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Extended phase graph formalism for systems with magnetization transfer and exchange

Research output: Contribution to journalArticle

Original languageEnglish
Pages (from-to)767-779
JournalMagnetic Resonance in Medicine
Issue number2
Early online date15 Dec 2017
Publication statusE-pub ahead of print - 15 Dec 2017


King's Authors


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 T2 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 T2 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.

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