Ricardo Coronado-Leija^{1}, Alonso Ramirez-Manzanares^{1}, and Jose Luis Marroquin^{1}

A stable, accurate and robust-to-noise general framework for the estimation of the intra-voxel axial and radial diffusivity parameters for diffusion-weighted magnetic resonance imaging is presented. The method estimates the diffusion profiles at multi-fiber voxels, improving the estimation of the intra-voxel geometry at challenging microstructure configurations. It naturally constrains the sparsity on the recovered solutions and exploits the spatial redundancy of the axon packs. A useful evaluation metric is proposed: it combines the information of the success rate of the number of bundles and their angular error. A new evaluation method for the in-vivo estimations on large datasets is also proposed.

Introduction and Purpose

The estimation of water molecular displacements from DW-MRI allows inferring the neuronal connections architecture. Spherical Deconvolution (CSD)Methods

This work illustrates the estimation of the axial and radial diffusivity from a Gaussian Mixture Model (GMM), however our framework can be used for different tissue models. Given a robust estimation of the bundles number and orientations provided by the fixed-response-function MRDSGold Standards for the validation on in-vivo data

The proper validation of estimations on in-vivo data is still a challenging open problem. Here we propose a methodology to create robust Gold Standards (GS) from the MASSIVE data setExperiments and Results

Realistic synthetic MR signals are generated from state-of-the-art multi-compartment models with intra/extra/isotropic compartmentsConclusions

An accurate and robust-to-noise algorithm and a framework for the validation on large in-vivo datasets is presented. It improves the existing approaches in the estimation of the number of axon bundles, their orientation and radial/axial diffusivities at challenging configurations: small crossing angles and different voxel-wise anisotropic diffusion profiles.1. Tournier J. D. , Yeh C. H., et al. Resolving crossing fibres using constrained spherical deconvolution: Validation using diffusion-weighted imaging phantom data. NeuroImage. 2008;42(2): 617-625.

2. Gulani V. and Webb A.G., et al. Apparent diffusion tensor measurements in myelin-deficient rat spinal cords. Mag. Reson. in Med. 2001;45(2): 191-195.

3. Parker G.D., Marshall D., et al. A pitfall in the reconstruction of fibre ODFs using spherical deconvolution of diffusion MRI data. NeuroImage. 2013; 65(1): 433-448.

4. Ramirez-Manzanares A., Cook, P. A., et al. Resolving axon fiber crossings at clinical b-values: An evaluation study. Medical Physics. 2011; 38(9): 5239-5253.

5. Daducci A., Canales-Rodríguez E.J., et al. Quantitative Comparison of Reconstruction Methods for Intra-Voxel Fiber Recovery From Diffusion MRI. IEEE Trans. on Med. Imag. 2014;33(2): 384-399.

6. Coronado-Leija R., Ramirez-Manzanares A., et al. Accurate Multi-resolution Discrete Search Method to Estimate the Number and Directions of Axon Packs from DWMRI . Proc. Intl. Soc. Mag. Reson. Med. 23. 2015:565.

7. Burnham K. Model selection and multimodel inference : a practical information-theoretic approach. Springer, New York. 2002.

8. Froeling M., Tax C.M.W., et al. MASSIVE Brain Dataset: Multiple Acquisitions for Standardization of Structural Imaging Validation and Evaluation. Mag. Reson. in Med. 2016; DOI:10.1002/mrm.26259.

9. Panagiotaki E., Schneider T., et al. Compartment models of the diffusion MR signal in brain white matter: A taxonomy and comparison. NeuroImage. 2012; 59(3): 224-2254.

10. Jeurissen, B., Tournier J.D., et al. Multi-tissue constrained spherical deconvolution for improved analysis of multi-shell diffusion MRI data. NeuroImage. 2014;103:411-426.

Figure
1. Importance of the response function estimation. $$$SR^{10^{\circ}}$$$ for
MRDS with estimation of axial and radial diffusivities,
MRDS-fixed-response-function, and CSD methods. TOP SNR = 15, BOTTOM SNR = 25.
Even with a fixed response function, the performance of MRDS is better than
that of CSD, but this difference significantly increases when the diffusion profile
$$$\left\{ \lambda^{\|},\lambda^{\bot} \right\}$$$ is estimated. CSD and MRDS
with fixed response function have good
performances only when the diffusion profile in the signals and in the response
function are similar, as reported in^{3}. The performance is worse when the FA decreases.

Figure 2. Overall results (MRDS-SDF, MRDS and
CSD) on the phantom in^{5} with synthetic multi-compartment signals, FA in [0.75,0.90]. Error metrics as in^{5}. Voxel-wise
MRDS shows better performance than CSD for all the SNR ($$$x$$$-axis) for most
of the cases. MRDS-SDF improves the performance for low SNRs presenting
better results than both CSD and MRDS. More importantly, the estimation of the
eigenvalues of the multi-tensors was also better using MRDS-SDF. The improvements
are achieved even when the eigenvalues are obtained using only the information
of the signal in its own voxel without using spatial regularization on this
estimation stage.

Table
1. GSA, ARA and ARC for the GSs on the challenging spatially coherent phantom
used in^{5}. Results are in the format
MRDS-SDF/MRDS/CSD (best result per category in bold). Error metrics as in Figure 2, $$$\sigma$$$=*std*. MRDS-SDF performs
best for almost all metrics, demonstrating the advantages
of the integration of spatial information. Comparing MRDS against CSD, MRDS is
better for GSA and ARA, i.e. MRDS is more accurate than CSD. For ARC, CSD is
slightly more consistent on each sample than MRDS. MRDS and MRDS-SDF
report accurate and consistent results on the estimation of the axial/radial diffusivities.

Figure 3. Comparison with the GS from the MASSIVE
dataset. Reconstructions of the sagittal dODFs are shown for MRDS-SDF GS
(the pseudo GT from Bootstrap) and for CSD, MRDS and MRDS-SDF single samples (80 DWIs). CSD
shows zones in which fiber bundles appear discontinuous, while MRDS and
MRDS-SDF capture those and additional fiber bundles. More importantly, the
extra fiber bundles reported by MRDS and MRDS-SDF show good spatial coherence
and are in correspondence with the GS, which indicates that these bundles are
very likely to be present, showing a qualitatively smoother dODF field.

Figure
4. $$$\lambda^{\|}, \lambda^{\bot}$$$, FA and $$$T_{1}$$$ (left to right) maps
for a single Boostrap sample (80 DWIs) from the MASSIVE dataset using the
MRDS-SDF method. From top to bottom: coronal, sagittal and axial slices.
Diffusivity units are in $$$mm^{2}/s$$$. The maps are smooth and the
diffusivities $$$\lambda^{\|}, \lambda^{\bot}$$$ in the WM are inside the plausible
ranges. A $$$T_{1}$$$ weighted image is also provided to demonstrate how the FA
is high in the voxels that belong to the WM independently of the existence of
crossing fiber bundles, and it is low when the voxel belongs to GM and CSF.