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Mode Vibrations of a Matrix Transducer for Three-Dimensional Second Harmonic Transesophageal Echocardiography
Ultrasound in Med. & Biol., Vol. 38, No. 10, pp. 1820–1832, 2012 Copyright Ó 2012 World Federation for Ultrasound in Medicine & Biology Printed in the USA. All rights reserved 0301-5629/$ - see front matter
http://dx.doi.org/10.1016/j.ultrasmedbio.2012.06.007
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Original Contribution MODE VIBRATIONS OF A MATRIX TRANSDUCER FOR THREE-DIMENSIONAL SECOND HARMONIC TRANSESOPHAGEAL ECHOCARDIOGRAPHY PAUL L. M. J. VAN NEER,*1 SANDRA BLAAK,* JOHAN G. BOSCH,* CHARLES T. LANCEE,* CHRISTIAN PRINS,y ANTON F. W. VAN DER STEEN,* and NICO DE JONG* * Department of Biomedical Engineering, Erasmus Medical Centre, Rotterdam, The Netherlands; and y Oldelft Ultrasound, Delft, The Netherlands (Received 20 December 2011; revised 30 May 2012; in final form 18 June 2012)
Abstract—Transesophageal echocardiography (TEE) uses the esophagus as an imaging window to the heart. This enables cardiac imaging without interference from the ribs or lungs and allows for higher frequency ultrasound to be used compared with transthoracic echocardiography (TTE). TEE facilitates the successful imaging of obese or elderly patients, where TTE may be unable to produce images of satisfactory quality. Recently, three-dimensional (3-D) TEE has been introduced, which greatly improves the image quality and diagnostic value of TEE by adding an extra dimension. Further improvement could be achieved by optimizing 3-D TEE for harmonic imaging. This article describes the optimal geometry and element configuration for a matrix probe for 3-D second harmonic TEE. The array concept features separated transmit and receive subarrays. The element geometry was studied using finite element modeling and a transmit subarray prototype was examined both acoustically and with laser interferometry. The transmit subarray is suitable for its role, with a 3 MHz resonance frequency, a 40%–50% 23 dB bandwidth and crosstalk levels ,227 dB. The proposed concept for the receive subarray has a 5.6 MHz center frequency and a 50% 23 dB bandwidth. (E-mail: [email protected]) Ó 2012 World Federation for Ultrasound in Medicine & Biology. Key Words: Transesophageal echocardiography, TEE, Matrix array transducer, 3-D imaging.
et al. 1999] in fundamental mode), because of the smaller distance between the array transducer and the structures of the heart (Lancee 1987). This increase in transmission frequency directly translates into higher axial and lateral resolutions (Lancee 1987; Seward 1988) and improved sensitivity (Lancee 1987), crucial for imaging fine structures such as the mitral valve. The combination of these two advantages allows for the successful imaging of obese or elderly patients, where TTE may have unsatisfactory results (Lutz and Gharbi 2006). In the last 15 years three-dimensional (3-D) echocardiography has received considerable attention. The 3-D visualization of organs offers a perspective closer to the real anatomy than two-dimensional (2-D) imaging. Moreover, the possibility of virtually removing structures to view inner parts of organs offers surgeons information on structure morphology and functionality, which helps in the preparation of surgical intervention (Roelandt 2000). In addition, 3-D imaging considerably increases the quantification accuracy of cardiac structures and parameters compared with 2-D imaging (Krenning et al. 2003; Voormolen 2007). Three-dimensional TEE
INTRODUCTION Echocardiography is of large clinical significance in cardiology as a diagnostic modality to assess the physiologic function of the heart and its disorders (Feigenbaum 1986; Kisslo et al. 2006). Most echocardiographic examinations are performed using an imaging window between the ribs near the thorax, so called transthoracic (or precordial) echocardiography (TTE). Transesophageal echocardiography (TEE) is an alternative technique, which uses the esophagus as an imaging window to the heart. As the esophagus wall is located directly posterior to the heart, cardiac imaging can be performed without interference from the ribs or the lungs. Moreover, TEE allows for higher frequency ultrasound to be used compared with TTE (5–6 MHz vs. 3.5 MHz [Kasprzak
Address correspondence to: Nico de Jong, Department of Biomedical Engineering, Erasmus Medical Centre, P.O. Box 2040, 3000 CA Rotterdam, The Netherlands. E-mail: [email protected] 1 Works now at the Department of Process Intensification and Instrumentation, TNO, Delft, The Netherlands. 1820
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could combine the advantages of 3-D echocardiography with the high resolution and sensitivity of TEE imaging. Two types of 3-D TEE methods have been reported in the literature (Nathanail et al. 2008; Pua et al. 2004; Sugeng et al. 2008). The first is mechanical; four-dimensional (4-D) datasets (3-D 1 time) are created by mechanically rotating a modified multiplane 2-D TEE probe. Preliminary in vivo results were presented, showing valvular images with good diagnostic accuracy and high temporal and spatial resolution (Nathanail et al. 2008). The second method is based on a matrix array transducer, where 4-D datasets are created by steering the ultrasound beam in two orthogonal directions. Both sparse arrays (Pua et al. 2004) and fully sampled array designs (Savord 2003) have been published. Such a probe can provide excellent real-time 3-D visualization of the mitral valve, interatrial septum, left atrium and left ventricle (Sugeng et al. 2008). An advantage of matrix 3-D TEE is that it can provide real-time or near-real-time 4-D datasets. The main drawback of the matrix approach is the cost of the probe and the high-end ultrasound system. Currently (March 2012), Philips Healthcare (Best, Noord-Brabant, the Netherlands) is the only commercial supplier of matrix 3-D TEE equipment (X7-2t transducer). Generally, TEE transducers operate in fundamental mode (i.e., the ultrasound received at the transmitted frequency is used to create an image). However, ultrasound image quality can often be improved by exploiting the nonlinear nature of wave propagation (Zemp et al. 2003; Tranquart et al. 1999; Shapiro et al. 1998; Thomas and Rubin 1998). Tissue second harmonic imaging is based on the selective imaging of the second harmonic frequency (Tranquart et al. 1999). Compared with fundamental imaging, second harmonic imaging has a higher resolution and is less sensitive to near-field artifacts, clutter and off-axis scatterers (Zemp et al. 2003; Tranquart et al. 1999; Humphrey 2000). As a result second harmonic imaging has become the standard in transthoracic tissue imaging since the late 1990s (Monaghan 2000). The main challenge for any design of a matrix array transducer optimized for 3-D second harmonic TEE imaging is the size constraint associated with TEE operation. Since a TEE probe consists of a flexible endoscope with the array located at the tip, the whole device has to fit in the esophagus. Therefore, the total array footprint is limited to about 10 3 10 mm. To obtain the highest possible pressure and resolution, the array should occupy this maximum available area. To enable steering of the acoustic beam to large angles without compromising the beam shape, the directivity of the elements should be weak and therefore the element should be small. Furthermore, for fundamental imaging the pitch of the elements should be smaller than half the wavelength to
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avoid grating lobes. However, since second harmonic imaging is less sensitive to grating lobe artifacts (Matte et al. 2011), this requirement can be significantly relaxed. For a 6 MHz transducer, the element width should be in the order of 0.2 mm. Consequently, the transducer should consist of several thousand elements to create an aperture of approximately 10 3 10 mm. It is impossible to connect this large number of elements to an external imaging system via coaxial cables in the gastroscopic tube. Therefore, some form of microbeamforming in the probe head is required. The chosen array concept: separate transmit and receive subarrays A considerable body of literature exists on the design of matrix array transducers with a minimized number of elements (Smith et al. 1991; Turnbull and Foster 1991; Lockwood et al. 1998; Smith et al. 2002) to simplify the ultrasound system and element interconnections and to minimize costs (Light et al. 1998). Most element reduction methods use sparse array transducers with the connected elements distributed in a variety of ways (Smith et al. 1991; Turnbull and Foster 1991; Lockwood et al. 1998; Smith et al. 2002; Pua et al. 2004). In our design, the transmit and receive are physically separated, which makes acoustic and electronic tuning much more efficient. Also, the separation minimizes the crosstalk between the elements of both subarrays. The two-way 70%–80% 26 dB bandwidth required to perform second harmonic imaging is now split: both the transmit and receive subarrays should have a one-way 23 dB bandwidth of 50%. The transmit subarray is located adjacent to the receive subarray. A schematic image of the endoscope tip including the subarray layout is shown in Figure 1. The maximum number of coaxial cables within the gastroscope tube is 250, as the shaft has to remain flexible enough for insertion into the esophagus. For the transmit subarray a 1.75 D array topology is chosen. This allows for electronic focusing and steering in the lateral dimension. In the elevation dimension, it produces a broad beam and allows for limited steering. The broad beam in the elevation dimension makes parallel beamforming in
Fig. 1. Schematic image of the endoscope tip including the matrix array transducer.
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reception possible, in a similar manner as presented by von Ramm et al. (1991). For the receive subarray, a full 2-D array topology is chosen allowing for receive focusing in both the lateral and elevation dimensions to construct a 3-D dataset. Figure 2 shows the subarray concept and the produced beams schematically, thus, detailing how the transducer will image a volume. The light gray beam indicates the –3 dB beam size of the transmit beam, thus representing the 26 dB beam size of the second harmonic component generated through nonlinear propagation. The dark gray beams indicate the parallel receive beams. Since the centers of the subarrays do not coincide, there is insufficient overlap of the transmit beam and the receive beam close to the transducer surface. With this concept, imaging can be performed for axial distances larger than 15 mm (see Discussion section, Receive subarray, Predicted performance). Microbeamforming will be used to reduce the channel count from 2025 (the number of receive elements) to 225 (the number of connecting coaxial cables) (Savord 2003; Blaak et al. 2009). The concept of microbeamforming entails that the elements are arranged in groups and that the delay is divided into a coarse delay common for all elements in the group and a fine delay for each individual element in the group. The fine delays and the element summing are applied by use of a chip in the tip of the gastroscope (Savord 2003; Blaak et al. 2009). The signals of the N elements in a group are then summed reducing the number of required channels by a factor of N. To keep the effects of microbeamforming on the beam equal in the lateral and elevation directions, only square configurations (2 3 2, 3 3 3 and 4 3 4 elements) were investigated by Blaak et al.
Fig. 2. Schematic of the transducer concept and the produced beams. The light gray beam indicates the 26 dB beam width of the 2nd harmonic component of the transmitted field. To insonify a cone from 15 mm to 15 cm with an opening angle of 90 , the transmit beam is steered from 237 to 45 in the elevation dimension and from 245 to 45 in the lateral dimension. The dark gray beams indicate the parallel receive beams, which are steered from 245 to 45 in both elevation and lateral dimensions.
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(2009). A 2 3 2 group configuration would provide an insufficient reduction in channels. A 9:1 channel reduction by a 3 3 3 group configuration has been shown to produce a suitable acoustic field, with a peak grating lobe level of 227 dB relative to the main beam (Blaak et al. 2009). A 16:1 channel reduction by a 4 3 4 group configuration would produce unacceptably high grating lobe levels. A 3 3 3 group configuration limits the number of elements to a maximum of 2250. The transmitted and received signals will use the same cables and will be separated by diode limiters in the probe head. Resonance frequencies TEE transducers based on the selective imaging of the fundamental band have been reported to use transmission frequencies of 5 MHz (Currie 1989)25.6 MHz (Lancee, 1987; Lancee et al. 1988). The optimal transmission frequency for tissue second harmonic imaging depends on the level of the second harmonic at distances typical for TEE imaging, which is determined by two competing phenomena—nonlinear propagation and attenuation. In the case of fundamental TTE, it was found that for the visualization of the left ventricular endocardial border during echocardiography (imaging depths of 10– 15 cm) a transmission frequency of 3.5 MHz yielded the best results (Kasprzak et al. 1999). However, in the same study it was found that for second harmonic TTE a reception frequency of 3.2–3.6 MHz provided the optimum results (Kasprzak et al. 1999). The latter was also found by Matte et al. (2011) in a systematic study on the optimal transmission frequencies for harmonic TTE. Similarly, for TEE we choose the frequency of the second harmonic (6 MHz) to be close to the frequency used in fundamental imaging (5–5.6 MHz). Thus, the chosen resonance frequencies are 3 MHz and 6 MHz for the transmit and receive subarrays, respectively. Consequences for the element vibration An element size in the order of 0.2 mm combined with the 3–6 MHz at which TEE operates, means that the elements vibrate between 33-mode and plate mode. Therefore, lateral modes can exist and should be considered when designing the elements. The influence of geometry on this issue cannot be determined using onedimensional (1-D) models, such as the KLM model, and requires a 3-D approach. Another important issue is the crosstalk between the elements. Crosstalk lengthens the ring down of elements through delayed signals from neighboring elements and limits angular dispersion by increasing the effective element size (Turnbull and Foster 1992). Recently, techniques such as laser interferometry and 3-D finite element modeling (FEM) have gained popularity in the understanding of these complex vibration modes and crosstalk of phased arrays based on
Matrix probe for 3-D second harmonic TEE d P. L. M. J. VAN NEER et al.
piezo material and cMUTs (Goldberg et al. 1997; Caronti et al. 2005). Goal This article describes a geometry and element configuration for a matrix probe consisting of two subarrays optimized for 3-D second harmonic TEE, predicting the mode vibration of single elements using FEM and documenting the performance of the transmitter using laser interferometry and acoustic measurements. The method of interconnection and the implemented electronics is beyond the scope of this article. METHODS Finite element model - element geometry optimization The optimal element geometries for elements of the transmit and receive subarrays were investigated using 3-D FEM simulations based on the ANSYS 11 FEM package (ANSYS Inc., Canonsburg, PA, USA). In these simulations, a single element was modeled: the geometry consisted of a piece of piezo material and a backing (see Fig. 3a). The piezo material properties used were those of 3203HD piezo material (CTS, Bloomingdale, IL, USA). The material of the backing was assumed to be isotropic and was modeled using linear elasticity. The transducer element was loaded by air, which was not modeled. The piezo element was a pillar with square top and bottom surfaces. In the case that a transmit subarray element was modeled, the piezo material thickness was
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0.47 mm and the width was varied between 0.068 mm and 0.81 mm. For a receive subarray element the piezo material thickness was 0.29 mm and the width was varied between 0.054 mm and 0.24 mm. The thickness of the backing was 8 mm, such that reflections from the backing did not affect the displacement of the element surface during the simulation time. Only a quarter of the element needed to be modeled due to symmetry. To ensure that the lateral mode resonance could always be resolved, 40 nodes were used in the width dimensions. Forty-one nodes were used in the thickness dimension of the piezo material. The thickness of the transducer electrodes (300 nm) was much smaller than the considered ultrasound wavelengths (0.3–1 mm) and, therefore, the electrodes were omitted from the model. The transducer element was excited by an impulse of amplitude 270 V. The time sample frequency was 100 MHz. The mesh and material properties are summarized in Tables 1 and 4, respectively. Finite element model–Final concept A single array element of both the final transmit and receive subarrays was modeled using the ANSYS 11 FEM package. An element of the transmit subarray consisted of four layers: a matching layer, the piezo material, a connection layer and the backing. A schematic of the geometry of an element of the transmit subarray in air is displayed in Figure 3b and a schematic of the geometry of the same element in water including the boundary conditions is shown in Figure 3c. An element of the
Fig. 3. (a) FEM model geometry of a piezo element for element width optimization (the width of an element is equal to its length). (b) FEM model geometry of an element of the transmit subarray in air. (c) FEM model geometry of an element of the transmit subarray in water including the boundary conditions. N indicates a nonreflective boundary condition on a surface, S is a symmetry boundary condition - displacement in direction perpendicular to the surface is 0, F stands for a free boundary - force in direction perpendicular to the surface is 0, P indicates that the pressure is 0 at this boundary surface, V is a voltage boundary condition on a surface and K is a boundary condition for a single node having 0 displacement in all directions.
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Table 1. Standard geometry and mesh parameters used in the FEM simulations Properties Total element Piezomaterial Matching layer Connection layer Backing Water Nonreflecting boundary (water)
width Thickness Element type Thickness Element type Thickness Element type Thickness Element type Radius Element type Element type
Unit [m] [m] – [m] – [m] – [m] – [m] – –
Transmit subarray 26
135.10 467.1026 20 node, 3-D SOLID226 120.1026 20 node, 3-D SOLID186 25.1026 20 node, 3-D SOLID186 2.1023 (prototype) / 8.1023 (FEM) 20 node, 3-D SOLID186 1.1023 8 node, 3-D FLUID30 4 node, 2-D boundary FLUID130
receive subarray consisted of three layers: a matching layer, the piezo material and the backing. The load of the element was either vacuum (representing an air load) or water. The water domain was surrounded by an nonreflecting boundary layer. The 2100 V impulse excitation recorded in the laser interferometer experiments were used for the voltage boundary condition. The time sampling frequency was 100 MHz. Transmit subarray prototype Based on the results of the finite element simulations a transmit subarray prototype was built. The transmit subarray consisted of four rows of 32 elements each, which results in a total of 128 elements. The array was built using CTS 3203HD piezo material. The resonance frequency of the transmit subarray was 2.7 MHz. Each element had a matching layer of 6.5 MRayl and a backing of 3.4 MRayl. In between the piezo material and the backing was a connection layer, which was a thin electrically conductive layer facilitating the connection between the elements and the flexible printed circuits. Also, a light-reflecting foil was glued on top of the elements. No lens was mounted. The width and length of the elements were both 0.27 mm. The elements were
Fig. 4. A picture of the transmit subarray prototype without the light-reflecting foil. The schematic on the bottom right shows the numbering of the elements.
Receive subarray 85.1026 292.1026 20 node, 3-D SOLID226 80.1026 20 node, 3-D SOLID186 23 2.10 (prototype) / 8.1023 (FEM) 20 node, 3-D SOLID186 1.1023 8 node, 3-D FLUID30 4 node, 2-D boundary FLUID130
diced into the backing using a diamond saw and were fully acoustically isolated from each other. The kerf was 40 mm and no kerf filler material was used. The total footprint of the transmit subarray was 9.9 3 1.2 mm. A picture of the array is displayed in Figure 4. The properties of the materials used in the subarray elements are given in Table 4 of Appendix: Material Properties. The transducer was manufactured by Oldelft Ultrasound, Delft, The Netherlands. Setup for optical characterization The space and time dependant out-of-plane surface displacement (henceforth, denoted as axial surface displacement) of the elements of the transmit subarray prototype was studied in air using a laser interferometer system. A schematic of the optical setup is displayed in Figure 5. The system was based on a Polytec MSV-300 laser scanning vibrometer system (Polytec GmbH, Waldbronn, Germany). The laser interferometer consisted of
Fig. 5. A schematic of the laser interferometer setup. Dotted arrows are trigger signals.
Matrix probe for 3-D second harmonic TEE d P. L. M. J. VAN NEER et al.
a Polytec OFV 512 fiber interferometer connected to a Polytec OFV 5000 vibrometer controller equipped with a displacement decoder with an upper frequency limit of 20 MHz. The fiber interferometer was connected to the MSA-400 scan head, which functioned as a microscope. The continuous analog output produced by the vibrometer controller was captured by a digitizer card (DP235; Acqiris, Geneva, Switzerland) at a sampling rate of 100 MHz. The digitizer was triggered by either an arbitrary waveform generator or a pulser/receiver. For amplitude transfer function measurements the array element was excited by 35-cycle sinusoids with amplitude 5 V generated by an arbitrary waveform generator (33250A; Agilent, Loveland, CO). For crosstalk measurements the element was excited by a pulser/ receiver (5800; Panametrics, Waltham, MA, USA), which produced 2100 V spikes with a width of 0.3 ms. The array was mounted on two orthogonal motorized translation stages (PT1-Z8; Thorlabs GmbH, Munich, Germany). The displacement of the array elements was studied using a laser spot diameter of 20 mm and a translation step size of 30 mm. The received signals were averaged 1000 times for each measurement position to reduce the effects of variance in signal quality due to the variability of element surface reflectivity and surface roughness. The pulse repetition frequency was 1 kHz. The electrical impedances of the equipment used were measured using a vector impedance meter (4193A; Hewlett Packard, Yokogawa, Japan). Setup for acoustic characterization The acoustic measurements were performed in a water tank using a hydrophone setup. The pressure transmit transfer function was determined by measuring the responses of individual elements to 30-cycle sine bursts with amplitude 5 V, the frequency of which was varied from 1 to 10 MHz. The emitted pressure field was measured at a distance of 4 cm using a calibrated hydrophone (diameter 0.2 mm; Precision Acoustics, Dorchester, UK) that was mounted in a custom built xyzsystem. The hydrophone signals were amplified by a low noise amplifier (AU-3A-0110-BNC; Miteq, Hauppauge, NY, USA) and digitized by an oscilloscope (DSO6034A; Agilent Technologies, Palo Alto, CA, USA). The transfer functions were calculated using the methods described by van Neer et al. (2007), where the Fraunhofer approximation for the pressure distribution of a flat rectangular piston transducer excited by continuous wave excitation (Cobbold 2007) was used to obtain the diffraction correction function. The electrical impedances of the equipment used were measured using a vector impedance meter (4193A; Hewlett Packard).
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RESULTS Transmit subarray Element geometry optimization. The resonance frequencies of the fundamental and lateral modes as a function of a piezo element’s width, which were simulated using 3-D FEM simulations, are plotted in Figure 6. For example, an element width of 0.27 mm gives a fundamental mode resonance of 2.7 MHz and a lateral mode resonance of 6 MHz. Figure 6 shows that as a piezo element’s width increases, the fundamental and lateral mode resonance frequencies approach each other. This was also reported in the literature (Onoe and Tiersten 1963; De Jong et al. 1985). Therefore, the desire to separate the fundamental and lateral mode resonances puts an upper limit on an element’s width. Performance. The amplitude transmit transfer functions of the transmit subarray elements produced by the optical measurements and FEM simulations are shown in Figure 7a. The elements were loaded by air. The experimental results were based on measurements of four elements, each excited individually. The maximum amplitude transmit transfer was 3 nm/V. Two peaks were visible in the spectra, the first on 2.4 MHz (measurements and simulation) and the second on 3.9 MHz (measurements) or 4.1 MHz (simulation). The experimental results showed a large spread around the second peak as indicated by the standard deviation of 0.7 nm/V vs. a mean of 2 nm/V (see Fig. 7a). This may have been
Fig. 6. The relation between an element’s width and resonance frequency of the fundamental mode (black plusses) and lateral mode (gray crosses) as calculated using FEM simulations for the elements of the transmit subarray. The dotted black lines show the 23 dB bandwidth requirement for the fundamental. The chosen width of 0.27 mm is indicated by black arrows and gives a fundamental mode resonance of 2.7 MHz and a lateral mode resonance of 6.0 MHz. The thickness of the element was 0.47 mm.
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Fig. 7. (a) Amplitude transmit transfer function (Tta ðuÞ) of the axial surface displacement of transmit subarray elements vibrating in air. The dashed gray line is the mean axial displacement of 4 elements, the gray area is the standard deviation around the mean (optical measurements). The solid black line is the result of the FEM simulation. (b) Transmit transfer function (Tt ðuÞ) of transmit subarray elements vibrating in water. The dashed gray line is the mean transmit transfer of four elements, the gray area is the standard deviation around the mean (acoustic measurements). The solid black line is the result of the FEM simulation.
caused by a nonuniform adhesion between the matching layer and the piezo material, or by damage related to dicing. The agreement between the optical measurements and the FEM simulation was good, especially at frequencies below 5 MHz. The spikiness of the results above 5 MHz was caused by the lack of damping in the FEM model combined with the interaction of the axial surface displacement and a lateral mode around 6 MHz. The transmit transfer functions of transmit subarray elements vibrating in water produced by acoustic measurements and modeled by a FEM simulations are shown in Figure 7b. The experimental results were based on measurements of four elements, each excited individually. The peak transmit transfer as determined by the FEM simulations was 43 kPa/V at 2.3 MHz vs. an exper-
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imentally determined peak mean transmit transfer of 54 kPa/V at 2.5 MHz. This difference is caused by crosstalk. The standard deviation in the experimental results may be caused by nonuniform adhesion, variations in dicing or the variations in the thin silicone layer which was applied on top of the transmit subarray to create a watertight seal. The 23 dB bandwidth as calculated by FEM simulations was 64% around a center frequency of 3 MHz vs. an experimentally determined average 23 dB bandwidth of 65% around the same center frequency. Figure 8a shows the magnitude of the electrical impedance of the transmit subarray elements measured in air, while Figure 8b shows the phase of the electrical impedance of the transmit subarray elements measured in air. These results were based on measurements of five individual elements. The two fundamental resonance peaks at 2.4 MHz and 3.9 MHz, as observed in the measured amplitude transfer functions (see Fig. 7a), are clearly observable in Figure 8a. Moreover, the impedance spectrum shows a third harmonic mode at about 7.1 MHz. There is a small peak in the phase spectrum (see Fig. 8b) at 5.6 MHz, which is likely caused by a lateral mode. The average coupling coefficient k33, calculated from the experimentally determined electrical impedances using the formula given for bar mode vibration by De Jong et al. (1985), was 0.66. The manufacturer of the piezo material used (CTS 3203HD) states in the specifications of the material a k33 of 0.75. Therefore, the efficiency is close to that of an ideal element vibrating in the 33-mode. Figure 9 shows the normalized maximum axial surface displacement of element 28 and element 93, as measured with the laser interferometer. The elements were excited by 2100 V impulses. Element 28 was located on the edge of the array and element 93 in the middle. The peak displacement of elements 28 and 93 were 63.4 nm and 52.5 nm, respectively. Four elements were examined (the displacement of only two elements is shown in Fig. 9) and their peak displacements varied from 52 to 64 nm. The displacement pattern clearly reflected the element distribution. The axial displacement due to crosstalk in the lateral direction was higher than in the elevation direction. This was visible in the displacement pattern produced by element 93 (Fig. 9b) but less obvious in the displacement pattern produced by element 28 (Fig. 9a). There was no discernible time delay in the time signals of the neighboring elements suggesting primarily electrical rather than mechanical crosstalk. The frequency dependency of the crosstalk from an excited element to a neighboring element is shown in Figure 10 for elements 28 and 93. This was calculated by taking the Fourier transform of the mean surface displacement of an element neighboring the excited element and normalizing that to the Fourier transform of the mean surface displacement of the excited element.
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Table 2. Normalized crosstalk level of excited element to neighboring element averaged over a frequency band of 1–5 MHz Crosstalk in lateral direction (dB)
Crosstalk in elevation direction (dB)
218 217 220 216 218
226 238 218 228 227
Element 28 Element 85 Element 87 Element 93 Average
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Predicted performance. The receive transfer function of an element of the receive subarray with the chosen width of 0.17 mm as simulated using FEM modeling is displayed in Figure 12. The element was loaded by water. The receive transfer function had a maximum of 24.8 mV/Pa at 5.3 MHz. The center frequency of the element was 5.6 MHz. Its 23 dB bandwidth was 50% and stretched from 4.2 MHz to 7 MHz. DISCUSSION Transmit subarray
The crosstalk was higher in the lateral direction than in the elevation direction. In the case element 28 was excited the crosstalk averaged over 1–5 MHz was 218 dB and 226 dB in the lateral and elevation directions, respectively. For element 93 this was 216 dB and 228 dB in the lateral and elevation directions, respectively. The crosstalk showed a frequency dependency, being highest between 3 and 4 MHz (element 28:28 and 214 dB for the lateral and elevation directions) and lowest between 1 and 2 MHz (element 28: 225 dB and 233 dB for the lateral and elevation directions). These crosstalk measurements were performed for four excited elements. The average crosstalk over a 1–5 MHz band is summarized in Table 2 for the lateral and elevation dimensions. The average crosstalk from the excited element to a neighboring element was 218 dB and 227 dB for the lateral and elevation directions respectively. Receive subarray Element geometry optimization. The resonance frequencies of the fundamental and lateral modes as a function of a piezo element’s width, which were simulated using 3-D FEM simulations, are plotted in Figure 11. For example, an element with a width of 0.17 mm gives a fundamental mode resonance of 6.3 MHz and a lateral mode resonance of 9.4 MHz. Similar to the transmit array, the fundamental and lateral mode resonance frequencies approach each other as the element width increases.
Element geometry optimization. The optimal element width of the transmit subarray is the result of a trade-off. On the one hand, the element should be small enough to avoid interference from the fundamental and lateral mode resonances of the element. Furthermore, smaller elements ensure sufficient element omnidirectionality to steer the ultrasound beam and reduce the pitch, leading to lower grating lobe levels. On the other hand, choosing the elements too small leads to either an aperture that is unable to generate sufficient pressure or contains too many elements. The chosen width for the elements of the transmit subarray is 0.27 mm. The fundamental resonance frequency of the piezo element in air is at 2.7 MHz. The lateral mode resonance is outside the 23 dB bandwidth, at 6 MHz. The center frequency of the element, including matching layers, in water is 3 MHz. The chosen width is only slightly larger than half the wavelengths at 3 MHz, which is 0.25 mm, ensuring sufficiently weak element directivity for beam steering. Practical experience shows that the smallest kerf width, which still results in reliable array construction, is 40 mm. Even though the resulting pitch is somewhat larger than half the wavelength of the emitted ultrasound, grating lobes are not expected to be a problem with this element configuration as the array is intended for second harmonic imaging. The final transmit subarray consists of 32 3 4 elements, with a size of 0.27 3 0.27 3 0.47 mm. In combination with a kerf size of 40 mm this yields a subarray footprint of 9.9 3 1.2 mm. A summary of the parameters of final transmit and receive subarrays is given in Table 3.
Table 3. Parameters of the final transmit and receive subarrays Properties
Unit
Transmit subarray
Receive subarray
Center frequency Piezo element size Kerf size Element layout Total no. of elements Footprint size Channel reduction No. of connecting channels
[MHz] [mm] [mm] [–] [–] [mm] [–] [–]
3 0.27 3 0.27 3 0.47 40 32 3 4 128 9.9 3 1.2 1:1 128
5.6 0.17 3 0.17 3 0.29 30 45 3 45 2025 9.0 3 9.0 9:1 225
Note that the total amount of coaxial cables connecting the combined arrays is 225.
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Fig. 9. (a) Normalized maximum axial displacement of transmit subarray element 28. (b) Normalized maximum axial displacement of transmit subarray element 93. The normalized axial displacement in dB is encoded by gray values. The elevation and lateral dimensions are relative to the bottom right corner of element 1 (see the picture of the prototype in Fig. 4). The element displacement in air was measured using the laser interferometer setup.
Fig. 8. (a) Magnitude of electrical impedance of transmit subarray elements, measured in air. The dashed gray line is the mean of measurements on five individual elements, the gray area is the standard deviation around the mean. (b) Phase of electrical impedance of five transmit subarray elements measured in air.
Performance. The amplitude transmit transfer function of the transmit subarray elements (in air, shown in Fig. 7a) showed a considerable dip between the peak at 2.4 MHz and the peak at 3.9 MHz. However, the peak at 3.9 MHz was smoothed and lowered, when the elements were loaded by water (Fig. 7b). The experimentally determined average peak transmit transfer of a transmit subarray element was 54 kPa/V at 2.5 MHz. In the future, the transmit subarray elements will be electrically matched to the transmitters using coils. This will lower the bandwidth to 40%–50% and increase the efficiency of the elements compared to the transfer function shown in Figure 7b. In recent work it has been shown that the full unsteered, unfocused and untuned transmit subarray produced 0.7 MPa using 95 Vpp excitation signals at an axial distance of 60 mm in water (Blaak et al. 2011b). After filtering of the second harmonic band in this data it was found to have a peak amplitude of 120 kPa. Through electrical tuning and an increase in excitation
voltage to 120 Vpp we expect to increase these amplitudes two to three times, giving a second harmonic pressure in the order of 300 kPa. The crosstalk between the array elements is important because it has a detrimental effect on the transducer’s ability to perform beam steering by effectively making the elements larger and, thus, less omnidirectional. McKeighen (1998) reported that crosstalk values of 230 dB are considered acceptable for most imaging situations. Electrical crosstalk appears to be the largest contributor to the total crosstalk and efforts should be made to reduce it by improving the electrical shielding of the elements and connecting wires. Moreover, the crosstalk in the lateral direction is higher than in the elevation direction. This corresponds to the direction of the flexible printed circuits. Since beam steering will mostly be applied in the lateral direction, it may be beneficial to connect the flexible printed circuits in the elevation direction to the elements. The crosstalk in the steering direction will be at 227 dB close to the required 230 dB. Preliminary measurements of the acoustic field produced by single transmit subarray elements showed an opening angle of 60 , which is sufficient for volumetric imaging (Blaak et al. 2010). The crosstalk has a strong frequency dependency as shown in Figure 10, with a shape roughly similar to
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Fig. 10. The transmit array surface displacement due to crosstalk to a neighboring element normalized to the displacement of the excited element plotted vs. the frequency, for elements 28 (a) and 93 (b). The mean crosstalk to a neighboring element in the lateral direction is denoted by a black solid line and the crosstalk to an element in the elevation direction is denoted by a gray dashed line. The element displacement in air was measured using the laser interferometer setup.
magnitude of the electrical impedance of an element (see Fig. 8a). For the typical 3 MHz imaging bursts with 50% 23 dB bandwidth, the crosstalk will be close to the reported mean values (227 dB, see Table 2). However, for applications requiring narrowband excitation (e.g., Doppler), the 20 dB crosstalk variance due to the frequency (see Fig. 10) should be taken into account. A 2.5 MHz excitation frequency would provide low crosstalk and a good transmission efficiency.
Fig. 11. The relation between element’s width and resonance frequency of the fundamental mode (black plusses) and lateral mode (gray crosses) as calculated using FEM simulations for the elements of the receive subarray. The dotted black lines show the 23 dB bandwidth requirement for the fundamental. The chosen width of 0.17 mm is indicated by black arrows and gives a fundamental mode resonance of 6.3 MHz and a lateral mode resonance of 9.4 MHz. The thickness of the element was 0.29 mm.
Receive subarray Element geometry optimization. The optimal width of the receive subarray elements is a compromise between the element count, the footprint size and minimizing the effects of lateral resonance modes. Other important factors are a weak element directivity for beam steering and a sufficiently small pitch to avoid grating lobes. The chosen width for the elements of the receive subarray is 0.17 mm. For this element width, the fundamental resonance frequency of the piezo element in air is at 6.3 MHz and the lateral mode resonance is at 9.4 MHz, which is outside the 23 dB bandwidth. The center frequency of the element, including
Fig. 12. The receive transfer function (Tr ðuÞ) of the axial surface displacement of an element of the receive subarray, obtained using FEM simulations. The element was loaded by water.
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matching layers, is in water 5.6 MHz. This is close to the intended 6 MHz. Awidth of 0.17 mm corresponds to 0.7 wavelength, which ensures sufficiently weak element directivity to allow for steering between 245 and 45 . Although this is larger than half the wavelength of the received ultrasound, grating lobes are not expected to be a problem, since they are unlikely to overlap with the grating lobes produced by the transmit subarray. The outer dimension of the tip of an adult TEE probe is 15 mm, therefore, the total aperture of the array can only be 10 3 10 mm. This results in a total of 45 3 45 elements each with a size of 0.17 3 0.17 3 0.29 mm. Combined with a kerf of 30 mm this yields a footprint of the receive subarray of 9.0 3 9.0 mm. Using 9:1 channel reduction based on microbeamforming the total number of required wires is 225, which fits in the gastroscope tube. The footprint of the transmit and receive subarrays combined amounts to 9.9 3 10.2 mm, which is comparable to the footprint of conventional TEE transducers. A summary of the parameters of final transmit and receive subarrays is given in Table 3. Predicted performance. The center frequency of 5.6 MHz found for the modeled element of the receive subarray is slightly lower than the intended 6 MHz, but still acceptable. The FEM simulations of a single receive subarray element show a peak receive sensitivity of 25 mV/Pa. To judge whether this is sufficient, the entire imaging chain should be considered. The transmit subarray is expected to produce second harmonic pressures of 300 kPa (see Discussion section, Transmit subarray, Performance). Applying the formula and cardiac tissue properties in Table 4.22 from Duck (1990) on our array concept and imaging situation, the backscattered intensity is 40–60 dB lower than the intensity impinging on a scatterer. This means that the highest received second harmonic pressure will be 3 kPa. With 25 mV/Pa sensitivity this corresponds to a signal of 75 mV. The noise level of commercial TEE systems is 100 mVrms. That means that the dynamic range of our system is 57 dB, which is more than can be indicated using gray levels in a B-mode image (256 gray levels is 48 dB). Therefore, the sensitivity of the receive elements is expected to be sufficient. The distance between the centers of the transmit and receive subarrays is 5.1 mm and the maximum steering angle of the receive subarray is 45 . At larger steering angles, the grating lobe level increases to unacceptable levels due to the microbeamforming used for channel reduction (Blaak et al. 2009). We expect to steer the transmit subarray beam in the elevation dimension between 237 and 45 . Preliminary acoustic measurements on the entire transmit subarray showed an elevation length and a lateral width of the second harmonic of 12.2 mm and 6.2 mm at an axial distance of 40 mm, respectively
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(based on data used in Figure 5a of Blaak et al. [2011b]). Hence, the transmit and receive beams start to overlap at an axial distance of 15 mm (Blaak et al. 2011a). Laser interferometer measurements The signal-to-noise-ratio (SNR) of the laser interferometer measurements was mainly determined by the amount of light reflected back into the detector. The prototype array was covered by a highly reflective aluminum foil, which was stretched and smoothed as much as possible during production. Even so, the irregularity of the top surface (e.g., due to folds in the aluminum) relative to the size of the laser spot (20 mm) occasionally caused little light to be reflected back to the detector. This effect was visible in the maximum displacement plots of Figure 9 as spots with an unexpectedly low displacement. During the total time of the measurements (2 weeks), the reflectivity of the aluminum foil deteriorated due to handling and temperature influences decreasing the SNR by 2 dB. However, this reduction in SNR was not significant, as the peak SNR was about 55 dB after averaging. CONCLUSION The presented transmit subarray in combination with appropriate electrical tuning is expected to be suitable for its role, with a 3 MHz resonance frequency, 40%–50% 23 dB bandwidth and ,227 dB crosstalk levels in the lateral steering direction. The proposed concept for the receive subarray has a 5.6 MHz center frequency and a 50% 23 dB bandwidth. Acknowledgments—The authors acknowledge the technical support of J. Ponte, G. Springeling and M. Manten. They thank S.L. Paalvast and Prof. D. Rixen from the faculty of Mechanical, Maritime and Materials Engineering, Delft University of Technology for providing the laser interferometer setup.
REFERENCES Blaak S, Lancee C, Bosch J, Prins C, van der Steen A, De Jong N. A matrix transducer for 3-D transesophageal echocardiography with a separate transmit and receive subarray. Orlando, Florida: USA. Proc IEEE Ultrason Symp 2011a:2341–2344. Blaak S, van Neer P, Prins C, Bosch J, Lancee C, De Jong N. Transducer design for second harmonic 3-D transesophageal echocardiography. San Diego, USA: Proc IEEE Ultrason Symp 2010:1218–1221. Blaak S, van Neer PLMJ, Prins C, Bosch JG, Lancee CT, van der Steen AFW, de Jong N. Design of a matrix transducer for threedimensional second harmonic transesophageal echocardiography. Acoustical Imaging 2012;31:341–349. Blaak S, Yu Z, Meijer G, Prins C, Lancee C, Bosch J, De Jong N. Design of a micro-beamformer for a 2D piezoelectric ultrasound transducer. In: Proc. IEEE Ultrason Symp Rome, Italy, 2009:1338–1341. Briggs A. Acoustic microscopy. New York: Oxford University Press; 1992. Caronti A, Savoia A, Caliano G, Pappalardo M. Acoustic coupling in capacitive microfabricated ultrasonic transducers: Modeling and experiments. IEEE Trans Ultrason Ferroelectr Freq Control 2005; 5212:2220–2234.
Matrix probe for 3-D second harmonic TEE d P. L. M. J. VAN NEER et al. Cobbold R. Foundations of biomedical ultrasound. Oxford, New York: Oxford University Press, Inc.; 2007. Currie P. Transesophageal echocardiography. new window to the heart. Circulation 1989;80:215–217. De Jong N, Souquet J, Faber G, Bom N. Transducers in medical ultrasound: Part two vibration modes, matching layers and grating lobes. Ultrasonics 1985;234:176–182. Duck F. Physical properties of tissues. San Diego: Academic Press, Inc.; 1990. Feigenbaum H. Echocardiography. 4th edition. Philadelphia: Lea & Febiger; 1986. Goldberg RL, Jurgens M, Mills D, Henriquez C, Vaughan D, Smith S. Modeling of piezoelectric multilayer ceramics using finite element analysis. IEEE Trans Ultrason Ferroelectr Freq Control 1997;446: 1204–1214. Humphrey V. Nonlinear propagation in ultrasonic fields: Measurements modelling and harmonic imaging. Ultrasonics 2000;38:267–272. Kasprzak J, Paelinck B, Ten Cate F, Vletter W, De Jong N, Poldermans D, Elhendy A, Bouakaz A, Roelandt J. Comparison of native and contrast-enhanced harmonic echocardiography for visualization of left ventricular endocardial border. Am J Cardiol 1999;832:211–217. Kisslo J, Adams D, Leech G. Two-dimensional echocardiography in the normal heart. In: Echo in Context - 21st Annual Satellite Video Teleconference, 2006. Krenning B, Voormolen M, Roelandt J. Assessment of left ventricular function by three-dimensional echocardiography. Cardiovasc Ultrasound 2003;1–12. Lancee C. A transesophageal phased array transducer for ultrasonic imaging of the heart. PhD Thesis, Erasmus University Rotterdam, 1987. Lancee C, de Jong N, Bom N. Design and construction of an esophageal phased array probe. Med Prog Technol 1988;133:139–148. Light E, Davidsen R, Fiering J, Hruschka T, Smith S. Progress in twodimensional arrays for real-time volumetric imaging. Ultrason Imaging 1998;201:1–15. Lockwood G, Talman J, Brunke S. Real-time 3-D ultrasound imaging using sparse synthetic aperture beamforming. IEEE Trans Ultrason Ferroelectr Freq Control 1998;454:980–988. Lutz H, Gharbi H. Manual of diagnostic ultrasound in infectious tropical diseases. Berlin Heidelberg, Germany: Springer-Verlag; 2006. Matte G, van Neer P, Danilouchkine M, Huijssen J, Verweij M, de Jong N. Optimization of a phased-array-transducer for multiple harmonic imaging in medical applications: Frequency and topology. IEEE Trans Ultrason Ferroelectr Freq Control 2011;583:533–546. McKeighen R. Design guidelines for medical ultrasonic arrays. San Diego, USA. Proc SPIE 1998;3341:2–18. Monaghan M. Second harmonic imaging: A new tune for an old fiddle? Heart 2000;83:131–132. Nathanail K, van Stralen M, Prins C, van den Adel F, French P, De Jong N, van der Steen A, Bosch J. Rapid 3-D transesophageal echocardiography using a fast-rotating multiplane transducer. Beijing, China. Proc IEEE Ultrason Symp 2008:848–851. Onoe M, Tiersten H. Resonant frequencies of finite piezoelectric ceramic vibrators with high electromechanical coupling. IEEE Trans Ultrason Eng 1963;10:32–39. Pua E, Idreiss S, Wolf P, Smith S. Real-time 3-D transesophageal echocardiography. Ultrason Imaging 2004;26:217–232. Roelandt J. Three-dimensional echocardiography: The future today! Comput Graph 2000;245:715–729. Savord B. Fully sampled matrix transducer for real time 3-D ultrasonic imaging. Hawaii, USA: Proc IEEE Ultrason Symp; 2003:945–953. Selfridge A. Approximate material properties in isotropic materials. IEEE Trans Sonics Ultrason 1985;SU-323:381–394. Seward J. Transesophageal echocardiography: Technique, anatomic correlations, implementation and clinical applications. Mayo Clin Proc 1988;63:649–680. Shapiro R, Wagreich J, Parsons R, Stancato-Pasik A, Yeh H, Lao R. Tissue harmonic imaging sonography: Evaluation of image quality compared with conventional sonography. AJR 1998;171: 1203–1206.
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Sherrit S, Wiederick H, Mukherjee B. A complete characterization of the piezoelectric dielectric and elastic properties of Motorola pzt 3203 hd including losses and dispersion. Newport Beach. Proc SPIE 1997;3037:158–169. Smith S, Lee W, Light E, Yen J, Wolf P, Idriss S. Two dimensional arrays for 3-D ultrasound imaging. Proc. IEEE Ultrason Symp 2002;2: 1545–1553. Smith S, Pavy H Jr, von Ramm O. High-speed ultrasound volumetric imaging system-part i: Transducer design and beam steering. IEEE Trans Ultrason Ferroelectr Freq Control 1991;382:100–108. Sugeng L, Shernan S, Salgo I, Weinert L, Shook D, Raman J, Jeevanandam V, DuPont F, Settlemier S, Savord B, Fox J, Mor-Avi V, Lang R. Live 3-dimensional transesophageal echocardiography: Initial experience using the fully-sampled matrix array probe. JACC 2008;526:446–449. Thomas J, Rubin D. Tissue harmonic imaging: Why does it work? J Am Soc Echocardiogr 1998;118:803–808. Tranquart F, Grenier N, Eder V, Pourcelot L. Clinical use of ultrasound tissue harmonic imaging. Ultrasound Med Biol 1999;256:889–894. Turnbull D, Foster F. Beam steering with pulsed two-dimensional transducer arrays. IEEE Trans Ultrason Ferroelectr Freq Control 1991; 384:320–333. Turnbull D, Foster F. Fabrication and characterization of transducer elements in two-dimensional arrays for medical ultrasound imaging. IEEE Trans Ultrason Ferroelectr Freq Control 1992;394:464–475. van Neer P, Matte G, Sijl J, Borsboom J, de Jong N. Transfer functions of us transducers for harmonic imaging and bubble responses. Ultrasonics 2007;464:336–340. von Ramm O, Smith S, Pavy H Jr. High-speed ultrasound volumetric imaging system-part 11: Parallel processing and image display. IEEE Trans Ultrason Ferroelectr Freq Control 1991;382:109–115. Voormolen M. 3-D harmonic echocardiography. PhD Thesis. Erasmus University Rotterdam; 2007. Zemp R, Tavakkoli J, Cobbold R. Modeling of nonlinear ultrasound propagation in tissue from array transducers. J Acoust Soc Am 2003;1131:139–152.
APPENDIX TRANSFER FUNCTION DEFINITIONS The transducer transmit transfer function (Tt ðuÞ) was defined as (van Neer et al. 2007): Tt ðuÞ 5
jp0 ðuÞj ; jVT ðuÞj
(1)
with p0 ðuÞ the pressure at the transducer surface and VT ðuÞ the voltage over the transducer electrodes. The receive transfer function (Tr ðuÞ) was defined as (van Neer et al. 2007): VT2open ðuÞ ; (2) Tr ðuÞ 5 jpa ðuÞj with VT2open ðuÞ the open circuit voltage produced by the transducer and pa ðuÞ the pressure received on the transducer surface. The amplitude transmit transfer function of a transducer (Tta ðuÞ) was defined as: a u ðuÞ 33 a ; (3) Tt ðuÞ 5 jVT ðuÞj with ua33 the mean axial displacement of the transducer surface.
MATERIAL PROPERTIES The properties of the CTS 3203HD piezo material used in both subarrays were based on the values reported by Sherrit et al. (1997).
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Table 4. The properties of the materials used in the simulations and the prototype Property Piezomaterial
Matching layer Connection layer Backing Water
Unit 2
Value 211
Elastic compliance (sE )
[m /N.10
Piezoelectric strain coefficient (d) Relative permittivity (K T ) Density (r) Dielectric loss (tande ) Mechanical quality factor (Qm ) Longitudinal wave speed (y33 ) Poisson ratio (n) Density (r) Longitudinal wave speed (y33 ) Poisson ratio (n) Density (r) Longitudinal wave speed (y33 ) Poisson ratio (n) Density (r) Longitudinal wave speed (y33 ) Density (r)
[C/N.10210] – [kg/m3] – – [m.s21] – [kg.m23] [m.s21] – [kg.m23] [m.s21] – [kg.m23] [m.s21] [kg.m23]
The materials used for the matching layer and backing were assumed to be homogeneous and isotropic. The longitudinal wave speed (y33 ) of these materials was determined using the method of Selfridge (1985). The density (r) was determined using Archimedes’ method (Selfridge
]
sE11 5 1.56, sE12 5 20.420, sE13 5 20.823, sE33 5 1.89, sE55 5 3.92, sE66 5 3.98 d13 5 2.95, d33 5 5.64, d15 5 5.60 T T K11 5 2417, K33 5 3331 7800 0.028 66 2066 0.35 3146 2066 0.35 3146 1818 0.35 1870 1490 1000
1985). Using y33 and r the axial modulus was calculated (Briggs 1992; Cobbold 2007). The Poisson ratio (n) of the passive materials was estimated at 0.35. A summary of the material properties is given in Table 4.
http://dx.doi.org/10.1016/j.ultrasmedbio.2012.06.007
d
Original Contribution MODE VIBRATIONS OF A MATRIX TRANSDUCER FOR THREE-DIMENSIONAL SECOND HARMONIC TRANSESOPHAGEAL ECHOCARDIOGRAPHY PAUL L. M. J. VAN NEER,*1 SANDRA BLAAK,* JOHAN G. BOSCH,* CHARLES T. LANCEE,* CHRISTIAN PRINS,y ANTON F. W. VAN DER STEEN,* and NICO DE JONG* * Department of Biomedical Engineering, Erasmus Medical Centre, Rotterdam, The Netherlands; and y Oldelft Ultrasound, Delft, The Netherlands (Received 20 December 2011; revised 30 May 2012; in final form 18 June 2012)
Abstract—Transesophageal echocardiography (TEE) uses the esophagus as an imaging window to the heart. This enables cardiac imaging without interference from the ribs or lungs and allows for higher frequency ultrasound to be used compared with transthoracic echocardiography (TTE). TEE facilitates the successful imaging of obese or elderly patients, where TTE may be unable to produce images of satisfactory quality. Recently, three-dimensional (3-D) TEE has been introduced, which greatly improves the image quality and diagnostic value of TEE by adding an extra dimension. Further improvement could be achieved by optimizing 3-D TEE for harmonic imaging. This article describes the optimal geometry and element configuration for a matrix probe for 3-D second harmonic TEE. The array concept features separated transmit and receive subarrays. The element geometry was studied using finite element modeling and a transmit subarray prototype was examined both acoustically and with laser interferometry. The transmit subarray is suitable for its role, with a 3 MHz resonance frequency, a 40%–50% 23 dB bandwidth and crosstalk levels ,227 dB. The proposed concept for the receive subarray has a 5.6 MHz center frequency and a 50% 23 dB bandwidth. (E-mail: [email protected]) Ó 2012 World Federation for Ultrasound in Medicine & Biology. Key Words: Transesophageal echocardiography, TEE, Matrix array transducer, 3-D imaging.
et al. 1999] in fundamental mode), because of the smaller distance between the array transducer and the structures of the heart (Lancee 1987). This increase in transmission frequency directly translates into higher axial and lateral resolutions (Lancee 1987; Seward 1988) and improved sensitivity (Lancee 1987), crucial for imaging fine structures such as the mitral valve. The combination of these two advantages allows for the successful imaging of obese or elderly patients, where TTE may have unsatisfactory results (Lutz and Gharbi 2006). In the last 15 years three-dimensional (3-D) echocardiography has received considerable attention. The 3-D visualization of organs offers a perspective closer to the real anatomy than two-dimensional (2-D) imaging. Moreover, the possibility of virtually removing structures to view inner parts of organs offers surgeons information on structure morphology and functionality, which helps in the preparation of surgical intervention (Roelandt 2000). In addition, 3-D imaging considerably increases the quantification accuracy of cardiac structures and parameters compared with 2-D imaging (Krenning et al. 2003; Voormolen 2007). Three-dimensional TEE
INTRODUCTION Echocardiography is of large clinical significance in cardiology as a diagnostic modality to assess the physiologic function of the heart and its disorders (Feigenbaum 1986; Kisslo et al. 2006). Most echocardiographic examinations are performed using an imaging window between the ribs near the thorax, so called transthoracic (or precordial) echocardiography (TTE). Transesophageal echocardiography (TEE) is an alternative technique, which uses the esophagus as an imaging window to the heart. As the esophagus wall is located directly posterior to the heart, cardiac imaging can be performed without interference from the ribs or the lungs. Moreover, TEE allows for higher frequency ultrasound to be used compared with TTE (5–6 MHz vs. 3.5 MHz [Kasprzak
Address correspondence to: Nico de Jong, Department of Biomedical Engineering, Erasmus Medical Centre, P.O. Box 2040, 3000 CA Rotterdam, The Netherlands. E-mail: [email protected] 1 Works now at the Department of Process Intensification and Instrumentation, TNO, Delft, The Netherlands. 1820
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could combine the advantages of 3-D echocardiography with the high resolution and sensitivity of TEE imaging. Two types of 3-D TEE methods have been reported in the literature (Nathanail et al. 2008; Pua et al. 2004; Sugeng et al. 2008). The first is mechanical; four-dimensional (4-D) datasets (3-D 1 time) are created by mechanically rotating a modified multiplane 2-D TEE probe. Preliminary in vivo results were presented, showing valvular images with good diagnostic accuracy and high temporal and spatial resolution (Nathanail et al. 2008). The second method is based on a matrix array transducer, where 4-D datasets are created by steering the ultrasound beam in two orthogonal directions. Both sparse arrays (Pua et al. 2004) and fully sampled array designs (Savord 2003) have been published. Such a probe can provide excellent real-time 3-D visualization of the mitral valve, interatrial septum, left atrium and left ventricle (Sugeng et al. 2008). An advantage of matrix 3-D TEE is that it can provide real-time or near-real-time 4-D datasets. The main drawback of the matrix approach is the cost of the probe and the high-end ultrasound system. Currently (March 2012), Philips Healthcare (Best, Noord-Brabant, the Netherlands) is the only commercial supplier of matrix 3-D TEE equipment (X7-2t transducer). Generally, TEE transducers operate in fundamental mode (i.e., the ultrasound received at the transmitted frequency is used to create an image). However, ultrasound image quality can often be improved by exploiting the nonlinear nature of wave propagation (Zemp et al. 2003; Tranquart et al. 1999; Shapiro et al. 1998; Thomas and Rubin 1998). Tissue second harmonic imaging is based on the selective imaging of the second harmonic frequency (Tranquart et al. 1999). Compared with fundamental imaging, second harmonic imaging has a higher resolution and is less sensitive to near-field artifacts, clutter and off-axis scatterers (Zemp et al. 2003; Tranquart et al. 1999; Humphrey 2000). As a result second harmonic imaging has become the standard in transthoracic tissue imaging since the late 1990s (Monaghan 2000). The main challenge for any design of a matrix array transducer optimized for 3-D second harmonic TEE imaging is the size constraint associated with TEE operation. Since a TEE probe consists of a flexible endoscope with the array located at the tip, the whole device has to fit in the esophagus. Therefore, the total array footprint is limited to about 10 3 10 mm. To obtain the highest possible pressure and resolution, the array should occupy this maximum available area. To enable steering of the acoustic beam to large angles without compromising the beam shape, the directivity of the elements should be weak and therefore the element should be small. Furthermore, for fundamental imaging the pitch of the elements should be smaller than half the wavelength to
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avoid grating lobes. However, since second harmonic imaging is less sensitive to grating lobe artifacts (Matte et al. 2011), this requirement can be significantly relaxed. For a 6 MHz transducer, the element width should be in the order of 0.2 mm. Consequently, the transducer should consist of several thousand elements to create an aperture of approximately 10 3 10 mm. It is impossible to connect this large number of elements to an external imaging system via coaxial cables in the gastroscopic tube. Therefore, some form of microbeamforming in the probe head is required. The chosen array concept: separate transmit and receive subarrays A considerable body of literature exists on the design of matrix array transducers with a minimized number of elements (Smith et al. 1991; Turnbull and Foster 1991; Lockwood et al. 1998; Smith et al. 2002) to simplify the ultrasound system and element interconnections and to minimize costs (Light et al. 1998). Most element reduction methods use sparse array transducers with the connected elements distributed in a variety of ways (Smith et al. 1991; Turnbull and Foster 1991; Lockwood et al. 1998; Smith et al. 2002; Pua et al. 2004). In our design, the transmit and receive are physically separated, which makes acoustic and electronic tuning much more efficient. Also, the separation minimizes the crosstalk between the elements of both subarrays. The two-way 70%–80% 26 dB bandwidth required to perform second harmonic imaging is now split: both the transmit and receive subarrays should have a one-way 23 dB bandwidth of 50%. The transmit subarray is located adjacent to the receive subarray. A schematic image of the endoscope tip including the subarray layout is shown in Figure 1. The maximum number of coaxial cables within the gastroscope tube is 250, as the shaft has to remain flexible enough for insertion into the esophagus. For the transmit subarray a 1.75 D array topology is chosen. This allows for electronic focusing and steering in the lateral dimension. In the elevation dimension, it produces a broad beam and allows for limited steering. The broad beam in the elevation dimension makes parallel beamforming in
Fig. 1. Schematic image of the endoscope tip including the matrix array transducer.
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reception possible, in a similar manner as presented by von Ramm et al. (1991). For the receive subarray, a full 2-D array topology is chosen allowing for receive focusing in both the lateral and elevation dimensions to construct a 3-D dataset. Figure 2 shows the subarray concept and the produced beams schematically, thus, detailing how the transducer will image a volume. The light gray beam indicates the –3 dB beam size of the transmit beam, thus representing the 26 dB beam size of the second harmonic component generated through nonlinear propagation. The dark gray beams indicate the parallel receive beams. Since the centers of the subarrays do not coincide, there is insufficient overlap of the transmit beam and the receive beam close to the transducer surface. With this concept, imaging can be performed for axial distances larger than 15 mm (see Discussion section, Receive subarray, Predicted performance). Microbeamforming will be used to reduce the channel count from 2025 (the number of receive elements) to 225 (the number of connecting coaxial cables) (Savord 2003; Blaak et al. 2009). The concept of microbeamforming entails that the elements are arranged in groups and that the delay is divided into a coarse delay common for all elements in the group and a fine delay for each individual element in the group. The fine delays and the element summing are applied by use of a chip in the tip of the gastroscope (Savord 2003; Blaak et al. 2009). The signals of the N elements in a group are then summed reducing the number of required channels by a factor of N. To keep the effects of microbeamforming on the beam equal in the lateral and elevation directions, only square configurations (2 3 2, 3 3 3 and 4 3 4 elements) were investigated by Blaak et al.
Fig. 2. Schematic of the transducer concept and the produced beams. The light gray beam indicates the 26 dB beam width of the 2nd harmonic component of the transmitted field. To insonify a cone from 15 mm to 15 cm with an opening angle of 90 , the transmit beam is steered from 237 to 45 in the elevation dimension and from 245 to 45 in the lateral dimension. The dark gray beams indicate the parallel receive beams, which are steered from 245 to 45 in both elevation and lateral dimensions.
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(2009). A 2 3 2 group configuration would provide an insufficient reduction in channels. A 9:1 channel reduction by a 3 3 3 group configuration has been shown to produce a suitable acoustic field, with a peak grating lobe level of 227 dB relative to the main beam (Blaak et al. 2009). A 16:1 channel reduction by a 4 3 4 group configuration would produce unacceptably high grating lobe levels. A 3 3 3 group configuration limits the number of elements to a maximum of 2250. The transmitted and received signals will use the same cables and will be separated by diode limiters in the probe head. Resonance frequencies TEE transducers based on the selective imaging of the fundamental band have been reported to use transmission frequencies of 5 MHz (Currie 1989)25.6 MHz (Lancee, 1987; Lancee et al. 1988). The optimal transmission frequency for tissue second harmonic imaging depends on the level of the second harmonic at distances typical for TEE imaging, which is determined by two competing phenomena—nonlinear propagation and attenuation. In the case of fundamental TTE, it was found that for the visualization of the left ventricular endocardial border during echocardiography (imaging depths of 10– 15 cm) a transmission frequency of 3.5 MHz yielded the best results (Kasprzak et al. 1999). However, in the same study it was found that for second harmonic TTE a reception frequency of 3.2–3.6 MHz provided the optimum results (Kasprzak et al. 1999). The latter was also found by Matte et al. (2011) in a systematic study on the optimal transmission frequencies for harmonic TTE. Similarly, for TEE we choose the frequency of the second harmonic (6 MHz) to be close to the frequency used in fundamental imaging (5–5.6 MHz). Thus, the chosen resonance frequencies are 3 MHz and 6 MHz for the transmit and receive subarrays, respectively. Consequences for the element vibration An element size in the order of 0.2 mm combined with the 3–6 MHz at which TEE operates, means that the elements vibrate between 33-mode and plate mode. Therefore, lateral modes can exist and should be considered when designing the elements. The influence of geometry on this issue cannot be determined using onedimensional (1-D) models, such as the KLM model, and requires a 3-D approach. Another important issue is the crosstalk between the elements. Crosstalk lengthens the ring down of elements through delayed signals from neighboring elements and limits angular dispersion by increasing the effective element size (Turnbull and Foster 1992). Recently, techniques such as laser interferometry and 3-D finite element modeling (FEM) have gained popularity in the understanding of these complex vibration modes and crosstalk of phased arrays based on
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piezo material and cMUTs (Goldberg et al. 1997; Caronti et al. 2005). Goal This article describes a geometry and element configuration for a matrix probe consisting of two subarrays optimized for 3-D second harmonic TEE, predicting the mode vibration of single elements using FEM and documenting the performance of the transmitter using laser interferometry and acoustic measurements. The method of interconnection and the implemented electronics is beyond the scope of this article. METHODS Finite element model - element geometry optimization The optimal element geometries for elements of the transmit and receive subarrays were investigated using 3-D FEM simulations based on the ANSYS 11 FEM package (ANSYS Inc., Canonsburg, PA, USA). In these simulations, a single element was modeled: the geometry consisted of a piece of piezo material and a backing (see Fig. 3a). The piezo material properties used were those of 3203HD piezo material (CTS, Bloomingdale, IL, USA). The material of the backing was assumed to be isotropic and was modeled using linear elasticity. The transducer element was loaded by air, which was not modeled. The piezo element was a pillar with square top and bottom surfaces. In the case that a transmit subarray element was modeled, the piezo material thickness was
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0.47 mm and the width was varied between 0.068 mm and 0.81 mm. For a receive subarray element the piezo material thickness was 0.29 mm and the width was varied between 0.054 mm and 0.24 mm. The thickness of the backing was 8 mm, such that reflections from the backing did not affect the displacement of the element surface during the simulation time. Only a quarter of the element needed to be modeled due to symmetry. To ensure that the lateral mode resonance could always be resolved, 40 nodes were used in the width dimensions. Forty-one nodes were used in the thickness dimension of the piezo material. The thickness of the transducer electrodes (300 nm) was much smaller than the considered ultrasound wavelengths (0.3–1 mm) and, therefore, the electrodes were omitted from the model. The transducer element was excited by an impulse of amplitude 270 V. The time sample frequency was 100 MHz. The mesh and material properties are summarized in Tables 1 and 4, respectively. Finite element model–Final concept A single array element of both the final transmit and receive subarrays was modeled using the ANSYS 11 FEM package. An element of the transmit subarray consisted of four layers: a matching layer, the piezo material, a connection layer and the backing. A schematic of the geometry of an element of the transmit subarray in air is displayed in Figure 3b and a schematic of the geometry of the same element in water including the boundary conditions is shown in Figure 3c. An element of the
Fig. 3. (a) FEM model geometry of a piezo element for element width optimization (the width of an element is equal to its length). (b) FEM model geometry of an element of the transmit subarray in air. (c) FEM model geometry of an element of the transmit subarray in water including the boundary conditions. N indicates a nonreflective boundary condition on a surface, S is a symmetry boundary condition - displacement in direction perpendicular to the surface is 0, F stands for a free boundary - force in direction perpendicular to the surface is 0, P indicates that the pressure is 0 at this boundary surface, V is a voltage boundary condition on a surface and K is a boundary condition for a single node having 0 displacement in all directions.
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Table 1. Standard geometry and mesh parameters used in the FEM simulations Properties Total element Piezomaterial Matching layer Connection layer Backing Water Nonreflecting boundary (water)
width Thickness Element type Thickness Element type Thickness Element type Thickness Element type Radius Element type Element type
Unit [m] [m] – [m] – [m] – [m] – [m] – –
Transmit subarray 26
135.10 467.1026 20 node, 3-D SOLID226 120.1026 20 node, 3-D SOLID186 25.1026 20 node, 3-D SOLID186 2.1023 (prototype) / 8.1023 (FEM) 20 node, 3-D SOLID186 1.1023 8 node, 3-D FLUID30 4 node, 2-D boundary FLUID130
receive subarray consisted of three layers: a matching layer, the piezo material and the backing. The load of the element was either vacuum (representing an air load) or water. The water domain was surrounded by an nonreflecting boundary layer. The 2100 V impulse excitation recorded in the laser interferometer experiments were used for the voltage boundary condition. The time sampling frequency was 100 MHz. Transmit subarray prototype Based on the results of the finite element simulations a transmit subarray prototype was built. The transmit subarray consisted of four rows of 32 elements each, which results in a total of 128 elements. The array was built using CTS 3203HD piezo material. The resonance frequency of the transmit subarray was 2.7 MHz. Each element had a matching layer of 6.5 MRayl and a backing of 3.4 MRayl. In between the piezo material and the backing was a connection layer, which was a thin electrically conductive layer facilitating the connection between the elements and the flexible printed circuits. Also, a light-reflecting foil was glued on top of the elements. No lens was mounted. The width and length of the elements were both 0.27 mm. The elements were
Fig. 4. A picture of the transmit subarray prototype without the light-reflecting foil. The schematic on the bottom right shows the numbering of the elements.
Receive subarray 85.1026 292.1026 20 node, 3-D SOLID226 80.1026 20 node, 3-D SOLID186 23 2.10 (prototype) / 8.1023 (FEM) 20 node, 3-D SOLID186 1.1023 8 node, 3-D FLUID30 4 node, 2-D boundary FLUID130
diced into the backing using a diamond saw and were fully acoustically isolated from each other. The kerf was 40 mm and no kerf filler material was used. The total footprint of the transmit subarray was 9.9 3 1.2 mm. A picture of the array is displayed in Figure 4. The properties of the materials used in the subarray elements are given in Table 4 of Appendix: Material Properties. The transducer was manufactured by Oldelft Ultrasound, Delft, The Netherlands. Setup for optical characterization The space and time dependant out-of-plane surface displacement (henceforth, denoted as axial surface displacement) of the elements of the transmit subarray prototype was studied in air using a laser interferometer system. A schematic of the optical setup is displayed in Figure 5. The system was based on a Polytec MSV-300 laser scanning vibrometer system (Polytec GmbH, Waldbronn, Germany). The laser interferometer consisted of
Fig. 5. A schematic of the laser interferometer setup. Dotted arrows are trigger signals.
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a Polytec OFV 512 fiber interferometer connected to a Polytec OFV 5000 vibrometer controller equipped with a displacement decoder with an upper frequency limit of 20 MHz. The fiber interferometer was connected to the MSA-400 scan head, which functioned as a microscope. The continuous analog output produced by the vibrometer controller was captured by a digitizer card (DP235; Acqiris, Geneva, Switzerland) at a sampling rate of 100 MHz. The digitizer was triggered by either an arbitrary waveform generator or a pulser/receiver. For amplitude transfer function measurements the array element was excited by 35-cycle sinusoids with amplitude 5 V generated by an arbitrary waveform generator (33250A; Agilent, Loveland, CO). For crosstalk measurements the element was excited by a pulser/ receiver (5800; Panametrics, Waltham, MA, USA), which produced 2100 V spikes with a width of 0.3 ms. The array was mounted on two orthogonal motorized translation stages (PT1-Z8; Thorlabs GmbH, Munich, Germany). The displacement of the array elements was studied using a laser spot diameter of 20 mm and a translation step size of 30 mm. The received signals were averaged 1000 times for each measurement position to reduce the effects of variance in signal quality due to the variability of element surface reflectivity and surface roughness. The pulse repetition frequency was 1 kHz. The electrical impedances of the equipment used were measured using a vector impedance meter (4193A; Hewlett Packard, Yokogawa, Japan). Setup for acoustic characterization The acoustic measurements were performed in a water tank using a hydrophone setup. The pressure transmit transfer function was determined by measuring the responses of individual elements to 30-cycle sine bursts with amplitude 5 V, the frequency of which was varied from 1 to 10 MHz. The emitted pressure field was measured at a distance of 4 cm using a calibrated hydrophone (diameter 0.2 mm; Precision Acoustics, Dorchester, UK) that was mounted in a custom built xyzsystem. The hydrophone signals were amplified by a low noise amplifier (AU-3A-0110-BNC; Miteq, Hauppauge, NY, USA) and digitized by an oscilloscope (DSO6034A; Agilent Technologies, Palo Alto, CA, USA). The transfer functions were calculated using the methods described by van Neer et al. (2007), where the Fraunhofer approximation for the pressure distribution of a flat rectangular piston transducer excited by continuous wave excitation (Cobbold 2007) was used to obtain the diffraction correction function. The electrical impedances of the equipment used were measured using a vector impedance meter (4193A; Hewlett Packard).
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RESULTS Transmit subarray Element geometry optimization. The resonance frequencies of the fundamental and lateral modes as a function of a piezo element’s width, which were simulated using 3-D FEM simulations, are plotted in Figure 6. For example, an element width of 0.27 mm gives a fundamental mode resonance of 2.7 MHz and a lateral mode resonance of 6 MHz. Figure 6 shows that as a piezo element’s width increases, the fundamental and lateral mode resonance frequencies approach each other. This was also reported in the literature (Onoe and Tiersten 1963; De Jong et al. 1985). Therefore, the desire to separate the fundamental and lateral mode resonances puts an upper limit on an element’s width. Performance. The amplitude transmit transfer functions of the transmit subarray elements produced by the optical measurements and FEM simulations are shown in Figure 7a. The elements were loaded by air. The experimental results were based on measurements of four elements, each excited individually. The maximum amplitude transmit transfer was 3 nm/V. Two peaks were visible in the spectra, the first on 2.4 MHz (measurements and simulation) and the second on 3.9 MHz (measurements) or 4.1 MHz (simulation). The experimental results showed a large spread around the second peak as indicated by the standard deviation of 0.7 nm/V vs. a mean of 2 nm/V (see Fig. 7a). This may have been
Fig. 6. The relation between an element’s width and resonance frequency of the fundamental mode (black plusses) and lateral mode (gray crosses) as calculated using FEM simulations for the elements of the transmit subarray. The dotted black lines show the 23 dB bandwidth requirement for the fundamental. The chosen width of 0.27 mm is indicated by black arrows and gives a fundamental mode resonance of 2.7 MHz and a lateral mode resonance of 6.0 MHz. The thickness of the element was 0.47 mm.
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Fig. 7. (a) Amplitude transmit transfer function (Tta ðuÞ) of the axial surface displacement of transmit subarray elements vibrating in air. The dashed gray line is the mean axial displacement of 4 elements, the gray area is the standard deviation around the mean (optical measurements). The solid black line is the result of the FEM simulation. (b) Transmit transfer function (Tt ðuÞ) of transmit subarray elements vibrating in water. The dashed gray line is the mean transmit transfer of four elements, the gray area is the standard deviation around the mean (acoustic measurements). The solid black line is the result of the FEM simulation.
caused by a nonuniform adhesion between the matching layer and the piezo material, or by damage related to dicing. The agreement between the optical measurements and the FEM simulation was good, especially at frequencies below 5 MHz. The spikiness of the results above 5 MHz was caused by the lack of damping in the FEM model combined with the interaction of the axial surface displacement and a lateral mode around 6 MHz. The transmit transfer functions of transmit subarray elements vibrating in water produced by acoustic measurements and modeled by a FEM simulations are shown in Figure 7b. The experimental results were based on measurements of four elements, each excited individually. The peak transmit transfer as determined by the FEM simulations was 43 kPa/V at 2.3 MHz vs. an exper-
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imentally determined peak mean transmit transfer of 54 kPa/V at 2.5 MHz. This difference is caused by crosstalk. The standard deviation in the experimental results may be caused by nonuniform adhesion, variations in dicing or the variations in the thin silicone layer which was applied on top of the transmit subarray to create a watertight seal. The 23 dB bandwidth as calculated by FEM simulations was 64% around a center frequency of 3 MHz vs. an experimentally determined average 23 dB bandwidth of 65% around the same center frequency. Figure 8a shows the magnitude of the electrical impedance of the transmit subarray elements measured in air, while Figure 8b shows the phase of the electrical impedance of the transmit subarray elements measured in air. These results were based on measurements of five individual elements. The two fundamental resonance peaks at 2.4 MHz and 3.9 MHz, as observed in the measured amplitude transfer functions (see Fig. 7a), are clearly observable in Figure 8a. Moreover, the impedance spectrum shows a third harmonic mode at about 7.1 MHz. There is a small peak in the phase spectrum (see Fig. 8b) at 5.6 MHz, which is likely caused by a lateral mode. The average coupling coefficient k33, calculated from the experimentally determined electrical impedances using the formula given for bar mode vibration by De Jong et al. (1985), was 0.66. The manufacturer of the piezo material used (CTS 3203HD) states in the specifications of the material a k33 of 0.75. Therefore, the efficiency is close to that of an ideal element vibrating in the 33-mode. Figure 9 shows the normalized maximum axial surface displacement of element 28 and element 93, as measured with the laser interferometer. The elements were excited by 2100 V impulses. Element 28 was located on the edge of the array and element 93 in the middle. The peak displacement of elements 28 and 93 were 63.4 nm and 52.5 nm, respectively. Four elements were examined (the displacement of only two elements is shown in Fig. 9) and their peak displacements varied from 52 to 64 nm. The displacement pattern clearly reflected the element distribution. The axial displacement due to crosstalk in the lateral direction was higher than in the elevation direction. This was visible in the displacement pattern produced by element 93 (Fig. 9b) but less obvious in the displacement pattern produced by element 28 (Fig. 9a). There was no discernible time delay in the time signals of the neighboring elements suggesting primarily electrical rather than mechanical crosstalk. The frequency dependency of the crosstalk from an excited element to a neighboring element is shown in Figure 10 for elements 28 and 93. This was calculated by taking the Fourier transform of the mean surface displacement of an element neighboring the excited element and normalizing that to the Fourier transform of the mean surface displacement of the excited element.
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Table 2. Normalized crosstalk level of excited element to neighboring element averaged over a frequency band of 1–5 MHz Crosstalk in lateral direction (dB)
Crosstalk in elevation direction (dB)
218 217 220 216 218
226 238 218 228 227
Element 28 Element 85 Element 87 Element 93 Average
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Predicted performance. The receive transfer function of an element of the receive subarray with the chosen width of 0.17 mm as simulated using FEM modeling is displayed in Figure 12. The element was loaded by water. The receive transfer function had a maximum of 24.8 mV/Pa at 5.3 MHz. The center frequency of the element was 5.6 MHz. Its 23 dB bandwidth was 50% and stretched from 4.2 MHz to 7 MHz. DISCUSSION Transmit subarray
The crosstalk was higher in the lateral direction than in the elevation direction. In the case element 28 was excited the crosstalk averaged over 1–5 MHz was 218 dB and 226 dB in the lateral and elevation directions, respectively. For element 93 this was 216 dB and 228 dB in the lateral and elevation directions, respectively. The crosstalk showed a frequency dependency, being highest between 3 and 4 MHz (element 28:28 and 214 dB for the lateral and elevation directions) and lowest between 1 and 2 MHz (element 28: 225 dB and 233 dB for the lateral and elevation directions). These crosstalk measurements were performed for four excited elements. The average crosstalk over a 1–5 MHz band is summarized in Table 2 for the lateral and elevation dimensions. The average crosstalk from the excited element to a neighboring element was 218 dB and 227 dB for the lateral and elevation directions respectively. Receive subarray Element geometry optimization. The resonance frequencies of the fundamental and lateral modes as a function of a piezo element’s width, which were simulated using 3-D FEM simulations, are plotted in Figure 11. For example, an element with a width of 0.17 mm gives a fundamental mode resonance of 6.3 MHz and a lateral mode resonance of 9.4 MHz. Similar to the transmit array, the fundamental and lateral mode resonance frequencies approach each other as the element width increases.
Element geometry optimization. The optimal element width of the transmit subarray is the result of a trade-off. On the one hand, the element should be small enough to avoid interference from the fundamental and lateral mode resonances of the element. Furthermore, smaller elements ensure sufficient element omnidirectionality to steer the ultrasound beam and reduce the pitch, leading to lower grating lobe levels. On the other hand, choosing the elements too small leads to either an aperture that is unable to generate sufficient pressure or contains too many elements. The chosen width for the elements of the transmit subarray is 0.27 mm. The fundamental resonance frequency of the piezo element in air is at 2.7 MHz. The lateral mode resonance is outside the 23 dB bandwidth, at 6 MHz. The center frequency of the element, including matching layers, in water is 3 MHz. The chosen width is only slightly larger than half the wavelengths at 3 MHz, which is 0.25 mm, ensuring sufficiently weak element directivity for beam steering. Practical experience shows that the smallest kerf width, which still results in reliable array construction, is 40 mm. Even though the resulting pitch is somewhat larger than half the wavelength of the emitted ultrasound, grating lobes are not expected to be a problem with this element configuration as the array is intended for second harmonic imaging. The final transmit subarray consists of 32 3 4 elements, with a size of 0.27 3 0.27 3 0.47 mm. In combination with a kerf size of 40 mm this yields a subarray footprint of 9.9 3 1.2 mm. A summary of the parameters of final transmit and receive subarrays is given in Table 3.
Table 3. Parameters of the final transmit and receive subarrays Properties
Unit
Transmit subarray
Receive subarray
Center frequency Piezo element size Kerf size Element layout Total no. of elements Footprint size Channel reduction No. of connecting channels
[MHz] [mm] [mm] [–] [–] [mm] [–] [–]
3 0.27 3 0.27 3 0.47 40 32 3 4 128 9.9 3 1.2 1:1 128
5.6 0.17 3 0.17 3 0.29 30 45 3 45 2025 9.0 3 9.0 9:1 225
Note that the total amount of coaxial cables connecting the combined arrays is 225.
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Fig. 9. (a) Normalized maximum axial displacement of transmit subarray element 28. (b) Normalized maximum axial displacement of transmit subarray element 93. The normalized axial displacement in dB is encoded by gray values. The elevation and lateral dimensions are relative to the bottom right corner of element 1 (see the picture of the prototype in Fig. 4). The element displacement in air was measured using the laser interferometer setup.
Fig. 8. (a) Magnitude of electrical impedance of transmit subarray elements, measured in air. The dashed gray line is the mean of measurements on five individual elements, the gray area is the standard deviation around the mean. (b) Phase of electrical impedance of five transmit subarray elements measured in air.
Performance. The amplitude transmit transfer function of the transmit subarray elements (in air, shown in Fig. 7a) showed a considerable dip between the peak at 2.4 MHz and the peak at 3.9 MHz. However, the peak at 3.9 MHz was smoothed and lowered, when the elements were loaded by water (Fig. 7b). The experimentally determined average peak transmit transfer of a transmit subarray element was 54 kPa/V at 2.5 MHz. In the future, the transmit subarray elements will be electrically matched to the transmitters using coils. This will lower the bandwidth to 40%–50% and increase the efficiency of the elements compared to the transfer function shown in Figure 7b. In recent work it has been shown that the full unsteered, unfocused and untuned transmit subarray produced 0.7 MPa using 95 Vpp excitation signals at an axial distance of 60 mm in water (Blaak et al. 2011b). After filtering of the second harmonic band in this data it was found to have a peak amplitude of 120 kPa. Through electrical tuning and an increase in excitation
voltage to 120 Vpp we expect to increase these amplitudes two to three times, giving a second harmonic pressure in the order of 300 kPa. The crosstalk between the array elements is important because it has a detrimental effect on the transducer’s ability to perform beam steering by effectively making the elements larger and, thus, less omnidirectional. McKeighen (1998) reported that crosstalk values of 230 dB are considered acceptable for most imaging situations. Electrical crosstalk appears to be the largest contributor to the total crosstalk and efforts should be made to reduce it by improving the electrical shielding of the elements and connecting wires. Moreover, the crosstalk in the lateral direction is higher than in the elevation direction. This corresponds to the direction of the flexible printed circuits. Since beam steering will mostly be applied in the lateral direction, it may be beneficial to connect the flexible printed circuits in the elevation direction to the elements. The crosstalk in the steering direction will be at 227 dB close to the required 230 dB. Preliminary measurements of the acoustic field produced by single transmit subarray elements showed an opening angle of 60 , which is sufficient for volumetric imaging (Blaak et al. 2010). The crosstalk has a strong frequency dependency as shown in Figure 10, with a shape roughly similar to
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Fig. 10. The transmit array surface displacement due to crosstalk to a neighboring element normalized to the displacement of the excited element plotted vs. the frequency, for elements 28 (a) and 93 (b). The mean crosstalk to a neighboring element in the lateral direction is denoted by a black solid line and the crosstalk to an element in the elevation direction is denoted by a gray dashed line. The element displacement in air was measured using the laser interferometer setup.
magnitude of the electrical impedance of an element (see Fig. 8a). For the typical 3 MHz imaging bursts with 50% 23 dB bandwidth, the crosstalk will be close to the reported mean values (227 dB, see Table 2). However, for applications requiring narrowband excitation (e.g., Doppler), the 20 dB crosstalk variance due to the frequency (see Fig. 10) should be taken into account. A 2.5 MHz excitation frequency would provide low crosstalk and a good transmission efficiency.
Fig. 11. The relation between element’s width and resonance frequency of the fundamental mode (black plusses) and lateral mode (gray crosses) as calculated using FEM simulations for the elements of the receive subarray. The dotted black lines show the 23 dB bandwidth requirement for the fundamental. The chosen width of 0.17 mm is indicated by black arrows and gives a fundamental mode resonance of 6.3 MHz and a lateral mode resonance of 9.4 MHz. The thickness of the element was 0.29 mm.
Receive subarray Element geometry optimization. The optimal width of the receive subarray elements is a compromise between the element count, the footprint size and minimizing the effects of lateral resonance modes. Other important factors are a weak element directivity for beam steering and a sufficiently small pitch to avoid grating lobes. The chosen width for the elements of the receive subarray is 0.17 mm. For this element width, the fundamental resonance frequency of the piezo element in air is at 6.3 MHz and the lateral mode resonance is at 9.4 MHz, which is outside the 23 dB bandwidth. The center frequency of the element, including
Fig. 12. The receive transfer function (Tr ðuÞ) of the axial surface displacement of an element of the receive subarray, obtained using FEM simulations. The element was loaded by water.
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matching layers, is in water 5.6 MHz. This is close to the intended 6 MHz. Awidth of 0.17 mm corresponds to 0.7 wavelength, which ensures sufficiently weak element directivity to allow for steering between 245 and 45 . Although this is larger than half the wavelength of the received ultrasound, grating lobes are not expected to be a problem, since they are unlikely to overlap with the grating lobes produced by the transmit subarray. The outer dimension of the tip of an adult TEE probe is 15 mm, therefore, the total aperture of the array can only be 10 3 10 mm. This results in a total of 45 3 45 elements each with a size of 0.17 3 0.17 3 0.29 mm. Combined with a kerf of 30 mm this yields a footprint of the receive subarray of 9.0 3 9.0 mm. Using 9:1 channel reduction based on microbeamforming the total number of required wires is 225, which fits in the gastroscope tube. The footprint of the transmit and receive subarrays combined amounts to 9.9 3 10.2 mm, which is comparable to the footprint of conventional TEE transducers. A summary of the parameters of final transmit and receive subarrays is given in Table 3. Predicted performance. The center frequency of 5.6 MHz found for the modeled element of the receive subarray is slightly lower than the intended 6 MHz, but still acceptable. The FEM simulations of a single receive subarray element show a peak receive sensitivity of 25 mV/Pa. To judge whether this is sufficient, the entire imaging chain should be considered. The transmit subarray is expected to produce second harmonic pressures of 300 kPa (see Discussion section, Transmit subarray, Performance). Applying the formula and cardiac tissue properties in Table 4.22 from Duck (1990) on our array concept and imaging situation, the backscattered intensity is 40–60 dB lower than the intensity impinging on a scatterer. This means that the highest received second harmonic pressure will be 3 kPa. With 25 mV/Pa sensitivity this corresponds to a signal of 75 mV. The noise level of commercial TEE systems is 100 mVrms. That means that the dynamic range of our system is 57 dB, which is more than can be indicated using gray levels in a B-mode image (256 gray levels is 48 dB). Therefore, the sensitivity of the receive elements is expected to be sufficient. The distance between the centers of the transmit and receive subarrays is 5.1 mm and the maximum steering angle of the receive subarray is 45 . At larger steering angles, the grating lobe level increases to unacceptable levels due to the microbeamforming used for channel reduction (Blaak et al. 2009). We expect to steer the transmit subarray beam in the elevation dimension between 237 and 45 . Preliminary acoustic measurements on the entire transmit subarray showed an elevation length and a lateral width of the second harmonic of 12.2 mm and 6.2 mm at an axial distance of 40 mm, respectively
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(based on data used in Figure 5a of Blaak et al. [2011b]). Hence, the transmit and receive beams start to overlap at an axial distance of 15 mm (Blaak et al. 2011a). Laser interferometer measurements The signal-to-noise-ratio (SNR) of the laser interferometer measurements was mainly determined by the amount of light reflected back into the detector. The prototype array was covered by a highly reflective aluminum foil, which was stretched and smoothed as much as possible during production. Even so, the irregularity of the top surface (e.g., due to folds in the aluminum) relative to the size of the laser spot (20 mm) occasionally caused little light to be reflected back to the detector. This effect was visible in the maximum displacement plots of Figure 9 as spots with an unexpectedly low displacement. During the total time of the measurements (2 weeks), the reflectivity of the aluminum foil deteriorated due to handling and temperature influences decreasing the SNR by 2 dB. However, this reduction in SNR was not significant, as the peak SNR was about 55 dB after averaging. CONCLUSION The presented transmit subarray in combination with appropriate electrical tuning is expected to be suitable for its role, with a 3 MHz resonance frequency, 40%–50% 23 dB bandwidth and ,227 dB crosstalk levels in the lateral steering direction. The proposed concept for the receive subarray has a 5.6 MHz center frequency and a 50% 23 dB bandwidth. Acknowledgments—The authors acknowledge the technical support of J. Ponte, G. Springeling and M. Manten. They thank S.L. Paalvast and Prof. D. Rixen from the faculty of Mechanical, Maritime and Materials Engineering, Delft University of Technology for providing the laser interferometer setup.
REFERENCES Blaak S, Lancee C, Bosch J, Prins C, van der Steen A, De Jong N. A matrix transducer for 3-D transesophageal echocardiography with a separate transmit and receive subarray. Orlando, Florida: USA. Proc IEEE Ultrason Symp 2011a:2341–2344. Blaak S, van Neer P, Prins C, Bosch J, Lancee C, De Jong N. Transducer design for second harmonic 3-D transesophageal echocardiography. San Diego, USA: Proc IEEE Ultrason Symp 2010:1218–1221. Blaak S, van Neer PLMJ, Prins C, Bosch JG, Lancee CT, van der Steen AFW, de Jong N. Design of a matrix transducer for threedimensional second harmonic transesophageal echocardiography. Acoustical Imaging 2012;31:341–349. Blaak S, Yu Z, Meijer G, Prins C, Lancee C, Bosch J, De Jong N. Design of a micro-beamformer for a 2D piezoelectric ultrasound transducer. In: Proc. IEEE Ultrason Symp Rome, Italy, 2009:1338–1341. Briggs A. Acoustic microscopy. New York: Oxford University Press; 1992. Caronti A, Savoia A, Caliano G, Pappalardo M. Acoustic coupling in capacitive microfabricated ultrasonic transducers: Modeling and experiments. IEEE Trans Ultrason Ferroelectr Freq Control 2005; 5212:2220–2234.
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Sherrit S, Wiederick H, Mukherjee B. A complete characterization of the piezoelectric dielectric and elastic properties of Motorola pzt 3203 hd including losses and dispersion. Newport Beach. Proc SPIE 1997;3037:158–169. Smith S, Lee W, Light E, Yen J, Wolf P, Idriss S. Two dimensional arrays for 3-D ultrasound imaging. Proc. IEEE Ultrason Symp 2002;2: 1545–1553. Smith S, Pavy H Jr, von Ramm O. High-speed ultrasound volumetric imaging system-part i: Transducer design and beam steering. IEEE Trans Ultrason Ferroelectr Freq Control 1991;382:100–108. Sugeng L, Shernan S, Salgo I, Weinert L, Shook D, Raman J, Jeevanandam V, DuPont F, Settlemier S, Savord B, Fox J, Mor-Avi V, Lang R. Live 3-dimensional transesophageal echocardiography: Initial experience using the fully-sampled matrix array probe. JACC 2008;526:446–449. Thomas J, Rubin D. Tissue harmonic imaging: Why does it work? J Am Soc Echocardiogr 1998;118:803–808. Tranquart F, Grenier N, Eder V, Pourcelot L. Clinical use of ultrasound tissue harmonic imaging. Ultrasound Med Biol 1999;256:889–894. Turnbull D, Foster F. Beam steering with pulsed two-dimensional transducer arrays. IEEE Trans Ultrason Ferroelectr Freq Control 1991; 384:320–333. Turnbull D, Foster F. Fabrication and characterization of transducer elements in two-dimensional arrays for medical ultrasound imaging. IEEE Trans Ultrason Ferroelectr Freq Control 1992;394:464–475. van Neer P, Matte G, Sijl J, Borsboom J, de Jong N. Transfer functions of us transducers for harmonic imaging and bubble responses. Ultrasonics 2007;464:336–340. von Ramm O, Smith S, Pavy H Jr. High-speed ultrasound volumetric imaging system-part 11: Parallel processing and image display. IEEE Trans Ultrason Ferroelectr Freq Control 1991;382:109–115. Voormolen M. 3-D harmonic echocardiography. PhD Thesis. Erasmus University Rotterdam; 2007. Zemp R, Tavakkoli J, Cobbold R. Modeling of nonlinear ultrasound propagation in tissue from array transducers. J Acoust Soc Am 2003;1131:139–152.
APPENDIX TRANSFER FUNCTION DEFINITIONS The transducer transmit transfer function (Tt ðuÞ) was defined as (van Neer et al. 2007): Tt ðuÞ 5
jp0 ðuÞj ; jVT ðuÞj
(1)
with p0 ðuÞ the pressure at the transducer surface and VT ðuÞ the voltage over the transducer electrodes. The receive transfer function (Tr ðuÞ) was defined as (van Neer et al. 2007): VT2open ðuÞ ; (2) Tr ðuÞ 5 jpa ðuÞj with VT2open ðuÞ the open circuit voltage produced by the transducer and pa ðuÞ the pressure received on the transducer surface. The amplitude transmit transfer function of a transducer (Tta ðuÞ) was defined as: a u ðuÞ 33 a ; (3) Tt ðuÞ 5 jVT ðuÞj with ua33 the mean axial displacement of the transducer surface.
MATERIAL PROPERTIES The properties of the CTS 3203HD piezo material used in both subarrays were based on the values reported by Sherrit et al. (1997).
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Table 4. The properties of the materials used in the simulations and the prototype Property Piezomaterial
Matching layer Connection layer Backing Water
Unit 2
Value 211
Elastic compliance (sE )
[m /N.10
Piezoelectric strain coefficient (d) Relative permittivity (K T ) Density (r) Dielectric loss (tande ) Mechanical quality factor (Qm ) Longitudinal wave speed (y33 ) Poisson ratio (n) Density (r) Longitudinal wave speed (y33 ) Poisson ratio (n) Density (r) Longitudinal wave speed (y33 ) Poisson ratio (n) Density (r) Longitudinal wave speed (y33 ) Density (r)
[C/N.10210] – [kg/m3] – – [m.s21] – [kg.m23] [m.s21] – [kg.m23] [m.s21] – [kg.m23] [m.s21] [kg.m23]
The materials used for the matching layer and backing were assumed to be homogeneous and isotropic. The longitudinal wave speed (y33 ) of these materials was determined using the method of Selfridge (1985). The density (r) was determined using Archimedes’ method (Selfridge
]
sE11 5 1.56, sE12 5 20.420, sE13 5 20.823, sE33 5 1.89, sE55 5 3.92, sE66 5 3.98 d13 5 2.95, d33 5 5.64, d15 5 5.60 T T K11 5 2417, K33 5 3331 7800 0.028 66 2066 0.35 3146 2066 0.35 3146 1818 0.35 1870 1490 1000
1985). Using y33 and r the axial modulus was calculated (Briggs 1992; Cobbold 2007). The Poisson ratio (n) of the passive materials was estimated at 0.35. A summary of the material properties is given in Table 4.