A posteriori accuracy estimation of ultrasonic vector-flow mapping (VFM)

Figures

• 

  Fig. 1. Schematics of a posteriori method for evaluating VFM accuracy. The left figure shows a typical ultrasound image for a transmitral flow from the left atrium to the left ventricle. The background blue/red color denotes the direction of the flows measured by the color-Doppler technique. The yellow vectors are obtained by VFM. Also, VAE method focuses on estimating the uncertainty of the obtained vectors as in a box showing “uncertainty xx (m/s)”. The right figure is a flow chart of VFM derivation

• 

  Fig. 2. Schematic of VFM calculation for an integration path. Cross-beam, or azimuthal, velocities are calculated by successively integrating the mass-conservation equation. The wall used for the BC is called the “start wall.” The uncorrected VFM velocities starting from the start wall are displayed as cyan arrows. Mainly due to errors in the VFM calculation, resultant VFM azimuth velocity at the other side of the wall (end wall), \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$v_{{\theta ,{\text{en}}}}^{\text{st}} (r)$$\end{document}vθ,enst(r), is not the same as the wall azimuthal velocity measured by tissue tracking, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$v_{{\theta ,{\text{en}}}}^{T} (r)$$\end{document}vθ,enT(r), because of the error accumulations during the integration procedures. Therefore, another uncorrected VFM…

• 

  Fig. 3. Experimental system: a schematics of the experimental setup, which consists of an LV phantom, an ultrasound scanner, and a PIV. A pulse signal mimicking an R-wave generated by an activator synchronizes all three systems at 1 Hz. b LV phantom in air (left) and in PEG400 (right). c Schematics of the imaged planes

• 

  Fig. 4. Comparison between VFM (black) and PIV (red) vectors for the case in which the image plane is parallel to the valve alignment. The apex is at the bottom

• 

  Fig. 5. Probability density function of the corrected VFM uncertainty for imaged planes a parallel and b normal to the valve alignment

• 

  Fig. 6. Correlation of measured and estimated uncertainties for cases with imaged plane a parallel to the valve alignment at a frame rate of 33 Hz, b parallel to the valve alignment at a frame rate of 17 Hz, c normal to the valve alignment at a frame rate of 26 Hz, and d normal to the valve alignment at a frame rate of 14 Hz. The solid line depicts a line with slope of unity. The dashed line denotes the fitted line of the correlation plots

• 

  Fig. 7. Correlation of measured and estimated uncertainties for cases with imaged plane normal to the valve alignment at a frame rate of 14 Hz using several (from 1 to 4) frames. The solid line depicts a line with slope of unity. The dashed line denotes the fitted line of the correlation plots

• 

  Fig. 8. Schematic of VFM calculation domain in the LV, where velocity-error source, s, is distributed.

• 

  Fig. 9. Schematics of the mean VFM-velocity error

• 

  Fig. 10. Simulation results. Contour plots of a vector error source, s, for S.D. of 10, b integrated vector-error source, and c corrected VFM error with bias errors. d Probability density function of uncorrected VFM error and corrected VFM uncertainty. e Standard deviations in each beam line. The S.D. was calculated using the samples in the same beam in the depth direction, f Standard deviations for the corrected VFM error and the estimated value as a function of N