随机相控高强度聚焦超声换能器的栅瓣抑制

采用3种随机排列策略形成相控阵元线性排列结构抑制高强度聚焦超声(HIFU)相控阵栅瓣。第1种和第2种策略中阵元基于规则排列随机移动,而第3种策略中阵元则直接进行随机移动,阵元可移动范围依次为:第1种<第2种<第3种。采用瑞利积分和非线性Westervelt方程分别计算了3种策略对应随机相控阵产生的线性和非线性声场,并通过归一化栅瓣最大声压、归一化栅瓣平均声强和归一化旁瓣平均声强3个参量,对栅瓣抑制效果进行评价。结果表明:线性声场中,阵元可移动范围的增加有利于栅瓣抑制,3种随机策略的归一化栅瓣最大声压相比规则排列分别降低30.7%,53.8%和55.8%;非线性声场中对于同一种随机排列策略,随机度的增加可以改善栅瓣抑制效果。例如,第3种随机策略在随机度为0.9时正负压的归一化栅瓣最大声压相比规则排列分别降低55.6%和54.8%。进一步讨论了焦点偏移时随机相控阵的非线性声场,以-8 dB作为栅瓣的安全标准,第2种和第3种随机策略可以满足要求,横向偏移分别为6 mm和10 mm。本文的工作为抑制栅瓣提供了新思路,有利于随机HIFU相控阵的设计优化。     

Analytical method for evaluating the quality of acoustic fields radiated by a multielement therapeutic array with electronic focus steering

The paper presents an analytical method for calculating and analyzing the quality of 3-D acoustic fields of multielement phased arrays used in noninvasive ultrasound surgical devices. An analytical solution for the far field of each of its elements is used when calculating the array field. This method significantly accelerates calculations while preserving the high accuracy of results as compared to conventional direct numerical integration. Radiation from typical phased arrays is calculated using this approach, and the quality of their dynamic focusing is analyzed. Undesired diffraction effects caused by electronic focus steering are considered: an amplitude decrease in the main maximum and the appearance of grating lobes. The quality of dynamic focusing of the acoustic fields of two practically interesting arrays with a quasi-random element distribution (256 and 1024 elements, respectively), as well as of the regular array consisting of 256 elements is compared. In addition as well, a study is made of how the dimensions of the array elements and their spatial distributions affect the dimensions of the areas in which dynamic focusing is possible without occurrence of strong grating lobes and significant decrease in pressure amplitude at the main focus.

     

Characterization of high intensity focused ultrasound transducers using acoustic streaming

A new approach for characterizing high intensity focused ultrasound (HIFU) transducers is presented. The technique is based upon the acoustic streaming field generated by absorption of the HIFU beam in a liquid medium. The streaming field is quantified using digital particle image velocimetry, and a numerical algorithm is employed to compute the acoustic intensity field giving rise to the observed streaming field. The method as presented here is applicable to moderate intensity regimes, above the intensities which may be damaging to conventional hydrophones, but below the levels where nonlinear propagation effects are appreciable. Intensity fields and acoustic powers predicted using the streaming method were found to agree within 10% with measurements obtained using hydrophones and radiation force balances. Besides acoustic intensity fields, the streaming technique may be used to determine other important HIFU parameters, such as beam tilt angle or absorption of the propagation medium.     

Two-dimensional phased arrays for surgery: Movement of a single focus

Numerical simulation and comparative analysis of acoustic fields generated by two-dimensional phased arrays designed for ultrasonic surgery is conducted. The case of movement of a single focus by an array with the surface shaped as a part of a spherical shell with the curvature radius 120 mm is considered. The influence of the number of elements (varying from 64 to 1024), their diameter (from 2.5 to 10 mm), frequency (from 1 to 2 MHz), and the degree of sparseness of the elements at the array surface on the field characteristics is studied. The calculations are performed for arrays with elements positioned at the surface both regularly (in square, annular, or hexagonal patterns) and randomly. Criteria for the evaluation of the “quality” of intensity distributions in the field generated by an array in the case of movement of a single focus are suggested. Of all arrays studied, the best quality of distributions is obtained for an array containing 256 elements of diameter 5 mm randomly positioned at the array surface. The quality of the intensity distributions for arrays consisting of 255, 256, and 1024 elements positioned regularly (in square, annular, and hexagonal patterns) is inferior to the corresponding quality for arrays with randomly positioned elements. The irregularity in elements’ positioning considerably improves the distribution quality by suppressing the secondary intensity peaks in the field generated by the array; or, alternatively, it provides an opportunity to obtain the same distribution quality with a fraction of the number of elements in the array. The effects of the number and shape of elements, errors in phase setting, frequency modulation of signals, and non-uniform distribution of amplitudes over the array surface on the distribution quality are analyzed.     

A derating method for therapeutic applications of high intensity focused ultrasound

Current methods of determining high intensity focused ultrasound (HIFU) fields in tissue rely on extrapolation of measurements in water assuming linear wave propagation both in water and in tissue. Neglecting nonlinear propagation effects in the derating process can result in significant errors. A new method based on scaling the source amplitude is introduced to estimate focal parameters of nonlinear HIFU fields in tissue. Focal values of acoustic field parameters in absorptive tissue are obtained from a numerical solution to a KZK-type equation and are compared to those simulated for propagation in water. Focal wave-forms, peak pressures, and intensities are calculated over a wide range of source outputs and linear focusing gains. Our modeling indicates, that for the high gain sources which are typically used in therapeutic medical applications, the focal field parameters derated with our method agree well with numerical simulation in tissue. The feasibility of the derating method is demonstrated experimentally in excised bovine liver tissue.     

Nonlinear absorption in biological tissue for high intensity focused ultrasound

In recent years the propagation of the high intensity focused ultrasound (HIFU) in biological tissue is an interesting area due to its potential applications in non-invasive treatment of disease. The base principle of these applications is the heat effect generated by ultrasound absorption. In order to control therapeutic efficiency, it is important to evaluate the heat generation in biological tissue irradiated by ultrasound. In his paper, based on the Khokhlov-Zabolotkaya-Kuznetsov (KZK) equation in frequency-domain, the numerical simulations of nonlinear absorption in biological tissues for high intensity focused ultrasound are performed. We find that ultrasound thermal transfer effect will be enhanced with the increasing of initial acoustic intensity due to the high harmonic generation. The concept of extra absorption factor is introduced to describe nonlinear absorption in biological tissue for HIFU. The theoretical results show that the heat deposition induced by the nonlinear theory can be nearly two times as large as that predicated by linear theory. Then, the influence of the diffraction effect on the position of the focus in HIFU is investigated. It is shown that the sound focus moves toward the transducer compared with the geometry focus because of the diffraction of the sound wave. The position of the maximum heat deposition is shifted to the geometry focus with the increase of initial acoustic intensity because the high harmonics are less diffraction. Finally, the temperature in the porcine fat tissue changing with the time is predicated by Pennes' equation and the experimental results verify the nonlinear theoretical prediction.     

Physical mechanisms of the therapeutic effect of ultrasound (a review)

Therapeutic ultrasound is an emerging field with many medical applications. High intensity focused ultrasound (HIFU) provides the ability to localize the deposition of acoustic energy within the body, which can cause tissue necrosis and hemostasis. Similarly, shock waves from a lithotripter penetrate the body to comminute kidney stones, and transcutaneous ultrasound enhances the transport of chemotherapy agents. New medical applications have required advances in transducer design and advances in numerical and experimental studies of the interaction of sound with biological tissues and fluids. The primary physical mechanism in HIFU is the conversion of acoustic energy into heat, which is often enhanced by nonlinear acoustic propagation and nonlinear scattering from bubbles. Other mechanical effects from ultrasound appear to stimulate an immune response, and bubble dynamics play an important role in lithotripsy and ultrasound-enhanced drug delivery. A dramatic shift to understand and exploit these nonlinear and mechanical mechanisms has occurred over the last few years. Specific challenges remain, such as treatment protocol planning and real-time treatment monitoring. An improved understanding of the physical mechanisms is essential to meet these challenges and to further advance therapeutic ultrasound.     

Diffraction of high-intensity field in focal region as dynamics of nonlinear system with low-frequency dispersion

The stationary profile in the focal region of a focused nonlinear acoustic wave is described. Three models following from the Khokhlov-Zabolotskaya (KZ) equation with three independent variables are used: (i) the simplified one-dimensional Ostrovsky-Vakhnenko equation, (ii) the system of equations for paraxial series expansion of the acoustic field in powers of transverse coordinates, and (iii) the KZ equation reduced to two independent variables. The structure of the last equation is analogous to the Westervelt equation. Linearization through the Legendre transformation and reduction to the well-studied Euler-Tricomi equation is shown. At high intensities the stationary profiles are periodic sequences of arc sections having singularities of derivative in their matching points. The occurrence of arc profiles was pointed out by Makov. These appear in different nonlinear systems with low-frequency dispersion. Profiles containing discontinuities (shock fronts) change their form while passing through the focal region and are non-stationary waves. The numerical estimations of maximum pressure and intensity in the focus agree with computer calculations and experimental measurements.

     

Mechanisms for saturation of nonlinear pulsed and periodic signals in focused acoustic beams

Acoustic fields of powerful ultrasound sources with Gaussian spatial apodization and initial excitation in the form of a periodic wave or single pulse are examined based on the numerical solution of the Khokhlov-Zabolotskaya-Kuznetsov equation. The influence of nonlinear effects on the spatial structure of focused beams, as well as on the limiting values of the acoustic field parameters is compared. It is demonstrated that pressure saturation in periodic fields is mainly due to the effect of nonlinear absorption at a shock front, while in pulsed fields is due to the effect of nonlinear refraction. The limiting attainable values for the peak positive pressure in periodic fields turned out to be higher than the analogous values in pulsed acoustic fields. The total energy in a beam of periodic waves decreases with the distance from the source faster than in the case of a pulsed field, but it becomes concentrated within much smaller spatial region in the vicinity of the focus. These special features of nonlinear effect manifestation provide an opportunity to use pulsed beams for more efficient delivery of wave energy to the focus and to use periodic beams for attaining higher values of pressure in the focal region.     

时间反转方法用于高强度聚焦超声的焦点偏移补偿

传统的高强度聚焦超声(HIFU)治疗中实际焦点和预设焦点容易出现偏移,为考察时间反转方法对HIFU治疗中焦点偏移的补偿效果,采用时域有限差分方法求解Westervelt方程,建立高强度聚焦声场数值模型。数值计算得到在人体软组织中进行HIFU治疗时,采用时间反转方法后焦点偏移距离最大仅为1.6 mm。脂肪层厚度及声源强度改变对时间反转聚焦精度影响不大,F数(焦点距离同换能器孔径的比值)降低时,焦点偏移减小。研究表明在人体软组织吸收系数和非线性系数范围内,时间反转方法可有效补偿焦点偏移,达到更好的聚焦效果。     

A novel method for estimating the focal size of two confocal high-intensity focused ultrasound transducers

Estimating the focal size and position of a high-intensity focused ultrasound (HIFU) transducer remains a challenge since traditional methods, such as hydrophone scanning or schlieren imaging, cannot tolerate high pressures, are directional, or provide low resolution. The difficulties increase when dealing with the complex beam pattern of a multielement HIFU transducer array, e.g., two transducers facing each other. In the present study we show a novel approach to the visualization of the HIFU focus by using shockwave-generated bubbles and a diagnostic B-mode scanner. Bubbles were generated and pushed by shock waves toward the HIFU beam, and were trapped in its pressure valleys. These trapped bubbles moved along the pressure valleys and thereby delineated the shape and size of the HIFU beam. The main and sidelobes of 1.1- and 3.5 MHz HIFU beams were clearly visible, and could be measured with a millimeter resolution. The combined foci could also be visualized by observing the generation of sustained inertial cavitation and enhanced scattering. The results of this study further demonstrate the possibility of reducing the inertial cavitation threshold by the local introduction of shock wave-generated bubbles, which might be useful when bubble generation and cavitation-related bioeffects are intended within a small region in vivo.     

高斯叠代法研究相控阵非线性声场

相控阵在聚焦超声治疗应用中不可避免地受到非线性影响,提出了采用高斯叠代法计算相控阵的非线性声场。在该方法中,利用预设焦点参数并应用伪逆矩阵算法得到阵元的激励参数;然后将阵元近似拟合成一组高斯声束的叠加,通过高斯声束叠代计算非线性声场。数值计算中以64阵元一维相控阵为研究对象;线性条件下,高斯叠代法结果与菲涅耳积分结果的误差低于0.5%,验证了该方法的可行性;单焦点及双焦点模式的相控阵非线性声场结果表明非线性效应能提高焦点聚焦性能,并且非线性效应与激励声压及激励频率成正比。     

Ultrasound phased arrays for prostate treatment.

The effect of array geometry on the steering performance of ultrasound phased arrays is examined theoretically, in order to maximize array performance under the given anatomical constraints. This paper evaluates the performance of arrays with spherical and cylindrical geometry, determined by using computer simulations of the pressure fields produced at various extremes of steering. The spherical segment arrays were truncated for insertion into the rectum, and contained either annular or linear elements. The cylindrical arrays were either flat or had a variable curvature applied along their length. Fields were computed by dividing the array elements into many point sources. The effectiveness of an array configuration when steered to a particular focal location was assessed by defining a parameter, G, as the ratio of the intensity at the desired focus to the maximum intensity of any unwanted lobes. The performance of truncated spherical arrays with annular elements was evaluated for focal steering along the array axis (in depth, in the z direction). When steered 15 mm toward the source, these truncated spherical annular arrays exhibited excellent performance, with G>5.7 for arrays containing more than 10 elements. Similarly, the spherical arrays with linear elements performed well when steered along the array axis to the same degree, with G>7 (for element widths up to 3 lambda), though many more array elements were required. However, when these arrays were steered 15 mm laterally, along the length of the prostate (the y direction), the value for G fell below 1 for element widths greater than about 1.6 lambda. It was found that the cylindrical arrays performed much better for y-direction steering (G>4, for 60 mm arrays with an element width of 1.75 lambda), but their performance was poorer when steered in the z direction (G approximately 4 for an element width of 1.5 lambda). In order to find a compromise between these extremes, a curved cylindrical array was examined, which was a cylindrical array with additional curvature along its length. These curved cylindrical arrays yielded performance between that of spherical linear arrays and cylindrical arrays, with better steering along the y direction than the spherical arrays and better z-direction steering than the cylindrical arrays.     

球形腔聚焦换能器的非线性声场建模

球形腔聚焦换能器是一种特殊形式的聚焦换能器。为理论证实球形腔聚焦换能器能突破传统超声聚焦在聚焦精度和聚焦增益上的限制,采用Westervelt非线性方程并结合时域有限差分法,建立了球形腔聚焦换能器的非线性声场的数值模型。数值计算了直径为120 mm的0.6 MHz球形腔聚焦换能器的非线性声场,并与传统球壳形聚焦换能器进行了对比。当激励声压为100 kPa时,球形腔聚焦换能器与同尺寸壳形聚焦换能器相比,焦点正声压增益提高约8.5倍,且焦域精度更高,-6 dB聚焦区域在z方向减小约20倍,达到次波长尺度。研究表明球形腔聚焦换能器在高强度聚焦超声精细治疗上具有潜在的应用前景。     

New Techniques and Designs of Focusing Piezoelectric Transducers for Ultrasonic Diagnostics and Therapy

New techniques of forming high intensity focused ultrasound (HIFU) fields using dynamic focusing and harmonic multifrequency excitation are developed for ultrasonic diagnostics and therapy. New designs of HIFU transducers based on high-performance composite materials are developed and studied. Finite-element and finite-difference simulations of HIFU transducers and processes of ultrasonic wave propagation in biological tissues are performed. The parameters of piezoceramic materials, piezoelements, and the acoustic fields of focusing ultrasonic transducers are measured. Experiments are performed on biological tissues ex vivo that confirm the efficiency, selectivity, and safety of the developed HIFU transducers and techniques of forming acoustic fields.     

Counterpropagation of waves with shock fronts in a nonlinear tissue-like medium

A numerical model for describing the counterpropagation of one-dimensional waves in a nonlinear medium with an arbitrary power law absorption and corresponding dispersion is developed. The model is based on general one-dimensional Navier-Stokes equations with absorption in the form of a time-domain convolution operator in the equation of state. The developed algorithm makes it possible to describe wave interactions in the presence of shock fronts in media like biological tissue. Numerical modeling is conducted by the finite difference method on a staggered grid; absorption and sound speed dispersion are taken into account using the causal memory function. The developed model is used for numerical calculations, which demonstrate the absorption and dispersion effects on nonlinear propagation of differently shaped pulses, as well as their reflection from impedance acoustic boundaries.     

Frequency down-conversion using cascading arrays of coupled nonlinear oscillators

A novel coupling scheme using M≥2 arrays of coupled nonlinear elements arranged in a specific configuration can produce multifrequency patterns or a frequency down-converting effect on an external (input) signal. In such a configuration, each array contains N≥3 nonlinear elements with similar dynamics and each element is coupled unidirectionally within the array. The subsequent arrays in the cascade are coupled in a similar fashion except that the coupling direction is arranged in the opposite direction with respect to that of the preceding array. Previous theoretical work and numerical results have already been reported in [P. Longhini, A. Palacios, V. In, J. Neff, A. Kho, A. Bulsara, Exploiting dynamical symmetry in coupled nonlinear elements for efficient frequency down-conversion, Phys. Rev. E 76 (2007) 026201]. This paper is focused on results of experiments implemented on two distinct systems: the first system is fabricated using discrete component circuits to approximate an overdamped bistable Duffing oscillator described by a quartic potential system, and the second system is built in a microcircuit, where the nonlinearity is described by a hyperbolic tangent function, with the option of applying an external signal to investigate resonant effects. In particular, the circuit implementations for each case use M=2 arrays, but their voltage oscillations already demonstrate that the frequency relations between each of the successive arrays decrease by a rational factor, conforming to earlier theoretical and numerical results for the general case containing M arrays. This behavior is important for efficient frequency down-converting applications which are essential in many communication systems where heterodyning is typically used and it involves multi-step processes with complicated circuitry.     

Two-dimensional phased arrays for surgical applications: Multiple focus generation and scanning

A numerical simulation and a comparative analysis of the acoustic fields produced by two-dimensional phased arrays intended for ultrasonic surgery are performed for the case of a multiple focus (in particular, 25 foci) generation. The calculations were conducted for arrays (with an operating frequency of 1.5 MHz) consisting of 256 elements 5 mm in diameter, which were positioned on the array surface both regularly and randomly. The array foci can be formed simultaneously, but, in this case, the intensity levels of the secondary peaks in the ultrasonic field can exceed the values that guarantee the safe application of this method in surgery. A much safer way is to synthesize many foci with the use of several configurations, each of which contains a smaller number of foci. The number of foci in individual configurations must be approximately the same. It is demonstrated that randomization of the element distribution over the array surface provides an opportunity to improve the array performance, to reduce the intensity levels of secondary peaks in the acoustic field, and to increase the array capability for multiple focus scanning off the array axis.     

Phased Array Beam Fields of Nonlinear Rayleigh Surface Waves

This study concerns calculation of phased array beam fields of the nonlinear Rayleigh surface waves based on the integral solutions for a nonparaxial wave equation.Since the parabolic approximation model for describing the nonlinear Rayleigh waves has certain limitations in modeling the sound beam fields of phased arrays,a more general model equation and integral forms of quasilinear solutions are introduced.Some features of steered and focused beam Gelds radiated from a linear phased array of the second harmonic Rayleigh wave are presented.