Shock-induced collapse of a bubble inside a deformable vessel

Collapsing behavior of spark-induced cavitation bubble in rigid tube

The phenomenon of cavitation within tubes is a common scenario in the fields of medicine and industry. This paper focuses on the effects of rigid circular tube length, diameter and the distance of bubble - tube port on the behavior of bubble in tube. The low-voltage discharge technique was utilized to induce a cavitation bubble in deionized water. The effects of rigid tube lengths, diameters, and bubble-tube port distances on the morphology of bubbles are observed using high-speed camera. It has been found that as the length of the rigid tube increases, so does the period, and this effect is more pronounced in tubes with smaller diameters. Conversely, the cavitation bubble period decreased and then stabilized as the tube diameter increased, the ratio of tube radius and the bubble radius exceeds 4.8, the period of bubble in tube is similar to that of bubble in free field. Further analysis of the influence of tube characteristics on microjets reveals that a pair of oppositely microjets were formed along the tube axis by the bubble near the midpoint of the tube axis. Moreover, when the non-dimensional tube length η < 3.5, the increase tube diameter results in a decrease microjet velocity. It has also been observed that as the bubble gradually approaches the interior of the tube, the velocity of microjets directed inward decreases. Additionally, the smaller the diameter of the tube, the greater the bubble-tube port distance required for the microjets to reach the same level of velocity as bubble near the center of the tube axis. These findings hold theoretical implications for improvement of targeted drug delivery efficiency in medicine and enhance the operational efficiency of inertial micropumps in industries.

Investigation of the ultrasound-induced collapse of air bubbles near soft materials

A numerical investigation into the ultrasound-induced collapse of air bubbles near soft materials, utilizing a novel multi-material diffuse interface method (DIM) model with block-structured adaptive mesh refinement is presented. The present work expands from a previous five-equation DIM by incorporating Eulerian hyperelasticity. The model is applicable to any arbitrary number of interacting fluid and solid material. A single conservation law for the elastic stretch tensor enables tracking the deformations for all the solid materials. A series of benchmark cases are conducted, and the solution is found to be in excellent agreement against theoretical data. Subsequently, the ultrasound-induced bubble-tissue flow interactions are examined. The bubble radius was found to play a crucial role in dictating the stresses experienced by the tissue, underscoring its significance in medical applications. The results reveal that soft tissues primarily experience tensile forces during these interactions, suggesting potential tensile-driven injuries that may occur in relevant treatments. Moreover, regions of maximal tensile forces align with tissue elongation areas. It is documented that while early bubble dynamics remain relatively unaffected by changes in shear modulus, at later stages of the penetration processes and the deformation shapes, exhibit notable variations. Lastly, it is demonstrated that decreasing standoff distances enhances the interaction between bubbles and tissue, thereby increasing the stress levels in the tissue, although the behavior of the bubble dynamics remains largely unchanged.

Numerical investigation of acoustic cavitation and viscoelastic tissue deformation

Acoustic cavitation and tissue deformation are studied by modifying a level-set method for compressible two-phase flows to consider viscoelastic tissue deformation. The numerical simulations performed using different shear moduli and bubble-tissue distances demonstrate various interactions between bubble and viscoelastic tissue, including inverted cone-shape bubbles, bubble migration, liquid jet formation, compressive and expansive tissue deformation, and tissue perforation. The bubble is observed to grow larger with increasing tissue bulk modulus and density. The maximum tissue deformation generally increases with decreasing initial bubble-tissue distance and with increasing tissue bulk modulus and density. The tissue shear modulus conditions that maximize tissue deformation are in the range of 1-10 MPa, unless the tissue density is very large.

Experimental study on damage mechanism of blood vessel by cavitation bubbles

Ultrasound-induced cavitation in blood vessels is a common scenario in medical procedures. This paper focuses on understanding the mechanism of microscopic damage to vessel walls caused by the evolution of cavitation bubbles within the vessels. In this study, cavitation bubbles were generated using the low-voltage discharge method in 0.9% sodium chloride saline, and vessel models with wall thicknesses ranging from 0.7 mm to 2 mm were made using a 3D laminating process. The interaction between cavitation bubbles and vessel models with different wall thicknesses was observed using a combination of high-speed photography. Results show that cavitation bubble morphology and collapse time increased and then stabilized as the vessel wall thickness increased. When the cavitation bubble was located in vessel axial line, pair of opposing micro-jets were formed along the axis of the vessel, and the peak of micro-jet velocity decreased with increasing wall thickness. However, when the cavitation bubble deviated from the vessel model center, no micro-jet towards the vessel model wall was observed. Further analysis of the vessel wall deformation under varying distances from the cavitation bubble to the vessel wall revealed that the magnitude of vessel wall stretch due to the cavitation bubble expansion was greater than that of the contraction. A comparative analysis of the interaction of between the cavitation bubble and different forms of elastic membranes showed that the oscillation period of the cavitation bubble under the influence of elastic vessel model was lower than the elastic membrane. Furthermore, the degree of deformation of elastic vessel models under the expansion of the cavitation bubble was smaller than that of elastic membranes, whereas the degree of deformation of elastic vessel models in the contraction phase of the cavitation bubble was larger than that of elastic membranes. These new findings provide important theoretical insights into the microscopic mechanisms of blood vessel potential damage caused by ultrasound-induced cavitation bubble, as well as cavitation in pipelines in hydrodynamic systems.

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.

MFC: An open-source high-order multi-component, multi-phase, and multi-scale compressible flow solver

MFC is an open-source tool for solving multi-component, multi-phase, and bubbly compressible flows. It is capable of efficiently solving a wide range of flows, including droplet atomization, shock-bubble interaction, and bubble dynamics. We present the 5- and 6-equation thermodynamically-consistent diffuse-interface models we use to handle such flows, which are coupled to high-order interface-capturing methods, HLL-type Riemann solvers, and TVD time-integration schemes that are capable of simulating unsteady flows with strong shocks. The numerical methods are implemented in a flexible, modular framework that is amenable to future development. The methods we employ are validated via comparisons to experimental results for shock-bubble, shock-droplet, and shock-water-cylinder interaction problems and verified to be free of spurious oscillations for material-interface advection and gas-liquid Riemann problems. For smooth solutions, such as the advection of an isentropic vortex, the methods are verified to be high-order accurate. Illustrative examples involving shock-bubble-vessel-wall and acoustic-bubble-net interactions are used to demonstrate the full capabilities of MFC.

Shock-Induced Damage and Dynamic Fracture in Cylindrical Bodies Submerged in Liquid

Understanding the response of solid materials to shock loading is important for mitigating shock-induced damages and failures, as well as advancing the beneficial use of shock waves for material modifications. In this paper, we consider a representative brittle material, BegoStone, in the form of cylindrical bodies and submerged in water. We present a computational study on the causal relationship between the prescribed shock load and the resulting elastic waves and damage in the solid material. A recently developed three-dimensional computational framework, FIVER, is employed, which couples a finite volume compressible fluid solver with a finite element structural dynamics solver through the construction and solution of local, one-dimensional fluid-solid Riemann problems. The material damage and fracture are modeled and simulated using a continuum damage mechanics model and an element erosion method. The computational model is validated in the context of shock wave lithotripsy and the results are compared with experimental data. We first show that after calibrating the growth rate of microscopic damage and the threshold for macroscopic fracture, the computational framework is capable of capturing the location and shape of the shock-induced fracture observed in a laboratory experiment. Next, we introduce a new phenomenological model of shock waveform, and present a numerical parametric study on the effects of a single shock load, in which the shock waveform, magnitude, and the size of the target material are varied. In particular, we vary the waveform gradually from one that features non-monotonic decay with a tensile phase to one that exhibits monotonic decay without a tensile phase. The result suggests that when the length of the shock pulse is comparable to that of the target material, the former waveform may induce much more significant damage than the latter one, even if the two share the same magnitude, duration, and acoustic energy.

Modelling cavitation during drop impact on solid surfaces

The impact of liquid droplets on solid surfaces at conditions inducing cavitation inside their volume has rarely been addressed in the literature. A review is conducted on relevant studies, aiming to highlight the differences from non-cavitating impact cases. Focus is placed on the numerical models suitable for the simulation of droplet impact at such conditions. Further insight is given from the development of a purpose-built compressible two-phase flow solver that incorporates a phase-change model suitable for cavitation formation and collapse; thermodynamic closure is based on a barotropic Equation of State (EoS) representing the density and speed of sound of the co-existing liquid, gas and vapour phases as well as liquid-vapour mixture. To overcome the known problem of spurious oscillations occurring at the phase boundaries due to the rapid change in the acoustic impedance, a new hybrid numerical flux discretization scheme is proposed, based on approximate Riemann solvers; this is found to offer numerical stability and has allowed for simulations of cavitation formation during drop impact to be presented for the first time. Following a thorough justification of the validity of the model assumptions adopted for the cases of interest, numerical simulations are firstly compared against the Riemann problem, for which the exact solution has been derived for two materials with the same velocity and pressure fields. The model is validated against the single experimental data set available in the literature for a 2-D planar drop impact case. The results are found in good agreement against these data that depict the evolution of both the shock wave generated upon impact and the rarefaction waves, which are also captured reasonably well. Moreover, the location of cavitation formation inside the drop and the areas of possible erosion sites that may develop on the solid surface, are also well captured by the model. Following model validation, numerical experiments have examined the effect of impact conditions on the process, utilizing both planar and 2-D axisymmetric simulations. It is found that the absence of air between the drop and the wall at the initial configuration can generate cavitation regimes closer to the wall surface, which significantly increase the pressures induced on the solid wall surface, even for much lower impact velocities. A summary highlighting the open questions still remaining on the subject is given at the end.

Multiphase fluid-solid coupled analysis of shock-bubble-stone interaction in shockwave lithotripsy

A novel multiphase fluid-solid-coupled computational framework is applied to investigate the interaction of a kidney stone immersed in liquid with a lithotripsy shock wave (LSW) and a gas bubble near the stone. The main objective is to elucidate the effects of a bubble in the shock path to the elastic and fracture behaviors of the stone. The computational framework couples a finite volume 2-phase computational fluid dynamics solver with a finite element computational solid dynamics solver. The surface of the stone is represented as a dynamic embedded boundary in the computational fluid dynamics solver. The evolution of the bubble surface is captured by solving the level set equation. The interface conditions at the surfaces of the stone and the bubble are enforced through the construction and solution of local fluid-solid and 2-fluid Riemann problems. This computational framework is first verified for 3 example problems including a 1D multimaterial Riemann problem, a 3D shock-stone interaction problem, and a 3D shock-bubble interaction problem. Next, a series of shock-bubble-stone-coupled simulations are presented. This study suggests that the dynamic response of a bubble to LSW varies dramatically depending on its initial size. Bubbles with an initial radius smaller than a threshold collapse within 1 μs after the passage of LSW, whereas larger bubbles do not. For a typical LSW generated by an electrohydraulic lithotripter (p_max  = 35.0MPa, p_min  =- 10.1MPa), this threshold is approximately 0.12mm. Moreover, this study suggests that a noncollapsing bubble imposes a negative effect on stone fracture as it shields part of the LSW from the stone. On the other hand, a collapsing bubble may promote fracture on the proximal surface of the stone, yet hinder fracture from stone interior.

Spiral computed tomography evaluation of rabbit VX2 hepatic tumors treated with 20 kHz ultrasound and microbubbles

The aim of the present study was to explore the therapeutic effect of 20 kHz ultrasound (US) and microbubbles (MBs) on rabbit VX2 liver tumors by spiral computed tomography (CT) scanning. A total of 16 New Zealand rabbits with hepatic VX2 tumors were divided into four groups: Control, MB, low-frequency US and US + MB. The treatment effect was evaluated by spiral CT scanning prior to, during and following treatment (at 0 weeks and the end of 1 and 2 weeks). The tumor growth rate was recorded. The specimens of VX2 tumors were collected for histological examination and transmission electron microscopy (TEM). No significant differences were observed between tumor areas measured by CT and pathology after 2-week treatment (P>0.05). The mean tumor growth rates in the control, MB, US and US + MB groups after 2 weeks of treatment were 385±21, 353±12, 302±14 and 154±9%, respectively (P<0.05, US + MB vs. the other three groups). Hematoxylin and eosin staining in the US + MB group revealed coagulation necrosis, interstitial hemorrhage and intravascular thrombosis. In the control, MB and US groups, tumor cells exhibited clear nuclear hyperchromatism. TEM of US + MB revealed vascular endothelial cell wall rupture, widened endothelial cell gaps, interstitial erythrocyte leakage and microvascular thrombosis, while intact vascular endothelial cells and normal erythrocytes in the tumor vessels were observed in the control, MB and US groups. A combination of 20 kHz US and MBs may effectively inhibit rabbit VX2 tumors. Spiral CT scanning is an ideal method to evaluate the US treatment on rabbit tumors.

Low-frequency ultrasound-mediated microvessel disruption combined with docetaxel to treat prostate carcinoma xenografts in nude mice: A novel type of chemoembolization

The aim of the present study was to investigate whether low-frequency ultrasound (US)-mediated microvessel disruption combined with docetaxel (DTX) can be used as a novel type of chemoembolization. Mice were assigned to four groups: i) The USMB group, treated with low-frequency US combined with microbubbles (USMB); ii) the DTX group, treated with DTX; iii) the USMB + DTX group, treated with combined therapy; and iv) the control group, which was untreated. Immediately after the first treatment, the average peak intensity (API) on contrast-enhanced US was calculated, and tumors were excised for hematoxylin and eosin (HE) staining. At 2 weeks post-treatment, the tumor volumes and wet weights were calculated, and tumors were excised for immunohistochemistry to calculate apoptotic index (AI), proliferative index (PI) and microvessel density (MVD) values. Immediately after the first treatment, in the DTX and control groups, the tumors demonstrated abundant perfusion enhancement, while in the USMB + DTX and USMB groups, blood perfusion of the tumors was interrupted. Compared with that of the control group, the API was significantly lower in the USMB + DTX USMB groups (all P<0.001). HE staining showed that tumor microvasculature was disrupted into flaky hematomas and severely dilated microvessels in the USMB + DTX and USMB groups. In the DTX and control groups, there was no distinct evidence of the disruption and dilation of blood microvessels. At the end of the treatment, the mean tumor inhibition ratio was 73.33, 46.67 and 33.33% for the USMB + DTX, DTX and USMB groups, respectively. The USMB + DTX group had the highest AI, and the lowest PI and MVD compared with the other groups, although the difference between the USMB + DTX and DTX groups with regard to PI and MVD was not significant (USMB + DTX vs. DTX group, P=0.345 and P=0.059, respectively). In conclusion, as a novel type of chemoembolization, USMB combined with DTX is more effective than USMB or DTX alone in inhibiting tumor growth via the enhancement of apoptosis, and the suppression of proliferation and angiogenesis.

Review on Lithotripsy and Cavitation in Urinary Stone Therapy

Cavitation is the sudden formation of vapor bubbles or voids in liquid media and occurs after rapid changes in pressure as a consequence of mechanical forces. It is mostly an undesirable phenomenon. Although the elimination of cavitation is a major topic in the study of fluid dynamics, its destructive nature could be exploited for therapeutic applications. Ultrasonic and hydrodynamic sources are two main origins for generating cavitation. The purpose of this review is to give the reader a general idea about the formation of cavitation phenomenon and existing biomedical applications of ultrasonic and hydrodynamic cavitation. Because of the high number of the studies on ultrasound cavitation in the literature, the main focus of this review is placed on the lithotripsy techniques, which have been widely used for the treatment of urinary stones. Accordingly, cavitation phenomenon and its basic concepts are presented in Section II. The significance of the ultrasound cavitation in the urinary stone treatment is discussed in Section III in detail and hydrodynamic cavitation as an important alternative for the ultrasound cavitation is included in Section IV. Finally, side effects of using both ultrasound and hydrodynamic cavitation in biomedical applications are presented in Section V.

Low-frequency and low-intensity ultrasound-mediated microvessel disruption enhance the effects of radiofrequency ablation on prostate cancer xenografts in nude mice

The aim of the present study was to examine the impact of low-frequency, low-intensity ultrasound (US)-stimulated microbubbles (USMB) on radiofrequency ablation (RFA) in the treatment of nude mice with human prostate cancer xenografts. The tumor‑bearing nude mice were divided into three groups: The USMB+RFA group was treated with USMB immediately followed by RFA, the RFA group was treated with RFA alone, and the control group remained untreated. The animals underwent enhanced US to calculate the tumor volumes, ablation volumes and ablation rates. Subsequently, the tumors were excised for hematoxylin and eosin staining, to identify necrosis in the tumors following the treatments, and immunohistochemical staining, to analyze the apoptotic index (AI), proliferative index (PI) and microvessel density (MVD) at 1, 4 and 7 days post-treatment. Each group contained five mice at each time‑point. Necrosis was apparent in the center of the tumors in the treatment groups. Ablation lesion volumes of the USMB+RFA group were larger than those in the RFA group at 1 and 4 days post‑treatment (P=0.002 and P=0.022, respectively), and the ablation rates of the USMB+RFA group were significantly higher, compared with the RFA group at the three time‑points (all P<0.001). There were fewer apoptotic cells and more proliferative cells in the RFA group, compared with the control group 1,4 and 7 days post‑treatment (all P<0.05). The AI of the USMB+RFA group was higher than that of the control group and lower than that of the RFA group 1 day post-treatment (P=0.034 and P=0.016, respectively). The PI of the USMB+RFA group was lower than that of the control group and higher than that of the RFA group 4 and 7 days post-treatment (all P<0.05). No significant differences were observed in MVD among the three groups throughout the experiment. In conclusion, exposure to USMB prior to RFA produced larger volumes of ablation, compared with treatment with RFA alone, and increased AI and reduced PI in the residual carcinoma cells induced by RFA.

Optimization of low-frequency low-intensity ultrasound-mediated microvessel disruption on prostate cancer xenografts in nude mice using an orthogonal experimental design

The present study aimed to provide a complete exploration of the effect of sound intensity, frequency, duty cycle, microbubble volume and irradiation time on low-frequency low-intensity ultrasound (US)-mediated microvessel disruption, and to identify an optimal combination of the five factors that maximize the blockage effect. An orthogonal experimental design approach was used. Enhanced US imaging and acoustic quantification were performed to assess tumor blood perfusion. In the confirmatory test, in addition to acoustic quantification, the specimens of the tumor were stained with hematoxylin and eosin and observed using light microscopy. The results revealed that sound intensity, frequency, duty cycle, microbubble volume and irradiation time had a significant effect on the average peak intensity (API). The extent of the impact of the variables on the API was in the following order: Sound intensity; frequency; duty cycle; microbubble volume; and irradiation time. The optimum conditions were found to be as follows: Sound intensity, 1.00 W/cm²; frequency, 20 Hz; duty cycle, 40%; microbubble volume, 0.20 ml; and irradiation time, 3 min. In the confirmatory test, the API was 19.97±2.66 immediately subsequent to treatment, and histological examination revealed signs of tumor blood vessel injury in the optimum parameter combination group. In conclusion, the Taguchi L₁₈ (3)⁶ orthogonal array design was successfully applied for determining the optimal parameter combination of API following treatment. Under the optimum orthogonal design condition, a minimum API of 19.97±2.66 subsequent to low-frequency and low-intensity mediated blood perfusion blockage was obtained.

Finite-volume WENO scheme for viscous compressible multicomponent flows

We develop a shock- and interface-capturing numerical method that is suitable for the simulation of multicomponent flows governed by the compressible Navier-Stokes equations. The numerical method is high-order accurate in smooth regions of the flow, discretely conserves the mass of each component, as well as the total momentum and energy, and is oscillation-free, i.e. it does not introduce spurious oscillations at the locations of shockwaves and/or material interfaces. The method is of Godunov-type and utilizes a fifth-order, finite-volume, weighted essentially non-oscillatory (WENO) scheme for the spatial reconstruction and a Harten-Lax-van Leer contact (HLLC) approximate Riemann solver to upwind the fluxes. A third-order total variation diminishing (TVD) Runge-Kutta (RK) algorithm is employed to march the solution in time. The derivation is generalized to three dimensions and nonuniform Cartesian grids. A two-point, fourth-order, Gaussian quadrature rule is utilized to build the spatial averages of the reconstructed variables inside the cells, as well as at cell boundaries. The algorithm is therefore fourth-order accurate in space and third-order accurate in time in smooth regions of the flow. We corroborate the properties of our numerical method by considering several challenging one-, two- and three-dimensional test cases, the most complex of which is the asymmetric collapse of an air bubble submerged in a cylindrical water cavity that is embedded in 10% gelatin.