MRI Pulse Sequence Design With First-Order Gradient Moment Nulling in Arbitrary Directions by Solving a Polynomial Program

We suggest a polynomial program for the calculation of optimized gradient waveforms for magnetic resonance tomography pulse sequences. Such non-linear mathematical programs can describe gradient system capabilities, meet k-space trajectory specifications, and capture sequence timing conditions. Moreover they allow the incorporation of gradient moment nulling constraints in one or several arbitrary spatial directions, which can reduce flow motion artifacts in the images. We report first experiences in solving such automatic pulse sequence design programs with the interior point solver Ipopt.

[1]  Tamás Terlaky,et al.  Optimizing Teardrop, an MRI sampling trajectory , 2008, Optim. Methods Softw..

[2]  Dwight G Nishimura,et al.  Time‐optimal multidimensional gradient waveform design for rapid imaging , 2004, Magnetic resonance in medicine.

[3]  J G Pipe,et al.  A progressive gradient moment nulling design technique , 1991, Magnetic resonance in medicine.

[4]  J L Duerk,et al.  In-plane flow velocity quantification along the phase encoding axis in MRI. , 1988, Magnetic resonance imaging.

[5]  R. S. Hinks,et al.  Gradient moment nulling in fast spin echo , 1994, Magnetic resonance in medicine.

[6]  R E Wendt,et al.  Interactive design of motion‐compensated gradient waveforms with a personal computer spreadsheet program , 1991, Journal of magnetic resonance imaging : JMRI.

[7]  Lorenz T. Biegler,et al.  On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming , 2006, Math. Program..

[8]  Dwight G Nishimura,et al.  Spiral balanced steady‐state free precession cardiac imaging , 2005, Magnetic resonance in medicine.

[9]  J L Duerk,et al.  MRI gradient waveform design by numerical optimization , 1993, Magnetic resonance in medicine.

[10]  Hanif D. Sherali,et al.  A global optimization algorithm for polynomial programming problems using a Reformulation-Linearization Technique , 1992, J. Glob. Optim..

[11]  Christopher Kumar Anand,et al.  Magnetic resonance tissue quantification using optimal bSSFP pulse-sequence design , 2007 .

[12]  Vira Chankong,et al.  An optimal design method for magnetic resonance imaging gradient waveforms , 1993, IEEE Trans. Medical Imaging.

[13]  G. Jahng,et al.  An optimized flow compensation scheme on the slice-selection axis for spin-echo MRI sequences , 2000, Proceedings of the IEEE 26th Annual Northeast Bioengineering Conference (Cat. No.00CH37114).

[14]  Jürgen Garloff,et al.  Rigorous Affine Lower Bound Functions for Multivariate Polynomials and Their Use in Global Optimisation , 2008 .

[15]  R L Ehman,et al.  Flow artifact reduction in MRI: A review of the roles of gradient moment nulling and spatial presaturation , 1990, Magnetic resonance in medicine.

[16]  Yu-Chung N. Cheng,et al.  Magnetic Resonance Imaging: Physical Principles and Sequence Design , 1999 .

[17]  Seung-Jean Kim,et al.  A fast method for designing time-optimal gradient waveforms for arbitrary k-space trajectories , 2008, IEEE Transactions on Medical Imaging.

[18]  J L Duerk,et al.  Significance of the point of expansion in interpretation of gradient moments and motion sensitivity , 1991, Journal of magnetic resonance imaging : JMRI.

[19]  Wilson Fong.  Handbook of MRI Pulse Sequences , 2005 .

[20]  J. Hogg.  Magnetic resonance imaging. , 1994, Journal of the Royal Naval Medical Service.