# Finite Element Model of Canine-Specific Vertebrae Incorporating Biomechanical Tissue Nonlinearity
## 2 Materials and Methods
### Creating the Geometry  
Our numerical model's construction began with a detailed CT scan analysis using \"Siemens SOMATOM syngo CT 2007P \" of software version Somaris/5.5. The segmentation of the lumbar spine vertebra was meticulously processed through \"3D Slicer 5.2.2\", followed by simplification in \"Meshlab 2023.12 release version\" to optimize the computational efficiency. The final geometry, analyzed in \"Solidworks 2022\", was pivotal in establishing a robust model foundation, incorporating varying cortical layer thicknesses and accurately simulating the vertebral trabeculae.  
CT scan data were used for the geometry, surface area, and vertebral height calculations. Three separate software applications were used, \"Osirix Lite\" 13.0, \"3D Slicer\" 5.2.2, and \"Fiji\" 2.15.0. A confidence interval was also calculated.  
The scan was performed using a Siemens CT scanner, with a slice thickness of 1.25 mm, using the B31s protocol. This protocol was designed for high-resolution imaging. A specialized bone reconstruction algorithm was used. This algorithm is designed to enhance the visibility and definition of bone structures in the scanned images. It optimizes the contrast and sharpness to accurately delineate the bone from other tissues, which is crucial for the precise 3D modeling and analysis of the bone anatomy.  
In particular, \"3D Slicer\" is an open-source software program that allows the segmentation and analysis of medical images acquired from MRI or CT scans [22]. Here, the CT DICOM images were processed by the \"3D Slicer\" program to isolate the lumbar spine vertebra. Figure 1 illustrates the whole segmentation procedure. All the necessary vertebra parts were removed.  
The segmented vertebral body was simplified using the \"Meshlab\" software, and the number of surface area components was decreased to 10,000. This simplification was conducted to reduce the computer resources required while retaining the model's original shape.  
The resultant geometry was analyzed using the \"Solidworks\" software and imported for theoretical calculations.  
Subsequently, four distinct models were constructed. Three of these models varied in the cortical layer thicknesses, specifically 0.2, 0.25, and 0.3 millimeters. Instead of using nonlinear analysis, these models were evaluated using a linear approach paired with a simplified method designed for the analysis of nonlinear lumbar vertebra behavior. A key observation from this study was the necessity to model the trabeculae as ellipses to  
Figure 1: Segmentation of the first canine lumbar vertebra.  
achieve the target porosity. Additionally, in the simplified verteb geometry, trabeculae were approached as a continuum material.  
The model was initially subjected to a linear static analysis in \"Solidworks\". Although our primary focus was on the nonlinear characteristics of the model, a linear analysis was performed to ensure the model's fundamental stability and structural integrity under typical loading conditions. The study ensured the veracity of the geometric model, boundary conditions, and loading parameters as a crucial first stage in the comparison procedure.  
Intervertebral discs were treated as linear material. This important component is situated between each verteb and functions to reduce friction and provide a damping system. Its mechanical properties were determined on the basis of the results of a literature review. Table 2 shows the mechanical properties of the vertebral body.  
We imported the geometry into the finite element analysis program \"Solidworks\", which also supports finite element analysis for studies. It was necessary to specify that the current model was a three-dimensional (3D) solid body model, and, after selecting these settings, a nonlinear dynamic model was chosen for the calculations.  
Not only are these characteristics necessary in predicting the likelihood of lumbar spine fractures in canines, but they also have the potential to contribute to the development of fracture prevention and treatment strategies.