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Estimation of multiple fiber orientation distributions (mFODs) from diffusion MRI data using spherical deconvolution
Alberto De Luca1, Fenghua Guo1, and Alexander Leemans1

1Image Sciences Institute, UMC Utrecht, Utrecht, Netherlands

Synopsis

Fiber orientation distributions (FODs) of white matter (WM) are commonly estimated from brain diffusion MRI data with spherical deconvolution (SD) approaches. Typically, only WM is considered to be anisotropic in SD, relying on suboptimal isotropic modeling of grey matter (GM). Here we present a general framework to reconstruct multiple anisotropic FODs (mFODs) from multiple response functions, allowing for the investigation of anisotropy in GM. The estimated mFODs were evaluated on a dataset from the HCP project with five response functions generated with the diffusion kurtosis and NODDI approaches, and their performances compared to state-of-the-art SD approaches.

Introduction

Spherical deconvolution (SD) approaches can be used to reconstruct fiber orientation distributions (FODs) in brain white matter (WM) from diffusion MRI (dMRI) data sampled with high angular resolution. In common SD techniques1,2, including multi-shell (MS) formulations, only WM is considered to be anisotropic, and a single anisotropic response function is assumed valid throughout the brain. However, appropriate fits of other tissues, such as grey matter (GM), are essential for structural connectivity reconstructions. In this work, we investigated the simultaneous fit and tracking of multiple anisotropic FODs to improve the characterization and the tracking outside WM.

Methods

SD was reformulated to account for n response functions, leading to the multiple FOD (mFODs) SD approach. The problem can be formally written as: $$$\sum_{i=1}^{n}{f_{i}K_{i}}$$$, where S is the MS dMRI signal, and fi is the signal fraction associated to each FOD. The approach was implemented within the modified Richardson-Lucy iterative scheme3,4.

For proof of concept, we considered 5 different response functions K. K1 described highly oriented fibers, and was generated with the DKI model using tensor and isotropic kurtosis values derived from the data within a WM mask. K2, K3 and K4 described three configurations of dispersed fibers generated with the NODDI model5 using default values but with an orientation dispersion value of 1.5 and with intra-cellular fractions of 0.9, 0.6 and 0.3, respectively. K5 was generated using the ADC model and with a diffusion value 3x10-3mm2/s to account for free water diffusion.

Data of a subject from the Human Connectome Project (HCP)6, acquired with resolution 1.25mm isotropic, 18 volumes at b=0s/mm2, 90 volumes at b=1000,2000,3000s/mm2 were fit with mFODs SD, resulting in 5 fractional maps and 4 anisotropic FODs. The fractional maps were compared to the anatomical segmentation obtained from the T1 data7.

Fiber tracking of each mFOD separately was performed in ExploreDTI8 using a 1.25mm seed resolution, 0.6mm step size and 45 degrees angle threshold. Tract density maps were computed for each tracking result and compared with results obtained with constrained SD (CSD) and MS-CSD. Subsequently, tracking was performed considering two strategies to track from the multiple FODs simultaneously: 1) considering their sum weighted by their corresponding signal fraction (mFODs-LI) and 2) choosing voxel-wise the FOD corresponding to the greatest signal fraction (mFODs-MAX). Tracks not traversing GM were discarded.

Results

Figure 1 shows the signal fractions obtained with mFODs SD. These fractions have an excellent spatial agreement with the fractions of WM, GM and CSF derived from the structural image. The mFOD1 and mFOD2 magnitudes were mostly non-zero in WM areas, whereas non-zero values in mFOD3 and mFOD4 mainly covered the cortical areas and subcortical GM, as shown in Figure 2. Further, the orientations of mFOD3 and mFOD4 were mostly perpendicular to the GM folding. Similar results were observed from the tracking of the individual FODs and their density maps, shown in Figure 3. The tracking of mFOD1 and mFOD2 covered large parts of the WM, whereas the tractograms of mFOD3 and mFOD4 contained many short connections (U-fibers) and large part of the cerebellar structure.

Figure 4 compares the FODs obtained with CSD, MS-CSD, mFOD-s-LI and mFODs-MAX on an axial slice. MS-CSD effectively suppressed CSF contamination, but both MS-CSD and CSD were characterized by a large number of spurious peaks in the GM. Conversely, both mFODs-LI and mFODs-MAX provided a cleaner characterization of GM FODs. The whole brain tracking obtained with CSD, MS-CSD and mFODs-MAX are shown in Figure 5. The tractogram provided by mFODs-MAX showed better description of the cerebellar structure and cleaner depiction of the cortical gyri, as shown by the tissue type encoded tractograms. Further, the transition of tracts from WM to GM appear to be better characterized with the mFODs-MAX approach.

Discussion

We have shown the feasibility of reconstructing multiple FODs in SD to achieve a better description of tissue types as GM. We generated five response functions with different diffusion models, which selectively explained the signals in anatomical areas compatible with their design. Compared to (MS-)CSD approaches, the mFODs resulted in less spurious orientations in GM areas and better tracking transition into GM areas. No differences were observed in WM across the different methods. Further investigation are needed to determine the appropriate number and type of response functions, and data requirements. Additionally, the effective improvement in the transition of tracts between GM and WM should be evaluated quantitatively.

Conclusions

Spherical deconvolution with multiple FODs is a promising tool to improve the characterization of multiple tissue types, ultimately improving the performances of tracking algorithms beyond white matter regions.

Acknowledgements

No acknowledgement found.

References

1. Tournier, J. D., Calamante, F. & Connelly, A. Robust determination of the fibre orientation distribution in diffusion MRI: Non-negativity constrained super-resolved spherical deconvolution. Neuroimage 35, 1459–1472 (2007).

2. Dell’Acqua, F. et al. A model-based deconvolution approach to solve fiber crossing in diffusion-weighted MR imaging. IEEE Trans. Biomed. Eng. 54, 462–72 (2007).

3. Dell’acqua, F. et al. A modified damped Richardson-Lucy algorithm to reduce isotropic background effects in spherical deconvolution. Neuroimage 49, 1446–58 (2010).

4. Guo, F., Leemans, A., Viergever, Max A, Dell’acqua, F. & De Luca, A. Damped Richardson-Lucy Deconvolution for Multi-Shell Diffusion MRI. in International Society for Magnetic Resonance in Medicine2 (2018).

5. Zhang, H. G., Schneider, T., Wheeler-Kingshott, C. a & Alexander, D. C. NODDI: practical in vivo neurite orientation dispersion and density imaging of the human brain. Neuroimage 61, 1000–16 (2012).

6. McNab, J. A. et al. The Human Connectome Project and beyond: initial applications of 300 mT/m gradients. Neuroimage 80, 234–45 (2013).

7. Zhang, Y., Brady, M. & Smith, S. Segmentation of brain MR images through a hidden Markov random field model and the expectation-maximization algorithm. IEEE Trans. Med. Imaging 20, 45–57 (2001).

8. Leemans, A., Jeurissen, B., Sijbers, J. & Jones, D. K. ExploreDTI: a graphical toolbox for processing, analyzing, and visualizing diffusion MR data. in 17th annual meeting of the International Society for Magnetic Resonance in Medicine, Honolulu, Hawaii, USA 3537 (2009).

Figures

Figure 1: An example axial slice of the fractional maps fi associated to each FOD in the multiple fiber orientation distribution (mFODs) method (first two rows) and to the T1 tissue type segmentation (bottom row). When combining the FODs that are obtained with similar response functions, fractional maps from the mFODs method reveal an excellent agreement with the T1 segmentation results.

Figure 2: Graphical representation of each FOD computed with the mFODs method in a middle brain axial slice. The first column shows an overview of the whole slice, magnified to highlight details in a posterior area (middle column) and on a cortical region (right column). The mFOD1 and mFOD2 mainly characterize white matter areas, in agreement with their “sharp” response function design. The mFOD3 and mFOD4 have non-zero values mainly in cortical and subcortical gray matter, and their orientation was mostly perpendicular to the cortical folding surface.

Figure 3: Whole brain tracking of the individual FODs mFOD1-2-3-4 (tracks are subsampled for clarity), and an example slice of their spatial density maps. The whole brain tractogram with mFOD1 was in agreement with established methods. Tracking of mFOD2 resulted in the cerebellar pathways, part of the corticospinal tract and of the anterior projections. Tracking of mFOD3 and mFOD4 mostly revealed trajectories of cerebellar pathways and short connections (U fibers).

Figure 4: Comparison of FODs derived with CSD (second row), MS-CSD (third row), linear interpolation of the mFODs (fourth row) and local selection of the maximal mFOD (last row). Both mFODs-LI and mFODs-MAX showed sharper and highly oriented FODs in GM than CSD methods, which conversely exhibited a large number of spurious peaks.

Figure 5: Whole brain tractogram obtained with CSD, MS-CSD and mFODs-MAX. The latter showed a clear delineation of the brain surface, result of a clearer transition of the tracts to the cortical folding, especially in the cerebellar cortex (white oval). Further, it was characterized by less spurious fibers, which, for instance, allowed to better visualize the transition of white matter tracts into the temporal cortex (yellow oval).

Proc. Intl. Soc. Mag. Reson. Med. 27 (2019)
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