A combined parabolic-integral equation approach to the acoustic simulation of vibro-acoustic imaging

This paper aims to model ultrasound vibro-acoustography to improve our understanding of the underlying physics of the technique thus facilitating the collection of better images. Ultrasound vibro-acoustography is a novel imaging technique combining the resolution of high-frequency imaging with the clean (speckle-free) images obtained with lower frequency techniques. The challenge in modeling such an experiment is in the variety of scales important to the final image. In contrast to other approaches for modeling such problems, we break the experiment into three parts: high-frequency propagation, non-linear interaction and the propagation of the low-frequency acoustic emission. We then apply different modeling strategies to each part. For the high-frequency propagation we choose a parabolic approximation as the field has a strong preferred direction and small propagation angles. The non-linear interaction is calculated directly with Fourier methods for computing derivatives. Because of the low-frequency omnidirectional nature of the acoustic emission field and the piecewise constant medium we model the low-frequency field with a surface integral approach. We use our model to compare with experimental data and to visualize the relevant fields at points in the experiment where laboratory data is difficult to collect, in particular the source of the low-frequency field. To simulate experimental conditions we perform the simulations with the two frequencies 3 and 3.05 MHz with an inclusion of varying velocity submerged in water.