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A porous material is considered to be a potential material that can be used to repair bone defects. However, the methods of designing of a highly porous structure within the allowable stress range remain to be researched.
Therefore, this study was aimed at presenting a method for generating a three-dimensional tetrahedral porous structure characterized by low peak stress and high porosity for the reconstruction of mandibular defects. Firstly, the initial tetrahedral porous structure was fabricated with the strut diameters set to 0.
Following this, the simulation analysis was carried out. Further, a homogenization algorithm was used for homogenizing the stress distribution, increasing porosity, and controlling peak stress of the porous structure by adjusting the strut diameters. The results showed that compared with the initial porous structure, the position of the large stress regions remained unchanged, and the peak stress fluctuated slightly in the mandible and fixation system with the optimized porous structure under two occlusions.
The optimized porous structure had a higher porosity and more uniform stress distribution, and the maximum stress was lower than the target stress value. The design and optimization technique of the porous structure presented in this paper can be used to control peak stress, improve porosity, and fabricate a lightweight scaffold, which provides a potential solution for mandibular reconstruction.
Treatment of large segmental bone defects in the mandible caused by trauma, benign or malignant tumor, remains a challenge for surgeons to date [ 1 ]. A microvascular-free fibular graft is considered to be the contemporary gold standard for the treatment of mandibular defects and has been widely used [ 2 ]. However, the shape and size of autogenous bone grafts differ significantly from that of mandibular defects, resulting in asymmetry of the postoperative facial contour and poor cosmetic effect on the patient [ 3 , 4 ].
Complications associated with the donor site, such as a decrease in walking endurance and strenuous exercise, are also seen [ 5 , 6 ]. Tissue engineering provides a solution for bone defects [ 7 ]. This new approach combines the advantages of both autografts and allografts and eliminates the problems of donor scarcity. Many studies were conducted on bone replacement materials due to limitations regarding biocompatibility, mechanical properties, and other factors.
Metal materials titanium alloy, cobalt-chromium alloy, L stainless, etc. Ti6Al4V is still considered the optimal material for the production of orthopedic implants due to its excellent combination of corrosion resistance, biocompatibility, and mechanical properties [ 8 , 9 ].
Moreover, the porous Ti6Al4V scaffolds with a wide range of morphological and mechanical properties can be made using additive manufacturing technology, which solves the difficulty in the preparation of mandibular prostheses [ 10 , 11 ].
Compared to the natural bone, a solid titanium implant shows a stronger stiffness and elastic modulus, which induces a stress shielding effect on its surrounding bone that leads to an implant failure [ 12 ].
Implant porosity affects the displacement, stresses, and strain intensity of surrounding bone, and the selection of an appropriate implant according to the type of bone is conducive to improving safety [ 13 ]. Ideally, implants must be highly porous to decrease the stress shielding and allow the ingrowth of the new bone. In addition, a high porosity implant possesses strong permeability, which facilitates the easy diffusion of nutrients and the delivery of sufficient cellular mass for tissue repair [ 14 , 15 ].
However, a high-porosity scaffold usually lacks mechanical strength and is prone to fatigue damage. Fatigue wear and fractures have been reported as the main problems during implant failure, and it remains difficult to design porous structures with high porosity within the allowable stress range [ 15 — 17 ].
Excellent design is a key factor in success. Otherwise, a longer healing time would lead to implant failure. We reviewed articles on the design and optimization of mandibular scaffolds up to June Based on the design method and characteristics, the current approaches were divided into three categories.
In type 1, the porous scaffolds were obtained by the Boolean operation between the uniform porous structure and the design model [ 18 ]. Free-ends and stepped surfaces are produced because the nodes of the periodic lattice structure show difficulty fitting the surface of the design model, resulting in a few risks during clinical use.
Xiao et al. In type 2, the mechanical properties of the scaffold could be improved by optimizing the plate configuration or combining topology optimization technology. The topological optimization design of the fixed structures of the porous mandibular scaffold was reported by Peng et al. Cheng et al. The results indicated that the peak stress and weight of the optimized scaffold were reduced compared with that of the initial scaffold.
Ferguson et al. An ideal scaffold has high porosity and uniform stress that stimulates bone growth rather than merely reducing the peak stress. In type 3, novel design or optimization methods are used to homogenize the stress distribution of the scaffold.
Luo et al. The maximum stress of the optimized scaffold decreased, and the porosity increased in comparison to that of the initial scaffold. Although the peak stress decreases after optimization, it does not converge within the target stress.
Gao et al. However, the maximum stress of the optimized scaffold was still high, and there was no analysis of porosity. To our knowledge, there is no excellent design and optimization method for a scaffold with smooth surfaces, controllable peak stress, and high porosity.
In light of previous studies [ 21 , 23 ], a finite element method was proposed in this paper to design and optimize the tetrahedral porous structure for the repair of mandibular defects. The strut diameters of the porous structure were optimized as per the numerical simulation results.
That is, high-stress struts are of large diameters, and low-stress struts are of small diameters to reduce material wastage as much as possible while maintaining their mechanical performance. The results showed that the maximum stress of the optimized porous structure was lower than the target stress value, and the porosity increased greatly, achieving the design goals.
Furthermore, the controllable peak stress and high porosity structure design algorithm proposed in this paper is suitable not only for mandibular prosthesis but also provides a reference for the lightweight design of the other scaffolds. The preparation of the structural design for mandibular defects is shown in Figure 1.
Data of a head CT scan was taken from a patient having oral squamous cell carcinoma as an example. Ethical approval and informed consent have been obtained for using the imaging data of the patient. The image contours of the maxilla and mandible were extracted using the Mimics To simplify the mandibular model, the dentition triangular slices were removed, and the cavities were sutured. Smooth the surface of the model and remove prominent features. Then, manually check and repair the cracks, reversals, and interference problems of the triangular slices to ensure the correctness of the mandibular model.
After a series of reverse modeling procedures, the original triangular slice model of the mandible in the STL format was transformed into an IGES format. The mandible resection planes were determined based on the tumor location by an experienced surgeon to obtain a design model Figure 1.
To reduce the effect of stress shielding, the plate was divided into two parts to facilitate stress transfer through the design model and connected to the surface of design model to form the scaffold. Six screws with a radius of 1.
The detailed design assembly of the mandibular framework consisting of the residual mandible, design model, plates, and screws is illustrated in Figure 2 a. Classify and number plates and screws according to their position. The tetrahedral element was used to design the porous structure in the design model, and the size of the porous structure is shown in Figure 2 b.
The porous structure was performed by using the design model to achieve an anatomically correct contour. A three-dimensional tetrahedral structure was applied to the open porous structure, and the cell size and the strut diameter were selected as the design parameters. The initial mean cell size was chosen to be 2.
To guarantee the quality and connectivity of the porous structure, the lower and upper strut diameters were set to 0. The diameter of the strut of the initial porous structure was set at 0. The porous structure was designed using the Ansys Based on the initial parameters, the design model was decomposed into an approximately uniform tetrahedral mesh with an edge length of 2.
The node coordinates of the tetrahedral mesh and the connection relationship between each node were recorded to establish the model line structure by programming. Each connection line was replaced with a cylinder cross-section strut with a 0. All the materials were considered to be isotropic, linear elastic, and homogeneous for simplifying the finite element analysis.
The plates were integrated with the porous structure to form the scaffold, and the contacts were made using the multipoint constraint algorithm. The reconstructed mandible was at a later stage, and the porous structure was fixed to the residual mandible. The cortical bone, plates, and screw were meshed with the tetrahedral element. To ensure the accuracy of the results, the mesh was refined in the regions having large feature mutations. The mesh sensitivity analysis results showed that the numerical simulation could converge precisely with the number of elements was in this study.
Finite element analysis was performed on a reconstructed model to evaluate the mechanical properties of the porous structure under physiological loading conditions Figure 4. All fixes limited the degrees of freedom of the corresponding nodes, and all muscle forces were applied equally to the corresponding nodes on the mandibular surface.
The values and directions of the normal muscle forces were obtained from relevant research [ 28 , 29 ]. After establishing the finite element model, the porous structure was optimized according to von Mises stress under the physiological loads. An optimization algorithm was proposed in this study to make the porous structure possess large porosity within the target stress range.
Within the porous structure, the struts meet the minimum weight requirements of the target stress range. The outer contour of the porous structure and the tetrahedral elements of the model remain unchanged, and the strut diameter is introduced as the design variable. The optimal design scheme was to achieve an expected goal among the feasible schemes to meet the requirements. The optimization process could be defined as follows: where is the total number of struts in the porous structure.
The strut diameters are between 0. The optimization algorithm and the design process could be divided into several steps, and the pseudocode for the entire process is provided by the algorithm shown in Algorithm 1. The initial strut diameters were set to 0. The optimization is aimed at realizing the homogeneous stress distribution of the porous structure within the target stress value, removing unnecessary materials, and increasing porosity.
As a result, optimal porous structures were achieved. The porosity of the porous structure was calculated using the following formula: where is the volume of the pores, is the overall volume of the design model The volumes were measured automatically by the software.
To obtain detail information about the influence of porous structure on mandible and fixation system, the results of the finite element analysis under two occlusal situations are shown in Figure 5. The distribution of the large stress areas of mandible and the fixation system was similar before and after the optimization of porous structure. Figure 5 a shows the stress distribution of each mandible and fixation system under INC occlusion.
The high stress of the mandible was mainly distributed at both condylar necks and near the chin screw 3.
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