Three-dimensional computation of fibre orientation, diameter and branching in segmented image stacks of fibrous networks

Fibre topography of the extracellular matrix governs local mechanical properties and cellular behaviour including migration and gene expression. While quantifying properties of the fibrous network provides valuable data that could be used across a breadth of biomedical disciplines, most available techniques are limited to two dimensions and, therefore, do not fully capture the architecture of three-dimensional (3D) tissue. The currently available 3D techniques have limited accuracy and applicability and many are restricted to a specific imaging modality. To address this need, we developed a novel fibre analysis algorithm capable of determining fibre orientation, fibre diameter and fibre branching on a voxel-wise basis in image stacks with distinct fibre populations. The accuracy of the technique is demonstrated on computer-generated phantom image stacks spanning a range of features and complexities, as well as on two-photon microscopy image stacks of elastic fibres in bovine tendon and dermis. Additionally, we propose a measure of axial spherical variance which can be used to define the degree of fibre alignment in a distribution of 3D orientations. This method provides a useful tool to quantify orientation distributions and variance on image stacks with distinguishable fibres or fibre-like structures.