Linked Life Data

20616401

Source:http://linkedlifedata.com/resource/pubmed/id/20616401

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PredicateObject
rdf:type
lifeskim:mentions
pubmed:issue
15
pubmed:dateCreated
2010-7-21
pubmed:abstractText
The Ernst equation for Fourier transform nuclear magnetic resonance (MR) describes the spoiled steady-state signal created by periodic partial excitation. In MR imaging (MRI), it is commonly applied to spoiled gradient-echo acquisition in the steady state, created by a small flip angle alpha at a repetition time TR much shorter than the longitudinal relaxation time T(1). We describe two parameter transformations of alpha and TR/T(1), which render the Ernst equation as a low-order rational function. Computer algebra can be readily applied for analytically solving protocol optimization, as shown for the dual flip angle experiment. These transformations are based on the half-angle tangent substitution and its hyperbolic analogue. They are monotonic and approach identity for small alpha and small TR/T(1) with a third-order error. Thus, the exact algebraization can be readily applied to fast gradient echo MRI to yield a rational approximation in alpha and TR/T(1). This reveals a fundamental relationship between the square of the flip angle and TR/T(1) which characterizes the Ernst angle, constant degree of T(1)-weighting and the influence of the local radio-frequency field.
pubmed:language
eng
pubmed:journal
pubmed:citationSubset
IM
pubmed:status
MEDLINE
pubmed:month
Aug
pubmed:issn
1361-6560
pubmed:author
pubmed:issnType
Electronic
pubmed:day
7
pubmed:volume
55
pubmed:owner
NLM
pubmed:authorsComplete
Y
pubmed:pagination
4231-45
pubmed:meshHeading
pubmed:year
2010
pubmed:articleTitle
Exact algebraization of the signal equation of spoiled gradient echo MRI.
pubmed:affiliation
Department of Orthodontics, Biomechanics Group, University Medical Centre, Göttingen, Germany.
pubmed:publicationType
Journal Article