International audienceA wide range of ultrasound methods has been proposed to assess the mechanical strength of bone. Axial transmission technique, which consists of measuring guided elastic modes through the cortical shell of long bones such as the radius and the tibia, has recently emerged as one of the most promising approaches of all bone exploration methods. Determination of dispersion curves of guided waves is therefore of prime interest as they provide a large set of input data required to perform inverse process, and hence to evaluate bone properties (elastic and geometric). The cortical thickness of long bones ranges from approximately 1 to 7 mm, resulting in wide inter-individual variability in the guided wave response. This variability can be overcome by using a single probe able to operate with a tunable central frequency typically, within the 100 kHz – 2 MHz frequency range. However, there are certain limitations in the design of low frequency arrays using traditional PZT technology, and these limitations have triggered active research to find alternative solutions. Capacitive Micromachined Ultrasonic Transducers (cMUTs) present the potential to overcome these limitations and to improve axial transmission measurement significantly. The aim of the study presented here was to design and construct a new cMUT-based axial transmission probe and to validate the approach. We report all the steps followed to construct such a prototype, from the description of the fabrication of the cMUT (based on a surface micromachining process) through to probe packaging. The fabricated device was carefully characterized using both electrical and optical measurements in order to check the homogeneity of the device first from cMUT to cMUT and then from element to element. Finally, axial transmission measurements carried out with the prototype cMUT probe are shown and compared to results obtained with a counterpart PZT-based array
We report a fast time-domain model of fluid-coupled cMUTs developed to predict the transient response-i.e., the impulse pressure response--of an element of a linear 1-D array. Mechanical equations of the cMUT diaphragm are solved with 2-D finite-difference schemes. The time-domain solving method is a fourth--order Runge-Kutta algorithm. The model takes into account the electrostatic nonlinearity and the contact with the bottom electrode when the membrane is collapsed. Mutual acoustic coupling between cells is introduced through the numerical implementation of analytical solutions of the impulse diffraction theory established in the case of acoustic sources with rectangular geometry. Processing times are very short: they vary from a few minutes for a single cell to a maximum of 30 min for one element of an array. After a description of the model, the impact of the nonlinearity and the pull-in/pull-out phenomena on the dynamic behavior of the cMUT diaphragm is discussed. Experimental results of mechanical displacements obtained by interferometric measurements and the acoustic pressure field are compared with simulations. Different excitation signals-high-frequency bandwidth pulses and toneburst excitations of varying central frequency-were chosen to compare theory with experimental results.
Design and modeling are key steps in the value chain of Capacitive Micromachined Ultrasonic Transducer (CMUT) arrays. Although CMUT array element models are very powerful, most of them are still limited in their use as tools for electronic design assistance. The electroacoustic equivalent circuits developed are mainly based on a distributed-element approach while lumped-parameter electrical circuits are better suited for electronic software design tools interoperations. To meet this need, the present study aims to implement an electroacoustic equivalent scheme of a full array element, based on a two-port network representation made of lumped-parameters. After an extensive bibliographical review of CMUT models, the new model is set-up from a fully distributed approach using Foldy's electroacoustic definitions at the element level. Transmit and receive modes are implemented using scalar equations given by the lumped parameters. Moreover, based on a reciprocity analysis, the performance of the complete measurement chain in emission and reception will be defined using the relevant transfer functions. Finally, to help one design CMUT array elements for a given application, a method based on the computation of membranes thickness-size master curves is proposed. The two-port network representation of a full CMUT-based array element allowed by the new lumped-parameter modeling opens a wide range of possibilities regarding array design, electronic integration, operations with acoustic propagation simulation tools and more.
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