Concomitant gradient terms in phase contrast MR: Analysis and correction

Matt A. Bernstein, Xiaohong Joe Zhou, Jason A. Polzin, Kevin F. King, Alexander Ganin, Norbert J. Pelc, Gary H. Glover

Research output: Contribution to journalArticlepeer-review

360 Scopus citations


Whenever a linear gradient is activated, concomitant magnetic fields with non-linear spatial dependence result. This is a consequence of Maxwell's equations, i.e., within the imaging volume the magnetic field must have zero divergence, and has negligible curl. The concomitant, or Maxwell field has been described in the MRI literature for over 10 years. In this paper, we theoretically and experimentally show the existence of two additional lowest- order terms in the concomitant field, which we call cross-terms. The concomitant gradient cross-terms only arise when the longitudinal gradient G(z) is simultaneously active with a transverse gradient (G(x) or G(y)). The effect of all of the concomitant gradient terms on phase contrast imaging is examined in detail. Several methods for reducing or eliminating phase errors arising from the concomitant magnetic field are described. The feasibility of a joint pulse sequence-reconstruction method, which requires no increase in minimum TE, is demonstrated. Since the lowest-order terms of the concomitant field are proportional to G2/B(o), the importance of concomitant gradient terms is expected to increase given the current interest in systems with stronger gradients and/or weaker main magnetic fields.

Original languageEnglish (US)
Pages (from-to)300-308
Number of pages9
JournalMagnetic Resonance in Medicine
Issue number2
StatePublished - Feb 1998


  • Concomitant field
  • Concomitant gradient terms
  • Maxwell terms
  • Phase contrast

ASJC Scopus subject areas

  • Radiology Nuclear Medicine and imaging


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