Finite-element analysis of capacitive micromachined ultrasonic transducers

In this paper, we present the results of finite-element analysis performed to investigate capacitive micromachined ultrasonic transducers (CMUTs). Both three-dimensional (3-D) and 2-D models were developed using a commercially available finite-element modeling (FEM) software. Depending on the dimensionality of the model, the membranes were constructed using plane or shell elements. The electrostatic gap was modeled using many parallel plate transducers. An axisymmetric model for a single membrane was built; the electrical input impedance of the device then was calculated in vacuum to investigate series and parallel resonant frequencies, where the input impedance has a minimum and a maximum, respectively. A method for decomposing the membrane capacitance into parasitic and active parts was demonstrated, and it was shown that the parallel resonant frequency shifted down with increased biased voltage. Calculations then were performed for immersion transducers. Acoustic wave propagation was simulated in the immersion medium, using appropriate elements in a 3-D model. Absorbing boundaries were implemented to avoid the reflections at the end of the medium mesh. One row of an array element, modeled with appropriate boundary conditions, was used to calculate the output pressure. The results were compared with a simpler model: a single membrane in immersion, with symmetry boundary conditions on the sidewalls that cause the calculations to reflect the properties of an infinitely large array. A 2-D model then was developed to demonstrate the effect of membrane dimensions on the output pressure and bandwidth. Our calculations revealed that the small signal transmit pressure was inversely proportional to the square root of gap height. We also compared FEM results with analytical and experimental results.     

Finite-element analysis of 1-3 composite transducers

The vibrational and electromechanical characteristics of a wide range of 1-3 composite structures, comprising ceramic pillars aligned within a polymer phase, are considered using finite-element analysis. The influence of pillar geometry, ceramic volume fraction, and pillar orientation is described in terms of overall transduction efficiency. It is shown that the finite-element method provides a versatile means of analysis and the results obtained permit a set of useful design guidelines to be developed. In general, a small pillar aspect ratio and a relatively high volume fraction provides the most satisfactory performance, in terms of electromechanical efficiency and uniformity of thickness dilation.     

Prediction of surface temperature rise of ultrasonic diagnostic array transducers

Temperature rise at the surface of an ultrasound transducer used for diagnostic imaging is an important factor in patient safety and regulatory compliance. This paper presents a semianalytical model that is derived from first principles of heat transfer and is simple enough to be implemented in a commercial ultrasound scanner for real-time forecasting of transducer surface temperature. For modeling purposes, one-dimensional array transducers radiating into still air are considered. Promising experimental verification data are shown and practical implementation benefits of the model for thermal design and management of ultrasonic array transducers are discussed. In particular, the reduction in the amount of thermal characterization data required, compared to empirical models, shows promise.     

High-frequency rapid B-mode ultrasound imaging for real-time monitoring of lesion formation and gas body activity during high-intensity focused ultrasound ablation

The goal of this study was to examine the ability of high-frame-rate, high-resolution imaging to monitor tissue necrosis and gas-body activities formed during high-intensity focused ultrasound (HIFU) application. Ex vivo porcine cardiac tissue specimens (n = 24) were treated with HIFU exposure (4.33 MHz, 77 to 130 Hz pulse repetition frequency (PRF), 25 to 50% duty cycle, 0.2 to 1 s, 2600 W/cm(2)). RF data from Bmode ultrasound imaging were obtained before, during, and after HIFU exposure at a frame rate ranging from 77 to 130 Hz using an ultrasound imaging system with a center frequency of 55 MHz. The time history of changes in the integrated backscatter (IBS), calibrated spectral parameters, and echo-decorrelation parameters of the RF data were assessed for lesion identification by comparison against gross sections. Temporal maximum IBS with +12 dB threshold achieved the best identification with a receiver-operating characteristic (ROC) curve area of 0.96. Frame-to-frame echo decorrelation identified and tracked transient gas-body activities. Macroscopic (millimetersized) cavities formed when the estimated initial expansion rate of gas bodies (rate of expansion in lateral-to-beam direction) crossed 0.8 mm/s. Together, these assessments provide a method for monitoring spatiotemporal evolution of lesion and gas-body activity and for predicting macroscopic cavity formation.     

Integrated catheter for 3-D intracardiac echocardiography and ultrasound ablation

A catheter device with integrated ultrasound imaging array and ultrasound ablation transducer is introduced. This device has been designed for use in interventional cardiac procedures in which the cardiac anatomy is first imaged using real-time three-dimensional (3-D) ultrasound, then ablated to treat arrhythmias. The imaging array includes 112 elements operating at 5.4 MHz arranged in a 2-D matrix. Individual elements have a bandwidth of 21% and an insertion loss of 80 dB. The array has an azimuth resolution of 12 degrees and an elevation resolution of 8.7 degrees. The ablation transducer is a concentric piezoelectric transducer PZT-4 ring (outside diameter (O.D.), 4.5 mm, inside diameter (I.D.), 3.1 mm) operating at 10 MHz that surrounds the imaging array. It can produce a spatial-peak, temporal-average intensity up to 16 W/cm2. The entire device fits into a 9 Fr lumen with a 14 Fr tip to accommodate the ablation ring. With this device we have imaged, in realtime 3-D, a variety of targets including wire phantoms, fixed sheep hearts, and fresh bovine tissue. The ablation ring has been used to heat tissue-mimicking rubber 14 degrees C, as well as create lesions in fresh bovine tissue.     

3-D ultrasound guidance of surgical robotics using catheter transducers: feasibility study

The goal of this study was to test the feasibility of using a real-time 3-D (RT3D) ultrasound scanner with matrix array catheter probes to guide a surgical robot. We tested the accuracy of using 3-D catheter transducers with the 3-D measurement software of the scanner to direct automatically a robot arm that touched two needle tips together within a water tank and inside a vascular graft. RMS measurement error ranged from 2.4 to 3.4 mm for two catheter designs.     

Finite-element simulation of transient heat response in ultrasonic transducers

The application of the finite-element method to a transient heat response problem in electrostrictive ultrasonic transducers during their pulsed operation is described. The temperature and thermal stress distribution are of practical importance for the design of the ultrasonic transducers when they are operated at intense levels. Mechanical vibratory loss is responsible for heat in the elastic parts, while dielectric loss is responsible in the ferroelectric parts. A finite-element computer model is proposed for the temperature change evaluation in the transducers with time. Natural and forced cooling convection and heat radiation from the transducers' boundaries are included. Simulation is made for Langevin-type transducer models, for which comparison is made with experimental data.     

Finite-element analysis of material and parameter effects in laser-based thermoelastic ultrasound generation

Laser-based, thermoelastic transduction methods have potential in very high frequency (>50 MHz), high-density two-dimensional (2-D) arrays for a variety of very high-resolution superficial imaging applications, including in vivo tissue sectioning. Previous studies of these transducers generally have been based on experimental measurements or theoretical analyses using various simplifying assumptions. These theoretical models are mostly 1-D and best matched to simple geometries with a minimum number of component materials. In this work, we use a new thermoelastic solver in a commercially available finite-element analysis (FEA) software package to analyze multidimensional effects in laser-based devices of arbitrary geometry with the potential for use with arbitrary material properties. The FEA approach was verified first against experimental data. Thereafter, we explored the impact of various design variables, including laser spot size and laser penetration depth.     

Soft tissue temperature rise caused by scanned, diagnostic ultrasound

An acoustic-thermal model was developed for scanned diagnostic ultrasound in soft tissue. An adiabatic surface between the transducer and the skin was justified, and the model accounted for attenuation and focusing. The temperature along the central plane of the temporally averaged acoustic field was calculated by integration of line sources of heat that result from the tissue's absorption of ultrasound. The temperature profiles were calculated for 1400 transducers. The results show that current diagnostic transducers heat more significantly at the transducer-tissue interface than at the focus. The temperature rise in the focal region is typically less than 25% of that at the surface. The acoustic power per scan length that results in a 1 degrees C temperature rise at the surface is calculated as (210 mW-MHz/cm)/f. These results apply to both linear arrays and sectorlike scan formats. The temperature rises for simultaneous multimode scanned beams are additive as the peak temperatures of each mode will occur on the surface. Consideration was given to the surface boundary condition for such models. This boundary is considered adiabatic for calculation of heating due to acoustic absorption alone. Additional heating or cooling resulting from the transducer can then be superimposed on this solution.     

Feasibility of noncontact intracardiac ultrasound ablation and imaging catheter for treatment of atrial fibrillation

Atrial fibrillation (AF) affects 1% of the population and results in a cost of 2.8 billion dollars from hospitalizations alone. Treatments that electrically isolate portions of the atria are clinically effective in curing AF. However, such minimally invasive catheter treatments face difficulties in mechanically positioning the catheter tip and visualizing the anatomy of the region. We propose a noncontact, intracardiac transducer that can ablate tissue and provide rudimentary imaging to guide therapy. Our design consists of a high-power, 20 mm by 2 mm, 128-element, transducer array placed on the side of 7-French catheter. The transducer will be used in imaging mode to locate the atrial wall; then, by focusing at that location, a lesion can be formed. Imaging of previously formed lesions could potentially guide placement of subsequent lesions. Successive rotations of the catheter will potentially enable a contiguous circular lesion to be created around the pulmonary vein. The challenge of intracardiac-sized transducers is achieving high intensities (300-5000 W/cm2) needed to raise the temperature of the tissue above 43 degrees C. In this paper, we demonstrate the feasibility of an intracardiac-sized transducer for treatment of atrial fibrillation. In simulations and proof-of-concept experiments, we show a 37 degrees C temperature rise in the lesion location and demonstrate the possibility of lesion imaging.     

Modeling and optimization of high-frequency ultrasound transducers

Obtaining an accurate transducer model for a high-frequency transducer can be troublesome using traditional models, such as the KLM model, since it is often difficult to measure precisely the piezoelectric, dielectric, and mechanical properties of the transducer. This paper describes an alternative method of modeling transducers using network theory. The network theory model for a transducer is determined from a measurement of the transducer impedance in water and the pulse-echo response of the system for a given electrical source and load. A discussion of how this model can be used to optimize the design of an electrical matching circuit is given. This method is illustrated by designing a two-element transmission line matching circuit for a miniature 53 MHz transducer. Excellent agreement between the network model prediction and the experimental response is obtained     

Design of focused ultrasound surgery transducers

High-intensity focused ultrasound surgery (FUS) has been developed for the extracorporeal treatment of various benign and malignant soft tissue tumors. The system developed at the Institute of Cancer Research/Royal Marsden (ICR/RM) National Health Service (NHS) Trust incorporates a 150 mm focal length focused bowl transducer operated at 1.7 MHz, and is currently undergoing Phase 1 clinical trials for the treatment of benign prostatic hyperplasia and superficial bladder cancer. However, the application of this transducer is limited by its focal length to a maximum depth of 100 mm, and by power absorption in the skin to a minimum depth of 40 mm. A computer model of acoustic fields, which assumes uniform excitation of the transducer over its entire surface, has previously been published. This has been used both to calculate the intensity in nonattenuating media, and to estimate the absorbed power per unit volume in homogeneous tissues in order to allow determination of the transducer configurations (frequency, focal length, and diameter) necessary for the treatment of both deep (~150 mm) and shallow (~20 mm) soft tissue tumors. These depths encompass the typical range for human tissues which are likely to be treated. Calculations cover the frequency range 0.5-4.5 MHz, focal lengths from 70 to 200 mm, and transducer diameters from 30 to 190 mm. The results show that appropriate transducers can be designed for the noninvasive treatment of tumors in specific organs     

Finite-element analysis of unsteady temperature fields in parts of gas turbine engines

A method is proposed for the numerical solution of a problem of unsteady heat conduction which arises in the analysis of the thermal strength of power-generating equipment. The method employs finite-element techniques. It is of secondorder accuracy and is absolutely stable. The method is compared with the traditional Euler, Galerkin, and Crank-Nicolson methods. It is shown that the new method is more advantageous for solving unsteady heat-conduction problems in which the boundary conditions change rapidly with time. Examples are presented to illustrate the high degree of accuracy and reliability of the method.Leningrad Polytechnic Institute. Translated from Problemy Prochnosti, No. 12, pp. 82–87, December, 1989.     

Theoretical study of steady-state temperature rise within the eye due to ultrasound insonation

The soft tissue thermal index (TIS), as defined in the AIUM/NEMA Output Display Standard, may not be relevant with respect to eye exposure, primarily because of differences in actual vs. assumed acoustic and thermal properties. Therefore, a theoretical study of temperature rise within the eye due to ultrasound insonation was undertaken to compare the TIS with more exact calculations. At each plane in the direction of propagation, the focused ultrasound beam was modeled as a disc of uniform intensity. Each disc becomes a heat source, and integration over all discs provides the total temperature rise at any axial position. Calculations were done assuming the ultrasound beam intersects the lens of the eye as well as for the case in which the beam does not intersect the lens. Results were found for frequencies of 7.0 MHZ to 40 MHZ, transducer diameters of 0.2 cm to 1.0 cm, and focal lengths ranging from 0.2 cm to 3.0 cm. Perfusion was assumed negligible and thermal and acoustic parameters were taken from reported studies. For every case, the ratio of maximum temperature rise to the TIS (assuming constant output power) was calculated. For the lens case, the ratio varied from 7.35 to 0.8. For the no-lens case, the ratio varied from 4.1 to 0.4. These results indicate that the TIS is not adequate to represent the temperature rise occurring within the eye upon insonation.     

A fast algorithm to calculate ultrasound pressure fields from single-element transducers

An algorithm for calculating the beam profile for a single-element circular transducer is reported here. It performs well in calculating the pressure everywhere in the field including the near field and points at large distances from the axis of the transducer. The algorithm is much faster than direct numerical methods currently in use. Lateral beam profiles computed using the fast algorithm are nearly identical to profiles computed using a 96-point Gaussian quadrature routine.     

Calculation of pressure fields from arbitrarily shaped, apodized, and excited ultrasound transducers

A method for simulation of pulsed pressure fields from arbitrarily shaped, apodized and excited ultrasound transducers is suggested. It relies on the Tupholme-Stepanishen method for calculating pulsed pressure fields, and can also handle the continuous wave and pulse-echo case. The field is calculated by dividing the surface into small rectangles and then Summing their response. A fast calculation is obtained by using the far-field approximation. Examples of the accuracy of the approach and actual calculation times are given.     

Modeling of received signals from annular array ultrasound transducers due to extended reflectors

This paper describes a computationally efficient numerical technique for calculating the received signal from a broadband annular array transducer operating in pulse-echo mode, due to a specified reflector. The technique is referred to as the Diffraction Response from Extended Area Method (DREAM) and operates by tessellating the reflector into planar tiles with a dimension of several wavelengths (at the highest frequency of interest) and finding the contribution from a given tile by a temporal low-pass filtering rather than spatial integration. In particular, this paper formulates the theory for the DREAM for tessellation into triangular tiles and demonstrates the improved performance with triangular tiles relative to square tiles. This paper also analyzes the mean square error of the received signal as a function of the diameters of the transmitting and the receiving transducers and the radial position and orientation of the tile. Based on this, a set of rules for the optimal tile size is developed. The power of the modeling technique is demonstrated by calculating the received signal from an annular array transducer due to three given extended reflectors in which the effect of the focal point location on the received signal is readily demonstrated.     

Finite-element analysis of a weld-penetration problem

The stress concentration factor for a weld penetration defect is calculated by the finite-element method. A stress intensity factor is computed by use of the finite-element solution and the J-integral. The results are compared with experimental results.