Frequency distribution and signal formation around a vessel

We describe the NMR signal formation properties of a single vessel. Instead of assuming the frequency distribution to be a simple Lorentzian or Gaussian one, we take into account that the frequency distribution around the vessel is a complex function. Considering the static dephasing regime we find a relationship between signal formation and frequency distribution. Analytical expressions for the frequency distribution in a voxel and the magnetization decay are obtained. In the case of small volume fractions of blood and week magnetic fields the results can be used for describing signal formation processes in a vascular network. A relationship between the frequency distribution and the properties of the vascular network is derived. The magnetization decay in different time regimes is discussed. The result is relevant for describing signal formation processes around a vessel for arbitrary pulse sequences.