Computing the Orientational-Average of Diffusion-Weighted MRI Signals: A Comparison of Different Techniques

Abstract

Numerous applications in diffusion MRI, from multi-compartment modeling to power-law analyses, involves computing the orientationally-averaged diffusion-weighted signal. Most approaches implicitly assume, for a given b-value, that the gradient sampling vectors are uniformly distributed on a sphere (or shell), computing the orientationally-averaged signal through simple arithmetic averaging. One challenge with this approach is that not all acquisition schemes have gradient sampling vectors distributed over perfect spheres (either by design, or due to gradient non-linearities). To ameliorate this challenge, alternative averaging methods include: weighted signal averaging; spherical harmonic representation of the signal in each shell; and using Mean Apparent Propagator MRI (MAP-MRI) to derive a three-dimensional signal representation and estimate its isotropic part. This latter approach can be applied to all q-space sampling schemes, making it suitable for multi-shell acquisitions when unwanted gradient non-linearities are present. Here, these different methods are compared under different signal-to-noise (SNR) realizations. With sufficiently dense sampling points (61points per shell), and isotropically-distributed sampling vectors, all methods give comparable results, (accuracy of MAP-MRI-based estimates being slightly higher albeit with slightly elevated bias as b-value increases). As the SNR and number of data points per shell are reduced, MAP-MRI-based approaches give pronounced improvements in accuracy over the other methods.