Jakob Assländer1,2, Cem Gultekin3, Sebastian Flassbeck1,2, Steffen J Glaser4, Daniel K Sodickson1,2. 1. Center for Biomedical Imaging, Department of Radiology, New York University Grossman School of Medicine, New York, New York, USA. 2. Center for Advanced Imaging Innovation and Research (CAI2R), Department of Radiology, New York University Grossman School of Medicine, New York, New York, USA. 3. Courant Institute of Mathematical Sciences, New York University, New York, New York, USA. 4. Department of Chemistry, Technische Universität München, Munich, Germany.
Abstract
PURPOSE: The paper introduces a classical model to describe the dynamics of large spin-1/2 ensembles associated with nuclei bound in large molecule structures, commonly referred to as the semi-solid spin pool, and their magnetization transfer (MT) to spins of nuclei in water. THEORY AND METHODS: Like quantum-mechanical descriptions of spin dynamics and like the original Bloch equations, but unlike existing MT models, the proposed model is based on the algebra of angular momentum in the sense that it explicitly models the rotations induced by radiofrequency (RF) pulses. It generalizes the original Bloch model to non-exponential decays, which are, for example, observed for semi-solid spin pools. The combination of rotations with non-exponential decays is facilitated by describing the latter as Green's functions, comprised in an integro-differential equation. RESULTS: Our model describes the data of an inversion-recovery magnetization-transfer experiment with varying durations of the inversion pulse substantially better than established models. We made this observation for all measured data, but in particular for pulse durations smaller than 300 μs. Furthermore, we provide a linear approximation of the generalized Bloch model that reduces the simulation time by approximately a factor 15,000, enabling simulation of the spin dynamics caused by a rectangular RF-pulse in roughly 2 μs. CONCLUSION: The proposed theory unifies the original Bloch model, Henkelman's steady-state theory for MT, and the commonly assumed rotation induced by hard pulses (i.e., strong and infinitesimally short applications of RF-fields) and describes experimental data better than previous models.
PURPOSE: The paper introduces a classical model to describe the dynamics of large spin-1/2 ensembles associated with nuclei bound in large molecule structures, commonly referred to as the semi-solid spin pool, and their magnetization transfer (MT) to spins of nuclei in water. THEORY AND METHODS: Like quantum-mechanical descriptions of spin dynamics and like the original Bloch equations, but unlike existing MT models, the proposed model is based on the algebra of angular momentum in the sense that it explicitly models the rotations induced by radiofrequency (RF) pulses. It generalizes the original Bloch model to non-exponential decays, which are, for example, observed for semi-solid spin pools. The combination of rotations with non-exponential decays is facilitated by describing the latter as Green's functions, comprised in an integro-differential equation. RESULTS: Our model describes the data of an inversion-recovery magnetization-transfer experiment with varying durations of the inversion pulse substantially better than established models. We made this observation for all measured data, but in particular for pulse durations smaller than 300 μs. Furthermore, we provide a linear approximation of the generalized Bloch model that reduces the simulation time by approximately a factor 15,000, enabling simulation of the spin dynamics caused by a rectangular RF-pulse in roughly 2 μs. CONCLUSION: The proposed theory unifies the original Bloch model, Henkelman's steady-state theory for MT, and the commonly assumed rotation induced by hard pulses (i.e., strong and infinitesimally short applications of RF-fields) and describes experimental data better than previous models.
Authors: Richard D Dortch; Ke Li; Daniel F Gochberg; E Brian Welch; Adrienne N Dula; Ashish A Tamhane; John C Gore; Seth A Smith Journal: Magn Reson Med Date: 2011-05-23 Impact factor: 4.668
Authors: Xiaoxia Zhang; Quentin Duchemin; Kangning Liu; Cem Gultekin; Sebastian Flassbeck; Carlos Fernandez-Granda; Jakob Assländer Journal: Magn Reson Med Date: 2022-03-28 Impact factor: 3.737