Studies On Applications Of Lattice Boltzmann Method In Modeling Of High-intensity Focused Ultrasound

High-intensity focused ultrasound(HIFU)is a breakthrough of noninvasive targeted therapeutic technique,and has been widely applied in tumor treatments.The operational procedure of HIFU is to concentrate acoustic energy by focused ultrasonic transducer into the focal region to destroy the tumor locally without damages to surrounding normal tissues.Hence,this paper focus on two issues of HIFU including:(1)The focused ultrasonic transducer determines the therapeutic effect of HIFU directly.Therefore,it is prerequisite to simulate the acoustic field numerically for estimating the performance,optimizing the parameters and reducing the design cost of the focused ultrasonic transducer.On the other hand,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 design some new kinds of focused ultrasonic transducers with better focusing performance.(2)The cavitation effect induced by extremely high acoustic pressure has shown great research significance and application value in HIFU or other fields of biomedical ultrasonic engineering.There have no perfect theoretical models for analyzing the cavitation effect so far,which makes it significant to investigate the cavitation effect numerically.Aiming at the above two issues,a numerical simulation method called the lattice Boltzmann method(LBM)was presented 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.LBM has shown great potential in numerical simulations of complex flows that would be difficult for traditional methods.In this paper,LBM was used to investigate some key topics in HIFU treatments,including the following three aspects:(1)The lattice Boltzmann equation(LBE)was derived to reveal the relationship between the LBM and the classical Boltzmann equation;Based on the D2Q9 lattice,two basic LBM models,including the single-relaxation-time(SRT)model and the multiple-relaxation-time(MRT)model,were built respectively,and the corresponding macroscopic Navier-Stokes equations were derived by using the Chapman-Enskog expansion;Based on the D2Q9 lattice,the Shan-Chen(SC)model was built for describing the multiphase flow,and the inherent thermodynamic inconsistence of the SC model was explained;some common boundary conditions and the unit conversion method of LBM were introduced;besides,the complete calculation process of LBM was presented.(2)An axisymmetric multiple-relaxation-time(AMRT)LBM model with a high-precision curve boundary condition called the Bouzidi-Firdaouss-Lallemand(BFL)scheme was build;the acoustic field generated by a conventional spherical transducer was simulated by the AMRT model to evaluate the influences of adjustable relaxation times on the results;the acoustic fields generated by spherical transducers of different field angles were simulated 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,and the spherical transducer of bigger field angle had a better focusing performance.(3)A novel spherical cavity transducer was presented to provide subwavelength focal region and sufficient pressure gain for HIFU treatments;the standing wave acoustic field generated by the spherical cavity transducer was numerically investigated by the AMRT model and experimental measurement;the acoustic nonlinearity was analyzed by the AMRT model;results indicated that the AMRT model could be used to describe the standing wave filed,and the spherical cavity transducer could meet the requirement of some sophisticated HIFU treatments.(4)A multiple-relaxation-time Shan-Chen(MRT-SC)LBM model with the Carnahan-Starling(CS)equation of state for real gas was built;the forcing term in the governing equation of the MRT-SC model was improved to overcome the inherent thermodynamics inconsistence;the Spinodal decompositions under different types of density perturbations at the initial time were simulated by the MRT-SC model to obtain the liquid-vapor coexistence densities and validate the Young-Laplace equation;the collapse of cavitation bubble near a solid wall was simulated by the MRT-SC model,and the result was compared with the standard result given by previous work;the influences of the initial internal-external pressure difference and the bubble-wall distance on the bubble collapse were discussed.Results indicated that the MRT-SC model could be used to describe the collapse of cavitation bubble near a solid wall,and the high-speed jet was excited by the bubble collapse.In this work,the LBM was adopted to investigate some key topics of HIFU treatments.The main aim of this work is to solve some practical problems for the numerical modeling of HIFU treatments and provide new sights into the acoustic simulations.