True energy-minimal and finite-size biplanar gradient coil design for MRI

Haiying Liu, Charles L. Truwit

Research output: Contribution to journalArticlepeer-review

22 Scopus citations


Finite-sized high-performance planar magnetic field gradient coils in today's open configuration magnetic resonance imaging (MRI) systems have always been desirable for ever demanding imaging applications. We present a Lagrange multiplier technique for designing a minimum-energy gradient coil under a finite-size planar geometry constraint in addition to a set of magnetic field constraints. In this new design methodology, the surface current density on a finite size plane is represented by a two-dimensional (2-D) Fourier series expansion. Following the standard approach, we construct a functional F in terms of the stored magnetic energy and a set of field constraint points which are chosen over the desired imaging volume. Minimizing F, we obtain the continuous current density distribution for the finitesize planar gradient coil. Applying the stream function technique to the resulting continuous current distribution, the discrete current pattern can be generated. Employing the Biot-Savart law to the discrete current loops, the gradient magnetic field has been re-evaluated in order to validate the theory. Using this approach, we have been able to design a finite-size biplanar z -gradient coil which is capable of generating a gradient field of 40 mT /m @ 266 A. The excellent agreement between the analytical and numerical results has been achieved.

Original languageEnglish (US)
Pages (from-to)826-830
Number of pages5
JournalIEEE Transactions on Medical Imaging
Issue number5
StatePublished - 1998


  • Finite-size coil
  • Interventional MRI
  • Magnetic energy minimization
  • Planar gradient coil


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