Effects of pore size and shape distributions on diffusion pore imaging by NMR

In medical imaging and porous media research, NMR diffusion measurements are extensively used to investigate the structure of diffusion restrictions such as cell membranes. Recently, several methods have been proposed to unambiguously determine the shape of closed pores or cells by NMR diffusion experiments. This could allow imaging porous media or measuring cells size distributions. The first approach uses a combination of a long and a short diffusion weighting gradient pulse [1] [2] [3], while the other techniques employ short gradient pulses only [4] [5]. The long-narrow approach is superior regarding the required signal; the short-gradient methods allow a more flexible sequence design, such as using stimulated echoes. While the eventual aim of these methods is to determine pore size and shape distributions, the focus has been so far on identical pores.

Thus, the aim of this work was to investigate the ability of the different pore imaging methods to resolve pore size and orientation distributions. Simulations were performed employing different distributions of pore size and orientation and varying timing parameters to compare the imaging approaches. The long-narrow gradient profile is most advantageous to image pore size distributions. For pores with different sizes in the considered volume element, the long-narrow approach yields an image showing the arithmetic average of the individual pore space functions. These images can be used to directly estimate pore size distributions.

In contrast, for the methods using several short gradient pulses, the Fourier transforms of the individual pore space functions contribute in a non-linear way to the signal. Thus, the reconstructed pore images deviate from the averaged pore shape. For pore size distributions, the short-gradient methods suppress larger pores or induce a considerable blurring. However, this effect also depends on the symmetry of the pores. Moreover, pore shape specific artifacts occur; for example, the central part of a distribution of cylinders may be largely underestimated. The effects occurring for pore rotations are also dependent on the symmetry and specific pore geometry.

Depending on the actual pore distribution, short-gradient methods may nonetheless yield good approximations of the average pore shape. Furthermore, the application of short-gradient methods can be advantageous to differentiate whether pore size or orientation distributions or identical pores with an inhomogeneous signal intensity, e.g. due to surface relaxation, are predominant.