About the origins of NMR diffusion-weighting induced by frequency-swept pulses

In the present work, the non-linear phase dispersion induced by slice selective frequency-swept pulses is analyzed, in order to assess NMR signal attenuation due to molecular diffusion during such pulses. In particular, theoretical considerations show that diffusion-weighting can be calculated based on the non-linear phase spatial derivative (i.e. the phase gradient), and that the phase of B1 field at the instant of the flip does not contribute to phase scrambling and diffusion-weighting, yielding a simple analytical expressions. The theory is validated by confrontation with numerical simulations of the Bloch equations including diffusion, performed for a pair of hyperbolic secant pulses and a pair of CHIRP pulses. The simple though general conceptual framework developed here should be useful for the understanding and the exact calculation of diffusion-weighting in NMR sequences using frequency-swept pulses.