Preprints
https://doi.org/10.5194/mr-2021-4
https://doi.org/10.5194/mr-2021-4

  15 Jan 2021

15 Jan 2021

Review status: this preprint is currently under review for the journal MR.

Approximate Representations of Shaped Pulses Using the Homotopy Analysis Method

Timothy Crawley and Arthur G. Palmer III Timothy Crawley and Arthur G. Palmer III
  • Department of Biochemistry and Molecular Biophysics, Columbia University, 630 West 168th Street, New York, NY 10032, United States

Abstract. The evolution of nuclear spin magnetization during a radiofrequency pulse in the absence of relaxation or coupling interactions can be described by three Euler angles. The Euler angles in turn can be obtained from the solution of a Riccati differential equation; however, analytic solutions exist only for rectangular and chirp pulses. The Homotopy Analysis Method is used to obtain new approximate solutions to the Riccati equation for shaped radiofrequency pulses in NMR spectroscopy. The results of even relatively low orders of approximation are highly accurate and can be calculated very efficiently. The Homotopy Analysis Method is powerful and flexible and is likely to have other applications in theoretical magnetic resonance.

Timothy Crawley and Arthur G. Palmer III

Status: open (until 02 Mar 2021)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on mr-2021-4', Fabien Ferrage, 01 Feb 2021 reply
  • RC2: 'Comment on mr-2021-4', Anonymous Referee #2, 17 Feb 2021 reply

Timothy Crawley and Arthur G. Palmer III

Timothy Crawley and Arthur G. Palmer III

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Short summary
Shaped radiofrequency pulses are widely used in NMR spectroscopy to provide selective excitation or inversion of magnetization. Efficient accurate methods for calculating the performance of such pulses enable understanding of existing pulses and facilitate optimization of new pulses. A new approach for approximating the effects of shaped pulses is introduced and applied to some popular shaped pulses as examples. This approach also will be useful in other areas of theoretical NMR spectroscopy.