# FEM-Based Compression Fracture Risk Assessment in Osteoporotic Lumbar Vertebra L1
## 3 Numerical Results and Discussion
### Validation of Mechanical Model  
Extracting physical and micro-geometrical properties of vertebrae is very complicated. If we want to know micro-geometry of human bones, quantitative computational tomography (QCT) can be used on leg or hand bones but not on whole human spine or one of vertebra. Therefore, an alternating methodology of investigation of vertebrae mechanical properties can be 3-D printing. As is stated in Reference [52], today, 3-D printing is practical, useful technology in surgical planing or spine implantation. Obviously, knowing mechanical characteristics, 3-D printed vertebrae is the basic step in successful applications of such kind of structures.  
The validation of numerical modelling was aided in our case by a physical test of the printed polylactide (PLA) vertebrae geometrical model (Figure 13a). The whole procedure took the following the steps:  
1. The printing of the vertebrae model;
2. The printing of the cylindrical PLA sample for mechanical properties of PLA to define;
3. The compression test of the printed PLA sample;
4. The compression test of the printed PLA vertebrae;
5. The determination of the mechanical properties of PLA by verifying the obtained load-displacement curve of the cylindrical sample;
6. The implementation of the defined stress-strain curve of PLA onto the numerical calculation;
7. The comparison of the results of the experimental and numerical studies.  
The printing process was realized by using self-made 3-D printer, based on Prusa-i3 model (Figure 13b). The selection of this device was justified by its parameters: printer type FDM, build volume, \(25\times 21\times 20\text{ cm}^{3}\), minimal layer height \(50\text{ }\upmu\text{m}\), and nozzle diameter \(0.2\text{ mm}\). The printing process took about \(20\text{ h}\), while the printing was completed. The properties of the osteopororic sample of vertebrae was as follow: thickness of cortical shell, \(0.5\text{ mm}\), \(0.1\text{ BV}/\text{TV ratio}\), and \(1.2\text{ TBS}\).  
The physical experiment was performed by using a MultiTest 2.5-i compression machine (Figure 14). The selection of this device was based on suitable range of load 0-2500 N and relatively high precision (\(\pm\)0.1% of full scale). The sample vertebra was tested under the constant loading speed (10 mm/min), and the displacement values were obtained: They are presented in Figure 14(a). The same test was accomplished for the printed cylindrical sample too.  
As Figure 14(a) shows, the nonlinear behaviour of the printed PLA was revealed. The mechanical properties of PLA were determined by processing the load-displacement curve of the cylindrical sample (20 mm length, 15 mm diameter), and the stress-strain relation of PLA was defined.  
The defined stress-strain curve of PLA (Figure 14(a)) was integrated into the numerical model of the vertebrae, and the finite element study was compared to the results of the physical experiment (Figure 14(b)).  
Figure 14: Testing of printed vertebrae by the compression machine.  
Figure 13: The 3-D printer and printed vertebra.  
Figure 15: The load-displacement curves.  
As Figure 15b shows, the curves present corresponding characters, and the biggest difference between the results is constant (about 4%) until the value of load becomes 700 N. Then, the curves demonstrate similar magnitudes of displacement values, which does not exceed 5%. These results approve the adequacy of finite element model and shows that the method offered for osteoporotic bone validation is reliable.