Comparison of Divergence-Free Filters for Cardiac 4D PC-MRI Data

  • Mickäel Francisco Sereno
  • Benjamin Köhler
  • Bernhard Preim
Conference paper
Part of the Informatik aktuell book series (INFORMAT)

Zusammenfassung

4D PC-MRI enables the measurement of time-resolved blood flow directions within a 3D volume. These data facilitate a comprehensive qualitative and quantitative analysis. However, noise is introduced, e.g., due to inhomogeneous magnetic field gradients. Blood is commonly assumed as a non-Newtonian fluid, thus, incompressible, and divergence should be zero. Divergence-free filters enforce this model assumption and have been shown to improve data quality. In this paper, we compare binomial smoothing and three of these techniques: The finite difference method (FDM), divergence-free radial basis functions (DFRBF) and divergence-free wavelets (DFW). The results show that average and maximum velocities tend to decrease, while average line lengths tend to increase slightly. We recommend FDM or DFW divergence-free filtering as an optional pre-processing step in 4D PC-MRI processing pipelines, as they have feasible computation times of few seconds.

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Literatur

  1. 1.
    Dyverfeldt P, Bissell M, Barker AJ, et al. 4D flow cardiovascular magnetic resonance consensus statement. J Cardiovasc Magn Reson. 2015;17(1):1–19.Google Scholar
  2. 2.
    Köhler B, Born S, Van Pelt RFP, et al. A survey of cardiac 4D PC-MRI data processing. Comput Graph Forum. 2017;36(6):5–35.Google Scholar
  3. 3.
    Song SM, Napel S, Glover GH, et al. Noise reduction in three-dimensional phasecontrast MR velocity measurements. J Magn Reson Imaging. 1993;3(4):587–96.Google Scholar
  4. 4.
    Busch J, Giese D, Wissmann L, et al. Reconstruction of divergence-free velocity fields from cine 3D phase-contrast flow measurements. J Magn Reson Imaging. 2013;69(1):200–10.Google Scholar
  5. 5.
    Paige CC, Saunders MA. LSQR: An algorithm for sparse linear equations and sparse least squares. ACM Trans Math Softw. 1982;8(1):43–71.Google Scholar
  6. 6.
    Ong F, Uecker M, Tariq U, et al. Robust 4D flow denoising using divergence-free wavelet transform. J Magn Reson Imaging. 2015;73(2):828–42.Google Scholar
  7. 7.
    Loecher M, Schrauben E, Johnson KM, et al. Phase unwrapping in 4D MR flow with a 4D single-step Laplacian algorithm. J Magn Reson Imaging. 2015;43(4):833–42.Google Scholar
  8. 8.
    Antiga L, Iordache EB, Remuzzi A. Computational geometry for patient-specific reconstruction and meshing of blood vessels from MR and CT angiography. IEEE Trans Med Imaging. 2003;22(5):674–84.Google Scholar
  9. 9.
    Donoho DL, Johnstone IM. Adapting to unknown smoothness via wavelet shrinkage. J Am Stat Assoc. 1995;90(432):1200–24.Google Scholar

Copyright information

© Springer-Verlag GmbH Deutschland 2018

Authors and Affiliations

  • Mickäel Francisco Sereno
    • 1
  • Benjamin Köhler
    • 2
  • Bernhard Preim
    • 2
  1. 1.Paris-Sud UniversityOrsayFrankreich
  2. 2.Deptartment of Simulation and GraphicsMagdeburg UniversityMagdeburgDeutschland

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