3D Finite Element Analysis of Long Spinal Fusion

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 formula [3 (link), 4 (link)] to determine the material properties of the finite elements. The Young's modulus E (MPa) is expressed as indicated in Formula 1, as follows: $$E=\left\{\begin{array}{c}0.001\left(\rho ,=,0\right)\\ 33900{\rho }^{2.20}\left(0,<,\rho ,\le ,0.27\right)\\ 5307\rho +469\left(0.27,<,\rho ,<,0.6\right)\\ 10200{\rho }^{2.01}\left(0.6,\le ,\rho \right)\end{array}\right)$$
Figures 1A and B 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.Fig. 1

Element segmentation diagram of multi-vertebrae and Young’s modulus distribution diagram. A FE models of spinal fusion. B Heterogeneous distribution of Young's modulus, E. FE, finite element; E, Young’s modulus (MPa)

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	7.5 MPa	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 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. The contact condition between implant and bone was set as bonding contact.