Spatial Configurations of 3D Extracellular Matrix Collagen Density and Anisotropy Simultaneously Guide Angiogenesis
Fig 7
Pseudo-deformation concept map & Monte-Carlo EFD sampling visualization.
A. EFD deformation & pseudo-deformation concept map. Vectors originating from the center of a unit sphere ΩI were mapped by P0 to the undeformed EFD Ω0. After deformation by F, the fibrils of Ω0 were stretched and rotated, yielding the deformed ODF Ω. The net mapping from ΩI to Ω was given by Fn. Polar decomposition of Fn yielded Fn = VnRn. An EFD Ωp that closely approximated Ω was found by applying the pseudo-deformation Fp = VnI to ΩI. B. Visualizations of EFD Monte-Carlo sampling are provided for the cases of transverse isotropy (semiprincipal axis lengths β1 = 5, β2 = β3 = 1) and orthotropy (semiprincipal axis lengths β1 = 5, β2 = 3, β3 = 1). Sampled directions were mapped onto the surface of a unit sphere. The ODF was generated by summing points on the surface of the unit sphere that corresponded to faces on an icosahedron.