Abstract
The soliton-lattice algorithm, an exact algebraic method of inverting the Bloch equation to obtain frequency-selective radio-frequency pulses is described. Some general properties of pulses are described that were obtained with the help of this algorithm. It is used to obtain two new pulses. A highly prefocused pulse is shown that can be used in short-echo-timein vivo 31P spectroscopic imaging, and an adiabatic selective inversion pulse is obtained.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Mansfield P, Morris PG (1982) NMR imaging in biomedicine. InAdvances in Magnetic Resonance (Suppl. 2). Orlando, FL: Academic Press.
Rourke DE, Morris PG (1992) Half-solitons as solutions to the Zakharov-Shabat eigenvalue problem for rational reflection coefficient, with application in the design of selective pulses in nmr.Phys Rev A 46(7): 3631–3636.
Rourke DE, Saunders JK (1994) Half-solitons as solutions to the Zakharov-Shabat eigenvalue problem for rational reflection coefficient. II. Potentials on infinite support.J Math Phys 35(2): 848–872.
Zakharov VE, Shabat AB (1972) Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media.Sov Phys JETP 34(1): 62–69.
Ablowitz MJ, Kaup DJ, Newell AC, Segur H (1974) The inverse scattering transform—Fourier analysis for nonlinear problems.Studies Appl Math 53(4): 249–315.
Rourke DE, Morris PG (1992) The inverse scattering transform and its use in the exact inversion of the Bloch equation for noninteracting spins.J Magn Reson 99 118–138.
Konopelchenko BG (1982) Elementary Bäckhand transformations, nonlinear superposition principle and solutions of the integrable equations.Phys Lett A 87(9): 445–448.
Calogero F, Degasperis A (1984) Elementary B äcklund transformations, nonlinear superposition formulae and algebraic constructions of solutions for the nonlinear evolution equations solvable by the Zakharov-Shabat spectral transform.Physica D 14 103–116.
Wang Z (1989) Theory of selective excitation by scaled frequency-amplitude sweep.J Magn Reson 81 617–622.
Ngo JT, Morris PG (1987) General solution to the nmr excitation problem for noninteracting spins.Magn Reson Med 5 217–237.
Kozlowski P, Rourke DE, Winsborrow BG, Saunders JK (1994) Highly prefocused selective pulses—a tool forin-vivo 31P spectroscopic imaging.J Magn Reson Ser B 104 280–283.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Rourke, D.E., Kozlowski, P., Winsborrow, B.G. et al. The soliton-lattice algorithm and selective pulses. MAGMA 2, 379–381 (1994). https://doi.org/10.1007/BF01705277
Issue Date:
DOI: https://doi.org/10.1007/BF01705277