Magnetic Resonance Imaging
Volume 28, Issue 2 , Pages 185-194 , February 2010

Registering spherical navigators with spherical harmonic expansions to measure three-dimensional rotations in magnetic resonance imaging

  • Andreu F. Costa

      Affiliations

    • Imaging Research Laboratories, Robarts Research Institute, University of Western Ontario, London, Ontario, Canada N6A 5K8
  • ,
  • Yi-Fen Yen

      Affiliations

    • Global Applied Science Laboratory, GE Healthcare, Menlo Park, CA 94025, USA
  • ,
  • Maria Drangova

      Affiliations

    • Imaging Research Laboratories, Robarts Research Institute, University of Western Ontario, London, Ontario, Canada N6A 5K8
    • Department of Medical Biophysics, University of Western Ontario, London, Ontario, Canada N6A 3K7
    • Department of Medical Imaging, University of Western Ontario, London, Ontario, Canada N6A 3K7
    • Corresponding Author InformationCorresponding author. Imaging Research Laboratories, Robarts Research Institute, P.O. Box 5015, London, Ontario, Canada N6A 5K8. Tel.: +1 519 663 5777x24064; fax: +1 519 931 5260.

Received 21 August 2008 ,Revised 20 January 2009 ,Accepted 18 July 2009.

References 

  1. Ehman RL, Felmlee JP. Adaptive technique for high-definition MR imaging of moving structures. Radiology. 1989;173(1):255–263
  2. Welch EB, Manduca A, Grimm RC, Ward HA, Jack CR. Spherical navigator echoes for full 3D rigid body motion measurement in MRI. Magn Reson Med. 2002;47(1):32–41
  3. Petrie DW, Costa AF, Takahashi A, Yen YF, Drangova M. Optimizing spherical navigator echoes for three-dimensional rigid-body motion detection. Magn Reson Med. 2005;53(5):1080–1087
  4. Shu Y, Elliott AM, Riederer SJ, Bernstein MA. Motion correction properties of the shells k-space trajectory. Magn Reson Imaging. 2006;24(6):739–749
  5. Wong ST, Roos MS. A strategy for sampling on a sphere applied to 3D selective RF pulse design. Magn Reson Med. 1994;32(6):778–784
  6. Costa AF, Yen YF, Petrie D, Drangova M. Fast motion tracking of a rigid body using MRI. In: Proceedings of the 11th Annual Meeting of ISMRM, Toronto, Canada. 2003;p. 1030
  7. Costa AF, Petrie DW, Yen YF, Drangova M. Using the axis of rotation of polar navigator echoes to rapidly measure 3D rigid-body motion. Magn Reson Med. 2005;53(1):150–158
  8. Costa AF, Petrie D, Drangova M. Variable-density oblique spherical navigator echoes to improve performance in measuring 3D motion. In: Proceedings of the 12th Annual Meeting of ISMRM, Kyoto, Japan. 2004;p. 2153
  9. Yen YF. 3D Rotation matching using spherical harmonic transformation of k-space navigator. In: Proceedings of the 12th Annual Meeting of ISMRM, Kyoto, Japan. 2004;p. 2154
  10. Driscoll JR, Healy DM. Computing Fourier transforms and convolutions on the 2-sphere. Adv Appl Math. 1994;15(2):202–250
  11. Kostelec PJ, Rockmore DN. FFTs on the rotation group. Santa Fe Institute Working Papers Series Paper #03-11-060 2003:1-27.
  12. Hobson EW. The Theory of Spherical and Ellipsoidal Harmonics. New York (NY): Chelsea Pub. Co.; 1955;
  13. Healy DM, Rockmore DN, Kostelec PJ, Moore SB. FFTs for the 2-sphere — improvements and variations. J Fourier Anal Appl. 2003;9(4):341–385
  14. Frigo M, Johnson SG. The design and implementation of FFTW3. Proc IEEE. 2005;93(2):216–231
  15. Renka RJ. Algorithm 772: STRIPACK: Delaunay triangulation and Voronoi diagram on the surface of a sphere. ACM Trans Math Softw. 1997;23(3):416–434
  16. Renka RJ. Algorithm 773: SSRFPACK: interpolation of scattered data on the surface of a sphere with a surface under tension. ACM Trans Math Softw. 1997;23(3):435–442
  17. Takahashi A, Peters T. Compensation of multi-dimensional selective excitation pulses using measured k-space trajectories. Magn Reson Med. 1995;34(3):446–456
  18. Alley MT, Glover GH, Pelc NJ. Gradient characterization using a Fourier-transform technique. Magn Reson Med. 1998;39(4):581–587
  19. Costa AF, Yen YF, Petrie D, Drangova M. Using the axis of rotation of polar navigator echoes to rapidly correct 3D subject motion. In: Proceedings of the 12th Annual Meeting of ISMRM, Kyoto, Japan. 2004;p. 2155
  20. Petrie D. Design and optimization of spherical navigator echoes for measurement of motion in magnetic resonance. M.S. Thesis: The Univ. of Western Ontario, London, Canada; 2003.

 Grant sponsors: The Canadian Institutes of Health Research (MGP-49536), The Ontario Research and Development Challenge Fund, The Whitaker Foundation (RG-00-0409). MD is a Career Investigator with the Heart and Stroke Foundation of Ontario.

PII: S0730-725X(09)00183-0

doi: 10.1016/j.mri.2009.07.010

Magnetic Resonance Imaging
Volume 28, Issue 2 , Pages 185-194 , February 2010