Spin echo analysis of restricted diffusion under generalized gradient waveforms for spherical pores with relaxivity and interconnections

The problem of restricted diffusion in spherical pores is examined under conditions of finite gradient pulse width in pulsed gradient spin echo (PGSE)-NMR experiments. Closed form analytic expressions are derived, and the case of interconnected pores is briefly examined. An expression, based on the pore hopping approximation, is presented that predicts the echo attenuation for diffusion between pores under any gradient waveform.