Diffusion Gradient Calibration Influences the Accuracy of Fibre Orientation Density Function Estimation: Validation by Efficiency Measure

Introduction. Diffusion-weighted (DW) MRI provides important information regarding the arrangement of white matter fibres. However, imperfections in the DW gradients may cause errors in the estimation of diffusion parameters. The sources of the gradient errors are various and may arise from long-term eddy currents, background gradients, imaging gradients, and spatial non-linearity and non-uniformity of the gradients. We present results demonstrating the influence of these errors into the accuracy of the fibre orientation density function (ODF) estimation. A DW gradient calibration scheme, which can be used to mitigate the gradient errors, is also described. We compare the reconstructed fibre ODFs from two datasets, acquired in vivo with and without the application of the diffusion gradient calibration scheme [1, 2] and calculated the statistical efficiency [3] of the unbiased fibre ODF estimators for these datasets. Methods. Several approaches for reconstructing fibre orientations from high angular resolution diffusion imaging (HARDI) have been proposed as alternative methods to diffusion tensor imaging (DTI) [4-8]. Here, we obtained the fibre ODF combining the general idea of spherical deconvolution [6] with the Funk-Hecke theorem [7], which leads to: