Computing the orientational-average of diffusion-weighted MRI signals: a comparison of different techniques

Maryam Afzali,Hans Knutsson,Derek K Jones,Evren Özarslan

doi:10.1038/s41598-021-93558-1

Maryam Afzali, Hans Knutsson + Show 2 more

Open Access

https://doi.org/10.1038/s41598-021-93558-1

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Abstract

Numerous applications in diffusion MRI involve 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. 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’. Here, these different methods are simulated and compared under different signal-to-noise (SNR) realizations. With sufficiently dense sampling points (61 orientations per shell), and isotropically-distributed sampling vectors, all averaging methods give comparable results, (MAP-MRI-based estimates give slightly higher accuracy, 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 significantly higher accuracy compared with the other methods. We also apply these approaches to in vivo data where the results are broadly consistent with our simulations. A statistical analysis of the simulated data shows that the orientationally-averaged signals at each b-value are largely Gaussian distributed.

Highlights

Diffusion MRI is a non-invasive technique that is sensitive to differences in tissue microstructure, which comprises a combination of micro-environments with potentially different orientational characteristics
To factor out the effect of macroscopic anisotropy in diffusion MRI, i.e., to estimate the signal for the “powdered” structure, two approaches have been proposed: (i) taking the “isotropic component” of the s ignal[3,4]; this is typically achieved by representing the signal with a series of spherical harmonics and keeping the leading term; and (ii) numerical computation of the orientational average of the diffusion-weighted signal profile[5,6]
MAP-based methods outperform the shell-by-shell estimates, and the regularization employed in MAPL method yields a further reduction in d1

Summary

Introduction

Diffusion MRI is a non-invasive technique that is sensitive to differences in tissue microstructure, which comprises a combination of micro-environments with potentially different orientational characteristics. To factor out the effect of macroscopic anisotropy in diffusion MRI, i.e., to estimate the signal for the “powdered” structure, two approaches have been proposed: (i) taking the “isotropic component” of the s ignal[3,4]; this is typically achieved by representing the signal with a series of spherical harmonics and keeping the leading (zeroth order) term; and (ii) numerical computation of the orientational average of the diffusion-weighted signal profile[5,6]. The accuracy of the powder-averaged signal depends on both the set of gradients employed in the data acquisition and the numerical method used to estimate the average Regarding the former, different strategies have been proposed to optimize the sampling strategy, the most well-known and widely-used of which is the electrostatic repulsion a lgorithm[17]. Our simulations feature varying levels of noise, to explore the performance of the different algorithms under different SNR levels

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