On the lorentzian versus Gaussian character of time‐domain spin‐echo signals from the brain as sampled by means of gradient‐echoes: Implications for quantitative transverse relaxation studies

Purpose To determine whether Lorentzian or Gaussian intra‐voxel frequency distributions are better suited for modeling data acquired with gradient‐echo sampling of single spin‐echoes for the simultaneous characterization of irreversible and reversible relaxation rates. Clinical studies (e.g., of brain iron deposition) using such acquisition schemes have typically assumed Lorentzian distributions. Theory and Methods Theoretical expressions of the time‐domain spin‐echo signal for intra‐voxel Lorentzian and Gaussian distributions were used to fit data from a human brain scanned at both 1.5 Tesla (T) and 3T, resulting in maps of irreversible and reversible relaxation rates for each model. The relative merits of the Lorentzian versus Gaussian model were compared by means of quality of fit considerations. Results Lorentzian fits were equivalent to Gaussian fits primarily in regions of the brain where irreversible relaxation dominated. In the multiple brain regions where reversible relaxation effects become prominent, however, Gaussian fits were clearly superior. Conclusion The widespread assumption that a Lorentzian distribution is suitable for quantitative transverse relaxation studies of the brain should be reconsidered, particularly at 3T and higher field strengths as reversible relaxation effects become more prominent. Gaussian distributions offer alternate fits of experimental data that should prove quite useful in general. Magn Reson Med 74:51–62, 2015. © 2014 Wiley Periodicals, Inc.