## 4 Discussion  
The patient-specific 3D printing fixation implant values applied in plastic surgery or mid-face repair are greatly improved because the implant geometry profile provided an adaptive interfacial fitness, both the positioning and fixation functions for the resting bone. However, patient-specific 3D printing implants must be well designed according to the patient's condition before surgery. However, there is currently no design criterion for applying 3D-printing technology to ZMC fracture repairs. According to the literature and biomechanical principles [2; 3; 7], the fixation implant needs to be designed as a thin plate, which should not be too rigid to produce a stress-shielding effect. Nor can it be too soft to induce repair instability, and must restore the intact bone mechanical function, i.e., buttress pillars in the mid-facial bones. This is the reason why topology optimization was combined with the FE analysis in the IFS model to verify the generated optimized structure (HS) model as feasible for representing the buttress. The PSBT implant was then designed according to the skeleton of the optimized structure (HS) model.  
The topology optimization is a design tool that can arrange a specified number of materials on a given design domain for giving loads, boundary conditions, and constraints to minimize the scalar objective function. This optimization algorithm was combined with the FE analysis in this study to identify optimal structures removing elements whose stress value was less than the constraint value [17]. The objective function was defined to minimize the volume of the intact skeletal structure.  
The topology optimization result for the IFS model obtained a HS model with a hollow skeleton structure. The stress pattern that was found through the mid-facial skeleton had similar specific osseous trajectories as the buttresses by occlusal forces. High stress distributions were found at the nasomaxillary and zygomaticomaxillary areas of the HS model and implied that these areas are similar to the position of the former cortical bone with the higher stress registered. The cortical bone with harder stiffness is the main skeleton structure, the adaptive position for screw anchors, and exhibited the highest compressive stress during occlusal. The small stress and large volume variation between the IFS and HS models indicated that many cancellous areas in the facial bone may not need to be transmitted as strength and the structure achieves lightweight neutrality. This point implied that the internal fixation implant contour design can follow the HS model skeleton position, i.e., nearly the buttress pillars in the IFS model.  
The maxillary and zygomatic bones received a bending moment under the loading condition in our simulation. Principal stresses were selected more suitable as the stress index of failure for brittle materials rather than von Mises stress. The simulated results clearly showed that the ZMC fracture repair mechanical behavior with the PSBT implant designed according to the HS model skeleton was similar to the IFS model regardless of the stress value and distribution in different positions. However, the use of a traditional mini-plate showed unsatisfactory results. This phenomenon confirms the hypothesis that we proposed the implant main structure or contour design that should be designed according to the buttress position and orientation.  
The results obtained in this study were only simulated under the condition of a uniform axial load applied to the posterior teeth, because the chewing condition occurs clinically most often, it was applied to simulate occlusal force. The structural optimization was obtained for explaining the buttress theory under chewing forces. However, this could not represent the actual individual occlusion situations. Well-controlled clinical/animal trials must be confirmed in a further study.