Abstract
A simulation method for forward propagation of acoustic pressure pulses in a medium with three-dimensional (3D) spatially-variable acoustic properties is presented. The intended application is to study aspects of ultrasound imaging of soft biological tissue. The forward wave propagation is modelled by a one-way wave equation. The equation describes tissue exhibiting nonlinear elasticity and arbitrary frequencydependent attenuation. A numerical solution to the equation is found by means of first-order accurate operator splitting and propagation along the spatial depth coordinate. Thus diffraction, nonlinearity and attenuation are solved independently at each propagation step, rendering their relative importance easy to monitor. The method is seen to yield an accurate simulation of the wave propagation when compared to numerical solutions of the full wave equation and experiments in a water tank. By this approach it is possible to simulate wave propagation over relatively large distances—typically several hundred wavelengths—at a modest computational complexity compared to solution of the full wave equation. It furthermore facilitates a high degree of parallelism, thus enabling efficient distribution of the required computations overmultiple processors.
Highlights
The quality of an ultrasound image is limited by the ability to transmit a focused sound beam through the body
The current paper presents a 3D implementation of a simulation model capable of describing wavefront aberration
Several authors have performed simulation of ultrasound wave propagation previously Tabei et al (2003), Masøy et al (2003), Nachman et al (1990), Christopher & Parker (1991), Berkhoff & Thijssen (1996), Wojcik et al (1998), Mast (2002). These simulations range from solving a full wave equation in a heterogeneous medium, to solving an approximate wave equation in a homogeneous medium
Summary
The quality of an ultrasound image is limited by the ability to transmit a focused sound beam through the body. Several authors have performed simulation of ultrasound wave propagation previously Tabei et al (2003), Masøy et al (2003), Nachman et al (1990), Christopher & Parker (1991), Berkhoff & Thijssen (1996), Wojcik et al (1998), Mast (2002) Depending on their objectives, these simulations range from solving a full wave equation in a heterogeneous medium, to solving an approximate wave equation in a homogeneous medium. Reverberations have been reported to produce only minor distortions of the forward propagating pulse in soft tissue Angelsen (2000), Hamilton & Blackstock (1997), Mast et al (1998) For this reason it is important to accurately model forward propagation, but of lesser importance to model multiple reflections. A derivation of the underlying wave equation is included in order to make available to the reader the approximations made in the modelling
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