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Algebraic description of spin 3/2 dynamics in NMR experiments

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Title: Algebraic description of spin 3/2 dynamics in NMR experiments
Authors: Tanase, Costin1,2 huiduhu@yahoo.com, Boada, Fernando E.2
Source: Journal of Magnetic Resonance. Apr2005, Vol. 173 Issue 2, p236-253. 18p.
Subjects: Algebra, Matrices (Mathematics), Magnetic fields, Mathematical analysis
Abstract: Abstract: The dynamics of spin 3/2 systems is analyzed using the density matrix theory of relaxation. By using the superoperator formalism, an algebraic formulation of the density matrix’s evolution is obtained, in which the contributions from free relaxation and RF application are easily factored out. As an intermediate step, an exact form for the propagator of the density matrix for a spin 3/2 system, in the presence of static quadrupolar coupling, inhomogeneous static magnetic field, and relaxation is demonstrated. Using this algebraic formulation, exact expressions for the behavior of the density matrix in the classical one-, two-, and three-pulse experiments are derived. These theoretical formulas are then used to illustrate the bias introduced on the measured relaxation parameters by the presence of large spatial variations in the B0 and B1 fields. The theoretical predictions are easily evaluated through simple matrix algebra and the results agree very well with the experimental observations. This approach could prove useful for the characterization of the spatial variations of the signal intensity in multiple quantum-filtered sodium MRI experiments. [Copyright &y& Elsevier]
Copyright of Journal of Magnetic Resonance is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Algebraic description of spin 3/2 dynamics in NMR experiments
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Magnetic+Resonance%22">Journal of Magnetic Resonance</searchLink>. Apr2005, Vol. 173 Issue 2, p236-253. 18p.
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  Data: Abstract: The dynamics of spin 3/2 systems is analyzed using the density matrix theory of relaxation. By using the superoperator formalism, an algebraic formulation of the density matrix’s evolution is obtained, in which the contributions from free relaxation and RF application are easily factored out. As an intermediate step, an exact form for the propagator of the density matrix for a spin 3/2 system, in the presence of static quadrupolar coupling, inhomogeneous static magnetic field, and relaxation is demonstrated. Using this algebraic formulation, exact expressions for the behavior of the density matrix in the classical one-, two-, and three-pulse experiments are derived. These theoretical formulas are then used to illustrate the bias introduced on the measured relaxation parameters by the presence of large spatial variations in the B0 and B1 fields. The theoretical predictions are easily evaluated through simple matrix algebra and the results agree very well with the experimental observations. This approach could prove useful for the characterization of the spatial variations of the signal intensity in multiple quantum-filtered sodium MRI experiments. [Copyright &y& Elsevier]
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  Data: <i>Copyright of Journal of Magnetic Resonance is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1016/j.jmr.2004.12.009
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      – SubjectFull: Magnetic fields
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              Text: Apr2005
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