# Computed Tomography-Driven Design and Fused Filament Fabrication of Graded Density Bone Scaffolds
## 3 Test Case and Discussion
### Preliminary Process Calibration  
The maximum extrusion width, \(E_{w,max}\), must be determined based on the specific extruder configuration and material characteristics, while \(E_{w,min}\) = 0.2 mm, according to Equation (3) and a previous study [42]. For Amazon White PLA filament, the maximum flow rate reachable at \(T_{ext}\) = 215 \({}^{\circ}\)C with the adopted hardware (Sprite Extruder with \(\varphi\) = 0.4 mm) is \(Q_{max}\) = 19.24 mm\({}^{3}\)/s. This value corresponds to the threshold beyond which the stepper motor begins to lose steps, indicating that a continuous material flow can no longer be maintained. Extrusion tests were carried out at various feed rates (F = 500, 1500, 3000, and 5000 mm/min), corresponding to the movement speed \(v_{sp}\) (mm/s), and at different target extrusion widths (\(E_{w}\) = 0.5, 1.2, 1.5, and 2 mm), all at \(T_{ext}\) = 215 \({}^{\circ}\)C. The quality of the deposition was evaluated by analyzing the actual \(E_{w}\) dimensions and the retention of the bead shape over a cross-section of 20-layer, single-bead samples. For every F, at \(E_{w}\) = 0.5 mm, the shape of the beads is retained (one example is shown in Figure 7a), and at \(E_{w}\) = 2 mm the bead shape is not retained (Figure 7d). For \(E_{w}\) = 1.2 and 1.5 mm (Figure 7b,c), tested only at 1500 mm/min, the shape is reasonably preserved but the actual \(E_{w}\) is lower than the designed one in the first layers (1.02 and 1.16 mm). After a few layers, however, the deposition becomes misaligned with the vertical direction and the beads are deposited on top of each other, resembling the designed \(E_{w}\), with a measured width of 1.37 and 1.66 mm. This behavior is more pronounced at higher F values, where misalignments in the upper layers occur, likely due to increased vibrations in the printer frame (or extruder) during deposition or flow instabilities [43]. Moreover, at \(E_{w}\) = 2 mm, visible underextrusion can be observed because the \(Q_{max}\) limit was reached. Therefore, at T = 215 \({}^{\circ}\)C, F values up to 1500 mm/min are suitable to reduce bead misalignment, while \(E_{w,max}\) should fall within the range of 1.2-1.5 mm. The approximation for \(E_{w,max}\) previously described in Equation (4) can also be used. The polygonized surface model was then extracted and the main steps of the process are shown in Figure 9, where the HU 3D scalar field is visualized using a grayscale. Figure 10 illustrates the main geometrical operations applied to the polygonized surface to isolate a portion of the femur bone, shown in green. The entire polygonized surface is cropped using a Boolean intersection with a box, i.e., the ROI (edges highlighted in red) (Figure 10a). Next, the medullary cavity is closed (Figure 10b). Optionally, a remesh command can be used to refine the polygonized surface (Figure 10c). Finally, the polygonized surface model is exported in.stl file format. In this case study, the ROI is a portion of the femur bone, consisting of the cortical bone, trabecular bone, and bone marrow. The bone marrow is contained within the medullary cavity, which is primarily a void, so we consider the highest porosity. The HU-\(\rho\) correlation  
Figure 10: Magnification of the ROI region of the extracted polygonized surface. Shown in green are the femur bone section and geometric modeling steps. The selected femur bone section (**a**), the closed model (**b**), and the final model after quad-remeshing (**c**) are presented. Figure 9: Visualization of the HU 3D scalar field [\(-\)1000–1562] in HUs (segmented bone tissue > 350 HU, isosurface at 350 HUs, and polygonized surface model + ROI). Despite the proposed method's results shown in the case study, it is important to note that it is not without its limitations, which require further investigation. For instance, it may happen that the values of the 3D scalar field are not adequately suited for the FFF AM process, such as lacking the desired gradient, so several modifications can be applied to adjust these values.