Shock wave-inertial microbubble interaction: a theoretical study based on the Gilmore formulation for bubble dynamics

The Gilmore formulation for bubble dynamics coupled with zeroth-order gas diffusion were used to investigate theoretically the cavitation activity produced by a modified XL-1 lithotripter [J. Acoust. Soc. Am. 105, 1997-2009 (1999)]. The model calculation confirms many of the basic features in bubble dynamics observed experimentally, in particular the strong secondary shock wave emission generated by in situ lithotripter shock wave-inertial microbubble interaction. In addition, shock wave-inertial microbubble interaction produced by a Dornier HM-3, the most commonly used clinical lithotripter, was evaluated. It was shown that the forced collapse of inertial microbubbles with strong secondary shock wave emission could be produced consistently, provided that an appropriate preceding shock wave and interpulse delay were used. Further, it was demonstrated that truncation of the tensile stress of the lithotripter shock wave could significantly reduce the large expansion of the bubble following shock wave-inertial microbubble interaction, which may alleviate the risk for vascular injury during shock wave exposure.     

Suppression of large intraluminal bubble expansion in shock wave lithotripsy without compromising stone comminution: methodology and in vitro experiments.

To reduce the potential of vascular injury without compromising the stone comminution capability of a Dornier HM-3 lithotripter, we have devised a method to suppress intraluminal bubble expansion via in situ pulse superposition. A thin shell ellipsoidal reflector insert was designed and fabricated to fit snugly into the original reflector of an HM-3 lithotripter. The inner surface of the reflector insert shares the same first focus with the original HM-3 reflector, but has its second focus located 5 mm proximal to the generator than that of the HM-3 reflector. With this modification, the original lithotripter shock wave is partitioned into a leading lithotripter pulse (peak positive pressure of 46 MPa and positive pulse duration of 1 micros at 24 kV) and an ensuing second compressive wave of 10 MPa peak pressure and 2 micros pulse duration, separated from each other by about 4 micros. Superposition of the two waves leads to a selective truncation of the trailing tensile component of the lithotripter shock wave, and consequently, a reduction in the maximum bubble expansion up to 41% compared to that produced by the original reflector. The pulse amplitude and -6 dB beam width of the leading lithotripter shock wave from the upgraded reflector at 24 kV are comparable to that produced by the original HM-3 reflector at 20 kV. At the lithotripter focus, while only about 30 shocks are needed to cause a rupture of a blood vessel phantom made of cellulose hollow fiber (i.d.=0.2 mm) using the original HM-3 reflector at 20 kV, no rupture could be produced after 200 shocks using the upgraded reflector at 24 kV. On the other hand, after 100 shocks the upgraded reflector at 24 kV can achieve a stone comminution efficiency of 22%, which is better than the 18% efficiency produced by the original reflector at 20 kV (p = 0.043). All together, it has been shown in vitro that the upgraded reflector can produce satisfactory stone comminution while significantly reducing the potential for vessel rupture in shock wave lithotripsy.     

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.     

Suppression of large intraluminal bubble expansion in shock wave lithotripsy without compromising stone comminution: refinement of reflector geometry

Using the Hamilton model [Hamilton, J. Acoust. Soc. Am. 93, 1256-1266 (1993)], the effects of reflector geometry on the pulse profile and sequence of the shock waves produced by the original and upgraded reflector of an HM-3 lithotripter were evaluated qualitatively. Guided by this analysis, we have refined the geometry of the upgraded reflector to enhance its suppressive effect on intraluminal bubble expansion without compromising stone comminution in shock wave lithotripsy. Using the original HM-3 reflector at 20 kV, rupture of a standard vessel phantom made of cellulose hollow fiber (i.d. = 0.2 mm), in which degassed water seeded with ultrasound contrast agents was circulated, was produced at the lithotripter focus after about 30 shocks. In contrast, using the upgraded reflector at 24 kV no rupture of the vessel phantom could be produced within a 20-mm diameter around the lithotripter focus even after 200 shocks. On the other hand, stone comminution was comparable between the two reflector configurations, although slightly larger fragments were produced by the upgraded reflector. After 2000 shocks, stone comminution efficiency produced by the original HM-3 reflector at 20 kV is 97.15 +/- 1.92% (mean +/- SD), compared to 90.35 +/- 1.96% produced by the upgraded reflector at 24 kV (p<0.02). All together, it was found that the upgraded reflector could significantly reduce the propensity for vessel rupture in shock wave lithotripsy while maintaining satisfactory stone comminution.     

Focusing of shock waves induced by optical breakdown in water

The focusing of laser-generated shock waves by a truncated ellipsoidal reflector was experimentally and numerically investigated. Pressure waveform and distribution around the first (F(1)) and second foci (F(2)) of the ellipsoidal reflector were measured. A neodymium doped yttrium aluminum garnet laser of 1046 nm wavelength and 5 ns pulse duration was used to create an optical breakdown at F(1), which generates a spherically diverging shock wave with a peak pressure of 2.1-5.9 MPa at 1.1 mm stand-off distance and a pulse width at half maximum of 36-65 ns. Upon reflection, a converging shock wave is produced which, upon arriving at F(2), has a leading compressive wave with a peak pressure of 26 MPa and a zero-crossing pulse duration of 0.1 mus, followed by a trailing tensile wave of -3.3 MPa peak pressure and 0.2 mus pulse duration. The -6 dB beam size of the focused shock wave field is 1.6 x 0.2 mm(2) along and transverse to the shock wave propagation direction. Formation of elongated plasmas at high laser energy levels limits the increase in the peak pressure at F(2). General features in the waveform profile of the converging shock wave are in qualitative agreement with numerical simulations based on the Hamilton model.     

The effect of reflector geometry on the acoustic field and bubble dynamics produced by an electrohydraulic shock wave lithotripter

A theoretical model for the propagation of shock wave from an axisymmetric reflector was developed by modifying the initial conditions for the conventional solution of a nonlinear parabolic wave equation (i.e., the Khokhlov-Zabolotskaya-Kuznestsov equation). The ellipsoidal reflector of an HM-3 lithotripter is modeled equivalently as a self-focusing spherically distributed pressure source. The pressure wave form generated by the spark discharge of the HM-3 electrode was measured by a fiber optic probe hydrophone and used as source conditions in the numerical calculation. The simulated pressure wave forms, accounting for the effects of diffraction, nonlinearity, and thermoviscous absorption in wave propagation and focusing, were compared with the measured results and a reasonably good agreement was found. Furthermore, the primary characteristics in the pressure wave forms produced by different reflector geometries, such as that produced by a reflector insert, can also be predicted by this model. It is interesting to note that when the interpulse delay time calculated by linear geometric model is less than about 1.5 micros, two pulses from the reflector insert and the uncovered bottom of the original HM-3 reflector will merge together. Coupling the simulated pressure wave form with the Gilmore model was carried out to evaluate the effect of reflector geometry on resultant bubble dynamics in a lithotripter field. Altogether, the equivalent reflector model was found to provide a useful tool for the prediction of pressure wave form generated in a lithotripter field. This model may be used to guide the design optimization of reflector geometries for improving the performance and safety of clinical lithotripters.     

A theoretical study of cavitation generated by an extracorporeal shock wave lithotripter

The intense acoustic wave generated at the focus of an extracorporeal shock wave lithotripter is modeled as the impulse response of a parallel RLC circuit. The shock wave consists of a zero rise time positive spike that falls to 0 at 1 microsecond followed by a negative pressure component 6 microseconds long with amplitudes scaled to +1000 and -160 bars, P+ and P-, respectively. This pressure wave drives the Gilmore-Akulichev formulation for bubble dynamics; the zero-order effect of gas diffusion on bubble response is included. The negative pressure component of a 1000-bar shock wave will cause a preexisting bubble in the 1- to 10-microns range to expand to over 100 times its initial size, R0, for 250 microseconds, with a peak radius of approximately 1400 microns, then collapse very violently, emitting far UV or soft x-ray photons (black body). Gas diffusion does not appreciably mitigate the amplitude of the pressure wave radiated at the primary collapse, but does significantly reduce the collapse temperature. Diffusion also increases the bubble radius from R0 up to 40 microns and extends the duration of ringing following the primary collapse, assuming that the bubble does not break up or shed microbubbles. Results are sensitive to P+/P- and to the duration of the negative pressure cycle but not to rise time.     

Acoustic characteristics of pulse detonation engine with ellipsoidal reflector

Acoustic characteristics of a pulse detonation engine(PDE) with and without an ellipsoidal reflector are numerically and experimentally investigated. A two-dimensional(2 D) non-splitting unstructured triangular mesh Euler solver based on the space-time conservation element and solution element(CE/SE) method is employed to simulate the flow field of a PDE.The numerical results clearly demonstrate the external flow field of the PDE. The effect of an ellipsoidal reflector on the flow field characteristic near the PDE exit is investigated. The formation process of reflected shock wave and reflected jet shock are reported in detail. An acoustic measurement system is established for the PDE acoustic testing. The experimental results show that the ellipsoidal reflector changes the sound waveform and directivity of PDE sound. The reflected shock wave and reflected jet shock result in two more positive pressure peaks in the sound waveform. The ellipsoidal reflector changes the directivity of PDE sound from 20 to 0. It is found that the peak sound pressure level(PSPL) and overall sound pressure level(OASPL) each obtain an increment when the PDE is installed with a reflector. The maximum relative increase ratio of PSPL and OASPL are obtained at the focus point F2, whose values are 6.1% and 6.84% respectively. The results of the duration of the PDE sound indicate that the reflecting and focusing wave generated by the reflector result in the increment of A duration and B duration before and near focus point F2. Results show that the ellipsoidal reflector has a great influence on the acoustic characteristic of PDE sound. The research is helpful for understanding the influence of an ellipsoidal reflector on the formation and propagation process of PDE sound.     

激波聚焦反射的实验和数值研究

 采用高速摄影技术和数值模拟方法,对入射激波在两种不同形状的抛物形反射器表面聚焦和反射的过程进行了研究,得到了激波聚焦反射过程的波系结构的实验阴影照片和数值计算结果,两者符合得很好。对激波聚焦形成的气体动力学焦点的特性进行了分析,结果表明,入射激波在两种反射器反射后聚焦所形成的气体动力学焦点均是由三波点在轴心处的会聚所导致的,气体动力学焦点位于相应的反射器壁面的几何焦点附近。不同的反射器中,激波聚焦前后的波系结构也不同,对较浅的反射器,入射激波反射前在反射器壁面形成了弓形激波,反射之后需要相对较长的时间完成聚焦,形成聚焦反射激波之后弓形激波仍未相交;对较深的反射器,入射激波反射后在更短的时间内聚焦,聚焦时弓形激波已经相交,聚焦反射激波之后的流场波系结构更加复杂。     

水下强声波脉冲负压的产生和空化气泡运动

首先利用高速摄影和压力传感器测量的方法, 对曲面反射式水下强声波脉冲的传播和聚焦过程进行了实验研究.实验研究发现, 椭球面反射罩在起到汇聚声能的作用的同时也将使得强声波脉冲在传播过程中形成负压区, 并由此而引发近场声传播通道上空化气泡群的产生. 在实验结果的基础上, 进一步利用基于Kirchhoff衍射定理的声传播模型和大振幅条件下的QX气泡运动方程, 对强声波脉冲负压区的形成原因及空化气泡的运动过程进行了数值计算和分析. 研究结果表明, 在焦前区, 源于反射罩内表面的"尾波"和出口处的"边缘波"在传播过程中将形成反射波中的负压区; 在焦后区, 源于反射罩顶点的"中心波"在传播过程中将形成反射波中的负压区. 在反射波作用下, 空化气泡体现出了"正压区受压缩并振荡, 负压区膨胀"的运动特点. 在反射波之后, 空化气泡将出现成长、坍缩和回弹等典型的物理过程. 研究结果对曲面反射式水下强声波传播物理规律的认识具有实际意义.     

Comparison of electrohydraulic lithotripters with rigid and pressure-release ellipsoidal reflectors. II. Cavitation fields.

Dramatically different cavitation was produced by two separate acoustic pulses that had different shapes but similar duration, frequency content, and peak positive and negative pressure. Both pulses were produced by a Dornier HM-3 style lithotripter: one pulse when the ellipsoidal reflector was rigid, the other when the reflector was pressure release. The cavitation, or bubble action, generated by the conventional rigid-reflector pulse was nearly 50 times longer lived and 3-13 times stronger than that produced by the pressure-release-reflector pulse. Cavitation durations measured by passive acoustic detection and high-speed video agreed with calculations based on the Gilmore equation. Cavitation intensity, or destructive potential, was judged (1) experimentally by the size of pits in aluminum foil detectors and (2) numerically by the calculated amplitude of the shock wave emitted by a collapsing bubble. The results indicate that the trailing positive spike in the pressure-release-reflector waveform stifles bubble growth and mitigates the collapse, whereas the trough after the positive spike in the rigid-reflector waveform triggers inertially driven growth and collapse. The two reflectors therefore provide a tool to compare effects in weakly and strongly cavitating fields and thereby help assess cavitation's role in lithotripsy.     

Comparison of electrohydraulic lithotripters with rigid and pressure-release ellipsoidal reflectors. I. Acoustic fields.

The most common lithotripter, a Dornier HM-3, utilizes an underwater spark to generate an acoustic pulse and a rigid ellipsoidal reflector to focus the pulse on the kidney stone to be comminuted. The pulse measured in water with a PVDF membrane hydrophone at the external focus of the ellipsoid was a 1-microsecond positive-pressure spike followed by a 3-microsecond negative-pressure trough. When we replaced the rigid reflector in our experimental lithotripter with a pressure-release reflector, the pulse was a 1.6-microsecond trough followed by a 0.6-microsecond positive spike. The waveforms are nearly time inverses (i.e., their spikes and troughs are reversed). The frequency spectra, the maximum peak positive pressures P+ (42 MPa, rigid and 43 MPa, pressure-release), and the maximum peak negative pressures P- (-12 MPa and -14 MPa) are comparable. The maximum P- occurred 20 mm closer to the reflector than did the maximum P+, for both reflectors. However, the spatial maxima of the peak pressures (P+ and P-) produced by the pressure-release reflector were located 20 mm nearer to the reflector than those produced by the rigid reflector. Qualitative explanation of the waveforms and the location of pressure maxima as well as comparison to previous theoretical and experimental results is given. The alternate waveform produced by the pressure-release reflector may be a tool in determining the role of cavitation in lithotripsy because cavitation is highly sensitive to waveform.     

Spherical focusing of acoustic pulses in a liquid

Nonlinear processes accompanying the focusing of a microsecond acoustic pulse produced by an electromagnetic source shaped as a spherical segment are investigated. The processes are considered to be far from the boundaries of a liquid, in the absence of cavitation. Detailed measurements of the pressure field by a fiber-optic sensor and high-speed photography of the shock front are performed. The pressure field is found to be determined by the nonlinear effects that occur in the course of the propagation of the initial converging compression wave and an edge rarefaction wave. The peak pressure amplitudes at the focus are 75 and ?42 MPa for the compression and rarefaction waves, respectively, at the maximum voltage of the pulse generator in use. The measured length of the compression wave front is equal to the response time of the sensor (8 ns). The pressure amplitude is shown to be limited by the irregularity of the propagation of a shock wave in the form of Mach’s disk. At the focus, the pressure gradient across the radiator axis reaches 0.5 atm/μm, while the diameter of the focal spot is 2.5±0.2 mm. The focus of the edge rarefaction wave formed due to diffraction is located closer to the radiator than the focus of the compression wave, which may facilitate the study of the biological effect of cavitation independently of the shear motion of the medium.     

Shock wave interaction with laser-generated single bubbles

The interaction of a lithotripter shock wave (LSW) with laser-generated single vapor bubbles in water is investigated using high-speed photography and pressure measurement via a fiber-optic probe hydrophone. The interaction leads to nonspherical collapse of the bubble with secondary shock wave emission and microjet formation along the LSW propagation direction. The maximum pressure amplification is produced during the collapse phase of the bubble oscillation when the compressive pulse duration of the LSW matches with the forced collapse time of the bubble.     

Computer simulation of perturbation of a shock wave in nitrogen by optical radiation

The possibility of a displacement of the front of a shock wave formed in a 1D nitrogen flow to the low gas pressure region (in front of the shock wave) upon absorption of the laser pulse energy in the region of the shock wave front is demonstrated using computer simulation based on the finite difference technique. The low-pressure region formed in the region of the initially high pressure under the action of a light pulse moves in the direction opposite to the direction of propagation of the shock wave front. Analysis is carried out for a typical experimental situation corresponding to the growth of carbon-nitride nanofilms.     

聚心火焰在共振腔作用下引发爆轰的数值研究

 基于带化学反应的二维轴对称Euler方程，利用带有Superbee限制函数的波传播算法，对共振腔中的氢气-空气预混气的聚心燃烧进行了数值模拟，讨论了共振腔不同抛物面对起爆的影响。数值结果表明，在开始阶段，燃烧诱导的激波在轴心、火焰和固壁的反射，使火焰失稳，随后共振腔中的抛物壁面上产生一定频率和强度的反射激波，不断穿越火焰，使火焰进一步失稳，加剧了燃烧速度，最终导致爆轰的形成。同时，火焰在与激波的作用过程中，形状扭曲变形，呈封闭端小敞口端大的扁平头部蘑菇云。共振腔抛物面的不同形状引起激波聚焦位置的变化，会影响激波和火焰的相互作用，使起爆提前或推迟，甚至不起爆。     

Time-resolved shadowgraphs and morphology analyses of aluminum ablation with multiple femtosecond laser pulses

Aluminum ablation by multiple femtosecond laser pulses is investigated via time-resolved shadowgraphs and scanning electron microscope(SEM) images of the ablation spot. The spatial distribution of the ejected material and the radius of the shock wave generated during the ablation are found to vary with the increase in the number of pulses. In the initial two pulses, nearly concentric and semicircular stripes within the shock wave front are observed, unlike in subsequent pulses. Ablation by multiple femtosecond pulses exhibits different characteristics compared with the case induced by single femtosecond pulse because of the changes to the aluminum target surface induced by the preceding pulses.     

Stationary and quasi-stationary waves in even-order dissipative systems

A new equation was recently suggested by Rudenko and Robsman [1] for describing the nonlinear wave propagation in scattering media that are characterized by weak sound signal attenuation proportional to the fourth power of frequency. General self-similar properties of the solutions to this equation were studied. It was shown that stationary solutions to this equation in the form of a shock wave exhibit unusual oscillations around the shock front, as distinct from the classical Burgers equation. Here, similar solutions are studied in detail for nonlinear waves in even-order dissipative media; namely, the solutions are compared for the media with absorption proportional to the second, fourth, and sixth powers of frequency. Based on the numerical results and the self-similar properties of the solutions, the fine structure of the shock front of stationary waves is studied for different absorption laws and magnitudes. It is shown that the amplitude and number of oscillations appearing in the stationary wave profile increase with increasing power of the frequency-dependent absorption term. For initial disturbances in the form of a harmonic wave and a pulse, quasi-stationary solutions are obtained at the stage of fully developed discontinuities and the evolution of the profile and width of the shock wave front is studied. It is shown that the smoothening of the shock front in the course of wave propagation is more pronounced when the absorption law is quadratic in frequency.     

Cylindrical cumulation of fast ions in a ring focus of a high-power subpicosecond laser

A new method of cylindrical cumulation of fast ions undergoing ponderomotive acceleration at the focus of a high-power subpicosecond laser is proposed. When a laser beam is focused in a preionized gas at a ring focus, radial acceleration of ions by the ponderomotive force occurs. The ions accelerated from the inner side of the ring form a cylindrical shock wave converging toward the axis. As the shock wave cumulates, the ion density increases rapidly and the ion-ion collision probability increases along with it. A numerical simulation for a ~100 TW subpicosecond laser pulse predicts the generation of up to 200 keV ions and up to 100-fold volume compression of the plasma in a cylinder ~1 μm in diameter. The lifetime of the dense plasma filament over the length of the laser caustic is several picoseconds. It is suggested that laser cumulation of ions be used for the production of a bright and compact subpicosecond source of fast neutrons, media for x-and γ-ray lasers, and multiply-charged ions and for the initiation of nuclear reactions. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 1, 20–25 (10 January 1999)     

激光引致激波演化数值研究

在高重复频率激光推进的研究中,激波的合并是发生在激波演化后期的,同时由于脉冲间隔短,脉冲宽度对流场演化的影响也需要详细研究。考虑了激光辐照过程对流场演化的影响,通过数值计算对激波演化特性进行了研究。结果表明,初期波阵面的椭球形状逐渐转化为一个球形,球心与击穿点的距离随时间逐渐减小并最终趋于稳定。基于激波合并的应用,当激波马赫数在1~2之间时,给出了激波波阵面半径随时间的变化规律,以及激波高压区长度和波峰压强随激波波阵面半径变化规律的经验公式。