Universal equations for linear adiabatic pulses and characterization of partial adiabaticity

Tesiram, Yasvir A. and Bendall, M. Robin (2002) Universal equations for linear adiabatic pulses and characterization of partial adiabaticity. Journal of Magnetic Resonance, 156 1: 26-40. doi:10.1006/jmre.2002.2531


Author Tesiram, Yasvir A.
Bendall, M. Robin
Title Universal equations for linear adiabatic pulses and characterization of partial adiabaticity
Journal name Journal of Magnetic Resonance   Check publisher's open access policy
ISSN 1090-7807
1096-0856
Publication date 2002-05-01
Sub-type Article (original research)
DOI 10.1006/jmre.2002.2531
Volume 156
Issue 1
Start page 26
End page 40
Total pages 15
Place of publication Maryland Heights, MO, United States
Publisher Academic Press
Language eng
Formatted abstract
A numerical analysis of the sech/tanh (or hyperbolic secant) and tanh/tan adiabatic inversion pulses provides a set of master equations for each type of pulse that guarantee their optimal implementation over a wide range of practical conditions without needing to further simulate the inversion profiles of the pulses. These simple equations determine the necessary maximum RF amplitude (RFmax) required for a preselected degree of inversion across a chosen effective bandwidth (bweff) and for a chosen pulse length (Tp). The two types of pulse function differently: The sech/tanh pulse provides a rectangular inversion profile with bweff being a large fraction of the adiabatic frequency sweep (bwdth), whereas for tanh/tan bweff is ≤bwdth/20. If the quality of inversion is defined as the minimum allowable extent of inversion, ιbw, at the boundaries of bweff, two basic linear equations are found for both types of pulse and these are of the form (RFmaxTp)2=m1Tpbwdth+c1 and Tpbwdth=m3Tpbweff+c3. The different behavior of the two pulses is expressed as different dependencies of the slopes mn and intercepts cn on ιbw and allowances are made for second order effects within these equations. The availability of these master relationships enables a direct comparison of the two types of adiabatic pulse and it is found that tanh/tan requires about half the pulse length of an equivalent sech/tanh pulse and also has the advantage of being less sensitive to the effects of scalar coupling. In contrast sech/tanh delivers about half the total RF power of an equivalent tanh/tan pulse. It is expected that the forms of these two basic linear equations are generally applicable to adiabatic inversion pulses and thus define the concept of “linear adiabaticity.” At low values of Tpbwdth or Tpbweff the linear equations no longer apply, defining a region of “partial adiabaticity.” Normal adiabatic pulses in the middle of this partial region are more efficient in terms of RFmax or Tp but are moderately less tolerant to RF inhomogeneity. A class of numerically optimized pulses has recently been developed that specifically trades adiabaticity in an attempt to gain RFmax or Tp efficiency. In comparison to normal adiabatic pulses implemented under optimal conditions, these new partially adiabatic pulses show only marginal improvements; they are restricted to single values of Tpbweff, and they are vastly less tolerant to RF inhomogeneity. These comparisons, and direct comparisons between any types of inversion pulse, adiabatic or otherwise, can be made using plots of (RFmaxTp)2 or (Total Power) Tp versus Tpbweff.
Keyword Adiabatic pulses
Sech/tanh
Tanh/tan
Master equations
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Non-UQ

Document type: Journal Article
Sub-type: Article (original research)
Collection: Centre for Advanced Imaging Publications
 
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Created: Tue, 15 May 2012, 01:09:44 EST by Sandrine Ducrot on behalf of Centre for Advanced Imaging