Bundle-specific Tractogram Distribution Estimation Using Higher-order Streamline Differential Equation

TL;DR

diffusion MRI tractography suffers from ambiguous voxel-level diffusion directions and global inconsistency. The paper introduces Bundle-specific Tractogram Distribution (BTD), a framework that uses a higher-order streamline differential equation on the diffusion tensor vector field $v(x,y,z)$ and estimates BTD coefficients by energy minimization with anatomical priors. Contributions include a unified higher-order formulation, a divergence-free spatial continuity constraint, and a two-stage LS-plus-integration pipeline to reconstruct complex bundles. Across simulated and in vivo datasets, BTD yields improved reconstruction of long-range, twisting, and fanning tracts with better spatial fidelity, supported by open-source code.

Abstract

Tractography traces the peak directions extracted from fiber orientation distribution (FOD) suffering from ambiguous spatial correspondences between diffusion directions and fiber geometry, which is prone to producing erroneous tracks while missing true positive connections. The peaks-based tractography methods 'locally' reconstructed streamlines in 'single to single' manner, thus lacking of global information about the trend of the whole fiber bundle. In this work, we propose a novel tractography method based on a bundle-specific tractogram distribution function by using a higher-order streamline differential equation, which reconstructs the streamline bundles in 'cluster to cluster' manner. A unified framework for any higher-order streamline differential equation is presented to describe the fiber bundles with disjoint streamlines defined based on the diffusion tensor vector field. At the global level, the tractography process is simplified as the estimation of bundle-specific tractogram distribution (BTD) coefficients by minimizing the energy optimization model, and is used to characterize the relations between BTD and diffusion tensor vector under the prior guidance by introducing the tractogram bundle information to provide anatomic priors. Experiments are performed on simulated Hough, Sine, Circle data, ISMRM 2015 Tractography Challenge data, FiberCup data, and in vivo data from the Human Connectome Project (HCP) data for qualitative and quantitative evaluation. The results demonstrate that our approach can reconstruct the complex global fiber bundles directly. BTD reduces the error deviation and accumulation at the local level and shows better results in reconstructing long-range, twisting, and large fanning tracts.

Figures (10)

• Figure 1: Schematic representation of different tractography methods.
• Figure 2: Comparison of tractography results of BTD with iFOD2 and SD_Stream at different SNRs using the Hough data.
• Figure 3: Comparison of tractography results of BTD with iFOD2 and SD_Stream at different SNRs using the Sine data ($\alpha=0.3$).
• Figure 4: Comparison of tractography results of BTD with iFOD2 and SD_Stream at different $\alpha$ using Sine data (SNR=10).
• Figure 5: Comparison of tractography results of the BTD (5th-order) with iFOD2 and SD_Stream at SNRs of 10, 20, and $+ \infty$ using Circle data. The blue color fibers (from the same starting area) are used to visualize the tractography deviation with different methods.