Simulation of cavitation enhanced temperature elevation in a soft tissue during high-intensity focused ultrasound thermal therapy

The present study aims to investigate temperature distribution caused by bubble oscillations in a soft tissue during focused ultrasound therapy by introducing a coupled temperature-cavitation model. The proposed model is capable of describing bubble dynamics, viscoelastic properties of surrounding tissue-like medium, temperature distribution inside and outside the bubble, vapor diffusion within the bubble and vapor flux through the bubble wall to the exterior. The continuous temperature distribution inside and outside the oscillating bubble in soft tissue subject to ultrasound wave with high acoustic pressure is presented. The temperature close to the bubble wall can reach the value of about 10³ K. The elasticity of soft tissue reduces temperature values. The relaxation time effect strongly depends on the period of the ultrasound wave. If the vapor mass flux effect is taken into account in the simulations, the rectified growth effect can be observed, which can lead to the decrease of the temperature values. Due to the growth of the bubble, the effects of elasticity and relaxation time on the temperature become less prominent during several bubble oscillation cycles. The impact of cavitation heat source terms on the exterior temperature was examined and led us to draw conclusion that, even though these heat sources can increase the outside temperature values, they can not be treated as main mechanisms for the temperature elevation during a few microseconds. The performed comparison with uncoupled conventional model for the outside temperature calculation revealed that coupling with inside temperature model delivers incomparably higher values to the bubble's exterior and, therefore, it is essential for the accurate description of the treatment process.

Dynamics of bubble-bubble interactions experiencing viscoelastic drag

The subject of the present theoretical study is the dynamics of bubble-bubble interactions in a viscoelastic medium. First, new equations for calculating the viscoelastic drag exerted on bubbles during their translational motion in a viscoelastic medium are derived. The drag equations are incorporated in the bubble-bubble interaction model in which, thereby, both the translational and radial motions of the bubbles are affected by the viscoelastic features of the medium. Second, the derived equations are applied to investigate how the viscoelastic properties of the medium can affect the dynamics of multiple bubbles, as well as how the bubbles can affect each other. It was discovered that the bubble-bubble interaction can significantly influence the dynamics of a single bubble. As the distance between the bubbles increases, their effect on each other decreases, and at a distance of several millimeters, this effect can be neglected. Moreover, it was concluded that with increasing elasticity and viscosity of the medium, as well with decreasing relaxation time, the effects of other bubbles on the current bubble's radial motion can become negligible. The translational motion of the bubbles was investigated for different viscoelastic models. The elasticity resists the motion of bubbles in space, resulting in a dynamical steady state of the distance between the bubbles at high elasticity values. The relaxation time of the medium was also found to be important in terms of the bubbles' translational movement.

Bubble dynamics in viscoelastic soft tissue in high-intensity focal ultrasound thermal therapy

The present study is aimed to investigate bubble dynamics in a soft tissue, to which HIFU's continuous harmonic pulse is applied by introducing a viscoelastic cavitation model. After a comparison of some existing cavitation models, we decided to employ Gilmore-Akulichev model. This chosen cavitation model should be coupled with the Zener viscoelastic model in order to be able to simulate soft tissue features such as elasticity and relaxation time. The proposed Gilmore-Akulichev-Zener model was investigated for exploring cavitation dynamics. The parametric study led us to the conclusion that the elasticity and viscosity both damp bubble oscillations, whereas the relaxation effect depends mainly on the period of the ultrasound wave. The similar influence of elasticity, viscosity and relaxation time on the temperature inside the bubble can be observed. Cavitation heat source terms (corresponding to viscous damping and pressure wave radiated by bubble collapse) were obtained based on the proposed model to examine the cavitation significance during the treatment process. Their maximum values both overdominate the acoustic ultrasound term in HIFU applications. Elasticity was revealed to damp a certain amount of deposited heat for both cavitation terms.

Refined energy-conserving dissipative particle dynamics model with temperature-dependent properties and its application in solidification problem

It has been observed previously that the physical behaviors of Schmidt number (Sc) and Prandtl number (Pr) of an energy-conserving dissipative particle dynamics (eDPD) fluid can be reproduced by the temperature-dependent weight function appearing in the dissipative force term. In this paper, we proposed a simple and systematic method to develop the temperature-dependent weight function in order to better reproduce the physical fluid properties. The method was then used to study a variety of phase-change problems involving solidification. The concept of the "mushy" eDPD particle was introduced in order to better capture the temperature profile in the vicinity of the solid-liquid interface, particularly for the case involving high thermal conductivity ratio. Meanwhile, a way to implement the constant temperature boundary condition at the wall was presented. The numerical solutions of one- and two-dimensional solidification problems were then compared with the analytical solutions and/or experimental results and the agreements were promising.

Simulation of nonlinear Westervelt equation for the investigation of acoustic streaming and nonlinear propagation effects

This study investigates the influence of blood flow on temperature distribution during high-intensity focused ultrasound (HIFU) ablation of liver tumors. A three-dimensional acoustic-thermal-hydrodynamic coupling model is developed to compute the temperature field in the hepatic cancerous region. The model is based on the nonlinear Westervelt equation, bioheat equations for the perfused tissue and blood flow domains. The nonlinear Navier-Stokes equations are employed to describe the flow in large blood vessels. The effect of acoustic streaming is also taken into account in the present HIFU simulation study. A simulation of the Westervelt equation requires a prohibitively large amount of computer resources. Therefore a sixth-order accurate acoustic scheme in three-point stencil was developed for effectively solving the nonlinear wave equation. Results show that focused ultrasound beam with the peak intensity 2470 W/cm(2) can induce acoustic streaming velocities up to 75 cm/s in the vessel with a diameter of 3 mm. The predicted temperature difference for the cases considered with and without acoustic streaming effect is 13.5 °C or 81% on the blood vessel wall for the vein. Tumor necrosis was studied in a region close to major vessels. The theoretical feasibility to safely necrotize the tumors close to major hepatic arteries and veins was shown.

Prediction of strong-shock structure using the bimodal distribution function

A modified Mott-Smith method for predicting the one-dimensional shock wave solution at very high Mach numbers is constructed by developing a system of fluid dynamics equations. The predicted shock solutions in a gas of Maxwell molecules, a hard-sphere gas, and in argon using the newly proposed formalism are compared with the experimental data, direct-simulation Monte Carlo (DSMC) solution, and other solutions computed from some existing theories for Mach numbers M<50. In the limit of an infinitely large Mach number, the predicted shock profiles are also compared with the DSMC solution. The density, temperature and heat flux profiles calculated at different Mach numbers have been shown to have good agreement with the experimental and DSMC solutions.

Prediction of shock structure using the bimodal distribution function

A modification of Mott-Smith method for predicting the one-dimensional shock wave solution is presented. Mott-Smith distribution function is used to construct the system of moment equations to study the steady-state structure of shock wave in a gas of Maxwell molecules and in argon. The predicted shock solutions using the newly proposed formalism are compared to the experimental data, direct-simulation Monte Carlo (DSMC) solution, and the solutions predicted by other existing theories for Mach numbers M<11 . The density, temperature, heat flux profiles, and shock thickness calculated at different Mach numbers have been shown to have good agreement with the experimental and DSMC solutions. In addition, the predicted shock thickness is in good agreement with the DSMC simulation result at low Mach numbers.

Numerical investigation of non-Newtonian microcirculatory blood flow in hepatic lobule

The circulation in the liver is unique at macroscopic and microscopic levels. At the macroscopic level, there is an unusual presence of portal and arterial inputs rather than a single arterial input. At the microscopic level, a series of microenvironments in the acinar system is essential in controlling the functional characteristics of hepatic parenchymal cells. Since the hemodynamics is much less studied in the multifunctional liver, an attempt is made to study the hepatic hemodynamics in a segment of a hepatic lobular structure, that is made up of high-pressure oxygenated arteriole, low-pressure nutrient-rich portal venule, fenestrated sinusoidal space and hepatic venule. Our goal is to dispel some of the myths of this complex vascular bed by means of finite volume blood flow simulation. Flow features like high-velocity gradients near the fenestrations, flow reversal and Dean vortices in the sinusoidal space are analyzed within the non-Newtonian framework. Since no distinct exact or numerical solutions are available for this complex vascular bed, the present simulated results are compared with the available clinical observations. Results revealed that the pressure plays a key role in hepatic blood flow.

Three-dimensional analysis for radio-frequency ablation of liver tumor with blood perfusion effect

Increase of temperature above 50 approximately 60 degrees C for few minutes by the emitted radio-frequency (RF) energy has been shown to be able to denaturate the intracellular proteins and destruct membranes of tumor cells. To improve the efficacy of this thermal therapy, it is important to investigate factors that may affect the RF heating characteristics for the hepatocellular carcinoma and metastatic liver tumors. In order to make sure the applied RF energy is adequate to ablate the target tumor, a 3D thermoelectric analysis for the system consisting of liver, liver arteries and 4 mm diameter tumor is conducted. The effect of blood perfusion is addressed in this study.

Three-dimensional simulation of square jets in cross-flow

Direct numerical simulations are performed to predict the three-dimensional unsteady flow interactions in the near-field of a square jet issuing normal to a cross-flow. The simulated flow features reveal the formation of an upstream horseshoe vortex system, which is the result of an interaction between the oncoming channel floor shear layer and the transverse jet; the growth of a sequence of Kelvin-Helmholtz instability-induced vortical rollers in the mixing layer between the jet and the cross-flow, which wrap around the front side of the jet; and the inception process of the counter-rotating vortex pair (CVP), which is initiated through the folding of the lateral jet shear layers. It has been observed that for a square jet in cross-flow, the developed Kelvin-Helmholtz instability induced shear layer rollers do not form closed circumferential vortex rings. Along the downstream side of the jet, the extended tails of such rollers gradually join the locally evolving CVP. The very inception of the CVP is, however, observed to take place within the cross-flow-induced skewed lateral jet shear layers, and such inception was seen to occur slightly below the jet orifice. The simulated results also reveal the growth of the upright wake vortices from the topological singular points that developed on the cross-flow floor boundary layer. The accumulated floor vortices are seen to spiral around the critical points and subsequently leave the channel floor uprightly. During upward motion these vortices eventually get entrained into the CVP core. It has been made clear topologically that the unstable local surface excitations are the seeds from which upright vortices grow. Interestingly, such findings remain quite consistent with the existing experimental predictions for a round jet. Simulations were performed for two moderate values of the Reynolds number 225 and 300, based on the jet width and the average cross-flow inlet velocity, and for two different values of the jet to cross-stream velocity ratio, 2.5 and 3.5.

Interaction of trailing vortices in the wake of a wall-mounted rectangular cylinder

Numerical simulations are performed to investigate three-dimensional unsteady vortex-vortex and vortex-surface interactions in the near field of a wall-mounted rectangular cylinder placed inside a channel. The generation mechanism of the upstream and the trailing vortices from the topologically important critical points and their near-wall evolution pattern have been examined in detail. In the upstream region, a laminar necklace vortex system formed around the junction between the rectangular block (cylinder) and the flat channel floor. A sequence of streamwise vortical rollers dominated the downstream interaction region, and they exhibited strong unsteady vortex-surface interaction. Streamwise vortices which formed upstream of the obstacle exhibited quadrupole structure with the dominant pair being central downwash, whereas those lifting the flow behind the obstacle were of predominantly central upwash. Notably, at some downstream location, the near-wall wake structure was observed to locally disappear due to mutual interaction and annihilation by opposite strength vortices on either side of the wake centerline. During the entire course of unsteady flow evolution, such a disappearance of the wake remained closely associated with local contraction of the limiting streamlines on the channel floor, the development of a pair of topologically important floor critical points (saddles), and the presence of a near-wall node on the vertical symmetry plane. The dominance of inward transverse flow toward these saddles together with flow evolution from the downstream node on the vertical symmetry plane were found to be particularly responsible for facilitating the local interaction of various vortices of opposite strength, leading to significant vorticity cancellation in the region. Moreover, the basic source of the wake vortices and their nature of evolution behind the cylinder were also investigated here, and they were found to be fundamentally different from what one usually observes in the near-wake of a transverse jet. However, the growth of a pair of vertically lifting vortices from the spiraling shear layer nodes just behind the downstream edge of the cylinder base was detected in this flow configuration also.

Spanwise bifurcation in plane-symmetric sudden-expansion flows

Present computational investigation reports a steady bifurcation phenomenon for three-dimensional flows through a plane-symmetric sudden expansion. When the channel aspect ratio exceeds a critical value, the well-known step height (pitchfork) bifurcation evolves with different symmetry breaking orientations on the left and right sides of the channel and bifurcates in the spanwise direction. For the channel aspect ratio less than the critical value, the originally occurring spanwise bifurcation cannot be stably retained and evolves eventually to a step height bifurcation. Compared to step height bifurcation, the spanwise bifurcation is found to be more difficult to obtain, because the symmetric flow present on the spanwise symmetry plane is unstable in two dimensions. For completeness, an extensive analysis of the observed spanwise bifurcation, covering its transient behavior, dependence on flow Reynolds number, channel aspect ratio, and expansion ratio, is included.