格子Boltzmann方法及其在高强度聚焦超声声场建模的应用

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

格子Boltzmann方法(lattice Boltzmann method,LBM)是一种新型的流体力学模拟工具.基于介观动力学理论,LBM具有物理意义清晰、程序易于实施、边界易于处理和并行性能好等优势,因而在许多传统方法难以胜任的复杂流动领域得到了广泛应用.本文首先综述了LBM的诞生、发展以及现况,并阐述了LBM的理论和基本模型;随后,介绍了LBM在高强度聚焦超声(high-intensity focused ultrasound,HIFU)领域中的相关应用.基于LBM基本模型,构建了一种轴对称多弛豫时间(axisymmetric multiple-relaxation-time,AMRT)模型,并在模型中采用了具有二阶精度的Bouzidi-Firdaouss-Lallemand(BFL)边界处理格式.利用AMRT模拟了常见球面聚焦换能器产生的行波聚焦声场,并与传统声学方法进行了对比,验证了AMRT模型的有效性;随后又模拟了一种新型的球腔聚焦换能器产生的驻波聚焦声场,探讨了该类型换能器在HIFU治疗中的应用价值.本文结果旨在推动LBM成为一种全新的有效的声学仿真手段.

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℃ 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.