Bundle-specific tractogram distribution estimation using higher-order streamline differential equation

Streamline tractography locally traces peak directions extracted from fiber orientation distribution (FOD) functions, lacking global information about the trend of the whole fiber bundle. Therefore, it is prone to producing erroneous tracks while missing true positive connections. In this work, we propose a new bundle-specific tractography (BST) method based on a bundle-specific tractogram distribution (BTD) function, which directly reconstructs the fiber trajectory from the start region to the termination region by incorporating the global information in the fiber bundle mask. 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 vectorial field. At the global level, the tractography process is simplified as the estimation of 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) for qualitative and quantitative evaluation. Results demonstrate that our approach reconstructs complex fiber geometry more accurately. BTD reduces the error deviation and accumulation at the local level and shows better results in reconstructing long-range, twisting, and large fanning tracts.