Introduction

The estimation of axon bundle-specific microstructure descriptors is an important research area. Those descriptors are useful to understand the global brain connectivity profiles as well as the dynamics of neuropathological processes. Multi-Resolution Discrete-Search (MRDS)¹ is a method to solve the multi-tensor model of the diffusion MRI signal. It is able to provide DTI-like metrics, such FA and MD, for each bundle in individual voxels. MRDS provides similar information like DIAMOND⁸ and CSD¹⁰ methods for computing individual diffusion descriptors, however it has shown to be more robust to noise^1,9. We use the MRDS multi-tensor maps to develop a novel bundle-wise segmentation. Our segmentation allows us to compute robust averaged-based estimators of the per-bundle FA as well as to reinform the MRDS solution to improve the recovered data.

Methods

The methodology is structured in 5 stages executed in the original spatial resolution. The stages are described in sequential order as following:

Denoising: Using MRtrix3⁶.

Bias Correction: Applying the Gudbjartsson’s scheme⁵.

Local Modelling: Voxel wise multi-tensor modelling with MRDS method¹. After fitting the model, a multi-tensor field (MTF) is obtained. MRDS also provides metrics of the tensors like FA and MD.

Bundle Segmentation: We defined a distance function² between two neighboring tensors $$$T$$$ and $$$P$$$ in the MTF

$$D(T,P) = \frac{||pos(T)-pos(P)||^2}{d^2} + \frac{angle(T,P)}{\theta} + \frac{|FA(T)-FA(P)|}{f} + \frac{|MD(T)-MD(P)|}{m}$$

where angle() gives the angle between the direction of the tensors and $$$d$$$, $$$\theta$$$, $$$f$$$ and $$$m$$$ are user defined parameters. Then, a similarity function is defined as $$$S(T,P)=exp(-D(T,P))$$$. Two tensors T and P in the MTF are connected if they belong to two neighboring voxels (in the 2nd order voxel’s neighborhood) and $$$S(T,P)>E$$$ where $$$E$$$ is a user defined threshold value.Using the MTF from MRDS and the similarity function $$$S$$$, our segmentation problem can be formulated as a MTF segmentation problem. The compartments of each multi-tensor belong to a class (bundle). The segmentation is performed by a flood-fill based algorithm. Given an initial tensor in the MTF, the algorithm looks for all the tensors in the neighboring voxels and determines the connected tensors to the initial one. Then, the process is recursively repeated also for the connected neighbors tensors. Every connected cluster of tensors represents a fiber bundle in the white-matter.

Filtering: The filtering stage is used to enhance the results in the estimation stage by using the information obtained in the segmentation stage. Given the segmentation in bundles of the tensors in the MTF, the FA value of every tensor is averaged with the FA value of its 2nd order neighbors within the same bundle. This filtering method is helpful to remove the dispersion when estimating the FA value for each tensor while keeping the local spatial properties.

The methodology was tested on the Penthera3T dataset⁷. The DWI (112x112 matrix, TR 5615 ms, TE 95 ms, SENSE factor of 2) were acquired on a 3 Tesla MRI (Philips, Ingenia) with a single-shot echo-planar imaging sequence having 3 different shells, b=300, 1000, 2000 mm^2/s with respectively 8, 32 and 60 directions evenly distributed, and 7 b=0 mm2/s with a 2 mm isotropic spatial resolution. For the validation on synthetic data, the HARDI reconstruction workshop phantom⁴ was used. The acquisition scheme used to generate the phantom corresponds with the scheme of the Penthera3T dataset. We set the FA values different for each bundle in order to simulate per-bundle damages as we detail below. One of the bundles has a low FA value along the entire bundle, simulating a completely damaged bundle. Besides, we have one bundle with a normal FA value in most of the bundle, except for a compact connected region where the FA is lower, simulating a partially damaged bundle. The third bundle has a normal FA value across all the bundle, simulating a healthy bundle. Finally, Rician noise was added with a SNR =12 according to the noise level estimated on the Phentera3T dataset.

Results and Discussion

The obtained segmentation is visually correct, see Fig. 1. However, it struggles recovering the partially damaged bundle. In fact, it lets see where the damaged region is in the red bundle. It can be observed from Fig. 2 that the estimation stage allows for an accurate estimation of the per-bundle-FA profiles. Plots in Fig. 3 for the FA values along each bundle report robustness to fiber crossing and, even before the filtering stage, it is easy to identify which bundle is healthy (blue profile), partially damaged (protuberance in the red profile) or fully damaged (green profile). Both Fig. 2 and Fig. 3 illustrate the effectiveness of the filtering stage decreasing dispersion while maintaining the appreciation of the local and global damages. Finally, Fig. 4 and Fig. 5 show promising results on real data.

Conclusions
In this work, we showed that fascicle-based FA can be recovered. Results of the proposed methodology on synthetic data demonstrated that it is robust to noise (SNR=12) and able to detect challenging FA variations along the bundles. Results on real data make our methodology a suite candidate for detecting local and global FA profiles along the individual bundle associated with, for instance, tissue damage.

Acknowledgements

AR was supported by CONACyT Mexico and the National Laboratory for Magnetic Resonance Imaging (Conacyt, UNAM, CIMAT, UAQ).