Streamfunction-Vorticity Flow Reconstruction for Color Doppler Ultrasound Velocimetry
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Streamfunction-Vorticity Flow Reconstruction for Color Doppler Ultrasound Velocimetry

Visualization and quantitation of multi-directional cardiovascular flow without the need for sedation or contrast is desirable across all practices of cardiology. Intraventricular flow mapping (iVFM) is one such method for multi-direction visualization. iVFM estimates the transverse flow from color Doppler ultrasound using the continuity equation. iVFM has been adopted as an effective research tool, and studies have demonstrated qualitatively accurate results. However, this formulation over-simplifies influence of global wall and surrounding blood motions on local reconstruction estimates, which produces large, non-physical gradients that corrupt other flow measurements of interest such as vorticity, vortex strength, and pressure estimation. We have developed a Doppler velocity vector field reconstruction algorithm based on the streamfunction-vorticity (ψ-ω) equation. Our algorithm, herein referred to as Doppler Velocity Reconstruction (DoVeR), improves on limitations inherent to iVFM methods. We validated DoVeR using artificial color Doppler images generated from computational fluid dynamics models of left ventricle (LV) and carotid artery flows. Conventional iVFM (iVFM1D) and reformulated iVFM (iVFM2D) were employed for comparison. LV model analysis showed DoVeR is robust to noise and probe placement (nRMSE: 3.81%-6.67%); iVFM method performance differed across conditions (nRMSE­­–iVFM1D:4.16%-24.17%, iVFM2D:4.06%-400.21%). Carotid model analysis showed DoVeR yields less bias and random error (LoA:-16.80%–15.19%) compared to iVFM methods (LoA–iVFM1D:-9.57%–51.34%, iVFM1D:-6.25%–56.55%). The DoVeR method yielded physiologically accurate reconstructions, which will enable more robust quantitative cardiovascular metrics and improve diagnostic capabilities.

The DoVeR method uses (a) color Doppler ultrasound images to (b) construct appropriate boundary and initial conditions used to (c) reconstruct the underlying flowfield through the streamfunction-vorticity  equation. Comparison of reconstruction methods against ground truth for (d) LV and (e) carotid artery flows. RMS error CDFs indicate (f) a two-fold to (g) a five-fold improvement in accuracy by DoVeR.

Paper Reference

Meyers BA, Goergen CJ, Segers P, Vlachos PP. Colour-Doppler echocardiography flow field velocity reconstruction using a streamfunction–vorticity formulation. Journal of the Royal Society Interface. 2020 Dec 23;17(173):20200741.

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