Design and performance analysis of bionic trabecular bone scaffold structure based on Voronoi

Abstract

Background

The structural parameters of porous scaffolds are crucial to both their mechanical and biological properties. However, the influence mechanism of random number points and porosity of bionic trabecular bone scaffolds designed by the Voronoi on the scaffold performance is currently unclear.

Methods

In this paper, bionic trabecular bone scaffolds with different random number points and porosity were designed by the Voronoi, and the scaffolds were fabricated via the selective laser melting (SLM) technology. Subsequently, the mechanical and bone ingrowth properties of scaffolds with different parameters were analyzed. Meanwhile, the internal fluid characteristics of scaffolds with the different parameters were studied by using the Computational Fluid Dynamics (CFD) method.

Results

The results show that at low porosity, the fewer the random number of points, the better the mechanical properties. When the porosity is 50%, the yield strength of the scaffolds with random points 10 is approximately 200 MPa, while the scaffolds with random points 20 and 30 have a yield strength of only about 130 MPa. With the increase of the random number of points, the flow field inside the porous structure becomes more uniform. When the porosity is low, the bone ingrowth performance of the scaffold with a random number of 20 is the best; when the porosity is high, the bone penetration performance of the scaffold with a random number of 30 is the best.

Conclusion

The mechanical and biological properties of bionic scaffolds are greatly influenced by the random number of points and porosity. Bionic scaffolds with fewer points have good mechanical properties, while those with more points and higher porosity have good biological properties. The parameters of the scaffold need to be selected according to the requirements of the bone repair site.

Introduction

The repair of large bone defects has always been a rather difficult type of problem for clinicians. The use of artificial bone scaffolds for repair is usually regarded as having more advantages than traditional autologous bone and allogeneic bone transplantation [1–5]. With the development of 3D printing technology, 3D printed porous titanium alloy bone scaffolds have been increasingly applied in clinical practice [6–8]. The 3D printed porous titanium alloy scaffold can match the elastic modulus of bone tissue by adjusting the porosity of the scaffold to eliminate the stress shielding effect [9–11]. Meanwhile, the porous structure allows bone tissue to grow in, enabling the scaffold to form biological fixation with the surrounding bone tissue, thereby achieving the goal of long-term implantation [12, 13].

The design parameters such as porosity, pore size, structure and permeability of porous structure scaffolds determine their mechanical and biological properties [14–17]. There are two types of porous structures: regular structures and irregular structures. The struts inside regular structures have definite directions and positions, and their mechanical properties are better than those of irregular structures, but their biological properties are poorer [18, 19]. For large-segment bone scaffolds, the bone scaffolds usually need to have good mechanical properties to provide mechanical support at the bone defect site, and at the same time, they also need to have good biological properties to improve the osseointegration performance of the scaffolds [20–22].

To enhance the biological performance of porous scaffolds, some scholars have proposed that the biomimetic trabecular bone method can be utilized to design the porous structure of bone scaffolds [23–25]. The natural irregular pore size and structure of trabeculae provide an ideal site for the adhesion and proliferation of bone tissue cells, making it a relatively ideal design scheme for a porous structure scaffold [26, 27]. Compared with the modeling methods of regular structures, the biomimetic trabecular bone has good performances in terms of porous mechanical and biological properties [28–30]. Constructing porous scaffolds with trabecular bone structures by CT reconstruction is neither convenient nor flexible, and the porosity and pore size of the constructed trabecular bone structures are uncontrollable [31, 32]. At present, a design method of bionic trabecular bone porous structure based on the Voronoi has solved this problem. The Voronoi algorithm is a spatial segmentation algorithm based on seed point sets. By using this algorithm, the pore size and porosity of trabecular bone structures can be accurately controlled [33]. Liu et al. [34] investigated the differences in mechanical and biological properties of porous structure scaffolds with different porosities prepared by the Voronoi. The results indicated that the biomimetic porous structure had good comprehensive performance under an appropriate porosity. Chao et al. [35] studied the effects of different bone trabecular porous structures prepared by the Voronoi on the stress distribution of the scaffold at different number points and different porosity, and proved that the bone trabecular structures prepared by the Voronoi have a good matching with the mechanical properties of human bone tissue. Li et al. [36] designed a method for the random distribution of spherical spatial control points to achieve the parametric design of Voronoi trabecular bone structures, and its mechanical properties met the requirements of bone grafting. However, these studies did not explain the influence of random number points on the mechanical and biological properties of the constructed trabecular bone structure.

In this paper, we generated 10, 20 and 30 random points respectively in a three-dimensional closed space (2 × 2 × 2 mm), used these random points to construct the Voronoi bionic trabecular bone porous structure, and studied the performance differences of it as a bone scaffold. We focus on the influence of two factors, namely random number of points and porosity, on the mechanical properties of porous scaffolds. The permeability and wall shear stress (WSS) within the porous structure have a significant impact on bone tissue ingrowth. Therefore, we analyzed the flow field inside the biomimetic porous structure under different random number points and different porosity conditions by using the Computational Fluid Dynamics (CFD) method, and compared the permeability and WSS inside the porous structure under different biomimetic trabecular bone design parameters. Finally, the porous scaffolds were implanted into the femoral condyles of rabbits to investigate the effects of random point number and porosity on the in vivo bone ingrowth performance of the Voronoi bionic trabecular porous structure.

Materials and methods

Design of the bone trabecular structure

Generate a certain number of random points (e.g., 10) in a three-dimensional closed space (2 × 2 × 2 mm), and then use these points to create Voronoi polygons. At this point, these Voronoi polygons are connected and cannot generate struts. Therefore, we decomposed the polygons and extracted the boundaries of the polygons. The boundaries of the Voronoi polygon were obtained as some lines. These lines were replaced by cylindrical struts, and finally a Voronoi bionic trabecular porous scaffold was obtained, as shown in Fig. 1. The marking of porous structures is determined based on the number of random points and porosity within a 2 × 2 × 2 mm unit cell. For example, 10–52% indicates that the number of random points is 10 and the porosity is 52%.

Fig. 1.

Modeling process of Voronoi bionic trabecular porous scaffold

Preparation and mechanical property analysis of the scaffold

Preparation of the scaffold

The designed scaffold was prepared by selective laser melting (SLM) technology. The SLM process was conducted on a XDM 120 system, which is provided by Suzhou XDM 3D Printing Technology Co., Ltd. The machine was equipped with a 500 W laser with a spot size of 55 μm, the layer thickness is 20 μm.

Mechanical property analysis of the scaffold

According to the ISO 13314:2011 standard, rectangular scaffolds (n = 3, 10 × 10 × 10 mm) were fabricated to measure the equivalent elastic modulus and compressive strength of porous scaffolds.

Here, cubic specimens were selected for the experiment, while subsequent animal experiments used cylindrical specimens. To verify the influence of sample shape and size on mechanical properties, we conducted mechanical analysis using the finite element method. The lower end of the model was fixed and the upper end was subjected to the same displacement of 0.001 mm or the same stress of 3.1 MPa. As shown in Fig. 2(a) and (b), these are the finite element analysis boundary conditions for different specimens’ shapes and sizes of the 10–52% model. The finite element analysis was carried out using the ANSYS 18.2 software for the calculation.

Fig. 2.

(a) Boundary conditions of the cubic simulation model; (b) Boundary conditions of the cylindrical simulation model; (c) Compression testing machine; (d) Representative stress-strain curves

The mechanical experiments were completed on the universal testing machine for materials (MIT-100, Changzhou sanfeng instrument technology Co., Ltd), as shown in Fig. 2 (c). At room temperature, the indenter was subjected to uniaxial quasi-static compression tests at a speed of 1 mm·min⁻¹ until the sample was completely crushed. The value at 0.2% of the strain offset in the stress-strain curve was taken as the yield strength of the sample, and the equivalent elastic modulus of the sample was the value of the slope of the elastic deformation stage in the stress-strain curve, as shown in Fig. 2(d), the stress-strain curve of the cubic specimens (20–59%) is presented. The temperature and humidity in the experiment had little effect on the results. In this experiment, the temperature was 20℃ and the relative humidity was 60%.

Fluid simulation

Computational Fluid Dynamics (CFD) has been used to evaluate the biological performance of porous bone scaffold structures and has been verified by animal experiments [18]. CFD analysis can be utilized to analyze the wall shear stress (WSS) and flow field within porous structures, thereby analyzing the influence of the topological structure of porous structures on the transport of oxygen and nutrients required for cell growth, providing design ideas for the improvement of porous structures [16, 37]. The permeability, WSS, and velocity streamline inside different porous structures were analyzed by ANSYS Fluent software. Since the porous scaffold is of an array structure, to reduce the computational load, we only selected two of the units for analysis. Fluids are regarded as incompressible. In CFD, the Navier-Stokes equation defined by Eq. (1) is adopted for solution.

1

where: represents the fluid density (kg·m^− 3); v is the fluid velocity (mm·s^− 1); t is time (s); µ is the hydrodynamic viscosity (Pa·s); ∇p is the pressure difference (Pa); F is force (N).

To simulate the flow of cells within the porous scaffold, the fluid parameters adopted were the liquid parameters of the cell culture medium with 5%wt/wt dextran at 37℃ (µ = 0.0037 Pa·s; ρ = 1000 kg·m^{− 3}) [18, 38]. The boundary conditions for fluid calculation are shown in Fig. 3. The inlet velocity of the fluid is set at 0.1 mm·s^{− 1}, the outlet pressure is set at 0 Pa, scaffold strut surfaces were modeled with a no-slip boundary condition, and symmetrical boundary conditions are used around the fluid domain to indicate that the fluid domain can extend infinitely. The analysis was conducted using the Fluent module in ANSYS 18.2 software. The mesh type was tetrahedral mesh, and the meshing was carried out by the software’s automatic method. Table 1 shows the number of elements for different cubic specimens during the CFD analysis. Due to the varying complexity of different parts of the model, the mesh sizes for the same model in different parts were also different. The convergence residual value of the CFD simulation analysis is 1e^{− 5}. The porous structure unit is a cubic unit. Therefore, in this CFD analysis, cubic specimens were used for the analysis. To verify the differences between the cubic specimens and the cylindrical specimens in the CFD analysis, we first analyzed the results of the 10–52% model under different sizes and shapes. The CFD analysis boundary conditions of the cubic specimens and the cylindrical specimens are shown in Fig. 3(a) and (b), respectively.

Fig. 3.

Boundary conditions of fluid analysis: (a) cubic specimens; (b) cylindrical specimens

Table 1.

Number of elements in each model

Architecture	10–52%	10–61%	10–70%	20–51%	20–59%	20–70%	30–51%	30–60%	30–72%
Number of elements	202,776	283,766	412,915	416,817	551,665	948,727	546,761	786,312	1,439,757

The unit permeability K is calculated by defining Darcy’s Law through Eq. (2):

2

here: Q, L, A and ∆P represent the inlet fluid flow rate (m³·s), model length (m), inlet cross-sectional area (m²) and pressure difference (MPa) respectively.

Evaluation of bone ingrowth performance in the scaffold

The animal experiments were conducted at the Animal Experiment Center of Southwest Medical University and were approved by the Ethics Committee of Southwest Medical University (Ethical Number: SWMU20240003). Forty-six three-month-old New Zealand white rabbits (weighing 2.5–3.0 kg) were divided into two groups, with 23 rabbits in each group corresponding to two time points (4 weeks and 12 weeks) respectively. The 46 femurs of 23 rabbits in each group corresponded to 9 different cylindrical porous scaffolds (∅5 × 8 mm) respectively, and each scaffold was repeated 5 times. After general anesthesia was administered to rabbits with 3% pent barbiturate sodium (30 mg/kg), a cylindrical defect (∅5 × 8 mm) was fabricated in the femoral condyle of the rabbits using an electric drill, and a cylindrical porous scaffold was randomly implanted, as shown in Fig. 4. After implantation, the wounds were sutured, ear tags were placed on each group of rabbits for numbering, and the types of scaffolds implanted in the left and right legs were recorded. After the operation, each rabbit was raised alone and treated continuously with penicillin for three days. After implantation, the rabbits were sacrificed by injecting excessive sodium pentobarbital at the 4th and 12th weeks respectively. The entire femoral condyle was removed and fixed in a 10% formalin solution for subsequent experimental analysis.

Fig. 4.

(a) Create bone defects; (b) Implant porous bone scaffolds; (c) Suture the wound

Micro-CT reconstruction

Microcomputed tomography (Micro-CT) is used to analyze the internal structure of porous scaffolds and the growth of surrounding bone tissue after implantation in animals. During the scanning process, the X-ray voltage was set at 90 kV, the beam current was 200 µA, and the resolution was 17.2 μm. Through 3D reconstruction, the bone volume (BV) value of the new bone was measured. The total void volume (TV) of the scaffold is known. Evaluate the bone ingrowth of porous scaffolds by using the ratio of BV to TV. The higher the BV/TV value, the better the biological performance of the porous scaffold.

Histological evaluation

After the rabbit’s femur was completely removed, the specimen was first subjected to graded ethanol dehydration treatment (70% − 100%). Then, the sample was immersed in a 37 °C methacrylic acid methyl ester solution for one week. Using a hard tissue sectioning machine (SP1600, Leica, Germany), thin Sect. 50 μm thick were cut along the long axis of the cylindrical scaffold. The sections were stained with Van-Gieson (1.2% trinitrophenol and 1% acid fuchsin) and observed under an optical microscope (DMLA, Leica, DM2500, Germany) to examine the process of bone tissue ingrowth.

Statistical analysis

The analysis was performed using SPSS software. All the data were expressed as mean ± standard deviation and analyzed with the one-way analysis of variance (ANOVA). In all cases, the results were considered statistically significant with a p-value less than 0.05.

Results

Characterization of scaffold structure and morphology

As shown in Table 2, the design parameters of the porous strut for the cubic specimens and the corresponding relationship between the strut diameter and porosity are presented. The porosity of porous scaffolds with the same number of points is changed by altering the diameter of the struts. Due to the large number of random struts, changing the diameter of the struts will cause significant fluctuations in their porosity. Therefore, we cannot accurately meet the porosity requirements of all structures at 50%, 60%, and 70%. We can only make the porosity of the structures close to the required porosity. It can be seen from the table that with the increase of random points, the diameter of the strut of the porous structure is approximately smaller at the same porosity. As the number of random points increases, the number of internal struts in the porous structure also increases, and its internal surface area becomes larger.

Table 2.

Design parameters of porous structures

Porous structure scaffold	Number of random points	Strut diameter/mm	Porosity/%	Surface area/mm2
10–52%	10	0.46	52	560
10–61%		0.4	61	549
10–70%		0.34	70	517
20–51%	20	0.36	51	686
20–59%		0.32	59	681
20–71%		0.26	71	644
30–51%	30	0.32	51	744
30–60%		0.28	60	743
30–72%		0.22	72	692

Figure 5 (a) shows samples of scaffolds with different parameters in animal experiments, Fig. 5 (b) shows samples of scaffolds with different parameters in mechanical experiments, and Fig. 5 (c) shows the three-dimensional reconstruction model of the implanted samples of porous scaffolds prepared by 3D printing using Micro-CT. It can be seen from the figures that the printed porous structure scaffolds have a good pore structure. From the figure, we can see that the reconstructed porous scaffold has a clear pore structure, which accurately and perfectly replicates the designed structure. The design model of the porous structure has been well restored.

Fig. 5.

Characterization of the scaffold: (a) Animal experiment samples; (b) Mechanical experiment samples; (c) Three-dimensional reconstruction of the scaffold by Micro-CT

Mechanical properties of the scaffold

Figure 6(a) shows the displacement of specimens of different shapes along the direction of force application under the same stress (3.12 MPa). Figure 6(b) shows the stress distribution maps of different specimens under the same displacement (0.001 mm). From the figures, it can be seen that the displacements and stresses of the porous structures of different shapes under the force action are not significantly different, and the error between the two is less than 5%. As shown in Fig. 6(c), the stress-strain curves of the biomimetic porous structure scaffolds of cubic specimens with porosity of 50%, 60%, and 70% are presented at different random points. It can be seen from the figure that as the porosity increases, the yield strength of the porous structure also decreases.

Fig. 6.

(a) Displacement cloud chart of samples with different shapes under the same stress; (b) Stress cloud chart of samples with different shapes under the same displacement; (c)Stress-strain curves of porous structure scaffolds with different parameter

Fluid flow characterization

To study the bone ingrowth mechanism inside scaffolds with different parameters, the fluid characteristics inside different scaffolds were analyzed by using CFD analysis. Figure 7 shows the comparison of CFD analysis results for cubic specimens and cylindrical specimens. From the Fig. 7(a) and Fig. 7(b), it can be seen that the calculation results of different shapes have no significant impact on the pressure cloud chart and velocity streamlines. The maximum stress of the WSS cloud chart is somewhat affected (Fig. 7(c)), which is due to the fact that the maximum stress of the cubic specimens occurs at the edge while the cylindrical model does not have this area. From the results of the WSS stress statistical analysis in Fig. 7(d), this influence is only local. The stress magnitudes at different stages in different shape specimens do not differ greatly, and do not have a significant impact on the overall distribution of WSS.

Fig. 7.

Comparison of CFD analysis results for cubic specimen and cylindrical specimen: (a) Pressure cloud chart; (b) Distribution diagram of velocity streamline; (c) WSS cloud chart; (d) Different percentages of WSS

As shown in Fig. 8 (a), it is the pressure drop of the scaffolds with different parameters when the inlet flow velocity is 0.1 mm/s. It can be seen from the figure that the pressure distribution of the porous supports with different parameters is uniform, and the pressure decreases uniformly from the inlet to the outlet. Figure 8 (b) shows the distribution of fluid flow lines inside the porous structure. It can be seen from the figure that as the number of points increases, the distribution of fluid flow lines inside the porous structure becomes more uniform.

Fig. 8.

CFD analysis results of porous structure scaffolds with different parameters: (a) Pressure cloud chart; (b) Distribution diagram of velocity streamline

Figure 9 shows the pressure drop and permeability of the cubic specimens analyzed by CFD in Fig. 8. Figure 9 (a) shows the pressure drop from the inlet to the outlet of the scaffold with different parameters. It can be seen from the figure that for different number points, the pressure drops decreases with the increase of porosity. Under the condition of the same porosity, the pressure drop gradually increases with the increase of number points. Figure 9 (b) shows the permeability of scaffolds with different parameters calculated using the permeability formula. Corresponding to the pressure drop, under the same number of points, the permeability gradually increases with the increase of porosity, and under the same porosity, the permeability gradually decreases with the increase of number of points.

Fig. 9.

Pressure drop and permeability of porous structure scaffolds with different parameters: (a) Pressure drop; (b) Penetration rate

Figure 10 shows the WSS conditions of porous structures with different parameters when the fluid inlet flow velocity is 0.1 mm/s. The WSS diagram can represent the distribution of shear stress conditions of the fluid inside the porous structure. It can be seen from Fig. 10(a) that as the number of points increases, the number of porous structure struts also increases. Correspondingly, the flow of the fluid inside the structure becomes more uniform, and the generated WSS is also more uniform. Figure 10 (b) shows the percentages of different ranges of shear stress on the wall of the support with different parameters. The results from in vitro bioreactors indicate that a pressure of less than 15 mPa is more conducive to the growth of BMSCS [39, 40]. These research findings are on the same order of magnitude as the WSS values calculated in this study.

Fig. 10.

Wall shear stress conditions of porous structure scaffolds with different parameters: (a) WSS cloud map; (b) Different percentages of WSS

As shown in Table 3, the statistical analysis of WSS for the cubic specimens in Fig. 10 is presented. The WSS Standard Deviation (SD), Mean Value, Coefficient of Variance (CV) analyses of scaffolds with different parameters are presented. SD reflects the degree of dispersion of the shear stress value inside the scaffold, Mean Value reflects the average value of the shear stress inside the scaffold, and CV is a normalized measure of the degree of data dispersion, which is the ratio of the standard deviation to the average value, eliminating the influence of the data dimension and the mean. The smaller the CV value is, the more uniform the distribution of WSS inside the porous scaffold is.

Table 3.

Statistical analysis of WSS of scaffolds with different parameters

Scaffold	0-15mpa percentage	Standard Deviation (SD)	Mean Value	Coefficient of Variance (CV)
10–52%	81.1	9.69	8.31	1.16
10–61%	85.9	7.38	7.00	1.05
10–70%	89.9	5.87	6.27	0.94
20–51%	73.4	17.023	13.2	1.29
20–59%	76.4	12.5	10.6	1.18
20–70%	81.7	8.486	8.21	1.03
30–51%	64.9	17.7	15.4	1.14
30–60%	70.4	12.8	12.2	1.05
30–72%	81.1	7.82	8.26	0.95

Analysis of bone ingrowth performance of the scaffold

The reconstruction of porous scaffolds after implantation using Micro-CT scan quantitatively analyze the bone penetration of porous scaffolds with different parameters. Figure 11 shows the Micro-CT three-dimensional reconstruction images of scaffolds with different parameters implanted in the rabbit femur at 4 weeks (4 W) and 12 weeks (12 W).

Fig. 11.

(a) Micro-CT three-dimensional reconstruction of rabbit femurs after implantation of porous structure scaffolds with different parameters for 4 W and 12 W (the green part is the 3D printed porous scaffold, and the yellow part is the new bone); (b) BV/TV values of porous structure scaffolds with different parameters at 4 W and 12 W (*p < 0.05 compared with 10–52%, **p < 0.05 compared with 10–52%)

Figure 12 shows the VG staining images of the scaffolds with different parameters after being implanted into the femur of rabbits at 4 W and 12 W. It can be seen from the figure, in the 4 W, there is new bone tissue adhering to the edge of the scaffold, showing a tendency to grow inward. In the 12 W, a large amount of new bone tissue appeared inside the porous scaffold. Meanwhile, it was found that the greater the porosity, the more bone tissue there was inside the scaffold, which was consistent with the results of Micro-CT three-dimensional reconstruction analysis. As time went on, cells also appeared inside the stent at 12 weeks, and the number of cells inside the high-porosity stent was significantly higher than that in the low-porosity scaffold.

Fig. 12.

VG staining plots of hard tissue sections of scaffolds with different parameters at 4 W and 12 W. (The black part is the scaffold, the pink part is the new bone, and the blue part is the fibrous tissue, the scale bars is 500 μm)

Discussion

In this paper, we investigated the influence of the number of random points and porosity of bionic trabecular bone scaffolds on bone penetration performance. From the simulation analysis results in Fig. 6(a), (b) and Fig. 7, it can be seen that there are no significant differences in mechanical properties and CFD analysis results between the cubic specimens and the cylindrical specimens, indicating that the size and shape of the samples do not affect the experimental results. From the results of the mechanical property analysis in Fig. 6(c), when the porosity is 60% and 70%, the number of random points has little influence on its compression performance, and the compression mechanical curves with different numbers of random points are relatively close. However, when the porosity is small, the elastic modulus and yield strength of the scaffold with 10 random points are significantly higher than those of the two groups with 20 and 30 random points. This situation occurs because when the number of random points is small, to ensure the same porosity, the fewer the number of points, the fewer the number of struts, and the larger the diameter of the strut. Such larger struts have a greater strength when subjected to force compared to the two groups with smaller strut diameters.

From the analysis results of fluid mechanics, with the increase of porosity, the pressure drop of the porous structure scaffold gradually decreases and the permeability gradually increases. Under the same porosity conditions, the permeability of the porous structure with a random number of 10 points is higher than that of the porous structures with random number of 20 and 30 points. This is because under the condition of the same porosity, the more random points there are, the more struts there will be, the greater the obstruction to the fluid will be, and thus the lower the permeability will be. In the porous structures with 20 and 30 random points, the permeability difference under each porosity condition is not significant. The permeability of the porous structure with 20 random points is slightly higher than that of the porous structure with 30 random points. This phenomenon may occur because when the number of random points reaches a certain level, the main factor affecting the permeability is not the number of struts inside the porous structure. From the results of the fluid flow lines inside the porous structure in Fig. 8, the internal flow lines of the porous structure with 10 random points are not uniform, and most of the fluid flows out from the left side of the figure. However, the porous structures with 20 and 30 random points have more struts inside, so the fluid inside is more uniform.

Figure 9 shows the calculation of pressure drop and permeability of scaffolds with different parameters using CFD. The greater the pressure drop, the more difficult it is for the fluid to flow out of the pores, and it is inversely proportional to the permeability. The permeability range of all the porous structures is from 1 × 10^{− 9} m² to 6 × 10^{− 9} m², which is consistent with the permeability range of natural cancellous bone, indicating that the several biomimetic trabecular bone scaffolds established all meet the implantation conditions in terms of permeability. The WSS within the porous structure plays a crucial role in the growth and reproduction of osteocytes on the structural surface [41]. Figure 10 shows the distribution of WSS inside structures with different parameters. It can be seen from the figure that as the number of points increases, the distribution of struts inside the porous structure becomes more uniform, and at the same time, the distribution of WSS inside the porous structure also becomes more uniform. Table 2 presents the statistical analysis of WSS for porous structures with different parameters. As the number of random points increases, the WSS value distribution within the porous structure gradually decreases in the range of 0-15mpa. The WSS value within this range has been considered to be conducive to the differentiation of osteocytes [42]. In the group of 30–51%, only 64.9% of the WSS values were distributed within the range of 0-15mpa, while in each group of porous scaffolds with a random number of 10, more than 80% of the WSS values were within this range. The WSS values within the range of 0–15 mPa have been proven to be beneficial for cell proliferation and differentiation [43, 44]. It is worth noting here that in Table 1, the different parameters of the porous structure surface area parameters show that as the number of random points increases, the surface area inside the porous structure becomes larger. Therefore, although the proportion of porous structures with 30 random points in the 0-15mpa range is relatively low, it does not mean that the area available for the growth and reproduction of bone cells is small. The CV value quantifies the WSS distribution inside the porous structure. The smaller the CV value, the more uniform the distribution. The CV value of the random number 30 is slightly smaller than that of the random points 10 and 20, but the difference is not significant, indicating that the WSS distribution inside the porous structure scaffold generated by the random points is relatively uniform.

Figure 11 (a) shows the Micro-CT three-dimensional reconstruction images of the porous structures implanted in the femoral condyle of rabbits at 4 W and 12 W with different parameters. It can be seen from the figure that the bone tissue gradually increases over time and is closely combined with the scaffold, demonstrating the good histocompatibility of the porous structure of the 3D printed porous titanium alloy. Figure 11 (b) shows the BV/TV values of porous scaffolds with different parameters at 4 W and 12 W. It can be seen from the figure that for porous structures with different parameters, the values of BV/TV increase with the increase of porosity. It is indicated that within the range of porosity 50%-70%, the bone ingrowth performance of the bone scaffold becomes better with the increase of porosity. Under the two porosities of 50% and 60%, the bone ingrowth performance of the porous structure with a random number of 20 is the best, while that of the porous structure with a random number of 30 is the worst. This might be because the porous structure with a random point of 30 has a higher number of struts when the porosity is 50% or 60%. Moreover, the pores within the porous structure are smaller, which affects the infiltration of bone cells. Although the porous structure with a random point of 10 has a larger pore structure, its internal surface area is smaller, and the space available for the growth and attachment of bone cells is also smaller, thus resulting in a weaker bone ingrowth performance than the porous structure with a random point of 20. When the porosity is 70%, the BV/TV values of the porous structure with a random point of 30 at 4 W and 12 W are both higher than those of the porous structures with random points of 10 and 20. This might be because when the porosity is large, the pore size of the porous structure with a random point of 30 will also be large. At the same time, the internal surface area of its structure is large, which can provide sufficient space for bone cells to grow and attach. Therefore, its bone ingrowth performance is the best. Figure 12 shows the staining of hard tissue sections of the porous scaffold at 4 W and 12 W after implantation of the femoral condyle in rabbits. It can be seen from the figure that the bone cells are closely attached to the porous structure prepared by 3D printing and have penetrated deep into the interior of the porous structure, demonstrating its good histocompatibility. From the perspective of bone tissue penetration, when the porosity is 70%, due to the larger growth space, the bone tissue penetration of porous scaffolds with different random number points is better than that of other porosity rates. More bone tissue can be seen at the strut intersections, possibly due to the larger attachment area and more suitable fluid flow rate at the intersections.

The samples used in this study were not subjected to heat treatment, thus there are unmelted metal particles on the surface of the scaffolds. Existing research indicates that these unmelted metal particles can enhance the cell attachment ability [45], but they also reduce the mechanical properties of the scaffolds [46]. However, these effects were not included in this study. This study did not consider the influence of manufacturing tolerance on the mechanical and biological properties of the scaffolds. The mechanical experiments and animal experiments in this study used small samples size (n = 3), which might have certain impacts on the experimental results. In subsequent studies, we will conduct research on this issue. Additionally, due to limitations in computing power, no mesh-independence tests were conducted during the CFD analysis.

Conclusion

In this paper, we prepared bionic trabecular bone porous structures with different parameters by the Voronoi. The porous structure scaffolds prepared by the SLM technology were characterized by Micro-CT, and the influence of porous structure parameters on the mechanics and osteogenic properties of the scaffolds was studied. The fluid characteristics inside the porous structure were analyzed by CFD to explore their relationship with bone ingrowth performance. The main conclusions are as follows:

1. SLM successfully fabricated scaffolds with geometry replicating CAD models, and the printing accuracy meets the implantation requirements.

2. Under the same porosity conditions, the fewer the random number of points, the larger the diameter of the strut, and the higher the elastic modulus and compressive strength of the scaffold. With the increase of porosity, the influence of strut diameter weakens and has no obvious effect on mechanical properties.

3. Under the same porosity conditions, the number of points will directly affect the situation of bone ingrowth. When the porosity was 50% and 60%, the bone ingrowth performance of the porous structure with a random number of 20 was higher than that of the other groups, while when the porosity was 70%, the bone ingrowth performance of the porous structure with a random number of 30 was the best. This is closely related to the pore size, permeability, surface area and WSS inside the scaffold. It indicates that scaffolds with more random points are more suitable for implantation when the porosity is high.

4. As the random point numbers increase, the internal surface area of the porous structure becomes larger, the flow field becomes more uniform, and the WSS distribution becomes more uniform, which is more conducive to the growth and reproduction of bone tissue.

Author contributions

L. L: Conceptualization, Methodology, Writing - original draft, Formal analysis, Writing - review & editing. S. W: Validation, Data curation, Conceptualization. X. W: Formal analysis, Supervision, Investigation. J. L. Investigation, Visualization, Resources, Supervision. All authors reviewed the manuscript.

Funding

This work was supported by China Postdoctoral Science Foundation (2023MD744134), Sichuan Science and Technology Program (2024YFHZ0067), Chongqing Natural Science Foundation (CSTB2025NSCQ-GPX1296), Natural Science Foundation of China (52205553), Special Funding for Postdoctoral Research Projects in Chongqing (2023CQBSHTB3018), Science and technology research project of Chongqing Education Commission (KJQN202500641 and KJQN202300628), Science and Technology Research Program of Chongqing Municipal Education Commission (KJQN202200628), Chongqing Postdoctoral Science Foundation, China (CSTB2023NSCQ-BHX0157).

Data availability

The data can be obtained from the corresponding author upon reasonable request.

Declarations

Ethics approval and consent to participate

The animal experiments were conducted at the Animal Experiment Center of Southwest Medical University and were approved by the Ethics Committee of Southwest Medical University (Ethical Number: SWMU20240003).

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.