## 1 Introduction
[18; 19] explored the potential of biomimetic smart materials in 4D printing technology, highlighting the transformative role of these materials in a number of fields, including regenerative medicine, robotics, architecture, and aerospace, which will drive breakthroughs in areas such as personalized medicine, adaptive robotics, and sustainable architecture. Despite these promising developments, current studies focus primarily on improving biomechanical properties and biocompatibility, rather than addressing the critical need for the accurate replication of patient-specific bone densities and microstructures in the context of robotic-assisted surgeries. The lack of precise bone density matching between artificial models and real vertebrae significantly hinders the application of these models in robotic osteotomy and surgical planning, as bone density directly influences the cutting force and tactile control in robotic surgeries. It is evident that while 3D printing has been widely applied to produce medical models, surgical guides, artificial bone implants, and bioskeletal scaffolds, the primary focus has been on achieving adequate biomechanical properties and biocompatibility, rather than precisely replicating patient-specific bone densities and microstructures for robotic surgical applications. In robotic osteotomy, the cutting force is influenced by physical attributes such as bone density, underscoring the necessity for a bone surrogate material with equivalent bone density for robotic surgical planning and tactile control research. Thus, a novel approach is required to address these challenges by developing artificial vertebrae that precisely mimic both the geometric structure and bone density of natural vertebrae for use in robotic-assisted surgeries. Given that the bone density of artificial vertebrae is significantly influenced by the parameters of the 3D printing process, achieving artificial vertebrae with a targeted bone density proves challenging. Consequently, there is a pressing need to investigate a method for personalized 3D printing of artificial vertebrae based on bone density prediction. Through a bone density prediction model, one can derive the 3D printing process parameters tailoring the structure of the 3D printing process, and the 3D printing process parameters tailoring the structure of the 3D printing process. lored to individual patients, ensuring that the density and geometric accuracy of artificial vertebrae closely match those of actual human bone. This forms a solid foundation for predictive modeling of robotic vertebral plate cutting force and bone identification. Utilizing the response surface method to construct a predictive model between bone density and printing process parameters can offer extensive data support. By incorporating new sample data, this method facilitates deep learning and training, gradually enhancing the accuracy of model predictions. As a result, this approach overcomes the limitations of conventional prediction methods, substantially reduces the number of required experiments, improves operational efficiency, and presents a novel solution for bone density prediction [20]. The density of artificial vertebrae is contingent upon numerous 3D printing process parameters, and acquiring the specific densities of artificial vertebrae models demands precise control over these parameters. Traditional prediction methods, such as univariate and orthogonal testing, typically require substantial experimental resources and exhibit low prediction accuracy. In this regard, the integration of intelligent computing techniques like neural networks and genetic algorithms holds significant potential for enhancing precision. Methods that integrate neural networks and genetic algorithms require only a small dataset, effectively constructing models linking process parameters to the densities of finished products. These methods boost significant advantages in parameter optimization and performance prediction. [PERSON] et al.