## 2 Three-Dimensional Printing Program of Artificial Vertebrae and Analysis of Influencing Factors  
### Three-Dimensional Printing Program of Artificial Vertebrae  
Based on the anatomical structure of the human lumbar vertebrae and adhering to the principles of the 3D printing process, a comprehensive strategy has been developed to fabricate an artificial vertebral model with targeted bone density. As illustrated in Figure 1, this approach is divided into two key components: the 3D modeling of the lumbar vertebrae, which involves digital reconstruction and density mapping, and the prediction of critical printing process parameters, which ensures precise control over bone density distribution during the fabrication process. (1) Lumbar spine 3D modeling program  
The image acquisition phase represents the initial step toward crafting a lumbar spine model. Initially, CT data of the human lumbar spine are acquired through imaging, with particular attention given to optimizing image resolution and selecting appropriate slice spacing during the scanning procedure. Following image acquisition, the process of image segmentation ensues, with the primary objective of isolating the region of interest amidst the intricate array of anatomical structures. Utilizing Materialise Mimics 21.0 medical modeling software, the lumbar spine's 3D model is generated by judiciously setting the threshold range to delineate the desired area. Through image segmentation, the target region is extracted, culminating in the production of a preliminary model. Ultimately, to refine the surface quality and geometric precision of the model, Geomagic Studio 2012 reverse engineering software is employed. This software facilitates wrapping, smoothing, and reducing the number of triangular facets on the model's surface, thereby enhancing its overall fidelity. (2) Three-Dimensional printing process parameter prediction program  
Initially, a single-factor experiment is conducted to identify the pivotal printing process parameters that significantly impact the specimen's density. Subsequently, Response Surface Methodology is applied, opting for a central composite design coupled with a quadratic polynomial response surface model. Here, principal printing process parameters serve as independent variables, while the density of the printed specimen acts as the dependent variable or response. Distinct prediction models are then formulated for both cortical and cancellous bone densities. These models provide a theoretical foundation for forecasting the printing process parameters required to achieve a specified bone density, thus enabling the more accurate and efficient production of bone-mimetic structures. Based on the established bone density prediction model, data are randomly divided into training and test samples. A Back Propagation (BP) neural network model is then constructed using these samples. This model serves as the foundation for deriving the fitness function for the genetic algorithm (GA). To establish a bone density prediction and optimization model, we combined several algorithms. First, we collected data on how different printing parameters (such as filling density, layer height, and material flow rate) affect the density of printed samples. Next, we used Response Surface Methodology (RSM) to analyze the relationship between these parameters and bone density, helping us find the best settings. Then, we employed a Back Propagation (BP) neural network to learn from  
Figure 1: Schematic representation of artificial verteb preparation strategy. these data and identify patterns between the input parameters and bone density. Finally, we applied a genetic algorithm (GA) to further optimize the printing parameters, simulating the process of natural selection to find the most effective combinations. By integrating these methods, we can accurately predict and optimize the bone density of 3D-printed artificial vertebrae, ensuring their quality.