Generalized equation for describing the magnetization in spoiled gradient-echo imaging

• Published in: Magnetic resonance imaging Vol. 29; no. 5; pp. 723 - 730
• Main Author: Murase, Kenya
• Format: Journal Article
• Language: English
• Published: Netherlands Elsevier Inc 01.06.2011
• Subjects: Algorithms; Bloch equations; Echo-Planar Imaging - methods; Equipment Design; Humans; Image Processing, Computer-Assisted - methods; In-pulse relaxation; Magnetic Resonance Imaging - methods; Magnetics; Magnetization; Magnetization transfer; Models, Statistical; Models, Theoretical; Radio Waves; Radiology; Signal Processing, Computer-Assisted; Spoiled gradient-echo imaging; In-pulse relaxation; Magnetization transfer; Spoiled gradient-echo imaging; Bloch equations; Magnetization
• ISSN: 0730-725X; 1873-5894
• DOI: 10.1016/j.mri.2011.02.005

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.