Shock wave–bubble interaction near soft and rigid boundaries during lithotripsy: numerical analysis by the improved ghost fluid method

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.

Numerical investigation of two-microbubble collapse and cell deformation in an ultrasonic field

Two-microbubble collapse near a spherical cell in an ultrasonic field is numerically analyzed by extending a level-set method for compressible multiphase flows with bubble and cell multiple interfaces. Computations performed with different bubble-bubble distances and size ratios demonstrate various bubble-bubble interactions, such as bubble coalescence, bubble repulsion and attraction, jet penetration into the bubble, and jet collision. The interactions between collapsing bubbles are found to produce strong liquid jet formation and result in significant cell deformation compared to single-bubble collapse. The optimal bubble-bubble distance and size ratio for cell deformation are presented via contour maps based on extensive computations. The influences of the ultrasonic amplitude and frequency on cell deformation are further investigated.

Bubble dynamic evolution, material strengthening and chemical effect induced by laser cavitation peening

The mechanism of laser cavitation peening (LCP) including laser shock wave, bubble collapse shock wave, and water-jet was investigated at various stand-off distances (γ) combined with experiment and simulation. The dynamic characteristics, pressure field, and temperature field of cavitation bubble were investigated. The Q235 steel was impacted by LCP and the strengthening mechanism was analyzed, and the chemical effect in LCP was discussed. The results found that the pressure intensity of shock wave and water-jet decreases with increasing the γ. At γ=0, the laser shock wave, bubble collapse shock wave, and water-jet are 989 Mpa, 763 Mpa, and 369 Mpa respectively. The pressure and temperature of the bubble decrease obviously in the second and third pulsations. The impact of LCP causes plastic deformation on the Q235 steel surface and refines the grains on the surface layer within a depth of 20-30 μm. The enhancement of microhardness and the residual stress increases with the increase of γ, and the optimal value for LCPwc is 0.4. The degradation rate of MB solution in the infinite domain, LCPwc, and LCP is 26.4%, 41.7%, and 34.5%.

A simple model of bubble cluster dynamics in an acoustic field

The dynamics of bubble clouds induced by ultrasound field are investigated in a regime where the cloud size is much smaller than the ultrasound wavelength. Two frequently used models describing the dynamics of individual bubbles inside a bubble cluster in an acoustic field are studied, one based on the homogeneity assumption, and the other based on the simultaneous motion assumption. A modified formula of the homogenization-based model is presented, and an inherent distinction in bubble-bubble interaction term is found in comparison to the simultaneous motion model. To gain insight into the mechanisms of such distinction, a reduced model unifying these two models is presented, and such distinction is explained by the spatial dependence of the bubble-bubble interaction in a bubble cluster accordingly. To validate the reduced model, the normalized distance γ_bb and the cloud interaction parameter B₀ are used as two scaling parameters, and the comparison between the present model and the coupled Rayleigh-Plesset type equations is made. A conclusion is that, in the weak bubble-bubble interaction case (γ_bb>10), the reduced model can well reproduce the radial motion of bubbles in the cluster during the growth stage and the collapse stage in each acoustic cycle; in the strong bubble-bubble interaction case (γ_bb<10), the growth phase of bubbles in the cluster can be accurately predicted by the reduced model only if B₀ or the amplitude of driving field is small.

High-speed video microscopy and numerical modeling of bubble dynamics near a surface of urinary stone

Ultra-high-speed video microscopy and numerical modeling were used to assess the dynamics of microbubbles at the surface of urinary stones. Lipid-shell microbubbles designed to accumulate on stone surfaces were driven by bursts of ultrasound in the sub-MHz range with pressure amplitudes on the order of 1 MPa. Microbubbles were observed to undergo repeated cycles of expansion and violent collapse. At maximum expansion, the microbubbles' cross-section resembled an ellipse truncated by the stone. Approximating the bubble shape as an oblate spheroid, this study modeled the collapse by solving the multicomponent Euler equations with a two-dimensional-axisymmetric code with adaptive mesh refinement for fine resolution of the gas-liquid interface. Modeled bubble collapse and high-speed video microscopy showed a distinctive circumferential pinching during the collapse. In the numerical model, this pinching was associated with bidirectional microjetting normal to the rigid surface and toroidal collapse of the bubble. Modeled pressure spikes had amplitudes two-to-three orders of magnitude greater than that of the driving wave. Micro-computed tomography was used to study surface erosion and formation of microcracks from the action of microbubbles. This study suggests that engineered microbubbles enable stone-treatment modalities with driving pressures significantly lower than those required without the microbubbles.

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.

Numerical studies of cavitation erosion on an elastic–plastic material caused by shock-induced bubble collapse

We present a study of shock-induced collapse of single bubbles near/attached to an elastic–plastic solid using the free-Lagrange method, which forms the latest part of our shock-induced collapse studies. We simulated the collapse of 40 μm radius single bubbles near/attached to rigid and aluminium walls by a 60 MPa lithotripter shock for various scenarios based on bubble–wall separations, and the collapse of a 255 μm radius bubble attached to aluminium foil with a 65 MPa lithotripter shock. The coupling of the multi-phases, compressibility, axisymmetric geometry and elastic–plastic material model within a single solver has enabled us to examine the impingement of high-speed liquid jets from the shock-induced collapsing bubbles, which imposes an extreme compression in the aluminium that leads to pitting and plastic deformation. For certain scenarios, instead of the high-speed jet, a radially inwards flow along the aluminium surface contracts the bubble to produce a ‘mushroom shape’. This work provides methods for quantifying which parameters (e.g. bubble sizes and separations from the solid) might promote or inhibit erosion on solid surfaces.

Predicting the effectiveness of extracorporeal shock wave lithotripsy on urinary tract stones. Risk groups for accurate retreatment

INTRODUCTION

Extracorporeal shock wave lithotripsy (ESWL) is a non-invasive, safe and effective treatment for urinary tract lithiasis. Its effectiveness varies depending on the location and size of the stones as well as other factors; several sessions are occasionally required. The objective is to attempt to predict its success or failure, when the influential variables are known beforehand.

MATERIAL AND METHODS

We analysed 211 patients who had had previous CT scans and were treated with ESWL between 2010 and 2014. The influential variables in requiring retreatment were studied using binary logistic regression models (univariate and multivariate analysis): maximum density, maximum diameter, area, location, disintegration and distance from the adipose panniculus. With the influential variables, a risk model was designed by assessing all possible combinations with logistic regression (version 20.0 IBM SPSS).

RESULTS

The independent influential variables on the need for retreatment are: maximum density >864HU, maximum diameter >7.5mm and pyelocaliceal location. Using these variables, the best model includes 3risk groups with a probability of requiring significantly different retreatment: group 1-low risk (0 variables) with 20.2%; group 2-intermediate risk (1-2 variables) with 49.2%; and group 3-high risk (3 variables) with 62.5%.

CONCLUSIONS

The density, maximum diameter and pyelocaliceal location of the stones are determinant factors in terms of the effectiveness of treatment with ESWL. Using these variables, which can be obtained in advance of deciding on a treatment, the designed risk model provides a precise approach in choosing the most appropriate treatment for each particular case.

Shock-induced collapse of a bubble inside a deformable vessel

Shockwave lithotripsy repeatedly focuses shockwaves on kidney stones to induce their fracture, partially through cavitation erosion. A typical side effect of the procedure is hemorrhage, which is potentially the result of the growth and collapse of bubbles inside blood vessels. To identify the mechanisms by which shock-induced collapse could lead to the onset of injury, we study an idealized problem involving a preexisting bubble in a deformable vessel. We utilize a high-order accurate, shock- and interface-capturing, finite-volume scheme and simulate the three-dimensional shock-induced collapse of an air bubble immersed in a cylindrical water column which is embedded in a gelatin/water mixture. The mixture is a soft tissue simulant, 10% gelatin by weight, and is modeled by the stiffened gas equation of state. The bubble dynamics of this model configuration are characterized by the collapse of the bubble and its subsequent jetting in the direction of the propagation of the shockwave. The vessel wall, which is defined by the material interface between the water and gelatin/water mixture, is invaginated by the collapse and distended by the impact of the jet. The present results show that the highest measured pressures and deformations occur when the volumetric confinement of the bubble is strongest, the bubble is nearest the vessel wall and/or the angle of incidence of the shockwave reduces the distance between the jet tip and the nearest vessel surface. For a particular case considered, the 40 MPa shockwave utilized in this study to collapse the bubble generated a vessel wall pressure of almost 450 MPa and produced both an invagination and distention of nearly 50% of the initial vessel radius on a 𝒪(10) ns timescale. These results are indicative of the significant potential of shock-induced collapse to contribute to the injury of blood vessels in shockwave lithotripsy.