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Sensitivity of the NMR density matrix to pulse sequence parameters : a simplified analytic approach

Momot, Konstantin I. & Takegoshi, Kiyonori (2012) Sensitivity of the NMR density matrix to pulse sequence parameters : a simplified analytic approach. Journal of Magnetic Resonance, 221, pp. 57-68.

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Abstract

We present a formalism for the analysis of sensitivity of nuclear magnetic resonance pulse sequences to variations of pulse sequence parameters, such as radiofrequency pulses, gradient pulses or evolution delays. The formalism enables the calculation of compact, analytic expressions for the derivatives of the density matrix and the observed signal with respect to the parameters varied. The analysis is based on two constructs computed in the course of modified density-matrix simulations: the error interrogation operators and error commutators. The approach presented is consequently named the Error Commutator Formalism (ECF). It is used to evaluate the sensitivity of the density matrix to parameter variation based on the simulations carried out for the ideal parameters, obviating the need for finite-difference calculations of signal errors. The ECF analysis therefore carries a computational cost comparable to a single density-matrix or product-operator simulation. Its application is illustrated using a number of examples from basic NMR spectroscopy. We show that the strength of the ECF is its ability to provide analytic insights into the propagation of errors through pulse sequences and the behaviour of signal errors under phase cycling. Furthermore, the approach is algorithmic and easily amenable to implementation in the form of a programming code. It is envisaged that it could be incorporated into standard NMR product-operator simulation packages.

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ID Code: 51612
Item Type: Journal Article
Keywords: Carr-Purcell-Meiboom-Gill (CPMG), Spin density matrix, Product operator formalism, Unitary transformation, NMR quantum computing, NMR pulse sequence design
DOI: 10.1016/j.jmr.2012.05.004
ISSN: 1090-7807
Subjects: Australian and New Zealand Standard Research Classification > PHYSICAL SCIENCES (020000) > OTHER PHYSICAL SCIENCES (029900) > Physical Sciences not elsewhere classified (029999)
Divisions: Current > Schools > School of Chemistry, Physics & Mechanical Engineering
Current > Institutes > Institute of Health and Biomedical Innovation
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: Copyright 2012 Elsevier Inc.
Copyright Statement: This is the author’s version of a work that was accepted for publication in Journal of Magnetic Resonance. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Magnetic Resonance, [VOL 221, ISSUE , (2012)] DOI: 10.1016/j.jmr.2012.05.004
Deposited On: 16 Jul 2012 08:50
Last Modified: 16 Sep 2013 06:40

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