title: Extended phase graphs with anisotropic diffusion.
abstract: The extended phase graph (EPG) calculus gives an elegant pictorial description of magnetization response in multi-pulse MR sequences. The use of the EPG calculus enables a high computational efficiency for the quantitation of echo intensities even for complex sequences with multiple refocusing pulses with arbitrary flip angles. In this work, the EPG concept dealing with RF pulses with arbitrary flip angles and phases is extended to account for anisotropic diffusion in the presence of arbitrary varying gradients. The diffusion effect can be expressed by specific diffusion weightings of individual magnetization pathways. This can be represented as an action of a linear operator on the magnetization state. The algorithm allows easy integration of diffusion anisotropy effects. The formalism is validated on known examples from literature and used to calculate the effective diffusion weighting in multi-echo sequences with arbitrary refocusing flip angles.
authors.affiliation: University Hospital Freiburg, Department of Radiology, Medical Physics, Breisacher Strasse 60a, 79106 Freiburg, Germany. Matthias.Weigel@uniklinik-freiburg.de
authors.forename: M
authors.initials: M
authors.lastname: Weigel
authors.forename: S
authors.initials: S
authors.lastname: Schwenk
authors.forename: V G
authors.initials: VG
authors.lastname: Kiselev
authors.forename: K
authors.initials: K
authors.lastname: Scheffler
authors.forename: J
authors.initials: J
authors.lastname: Hennig
mesh_terms: D000465:Algorithms; D016880:Anisotropy; D004058:Diffusion; D004574:Electromagnetic Fields; D004578:Electron Spin Resonance Spectroscopy; D009682:Magnetic Resonance Spectroscopy / Q000379:methods* / Q000706:statistics & numerical data; D015233:Models, Statistical