title: Generalized equation for describing the magnetization in spoiled gradient-echo imaging.
abstract: The purpose of this study was to demonstrate a generalized equation for describing the magnetization in spoiled gradient-echo (SPGR) imaging in which the in-pulse relaxation and magnetization transfer (MT) effects are taken into account. First, the time-dependent Bloch equations for the two-pool exchange model with MT effect were reduced to an inhomogeneous linear differential equation, and then a simple equation was derived to solve it using a matrix operation. Second, the equations describing the magnetization before and after the radiofrequency (RF) pulse were derived based on the above solution for the RF-pulse excitation and evolution phases. Finally, a generalized equation describing the steady-state magnetization was derived. The validity of this equation was investigated by comparing with the transverse magnetization obtained by the regular Ernst equation and analytical solution in which the in-pulse transverse relaxation is considered. When the same assumption was made in our method, there were good agreements between them, indicating the validity of our method. The in-pulse transverse and longitudinal relaxations decreased the transverse magnetization compared to the case in which these effects were neglected, whereas MT increased it. In conclusion, we derived a generalized equation for describing the magnetization in SPGR imaging. This equation will provide a suitable basis for understanding the signal intensity in SPGR imaging and/or T1 measurement using an SPGR sequence in cases in which the effect of in-pulse relaxation and/or MT cannot be neglected.
authors.affiliation: Department of Medical Physics and Engineering, Division of Medical Technology and Science, Faculty of Health Science, Graduate School of Medicine, Osaka University, 1-7 Yamadaoka, Suita, Osaka 565-0871, Japan. murase@sahs.med.osaka-u.ac.jp
authors.forename: Kenya
authors.initials: K
authors.lastname: Murase
mesh_terms: D000465:Algorithms; D017352:Echo-Planar Imaging / Q000379:methods*; D004867:Equipment Design; D006801:Humans; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D008279:Magnetic Resonance Imaging / Q000379:methods*; D008280:Magnetics; D015233:Models, Statistical; D008962:Models, Theoretical; D011846:Radio Waves; D012815:Signal Processing, Computer-Assisted