Thirty-four patients (21 females and 13 males) hospitalized for degenerative spinal diseases (DSDs) were included in the study. All patients underwent lumbar spine CT and MRI examinations when admitted to the hospital. The age of the patients ranged from 33 to 73 years (Table 1). Approval of the experimental design was obtained by the appropriate Institutional Review Board prior to the initiation of the study. A written consent was obtained from each subject before the study.
Exclusion criteria included the presence of other spinal diseases including lumbar spinal infection, fracture of the lumbar vertebrae, lumbar scoliosis with a Cobb angle larger than 10°, isthmic spondylolisthesis and previous spinal surgery.The presence of back pain which affects lumbar movements taking about 15 minutes was used as indications for exclusion from the study. All CTs and MRIs were read by two senior spinal surgeons with >15 years experience who were blinded to clinical patient information and the research hypothesis. The investigators independently read the CTs and MRIs in the same random order on a clinical Picture Archiving and Communication System (PACS) unit. When disagreements arose, another experienced radiologist (with over >20 years experience) was consulted to provide consensus.
Facet-joint degeneration grading scores, facet sagittal angles, and disc degeneration degree were obtained from CT and MRI images. A number of studies have found a higher accuracy when evaluating facet joint degeneration with a CT image [9,10]. In addition, Fujiwara et al.  showed that an MRI may underestimate the severity of osteoarthritis compared to CT images. Therefore, the degree of degeneration in the L3-S1 facet joints and discs were graded according to Weishaupt scales  and the Pffirmann classification, respectively. The degree of bilateral facet-joint degeneration was scored for each L3-S1 segment, and scores from 0 to 3 were matched to the grades of the same number. The scores from the left and right sides of the facet joints were summed and defined the 3 degeneration groups. Mild degeneration was scored from 1-2 points, moderate degeneration from 3-4 points, and severe degeneration from 5-6 points. The left and right facet-joint degeneration scores were usually either equal or differed by 1 point at each segment. However, there were 2 segments where one side had a score of 1and the other had a score of 3. In total, 102 segments from 34 DSD patients were divided into three groups at the L3-L4, L4-L5 and L5-S1 levels (Table 1).
CT-based, three-dimensional (3D) geometric model of the vertebrae
To construct 3D lumbar-spine models of L3-S1, CT images (Fig. 1a) with a thickness of 0.75 mm, without a gap and with a resolution of 512 × 512 pixels were imported into the modeling software program Mimics version 17.0 (Materialise, Leuven, Belgium) using an established, validated protocol .
Dual fluoroscopic imaging and the establishment of virtual locations of vertebral positions
Following the completion of the 3D modeling (Fig. 1b), a dual fluoroscopic imaging system [14-16] was used to image the lumbar spines at different postures: upright standing position, maximum trunk flexion-extension, maximum left-right bending, and maximum left-right twisting (Fig. 2a). For subjects who experienced symptoms of lower back pain during functional activity, oral painkillers (Celebrex 200mg) were administered to enable them to complete the 15 minutes exercises. Two fluoroscopes (Ziehm 8000; Ziehm imaging, Nuremberg, Germany) were positioned with their image intensifiers perpendicular to each other to obtain orthogonal images of the L3-S1 segments at different postures. The subjects remained still for several seconds during each target posture while the two fluoroscopes took images. To successfully image subjects while performing different postures, a distance of approximately 1 m was kept between the X-ray source and the receiver. To maximize the motion of the lower lumbar spine and maintain the spinal segments within the field of view of the two fluoroscopes, subjects were requested to minimize their hip movements.
The in vivo motions of the lumbar spine at different functional positions were reproduced with Rhinoceros version 5.0 modeling software (Robert McNeel & Associates, Seattle, WA, USA) (Fig.2b) using the 3D vertebral models and orthogonal fluoroscopic images and an established protocol. Briefly, the CT image-based 3D models of the L3-S1 were independently translated and rotated in 6 degrees of freedom (6DOF) with increments of 0.01 mm and 0.01° until their outlines matched the osseous contours positioned on the 2 fluoroscopic images [13,16].
Relative motion measurements of the vertebrae
Right-handed Cartesian coordinate systems were used to quantify the 6DOF motions for the L3-S1 segments . In an upright position, the volumetric center of the vertebral body was chosen as the origin of the coordinate systems for each segment level. The X-axis was in the frontal plane and pointed in the left direction. The Y-axis was in the sagittal plane and pointed in the posterior direction. The Z-axis was vertical to the X–Y plane and pointed proximally (Fig.3a). Following reproduction of the in vivo vertebral positions, the motions of the lumbar vertebrae were measured from the coordinate system of the proximal vertebrae with respect to the distal vertebrae at the 3 vertebral levels: L3-L4, L4-L5, and L5-S1 (Fig.3b). Three translations were defined as the motions of the proximal vertebral coordinate system origin in the distal coordinate system: anterior-posterior, left-right, and distal-proximal. The 3 rotations defined as the orientations of the proximal vertebral coordinate system in the distal vertebral coordinate system using Euler angles (in X–Y–Z sequence) were: flexion-extension, left-right bending, and left-right twisting. The ROMs of L3-S1 were then determined from the ending ROM of flexion-extension, left-right bending, left-right twisting positions, and included both the primary translations and rotations, as well as the coupled translations and rotations in all 6 DOFs.
Continuous variables were measured as means ± SDs and a repeated measures ANOVA was used to compare the dynamic ROMs of the 3 facet-joint groups for all segment levels. When a statistically significant difference was detected, a post hoc Newman–Keuls test was performed. Statistical significance was set at p<0.05. All statistical analyses were performed using SPSS 24.0 statistical software (SPSS Inc., Chicago, IL, USA).