A mathematical model of diamagnetic line broadening in lung tissue and similar heterogeneous systems: Calculations and measurements

Abstract In order to explain recently observed internal inhomogeneous broadening in lung tissue, we constructed and calculated diamagnetic field shifts for models consisting of a spherical shell of water and a hexagonally packed array of spherical air bubbles in water. For the spherical-shell model, the field equations were solved exactly for an arbitrary number of concentric shells. In contrast, in the hexagonal model, a Monte Carlo algorithm was used to pick points within the specimen at which the field was calculated to first order by adding together contributions from all the spheres. The linewidth calculated for the spherical-shell model agrees well with the results of our experimental measurements. Furthermore, the hexagonal model accurately predicts the observed linewidth in rat lung. These models can be used in correlating the NMR linewidth with the state of inflation or injury of the lung. They also may have application in a broad class of heterogeneous systems (e.g., slurries, bone).