Nucleus Size Determination in Q-Space Analysis of Three-Dimensional Cells

Gregory S. Duane¹, Yanwei W. Wang, Blake R. Walters, Jae K. Kim

The impulse-propagator (matrix) method is extended to a three-dimensional idealized cell geometry describing nucleus, cytoplasm, and extracellular fluid. A basis is constructed, appropriate for the boundary conditions specified on spheres, consisting of spherical Bessel functions of radius multiplied by spherical harmonics in the angular variables. For a PGSE sequence, clear diffraction patterns are obtained for both nucleus and cytoplasm, with cytoplasm dominating the total signal. Results compare favorably with Monte Carlo simulation results. With OGSE, the nuclear diffraction pattern dominates. In either case, vestiges of the diffraction pattern in the total signal could potentially be used to assess nucleus size.