An algorithm for the calculation of three‐dimensional collagen fiber orientation in ligaments using angle‐sensitive MRI

Abstract

A method based on angle-sensitive magnetic resonance imaging for determining unknown orientations of collagen fibers in ligaments is presented. Collagen fibers were stepwise rotated around two independent axes within a 3T magnetic resonance tomograph (from 0° to 180°, step size=10°). Analyzing the magnetic resonance signal intensity of each voxel as a function of the rotation angle, directions were calculated by means of a computational algorithm. The accuracy of the algorithm was validated using 1000 random test directions, revealing an average deviation of 4.4° (median±standard deviation: 2.7°±9°). Subsequently, the presented method was applied to three specimens of the human iliotibial tract mounted in different directions in a rotatable plastic box. Polarized light microscopy was used to verify parallel alignment of the collagen fibers in the three specimens. The calculated directions were compared with the directions of the specimens. Analyzing each voxel separately, average deviations (median±standard deviation) in the three specimens were: 11.2° (3.6°±20.4°), 12° (5°±24.1°), and 20.4° (8.7°±27°). If the magnetic resonance signal intensity of each voxel was averaged with the intensity of immediately neighboring voxels, average deviations (median±standard deviation) were 8.5° (3.6°±17.4°), 6.2° (0°±18°), and 9.2° (5°±19.2°). The presented method has the potential to be applied in situ to anatomical structures like cartilage, ligaments, tendons and fascia.