Temperature rise induced by an annular focused transducer with a wide aperture angle in multi-layer tissue

In order to improve the operability and accuracy of high-intensity focused ultrasound(HIFU), an annular focused transducer, whereby a B-ultrasound probe is placed in its center, is used to realize the real time monitoring and control of the treatment. In this paper, the spheroidal beam equation(SBE) was used to calculate the sound field by an annular focused transducer with a wide aperture angle to first derive the heat deposition and the Pennes equation was used to calculate the temperature field in multi-layer tissue. We studied the effect of different parameters on the temperature of the tissues. The result shows that the focal length has a significant influence on both maximum liver temperature rise and skin temperature rise, and both increase with the increase in the focal length. When the frequency increases, the temperature rise first undergoes a rapid increase before gradually reaching a maximum, and then finally decreasing. The temperature rise increases while the inner radius decreases or the sound pressure increases. By choosing suitable parameters, the proper temperature rise both on the target tissue and skin via an annular focused transducer with a wide aperture angle can be obtained.     

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 partial elements excitation for hemispherical high-intensity focused ultrasound phased transducer

The hemispherical phased transducer maximizes the coverage of the skull and the ultrasonic energy per unit area of the skull is minimized, thereby reducing the risk of skull burns, but the transducer has a small focal area adjustment range, increasing the focal length of treatment is an urgent question for this type of transducer. In this paper, a three-dimensional high-intensity focused ultrasound (HIFU) transcranial propagation model is established based on the human head structure. The finite difference time domain (FDTD) is combined with the Westervelt acoustic wave nonlinear propagation equation and Penne's biological heat conduction equation for numerical simulation of the sound pressure field and temperature field. Forming a treatable focal area in a small-opening hemispherical transducer with a small amount of numerical simulation calculation focusing at a set position to determine the minimum partial excitation area ratio of focusing. And then, applying these preliminary results to a large-opening diameter hemispherical transducer and the temperature field formed by it or full excitation is studied. The results show that the focus area with the excitation area ratio of less than 22% moves forward to the transducer side when the excitation sound is formed. When the excitation area ratio is greater than or equal to 23%, it focuses at the set position. In the case of partial incentives, using 23% of the partial array, the adjustable range of the treatable focal area formed in the three-dimensional space is larger than that of the full excitation.     

聚焦超声源对生物媒质加热的理论研究

用差分法求解生物热传导方程,研究了凹球面聚焦超声换能器用于热疗时在人体组织内产生的稳态温度场.引入热焦距及等温线,分析了换能器参数、生物组织特性参数对有效治疗区的影响,并对声场和温度场特征进行了比较 关键词： 聚焦超声 热疗 生物组织 温度场     

Simulation of sound field in a tissue medium generated by a concave spherically annular transducer

The concave spherically annular transducer is regarded as a negative and a positive concave spherical transducer, and the spheroidal beam equation is used to simulate the linear and nonlinear sound field in a tissue medium generated by this transducer. It is found that the acoustic focus of the ring does not coincide with the acoustic focus of its central part. If the width of the ring increases, its acoustic focus will move toward the geometric focus and the amplitudes of nonlinear harmonics will increase obviously. If there are several coaxial rings placed on the concave spherical surface, more than one peak will appear along the axial direction for the fundamental, and high harmonics focus better. The distribution of sound field will change with the number and the excited signals of rings, so it maybe is a potential approach to treat locally big tumors.     

Finite difference modelling of the temperature rise in non-linear medical ultrasound fields

Non-linear propagation of ultrasound can lead to increased heat generation in medical diagnostic imaging due to the preferential absorption of harmonics of the original frequency. A numerical model has been developed and tested that is capable of predicting the temperature rise due to a high amplitude ultrasound field. The acoustic field is modelled using a numerical solution to the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation, known as the Bergen Code, which is implemented in cylindrical symmetric form. A finite difference representation of the thermal equations is used to calculate the resulting temperature rises. The model allows for the inclusion of a number of layers of tissue with different acoustic and thermal properties and accounts for the effects of non-linear propagation, direct heating by the transducer, thermal diffusion and perfusion in different tissues. The effect of temperature-dependent skin perfusion and variation in background temperature between the skin and deeper layers of the body are included. The model has been tested against analytic solutions for simple configurations and then used to estimate temperature rises in realistic obstetric situations. A pulsed 3 MHz transducer operating with an average acoustic power of 200 mW leads to a maximum steady state temperature rise inside the foetus of 1.25 degrees C compared with a 0.6 degree C rise for the same transmitted power under linear propagation conditions. The largest temperature rise occurs at the skin surface, with the temperature rise at the foetus limited to less than 2 degrees C for the range of conditions considered.     

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.     

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。      

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.     

微泡对高强度聚焦超声声压场影响的仿真研究*

微泡对高强度聚焦超声(HIFU)治疗焦域具有增效作用,而HIFU治疗中不同声学条件下微泡对HIFU形成声压场的影响尚不清楚。本文基于气液混合声波传播方程、Keller气泡运动方程、时域有限差分(FDTD)法和龙格-库塔(RK)法数值仿真研究输入声压、激励频率、气泡初始空隙率和气泡初始半径对HIFU形成声压场的影响。研究结果表明,随着输入声压的增大,焦点处声压升高但焦点处最大声压与输入声压的比值减小,焦点位置几乎不变;随着激励频率和气泡初始半径的增大,焦点处声压升高且焦点位置向远离换能器方向移动;随着气泡初始空隙率的增大,焦点处声压降低且焦点位置向换能器方向移动。     

超声吸收体物理参数对红外热成像测量高强度聚焦超声声场的影响

超声吸收体的物理参数对利用水听器和红外热成像技术的高强度聚焦超声(High-Intensity Focused Ultrasound,HIFU)声场测量结果具有重要影响。为了探索超声吸收体的物理参数(密度、声速、衰减系数、热扩散系数、定压比热容)对测量结果的影响规律,本文根据层状模型计算出相同声源功率输出时不同物理参数对应的超声吸收体内部声场和热场,利用有限差分法计算出超声吸收体表面在辐照过程中的温度变化;利用基于水听器和红外热成像技术的聚焦声场测量方法测量出焦域内不同位置上声场特征值(轴线声强和-6 dB声束宽度),与通过理论计算得到的声源在纯水中声场特征值进行比较,分析了不同物理参数对测量结果的影响。超声吸收体的声、热学参数中除了声速外,其它物理参数的变化引起声场特征值的测量造成最大相对差异率小于15%。因为声波传播速度的改变会导致超声吸收体内部热场分布变化,使测量结果与理论计算值有较大偏差,其中-6 dB声束宽度和轴线声强最大相对差异率为95.37%和69.97%。因此在选择超声吸收体的声、热学参数时应重点关注声波在吸收体内声速的影响。超声吸收体的声学参数与水的声学参数相近时,可以在焦域内获得较好的测量结果。      

Modeling of an electrohydraulic lithotripter with the KZK equation.

The acoustic pressure field of an electrohydraulic extracorporeal shock wave lithotripter is modeled with a nonlinear parabolic wave equation (the KZK equation). The model accounts for diffraction, nonlinearity, and thermoviscous absorption. A numerical algorithm for solving the KZK equation in the time domain is used to model sound propagation from the mouth of the ellipsoidal reflector of the lithotripter. Propagation within the reflector is modeled with geometrical acoustics. It is shown that nonlinear distortion within the ellipsoidal reflector can play an important role for certain parameters. Calculated waveforms are compared with waveforms measured in a clinical lithotripter and good agreement is found. It is shown that the spatial location of the maximum negative pressure occurs pre-focally which suggests that the strongest cavitation activity will also be in front of the focus. Propagation of shock waves from a lithotripter with a pressure release reflector is considered and because of nonlinear propagation the focal waveform is not the inverse of the rigid reflector. Results from propagation through tissue are presented; waveforms are similar to those predicted in water except that the higher absorption in the tissue decreases the peak amplitude and lengthens the rise time of the shock.     

微纳相控线阵超声换能器参数的理论分析*

微纳相控线阵超声换能器参数(阵元数目、阵元宽度及阵元间距)直接影响其横向声场分布,而其横向声场分布是能否实现高成像分辨率、大探测深度的决定性因素,也是制备换能器的主要依据。该文利用数值模拟研究微纳相控线阵超声换能器阵元参数对其横向声场中主瓣强度、-3 dB主瓣宽度、第一级旁瓣及栅瓣的影响。结果表明,主瓣强度随着阵元数目增加而增大,随阵元间距减小而增大,随着阵元宽度的增大呈现先增大后减小的趋势;-3 dB主瓣宽度随着阵元数目和阵元间距的增大而减小,随着阵元宽度的减小而减小;此外,减小阵元数目、减小阵元间距或增大阵元宽度均可以抑制旁瓣;栅瓣在阵元间距满足一定条件时可以完全消除。通过这些研究为微纳相控线阵超声换能器的优化设计与制备提供理论参考。     

剪切波对HIFU经颅聚焦形成温度场影响的数值仿真研究

在高强度聚焦超声经颅治疗时,既有纵波又有剪切波,为了保障该治疗方法的安全有效性,有必要分析剪切波对HIFU治疗温度场的影响。该文基于人体头颅CT数据和曲率半径为150 mm的256阵元的半球相控换能器建立三维高强度聚焦超声经颅声波传播模型,利用时域有限差分法结合Westervelt声波非线性传播方程、动量方程、质量守恒方程和Pennes生物热传导方程数值仿真其形成温度场,研究在相同输入功率、不同聚焦角度条件下对应阵元数进行激励时,剪切波对换能器形成温度场的影响。结果表明,随换能器聚焦角度减小,在几何焦点处形成的焦域面积逐渐增大,考虑剪切波形成的温度场达到65?C所需时间逐渐延长,焦点前移程度越大;在相同聚焦角度条件下,考虑剪切波的温度场达到65?C所需时间更短,旁瓣更少,在颅骨处的温度更高,对焦点前移几乎没有影响;随换能器聚焦角度减小,考虑剪切波的模型形成的焦域面积变化范围更大;幂指数函数形式对不同聚焦角度下焦域面积大小的拟合优度高,可预测不同聚焦角度换能器形成的焦域面积。     

时间反转聚焦在组织中形成损伤的数值建模

为考察基于时间反转方法的高强度聚焦超声治疗在预设目标点处的组织损伤情况,使用三维有限差分算法求解Westervelt方程,建立非线性声波传播数值模型,采用97阵元相控阵结合虚拟源的时间反转方法进行超声聚焦,分析其形成的声场和热场,并考察目标点偏离轴线时的组织损伤形成规律。结果表明随着目标点偏轴距离的增大,声压旁瓣开始增多。旁瓣的温升较低,不足以形成组织损伤。时间反转方法可用于多点聚焦,在一定的范围内,形成多点目标损伤而不产生额外的周围组织损伤。同时多点聚焦可以形成一个较大的损伤区域,减少超声治疗时间。     

1-3型二维柱形凹面线聚焦换能器声场特性

设计并研制了柱面结构的1-3型复合材料凹面线聚焦换能器,在提高换能器带宽的同时,可以实现声场的线聚焦。将换能器内部PZT柱作为独立声源,应用瑞利积分和叠加原理,推导出了柱形凹面换能器总声场的理论表达式。通过仿真计算分析了换能器在聚焦线上的声场特点以及相关参数对聚焦性能的影响。对换能器参数做出合理设计,使换能器在实现线聚焦的同时,声场在聚焦线上的起伏较小,从而设计并制作出聚焦性能良好的线聚焦凹面换能器探头。实验测试结果表明采用本文方法计算得到的换能器声场与实测的声场分布基本符合,柱形凹面换能器在其几何焦点附近范围内均可实现聚焦,并在侧向上形成清晰的聚焦线,其聚焦线长度为换能器的侧向结构长度,在聚焦线上声场分布起伏较小。      

颗粒填充对介质阻挡放电制臭氧性能的影响

在同轴圆柱单介质内外双水冷结构的DBD臭氧发生器的放电间隙内分别填充玻璃珠、高铝瓷、石英砂和熔融石英砂等颗粒,研究填充颗粒材料、粒径大小、间隙宽度等参数对臭氧生成效率的影响。结果表明：颗粒材料的介电常数是影响其臭氧制取效果的主要因素,随着介电常数的增加,间隙击穿电压降低,但由于颗粒导致电场的畸变,间隙折合场强增加,臭氧生成的最大能效降低,饱和浓度提升;高铝瓷具有最高的臭氧饱和浓度,与未填充的空床相比,饱和浓度提升136%;对于填充不同粒径熔融石英砂颗粒,随着粒径的增加,间隙击穿电压上升,间隙的折合场强提高,臭氧生成的最大能效降低,而饱和浓度提升;通过在宽间隙内填充介质颗粒可以得到窄间隙宽度的臭氧制取效果。     

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在同轴圆柱单介质内外双水冷结构的DBD臭氧发生器的放电间隙内分别填充玻璃珠、高铝瓷、石英砂和熔融石英砂等颗粒,研究填充颗粒材料、粒径大小、间隙宽度等参数对臭氧生成效率的影响.结果表明:颗粒材料的介电常数是影响其臭氧制取效果的主要因素,随着介电常数的增加,间隙击穿电压降低,但由于颗粒导致电场的畸变,间隙折合场强增加,臭氧生成的最大能效降低,饱和浓度提升;高铝瓷具有最高的臭氧饱和浓度,与未填充的空床相比,饱和浓度提升136％;对于填充不同粒径熔融石英砂颗粒,随着粒径的增加,间隙击穿电压上升,间隙的折合场强提高,臭氧生成的最大能效降低,而饱和浓度提升;通过在宽间隙内填充介质颗粒可以得到窄间隙宽度的臭氧制取效果.     

离散坐标法在计算生物组织内光场空间角分布中的应用

从辐射传输理论出发,研究了准直光照下层状生物组织内漫射光场的角分布.在辐射传输方程的基础上,采用离散坐标法得到了描述层状生物组织内漫射光传输问题的微分方程组形式,并用特征值-特征矢量方法对其进行了求解,给出了通解形式.结合边界条件对两类典型生物组织内漫射光场角分布进行了数值计算-各向同性组织和前向散射组织,给出了组织内不同深度处漫射光场空间角分布曲线.通过对计算结果比较分析,得到了生物组织内漫射光场空间角分布随深度的变化规律,及边界效应和光学参量对组织内漫射光场空间角分布的影响.     

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.