A spline-based spatial impulse response simulator

Abstract

The spatial impulse response (SIR) method is a well-known approach to calculate transient acoustic fields of arbitrary-shape transducers. It involves the evaluation of a time-dependent surface integral. Although analytic expressions of the SIR exist for some geometries, numerical methods based on the discretization of transducer surfaces have become the standard. The proposed method consists of representing the transducer as a non-uniform rational B-spline (NURBS) surface, and decomposing it into smooth Bézier patches onto which quadrature rules can be deployed. The evaluation of the SIR can then be expressed in B-spline bases, resulting in a sum of shifted-and-weighted basis functions. Field signals are eventually obtained by a convolution of the basis coefficients, derived from the excitation waveform, and the basis SIR. The use of NURBS enables exact representations of common transducer elements. High-order Gaussian quadrature rules enable high accuracy with few quadrature points. High-order B-spline bases are ideally suited to exploit efficiently the bandlimited property of excitation waveforms. Numerical experiments demonstrate that the proposed approach enables sampling the SIR at low sampling rates, as required by the excitation waveform, without introducing additional errors on simulated field signals.[https://doi.org(DOI number)][XYZ] Pages: 1-12The need for fast and accurate ultrasound (US) simulation tools is as great as ever. Such tools have been and continue to be extensively used for the design and characterization of US transducers (Hunt et al., 1983;Kino, 1987). The use of end-to-end US scanner simulators is also increasing for the training and evaluation of physicians and sonographers (Lewiss et al., 2014;Ziv et al., 2006), as they eliminate the need for volunteers or patients and can provide on-demand exposure to specific care and diagnosis scenarios. Simulation tools are also crucial for the development, assessment, and validation of image analysis and image reconstruction methods. This includes, for example, the analysis and characterization of speckle patterns (Foster et al., 1983;Wagner et al., 1983), the optimization of application-specific acquisition sequences (Jensen et al., 2016), the fine-tuning and benchmarking of image reconstruction parameters and methods (Rindal et al., 2019), or the development of image quality metrics (Rodriguez-Molares et al., 2020). The recent breakthrough of deep learning-based methods in medical image analysis (