A new concept for improved quantitative analysis of reversible transverse relaxation in tissues with variable microscopic field distribution

Purpose: The intravoxel distribution of the magnetic field strongly influences signal dephasing after RF excitation and the resulting signal decay in gradient echo-based MRI. In this work, several different field distribution models were applied and tested for analysis of microscopic field characteristics within pixels.

Theory: A flexible model for improved pixel-wise characterization of the underlying field distribution is introduced. The proposed symmetric alpha-stable (SαS) distribution covers Lorentzian, Gaussian, and intermediate field distributions in a continuous way using a two-parametric (width and shape) function.

Methods: The new model was applied on human brain, potatoes (homogeneous isotropic tissue), and stems of pineapple (anisotropic fibrous tissue). Effects of microscopic structure and background gradients on the shape and the widths of the microscopic field distribution were analyzed using gradient echo sampling of the spin echo and multigradient-echo sequences. Effects of non-Lorentzian shapes of microscopic field distributions on the results of common $T_2^{\ast }$ measurements with mono-exponential fitting of signal values were tested.

Results: Many pixels of the examined objects showed field characteristics in between Lorentzian and Gaussian shapes. Microscopic field inhomogeneities caused by microscopic susceptibility effects and background gradients sometimes led to rather Gaussian than Lorentzian field distribution. In cases with nearly Gaussian field distribution, mono-exponential fitting of the signal decay resulted in different $T_2^{\ast }$ values, depending on the sampling points.

Conclusions: Using the concept of more flexible distributions for characterization of microscopic susceptibility effects in tissue provides better fitting of data and nearly sampling point-independent results than common $T_2^{\ast }$ measurements with mono-exponential fitting.