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
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 radio-frequency (RF) pulses. It
generalizes the original Bloch model to non-exponential decays, which are,
e.g., 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 small than 300μs.
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
2μs.
Conclusion: The proposed theory unifies the original Bloch model, Henkelman's
steady-state theory for magnetization transfer, 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