Use of the alpha shape to quantify finite helical axis dispersion during simulated spine movements

In biomechanical studies examining joint kinematics the most common measurement is range of motion (ROM), yet other techniques, such as the finite helical axis (FHA), may elucidate the changes in the 3D motion pathology more effectively. One of the deficiencies with the FHA technique is in quantifying the axes generated throughout a motion sequence. This study attempted to solve this issue via a computational geometric technique known as the alpha shape, which bounds a set of point data within a closed boundary similar to a convex hull. The purpose of this study was to use the alpha shape as an additional tool to visualize and quantify FHA dispersion between intact and injured cadaveric spine movements and compare these changes to the gold-standard ROM measurements. Flexion-extension, axial rotation, and lateral bending were simulated with five C5-C6 motion segments using a spinal loading simulator and Optotrak motion tracking system. Specimens were first tested intact followed by a simulated injury model. ROM and the FHAs were calculated post-hoc, with alpha shapes and convex hulls generated from the anatomic planar intercept points of the FHAs. While both ROM and the boundary shape areas increased with injury (p<0.05), no consistent geometric trends in the alpha shape growth were identified. The alpha shape area was sensitive to the alpha value chosen and values examined below 2.5 created more than one closed boundary. Ultimately, the alpha shape presents as a useful technique to quantify sequences of joint kinematics described by scatter plots such as FHA intercept data.