## 5 Personalized 3D Printing of Artificial Vertebrae
### Bone Density Measurement and 3D Printing  
Bone density includes several types such as apparent wet density, apparent dry density, gray density, and bone mineral density [27]. In this paper, the Quantitative Computed Tomography (QCT) method is utilized to quantify the CT value (expressed in Hounsfield Units, Hu) of bones, upon which the bone density value is calculated. With the apparent density serving as the principal investigative parameter, previous studies have conducted linear regression analyses to explore the relationship between CT values and apparent densities. This has led to the derivation of a linear regression equation linking the two variables, as referenced in [28]. \[\rho_{app}=0.896 CT+134, \tag{20}\]  
In this equation, \(\rho_{app}\) is the apparent density unit (mg/cm\({}^{3}\)) and CT is the CT value in Hounsfield Units (Hu). The D'ensity in Ellipse\({}^{\prime}\) tool within the Mimics 21.0 software is employed to designate regions of interest (ROIs) within each image slice. Upon selection, the system autonomously computes and displays the CT values, as exemplified in Figure 19. In this illustration, A'rea' denotes the extent of the delineated ROI, whereas M\({}^{\prime}\)ean (HU)  
Figure 17: Process of CT-based reconstruction of lumbar spine modeling. Figure 18: L4 lumbar spine model and anatomical structure. (**a**) L4 lumbar spine model; (**b**) anatomy of lumbar spine. signifies the arithmetic mean of the density readings in Hounsfield Units (HU). Specifically, the mean grayscale value of the cancellous bone within the current slice is quantified as 215.51 HU. In the realm of medical imaging, HU serves as a standardized metric to depict the relative density of tissues in CT scans. The computation of M\({}^{\prime}\)ean (HU)\({}^{\prime}\) involves aggregating a series of density measurements and dividing the sum by the total number of data points, yielding the average density. Conversely, S\({}^{\prime}\)td.Dev (HU)\({}^{\prime}\) represents the standard deviation of the density data, expressed in HU. Should the image quality be subpar, marked by the presence of streaks or other imaging artifacts, the affected layer must be excluded from the analysis. In such instances, the conversion of CT values should adhere to the methodology outlined by [PERSON] [29]. CT values for each slice are meticulously recorded in correspondence with their respective layer numbers. By averaging these values, a representative CT value for each bone segment is derived, facilitating a comprehensive assessment of bone density across the entire structure. The CT values of the cancellous and cortical bone for each layer were recorded following the aforementioned procedure, resulting in average CT values of 231 HU for cancellous bone and 1156 HU for cortical bone. Upon substituting these average CT values into the previously derived equation, the computed densities were 340.98 mg/cm\({}^{3}\) for cancellous bone and 1169.78 mg/cm\({}^{3}\) for cortical bone. After determining the densities of both cortical and cancellous bone, the anticipated printing process parameters are estimated through a hybrid approach combining a BP neural network analysis with genetic algorithm prediction. The resultant printing process parameters are tabulated in Table 10.  
For the fabrication of the vertebrae models, slicing software is employed to define and optimize the 3D printing parameters, ensuring accurate configuration and proper alignment within the build platform. The artificial vertebral bodies are subsequently constructed using 3D printing technology, as shown in Figure 20. Specifically, Figure 20 displays the cancellous bone model, and Figure 20 depicts the cortical bone model, while Figure 20,d present the composite models that integrate both the cancellous and cortical bone structures.