Recursive calibration of the fiber response function for spherical deconvolution of diffusion MRI data

There is accumulating evidence that at current acquisition resolutions for diffusion-weighted (DW) MRI, the vast majority of white matter voxels contains "crossing fibers", referring to complex fiber configurations in which multiple and distinctly differently oriented fiber populations exist. Spherical deconvolution based techniques are appealing to characterize this DW intra-voxel signal heterogeneity, as they provide a balanced trade-off between constraints on the required hardware performance and acquisition time on the one hand, and the reliability of the reconstructed fiber orientation distribution function (fODF) on the other hand. Recent findings, however, suggest that an inaccurate calibration of the response function (RF), which represents the DW signal profile of a single fiber orientation, can lead to the detection of spurious fODF peaks which, in turn, can have a severe impact on tractography results. Currently, the computation of this RF is either model-based or estimated from selected voxels that have a fractional anisotropy (FA) value above a predefined threshold. For both approaches, however, there are user-defined settings that affect the RF and, consequently, fODF estimation and tractography. Moreover, these settings still rely on the second-rank diffusion tensor, which may not be the appropriate model, especially at high b-values. In this work, we circumvent these issues for RF calibration by excluding "crossing fibers" voxels in a recursive framework. Our approach is evaluated with simulations and applied to in vivo and ex vivo data sets with different acquisition settings. The results demonstrate that with the proposed method the RF can be calibrated in a robust and automated way without needing to define ad-hoc FA threshold settings. Our framework facilitates the use of spherical deconvolution approaches in data sets in which it is not straightforward to define RF settings a priori.