Toward a real-time simulation of ultrasound image sequences based on a 3-D set of moving scatterers

Data simulation is an important research tool to evaluate algorithms. Two types of methods are currently used to simulate medical ultrasound data: those based on acoustic models and those based on convolution models. The simulation of ultrasound data sequences is very time-consuming. In addition, many applications require accounting for the out-of-plane motion induced by the 3-D displacement of scatterers. The purpose of this paper is to propose a model adapted to a fast simulation of ultrasonic data sequences with 3-D moving scatterers. Our approach is based on the convolution model. The scatterers are moved in a 3-D continuous medium between each pair of images and then projected onto the imaging plane before being convolved. This paper discusses the practical implementation of the convolution that can be performed directly or after a grid approximation. The grid approximation convolution is obviously faster than the direct convolution but generates errors resulting from the approximation to the grid´s nodes. We provide the analytical expression of these errors and then define 2 intensity-based criteria to quantify them as a function of the spatial sampling. The simulation of an image requires less than 2 s with oversampling, thus reducing these errors. The simulation model is validated with first- and second-order statistics. The positions of the scatterers at each imaging time can be provided by a displacement model. An example applied to flow imaging is proposed. Several cases are used to show that this displacement model provides realistic data. It is validated with speckle tracking, a well-known motion estimator in ultrasound imaging.