Matthias Weigel1,2,3,4
1Translational Imaging in Neurology (ThINk) Basel, Department of Biomedical Engineering, Faculty of Medicine, University Hospital Basel and University of Basel, Allschwil, Switzerland, 2Department of Neurology, University Hospital Basel, Basel, Switzerland, 3Research Center for Clinical Neuroimmunology and Neuroscience Basel (RC2NB), University Hospital Basel and University of Basel, Basel, Switzerland, 4Division of Radiological Physics, Dept. of Radiology, University Hospital Basel, Basel, Switzerland
Synopsis
Keywords: Physics & Engineering: Physics, Image acquisition: Sequences, Physics & Engineering: Nuclear Magnetic Resonance
The Extended Phase Graph (EPG) concept represents a powerful tool for depicting and understanding magnetization response of several MRI and MRS sequences. It allows pictorial understanding of echo generation, simple but elegant classification of echoes, and at the same time fast and accurate computation of echo intensities. It particularly demonstrates its advantages in the application for NMR sequences with multiple gradients and RF pulses. Motion effects (rigid body motion, flow, free diffusion) can also be considered. Overall, the EPG concept is really worth studying to get a deeper insight into the understanding and development of complex NMR sequences.
Overview
The extended phase graph (EPG) concept represents a powerful tool for depicting and understanding the magnetization response of a broad variety of magnetic resonance imaging (MRI) and magnetic resonance spectroscopy (MRS) sequences 1-7. EPGs focus on echo generation as well as on classification and use a Fourier based magnetization description in terms of “configurations states” 1-7. The effect of gradients, radiofrequency (RF) pulses, and relaxation during the MR sequence is characterized as the action of a few matrix operations ("operators") on these configuration states 1-7. Further operators for including more complex effects such as bulk motion, flow, diffusion, or magnetization transfer can be defined and be included in the EPG formalism in a relatively easy way 5-7. Thus, the EPG method allows for fast and precise quantitation of echo intensities even if several gradients and RF pulses are applied 1-7. EPG diagrams aid in the comprehension of different types of echoes and their corresponding echo time 1-7.
This lecture will introduce the idea of "phase-graphing", investigate some of its foundations and particularly highlight its strengths. The focus will be more on a pictorial and basic understanding. Different parts of the formalism and their application will be discussed. The lecture will closely follow some parts of the educational (not really being a "review") paper by M. Weigel 6.
Simple and representative software for a basic implementation of EPG formalism for the basic types of "gradient echo / steady state imaging" and "multiple spin echo imaging" can be found at http://epg.matthias-weigel.net/. The provided codes are in accordance with parts and examples of M. Weigel's manuscript 6.Acknowledgements
No acknowledgement found.References
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5. Weigel M, Schwenk S, Kiselev VG, Scheffler K, Hennig J. Extended phase graphs with anisotropic diffusion. J Magn Reson 2010;205:276–285.
6. Weigel M. Extended phase graphs: dephasing, RF pulses, and echoes - pure and simple. J Magn Reson Imaging 2015;41:266-95.
7. Malik SJ, Teixeira RPAG, Hajnal JV. Extended phase graph formalism for systems with magnetization transfer and exchange. Magn Reson Med 2018;80:767-779.