Lattice Boltzmann method and its application in the modelling of high intensity focused ultrasound (HIFU)

Abstract

High-intensity focused ultrasound (HIFU) is a breakthrough of noninvasive targeted therapeutic technique for tumor treatments. The operational procedure of HIFU is to concentrate the ultrasound energy into the focal region by using the ultrasound transducer, and the focused ultrasound energy is sufficient to rapidly rise the temperature of tumor located at the focal region up to above 65°C and locally destroy the tumor for coagulation necrosis. The ultrasound transducer is the key component in HIFU treatment to generate the high-intensity focused ultrasound energy, the dimension of focal region generated by the transducer is closely relevant to the safety of HIFU treatment. Therefore, it is necessary to simulate the acoustic field numerically for estimating the performance, optimizing the parameters and reducing the design cost of the focused ultrasound transducer. Besides, the common spherical transducer is the most widely used transducer in HIFU, but the size of its focal region still could not satisfy the requirements of some sophisticated applications. So, it is necessary to adopt some new kinds of focused ultrasound transducers with better focusing performance. Aiming at these issues, we presented a numerical simulation method called the lattice Boltzmann method (LBM) in this paper. It is a novel fluid dynamic simulation approach based on mesoscopic kinetic theory, which takes prominent advantages of distinct physical meaning, easy implementation and excellent parallel performance. The LBM has shown great potential in numerical simulations of complex flows that would be difficult for traditional methods. Firstly, we reviewed the developments and applications of the LBM. Then, we revealed the inherent relationship between the LBM and the Boltzmann equation, and presented two basic LBM models called the single-relaxation-time (SRT) model and multiple- relaxation-time (MRT) model, recovered the corresponding macroscopic Navier-Stokes equations respectively via the Chapman−Enskog expansion, presented two common boundary conditions called the non-equilibrium extrapolation scheme and the BFL scheme. Besides we introduced the conversion method between the physical units and lattice units based on dimensional analysis. After that, we built an axisymmetric multiple-relaxation-time (AMRT) LBM model with the BFL scheme, and simulated the acoustic fields generated by concave ultrasound transducers of different field angles respectively by the AMRT model, Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation and spheroidal beam equation (SBE). Results indicated that the AMRT model could be used to describe the acoustic field generated by the concave ultrasound transducer, and the transducer with bigger field angle had a better focusing performance. Lastly, we presented a novel spherical cavity transducer with two open ends for providing subwavelength focal region and sufficient pressure gain. We investigated the standing wave acoustic field generated by the spherical cavity ultrasound transducer via the AMRT model and experimental measurements. Results indicated that the AMRT model could be used to describe the standing wave filed generated by the spherical cavity ultrasound transducer, and this device exhibited much better focusing performance than the traditional concave ultrasound transducer, and could meet the requirement of some sophisticated HIFU treatments. The main aim of this work is to solve some practical problems for the numerical modeling of acoustic field in the HIFU treatments and provide new sights into the acoustic simulations.