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Exact algebraization of the signal equation of spoiled gradient echo MRI
- Dathe, Henning (author)
-
- Helms, Gunther (author)
- Lund University,Lunds universitet,Medicinsk strålningsfysik, Lund,Sektion V,Institutionen för kliniska vetenskaper, Lund,Medicinska fakulteten,Medical Radiation Physics, Lund,Section V,Department of Clinical Sciences, Lund,Faculty of Medicine
- (creator_code:org_t)
- 2010-07-08
- 2010
- English.
- In: Physics in Medicine and Biology. - : IOP Publishing. - 1361-6560 .- 0031-9155. ; 55, s. 4231-4245
- Journal article (peer-reviewed)
Abstract
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- 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 α at a repetition time TR much shorter than the longitudinal relaxation time T1. We describe two parameter transformations of α and TR/T1, 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 α and small TR/T1 with a third-order error. Thus, the exact algebraization can be readily applied to fast gradient echo MRI to yield a rational approximation in α and TR/T1. This reveals a fundamental relationship between the square of the flip angle and TR/T1 which characterizes the Ernst angle, constant degree of T1-weighting and the influence of the local radiofrequency field.
Subject headings
- NATURVETENSKAP -- Fysik -- Annan fysik (hsv//swe)
- NATURAL SCIENCES -- Physical Sciences -- Other Physics Topics (hsv//eng)
- TEKNIK OCH TEKNOLOGIER -- Medicinteknik -- Medicinsk bildbehandling (hsv//swe)
- ENGINEERING AND TECHNOLOGY -- Medical Engineering -- Medical Image Processing (hsv//eng)
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