Benjamin Ades-Aron1, Jelle Veraart1,2, Elias Kellner3, Yvonne W. Lui1, Dmitry S. Novikov1, and Els Fieremans1
1Center for Biomedical Imaging, New York University School of Medicine, New York, NY, United States, 2iMinds Vision Lab, University of Anterp, Antwerp, Belgium, 3Department of Radiology, University Medical Center Freiburg, Freiburg, Germany
Synopsis
We propose a new pipeline (DESIGNER) for diffusion
image processing that includes Marchenko Pastur denoising and Gibbs artifact removal,
and thereby improves the precision and accuracy of the diffusion tensor and
kurtosis tensor parameter estimation. In particular, our results show no notorious
black voxels on kurtosis maps, while the original resolution is maintained in
contrast to state-of-the-art processing methods that apply smoothing. Purpose
To
maximize the quality, precision, and accuracy of Diffusion Kurtosis parameters
derived from diffusion MRI (dMRI) data without compromising efficiency. Diffusion
Kurtosis Imaging (DKI) is a clinically feasible extension of conventional
Diffusion Tensor Imaging (DTI) that has recently emerged as a more
comprehensive and empirically useful method for evaluating brain tissue
microstructural complexity
1. Unfortunately, fitting the DKI signal
representation to dMRI data often results in physically and mathematically
implausible values, cf. negative diffusion and kurtosis coefficients often observed as black voxels in kurtosis maps (See
Figure). These physically implausible kurtosis parameters bias statistical
analysis, modeling and interpretation of dMRI data. The outliers particularly originate
from the combination of low radial diffusivities with thermal noise and/or
Gibbs ringing
2. Smoothing and imposing positivity constraints
3 on the DKI fit
are the current practice to clean up parametric maps
4. However, spatial
smoothing inherently lowers the spatial resolution of the image and introduces
additional partial volume effects that lead to complications in further
quantitative analyses or to biases in microstructural modeling. Furthermore,
constrained parameter fitting is time consuming and, more importantly, may bias
the estimator. Here we propose a new pipeline, dubbed DESIGNER, where we
decompose the problem in 2 independent steps: (a) denoising, including Rician
bias correction and (b) Gibbs correction. These two pre-processing steps alleviate
the need for smoothing and allow for unconstrained weighted linear least squares
fitting (WLLS) when performing the kurtosis tensor fit routine without lowering
the resolution of the data. We demonstrate here how our new pipeline enables the
robust estimation of parametric kurtosis metrics on clinically acquired DKI
datasets.
Methods
dMRI
with $$$b = 0, 0.25, 1, \mathrm{and}\ 2\ \mathrm{ms/\mu m}^{2}$$$ along $$$84$$$ directions in total was acquired in a volume of $$$50$$$ slices, $$$130\times 130$$$ matrix, with voxel size $$$ = 1.7\ \mathrm{mm} \times 1.7\ \mathrm{mm} \times 3\ \mathrm{mm}\ (8.6\ \mathrm{mm}^{3})$$$, TE $$$ = 70\ \mathrm{ms,\ and}$$$ TR $$$ = 3500\ \mathrm{ms}$$$, on a Magnetom Prisma 3T MRI system (Siemens AG, Healthcare Sector, Erlangen, Germany) on a
51 y/o female as part of a clinical study and analyzed retrospectively. Denoising: We adopt the idea of noise removal by means of
transforming a redundant data matrix into the local Principal Component
Analysis (PCA) domain and preserving only the principal components that exceed
a data-driven threshold. The threshold for PCA denoising is
based on the fact that noise-only eigenvalues obey the universal
Marchenko-Pastur (MP) law
5. Gibbs ringing
artifacts are subsequently removed by resampling the
denoised image such that sampling points coincide with the zero-crossings of
the sinc functions
6. EPI, eddy distortion and motion correction were performed
using FSL
7 prior to the final unconstrained weighted linear least squares fit.
Alternatively, the denoising and Gibbs removal were replaced by 2D Gaussian
smoothing using a full-width at half-maximum (FWHM) of 2 times the voxel size prior to a constrained WLLS
4.
Results
& Discussion
Figure 1 displays the different pipelines, along with
the resulting parametric mean kurtosis (MK) maps, either without any artifact
correction (a), or obtained after smoothing and imposing constraints in the fit
(the current state-of-the-art) (b), or after noise and Gibbs removal (DESIGNER)
(c). While both the state-of-the art (b) and DESIGNER pipeline (c) effectively
eliminate outliers in the MK map, the smoothing results in partial volume
effects and spurious deviations in grey/white matter values. Difference maps (Figure
2) showing the signal being removed by denoising and smoothing, also clearly
illustrate that smoothing eliminates anatomy features while our denoising
process removes only randomly distributed Rician noise. Figure 3 shows residual
histograms calculated for denoising, denoising + Gibbs correction, and smoothing. While noise and Gibbs
removal did not shift the distribution, smoothing introduces a systematic bias
to the dataset, which can potentially skew clinical analyses attempting to
correlate diffusion parameters with pathological patterns.
Conclusion
Instead of imposing constraints in fit routines and
smoothing to estimate diffusion tensor and kurtosis tensor parameters, we
propose here a new processing pipeline including Marchenko-Pastur noise and
Gibbs artifact removal that allows for a completely unconstrained model fit
4,8. Using
an unconstrained fit is advantageous as it can be computed more quickly and
makes the diffusion parameter estimates more likely to reflect true physiology.
Acknowledgements
This work was financially supported by R01-NS088040-02References
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