Calculation of diffusion effect for arbitrary pulse sequences

A method is presented for calculating the nuclear spin magnetization created by an arbitrary number of short radio frequency pulses and of piecewise constant gradient applied in a selected direction. The isotropic diffusion, the transverse and longitudinal relaxations as well as the global transport are taken into account. A thorough analysis of the magnetization density evolution results in an algorithm for the analytical calculation of final NMR signal. Computationally, it requires only accumulating numerical coefficients in the found analytical structure. For arbitrary sequences this is done with a computer program. This approach, which can be classified as symbolical computations, results in a high performance and in a practically unlimited accuracy. Results for sample pulse sequences are presented.