Rapid three-dimensional quantification of voxel-wise collagen fiber orientation

Defining fiber orientation at each voxel within a 3D biomedical image stack is potentially useful for a variety of applications, including cancer, wound healing and tissue regeneration. Current methods are typically computationally intensive or inaccurate. Herein, we present a 3D weighted orientation vector summation algorithm, which is a generalization of a previously reported 2D vector summation technique aimed at quantifying collagen fiber orientations simultaneously at each voxel of an image stack. As a result, voxel-wise fiber orientation information with 4° to 5° accuracy can be determined, and the computational time required to analyze a typical stack with the size of 512x512x100 voxels is less than 5 min. Thus, this technique enables the practical extraction of voxel-specific orientation data for characterizing structural anisotropy in 3D specimens. As examples, we use this approach to characterize the fiber organization in an excised mouse mammary gland and a 3D breast tissue model.