Simulation of circular array ultrasound transducers for intravascular applications

The beam shape of a circular array transducer that is commonly used in intravascular ultrasound catheters was investigated in linear mode of operation. For this use, a simulation program which can simulate the radio frequency (rf)-response of a number of scatterers has been developed. The program is based on the impulse response method, which is implemented in the frequency domain. Due to the unusual geometry of the transducer, the far field gets peculiarly shaped for large apertures. Instead of having a far field with its maximum intensity in a single lobe on the acoustical axis, the far field splits up into a dual-lobe far field with maximum intensity in two lobes off the acoustical axis. A formula is derived that predicts the occurrence of these beam shapes.     

Laser array beam propagation through liver tissue

Laser array beam propagating through mouse liver tissue is investigated. The turbulence power spectrum of the liver tissue is employed in the extended Huygens–Fresnel method to obtain an optical intensity profile and beam broadening at the observation point in biological liver tissue. Variations of the beam profile and the beam broadening are simulated based on the number of beamlets, source size, wavelength and the ring radius of the array. A biological tissue, illuminated by the laser array beam, exhibits different beam profiles and beam spot radius variations when the number of beamlets, source size, wavelength and the ring radius of the laser array beam are varied. Examining these variations observed in the propagated optical beam and comparing them with the test cases, abnormalities such as cancer and tumor in a biological liver tissue can be diagnosed.     

Modeling nonlinear ultrasound propagation in heterogeneous media with power law absorption using a k-space pseudospectral method

The simulation of nonlinear ultrasound propagation through tissue realistic media has a wide range of practical applications. However, this is a computationally difficult problem due to the large size of the computational domain compared to the acoustic wavelength. Here, the k-space pseudospectral method is used to reduce the number of grid points required per wavelength for accurate simulations. The model is based on coupled first-order acoustic equations valid for nonlinear wave propagation in heterogeneous media with power law absorption. These are derived from the equations of fluid mechanics and include a pressure-density relation that incorporates the effects of nonlinearity, power law absorption, and medium heterogeneities. The additional terms accounting for convective nonlinearity and power law absorption are expressed as spatial gradients making them efficient to numerically encode. The governing equations are then discretized using a k-space pseudospectral technique in which the spatial gradients are computed using the Fourier-collocation method. This increases the accuracy of the gradient calculation and thus relaxes the requirement for dense computational grids compared to conventional finite difference methods. The accuracy and utility of the developed model is demonstrated via several numerical experiments, including the 3D simulation of the beam pattern from a clinical ultrasound probe.     

Numerical approaches to simulating nonlinear ultrasound fields generated by diagnostic-type transducers

Two theoretical approaches for simulating nonlinear focused ultrasound fields generated by a diagnostic convex array are compared. The first model is based on the three-dimensional Westervelt equation and describes the full structure of the array field with high accuracy. However, it requires great computational resources and is technically difficult. The second model is based on an axially symmetric form of the parabolic KZK equation for estimating the strength of nonlinear effects in the focal region of a beam, which reduces the computational time by a factor of several hundreds. To establish the boundary conditions to the KZK model, the radius and the focal length of a circular piston source are defined such that the simulated field on the beam axis in the linear case fits the real structure of the field in the focal region. It is shown that the parabolic model can be used to accurately describe the spatial and temporal structure of the field generated by a diagnostic transducer in the focal region of the beam along its axis and in the plane of the beam’s electronic focusing.     

Increased heating by diagnostic ultrasound due to nonlinear propagation

The heating of tissues by the absorption of ultrasound is an important safety consideration in the use of diagnostic ultrasound. This paper shows that models of ultrasonic heating for this situation need to take account of nonlinear propagation. Measurements were made of the temperature rise in a sample of tissue-mimicking gel, caused by the application of 3.6-MHz focused ultrasonic beams for 3 min. The propagation path to the focus was in water, to mimic the situation where the fetus is scanned through the full bladder. The effect of nonlinear propagation was seen by changing the pressure amplitude of the pulse, while altering the pulsing regime to preserve a constant spatial-peak temporal-average intensity of 1 W cm-2. When nonlinear distortion was present, an enhancement in the temperature rise was observed, which correlated with the value of the shock parameter. The enhancement ratio was typically up to a factor of 3, and the maximum temperature rise observed was 2 degrees C. This enhanced heating was seen both at the surface of the tissue-mimicking gel and after propagation through 23 mm of the material. Under conditions of nonlinear propagation, the maximum heating usually occurs in the prefocal region, rather than at the focus.     

Modeling the propagation of nonlinear three-dimensional acoustic beams in inhomogeneous media

A three-dimensional model of the forward propagation of nonlinear sound beams in inhomogeneous media, a generalized Khokhlov-Zabolotskaya-Kuznetsov equation, is described. The Texas time-domain code (which accounts for paraxial diffraction, nonlinearity, thermoviscous absorption, and absorption and dispersion associated with multiple relaxation processes) was extended to solve for the propagation of nonlinear beams for the case where all medium properties vary in space. The code was validated with measurements of the nonlinear acoustic field generated by a phased array transducer operating at 2.5 MHz in water. A nonuniform layer of gel was employed to create an inhomogeneous medium. There was good agreement between the code and measurements in capturing the shift in the pressure distribution of both the fundamental and second harmonic due to the gel layer. The results indicate that the numerical tool described here is appropriate for propagation of nonlinear sound beams through weakly inhomogeneous media.     

Modeling of interaction between therapeutic ultrasound propagation and cavitation bubbles

In medical applications of high intense focused ultrasound the mechanism of interaction between ultrasound waves and cavitation bubbles is responsible for several therapeutic effects as well as for undesired side effects. Based on a two-phase continuum approach for bubbly liquids, in this paper a numerical model is presented to simulate these interactions. The numerical results demonstrate the influence of the cavitation bubble cloud on ultrasound propagation. In the case of a lithotripter pulse an increased bubble density leads to significant changes in the tensile part of the pressure waveform. The calculations are verified by measurements with a fiber optical hydrophone and by experimental results of the bubble cloud dynamics.     

A single-pole model for the propagation of ultrasound in soft tissue

A minimum-phase function, which characterizes the velocity dispersion in tissue was calculated from measured attenuation. This function was incorporated into a causal tissue model. Predictions of attenuation using the minimum-phase function with just a single pole matched measured attenuation in the 1- to 10-MHz range within a few percent. Dispersion of phase velocity predicted by the single-pole model was comparable to measured dispersion. The frequency associated with the single pole, which is a relaxation frequency, decreased with hemoglobin concentration and collagen content but increased with temperature. The electrical equivalent circuit for this model is a delay coupled with a low-pass filter which can be configured as a resistance in series with a parallel combination of resistance and capacitance.     

超声内镜换能器的应用进展

超声内镜集结了超声检查与内镜检查双重功能,可以获得腹部和胸腔内器官的高质量图像,是一种先进的医疗设备。超声内镜探头的核心部分是超声换能器。超声内镜检查需经过狭窄的消化道或内窥镜的活检通道伸进体内,由于工作环境的限制,超声内镜用换能器与普通超声成像换能器相比,工作频率更高、尺寸更小、制作工艺更精密。本文从超声内镜所用换能器的外形结构、内部组成、工作模式及材料等角度,对目前国内外超声内镜换能器的应用进展情况进行了描述,并根据超声内镜换能器的现状对未来的发展趋势进行了分析。     

Reflector-based phase calibration of ultrasound transducers

Recently, the measurement of phase transfer functions (PTFs) of piezoelectric transducers has received more attention. These PTFs are useful for e.g. coding and interference based imaging methods, and ultrasound contrast microbubble research. Several optical and acoustic methods to measure a transducer’s PTF have been reported in literature. The optical methods require a setup to which not all ultrasound laboratories have access to. The acoustic methods require accurate distance and acoustic wave speed measurements. A small error in these leads to a large error in phase, e.g. an accuracy of 0.1% on an axial distance of 10 cm leads to an uncertainty in the PTF measurement of ±97° at 4 MHz. In this paper we present an acoustic pulse-echo method to measure the PTF of a transducer, which is based on linear wave propagation and only requires an estimate of the wave travel distance and the acoustic wave speed. In our method the transducer is excited by a monofrequency sine burst with a rectangular envelope. The transducer initially vibrates at resonance (transient regime) prior to the forcing frequency response (steady state regime). The PTF value of the system is the difference between the phases deduced from the transient and the steady state regimes. Good agreement, to within 7°, was obtained between KLM simulations and measurements on two transducers in a 1-8 MHz frequency range. The reproducibility of the method was ±10°, with a systematic error of 2° at 1 MHz increasing to 16° at 8 MHz. This work demonstrates that the PTF of a transducer can be measured in a simple laboratory setting.     

A unified treatment of nonclassical nonlinear effects in the propagation of ultrasound in heterogeneous media

Recent experiments on rocks and other materials, such as soil, cement, concrete and damaged elastic materials, have led to the discovery of nonlinear (NL) hysteretic effects in their elastic behaviour. These observations suggest the existence of a NL mesoscopic elasticity universality class, to which all the aforementioned materials belong. The purpose of the present contribution is to search for the basic mathematical roots for nonclassical nonlinearity, in order to explain its universality, classify it and correlate it with the underlying meso- or microscopic interaction mechanisms. In our discussions we explicitly consider two quite different kinds of specimens: a two-bonded-elements structure and a thin multigrained bar. It is remarkable that, although the former includes only one interface and the latter very many interstices, the same "interaction box" formalism can be applied to both. Another important result of the proposed formalism is that the spectral contents of an arbitrary system for any input amplitude may be predicted, under certain assumptions, from the result of a single experiment at a higher amplitude.     

Influence of the abdominal wall on the nonlinear propagation of focused therapeutic ultrasound

This article theoretically studies the influence of inhomogeneous abdominal walls on focused therapeutic ultrasound based on the phase screen model. An inhomogeneous tissue is considered as a combination of a homogeneous medium and a phase aberration screen. Variations of acoustic parameters such as peak positive pressure, peak negative pressure, and acoustic intensity are discussed with respect to the phase screen statistics of human abdominal walls. Results indicate that the abdominal wall can result in energy loss of the sound in the focal plane. For a typical human abdominal wall with correlation length of 7.9~mm and variance of 0.36, the peak acoustic intensity radiated from a 1~MHz transmitter with a radius of 30~mm can be reduced by about 14% at the focal plane.     

Acoustic impedance matching of medical ultrasound transducers

Ultrasonic transducers for pulse-echo systems are studied both theoretically and experimentally. For the theoretical calculations the Mason model for thickness-mode disc transducers with and without backing and matching layers is used. By building several of the theoretically investigated transducer configurations it is shown that theory and experiment agree well. Thus the properties of a transducer can be predicted to a good approximation before its experimental realization. To find transducers with good sensitivity and short pulses, the pulse shape and frequency response for the following classes of transducers were studied both theoretically and experimentally: transducers with backing only, transducers with heavy backing and front matching layers, and air-backed transducers with front matching layers.     

Micromachined ultrasound transducers with improved coupling factors from a CMOS compatible process

For medical high frequency acoustic imaging purposes the reduction in size of a single transducer element for one-dimensional and even more for two-dimensional arrays is more and more limited by fabrication and cabling technology. In the fields of industrial distance measurement and simple object recognition low cost phased arrays are lacking. Both problems can be solved with micromachined ultrasound transducers (MUTs). A single transducer is made of a large number of microscopic elements. Because of the array structure of these transducers, groups of elements can be built up and used as a phased array. By integrating parts of the sensor electronics on chip, the cabling effort for arrays can be reduced markedly. In contrast to standard ultrasonic technology, which is based on massive thickness resonators, vibrating membranes are the radiating elements of the MUTs. New micromachining technologies have emerged, allowing a highly reproducible fabrication of electrostatically driven membranes with gap heights below 500 nm. A microelectronic BiCMOS process was extended for surface micromechanics (T. Scheiter et al., Proceedings 11th European Conference on Solid-State Transducers, Warsaw, Vol. 3, 1997, pp. 1595-1598). Additional process steps were included for the realization of the membranes which form sealed cavities with the underlying substrate. Membrane and substrate are the opposite electrodes of a capacitive transducer. The transducers can be integrated monolithically on one chip together with the driving, preamplifying and multiplexing circuitry, thus reducing parasitic capacities and noise level significantly. Owing to their low mass the transducers are very well matched to fluid loads, resulting in a very high bandwidth of 50-100% (C. Eccardt et al., Proceedings Ultrasonics Symposium, San Antonio, Vol. 2, 1996, pp. 959-962; P.C. Eccardt et al., Proceedings of the 1997 Ultrasonics Symposium, Toronto, Vol. 2, 1997, pp. 1609-1618). In the following it is shown how the BiCMOS process has been modified to meet the demands for ultrasound generation and reception. Bias and driving voltages have been reduced down to the 10 V range. The electromechanical coupling is now almost comparable with that for piezoelectric transducers. The measurements exhibit sound pressures and bandwidths that are at least comparable with those of conventional piezoelectric transducer arrays.     

Estimation of interference of piezoelectric ceramic transducers in a hydroacoustic array

A method for experimental estimation of intrinsic and mutual impedances of transducers in a shipborne multielement hydroacoustic array is proposed and investigated. It is shown that consideration of the transducer interactions increases the radiated power and suppresses the lateral field.     

Modeling of functionally graded piezoelectric ultrasonic transducers

The application of functionally graded material (FGM) concept to piezoelectric transducers allows the design of composite transducers without interfaces, due to the continuous change of property values. Thus, large improvements can be achieved, as reduction of stress concentration, increasing of bonding strength, and bandwidth. This work proposes to design and to model FGM piezoelectric transducers and to compare their performance with non-FGM ones. Analytical and finite element (FE) modeling of FGM piezoelectric transducers radiating a plane pressure wave in fluid medium are developed and their results are compared. The ANSYS software is used for the FE modeling. The analytical model is based on FGM-equivalent acoustic transmission-line model, which is implemented using MATLAB software. Two cases are considered: (i) the transducer emits a pressure wave in water and it is composed of a graded piezoceramic disk, and backing and matching layers made of homogeneous materials; (ii) the transducer has no backing and matching layer; in this case, no external load is simulated. Time and frequency pressure responses are obtained through a transient analysis. The material properties are graded along thickness direction. Linear and exponential gradation functions are implemented to illustrate the influence of gradation on the transducer pressure response, electrical impedance, and resonance frequencies.     

The characterization of an ultrasound spherical phased array for the ablation of deep-seated tissue

In this paper we have developed and evaluated a spherical phased array ultrasound applicator for deep tissue ablation. The 90-element prototype array has a 21 cm aperture and an 18 cm radius of curvature with a 5 cm wide central hole. Annular distribution with circular elements is used to reduce the number of elements. The array is constructed with piezoelectric (PZT-8) circular planar elements that are 1.4 cm in diameter and 0.2-cm thick. With the water-muscle propagation path, the array offers an effective beam focusing depth of at least 8 cm in the muscle layer. Simulation results show that the array provides good beam focusing and steering capability over a cylindrical volume of approximately π × 1 × 1 × 4 cm³ (up to 10 mm off center over ranges from 15 cm to 19 cm). We also present its beam focusing and steering capability in deep tissue through a series of ex vivo experiments by measuring discoloration areas after sonications. The ex vivo experiments show a similar focal range as that found in the simulations.