Introduction

Although tractography has seen a notable evolution, the reconstruction of the white matter (WM) pathways remains a challenging task¹. Global minimization methods have shown promising results by simultaneously performing tracking and signal reconstruction^2,3,4. These approaches model analytically the tracking process, which is often really complex and involves billions of parameters that need to be optimized, typically with stochastic procedures. Consequently, they are computationally heavy, and convergence is not guaranteed. Given these limitations, we present a method that tackles tractography from a different point of view. The main idea is to move from “tract-o-graphy” to “bundle-o-graphy”, i.e., track bundles directly instead of streamlines. The optimal configuration is sought by a global optimization process that shapes and adapts the bundles geometry to fit the observed dMRI data. This is achieved using a modified version of Convex Optimization Modelling for Microstructure Informed Tractography (COMMIT)⁵ to cope with bundles instead of streamlines. We tested our novel bundle-o-graphy both on synthetic and real data, showing it can dramatically reduce the number of parameters needed to explain the white-matter fiber configuration as good as streamline-based tractography methods.

Methods

In our bundle-o-graphy approach, a bundle is modeled by means of its centerline trajectory and the spatial extent for the signal contributions of the bundle to the voxels. Each trajectory is considered as the centroid of a blurred cylinder, with a constant radius, extending along the whole path (Fig.1B). Taking inspiration from⁶, we adopted a parametric representation of the centroids using cubic B-splines. The corresponding diffusion signal is analytically simulated mimicking a set of densely packed streamlines, aligned with the centroid and covering the whole volume. In particular, signal reconstruction is performed using a Gaussian blurring function centered on the streamline (Fig.1C). This implies that the local signal contribution decays exponentially as we move outward, becoming increasingly negligible while it remains constant along the path. Following this implementation, bundle simulation turns into modeling the space of influence of a streamline which requires only the variance as a parameter. Therefore, this extension allows the current streamline-based COMMIT to becoming a bundle-based algorithm. The bundle configuration is optimized following a Bayesian approach. In this context, the B-splines control points and the extent of the blur represent the parameters of our model $$$M$$$ that need to be optimized. According to the Bayesian theory, we can infer on the posterior distributions of these parameters based on the observed data $$$d$$$ and the data generated by $$$M$$$. The inference can be used to influence the parameters by back-propagation to minimize the cost function $$$f_T(M)$$$ defined as:
$$f_T(M) = {E_D(M,d)} + \lambda |M|$$
The first term defines the likelihood function, which scores how well a specific configuration $$$M$$$ explains $$$d$$$, while the second promotes the minimization of the number of bundles in the configuration. To assess the impact of bundle-o-graphy we tested it on a well-known synthetic phantom (Fig.2) used in⁷. Tractography was performed using iFOD2 of MRTrix3⁸, discarding streamlines prematurely stopping in WM. We compared the optimized configuration against the known ground-truth, reporting the number of bundles (VBs) and invalid bundles (IBs). In real data, we performed qualitative analysis on one HCP⁹ dataset (103818) using a tractogram with 3-million streamlines.

Results and Discussion

Bundle-o-graphy results on the synthetic phantom are reported in Fig.2. At the top of the first column, we show the input tractogram and, at the bottom, the bundle-based representation of the optimized one. In the second column, we compare the RMSE of the input configuration filtered by COMMIT, with the one of the optimized configuration. In the third column, we report connectivity graphs of each configuration. Results show how our method is able to remarkably filter out false positives while reducing the complexity of the tractogram. In fact, we needed only 0.94% of the streamlines to characterize all the connections, while shape and radius adaptation allowed to keep a comparable fitting error. Bundle-o-graphy results on the HCP data are shown in Fig.3, where we qualitatively assessed the impact of our method by comparing the RMSE maps of the input tractogram (left), with the one corresponding to the optimized configuration (right). With bundle-o-graphy, we were able to dramatically reduce the number of streamlines, decreasing from millions to tens of thousands for a whole-brain reconstruction while keeping a comparable RMSE. Lastly, Fig.4 is a visual representation of the impact of bundle-o-graphy on a section of the CST manually segmented from the input tractogram.

Conclusions

Bundle-o-graphy formulation allows to drastically reduce the number of parameters needed to track WM connections. This, in turn, allows exploiting the potentials of global optimization to incorporate and use prior knowledge to guide in real-time the reconstruction. Thanks to these two aspects, the proposed method is capable to locally well represent the underlying anatomy and, at the same time, remove global implausible connections. Bundle-o-graphy opens new avenues to global tractography inverse-problem resolution and represents a fundamental step forward to improve tractography sensitivity and specificity.

Acknowledgements

No acknowledgement found.