Linear rotationally invariant kurtosis measures from double diffusion encoding MRI

Purpose

To characterize the complete set of linear rotationally invariant kurtosis measures provided by double diffusion encoding (DDE) MRI, show their utility in distinguishing different types of multiple Gaussian compartment (MGC) models, and demonstrate simplified acquisition and analysis schemes for their estimation.

Theory and methods

The lowest order novel information obtainable with DDE MRI can be encapsulated in a six-dimensional kurtosis tensor. The most basic DDE MRI kurtosis measures are rotational invariants that are linear in this tensor while depending on no other physical quantities. We identify four such invariants and show that any others must be linear combinations of these. The invariants are applied to classify MGC models according to whether they include microscopic anisotropy or intercompartmental water exchange. In addition, they are used to investigate the effect of exchange on estimates of the microscopic fractional anisotropy (μFA). Simplified acquisition and analysis schemes for the invariants are proposed and demonstrated with human brain data obtained at 3 T.

Results

For the considered brain regions, the kurtosis invariants are found to be largely consistent with MGC models having microscopic anisotropy. They also indicate that water exchange in gray matter may affect estimates of μFA.

Conclusion

The kurtosis measures can classify MGC models according to whether they have microscopic anisotropy or water exchange, and they can be estimated with simple acquisition and analysis schemes. Measurements of the invariants in brain support the validity of MGC models with microscopic anisotropy and the importance of water exchange for modeling diffusion in gray matter.