Extended phase graph formalism for systems with magnetization transfer and exchange

Abstract

PurposeAn extended phase graph framework (EPG‐X) for modeling systems with exchange or magnetization transfer (MT) is proposed.TheoryEPG‐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.MethodsThe 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.ResultsEPG‐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.ConclusionsThe 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.

Magnetization transfer in magnetic resonance fingerprinting

“…The differences at the beginning of the sequence can be explained by a large saturation of the semi‐solid pool by the initial high‐power inversion pulse. This MT effect caused by the inversion pulse was also observed by Malik et al…”

“…When the signal evolutions of these MRI techniques are simulated using comprehensive models, a dependency of the model on additional experimental factors, such as properties of the RF pulses, becomes apparent. This dependency can influence the T 1 or T 2 estimation accuracy …”

FASt single‐breathhold 2D multislice myocardial T1 mapping (FAST1) at 1.5T for full left ventricular coverage in three breathholds

“…As FAST1 and MOLLI use analogous acquisition schemes, FAST1‐BS and FAST1‐IR may also be sensitive to magnetization transfer, which was shown to be the main contributor for the underestimation of in vivo native myocardial T 1 time using MOLLI . FAST1‐BS may thus have an advantage over FAST1‐IR, as it could enable the integration of the magnetization transfer effect in the creation of the signal dictionary …”

Fast model‐based T2 mapping using SAR‐reduced simultaneous multislice excitation

“…This effect may lead to different T 2 decays for the SMS sequence in comparison to the standard CPMG sequence, as the used MB pulse saturates the semisolid pool with high pulse power at 5 different frequencies, and the PINS pulses always saturate the semisolid‐pool on‐resonance. To study this effect, we simulated the magnetization of the free water and semisolid pool for both the standard and the SMS‐CPMG sequence in the presence of multiple components (i.e., intracellular/extracellular water [IE] and myelin [M] water) using the EPG‐X framework . The magnetization was simulated for a central slice within the FOV, and the saturation caused by the acquisition of neighboring slices was considered.…”

“…To study this effect, we simulated the magnetization of the free water and semisolid pool for both the standard and the SMS-CPMG sequence in the presence of multiple components (i.e., intracellular/extracellular water [IE] and myelin [M] water) using the EPG-X framework. 41 The magnetization was simulated for a central slice within the FOV, and the saturation caused by the acquisition of neighboring slices was considered. The following simulation parameters, similar to what could be expected in WM, 42 were used: T 2,IE = 60 ms, T 2,M = 10 ms, T 2,Semi-Solid = 12 µs, T 1,IE = 800 ms, T 1,M = 200 ms, MT exchange rate k IE = 5 s −1 , k M = 10 s −1 , fractional MT pool size F IE = 10%, and F M = 30%.…”