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Uniform Depth Channel Flow: Problem Solving01:18

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To calculate the flow rate for a trapezoidal channel, first, identify the bottom width, side slope, and flow depth of the channel. The cross-sectional area (A) corresponding to the depth of flow (y), channel bottom width (B), and side slope (θ) is determined by:Next, calculate the wetted perimeter, which includes the bottom width and the sloped side lengths in contact with the water. Using the values of the cross-sectional area and the wetted perimeter, determine the hydraulic radius by...
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Related Experiment Video

Updated: Sep 2, 2025

Human Fetal Blood Flow Quantification with Magnetic Resonance Imaging and Motion Compensation
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Fully automated background phase correction using M-estimate SAmple consensus (MSAC)-Application to 2D and 4D flow.

Carola Fischer1,2, Jens Wetzl2, Tobias Schaeffter1,3,4

  • 1Department of Medical Imaging, Technical University of Berlin, Berlin, Germany.

Magnetic Resonance in Medicine
|August 2, 2022
PubMed
Summary
This summary is machine-generated.

We developed a new method, M-estimate SAmple Consensus (MSAC), for automated background phase correction in phase-contrast MRI. MSAC effectively rejects outliers, improving flow quantification accuracy, especially in complex cases with artifacts.

Keywords:
background phasebackground phase correctioncardiovascular MRIeddy currentsflow quantificationoutlier rejection

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Area of Science:

  • Medical Imaging
  • Magnetic Resonance Imaging
  • Image Processing

Background:

  • Phase-contrast MRI (PC-MRI) is crucial for flow quantification.
  • Spatially varying background phase offsets are a major limitation in PC-MRI.
  • Existing correction methods using polynomial regression can be sensitive to outliers like wrap-around or constant flow.

Purpose of the Study:

  • To propose and evaluate M-estimate SAmple Consensus (MSAC) as an automated method for background phase correction in PC-MRI.
  • To improve the accuracy and robustness of flow quantification by effectively rejecting outliers.
  • To automate the background phase correction process for both 2D and 4D flow data.

Main Methods:

  • MSAC fits polynomials to random image samples, identifying consensus pixels and rejecting outliers.
  • Robustness was tested using third-order polynomial fits on 118 2D and 18 4D flow datasets (with and without wrap-around) at 1.5T and 3T.
  • Performance was compared against standard stationary tissue correction and phantom correction.

Main Results:

  • MSAC demonstrated robustness across various parameter choices, with a single set suitable for both 2D and 4D flow.
  • MSAC significantly reduced phase errors in 2D flow compared to stationary correction (p=0.005).
  • Stationary correction yielded larger errors in pulmonary/systemic flow ratios in 2D flow compared to MSAC; performance was similar in 4D flow.

Conclusions:

  • MSAC offers fully automated background phase correction for 2D and 4D flow MRI.
  • The MSAC method provides enhanced robustness over traditional stationary correction, particularly when outliers are present.
  • This technique improves the reliability of flow quantification in phase-contrast MRI.