Use of the Alpha Shape to Quantify Changes in the Finite Helical Axis during Simulated Spine Movements

Introduction: The finite helical axis (FHA) is a widely used kinematic technique to describe changes in joint motion. Specific to the spine, the most common application of the FHA has been to quantify changes in the location of instantaneous centre of rotation (ICR) of a motion segment while the spine completes a prescribed range of motion (e.g., flexion-extension trial) [1]. This measure can be sensitive to alterations in the kinematics of the motion segment resulting from trauma, degeneration, or the application of instrumentation [2]. Furthermore, with the development of many motion restoring (i.e., dynamic stabilization) devices, this measure is frequently reported as a parameter of interest for evaluating the device efficacy [3]. However, the ICR is typically only qualitatively reported, using 2D images of the motion segment to provide a visual of the changes in ICR location [4]. A potential improvement to this technique for describing changes in joint stability would be to quantify the scatter in the generated ICRs. One solution may be to determine the alpha shape, a computational geometric technique used to envelop a finite set of points in a series of curves [5]. The method requires a set of point data and a value of “alpha” as inputs, and uses them to define the level of detail in the outline shape of the point set. The purpose of this study was to investigate the applicability of the alpha shape to visualize and quantify changes in the helical axis of motion during intact and injured simulated spinal movements. It was hypothesized that the alpha shape could identify differences in the kinematic stability between these two states. Methods: Five fresh-frozen C4-C7 cadaveric cervical spine segments were used (mean age: 74±5 years). C4-C5 and C6-C7 segments were fixed with screws to isolate motion to C5-C6. Each specimen was then potted in 2.5cm thick, 10cm diameter PVC piping using DenstoneTM cement to hold the C4 and C7 vertebrae. Flexibility testing was performed on each specimen using a custom spinal loading simulator. Kinematics were captured using the Optotrak® CertusTM motion capture system (NDI, Waterloo, ON, Canada), with Optotrak® ‘Smart Markers’ rigidly attached to the C5 and C6 vertebrae. A testing protocol was designed to assess the kinematic stability of the intact and injured states. First, the intact kinematics were collected for flexion-extension, axial rotation, and lateral bending. Subsequently, a standardized injury model for a unilateral facet perch was then induced in the right facet joint at C5-C6 of each specimen as the injured state. Post-hoc data analysis to determine range of motion (ROM) was performed using custom-written LabVIEWTM software. In addition to the standard ROM analyses, finite helical axes (FHAs) were calculated for both the intact and injured states using a constant moving window size [6, 7]. The window size (in degrees) had to be determined post-hoc, as it was taken to be half of the smallest ROM from the intact data for each motion. From the FHAs calculated, the direction cosine vectors and corresponding alpha shapes enveloping the intercepts in a selected plane (i.e., X, Y, or Z = 0 of the C6 frame for lateral bending, flexion-extension, and axial rotation, respectively) were generated using MATLAB software. To generate the alpha shapes, the MATLAB program calls the alpha shape function “alphavol,” which was downloaded from the MATLAB File Exchange website. An “alpha” value of 2.5 was used, based on trial and error to generate the smallest single shape. Alpha shapes were quantified by determining their area and centroid location, and visualized over specimen-specific 3D bone models (generated from CT scans using Mimics software). Statistical analyses were performed using SigmaStat software. Intact versus injured ROM and alpha shape area were compared in a paired t-test (α=0.05). Results: Based on the calculated intact ROM, a moving window size of 2°, 3°, and 2° was used for flexion-extension, axial rotation, and lateral bending, respectively. In terms of the alpha shapes generated from the FHAs for each specimen, there was an increase in area for all motions between the intact and injured states (p<0.05) (Table 1). A representative increase between the intact and injured alpha shapes is shown in Figure 1. Between the intact and injured states, the largest shifts in the centroid location were a 9mm posterior shift for axial rotation, and 5mm superior and posterior shifts in flexion-extension.