Inductive measurement and encoding of k-space trajectories in MR raw data

  • Jan Ole Pedersen
  • Christian G. Hanson
  • Rong Xue
  • Lars G. HansonEmail author
Research Article



 The objective of this study was to concurrently acquire an inductive k-space trajectory measure and corresponding imaging data by an MR scanner.

Materials and methods

 1D gradient measures were obtained by digital integration, regularized using measured gradient coil currents and recorded individually by the scanner concurrently with raw MR data. Gradient measures were frequency modulated into an RF signal receivable by the scanner, yielding a k-space trajectory measure from the cumulative phase of the acquired data. Generation of the gradient measure and frequency modulation was performed by previously developed custom, versatile circuitry.


 For a normal echo planar imaging (EPI) sequence, the acquired k-space trajectory measure yielded slightly improved image quality compared to that obtained from using the scanner’s estimated eddy current-compensated k-space trajectory. For a spiral trajectory, the regularized inductive k-space trajectory measure lead to a 76% decrease in the root-mean-square error of the reconstructed image.


 While the proof-of-concept experiments show potential for further improvement, the feasibility of inductively measuring k-space trajectories and increasing the precision through regularization was demonstrated. The approach may offer an inexpensive method to acquire k-space trajectories concurrently with scanning.


Gradient imperfections Inductive measurement of k-space trajectories Encoding of signals in MRI raw data Regularization by current measure Magnetic resonance imaging 



We acknowledge Dr. Zhentao Zuo for his kind support. We would also like to thank the reviewers for their many good suggestions for improving the paper.

Author contributions

Study conception and design were performed by all authors. Acquisition of data was performed by Pedersen and L. Hanson using hardware developed by C. Hanson. Analysis and interpretation of data were done by all authors. Drafting of manuscript was done by Pedersen and L. Hanson. Critical revision was done by all authors.


This article is funded by Sino-Danish Center for Education and Research.

Compliance with ethical standards

Conflict of interest

After completion of the presented work, Pedersen has become an employee of Philips Healthcare.

Ethical approval

No human subjects or animals were scanned in this study.


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Copyright information

© European Society for Magnetic Resonance in Medicine and Biology (ESMRMB) 2019

Authors and Affiliations

  1. 1.Department of Health Technology, Center for Magnetic ResonanceTechnical University of DenmarkKongens LyngbyDenmark
  2. 2.Danish Research Centre for Magnetic Resonance, Centre for Functional and Diagnostic Imaging and ResearchCopenhagen University HospitalHvidovreDenmark
  3. 3.Sino-Danish Center for Education and ResearchAarhusDenmark
  4. 4.State Key Laboratory of Brain and Cognitive Science, Institute of BiophysicsChinese Academy of SciencesBeijingChina
  5. 5.Sino-Danish CollegeUniversity of Chinese Academy of SciencesBeijingChina
  6. 6.KøgeDenmark

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