The Drum is Visible in Nuclear Magnetic Resonance Diffusion Experiments

Frederik Bernd Laun¹, Wolfhard Semmler¹, Bram Stieltjes²

While nuclear magnetic resonance diffusion experiments are widely used to resolve the structure of cells and porous media, it has been elusive whether they can reveal the exact shape of boundaries confining the diffusion process. This question is mathematically closely related to Kacs hear the drum problem. Although the shape of the drum is not hearable, we show that the confining boundary in closed pores can indeed be detected using modified Stejskal-Tanner magnetic field gradients. These modified gradients can act like imaging gradients, and potentially allow novel imaging contrasts.