Computer simulation and six-dimensional spin density and velocity NMR microimaging of lacunar systems: A comparative analysis of percolation properties

Abstract

Using computer-simulated random site-percolation networks as a template, phantoms of lacunar systems were fabricated. The pore space was filled with water and experimentally investigated with the aid of nuclear magnetic resonance (NMR) microimaging. A pulse sequence providing six-dimensional spin density and velocity NMR image data was employed for the combined record of the three-dimensional spin-density distribution and the three-dimensional velocity vector field of water percolating through the pore networks. From these data, three-dimensional velocity magnitude images were derived. The exclusion of all voxels of the spin density images with velocities below the noise level provides an experimental means to directly image the percolation backbone. An evaluation procedure for the NMR image data was established that reliably renders the pair correlation function and the mean volume-averaged porosity as a function of the probe volume radius. Characteristic parameters refer to the fractal dimensionality, to the correlation length, and to the short-range order. The theoretical predictions can thus be compared directly with experiments. For comparison, the water-filled pore spaces of other, less random lacunar objects such as glass-bead agglomerates and a natural sponge were also examined with respect to percolation properties.