title: High tip angle approximation based on a modified Bloch-Riccati equation.
abstract: When designing a radio-frequency pulse to produce a desired dependence of magnetization on frequency or position, the small flip angle approximation is often used as a first step, and a Fourier relation between pulse and transverse magnetization is then invoked. However, common intuition often leads to linear scaling of the resulting pulse so as to produce a larger flip angle than the approximation warrants--with surprisingly good results. Starting from a modified version of the Bloch-Riccati equation, a differential equation in the flip angle itself, rather than in magnetization, is derived. As this equation has a substantial linear component that is an instance of Fourier's equation, the intuitive approach is seen to be justified. Examples of the accuracy of this higher tip angle approximation are given for both constant- and variable-phase pulses.
authors.affiliation: CEA, I2BM, NeuroSpin, LRMN, Gif sur Yvette, France. nicolas.boulant@cea.fr
authors.forename: Nicolas
authors.initials: N
authors.lastname: Boulant
authors.forename: David I
authors.initials: DI
authors.lastname: Hoult
mesh_terms: D000465:Algorithms; D016477:Artifacts; D005583:Fourier Analysis; D006801:Humans; D007089:Image Enhancement / Q000379:methods*; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D016014:Linear Models; D008279:Magnetic Resonance Imaging / Q000379:methods*; D008433:Mathematics; D057233:Radio Frequency Identification Device