gKFA: a geometric framework for kurtosis fractional anisotropy

Area of Science:

• Medical Imaging
• Biophysics
• Neuroimaging

Background:

• Diffusion tensor imaging (DTI) analyzes water diffusion in tissues.
• Diffusion kurtosis imaging (DKI) extends DTI by incorporating non-Gaussian diffusion effects.
• Analyzing the kurtosis tensor's geometric structure is complex.

Purpose of the Study:

• To investigate the 3D geometric structure of the kurtosis tensor.
• To introduce a geometry-inspired anisotropy descriptor for kurtosis.
• To define and evaluate geometric kurtosis fractional anisotropy (gKFA).

Main Methods:

• Mapped symmetric second-order quadratic forms were used to represent kurtosis anisotropy.
• Geometric kurtosis fractional anisotropy (gKFA) was defined as the geometric mean of fractional anisotropies from mapped quadratic forms.
• Evaluated using simulations, phantoms, and in vivo human and rodent brain data.

Main Results:

• gKFA demonstrated sensitivity to directional heterogeneity and tissue complexity in simulations and phantoms, surpassing conventional KFA.
• In human brain data, gKFA showed distinct behavior from KFA and standard kurtosis measures (MK, AK, RK).
• gKFA exhibited improved tissue contrast and complementary information compared to KFA in both human and rodent brains.

Conclusions:

• gKFA provides a novel kurtosis-anisotropy descriptor with a strong geometric basis.
• gKFA offers enhanced sensitivity and tissue contrast in neuroimaging applications.
• This approach facilitates a more nuanced understanding of tissue microstructure through DKI.