Fast time-domain modeling of fluid-coupled cMUT cells: from the single cell to the 1-D linear array element

Broad bandwidth air-coupled micromachined ultrasonic transducers for gas sensing

The present work aims to develop ultra-wide bandwidth air-coupled capacitive micromachined ultrasonic transducers (CMUTs) for binary gas mixture analysis. The detection principle is based on time-of-flight (ToF) measurements, in order to monitor gas ultrasound velocity variations. To perform such measurements, CMUTs were especially designed to work out of resonance mode, like a microphone. The chosen membrane size is 32 × 32 µm² and gap height is 250 nm. The resonance frequency and collapse voltage were found at 8 MHz and 58 V respectively. As mentioned, the CMUTs were exploited in quasi-static operating mode, in a very low frequency band, from 1 MHz to 1.5 MHz frequencies. The transducer impulse response was characterised, and a -6 dB relative fractional frequency bandwidth (FBW) higher than 100% was measured, enabling to use CMUT for the targeted application. Additionally, a measuring cell has been designed to hold the fabricated CMUT emitter and receiver prototypes facing each other. The volume inside the cell was kept lower than 3 mL and the surface of emitter/receiver was 1.6 × 8 mm². To validate the general principle of the proposed technique, two binary gas mixtures of CO₂/N₂ and H₂/N₂, with varying concentrations, have been tested. The results are very promising with a measured limit of detection (LOD) of 0.3% for CO₂ in N₂ and 0.15% for H₂ in N₂.

A Review on Analytical Modeling for Collapse Mode Capacitive Micromachined Ultrasonic Transducer of the Collapse Voltage and the Static Membrane Deflections

Analytical modeling of capacitive micromachined ultrasonic transducer (CMUT) is one of the commonly used modeling methods and has the advantages of intuitive understanding of the physics of CMUTs and convergent when modeling of collapse mode CMUT. This review article summarizes analytical modeling of the collapse voltage and shows that the collapse voltage of a CMUT correlates with the effective gap height and the electrode area. There are analytical expressions for the collapse voltage. Modeling of the membrane deflections are characterized by governing equations from Timoshenko, von Kármán equations and the 2D plate equation, and solved by various methods such as Galerkin’s method and perturbation method. Analytical expressions from Timoshenko’s equation can be used for small deflections, while analytical expression from von Kármán equations can be used for both small and large deflections.

An Improved CMUT Structure Enabling Release and Collapse of the Plate in the Same Tx/Rx Cycle for Dual-Frequency Acoustic Angiography

This study demonstrates, in detail, the potential of using capacitive micromachined ultrasonic transducers (CMUTs) for acoustic angiography of the microvasculature. It is known that when ultrasound contrast agents (microbubbles) are excited with moderate acoustic pressure around their resonance (2-4 MHz), they produce higher order harmonics (greater than third harmonic) due to their nonlinear behavior. To date, the fundamental challenge has been the availability of a transducer that can generate the transmit signals to excite the microbubbles at low frequencies and, in the same cycle, confocally detect harmonics in the higher frequencies. We present a novel device structure and dual-mode operation of a CMUT that operates with a center frequency of 4.3 MHz and 150% bandwidth in the conventional mode for transmitting and a center frequency of 9.8 MHz and a 125.5% bandwidth in collapse mode for receiving. Output pressure of 1.7 MPapp is achieved on the surface of a single unfocused transducer. The mechanical index at the transducer surface is 0.56. FEM simulations are performed first to show the functionality of the proposed device, and then, the device fabrication is described in detail. Finally, we experimentally demonstrate the ability to detect the microbubble signals with good contrast, and the background reflection is adequately suppressed, indicating the feasibility of the presented approach for acoustic angiography.

A Boundary Element Model for CMUT-Arrays Loaded by a Viscoelastic Medium

This work is an extension of a model previously developed by our group to simulate the electroacoustic response of capacitive micromachined ultrasonic transducer (CMUT)-based linear arrays acoustically loaded by a fluid medium. The goal is to introduce the viscoelasticity effects of the propagation medium into the modeling. These effects are mainly due to the passivation layer used to protect the transducer, i.e., a silicon polymer, a few hundred micrometers thick. The passivation layer is also required to ensure good acoustic coupling between the transducer front face and human skin. The theoretical approach relies on the determination of a new boundary matrix to simulate the acoustic coupling between the CMUT array and the viscoelastic medium. The complete numerical implementation of a 3-D Green's function for a viscoelastic half-space is hence described. In order to reduce computing time, an optimization was carried out through vectorization and parallelization methods. A comparison is then performed with the analytical solutions, from the literature, obtained for elastic half-space. An experimental validation of shear viscosity effects is performed through electrical impedance measurements of the CMUT linear arrays loaded by oils of varying viscosity. A very good agreement is obtained, showing that the model correctly takes the shear viscosity effects on the mechanical response of the CMUT into account, i.e., a shift in the resonance frequency and a diminution in the mechanical quality factor are observed.

A Hybrid Boundary Element Model for Simulation and Optimization of Large Piezoelectric Micromachined Ultrasonic Transducer Arrays

A hybrid boundary element model is proposed for the simulation of large piezoelectric micromachined ultrasonic transducer (PMUT) arrays in immersion. Multiphysics finite element method (FEM) simulation of a single-membrane structure is used to determine stiffness and piezoelectrically induced actuation loading of the membranes. To simulate the arrays of membranes in immersion, a boundary element method is employed, wherein membrane structures are modeled by a surface mesh that is coupled mechanically by mass, stiffness, and damping matrices, and acoustically by a mutual impedance matrix. A multilevel fast multipole algorithm speeds up computation time and reduces memory usage, enabling the simulation of thousands of membranes in a reasonable time. The model is validated with FEM for a small 3 3 matrix array for both square and circular membrane geometries. Two practical optimization examples of large PMUT arrays are demonstrated: membrane spacing of a 7 7 matrix array with circular membranes, and material choice and top electrode coverage of a 32-element linear array with 640 circular membranes. In addition, a simple analytical approach to electrode optimization based on normal mode theory is verified.

Unbiased Charged Circular CMUT Microphone: Lumped-Element Modeling and Performance

An energy-consistent lumped-element equivalent circuit model for charged circular capacitive micromachined ultrasonic transducer (CMUT) cell is derived and presented. It is analytically shown and experimentally verified that a series dc voltage source at the electrical terminals is sufficient to model the charging in CMUT. A model-based method for determining this potential from impedance measurements at low bias voltages is presented. The model is validated experimentally using an airborne CMUT, which resonates at 103 kHz. Impedance measurements, reception measurements at resonance and off-resonance, and the transient response of the CMUT are compared with the model predictions.

Capacitive Micromachined Ultrasound Transducers for Interstitial High-Intensity Ultrasound Therapies

Capacitive micromachined ultrasound transducers (CMUTs) exhibit several potential advantages over conventional piezo technologies for use in therapeutic ultrasound (US) devices, including ease of miniaturization and integration with electronics, broad bandwidth (>several megahertz), and compatibility with magnetic resonance imaging (MRI). In this paper, the electroacoustic performance of CMUTs designed for interstitial high-intensity contact US (HICU) applications was evaluated and the feasibility of generating US-induced heating and thermal destruction of biological tissues was studied. One-dimensional CMUT linear arrays as well as a prism-shaped 2-D array composed of multiple 1-D linear arrays mounted on a cylindrical catheter were fabricated. The electromechanical and acoustic characteristics of the CMUTs were first studied at low intensity. Then, the acoustic output during continuous wave (CW) driving was studied while varying the bias voltage ( V_DC ) and driving voltage ( V_AC ). US heating was performed in tissue-mimicking gel phantoms under infrared (IR) or MR-thermometry monitoring. Acoustic intensities compatible with thermal ablation were obtained by driving the CMUTs in the collapse-snapback operation mode ( [Formula: see text]). Hysteresis in the acoustic output was observed with varying V_DC . IR- and MR-thermometry monitoring showed directional US-induced heating patterns in tissue-mimicking phantoms (frequency: 6-8 MHz and exposure time: 60-240 s) extending over 1.5-cm depth from the CMUT surface. Irreversible thermal damage was produced in turkey breast tissue samples ( [Formula: see text]). Multidirectional US-induced heating was also achieved in 3-D with the CMUT catheter. These studies demonstrate that CMUTs can be integrated into HICU devices and be used for heating and destruction of tissue under MR guidance.

Investigation of Classical Pulse Sequences for Contrast-Enhanced Ultrasound Imaging With a cMUT Probe

Capacitive micromachined ultrasonic transducers (cMUTs) provide promising ultrasonic technology that could become an alternative to piezoelectric probes for medical applications. cMUTs could be very valuable for contrast-enhanced ultrasound imaging based on higher harmonics detection. However, their use is restricted by the intrinsic nonlinearity of the cMUT transmitters themselves, because it is difficult to distinguish between the nonlinearity of the microbubbles and the nonlinearity arising from the emitting transducer. A number of approaches have been proposed in recent years to cancel the nonlinearity of cMUTs. However, these techniques have limitations in terms of implementation with current ultrasound scanner electronics. The solution to be comparable with classical methods should not need precharacterization of the probe or changing the bias voltage (amplitude or polarity) but does need good sensitivity and a high frame rate to avoid motion artifacts. We propose here proof of a concept of an adapted amplitude modulation sequence with cMUT where transmit elements operate alternately. We show that this method, which is currently used with piezoelectric probes, is fully applicable to cMUT probes and the intrinsic nonlinearity of the transmitter is no longer an issue.

A nonlinear lumped model for ultrasound systems using CMUT arrays

We present a nonlinear lumped model that predicts the electrical input-output behavior of an ultrasonic system using CMUTs with arbitrary array/membrane/electrode geometry in different transmit-receive configurations and drive signals. The receive-only operation, where the electrical output signal of the CMUT array in response to incident pressure field is calculated, is included by modifying the boundary elementbased vibroacoustic formulation for a CMUT array in rigid baffle. Along with the accurate large signal transmit model, this formulation covers pitch-catch and pulse-echo operation when transmit and receive signals can be separated in time. In cases when this separation is not valid, such as CMUTs used in continuous wave transmit-receive mode, pulse-echo mode with a nearby hard or soft wall or in a bounded space such as in a microfluidic channel, an efficient formulation based on the method of images is used. Some of these particular applications and the overall modeling approach have been validated through comparison with finite element analysis on specific examples including CMUTs with multiple electrodes. To further demonstrate the capability of the model for imaging applications, the two-way response of a partial dual-ring intravascular ultrasound array is simulated using a parallel computing cluster, where the output currents of individual array elements are calculated for given input pulse and compared with experimental results. With its versatility, the presented model can be a useful tool for rapid iterative CMUT-based system design and simulation for a broad range of ultrasonic applications.

A cMUT probe for ultrasound-guided focused ultrasound targeted therapy

Ultrasound-mediated targeted therapy represents a promising strategy in the arsenal of modern therapy. Capacitive micromachined ultrasonic transducer (cMUT) technology could overcome some difficulties encountered by traditional piezoelectric transducers. In this study, we report on the design, fabrication, and characterization of an ultrasound-guided focused ultrasound (USgFUS) cMUT probe dedicated to preclinical evaluation of targeted therapy (hyperthermia, thermosensitive liposomes activation, and sonoporation) at low frequency (1 MHz) with simultaneous ultrasonic imaging and guidance (15 to 20 MHz). The probe embeds two types of cMUT arrays to perform the modalities of targeted therapy and imaging respectively. The wafer-bonding process flow employed for the manufacturing of the cMUTs is reported. One of its main features is the possibility of implementing two different gap heights on the same wafer. All the design and characterization steps of the devices are described and discussed, starting from the array design up to the first in vitro measurements: optical (microscopy) and electrical (impedance) measurements, arrays' electroacoustic responses, focused pressure field mapping (maximum peak-to-peak pressure = 2.5 MPa), and the first B-scan image of a wire-target phantom.

Automatic optimal input command for linearization of cMUT output by a temporal target

Capacitive micromachined ultrasonic transducers (cMUTs) are a promising alternative to the piezoelectric transducer. However, their native nonlinear behavior is a limitation for their use in medical ultrasound applications. Several methods based on the pre-compensation of a preselected input voltage have been proposed to cancel out the harmonic components generated. Unfortunately, these existing pre-compensation methods have two major flaws. The first is that the pre-compensation procedure is not generally automatic, and the second is that they can only reduce the second harmonic component. This can, therefore, limit their use for some imaging methods, which require a broader bandwidth, e.g., to receive the third harmonic component. In this study, we generalized the presetting methods to reduce all nonlinearities in the cMUT output. Our automatic pre-compensation method can work whatever the excitation waveform. The precompensation method is based on the nonlinear modeling of harmonic components from a Volterra decomposition in which the parameters are evaluated by using a Nelder-Mead algorithm. To validate the feasibility of this approach, the method was applied to an element of a linear array with several types of excitation often encountered in encoded ultrasound imaging. The results showed that the nonlinear components were reduced by up to 21.2 dB.

Evaluation of bias voltage modulation sequence for nonlinear contrast agent imaging using a capacitive micromachined ultrasonic transducer array

Many clinical diagnoses have now been improved thanks to the development of new techniques dedicated to contrast agent nonlinear imaging. Over the past few years, Capacitive Micromachined Ultrasonic Transducers (cMUTs) have emerged as a promising alternative to traditional piezoelectric transducers. One notable advantage of cMUTs is their wide frequency bandwidth. However, their use in nonlinear imaging approaches such as those used to detect contrast agents have been challenging due their intrinsic nonlinear character. We propose a new contrast imaging sequence, called bias voltage modulation (BVM), specifically developed for cMUTs to suppress their inherent nonlinear behavior. Theoretical and experimental results show that a complete cancellation of the nonlinear signal from the source can be reached when the BVM sequence is implemented. In-vitro validation of the sequence is performed using a cMUT probe connected to an open scanner and a flow phantom setup containing SonoVue microbubbles. Compared to the standard amplitude modulation imaging mode, a 6 dB increase of contrast-to-tissue ratio was achieved when the BVM sequence is applied. These results reveal that the problem of cMUT nonlinearity can be addressed, thus expanding the potential of this new transducer technology for nonlinear contrast agent detection and imaging.

A large-signal model for CMUT arrays with arbitrary membrane geometry operating in non-collapsed mode

A large-signal, transient model has been developed to predict the output characteristics of a CMUT array operated in the non-collapse mode. The model is based on separation of the nonlinear electrostatic voltage-to-force relation and the linear acoustic array response. For modeling of linear acoustic radiation and crosstalk effects, the boundary element method is used. The stiffness matrix in the vibroacoustics calculations is obtained using static finite element analysis of a single membrane which can have arbitrary geometry and boundary conditions. A lumped modeling approach is used to reduce the order of the system for modeling the transient nonlinear electrostatic actuation. To accurately capture the dynamics of the non-uniform electrostatic force distribution over the CMUT electrode during large deflections, the membrane electrode is divided into patches shaped to match higher order membrane modes, each introducing a variable to the system model. This reduced order nonlinear lumped model is solved in the time domain using commercial software. The model has two linear blocks to calculate the displacement profile of the electrode patches and the output pressure for a given force distribution over the array. The force-to-array-displacement block uses the linear acoustic model, and the Rayleigh integral is evaluated to calculate the pressure at any field point. Using the model, the time-domain transmitted pressure can be simulated for different large drive signal configurations. The acoustic model is verified by comparison to harmonic FEA in vacuum and fluid for high- and low-aspect-ratio membranes as well as mass-loaded membranes. The overall software model is verified by comparison to transient 3-D finite element analysis and experimental results for different large drive signals, and an example for a phased array simulation is given.