A pitfall in the reconstruction of fibre ODFs using spherical deconvolution of diffusion MRI data

Abstract

Diffusion weighted (DW) MRI facilitates non-invasive quantification of tissue microstructure and, in combination with appropriate signal processing, three-dimensional estimates of fibrous orientation. In recent years, attention has shifted from the diffusion tensor model, which assumes a unimodal Gaussian diffusion displacement profile to recover fibre orientation (with various well-documented limitations), towards more complex high angular resolution diffusion imaging (HARDI) analysis techniques.Spherical deconvolution (SD) approaches assume that the fibre orientation density function (fODF) within a voxel can be obtained by deconvolving a ‘common’ single fibre response function from the observed set of DW signals. In practice, this common response function is not known a priori and thus an estimated fibre response must be used. Here the establishment of this single-fibre response function is referred to as ‘calibration’. This work examines the vulnerability of two different SD approaches to inappropriate response function calibration: (1) constrained spherical harmonic deconvolution (CSHD)—a technique that exploits spherical harmonic basis sets and (2) damped Richardson–Lucy (dRL) deconvolution—a technique based on the standard Richardson–Lucy deconvolution.Through simulations, the impact of a discrepancy between the calibrated diffusion profiles and the observed (‘Target’) DW-signals in both single and crossing-fibre configurations was investigated. The results show that CSHD produces spurious fODF peaks (consistent with well known ringing artefacts) as the discrepancy between calibration and target response increases, while dRL demonstrates a lower over-all sensitivity to miscalibration (with a calibration response function for a highly anisotropic fibre being optimal). However, dRL demonstrates a reduced ability to resolve low anisotropy crossing-fibres compared to CSHD. It is concluded that the range and spatial-distribution of expected single-fibre anisotropies within an image must be carefully considered to ensure selection of the appropriate algorithm, parameters and calibration. Failure to choose the calibration response function carefully may severely impact the quality of any resultant tractography.

Auto-calibrating Spherical Deconvolution Based on ODF Sparsity

“…Results confirm a previous finding that even when noise is very low, deconvolution is unreliable when the kernel overestimates the true anisotropy [3]. Auto-calibration effectively ameliorates this problem, especially in the singlefiber case.…”

“…Even though f R is commonly constrained to represent a non-negative function F R (θ, φ) [1], it has been pointed out that this does not reliably prevent erroneous peaks in the fODF [5], especially when the kernel R overestimates the anisotropy of the true single fiber response [3]. We propose to reduce spurious peaks via an additional sparsity constraint on F R , by selecting a kernelR such that…”

“…Recently, it has been pointed out that a mismatch between the true fiber response and the kernel used in CSD can lead to spurious peaks in the fODF [3]. Therefore, a more careful choice of the deconvolution kernel has the potential to improve fODF estimates, especially in cases where white matter degradation is studied, since degraded fibers can have a significantly different MR response.…”

Beyond fractional anisotropy: Extraction of bundle-specific structural metrics from crossing fiber models

“…These are particularly dangerous, as these peaks cannot be discerned from peaks caused by the underlying microstructure. The stability and the occurrence of spurious peaks may also be ameliorated by using the damped Richardson-Lucy deconvolution (Dell'Acqua et al, 2007, Parker et al, 2013.…”

Convex Non-negative Spherical Factorization of Multi-Shell Diffusion-Weighted Images

“…On the other hand, spherical deconvolution (SD) approaches estimate the fibre orientation distribution function (ODF), given a fibre response function (RF) that is typically estimated from and hence adapted to the data at hand [4]. However, this calibration of the RF may severely impact the reconstructed fibre ODF [5,6]. Additionally, the presence of partial volume effects (PVE), originating from adjacent grey matter (GM) and cerebrospinal fluid (CSF), has been shown to affect SD [7].…”