

Quartz-enhanced photoacoustic spectroscopy (QEPAS) sensors are based on a recent approach to photoacoustic detection which employs a quartz tuning fork as an acoustic transducer. These sensors enable detection of trace gases for air quality monitoring, industrial process control, and medical diagnostics. To detect a trace gas, modulated laser radiation is directed between the tines of a tuning fork. The optical energy absorbed by the gas results in a periodic thermal expansion which gives rise to a weak acoustic pressure wave. This pressure wave excites a resonant vibration of the tuning fork thereby generating an electrical signal via the piezoelectric effect. This paper describes a theoretical model of a QEPAS sensor. By deriving analytical solutions for the partial differential equations in the model, we obtain a formula for the piezoelectric current in terms of the optical, mechanical, and electrical parameters of the system. We use the model to calculate the optimal position of the laser beam with respect to the tuning fork and the phase of the piezoelectric current. We also show that a QEPAS transducer with a particular 32.8 kHz tuning fork is 2–3 times as sensitive as one with a 4.25 kHz tuning fork. These simulation results closely match experimental data.     

Bipolar-power-transistor-based limiter for high frequency ultrasound imaging systems

High performance limiters are described in this paper for applications in high frequency ultrasound imaging systems. Limiters protect the ultrasound receiver from the high voltage (HV) spikes produced by the transmitter. We present a new bipolar power transistor (BPT) configuration and compare its design and performance to a diode limiter used in traditional ultrasound research and one commercially available limiter. Limiter performance depends greatly on the insertion loss (IL), total harmonic distortion (THD) and response time (RT), each of which will be evaluated in all the limiters. The results indicated that, compared with commercial limiter, BPT-based limiter had less IL (−7.7 dB), THD (−74.6 dB) and lower RT (43 ns) at 100 MHz. To evaluate the capability of these limiters, they were connected to a 100 MHz single element transducer and a two-way pulse-echo test was performed. It was found that the −6 dB bandwidth and sensitivity of the transducer using BPT-based limiter were better than those of the commercial limiter by 22% and 140%, respectively. Compared to the commercial limiter, BPT-based limiter is shown to be capable of minimizing signal attenuation, RT and THD at high frequencies and is thus suited for high frequency ultrasound applications.     

Micromachined high frequency PMN-PT/epoxy 1-3 composite ultrasonic annular array

This paper reports the design, fabrication, and performance of miniature micromachined high frequency PMN-PT/epoxy 1-3 composite ultrasonic annular arrays. The PMN-PT single crystal 1-3 composites were made with micromachining techniques. The area of a single crystal pillar was 9 × 9 μm. The width of the kerf among pillars was ∼5 μm and the kerfs were filled with a polymer. The composite thickness was 25 μm. A six-element annular transducer of equal element area of 0.2 mm² with 16 μm kerf widths between annuli was produced. The aperture size the array transducer is about 1.5 mm in diameter. A novel electrical interconnection strategy for high density array elements was implemented. After the transducer was attached to the electric connection board and packaged, the array transducer was tested in a pulse/echo arrangement, whereby the center frequency, bandwidth, two-way insertion loss (IL), and cross talk between adjacent elements were measured for each annulus. The center frequency was 50 MHz and −6 dB bandwidth was 90%. The average insertion loss was 19.5 dB at 50 MHz and the crosstalk between adjacent elements was about −35 dB. The micromachining techniques described in this paper are promising for the fabrication of other types of high frequency transducers, e.g. 1D and 2D arrays.     

Extension of the crosstalk cancellation method in ultrasonic transducer arrays from the harmonic regime to the transient one

This paper describes a procedure to extend the crosstalk correction method presented in a previous paper [A. Bybi, S. Grondel, J. Assaad, A.–C. Hladky-Hennion, M. Rguiti, Reducing crosstalk in array structures by controlling the excitation voltage of individual elements: a feasibility study, Ultrasonics, 53 (6) (2013) 1135–1140] from the harmonic regime to the transient one. For this purpose a part of an ultrasonic transducer array radiating in water is modeled around the frequency 0.5 MHz using the finite element method. The study is carried out at low frequency in order to respect the same operating conditions than the previous paper. This choice facilitated the fabrication of the transducer arrays and the comparison of the numerical results with the experimental ones. The modeled array is composed of seventeen elements with the central element excited, while the others are grounded. The matching layers and the backing are not taken into account which limits the crosstalk only to the piezoelectric elements and fluid. This consideration reduces the structure density mesh and results in faster computation time (about 25 min for each configuration using a computer with a processor Intel Core i5-3210M, frequency 2.5 GHz and having 4 Go memory (RAM)).