Synopsis

Volumetric analysis of bundles derived from tractography is a popular statistical measure used in neurological disorder studies. Recent research performed by Gauvin shows that different bundles saturate with different tractography parameters, however, to achieve that saturation millions of streamlines need to be computed. In this investigation, the aim was to use microstructure informed tractography, a novel technique that combine tractography and microstructure models, to study the saturation of the bundles. This study has found that generally microstructure informed tractography makes the volume estimation less sensitive to tracking parameters. The findings may have profound implications in volumetric analysis in group studies.

Purpose

Methods

COMMIT (Convex Optimization Modeling for Microstructure Informed Tractography)^4,5 is a recent framework proposed to combine both tractography and tissue microstructure estimation in a linear formulation: $$\boldsymbol{y}=\boldsymbol{A}\boldsymbol{x}+\eta\,,$$ where $$$\boldsymbol{A}$$$ is the linear operator implementing a generic multi-compartment model⁶ for the signal contributions of the streamlines in each voxel, $$$\boldsymbol{y}$$$ contains all dMRI measurements and $$$\eta$$$ is the acquisition noise. The contributions $$$\boldsymbol{x}$$$, that are used to filter the tractogram, are estimated solving a nonnegative least-squares problem: $$\underset{\boldsymbol{x}\ge0}{\operatorname{argmin}}\;||\boldsymbol{A}\boldsymbol{x}-\boldsymbol{y}||_2^2.$$ The linear operator $$$\boldsymbol{A}$$$ was build according to the StickZeppelinBall model⁶ that assumes zero radius cylinders with fixed longitudinal diffusivity $$$d_\parallel$$$ for the intra-axonal space, extra-axonal space modelled as anisotropic tensors with same $$$d_\parallel$$$ but different $$$d_\perp$$$, and isotropically restricted compartment. The code is freely-available at https://github.com/daducci/COMMIT.

We tested our approach on 6 healthy subjects with 2 time-points acquired on Siemens Magnetom Prisma system, according to the following protocol: $$$2.0\,\text{mm}$$$ isotropic resolution, 10 b0, 90 q-space samples over 2 shells with $$$b=\{700,2000\}\,\text{s/mm}^2$$$, $$$TE=78\text{ms}$$$ and $$$TR=7700\text{ms}$$$. All images were processed with the Connectome Mapping Toolkit⁷. The code is freely-available at https://www.cmtk.org. Whole-brain tractography was performed using the probabilistic iFOD2 algorithm⁸ with all the possible combinations of the following parameters: step size $$$1\text{mm}$$$, angle=(20,30,40,45,50,60), number of streamlines=(40K,75K,100K,125K, 250K,500K,1M,2M). Only streamlines for which the end points reach the grey matter up to $$$2\text{mm}$$$ of radial search were selected. The tissue model was set as follows: $$$d_\parallel=1.7\cdot10^{-3}\,\text{mm}^2/\text{s}$$$, $$$d_\text{iso}=(1.7,3.0)\cdot10^{-3}\,\text{mm}^2/\text{s}$$$ and 7 different values for $$$d_\perp$$$. Arcuate fascicles (AF), cortico spinal tract (CST), and superior longitudinal fasciculus (SLF) of the both hemispheres were extracted using the White Matter Query Language (WMQL)⁹.

Result and discussion

Figure 1 shows the volume variability of the AF left with respect to varying angles and number of streamlines for a single subject. Here, we compare the results between the original tractograms (left) and the streamlines filtered with COMMIT (right). The most obvious finding to emerge from this study is that with only tractography (left) the estimated volume increases with the number of streamlines and angle. However, if we use a framework that associate microstructure estimates (right), the volume bundle, compared to the original tractograms, saturate at lower stages and provide always measures. This new approach opens the possibility to develop more robust volumetric studies.

In Figure 2 we show the saturation curve for all the bundles for one subject with angle=30. To help visualization 2 color are chosen: red for the original tractogram and blue for the tractogram filtered with COMMIT. For each bundle, the points represent the volume related to number of streamline of that bundle. For each bundle, the progression of the points is related to the number of streamlines of the whole-brain tractogram. Here, we show that if we use a microstructure informed tractography technique, the volumes of all the bundle selected achieve saturation earlier(blue curves) compared to the method without microstructure filtering(red curves).

Ultimately, in Figure 3 we present a visual example on the AF. The comparison is done using number of streamlines=(125K,1M) and angle=(30,45) for one subject. The figure shows that the filtering done using microstructure information tend to preserve the core of the bundle. Anatomically, the AF arches down and comes to sit close the inferior-fronto-occipital fascilus (IFOF), which results inappropriate extension of AF fibers to the IFOF region highlighted by the red circles. The filtering performed by the COMMIT framework, in the red boxes, removes these green fibers from the AF bundle. However, this remains to be more extensively validated.

Conclusion

Acknowledgements

References

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