Extended phase graph formalism for systems with magnetization transfer and exchange

PURPOSE: An extended phase graph framework (EPG‐X) for modeling systems with exchange or magnetization transfer (MT) is proposed. THEORY: EPG‐X models coupled two‐compartment systems by describing each compartment with separate phase graphs that exchange during evolution periods. There are two variants: EPG‐X(BM) for systems governed by the Bloch‐McConnell equations, and EPG‐X(MT) for the pulsed MT formalism. For the MT case, the “bound” protons have no transverse components, so their phase graph consists of only longitudinal states. METHODS: The EPG‐X model was validated against steady‐state solutions and isochromat‐based simulation of gradient‐echo sequences. Three additional test cases were investigated: (i) MT effects in multislice turbo spin‐echo; (ii) variable flip angle gradient‐echo imaging of the type used for MR fingerprinting; and (iii) water exchange in multi‐echo spin‐echo T(2) relaxometry. RESULTS: EPG‐X was validated successfully against isochromat based transient simulations and known steady‐state solutions. EPG‐X(MT) simulations matched in‐vivo measurements of signal attenuation in white matter in multislice turbo spin‐echo images. Magnetic resonance fingerprinting–style experiments with a bovine serum albumin (MT) phantom showed that the data were not consistent with a single‐pool model, but EPG‐X(MT) could be used to fit the data well. The EPG‐X(BM) simulations of multi‐echo spin‐echo T(2) relaxometry suggest that exchange could lead to an underestimation of the myelin‐water fraction. CONCLUSIONS: The EPG‐X framework can be used for modeling both steady‐state and transient signal response of systems exhibiting exchange or MT. This may be particularly beneficial for relaxometry approaches that rely on characterizing transient rather than steady‐state sequences. Magn Reson Med 80:767–779, 2018. © 2017 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.