A pulse sequence optimization method for assessment of nucleus size in q-space analysis of idealized cells

To adjust pulse sequences that produce diffusion-weighted MRI signals for increased sensitivity to nucleus size, the impulse-propagator method in q-space is applied to a spherical geometry that would describe each member of a collection of cells and their nuclei, with several possible representations of the extracellular space. The method is extended to allow propagation between nucleus, cytoplasm, and extracellular space through semi-permeable membranes, using an approximate adjustment of intra-compartment propagators. Diffraction patterns are first calculated for the three compartments separately, for PGSE and OGSE pulse sequences, and verified by comparison with Monte Carlo simulations. The detailed patterns from the separate compartments determine the q value for maximum contrast in the total signal between large and small nuclei, an optimization that is not accurate in a Gaussian Phase Distribution (GPD) approximation. Then diffraction patterns are calculated for the case of linked compartments with semi-permeable membranes. The treatment of permeability adequately estimates pulse-sequence parameters for maximum contrast in calculated signal as nucleus size varies.