Simulation of ultrasound nonlinear propagation on GPU using a generalized angular spectrum method
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RESEARCH
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Simulation of ultrasound nonlinear propagation on GPU using a generalized angular spectrum method Francois Varray1,2*, Christian Cachard1, Alessandro Ramalli1,2, Piero Tortoli2 and Olivier Basset1
Abstract Acoustic simulation has always played an important role in the development of new ultrasound imaging techniques. In nonlinear ultrasound imaging particularly, the simulators are accurate but time-consuming, because of the high derivative order of the propagation equation and to the classic solution based on finite difference schemes. This article presents a fast 3D + t nonlinear ultrasound simulator, based on a generalized angular spectrum method, particularly fit for the graphics processing unit (GPU). Indeed, the Fourier domain approach decreases the derivative order of the propagation, thus significantly speeding up the simulation time. The simulator was implemented and optimized on a central processing unit (CPU) and a GPU, respectively. The processing times measured on two different graphic cards show that, compared to the CPU, GPU-based implementation is 3.5-13.6 times faster. 1. Introduction The use of harmonic imaging in ultrasound has become popular because of the improvement it offers in terms of axial and lateral resolution with respect to standard B-mode imaging [1]. The new modality exploits the nonlinear propagation of ultrasound waves in human tissues, yielding the presence of significant harmonics in the ultrasound echoes, which can be selected on the receiver. The great interest in nonlinear propagation and its applications has stimulated the development of simulation programs, capable of predicting the behavior of a large class of ultrasound waves in different tissues. The main strategies to simulate the distortion of a propagating wave are based on the finite difference approach [2] and the angular spectrum method (ASM) [3]. The former is more accurate, but requires a very long time to converge. On the other hand, the angular approach is faster because it solves the propagation equation in the Fourier domain, thus decreasing the derivative terms of the propagation equation. Furthermore, by considering the fundamental and the second harmonic distortion separately, simpler and faster * Correspondence: [email protected] 1 Université de Lyon, CREATIS; CNRS UMR5220; INSERM U1044; INSA-Lyon; Université Lyon 1; 7 av Jean Capelle, 69621 Villeurbanne, France Full list of author information is available at the end of the article
solutions [4-7] can be obtained. In the recent article by Wojcik et al. [8], the simulation time for a 4D (3D + time) ultrasound wave propagation was between 3 and 12 h. Although an ASM-based simulator decreases the computation time, for a 3D + t volume, it still takes about 2 h [9]. Work is required to optimize the ASM approach and to develop a fast simulation tool. In the last few years, the increased performance of graphics processor units (GPUs) has made them excellent candidates not only for display but also for intensive calculus
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