Real-time numerical simulation of Doppler ultrasound in the presence of nonaxial flow

Numerical simulations of Doppler ultrasound (DUS) relying on computational fluid dynamics (CFD) models of nonaxial flow have traditionally employed detailed (but computationally intensive) models of the DUS physics, or have sacrificed much of the physics in the interest of computational or conceptual simplicity. In this paper, we present a compromise between these extremes, with the objective of simulating the essential characteristics of DUS spectrograms in a real-time manner. Specifically, a precomputed pulsatile CFD velocity field is interrogated at some number, N, of discrete points distributed spatially within a sample volume of prescribed geometry and power distribution and temporally within a prescribed sampling window. Intrinsic spectral broadening is accounted for by convolving each of the point velocities with a semiempirical broadening function. Real-time performance is facilitated through the use of an efficient algorithm for interpolating the unstructured CFD data. A spherical sample volume with Gaussian power distribution, N = 1000 sampling points, and quadratic broadening function are shown to be adequate for simulating, at frame rates of 86 Hz on a 1.5 GHz desktop workstation, realistic-looking spectrograms at representative locations within a stenosed carotid bifurcation model. Via qualitative comparisons with matched in vitro data, these simulated spectrograms are shown to mimic the distinctive spectral envelopes, broadening and power characteristics associated with common carotid, stenotic jet and poststenotic recirculating flows. We conclude that the complex interaction between Doppler ultrasound and complicated clinically relevant blood flow dynamics can be simulated in real time via this relatively straightforward semiempirical approach.