No abstract

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.

A numerical investigation has been conducted to explore the complex nonlinear nature of flow in a backward-facing step channel by the simulated results, which include the bifurcation diagram, limit cycle oscillations, power spectrums, and phase portraits. For small values of Reynolds number, the flow was steady and laminar. When the Reynolds number was amplified, the flow becomes unsteady with the initiation of a supercritical Hopf bifurcation. The flow path is trapped by the stable limit cycles, and this system is made to proceed with a sustained oscillation. As the Reynolds number was amplified further, the stability of the investigated system keeps decreasing through a sequence of frequency-doubling bifurcations. The fundamental frequency of high amplitude was identical to the most amplified mode of Kelvin-Helmholtz instability oscillations in the shear layer. Frequencies with a small amplitude result in a slower development of the Kelvin-Helmholtz instability and are responsible for the roll-up of the shear layer. The phase portrait shows the evolution of a chaotic attractor from a simple periodic attractor. Prior to the onset of the chaotic motion, pitchfork bifurcation showed its existence.

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.