Single-Shell Return-to-the-Origin Probability Diffusion Mri Measure Under a Non-Stationary Rician Distributed Noise

The sensitivity of diffusion MRI to microstructural properties and experimental factors

“…This study was not confirmed by Fick et al (2016) , where significant deteriorations have been observed with the RTOP and RTAP. Further, Pieciak et al (2019) has shown that the relative error of the RTOP measure increases approximately linearly with decreasing the number of gradients once fixing the maximal b -value parameter.…”

“…Such techniques have also been recently introduced both for non-stationary Rician ( Maximov et al, 2012 , Veraart et al, 2013a , Aja-Fernández et al, 2015 , Pieciak et al, 2017 ) and non-stationary nc- χ noise ( Tabelow et al, 2015 , Veraart et al, 2016b , Pieciak et al, 2016 ). Unlike the variance-stabilizing approach (VST; Pieciak et al, 2016 , Pieciak et al, 2019 ) that firstly transforms the signal-dependent Rician/nc- χ noise to a signal-independent variate and then estimates the noise pattern, most approaches estimate noise maps assuming Gaussian distribution and then apply a post-hoc correction by Koay and Basser (2006) . As a side note, most of the methods intended for diffusion MRI estimate the spatially-variant noise map given all gradient directions at a certain b -value.…”

“… ( Li et al, 2018 ) SMT gradients The recommended number of uniformly distributed diffusion-sensitizing gradients defined in terms of CV < 0.05 to a reference is given by 10 × b / b 1 ( b 1 = 1000 s/mm 2 ) for a typical SNR ∼ 20 measured at the baseline. Decreasing the number of gradients increases at an exponential rate the CV of the signal ( Pieciak et al, 2019 ) MAP-MRI, MAPL Gradients Decreasing the number of diffusion-sensitizing gradients increases the mean relative error (up to 20% for 10% measurements out of 270) and the standard deviation of the RTOP both for the MAP-MRI and MAPL. The mean relative error of the RTOP increases approximately linearly in the function of the subsampled gradients ( Aja-Fernández et al, 2020 ) MAP-MRI, MAPL, RBFs Shells, gradients, b -value Increasing the maximal b -value parameter (i.e., number of shells and gradients) leads to the amplification of microstructural-related measures (RTOP, RTAP, RTPP) independently of the technique used to estimate the EAP function (MAP-MRI, MAPL, RBFs) Modalities: QBI – Q-ball imaging, SD – spherical deconvolution, NODDI – neurite orientation dispersion and density imaging, DKI – diffusion kurtosis imaging, 3CM – three-compartment model, SMT – spherical mean technique, MAP-MRI – mean apparent propagator MRI, MAPL – Laplacian MAP, RBFs – radial basis functions, 3D-SHORE – three-dimensional simple harmonic oscillator based reconstruction and estimation, AMICO – accelerated microstructure imaging via convex optimization.…”

“…The former group includes alternative measures that can be obtained for example from the q-space domain data representation ( Wu and Alexander, 2007 , Wu et al, 2008 , Aja-Fernández et al, 2018 , Pieciak et al, 2019 , Aja-Fernández et al, 2019 , Aja-Fernández et al, 2020 ). Illustrative examples are the average sample diffusion (ASD) and the diffusion coefficient of variation (CVD).…”

“…The alternative measures should exhibit unbiasedness in terms of one or multiple factors such as the noise (e.g., the expectation of log-Rician random variable is assumed to be unbiased for high SNR; see Aja-Fernández et al, 2018 ), the number of diffusion-sensitizing gradients or the b -value. Besides, they should provide new diagnostic information (see Aja-Fernández et al, 2019 ) previously hindered by other techniques or exhibit high correlations to community accepted quantities for instance DT-MRI-based parameters ( Aja-Fernández et al, 2018 ) or microstructural quantities derived from the MAP-MRI model like the RTOP, RTAP, and RTPP ( Pieciak et al, 2019 , Aja-Fernández et al, 2020 ).…”