Bundle-specific Tractogram Distribution Estimation Using Higher-order
  Streamline Differential Equation
Yuanjing Feng Lei Xie Jingqiang Wang Jianzhong He Fei Gao
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.