Color Flow Ultrasound Spatial Sampling Beam Density for Partial Volume-Corrected Three-Dimensional Volume Flow (3DVF): Theory, Simulation, and Experiment

Objective: The purpose of this study was to quantify the accuracy of partial volume-corrected three-dimensional volume flow (3DVF) measurements as a function of spatial sampling beam density using carefully-designed parametric analyses in order to inform the target applications of 3DVF.

Methods: Experimental investigations employed a mechanically-swept curvilinear ultrasound array to acquire 3D color flow (6.3 MHz) images in flow phantoms consisting of four lumen diameters (6.35, 4.88, 3.18 and 1.65 mm) with volume flow rates of 440, 260, 110 and 30 mL/min, respectively. Partial volume-corrected three-dimensional volume flow (3DVF) measurements, based on the Gaussian surface integration principle, were computed at five regions of interest positioned between depths of 2 and 6 cm in 1 cm increments. At each depth, the color flow beam point spread function (PSF) was also determined, using in-phase/quadrature data, such that 3DVF bias could then be related to spatial sampling beam density. Corresponding simulations were performed for a laminar parabolic flow profile that was sampled using the experimentally-measured PSFs. Volume flow was computed for all combinations of lumen diameters and the PSFs at each depth.

Results: Accurate 3DVF measurements, i.e., bias less than ±20%, were achieved for spatial sampling beam densities where at least 6 elevational color flow beams could be positioned across the lumen. In these cases, greater than 8 lateral color flow beams were present. PSF measurements showed an average lateral-to-elevational beam width asymmetry of 1:2. Volume flow measurement bias increased as the color flow beam spatial sampling density within the lumen decreased.

Conclusion: Applications of 3DVF, particularly those in the clinical domain, should focus on areas where a spatial sampling density of 6 × 6 (lateral x elevational) beams can be realized in order to minimize measurement bias. Matrix-based ultrasound arrays that possess symmetric PSFs may be advantageous to achieve adequate beam densities in smaller vessels.