Creation of a whole-spine model extending from the thoracic spine to the pelvis
In this study, we used 3D-FEA software (Mechanical Finder [MF], version 10.0, Extended Edition, RCCM Co. Ltd., Tokyo, Japan). We analyzed computed tomography (CT) data obtained from a 64-year-old woman with a bone mineral density of 0.717 g/cm2. CT was performed at 0.625-mm intervals from the cervical spine to the pelvis, and the CT data were transferred to MF. The ethics committee of our institute approved the use of this patient’s CT data (Approval No. 1748). We created 3D-FEA bone models from the first thoracic vertebra (T1) to the pelvis by extracting bone contour lines using MF. The models consisted of tetrahedral elements with a length of 1.4 mm.
We derived the mass density of the bone ρ (g/cm3) from the CT value (Hounsfield Unit, HU) and calculated the non-homogeneous Young's modulus distribution based on Keyak's formula3,4 to determine the material properties of the finite elements. The Young's modulus E (MPa) is expressed as indicated in Formula 1, as follows:
\(E= \left\{\begin{array}{c} 0.001 \left(\rho =0\right) \\ 33900{\rho }^{2.20} \left(0<\rho \le 0.27\right) \\ 5307\rho +469 \left(0.27<\rho <0.6\right)\\ 10200{\rho }^{2.01} \left(0.6\le \rho \right) \end{array} \right.\) (Formula 1)
Figures 1A and 1B show the diagrams of element decomposition and non-homogeneous Young's modulus distribution, respectively. Table 1 shows the Young's modulus and Poisson's ratio values for the vertebral body and intervertebral discs.
Table 1
Young's modulus and Poisson's ratio of each element
| Young’s modulus | Poisson’s ratio | Element type |
Cortical bone | Determined by Formula 1 | 0.4 | Tetrahedral |
Cancellous bone | Determined by Formula 1 | 0.4 | Tetrahedral |
Disc | 7.5M Pa | 0.4 | Tetrahedral |
We obtained imaging data for the implants used in the actual surgery via micro-CT, which included a pedicle screw (PS; screw), an S2-alar-iliac screw (S2AI), and a transverse hook (TH; hook). Computer-aided design (CAD) data for these implants were created based on the CT data. The CAD software SOLIDWORKS® (Concord, MA, USA) was used to create the implant models. The diameter of the screw analyzed in the current study was 5.5 mm, with a length ranging from 35 mm to 40 mm. The diameter and length of the S2AI screw were 8.5 and 90 mm, respectively. The diameter of the rod was 6.0 mm. After creating the implant models, we imported the bone and implant models into MF and created the FE models of long spinal fusion by combining these data. All screws and rods were fixed.
Creation of instrumented spinal fusion models and load constraint conditions
Spinal balance
We evaluated the following three different patterns of standing sagittal vertical axes (SVAs): neutral [SVA 0 mm], SVA 50 mm, and SVA 100 mm (Fig. 2).
Fusion length
We analyzed fusion length using the following two different conditions: from the second thoracic vertebra to the pelvis (T2-S2AI) and from the 10th thoracic vertebra to the pelvis (T10-S2AI) (Fig. 3).
Implant types in upper instrumented vertebrae (UIV)
We created the models by applying screw in each vertebra. We also developed the models using a hook at the UIV, instead of a screw (Fig. 3). Accordingly, we evaluated 12 models based on combinations of these conditions. Table 2 shows the number of nodes and tetrahedral elements for each model.
Table 2
Number of elements and nodes in each model
Fusion length | Implant types in UIV | Spinal balance | Number of nodes | Number of elements |
T2-S2AI | Pedicle screw (All PS) | Neutral (SVA 0 mm) | 1,544,795 | 7,481,374 |
SVA 50 mm |
SVA 100 mm |
Transverse hook (TH) | Neutral (SVA 0 mm) | 1,591,719 | 7,747,207 |
SVA 50 mm |
SVA 100 mm |
T10-S2AI | Pedicle screw (All PS) | Neutral (SVA 0 mm) | 1,381,316 | 6,662,229 |
SVA 50 mm |
SVA 100 mm |
Transverse hook (TH) | Neutral (SVA 0 mm) | 1,377,463 | 6,628,824 |
SVA 50 mm |
SVA 100 mm |
Boundary and loading conditions
For the boundary conditions, acetabular regions were constrained, a distributed load of 1,200 N was applied according to the number of nodes in the upper endplates of each vertebral body from T1 to L5, and static elastic stress analysis was performed. The loading method was applied based on that described in a previous study.5
Data extraction
For all 12 models, we selected and extracted the meshes of each vertebra from T2 to the sacrum. The total stress of the vertebral mesh was added and equalized according to the volume of each vertebra. We collected data on stress from the screws at each vertebra. The rod was extracted separately, and the mechanical stress was evaluated. We analyzed the mechanical stress on each vertebra and implant, focusing on the differences in spinal balance, fusion length, and implants in UIV. Previous studies have validated the use of FEM analysis for examining mechanical stress in the lumbar vertebrae.6–8