RF Pulse Design
Markus Barth1

1University of Queensland, Australia


This course part will cover the concepts to understand the theory and implementation of radiofrequency (RF) pulses including the small tip angle tip angle approximation, the Shinnar-LeRoux (SLR) algorithm and numerical methods.

Basic RF pulse properties

The concept of slice selective excitation using magnetic field gradients as well as Bloch equations and the rotating frame will be introduced. Bandwidth-time product, slice profile will be presented based on simple shaped RF pulse examples. In addition to excitation pulses, refocusing and inversion pulses as well as Variable-rate selective excitation (VERSE) will be discussed.

RF pulse design methods

As a basic concept to design RF pulses the small tip angle approximation will be used to show the Fourier relationship between the RF pulse shape and the pulse profile. The Shinnar-LeRoux (SLR) algorithm will be introduced for RF pulses larger than about 30 degrees. In case of more complex situations including e.g. multichannel excitation or 2D spatial selective pulses efficient numerical methods are increasingly used for optimized excitation profiles.

Advanced RF pulses

Adiabatic RF pulses: a class of RF pulses that can excite the magnetization uniformly across the volume of interest in situations of B1 inhomogeneities, e.g. due to coil properties such as for small surface coil designs.

Multiband (MB) pulses for simultaneous multi-slice (SMS) acquisition: Recently these RF pulses have increasingly been used to speed up MR imaging acquisition by simultaneously exciting multiple slices and disentangling the resulting images using coil sensitivity information.

Spatial-spectral pulses: this class can excite magnetization that has both a specified slice location and a specified spectral content, and can be used to excite a slice of magnetization from one chemical species (e.g. water) while leaving the magnetization from another (e.g. fat) largely unaffected.


No acknowledgement found.


Bendall, M. R., and Pegg, D. T. (1986) Uniform sample excitation with surface coils for in vivo spectroscopy by adiabatic rapid half passage. J. Magn. Reson. 67: 376-381.

Ugurbil, K., Garwood, M., and Bendall, R. (1987) Amplitude- and frequency-modulated pulses to achieve 90 degree plane rotation with inhomogeneous B1 fields.J. Magn. Reson. 72:177-185.

Shinnar M, Leigh JS. (1987) Frequency-response of soft pulses. J Magn Reson 75:502-505.

Conolly S, Nishimura D, Macovski A, Glover G. (1988) Variable-rate selective excitation. J Magn Reson 78:440–458.

Pauly JM, Nishimura D, Macovski A. (1989) A k-space analysis of small-tip-angle excitation. J Magn Reson 81:43-56.

Hardy CJ, Cline HE. (1989) Spatial Localization in Two Dimensions using NMR designer pulses. Journal of Magnetic Resonance 82:647-654.

Pauly J, Leroux P, Nishimura D, Macovski A. (1991) Parameter relations for the shinnar-leroux selective excitation pulse design algorithm. IEEE Trans Med Imaging 10:53–65

Katscher U, Bornert P, Leussler C, van den Brink J. (2003) Transmit SENSE. Magn Reson Med 49:144-150.

Bernstein M, King KF, Zhou XJ. (2004) Handbook of MRI Pulse Sequences. Ch. 2-6.

Yip CY, Fessler JA, Noll DC. (2005) Iterative RF pulse design for multidimensional, small-tip-angle selective excitation. Magn Reson Med 54:908-917.

Grissom, W. A., Yip, C. Y., Wright, S. M., Fessler, J. A., & Noll, D. C. (2008). Additive angle method for fast large-tip-angle RF pulse design in parallel excitation. Magn Reson Med 59:779-787.

Xu, D., King, K. F., Zhu, Y., McKinnon, G. C., & Liang, Z. P. (2008). Designing multichannel, multidimensional, arbitrary flip angle RF pulses using an optimal control approach. Magnetic Resonance in Medicine, 59(3), 547-560.

Grissom WA, Xu D, Kerr AB, Fessler JA, Noll, DC (2009). Fast large-tip-angle multidimensional and parallel RF pulse design in MRI. Medical Imaging, IEEE Transactions on, 28:1548-1559.

Proc. Intl. Soc. Mag. Reson. Med. 26 (2018)