Fast Ultrasound Image Simulation Using the Westervelt Equation

Abstract

Abstract. The simulation of ultrasound wave propagation is of high interest in fields as ultrasound system development and therapeutic ultrasound. From a computational point of view the requirements for realistic simulations are immense with processing time reaching even an entire day. In this work we present a framework for fast ultrasound image simulation covering the imaging pipeline from the initial pulse transmission to the final image formation. The propagation of ultrasound waves is modeled with the Westervelt equation, which is solved explicitly with a Finite Difference scheme. Solving this scheme in parallel on the Graphics Processing Unit allows us to simulate realistic ultrasound images in a short time.

Ultrasound Simulation on the Cell Broadband Engine Using the Westervelt Equation

“…The gradients are approximated using finite differences that are fourth-order accurate in space and second-order accurate in time [14]. This is the same as the schemes used in [6,15]. The finite differences generated by this algorithm and used in the code are:…”

“…This has helped with the floating point operations, however, memory bandwidth is still a bottleneck. Our research extends the GPGPU implementation discussed by Karamalis et al [6], and explores how the Westervelt Equation could be used to simulate ultrasound on the Cell processor. In this case, the Westervelt equation is solved with a FDTD scheme which can take advantage of important aspects of the Cell's hardware, including multiple cores, SIMD calculations, and asynchronous memory retrieval/storage.…”

“…To discretize domains of this size, a 2 dimensional finite-difference time-domain (FDTD) simulation can require grid sizes in excess of 1000 × 1000 grid points [4,5]. Similarly, the simulation of a single scan line in which waves propagate from the transducer into the medium and back can require more than 6000 time steps [6]. This is increased further if the simulation of nonlinear harmonics is required, or if the simulations are performed in 3 dimensions.…”

“…Recently, nonlinear ultrasound simulation on general-purpose graphics processing units (GPGPUs) have been attracting attention [5][6][7]. This has helped with the floating point operations, however, memory bandwidth is still a bottleneck.…”

Nonlinear Ultrasound Simulation Based on Full-Wave Model and Comparisons with KZK

“…However, the validity of the KZK is limited by the paraxial approximation to about 15~20° from the axis of the ultrasound beam [7]. For this reason, other models such as the Westervelt equation [8] and the full-wave equation [7] have been proposed.…”