Unbiasing the spherical variance of a diffusion-weighted MR signal: An application to intra-axonal T2 estimation

Motivation: The spherical variance (SV) from multiparametric diffusion MRI acquisitions enables the estimation of the axonal T2 relaxation time. The SV is prone to a noise-induced bias due to positively skewed Rician statistics, leading to overestimation in the axonal T2 parameter. Goal(s): To derive a method to mitigate the Rician bias in the SV parameter map. Approach: A closed-form formula to remove the Rician bias from the SV has been analytically derived and verified with in silico and in vivo data. Results: The bias-corrected SV reduces the estimation error compared to the SV, translating to a less pronounced misestimation in the axonal T2 parameter. Impact: The SV is a practical parameter to infer the properties of restricted compartments with diffusion MRI. This work shows a formula to remove the Rician bias from the SV. The correction can be used for other SV-based diffusion MRI measures.