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Consider a control volume, such as a pipe with solid boundaries, through which fluid flows and changes direction due to the impulse exerted by the resulting force from the pipe walls. In steady flow, the mass of fluid entering the control volume at a given time, t, with velocity v1, is equal to the mass leaving after infinitesimal time dt, with velocity v2.
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Understanding steady, laminar flow between parallel plates is essential for analyzing and designing flow in narrow rectangular channels, commonly found in various water conveyance and drainage systems. The Navier-Stokes equations govern fluid motion and are generally challenging to solve due to their nonlinearity. However, simplifications are possible in certain cases, like the steady laminar flow between parallel plates. For this scenario, we assume steady, incompressible, laminar flow.
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Related Experiment Video

Updated: Jan 28, 2026

Determining 3D Flow Fields via Multi-camera Light Field Imaging
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3D Phase Contrast Using Balanced Steady-State Free Precession (PC-SSFP) for Improved 4D Flow at Clinical Field

Jie Xiang1, Maolin Qiu2, Gigi Galiana1,2

  • 1Department of Biomedical Engineering, Yale University, New Haven, Connecticut, USA.

Magnetic Resonance in Medicine
|January 27, 2026
PubMed
Summary

This study developed a 4D flow balanced steady state free precession (bSSFP) MRI method for improved cardiovascular imaging. The new technique enhances signal-to-noise ratio and contrast, accurately measuring blood flow during diastole.

Keywords:
3 T4D flowPC‐SSFPdiastolic functionstroke volume

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Phase Contrast Magnetic Resonance Imaging in the Rat Common Carotid Artery
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Area of Science:

  • Cardiovascular Imaging
  • Magnetic Resonance Imaging
  • Fluid Dynamics

Background:

  • 4D flow MRI offers comprehensive cardiovascular flow assessment.
  • Intracardiac 4D flow is limited by poor blood-myocardial contrast.
  • 2D phase contrast using balanced steady state free precession (PC-SSFP) shows enhanced contrast and SNR.

Purpose of the Study:

  • Extend 2D PC-SSFP to 4D flow MRI at clinical field strengths.
  • Evaluate the 4D flow bSSFP method for diastolic function assessment.
  • Improve blood-myocardial contrast in intracardiac 4D flow MRI.

Main Methods:

  • Modified 4D flow sequence with four-point encoding for bSSFP contrast.
  • Validated pixel-wise velocities in a 3T flow phantom.
  • Compared mitral inflow velocities (E, A, e') and stroke volume (SV) with 2D and 4D GRE methods in 13 healthy subjects.

Main Results:

  • 4D flow bSSFP showed strong agreement with GRE in phantom studies (r > 0.9).
  • In vivo studies demonstrated significantly improved SNR and blood-tissue CNR.
  • Comparable measurements of E, A, e', and SV were achieved with 4D flow bSSFP compared to GRE and 2D methods.

Conclusions:

  • The developed 4D flow bSSFP method is feasible for cardiovascular imaging.
  • The technique achieves improved SNR and CNR.
  • Accurate measurement of mitral velocity and volume is possible at clinical field strengths.