Shock wave-inertial microbubble interaction: methodology, physical characterization, and bioeffect study

A method of generating in situ shock wave-inertial microbubble interaction by a modified electrohydraulic shock wave lithotripter is proposed and tested in vitro. An annular brass ellipsoidal reflector (thickness = 28 mm) that can be mounted on the aperture rim of a Dornier XL-1 lithotripter was designed and fabricated. This ring reflector shares the same foci with the XL-1 reflector, but is 15 mm short in major axis. Thus, a small portion of the spherical shock wave, generated by a spark discharge at the first focus (F1) of the reflector, is reflected and diffracted by the ring reflector, producing a weak shock wave approximately 8.5 microseconds in front of the lithotripter pulse. Based on the configuration of the ring reflector (different combinations of six identical segments), the peak negative pressure of the preceding weak shock wave at the second focus (F2) can be adjusted from -0.96 to -1.91 MPa, at an output voltage of 25 kV. The preceding shock wave induces inertial microbubbles, most of which expand to a maximum size of 100-200 microns, with a few expanding up to 400 microns before being collapsed in situ by the ensuing lithotripter pulse. Physical characterizations utilizing polyvinylidene difluoride (PVDF) membrane hydrophone, high-speed shadowgraph imaging, and passive cavitation detection have shown strong secondary shock wave emission immediately following the propagating lithotripter shock front, and microjet formation along the wave propagation direction. Using the modified reflector, injury to mouse lymphoid cells is significantly increased at high exposure (up to 50% with shock number > 100). With optimal pulse combination, the maximum efficiency of shock wave-induced membrane permeabilization can be enhanced substantially (up to 91%), achieved at a low exposure of 50 shocks. These results suggest that shock wave-inertial microbubble interaction may be used selectively to either enhance the efficiency of shock wave-mediated macromolecule delivery at low exposure or tissue destruction at high exposure.     

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.     

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.     

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.     

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.     

Numerical investigation of shock-induced bubble collapse dynamics and fluid–solid interactions during shock-wave lithotripsy

In this paper we investigate the bubble collapse dynamics under shock-induced loading near soft and rigid bio-materials, during shock wave lithotripsy. A novel numerical framework was developed, that employs a Diffuse Interface Method (DIM) accounting for the interaction across fluid–solid-gas interfaces. For the resolution of the extended variety of length scales, due to the dynamic and fine interfacial structures, an Adaptive Mesh Refinement (AMR) framework for unstructured grids was incorporated. This multi-material multi-scale approach aims to reduce the numerical diffusion and preserve sharp interfaces. The presented numerical framework is validated for cases of bubble dynamics, under high and low ambient pressure ratios, shock-induced collapses, and wave transmission problems across a fluid–solid interface, against theoretical and numerical results. Three different configurations of shock-induced collapse applications near a kidney stone and soft tissue have been simulated for different stand-off distances and bubble attachment configurations. The obtained results reveal the detailed collapse dynamics, jet formation, solid deformation, rebound, primary and secondary shock wave emissions, and secondary collapse that govern the near-solid collapse and penetration mechanisms. Significant correlations of the problem configuration to the overall collapse mechanisms were found, stemming from the contact angle/attachment of the bubble and from the properties of solid material. In general, bubbles with their center closer to the kidney stone surface produce more violent collapses. For the soft tissue, the bubble movement prior to the collapse is of great importance as new structures can emerge which can trap the liquid jet into induced crevices. Finally, the tissue penetration is examined for these cases and a novel tension-driven tissue injury mechanism is elucidated, emanating from the complex interaction of the bubble/tissue interaction during the secondary collapse phase of an entrapped bubble in an induced crevice with the liquid jet.     

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.     

Cavitation bubble dynamics

The dynamics of cavitation bubbles on water is investigated for bubbles produced optically and acoustically. Single bubble dynamics is studied with laser produced bubbles and high speed photography with framing rates up to 20.8 million frames per second. Examples for jet formation and shock wave emission are given. Acoustic cavitation is produced in water in the interior of piezoelectric cylinders of different sizes (up to 12 cm inner diameter). The filementary structure composed of bubbles is investigated and their light emission (sonoluminescence) studied for various driving strengths.     

Cavitation bubble dynamics studied by high speed photography and holography: part two

For a thorough study of bubble dynamics in cavitation bubble fields one has to resort to holography to circumvent the problems caused by bubbles moving out of focus during their three-dimensional motion. The development and application of high speed holography and holocinematography in cavitation physics is reviewed in this paper. The state of the art is that several thousand holograms with frame size a few square millimetres can be taken at rates up to 300 000 per second. Digital image processing, a valuable tool which is used to cope with the huge information content of series of holograms, is discussed. Results on bubble dynamics obtained via holography are presented, in particular on shock wave emission and bubble oscillation, splitting and interaction in a sound field. Global field dynamics and streamer stability are also discussed.     

Experimental investigation of primary and secondary features in high-mach-number shock-bubble interaction

Experiments to study the compression and unstable evolution of an isolated soap-film bubble containing helium, subjected to a strong planar shock wave (M=2.95) in ambient nitrogen, have been performed in a vertical shock tube of square internal cross section using planar laser diagnostics. The early phase of the interaction process is dominated by the formation of a primary vortex ring due to the baroclinic source of vorticity deposited during the shock-bubble interaction, and the mass transfer from the body of the bubble to the vortex ring. The late time (long after shock interaction) study reveals the presence of a secondary baroclinic source of vorticity at high Mach number which is responsible for the formation of counterrotating secondary and tertiary vortex rings and the subsequent larger rate of elongation of the bubble.     

A dual passive cavitation detector for localized detection of lithotripsy-induced cavitation in vitro

A passive cavitation detector (PCD) identifies cavitation events by sensing acoustic emissions generated by the collapse of bubbles. In this work, a dual passive cavitation detector (dual PCD), consisting of a pair of orthogonal confocal receivers, is described for use in shock wave lithotripsy. Cavitation events are detected by both receivers and can be localized to within 5 mm by the nature of the small intersecting volume of the focal areas of the two receivers in association with a coincidence detection algorithm. A calibration technique, based on the impulse response of the transducer, was employed to estimate radiated pressures at collapse near the bubble. Results are presented for the in vitro cavitation fields of both a clinical and a research electrohydraulic lithotripter. The measured lifetime of the primary growth-and-collapse of the cavitation bubbles increased from 180 to 420 microseconds as the power setting was increased from 12 to 24 kV. The measured lifetime compared well with calculations based on the Gilmore-Akulichev formulation for bubble dynamics. The radiated acoustic pressure 10 mm from the collapsing cavitation bubble was measured to vary from 4 to 16 MPa with increasing power setting; although the trends agreed with calculations, the predicted values were four times larger than measured values. The axial length of the cavitation field correlated well with the 6-dB region of the acoustic field. However, the width of the cavitation field (10 mm) was significantly narrower than the acoustic field (25 mm) as bubbles appeared to be drawn to the acoustic axis during the collapse. The dual PCD also detected signals from "rebounds," secondary and tertiary growth-and-collapse cycles. The measured rebound time did not agree with calculations from the single-bubble model. The rebounds could be fitted to a Rayleigh collapse model by considering the entire bubble cloud as an effective single bubble. The results from the dual PCD agreed well with images from high-speed photography. The results indicate that single-bubble theory is sufficient to model lithotripsy cavitation dynamics up to time of the main collapse, but that upon collapse bubble cloud dynamics becomes important.     

Fundamental study of sterilization effects on marine Vibrio sp. in a cylindrical water chamber with supply of only underwater shock waves

The effect of shock sterilization on marine Vibrio sp. is investigated by carrying out a bio-experiment based on a bubble-shockwave interaction. In the experiments, underwater shock waves with different strength and frequencies are produced by a high-voltage power supply in a cylindrical water chamber. The bio-experimental results show marine Vibrio sp. is completely inactivated in a short time by a 1.0-Hz electric discharge. However, a high sterilization effect requires a strong and high frequency of the bubble motion, and it also depends on the lifetime of the bubble. Subsequently, by an experiment with an air gap to prevent the underwater shock waves entering the cell suspension, it is found that the introduction of a strong shock pressure is not entirely required to obtain the effective sterilization. On the other hand, the direct effect of the sterilization by rebound shock wave resulting from the bubble-shock wave interaction is examined in the experiments. The results suggest that free radicals mainly contribute to killing marine bacteria, and direct mechanical effects of the bubble motion are not responsible. In addition, the creation of the OH radical is indirectly confirmed by measuring the H₂O₂ concentration. Finally, the Herring equation is solved to investigate the condition of free radical generation when considering the effect of thermal conductivity at the bubble interface. As a result, the effective sterilization conditions based on the bubble-shock wave interaction are clearly obtained.     

Physical investigation of acoustic waves induced by the oscillation and collapse of the single bubble

The objective of this paper is to apply both experimental and numerical methods to investigate acoustic waves induced by the oscillation and collapse of a single bubble. In the experiments, the schlieren technique is used to capture the temporal evolution of the bubble shapes, and the corresponding acoustic waves. The results are presented for the single bubble generated by a low-voltage bubble generator in the free field of water. During the numerical simulations, a three-dimensional (3D) weakly compressible model is introduced to investigate the single bubble dynamics, including the generation and propagation of acoustic waves. The results show that (1) Compression wave, rarefaction wave and shock wave are generated during expansion stage, collapse stage and rebound stage of the bubble respectively. (2) Compression waves are induced by the rapid expansion of the bubble and eventually steepen into one shock wave propagating outward in the liquid, then another strong shock wave is emitted at the final collapse stage. The velocity and pressure of the liquid field increases after the shock wave. (3) Rarefaction waves are generated during the collapse stage due to the contraction of the bubble. The rarefaction wave reduces the liquid pressure and its spatial distribution is dispersive. The pressure of these acoustic waves and their effect on the liquid velocity attenuate with the increase of propagation distance.     

Quantitative measurements of acoustic emissions from cavitation at the surface of a stone in response to a lithotripter shock wave

Measurements are presented of acoustic emissions from cavitation collapses on the surface of a synthetic kidney stone in response to shock waves (SWs) from an electrohydraulic lithotripter. A fiber optic probe hydrophone was used for pressure measurements, and passive cavitation detection was used to identify acoustic emissions from bubble collapse. At a lithotripter charging voltage of 20 kV, the focused SW incident on the stone surface resulted in a peak pressure of 43 +/- 6 MPa compared to 23 +/- 4 MPa in the free field. The focused SW incident upon the stone appeared to be enhanced due to the acoustic emissions from the forced cavitation collapse of the preexisting bubbles. The peak pressure of the acoustic emission from a bubble collapse was 34 +/- 15 MPa, that is, the same magnitude as the SWs incident on the stone. These data indicate that stresses induced by focused SWs and cavitation collapses are similar in magnitude thus likely play a similar role in stone fragmentation.     

Microimplosions: cavitation collapse and shock wave emission on a nanosecond time scale

A streak camera with high spatial and temporal resolution was used for imaging the dynamics of the violent collapse in single-bubble sonoluminescence. The high pressure in the last phase of the bubble collapse leads to the emission of a shock wave, which is launched with a shock velocity of almost 4000 m/s. The shock amplitude decays much faster than approximately 1/r. From the strongly nonlinear propagation the pressure in the vicinity of the bubble can be calculated to be in the range of 40-60 kbar.     

激波作用下SF6气泡界面演化和射流发展的数值模拟

 数值研究了平面激波冲击氮气环境中SF₆气泡界面的Richtmyer-Meshkov不稳定性,重点关注其中的激波聚焦及射流的产生和发展过程。在入射激波马赫数为1.23的情况下,给出了压力、密度、数值纹影和涡量等物理量的演化图像,定量分析了流场中压力最大值、密度最大值、射流速度、环量和斜压力矩随时间的变化关系。计算结果表明,平面激波冲击SF₆气泡过程有很强的聚能效应,在气泡内部靠近下游极点处发生激波近似理想聚焦和点爆炸现象,直接导致出现二次波系以及向下游运动的细长射流结构。相比入射激波,二次波系产生斜压力矩和涡量的能力要弱得多。     

Focusing of an oscillating shock wave emitted by a toroidal bubble cloud

An analysis of pressure-field dynamics is performed for an axially symmetric problem of interaction between a shock wave and a “free” bubble system (toroidal cluster) giving rise to a steady oscillating shock wave. The results of a numerical study of near-axis wave structure are presented for a focusing shock wave emitted by a bubble cluster. It is shown that the wave reflected from the axis has irregular structure. The Mach disk developing on the axis has a core of finite thickness with a nonuniform radial pressure distribution. The evolution of the Mach-disk core is analyzed, and the maximum pressure in the core is computed as a function of the gas volume fraction in the cluster. The effect of geometric parameters of the toroidal bubble cloud on the cumulative effect is examined.     

Interaction of strong converging shock wave with SF6gas bubble

Interaction of a strong converging shock wave with an SF6 gas bubble is studied, focusing on the effects of shock intensity and shock shape on interface evolution. Experimentally, the converging shock wave is generated by shock dynamics theory and the gas bubble is created by soap film technique. The post-shock flow field is captured by a schlieren photography combined with a high-speed video camera. Besides, a three-dimensional program is adopted to provide more details of flow field. After the strong converging shock wave impact, a wide and pronged outward jet, which differs from that in planar shock or weak converging shock condition, is derived from the downstream interface pole. This specific phenomenon is considered to be closely associated with shock intensity and shock curvature. Disturbed by the gas bubble, the converging shocks approaching the convergence center have polygonal shapes, and the relationship between shock intensity and shock radius verifies the applicability of polygonal converging shock theory. Subsequently, the motion of upstream point is discussed, and a modified nonlinear theory considering rarefaction wave and high amplitude effects is proposed. In addition, the effects of shock shape on interface morphology and interface scales are elucidated. These results indicate that the shape as well as shock strength plays an important role in interface evolution.     

Modified shock waves for extracorporeal shock wave lithotripsy: a simulation based on the Gilmore formulation

Extracorporeal shock wave lithotripsy (SWL) is a reliable therapy for the treatment of urolithiasis. Nevertheless, improvements to enhance stone fragmentation and reduce tissue damage are still needed. During SWL, cavitation is one of the most important stone fragmentation mechanisms. Bubbles with a diameter between about 7 and 55 μm have been reported to expand and collapse after shock wave passage, forming liquid microjets at velocities of up to 400 m/s that contribute to the pulverization of renal calculi. Several authors have reported that the fragmentation efficiency may be improved by using tandem shock waves. Tandem SWL is based on the fact that the collapse of a bubble can be intensified if a second shock wave arrives tenths or even a few hundredths of microseconds before its collapse. The object of this study is to determine if tandem pulses consisting of a conventional shock wave (estimated rise time between 1 and 20 ns), followed by a slower second pressure profile (0.8 μs rise time), have advantages over conventional tandem SWL. The Gilmore equation was used to simulate the influence of the modified pressure field on the dynamics of a single bubble immersed in water and compare the results with the behavior of the same bubble subjected to tandem shock waves. The influence of the delay between pulses on the dynamics of the collapsing bubble was also studied for both conventional and modified tandem waves. For a bubble of 0.07 mm, our results indicate that the modified pressure profile enhances cavitation compared to conventional tandem waves at a wide range of delays (10-280 μs). According to this, the proposed pressure profile could be more efficient for SWL than conventional tandem shock waves. Similar results were obtained for a ten times smaller bubble.     

Interaction of strong converging shock wave with SF<Subscript>6</Subscript> gas bubble

Interaction of a strong converging shock wave with an SF₆ gas bubble is studied, focusing on the effects of shock intensity and shock shape on interface evolution. Experimentally, the converging shock wave is generated by shock dynamics theory and the gas bubble is created by soap film technique. The post-shock flow field is captured by a schlieren photography combined with a high-speed video camera. Besides, a three-dimensional program is adopted to provide more details of flow field. After the strong converging shock wave impact, a wide and pronged outward jet, which differs from that in planar shock or weak converging shock condition, is derived from the downstream interface pole. This specific phenomenon is considered to be closely associated with shock intensity and shock curvature. Disturbed by the gas bubble, the converging shocks approaching the convergence center have polygonal shapes, and the relationship between shock intensity and shock radius verifies the applicability of polygonal converging shock theory. Subsequently, the motion of upstream point is discussed, and a modified nonlinear theory considering rarefaction wave and high amplitude effects is proposed. In addition, the effects of shock shape on interface morphology and interface scales are elucidated. These results indicate that the shape as well as shock strength plays an important role in interface evolution.