Auto-calibrating Spherical Deconvolution Based on ODF Sparsity

Abstract

Abstract. Spherical deconvolution models the diffusion MRI signal as the convolution of a fiber orientation density function (fODF) with a single fiber response. We propose a novel calibration procedure that automatically determines this fiber response. This has three advantages: First, the user no longer needs to provide an estimate of the response. Second, we estimate a per-voxel fiber response, which is more adequate for the analysis of patient data with focal white matter degeneration. Third, parameters of the estimated response reflect diffusion properties of the white matter tissue, and can be used for quantitative analysis. Our method works by finding a tradeoff between a low fitting error and a sparse fODF. Results on simulated data demonstrate that autocalibration successfully avoids erroneous fODF peaks that can occur with standard deconvolution, and that it resolves fiber crossings with better angular resolution than FORECAST, an alternative method. Parameter maps and tractography results corroborate applicability to clinical data.

Characterizing brain tissue by assessment of the distribution of anisotropic microstructural environments in diffusion‐compartment imaging (DIAMOND)

“…This is inconsistent with the known presence of many axonal diameters and many degrees of myelination throughout the brain , and the interpretation of extracted tissue parameters from the fascicle orientation distribution function remains unclear. While extracting a fascicle response function in each voxel was investigated recently , only a single fascicle response function can be used to deconvolve the signal in a voxel and the signal arising from two crossing fascicles with different characteristics (e.g., healthy and not healthy) cannot be modeled.…”

Modelling white matter with spherical deconvolution: How and why?

“…Nonetheless, some methods have been proposed to estimate a response function per voxel . This is a difficult problem to solve, given the tight relationship between the fODF and the response function: the signal is inherently smooth, and this smoothness can be captured in either the response or the fODF, without otherwise affecting the quality of the fit.…”

“…This is a difficult problem to solve, given the tight relationship between the fODF and the response function: the signal is inherently smooth, and this smoothness can be captured in either the response or the fODF, without otherwise affecting the quality of the fit. In Reference , the response is estimated based on the premise that the fODF is sharp, an assumption that will not in general hold in regions of curvature or dispersion. On the other hand, Reference relies on the observation that, when the response function is modelled as an axially symmetric tensor, the radial diffusivity and mean diffusivity uniquely determine the mean DWI signal (averaged over all orientations) relative to the b = 0 signal, irrespective of the fODF (similar to Reference ).…”

Convexity-constrained and nonnegativity-constrained spherical factorization in diffusion-weighted imaging

“…Originally, white matter (WM) fibre response functions were fitted to the DWI data in a single-fibre mask of high FA, after reorientation of the diffusion tensor eigenvectors (Tournier et al, 2004, 2007). Alternative recursive approaches have been introduced, which segment single-fibre voxels and reorient the data based on the peaks of the fibre ODFs iteratively (Tournier et al, 2013; Tax et al, 2014), or which calibrate the kernel anisotropy in each voxel separately under sparsity constraints (Schultz and Groeschel, 2013). However, these techniques do not directly generalize to other tissue types, such as grey matter (GM) and cerebrospinal fluid (CSF).…”