Diffusion-mediated nuclear spin phase decoherence in cylindrically porous materials

In NMR or MRI of complex materials, including biological tissues and porous materials, magnetic susceptibility differences within the material result in local magnetic field inhomogeneities, even if the applied magnetic field is homogeneous. Mobile nuclear spins move though the inhomogeneous field, by translational diffusion and other mechanisms, resulting in decoherence of nuclear spin phase more rapidly than transverse relaxation alone. The objective of this paper is to simulate this diffusion-mediated decoherence and demonstrate that it may substantially reduce coherence lifetimes of nuclear spin phase, in an anisotropic fashion. We do so using a model of cylindrical pores within an otherwise homogeneous material, and calculate the resulting magnetic field inhomogeneities. Our simulations show that diffusion-mediated decoherence in a system of parallel cylindrical pores is anisotropic, with coherence lifetime minimised when the array of cylindrical pores is perpendicular to B0. We also show that this anisotropy of coherence lifetime is reduced if the orientations of cylindrical pores are disordered within the system. In addition we characterise the dependence on B0, the magnetic susceptibility of the cylindrical pores relative to the surroundings, the diffusion coefficient and cylinder wall thickness. Our findings may aid in the interpretation of NMR and MRI relaxation data.