Meshfree simulations of ultrasound vector flow imaging using smoothed particle hydrodynamics

Before embarking on a series of in vivo tests, design of ultrasound-flow-imaging modalities are generally more efficient through computational models as multiple configurations can be tested methodically. To that end, simulation models must generate realistic blood flow dynamics and Doppler signals. The current in silico ultrasound simulation techniques suffer mainly from uncertainty in providing accurate trajectories of moving ultrasound scatterers. In mesh-based Eulerian methods, numerical truncation errors from the interpolated velocities, both in the time and space dimensions, can accumulate significantly and make the pathlines unreliable. These errors can distort beam-to-beam inter-correlation present in ultrasound flow imaging. It is thus a technical issue to model a correct motion of the scatterers by considering their interaction with boundaries and neighboring scatterers. We hypothesized that in silico analysis of emerging ultrasonic imaging modalities can be implemented more accurately with meshfree approaches. We developed an original fluid-ultrasound simulation environment based on a meshfree Lagrangian CFD (computational fluid dynamics) formulation, which allows analysis of ultrasound flow imaging. This simulator combines smoothed particle hydrodynamics (SPH) and Fourier-domain linear acoustics (SIMUS  =  simulator for ultrasound imaging). With such a particle-based computation, the fluid particles also acted as individual ultrasound scatterers, resulting in a direct and physically sound fluid-ultrasonic coupling. We used the in-house algorithms for fluid and ultrasound simulations to simulate high-frame-rate vector flow imaging. The potential of the particle-based method was tested in 2D simulations of vector Doppler for the intracarotid flow. The Doppler-based velocity fields were compared with those issued from SPH. The numerical evaluations showed that the vector flow fields obtained by vector Doppler components were in good agreement with the original SPH velocities, with relative errors less than 10% and 2% in the cross-beam and axial directions, respectively. Our results showed that SPH-SIMUS coupling enables direct and realistic simulations of ultrasound flow imaging. The proposed coupled algorithm has also the advantage to be 3D compatible and parallelizable.