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Analytical solution and verification of diffusion effect in SSFP
Author(s) -
Carney C. E.,
Wong S. T. S.,
Patz S.
Publication year - 1991
Publication title -
magnetic resonance in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.696
H-Index - 225
eISSN - 1522-2594
pISSN - 0740-3194
DOI - 10.1002/mrm.1910190209
Subject(s) - steady state free precession imaging , diffusion , steady state (chemistry) , magnetization , fourier transform , bloch equations , diffusion equation , fourier analysis , fick's laws of diffusion , mathematical analysis , sensitivity (control systems) , nuclear magnetic resonance , statistical physics , physics , mathematics , chemistry , thermodynamics , quantum mechanics , magnetic field , magnetic resonance imaging , radiology , medicine , economy , electronic engineering , service (business) , engineering , economics
Assuming that the SSFP magnetization response maintains a steady state which is penodic in the presence of diffusion, we can solve for the diffusion effect in such sequences. Formulating a Fourier series decomposition solution to the Bloch‐Torrey equation and imposing the steady‐state condition, analytical expressions describing the signal decay due to diffusion are developed. Magnetization responses for any system and sequence parameters can then be obtained. Also, sensitivity to b factor changes is quite different than standard diffusion measurement techniques. Assumptions made in the solution are verified via finite difference solutions and simulations of the Bloch‐Torrey equation.