MR Contrast Due to Microscopically Heterogeneous Magnetic Susceptibility: Numerical Simulations and Applications to Cerebral Physiology

We calculate the effects of subvoxel variations in magnetic susceptibility on MR image intensity for spin-echo (SE) and gradient-echo (GE) experiments for a range of microscopic physical parameters. The model used neglects the overlap of gradients from one magnetic inclusion to the next, and so is valid for low volume fractions and weak perturbations of the magnetic field. Transverse relaxation is predicted to deviate significantly from linear exponential decay in both SE and GE at a particle radius of 2.5 microns. Calculated changes in transverse relaxation rates for SE and GE increase linearly with volume fraction of high-susceptibility regions of 5 microns diameter, but increase with about the 3/2 power of volume fraction of regions with 15 micron spacing between centers. This sensitivity to the actual size and spacing of magnetized regions may allow them to be measured on the basis of contrast. without being resolved in images. GE and SE decay rates are approximately twice as sensitive to long cylinders of 5 microns diameter than to spheres of the same size, for diffusion constants of 2.5 micron 2/ms. Calculated changes in transverse decay rates increase with approximately the square of field and susceptibility variation for 5-microns spheres and a diffusion constant of 2.5 microns 2/ms. This exponent is smaller for cylindrical magnetized regions of the same size, and also depends on the diffusion constant. We discuss possible applications of our theoretical results to the analysis of the effects of high-susceptibility contrast agents in brain. Experimental data from the literature are compared with calculated signal changes according to the model. The monotonic dependence of decay rates on the volume of distribution of the contrast agent suggests that cerebral blood volume and flow could be measured using MR contrast.