title: Extended phase graphs: dephasing, RF pulses, and echoes - pure and simple.
abstract: The extended phase graph (EPG) concept represents a powerful tool for depicting and understanding the magnetization response of a broad variety of MR sequences. EPGs focus on echo generation as well as on classification and use a Fourier based magnetization description in terms of "configurations states". The effect of gradients, radiofrequency (RF) pulses, relaxation, and motion phenomena during the MR sequence is characterized as the action of a few matrix operations on these configuration states. Thus, the EPG method allows for fast and precise quantitation of echo intensities even if several gradients and RF pulses are applied. EPG diagrams aid in the comprehension of different types of echoes and their corresponding echo time. Despite its several benefits in regard to a large number of problems and issues, researchers and users still often refrain from applying EPGs. It seems that "phase graphing" is still seen as a kind of "magic." The present review investigates the foundation of EPGs and sheds light on prerequisites for adding more advanced phenomena such as diffusion. The links between diagrams and calculations are discussed. A further focus is on limitations and simplifications as well recent extensions within the EPG concept. To make the review complete, representative software for EPG coding is provided.
authors.affiliation: Department of Radiology, Medical Physics, University Medical Center Freiburg, Freiburg, Germany; Radiological Physics, University of Basel Hospital, Basel, Switzerland.
authors.forename: Matthias
authors.initials: M
authors.lastname: Weigel
mesh_terms: D000465:Algorithms; D016880:Anisotropy; D005583:Fourier Analysis; D008279:Magnetic Resonance Imaging / Q000379:methods*; D015233:Models, Statistical; D011846:Radio Waves; D012984:Software
keywords: Fourier space; configuration states; dephasing; extended phase graph; partitioning; phase graph