Model construction
The geometric properties of the bony tissue of the pelvis and lumbar spine of a healthy 30-year-old female were assessed by a CT scan with a slice thickness of 1 mm, and the imaging data were then converted into a coarse geometric model by using Mimics 17.0 (Materialise Technologies Company, Leuven, Belgium). The lumbar intervertebral disc cartilage, cortical bones, cancellous bones, articular cartilage, fiber rings and ligaments of the FE model were created based on the geometrical model in Hypermesh 14.0 (Altair Engineering Corp, Michigan, USA). The geometric model of the lumbar, ilium and sacrum was then refined with reverse engineering software (Geomagic 11.0, Geomagic Company. Morrisville, USA) and meshed into a finite element (FE) model with FE preprocessing software (Hyper Mesh 14.0, Altair Engineering Company, Michigan, USA). Based on the structure of the bone, an FE model of the cartilage and ligaments was created according to the anatomical studies [15–16] (Table 1).
Table 1
Material parameters and element types of the model
|
Unit type
|
Elastic modulus
|
Poisson’s ratio
|
thickness/mm
|
Cortical bone
|
S4R
|
12 000
|
0.3
|
0.5
|
Cancellous bone
|
C3D8R、C3D4
|
100
|
0.2
|
—
|
Rear structure
|
C3D8R、C3D4
|
3 500
|
0.25
|
—
|
Endplate
|
S4R
|
2500
|
0.25
|
0.5
|
Articular cartilage
|
C3D8R
|
25
|
0.4
|
—
|
Nucleus pulposus
|
C3D8R
|
1.0
|
0.499 9
|
—
|
Annulus
|
C3D8R
|
4.2
|
0.45
|
—
|
Anterior longitudinal ligament
|
T3D2
|
7.8
|
0.3
|
—
|
Posterior longitudinal ligament
|
T3D2
|
10
|
0.3
|
—
|
Ligamentum flavum
|
T3D2
|
15
|
0.3
|
—
|
Interspinous ligament
|
T3D2
|
10
|
0.3
|
—
|
Supraspinous ligament
|
T3D2
|
8
|
0.3
|
—
|
Intertransverse ligament
|
T3D2
|
10
|
0.3
|
—
|
Joint capsule ligament
|
T3D2
|
7.5
|
0.3
|
—
|
The following ligaments were constructed as 3D tension truss elements: iliolumbar ligament (IL), anterior sacroiliac ligament (ASL), interspinous ligament (ISL), long posterior sacroiliac ligament (LPSL), short posterior sacroiliac ligament (SPSL), sacrospinous ligament (SS), sacrotuberous ligament (ST), superior pubic (SP), arcuate pubic (AP), ligamentum flavum (LF), anterior longitudinal ligament (ALL), posterior longitudinal ligament (PLL), interspinous ligament (IL2), supraspinous ligament (SL), ligamenta intertransversaria (LI) and capsular ligament (CL). The regions were attached according to the methods described in previous studies [15, 16]. The entire model had 886554 elements and 241576 nodes.
Model validation
The FE model was built based on the methods described in a previous study [17]. The results were validated using in vitro data and the results of other simulation studies [18–20]. According to the in vitro study, the points loads on the ventral surface and dorsal surface of L4 were located in the midsagittal plane of the inferior S1 and superior S2 vertebrae. Five translational loads (294 N) and three rotational moments (42 N*m) (anterior, posterior, superior, inferior, mediolateral, flexion, extension, and axial rotation) were tested. The validation outcomes were satisfactory. The “H”- and “U”-shaped fracture lines and different fixation models of the pelvis were then built based on the intact model according to a previous study [21, 14] (Fig. 1).
Pelvic FE model of H- and U-type fracture injuries and three kinds of fixation
The model mimicked the standing position of a human. The model was loaded with a 500 N force, and the forces were directed straight downward and toward the center of the L4 superior endplate. Both sides of the ischial tuberosity were restricted to six degrees of freedom.
The H-type sacrum fracture involved a fracture line between the two S1 foramina and a vertical fracture line crossing both sides of the sacral foramina. (Fig. 2) The U-type sacrum fracture involved a fracture line between the two S2 foramina and a vertical fracture line from both sides of the top of the sacrum to the S2 foramina (Fig. 3).
Four points, A to D, were marked on the model of the H-type sacrum fracture. A was located at the top of the fracture line on the left. B was located at the top of the fracture line on the right. C was located at the bottom of the fracture line on the left. D was located at the bottom of the fracture line on the right. After loading, the displacement of the four points was recorded. The displacement values after loading were recorded as A1 to D1.
Three points, A to C, were marked on the model of the U-type sacrum fracture. A was located at the top of the fracture line on the left. B was located at the top of the fracture line on the right. C was located in the middle of the S2 horizon fracture line. After loading, the displacement of the three points was recorded. The displacement values before and after loading were recorded as A1 to C1.
We chose the following 4 typical methods of fixation that many clinical studies and biomechanical studies have used:single S1 transsacral-transiliac screw fixation,S1 and S2 transsacral-transiliac screw fixation (transsacral-transiliac S1 and S2 screw), L4-L5 pedicle screw and iliac screw lumbopelvic fixation (lumbopelvic fixation), S1 transsacral-transiliac screw combinations of L4-L5 pedicle screw and iliac screw lumbopelvic fixation( bilateral triangular fixation). We used single S1 transsacral-transiliac screw fixation for the U-type fractures but not for the H-type fractures.
The stress distribution of internal fixation and displacement of the points on the model were recorded to determine the biomechanical stability and loading situations.