An alternative approach to the simulation of magnetic resonance lineshapes and spin echoes in the presence of exchange

A new approach to the simulation of magnetic resonance lineshapes and analysis of transverse spin relaxation experiments is presented. An approximate solution to the stochastic Liouville equation is employed in which the time evolution of the magnetization is expressed as a Markov chain. It is shown that a good approximation can be obtained by choosing a sufficiently small time step to define the corresponding propagator matrix. The simulation of free induction decays and spin echoes is performed by computing successive powers of this matrix. Frequency spectra are then obtained by Fourier transformation of the time functions. The resulting algorithm is trivial to implement and runs efficiently.