格子玻尔兹曼方法对不同张角聚焦声束的建模

Modeling of focused acoustic beams with varied aperture angles using lattice Boltzmann method

高强度聚焦超声（HIFU）是一种新型的无创治疗肿瘤新技术,其中换能器声场数值计算能够为HIFU治疗提供重要的依据。传统非线性KZK和SBE模型广泛应用于换能器声场数值计算,但依然存在某些不足。我们采用一种介观尺度的新型流体力学方法,即格子Boltzmann方法（LBM）,基于2维9离散速度（D2Q9）格子构建了轴对称多弛豫参数LBM模型,并通过调节弛豫参数分析其对模型的影响;利用该模型对两个具有不同张角的球面聚焦换能器的声场进行数值模拟,并与KZK和SBE模型的计算结果进行比较。结果表明LBM模型能够很好地描述超声波的激发和传播机制,从流体力学的角度描述聚焦声场的分布,具有清晰的物理意义,且计算过程不受换能器张角的限制,在换能器声场的理论分析和模拟计算及其在HIFU治疗中的应用有着积极的意义。

High-intensity focused ultrasound （HIFU） has been demonstrated to be a novel technique of noninvasive targeted therapy. Considering of the deficiency in acoustic field modeling of the traditional Khokhlov-Zabolotskaya- Kuznetsov （KZK） and spheroidal beam equation （SBE） equations, the lattice Boltzmann method （LBM） often used in fluid mechanics with mesoscopic characteristics, is employed to simulate the acoustic field of focused ultrasound. With the 2-diemsnison 9-speed （D2Q9） lattice, the LBM model is constructed by axisymmetric flow equations in cylindrical coordinates and boundary schemes of focused transducer, and the adjustment of relaxation time is also conducted to realize parameter optimization. The calculations using the proposed LBM model are performed for two focused transducers with different aperture angles, and also compared with the results of the KZK and SBE models. It shows that the LBM model can describe the mechanism of ultrasound excitation and propagation, providing the distribution of acoustic field from the view of fluid mechanics with a clear physical meaning. Additionally, the calculation process of LBM is not affected by the aperture angle of the focused transducer. The proposed LBM exhibits good application potential in theoretical analysis and numerical simulation of acoustic field for HIFU therapy.