Gradient nonlinearity calibration and correction for a compact, asymmetric magnetic resonance imaging gradient system

S. Tao, J. D. Trzasko, J. L. Gunter, P. T. Weavers, Y. Shu, J. Huston, S. K. Lee, E. T. Tan, M. A. Bernstein

Research output: Contribution to journalArticlepeer-review

19 Scopus citations


Due to engineering limitations, the spatial encoding gradient fields in conventional magnetic resonance imaging cannot be perfectly linear and always contain higher-order, nonlinear components. If ignored during image reconstruction, gradient nonlinearity (GNL) manifests as image geometric distortion. Given an estimate of the GNL field, this distortion can be corrected to a degree proportional to the accuracy of the field estimate. The GNL of a gradient system is typically characterized using a spherical harmonic polynomial model with model coefficients obtained from electromagnetic simulation. Conventional whole-body gradient systems are symmetric in design; typically, only odd-order terms up to the 5th-order are required for GNL modeling. Recently, a high-performance, asymmetric gradient system was developed, which exhibits more complex GNL that requires higher-order terms including both odd- and even-orders for accurate modeling. This work characterizes the GNL of this system using an iterative calibration method and a fiducial phantom used in ADNI (Alzheimer's Disease Neuroimaging Initiative). The phantom was scanned at different locations inside the 26 cm diameter-spherical-volume of this gradient, and the positions of fiducials in the phantom were estimated. An iterative calibration procedure was utilized to identify the model coefficients that minimize the mean-squared-error between the true fiducial positions and the positions estimated from images corrected using these coefficients. To examine the effect of higher-order and even-order terms, this calibration was performed using spherical harmonic polynomial of different orders up to the 10th-order including even- and odd-order terms, or odd-order only. The results showed that the model coefficients of this gradient can be successfully estimated. The residual root-mean-squared-error after correction using up to the 10th-order coefficients was reduced to 0.36 mm, yielding spatial accuracy comparable to conventional whole-body gradients. The even-order terms were necessary for accurate GNL modeling. In addition, the calibrated coefficients improved image geometric accuracy compared with the simulation-based coefficients.

Original languageEnglish (US)
Pages (from-to)N18-N31
JournalPhysics in medicine and biology
Issue number2
StatePublished - Jan 21 2017


  • asymmetric gradient
  • compact 3T
  • gradient nonlinearity
  • head-only MRI system
  • image geometric distortion

ASJC Scopus subject areas

  • Radiological and Ultrasound Technology
  • Radiology Nuclear Medicine and imaging


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