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.     

Simulation of the acoustic field emitted from medical linear transducer in a heterogeneous tissue

A numerical model is developed to simulate the acoustic field in heterogeneous tissue from a medical linear transducer.The coupled full-wave equation for nonlinear ultrasound is solved using a staggered-grid finite difference time domain method.The distribution of acoustic pressure and power in human abdominal wall with heterogeneities in sound speed,density,and nonlinear parameter are obtained.Compared with homogeneous medium,when sound speed in tissue is uniform and density unchanged,the acoustic energy decreases only1.8 dB in the focal region;when density in tissue is uniform and sound speed unchanged,the energy decreases 3.8 dB in the focal region,which is almost the same as heterogeneous tissue.Thus,the primary factor of the aberration of focused beam is the heterogeneous distribution of the tissue sound speed.     

聚焦区域高声强声场分布的测量方法研究

常用的声场分布测量是采用水听器扫描声场的方法,该方法对于声能量密度较大的声场难以测量,因为在这种情况下声振幅比较大,水听器在这种声场中呈现非线性或遭到破坏。设计了一种用辐射压力测量高声强声场分布的方法,该方法利用一根微细管,直接测量声场的冲流压力,通过对声场进行扫描测量可以得到高声强声场压力分布。从理论上分析了这种测量方法的可行性,对测量基本要求及实验装置做了阐述。实验结果证实:该方法可以用来测量高声能密度声场压力分布;测量结果与水听器测量结果基本吻合;测量方法存在测量盲区。     

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。      

Effects of nonlinear propagation, cavitation, and boiling in lesion formation by high intensity focused ultrasound in a gel phantom

The importance of nonlinear acoustic wave propagation and ultrasound-induced cavitation in the acceleration of thermal lesion production by high intensity focused ultrasound was investigated experimentally and theoretically in a transparent protein-containing gel. A numerical model that accounted for nonlinear acoustic propagation was used to simulate experimental conditions. Various exposure regimes with equal total ultrasound energy but variable peak acoustic pressure were studied for single lesions and lesion stripes obtained by moving the transducer. Static overpressure was applied to suppress cavitation. Strong enhancement of lesion production was observed for high amplitude waves and was supported by modeling. Through overpressure experiments it was shown that both nonlinear propagation and cavitation mechanisms participate in accelerating lesion inception and growth. Using B-mode ultrasound, cavitation was observed at normal ambient pressure as weakly enhanced echogenicity in the focal region, but was not detected with overpressure. Formation of tadpole-shaped lesions, shifted toward the transducer, was always observed to be due to boiling. Boiling bubbles were visible in the gel and were evident as strongly echogenic regions in B-mode images. These experiments indicate that nonlinear propagation and cavitation accelerate heating, but no lesion displacement or distortion was observed in the absence of boiling.     

非均匀组织医学超声发射声场仿真

为了分析医学超声在非均匀组织中的分布特性,建立了超声发射声场的计算模型。采用交错网格有限差分法对耦合超声非线性方程进行数值求解,获得了声速、密度及非线性参数非均匀分布情况下人体腹壁组织内的超声声场分布数据。同均匀介质相比:当声速均匀而密度非均匀时,声束仍聚焦良好,焦点处声能下降了1.8 dB;当密度均匀而声速非均匀时,声束发散严重,焦点处声能下降了3.8 dB,下降程度与非均匀组织接近。组织声速在空间分布的非均匀性是导致聚焦声束能量分布畸变的主要原因。      

Optimal design and experimental investigation of surfactant encapsulated microbubbles

The diagnostic capabilities of ultrasound imaging can be improved with contrast-specific nonlinear imaging modalities such as harmonic and subharmonic imaging. The nonlinear response of an encapsulated microbubble in an acoustic field is strongly influenced by the shell viscoelastic properties that are determined by the shell composition and thickness. In this paper, the subharmonic performance of a surfactant encapsulated microbubble was optimized by choosing the appropriate composition of shell material with the aid of theoretical model. To study the effects of viscoelastic properties of microbubble shell materials on the nonlinear scattered response of microbubbles, a theoretical model-modified Herring equation for the oscillation of encapsulated microbubbles in the ultrasound field was employed. Based on this model, a computer aided design system was developed to optimize and analyze the acoustic properties, particularly subharmonic responses, of microbubbles under different shell parameters. Furthermore, surfactant encapsulated microbubbles with different viscoelastic properties were prepared by changing the shell composition. Their shell viscoelastic behavior was measured indirectly as dilational modulus of monolayer film formed with surfactant molecular. Moreover, in vitro quantitative acoustic properties measurements of these microbubbles were carried out to evaluate their subharmonic performance. Both of the theoretical simulation and acoustic measurement showed that the surfactant encapsulated microbubbles with good subharmonic properties could be designed and prepared by adjusting the shell material composition with the guide of the computer aided design system.     

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.     

Effect of acoustic nonlinearity on heating of biological tissue by high-intensity focused ultrasound

Effect of strong acoustic nonlinearity on the efficiency of heating of a biological tissue by high-intensity focused ultrasound in the modes of operation used in real clinical setups is studied. The spatial distributions of thermal sources and the corresponding temperature increments caused by ultrasonic absorption are analyzed. Numerical algorithms are developed for simulating the nonlinear focusing of ultrasound in the calculations of both the heat sources on the basis of the Khokhlov-Zabolotskaya-Kuznetsov-type equations and the temperature field in a tissue on the basis of an inhomogeneous thermal conduction equation with a relaxation term. It is demonstrated that in the mode of operation typical of acoustic surgery, the nonlinearity improves the locality of heating and leads to an increase in the power of thermal sources in the focus by approximately an order of magnitude. The diffusion phenomena in the tissue lead to a smoothing of the spatial temperature distributions, as compared to the distributions of thermal sources. In the case of one-second exposure in the nonlinear mode of focusing, the maximal temperature in the focus exceeds the values obtained in the approximation of linear wave propagation by a factor of three.     

高频聚焦超声声场和温度场的仿真研究*

为探究临床常用的7 MHz高频聚焦超声在多层生物组织中的声传播以及毫秒级时间内的生物传热规律问题,基于Westervelt方程和Pennes传热方程,使用有限元方法建立高频聚焦超声辐照多层组织的非线性热黏性声传播及传热模型。首先分析了线性模型和非线性模型之间的差异,然后在非线性模型下探究换能器的参数对声场和温度场的影响。仿真结果显示：在7 MHz频率下,当换能器输出声功率超过5 W时,声波传播的非线性效应不可忽视(p <0.05);当声功率从5 W增大到15 W时,非线性模型与线性模型预测的温度偏差从20%增加到34.703%;高频聚焦超声波的非线性行为比低频更加显著,基频能量向高次谐波转移的程度增大,声功率为10 W和15 W时4次谐波与基波之比分别达到7.33%和12.12%;高频换能器参数的改变对组织中声场和温度场分布的影响较大,换能器焦距从12 mm减小到11.2 mm,焦点处最高温度增加了77%。结果表明,7 MHz聚焦超声的非线性声传播需要考虑到4次谐波的影响。该文提出的多层组织非线性仿真模型可为高频聚焦超声换能器参数优化及制定安全、有效的术前治疗方案提供理论参考。     

Numerical simulations of stable cavitation bubble generation and primary Bjerknes forces in a three-dimensional nonlinear phased array focused ultrasound field

We present a model developed for studying the generation of stable cavitation bubbles and their motion in a three-dimensional volume of liquid with axial symmetry under the effect of finite-amplitude phased array focused ultrasound. The density of bubbles per unit volume is determined by a nonlinear law which is a threshold-dependent function of the negative acoustic pressure reached in the liquid, in which nuclei are initially distributed. The nonlinear mutual interaction of ultrasound and bubble oscillations is modeled by a nonlinear coupled differential system formed by the wave and a Rayleigh-Plesset equations, for which both the pressure and the bubble oscillation variables are unknown. The system, which accounts for nonlinearity, dispersion, and attenuation due to the bubbles, is solved by numerical approximations. The nonlinear acoustic pressure field is then used to evaluate the primary Bjerknes force field and to predict the subsequent motion of bubbles. In order to illustrate the procedure, a medium-high and a low ultrasonic frequency configurations are assumed. Simulation results show where bubbles are generated, the nonlinear effects they have on ultrasound, and where they are relocated. Despite many physical restrictions and thanks to its particularities (two nonlinear coupled fields, bubble generation, bubble motion), the numerical model used in this work gives results that show qualitative coherence with data observed experimentally in the framework of stable cavitation and suggest their usefulness in some application contexts.     

Forty years of nonlinear ultrasound

Nonlinear ultrasound forms an integrated discipline of nonlinear acoustics founded in 1755. A short outline of the state-of-the-art in nonlinear ultrasound in 1960 forms the introduction to this paper. Some of the most important contributions to the development in the theoretical, analytical and numerical basis of nonlinear ultrasound and in experimental investigations of nonlinear ultrasonic processes published during the period of 1960 through 2000 are discussed and their successes and failures in practical exploitation are illuminated. A more detailed treatment is given of research achievements in nonlinearity of fluids, in focused ultrasonic field, in parametric acoustic arrays and in thermoacoustics. An attempt is made to point out some fields of research in nonlinear ultrasound where future efforts should be concentrated.     

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.     

Experimental observation of blood erythrocyte structure in the field of standing surface acoustic waves

The paper presents experimental results of observing the structurization effect for one of the formed elements of blood—erythrocytes—in the field of standing surface acoustic waves. Characteristic images of the striated structures formed by erythrocytes on the surface of lithium niobate as result of ultrasound action have been obtained. The results on the ultrasound structurization of erythrocytes in a blood sample and of calcium carbonate particles in an aqueous colloid solution have been comparatively analyzed. It has been noted that the achieved effect agrees qualitatively with the theoretical model of the behavior of colloid particle ensembles in an acoustic field developed by O.V. Rudenko et al.     

Calibration of ultrasonic hydrophone probes up to 100 MHz using time gating frequency analysis and finite amplitude waves

A number of ultrasound imaging systems employs harmonic imaging to optimize the trade off between resolution and penetration depth and center frequencies as high as 15 MHz are now used in clinical practice. However, currently available measurement tools are not fully adequate to characterize the acoustic output of such nonlinear systems primarily due to the limited knowledge of the frequency responses beyond 20 MHz of the available piezoelectric hydrophone probes. In addition, ultrasound hydrophone probes need to be calibrated to eight times the center frequency of the imaging transducer. Time delay spectrometry (TDS) is capable of providing transduction factor of the probes beyond 20 MHz, however its use is in practice limited to 40 MHz. This paper describes a novel approach termed time gating frequency analysis (TGFA) that provides the transduction factor of the hydrophone probes in the frequency domain and significantly extends the quasi-continuous calibration of the probes up to 60 MHz. The verification of the TGFA data was performed using TDS calibration technique (up to 40 MHz) and a nonlinear calibration method (up to 100 MHz). The nonlinear technique was based on a novel wave propagation model capable of predicting the true pressure-time waveforms at virtually any point in the field. The spatial averaging effects introduced by the finite aperture hydrophones were also accounted for. TGFA calibration results were obtained for different PVDF probes, including needle and membrane designs with nominal diameters from 50 to 500 micro m. The results were compared with discrete calibration data obtained from an independent national laboratory and the overall uncertainty was determined to be +/-1.5 dB in the frequency range 40-60 MHz and less than +/-1 dB below 40 MHz.     

应用角谱方法研究聚焦声束在层状生物组织中的非线性声传播

应用角谱方法理论研究了聚焦声束在层状生物组织中的非线性传播特性，将声波分解为角谱，可计算垂直于声轴的任意平面的非线性声场。在圆形平面活塞聚焦换能器的焦区中插入多种生物组织样品，数值计算了样品内部及外部的二次谐波声场，并通过实验测量验证了理论方法的有效性。基于快速傅氏变换的角谱方法可直观地描述非线性声传播，对非线性声成像有指导作用。     

FDTD simulation of finite-amplitude pressure and temperature fields for biomedical ultrasound.

Full wave simulations provide a valuable tool for studying the spatial and temporal nature of an acoustic field. One method for producing such simulations is the finite-difference time-domain (FDTD) method. This method uses discrete differences to approximate derivatives in the governing partial differential equations. We used the FDTD method to model the propagation of finite-amplitude sound in a homogeneous thermoviscous fluid. The calculated acoustic pressure field was then used to compute the transient temperature rise in the fluid; the heating results from absorption of acoustic energy by the fluid. As an example, the transient temperature field was calculated in biological tissue in response to a pulse of focused ultrasound. Enhanced heating of the tissue from finite-amplitude effects was observed. The excess heating was attributed to the nonlinear generation of higher-frequency harmonics which are absorbed more readily than the fundamental. The effect of nonlinear distortion on temperature rise in tissue was observed to range from negligible at 1 MPa source pressure to an 80% increase in temperature elevation at 10 MPa source pressure.     

Nonlinear pulsed ultrasound beams radiated by rectangular focused diagnostic transducers

A numerical model for simulating nonlinear pulsed beams radiated by rectangular focused transducers, which are typical of diagnostic ultrasound systems, is presented. The model is based on a KZK-type nonlinear evolution equation generalized to an arbitrary frequency-dependent absorption. The method of fractional steps with an operator-splitting procedure is employed in the combined frequency-time domain algorithm. The diffraction is described using the implicit backward finite-difference scheme and the alternate direction implicit method. An analytic solution in the time domain is employed for the nonlinearity operator. The absorption and dispersion of the sound speed are also described using an analytic solution but in the frequency domain. Numerical solutions are obtained for the nonlinear acoustic field in a homogeneous tissue-like medium obeying a linear frequency law of absorption and in a thermoviscous fluid with a quadratic frequency law of absorption. The model is applied to study the spatial distributions of the fundamental and second harmonics for a typical diagnostic ultrasound source. The nonlinear distortion of pulses and their spectra due to the propagation in tissues are presented. A better understanding of nonlinear propagation in tissue may lead to improvements in nonlinear imaging and in specific tissue harmonic imaging. Published in Russian in Akusticheskiĭ Zhurnal, 2006, Vol. 52, No. 4, pp. 560–570. This article was translated by the authors.     

Contrast harmonic imaging

The behavior of ultrasound contrast agents depends highly on the acoustic pressure of the insonified ultrasound wave. For low pressure the expansion and compression is linear to the pressure, for medium acoustic pressure nonlinear behavior starts to occur and for high pressures, but still in the diagnostic range transient scattering can be noticed, resulting in an enhanced scattering followed by a disappearance of the bubble. The nonlinear and transient regime can be utilized for imaging of the contrast agent in or nearby tissue. The magnitude of the nonlinear signal from the contrast has to compete with the nonlinear component of the ultrasound wave, which is generated during propagation. It is shown that contrast is superior to tissue when using low frequencies and imaging the third or fourth harmonic of the transmitted frequency.     

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.