Diffusion parameter EStImation with Gibbs and NoisE Removal (DESIGNER)
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 complexity1. 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 ringing2. Smoothing and imposing positivity constraints3 on the DKI fit are the current practice to clean up parametric maps4. 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) law5. Gibbs ringing artifacts are subsequently removed by resampling the denoised image such that sampling points coincide with the zero-crossings of the sinc functions6. EPI, eddy distortion and motion correction were performed using FSL7 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 WLLS4.

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 fit4,8. 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-NS088040-02

References

1. Jensen J. H., Helpern J. A. (2010). MRI quantification of non-Gaussian water diffusion by kurtosis analysis. NMR Biomed. 23, 698–710.

2. Veraart, J., Fieremans, E., Jelescu, I. O., Knoll, F., & Novikov, D. S. (2015). Gibbs ringing in diffusion MRI. Magn. Reson. Med. In Press, published online.DOI: 10.1002/mrm.25866

3. Koay, Cheng Guan, et al. "A unifying theoretical and algorithmic framework for least squares methods of estimation in diffusion tensor imaging." Journal of Magnetic Resonance 182.1 (2006): 115-125.

4. Tabesh A., Jensen J. H., Ardekani B. A., Helpern J. A. (2011). Estimation of tensors and tensor-derived measures in diffusional kurtosis imaging. Magn. Reson. Med. 65, 823–836. 10.1002/mrm.22655

5. Veraart J., Fieremans E., Novikov S. D. (2015) Noise map estimation in diffusion MRI using Random Matrix Theory. ISMRM 2015 p. 1023 DOI: 10.1002/mrm26059

6. Kellner, Elias, Bibek Dhital, and Marco Reisert. "Gibbs-Ringing Artifact Removal Based on Local Subvoxel-shifts." arXiv preprint arXiv:1501.07758 (2015). Magn. Reson. Med. In Press

7. J.L.R. Andersson, S. Skare, J. Ashburner How to correct susceptibility distortions in spin-echo echo-planar images: application to diffusion tensor imaging. NeuroImage, 20(2):870-888, 2003.

8. Veraart J., Sijbers J., Sunaert S., Leemans A., Jeurissen B. (2013b). Weighted linear least squares estimation of diffusion MRI parameters: strengths, limitations, and pitfalls. Neuroimage 81, 335–346.

Figures

Comparison between different DKI post-processing algorithms. The main difference between the state-of-the-art pipeline and the newly proposed DESIGNER pipeline is the substitution of smoothing and constrained fitting for model independent noise estimation using the Marchenko-Pastur distribution and automatic Gibbs artifact removal. MK maps generated by the two pipelines as well as MK generated from unconstrained fitting of the original uncorrected dMRI images are shown as an illustration.

Left: residual noise map produced after the denoising step of the post-processing routine. Middle: residual noise map left after isotropic Gaussian smoothing. Right: Difference between denoising techniques. The rightmost image shows that low pass filtering kills anatomic signal that is preserved using the Marchenko-Pastur noise removal.

Histograms of residual differences between raw dMRI and each processing step show how each denoising routine affects the distribution of noise in the dataset. The left image shows $$$b = 0$$$ data and the right image shows $$$b = 2000\ \mathrm{s/mm}^{2}$$$ data for a single direction. Median values for the $$$b = 0$$$ data are $$$-3.559, 0.3901,\ \mathrm{and}\ 0.1492$$$ for the smoothed, Gibbs corrected and denoised images respectively.



Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)
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