Vessel radius mapping in an extended model of transverse relaxation

Spin dephasing of the local magnetization in blood vessel networks can be described in the static dephasing regime (where diffusion effects may be ignored) by the established model of Yablonskiy and Haacke. However, for small capillary radii, diffusion phenomena for spin-bearing particles are not negligible. In this work, we include diffusion effects for a set of randomly distributed capillaries and provide analytical expressions for the transverse relaxation times T2* and T2 in the strong collision approximation and the Gaussian approximation that relate MR signal properties with microstructural parameters such as the mean local capillary radius. Theoretical results are numerically validated with random walk simulations and are used to calculate capillary radius distribution maps for glioblastoma mouse brains at 9.4 T. For representative tumor regions, the capillary maps reveal a relative increase of mean radius for tumor tissue towards healthy brain tissue of (p < 0.001). The presented method may be used to quantify angiogenesis or the effects of antiangiogenic therapy in tumors whose growth is associated with significant microvascular changes.