Twelve subjects (seven males and five females, ages 25 to 39 years) were recruited. Inclusion criteria included: normal spine development, age 18 ~ 40 years old, BMI 18.5 ~ 25 Kg/m2, Pfirrmann grade ≤ II (MRI), normal bone density. Exclusion criteria included: current or prior low-back pain, previous spinal surgery, anatomic abnormalities, pregnancy, or any spinal disorders. All subjects received a supine CT scan (Sensation 16, Siemens AG, Germany). Parallel digital images of the lumbar spine with a thickness of 0.625 mm and a resolution of 512 × 512 pixels were obtained. These CT images were input into Mimics software (Mimics 19.0 Materialise’s Interactive Medical Image Control System, Belgium) for the construction of 3D models of the vertebrae from L3 to L5 (Fig. 1a). Experienced orthopedic surgeons and radiology specialist excluded 2 subjects with spinal deformities (facet joint disorders) based on CT and 3D models and obtained the final 10 asymptomatic subjects (five males and five females, age 32 ± 4 y, height 1.67 ± 0.09 m, weight 62.75 ± 10.30 kg). The study was approved by our IRB, and signed informed consent was obtained from each subject prior to the experiment. The shape of the lumbar disc was constructed by the three-dimensional volume between the adjacent upper and lower endplates (Fig. 1b). The lumbar disc deformations at the L3–4 and L4–5 segments were investigated, resulting in a total of 20 discs.
A Cartesian coordinate system was created independently for each vertebral body (L3 ~ 5), based on vertebral symmetry (Fig. 1a). In the plane parallel to the upper endplate surface, the x-axis was set to point left, and the y-axis was set to point posteriorly. The z-axis was oriented perpendicular to the x–y plane and pointed proximally [9]. The orientations of the upper vertebral coordinate system in the lower vertebral coordinate system were defined by three rotations using the Euler angles α, β, and γ (in the X–Y–Z sequence): flexion-extension, left-right bending, and left-right axial rotations [13]. The Z-axis difference between the corresponding points of the upper and lower endplates indicates the height of the intervertebral disc. To represent the deformational characteristics of different regions, 9 representative locations on the upper and lower endplates of the discs were chosen: left-anterior, anterior, right-anterior, left, center, right, left-posterior, posterior, and right-posterior (Fig. 1c). The coordinate system was placed at the 9 points and the center of the vertebral body.
The lumbar spine of each subject during axial rotations to the maximal left and maximal right in a standing position under weightbearing (0 kg) or a 10 kg load (carrying 5 kg sandbags front and back) was imaged using a dual fluoroscopic imaging system (DFIS). After unified instructional training, the subjects freely rotated their bodies from the standing position to the maximum position and maintained that position for a period of time, during which the researchers assisted in correcting the pelvis and buttocks. Custom-made lead clothing was used to protect the subjects’ thyroid and gonads (Fig. 2a). The two orthogonal fluoroscopic images (F1, F2) obtained at the maximum rotation positions had a resolution of 1024 × 1024 pixels with a pixel size of 0.3 × 0.3 mm2 (Fig. 2b).
Using the established protocol, the vertebral model and paired fluoroscopy images were used to reproduce the motion of the vertebral body in Rhinoceros software (version 5.0, Robert McNeel & Associates, United States) [9, 13, 14]. The pairs of fluoroscopic images were imported into the Rhinoceros software environment and rebuilt based on the actual positions of two fluoroscopes to mimic the experimental setup. The environmental files “setup.rvb” were calculated by the disc aligner and the square plate calibrator that was collected before each test. Each 3D model of L3 ~ 5 imported into the DFIS environment produced its own virtual projection images. The in vivo positions of the vertebral body were reproduced when the virtual projection image best matched the pairs of fluoroscopic images in terms of translation and rotation (Fig. 3). Then, the shape of the deformed lumbar disc was determined by the three-dimensional volume between the adjacent upper and lower endplates. The accuracy and repeatability have been validated using a series of experiments [12, 15, 16].
The disc deformation was calculated using mesh vertices evenly distributed on the upper and lower endplates (approximately 3000 points per surface). The coordinate system of the upper endplate surface of the lower vertebra was used as a reference for calculating the displacement of each corresponding point on the lower endplate of the upper vertebra (Fig. 1b). The non-weightbearing, supine position during the CT scan was used as a reference to calculate the shear and compression deformations of each point of the disc during axial rotation motion. Compression deformation represents the change in the disc height, that is, the change ratio of the disc height during axial body rotations to that during supine position. The symbols “+” and “-” mean tensile and compressive, respectively.
$$Tensile\ Deformation=\frac{\mathrm{Disc}\ \mathrm{Height}\left(\mathrm{axial}\ \mathrm{rotation}\right)-\mathrm{Disc}\ \mathrm{Height}\left(\mathrm{supine}\right)}{\mathrm{Disc}\ \mathrm{Height}\left(\mathrm{supine}\right)}$$
$$=\frac{\left|\mathrm{Z}\right|\left(\mathrm{axial}\ \mathrm{rotation}\right)-\left|\mathrm{Z}\right|\left(\mathrm{supine}\right)}{\left|\mathrm{Z}\right|\left(\mathrm{supine}\right)}\left(\%\right)$$
$$\left|\mathrm{Z}\right|=\left|\mathrm{Z}\left(\mathrm{Lower}\ \mathrm{Endplate}\kern0.5em \mathrm{of}\ \mathrm{the}\ \mathrm{Upper}\ \mathrm{Vertebra}\right)-\mathrm{Z}\left(\mathrm{Upper}\ \mathrm{Endplate}\kern0.5em \mathrm{of}\ \mathrm{the}\ \mathrm{Lower}\ \mathrm{Vertebra}\right)\right|$$
+, Tensile Deformation; -,Compressive Deformation. Tension (+) means that the disc height during rotation is greater than that during supine, and compression (−) means that the height during rotation is smaller than that of during supine.
The overall compression deformation was measured in the reference coordinate system along the z-axis and plotted on a heat map (Fig. 4). In addition, the overall distributions of shear deformation and compression deformation were analyzed from the average of all subjects based on the 9 representative points.
A two-way analysis of variance was used to compare the differences in shear and tensile deformation, as well as the coupled bending of the lumbar spine during axial rotation motion at different load-bearing levels. The statistical significance was set at p < 0.05. Statistical analysis was performed with SPSS 18.0 software (IBM Corp., Armonk, New York).