High fidelity fiber orientation density functions from fiber ball imaging

Abstract

The fiber orientation density function (fODF) in white matter is a primary physical quantity that can be estimated with diffusion MRI. It has often been employed for fiber tracking and microstructural modeling. Requirements for the construction of high fidelity fODFs, in the sense of having good angular resolution, adequate data to avoid sampling errors, and minimal noise artifacts, are described for fODFs calculated with fiber ball imaging. A criterion is formulated for the number of diffusion encoding directions needed to achieve a given angular resolution. The advantages of using large b-values (≥6000 s/mm 2 ) are also discussed. For the direct comparison of different fODFs, a method is developed for defining a local frame of reference tied to each voxel's individual axonal structure. The Matusita anisotropy axonal is proposed as a scalar fODF measure for quantifying angular variability. Experimental results, obtained at 3 T from human volunteers, are used as illustrations.

PyDesigner: A Pythonic Implementation of the DESIGNER Pipeline for Diffusion Tensor and Diffusional Kurtosis Imaging

“…However, it should be emphasized that the validity of WMTI is restricted to white matter regions with high FA (i.e., FA ≳ 0.4) and with some WMTI metrics having a limited accuracy due to assuming parallel alignment of axons in any given voxel. FBI (Jensen et al, 2016; Moss et al, 2019; Moss and Jensen, 2021) is a distinct dMRI method applicable throughout the cerebral white matter, which requires high b -value (i.e., b ≥ 4000 s/mm 2 ) dMRI data sampled with a minimum of about 64 diffusion encoding directions (along with data for b = 0). The main outputs of FBI are the fiber orientation density function (fODF) for each white matter voxel, which can be used for white matter tractography and serves as an input for FBWM, as well as the intra-axonal fractional anisotropy (FAA).…”

“…• Parameter extraction. Culmination of IRLLS, constrained tensor fitting, and brute-forced AKC correction yield biologically plausible tensors suitable for microstructural evaluation via DTI, DKI, fiber ball imaging (FBI, Jensen et al, 2016;Moss et al, 2019;Moss and Jensen, 2021) and fiber ball white matter modelling (FBWM, McKinnon et al, 2018). PyDesigner speeds up the tensor fitting regime by limiting computations within voxels that only contain brain tissue by This is done as DKE requires only a single b0 volume placed at the beginning of an input DWI for tensor fitting.…”

Impact of intra‐axonal kurtosis on fiber orientation density functions estimated with fiber ball imaging

“…The response kernel depends only on the dot product n ⋅ u as a consequence of rotational invariance along with an assumption that axons can be regarded as being effectively axisymmetric. We further assume the reflection symmetry F(−u) = F(u), which is typical for fODFs, 10 and, without loss of generality, the symmetry R(−x) = R(x) as well as the normalization condition,…”

“…As a consequence of this truncation, the estimated fODF will have a finite angular resolution of approximately 20 • -35 • depending on 2L. 10 In carrying out explicit calculations, it is convenient to apply the spherical harmonic addition theorem, 25…”

“…where 1 F 1 (a; b; x) is the confluent hypergeometric function of the first kind. A superscript (0) has been appended to the eigenvalue symbol to indicate that Equation (10) assumes K a = 0. It is important to appreciate that D a is regarded, from an FBI perspective, as an input parameter rather than a fitting parameter.…”