Abstract
Ultrasound waves have been widely used in diagnostic and therapeutic medical applications. Accurate and effective simulation of ultrasound beam propagation and its interaction with tissue has been proved to be important. The nonlinear nature of the ultrasound beam propagation, especially in the therapeutic regime, plays an important role in the mechanisms of interaction with tissue. There are three main approaches in current computational fluid dynamics (CFD) methods to model and simulate nonlinear ultrasound beams: macroscopic, mesoscopic and microscopic approaches. In this work, a mesoscopic CFD method based on the Lattice-Boltzmann model (LBM) was investigated. In the developed method, the Boltzmann equation is evolved to simulate the flow of a Newtonian fluid with the collision model instead of solving the Navier-Stokes, continuity and state equations which are used in conventional CFD methods. The LBM has some prominent advantages over conventional CFD methods, including: (1) its parallel computational nature; (2) taking microscopic boundaries into account; and (3) capability of simulating in porous and inhomogeneous media. In our proposed method, the propagating medium is discretized with a square grid in 2 dimensions with 9 velocity vectors for each node. Using the developed model, the nonlinear distortion and shock front development of a finiteamplitude diffractive ultrasonic beam in a dissipative fluid medium was computed and validated against the published data. The results confirm that the LBM is an accurate and effective approach to model and simulate nonlinearity in finite-amplitude ultrasound beams with Mach numbers of up to 0.01 which, among others, falls within the range of therapeutic ultrasound regime such as high intensity focused ultrasound (HIFU) beams. A comparison between the HIFU nonlinear beam simulations using the proposed model and pseudospectral methods in a 2D geometry is presented.
Highlights
high intensity focused ultrasound (HIFU) surgery is a procedure for noninvasive ablation of soft tissue [1]
A mesoscopic computational fluid dynamics (CFD) method based on the Lattice-Boltzmann model (LBM) was investigated
The Boltzmann equation is evolved to simulate the flow of a Newtonian fluid with the collision model instead of solving the Navier-Stokes, continuity and state equations which are used in conventional CFD methods
Summary
HIFU surgery is a procedure for noninvasive ablation of soft tissue [1]. Design and optimization of these treatment modalities is the main motivation for simulating nonlinear ultrasound. To develop an accurate model for simulating ultrasound propagation one needs to consider absorption, diffraction and nonlinearity effects [2]. The Navier-Stokes, continuity and state equations are a nonlinear set of equations from which many computational methods that describe flow of fluids are derived. These equations are based on the variation of flow velocity and density [3]. To simulate the dynamics of a fluid, there is variety of models, each operating on a different level
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