A method for designing bionic bone scaffolds based on gradient changes in unit cell size

Abstract

The present invention discloses a method for designing a bionic bone scaffold based on a gradient change in unit cell size, belonging to the field of biomaterial design. The method of the present invention comprises the following steps: calculating the overall wall thickness of FCC, TH and G unit cell size gradient models according to the required porosity; selecting a unit to make a radial gradient in unit cell size; designing the overall porous structure morphology as a cylindrical model to better simulate the natural bone structure; and designing the outer and inner unit cell sizes of each model according to the required requirements; all three novel porous structure scaffolds achieve an overall porosity of 55% by varying the wall thickness; and conducting mechanical property tests on the novel porous structures: observing the compression deformation behavior of each model and recording the numerical results of the elastic modulus and yield strength after simulation; the novel porous scaffold designed has different functional gradients in the radial direction, thereby expanding the application range of the energy-absorbing material unit in the design of bionic bone scaffolds.

Description

Technical Field

[0001] The invention relates to a method for designing a bionic bone scaffold based on gradient changes in unit cell size, and belongs to the field of biomaterial design. Background Art

[0002] Bone tissue injury is a common clinical disease. By building porous scaffolds to simulate the structure and function of bones, bone transplantation is used to help repair and reconstruct damaged bone tissue. Scaffold materials play a vital role in bone tissue engineering. They need to have good biocompatibility, degradability and appropriate mechanical strength. Scaffold materials should also have a three-dimensional porous structure to facilitate cell adhesion, proliferation and differentiation to meet the personalized needs of different patients.

[0003] Existing bionic bone scaffold structural designs mostly focus on three-periodic minimal surface (TPMS) material unit structures because the TPMS structure itself can be expressed by mathematical formulas composed of trigonometric functions. Researchers can use this feature to develop and apply porous structures in various ways, and the generated CAD model has overall and local controllability and smooth surfaces, which is very suitable for the structural design of porous bone scaffolds. However, the current TPMS structural designs are mostly homogeneous porous structures, which are inconsistent with the heterogeneity and anisotropy of natural bone. In addition, due to the lack of relevant mathematical formulas for expressing lattice material units and plate lattice material units, the design methods for porous structures generated by such structures as bionic bone scaffolds are relatively simple and usually focus on homogeneous porous structure design or a certain gradient design in the axial direction, such as gradually increasing wall thickness and unit cell density from top to bottom. The actual structure of the human femur can be viewed radially as consisting of an outer circular portion of cortical bone and an inner portion of cancellous bone. The cortical bone has a lower porosity and primarily bears the load, while the cancellous bone (bone marrow) has a porosity of 50% to 90%. Its higher porosity primarily transports nutrients and provides growth space and landing points for bone cell proliferation and differentiation. Therefore, the aforementioned porous structures designed based on TPMS, lattice structures, and plate lattices are significantly inconsistent with the actual femoral structure and fail to fully reflect this hierarchical structural characteristic.

[0004] In summary, existing research, particularly the use of lattice and plate lattice material units to create gradient porous structures by varying radial unit cell dimensions to mimic the hierarchical structure of natural bone, has yet to be designed. Therefore, a general method is proposed to design three common energy-absorbing material unit structures—TPMS unit structures, lattice unit structures, and plate lattice unit structures—into radial unit cell size gradient models. In the present invention, G units, FCC units, and TH units are used, respectively, to design porous structures with radial functional gradients to better simulate the characteristics of the femur. Summary of the Invention

[0005] The present invention discloses a method for designing a bionic bone scaffold based on a gradient change in unit cell size. The method can control the porosity of the entire bone scaffold by adjusting the wall thickness and designing a gradient change in unit cell size. The method specifically comprises the following steps:

[0006] (1) Calculate the overall wall thickness of the FCC, TH, and G unit cell size gradient models based on the required porosity;

[0007] (2) Create a cube CAD model in the Create module of the Ntopology software, then use the Graph UniteCell command to select the FCC unit cell and the TH unit cell, and then use the Rectangular Volume Lattice command to set the initial wall thickness parameters of each unit to generate the FCC and TH homogeneous unit porous structure models respectively; use the TPMS Unite cell withOffset command to select the G unit cell, and use the Rectangular Volume Lattice command to set the initial MidsurfaceOffset parameter to 0 to generate the G homogeneous porous structure model;

[0008] (3) Then, the Ramp and Remap Field commands in the Ntopology software were called out as innovation commands and relevant parameters were set. The two commands were used to generate the initial FCC, TH and G cubic cell size gradient CAD models. The relevant parameters in the Ramp command are as follows: the In Max parameter of 2mm acts on the original cubic model to grow symmetrically outward by 1mm in the x and y directions in the three-dimensional Cartesian space coordinate system while the z direction remains unchanged, forming a new cubic model, and the 1mm expanded outward acts as the outer layer; the Out parameter of 0.5 controls the cell size ratio, that is, the outer cell size / inner cell size = 0.5.

[0009] Preferably, when generating a porous structure model with a gradient change in FCC unit cell size, the relationship between the overall wall thickness B1 and the porosity P1 of the FCC unit cell size gradient model is as follows: P1 = (1.151298 - 1.9014 B1) × 100%.

[0010] Preferably, when generating a porous structure model with a TH cell size gradient, the relationship between the overall wall thickness B2 and the porosity P2 of the TH cell size gradient model is as follows: P2 = (0.79606-2.4998B2) × 100%

[0011] Preferably, when generating a porous structure model with a G cell size gradient, the relationship between the overall wall thickness B3 and the porosity P3 of the G cell size gradient model is as follows: P3 = (0.998205-1.9929B3) × 100%.

[0012] Preferably, a cylindrical porous structure model is prepared: based on step (3), a cylindrical CAD model is created in the Create module in the Ntopology software, and the initial FCC, TH and G unit cell size gradient models are merged with the cylinder using the Boolean Intersect command to form a final overall morphology of a cylindrical FCC, TH and G unit cell size gradient CAD model with a diameter and height of 7 mm × 10 mm.

[0013] Beneficial effects of the present invention

[0014] Compared with the traditional femoral porous structure, the bionic bone scaffold designed by the present invention based on the gradient change of unit cell size has the following advantages:

[0015] In terms of mechanical properties: the energy absorption characteristics are good, and the selected energy-absorbing material units can effectively absorb energy when subjected to external forces, providing for the internal structure; whether it is a three-period minimal surface G unit, a lattice material FCC unit or a plate lattice material triangular honeycomb TH structure, they all have unique mechanical properties and can disperse and absorb impact forces in different directions; the structural stability is high: the overall structure is a cylindrical structure, and the outer ring adopts a 1mm×1mm×1mm unit cell. This design can provide uniform support and enhance the stability of the structure; at the same time, the inner layer adopts a radial gradient change of 2mm×2mm×2mm unit cell size, which can better adapt to the stress conditions of different parts and improve the overall bearing capacity.

[0016] Advantages of bionic design: Imitation of natural structure: The design of porous scaffolds is inspired by biological structures in nature, such as bones and honeycombs; these natural structures have undergone long-term evolution and have efficient mechanical properties and functional adaptability; through bionic design, the scaffolds can better adapt to the human environment and improve their compatibility with human tissues; promote tissue growth: the porous structure is conducive to the attachment, growth and differentiation of cells, providing a good microenvironment for tissue regeneration; the different sizes of unit cells of the outer ring and the inner central small cylinder can simulate the hierarchical structure of natural tissues and promote the orderly growth of cells in the scaffold; it can be used in bone tissue engineering, cartilage repair and other fields; its good mechanical properties and biocompatibility can provide support and guidance for damaged tissues, and promote tissue regeneration and repair. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 (a), (b) and (c) are schematic diagrams of the porous structures of cylindrical FCC, TH and G homogeneous units, respectively (without unit cell size gradient change, the ratio of the inner and outer unit cell sizes is 1);

[0018] Figure 2 Fitting diagram of the relationship between wall thickness and porosity of the final cylindrical FCC, TH and G unit cell size gradient models Figure 3 Schematic diagram of the A1, A2 and A3 model structures;

[0019] Figure 3 Surface strain distribution diagrams of the finite element models of the porous structures A1, A2, and A3 under different strains in the elastic stage;

[0020] Figure 4 Yield strength and elastic modulus corresponding to the porous structures of A1, A2, and A3 after finite element simulation. DETAILED DESCRIPTION

[0021] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments, but the protection scope of the present invention is not limited to the contents described above.

[0022] Example 1

[0023] (1) First, create a cubic CAD model with a length, width and height of 5mm×5mm×10mm in the Create module of the Ntopology software, then use the Graph Unite Cell command to select the FCC unit cell and the TH unit cell, and then use the Rectangular Volume Lattice command to set their respective initial wall thickness parameters (Thickness) to 0.4mm and 0.2mm respectively (the initial wall thickness value can be set arbitrarily, as long as the wall thickness can generate the CAD model) to generate the FCC and TH homogeneous unit porous structure models respectively; similarly, use the TPMS Unite cell with Offset command to select the G unit cell, and use the Rectangular Volume Lattice command to set the initial Midsurface Offset parameter to 0 to generate the G homogeneous porous structure model. Other parameters in the Rectangular Volume Lattice command: the initial unit cell size (Unit Cell Size) is designed to be 1mm×1mm×1mm and the system default Trim command is canceled, while the Frame is set to the default setting.

[0024] (2) Then, call out Ramp and Remap Field in Ntopology software as innovation commands and set relevant parameters. These two commands are used to generate three 7mm×7mm×10mm cubic cell size gradient CAD models, namely FCC, TH and G. The relevant parameters in the Ramp command are as follows: In Max parameter 2mm acts on the original 5mm×5mm×10mm cubic model to grow symmetrically outward by 1mm in the x and y directions in the three-dimensional Cartesian space coordinate system, while the z direction remains unchanged, forming a cubic model with a length, width and height of 7mm×7mm×10mm, and the 1mm expanded outward acts as the outer layer area; Out parameter 0.5 controls the cell size ratio, that is, outer cell size / inner cell size = 0.5. Since the initial cell size is 1mm×1mm×1mm, the inner cell size is 2mm×2m at this time. m×2mm; this is because the femur is divided into cortical bone and cancellous bone structures. The outer cortical bone area has a low porosity and mainly plays the role of bearing loads, so the unit cell size of this area is designed to be L1=1mm×1mm×1mm, while the inner cancellous bone mainly provides development space for bone cell proliferation and differentiation and transports nutrients, and its porosity is relatively high, so the unit cell size of the inner layer is designed to be L2=2mm×2mm×2mm (the initial unit cell size, the size of the outward expansion area and the control unit cell size ratio can be adjusted according to research needs).

[0025] (3) Then, a cylindrical CAD model with a diameter and height of 7 mm × 10 mm was created in the Create module of the Ntopology software, and the initial FCC, TH and G unit cell size gradient models were merged with the 7 mm × 10 mm cylinder using the Boolean Intersect command to form a final overall morphology of a cylindrical FCC, TH and G unit cell size gradient CAD model with a diameter and height of 7 mm × 10 mm; the overall morphology of the three models is a cylindrical porous structure with a diameter and height of 7 mm × 10 mm according to the ISO 13314:2011 (E) standard. During compression, the height to diameter ratio of the plate should be between 1 and 2.

[0026] (4) After the FCC, TH and G unit cell size gradient models are formed, the relationship between the overall wall thickness (B) and porosity (P) of the FCC, TH and G unit cell size gradient models is fitted by changing the wall thickness parameter. The selected wall thickness values ​​and their corresponding porosities are shown in Table 1:

[0027] Table 1

[0028] <![CDATA[FCC unit B1 (mm)]]> 0.1 0.2 0.3 0.4 0.5 <![CDATA[FCC porosity P1 (%)]]> 94.21 79.34 59.42 38.2 19.71 <![CDATA[TH unit B2 (mm)]]> 0.1 0.15 0.2 0.25 0.3 <![CDATA[TH porosity P2 (%)]]> 57.51 40.65 26.71 15.68 7.5 <![CDATA[G cell B3 (mm)]]> 0.05 0.15 0.25 0.35 0.45 <![CDATA[G porosity P3 (%)]]> 90.09 69.46 50.00 30.53 9.91

[0029] The linear fitting results of the above data are as follows Figure 2As shown, they are P1=(1.151298-1.9014B1)×100%, P2=(0.79606-2.4998B2)×100% and P3=(0.998205-1.9929B3)×100%, respectively. The reliabilities of the fitting results are 99.998%, 99.998% and 98.156%, respectively, all of which are above 98% and meet the reliability requirements.

[0030] (5) Because the porosity of cancellous bone is between 50% and 90%, the overall final average porosity of the FCC, TH and G cell size gradient CAD models is designed to be 55%. The 55% porosity is used to explore the effect of porosity on the mechanical properties of porous scaffolds. The porosity of 55% is then adjusted to P1 = (1.151298-1.9014B1) × 100%, P2 = (0.79606-2.4998B2) × 100% and P3 = (0.998205-1.9929B3) × 100% to obtain the wall thickness parameters B1 = 0.32065mm, B2 = 0.10686mm and B3 = 2.4741mm. After readjusting the wall thickness parameters, three cell size gradient models are generated and named A1, A2 and A3, respectively. The models are as follows: Figure 3 shown.

[0031] When generating cylindrical FCC and TH unit cell size gradient CAD models, return to the Rectangular Volume Lattice command and reset the Thickness parameter to 0.32065 and 0.10686 respectively. However, when generating cylindrical G unit cell size gradient CAD model, because the Thickness in the Rectangular Volume Lattice command will become Midsurface Offset, you should fill in (2.4741-2.5=-0.0259)-0.0259 to make the G unit cell size gradient CAD model porosity 55%; this is because Midsurface Offset means that the wall thickness can be increased or decreased, and the initial unit cell size is 1mm×1mm×1mm, so in Midsurface When the Offset value is set to 0, the initial wall thickness is 0.25mm. When the value is set to -0.25, the actual wall thickness reaches 0. At this time, the theoretical porosity is 100%, but a solid CAD model cannot be created. When the value is set to 0.25, the actual wall thickness reaches 0.5mm. At this time, the theoretical porosity is 0, corresponding to a solid cube unit cell. When the parameter is set to -0.0259, the actual wall thickness of the G unit cell is -0.0259+0.25=2.4741mm.

[0032] (5) The Mesh form Implict Body command in the Ntopology software was used to preliminarily divide the meshes of the three cylindrical FCC, TH and G cell size gradient CAD model files with 55% porosity. Then, the Export FE Mesh command was used to generate the inp form CAD model file and import it into the HyperMesh software. The tetrahedral unit meshing method was used to re-divide it, and the mesh unit type was set to C3D4 and the size was set to 0.15 mm. Finally, the Export command in the HyperMesh software was used to export the model again as an inp form CAD model file. The inp form CAD model file was then imported into the dynamics module of the Abaqus software for quasi-static compression finite element simulation and the elastic modulus of 110 GPa, the Poisson's ratio of 0.3 and the density of 4.51 g / cm were set. 3 The material properties of Ti-6AL-4V were set, and the mesh unit yield failure occurred when the maximum deformation ratio was set to 1.5. The compression boundary conditions were then set: a 60% displacement load was applied to the top surface, and only the Z direction was free to move in the X, Y, and Z directions, while the X, Y, and Z rotations and X, Y movements were completely restricted. The top and bottom surfaces were set as rigid surfaces, the friction coefficient was 0.2, and the total simulation time was 0.006 seconds.

[0033] like Figure 4 The deformation behaviors of three new porous structures were analyzed through finite element simulation. The results showed that under load:

[0034] ① The outer ring adopts a unit cell structure of 1mm×1mm×1mm. In the initial stage, the material will undergo elastic deformation. As the pressure increases, the deformation gradually increases. As the compression continues, the energy-absorbing material begins to play a role and absorbs energy through its own structural deformation. The G unit will bend and fold, the FCC unit will experience lattice distortion and deformation, and the TH structure will experience honeycomb wall buckling. The small unit cell structure of the outer ring enables it to provide a higher specific surface area during compression, thereby increasing the efficiency of energy absorption.

[0035] ② The inner layer adopts a unit cell size of 2mm×2mm×2mm, and has a radial gradient change; during the compression process, the part with a smaller unit cell size in the outer layer will begin to deform first and absorb a certain amount of energy; as the pressure is transmitted, it gradually advances to the part with a larger unit cell size in the inner layer; due to the change in unit cell size, the deformation behavior of the inner layer will be different from that of the outer layer; the larger unit cell size will provide a higher load-bearing capacity, but at the same time it will also begin to deform significantly in the later stages of compression; the radial gradient change enables the entire inner small cylinder to achieve gradual energy absorption during the compression process, avoiding local stress concentration and improving the stability and reliability of the overall structure.

[0036] ③ When the overall cylindrical structure is compressed: the outer ring and the inner center will work together to jointly bear the compression load; due to the difference in unit cell structure of the outer ring and the unit cell size of the inner small cylinder, complex stress distribution and deformation pattern will be generated during the compression process; this design can effectively disperse stress and improve the compressive resistance of the structure; the entire bionic porous scaffold will exhibit good energy absorption characteristics during the compression process, and can convert external impact energy into deformation energy inside the material, thereby protecting the supported object or structure; in summary, this bionic porous scaffold with an overall cylindrical structure made of a single energy-absorbing material unit has the characteristics of elastic deformation, energy absorption, stress dispersion and gradual load-bearing in compression deformation behavior.

[0037] Table 2 shows the yield strength and elastic modulus values ​​of the three cell size gradient CAD models after quasi-static compression finite element simulations. In terms of yield strength, A1 and A3 are both within the cortical bone range (33-193 MPa), but A2 is greater than the cortical bone yield strength. In addition, in terms of elastic modulus, only A1 and A3 are within the cortical bone range (3-20 GPa), and A2 also exceeds the cortical bone elastic modulus range. The data show that at the same porosity of 55%, the mechanical properties (yield strength and elastic modulus) of the TH cell size gradient porous structure are almost three times that of the FCC and G cell size gradients, making it superior in terms of mechanical properties. However, as a porous scaffold bone implant, only A1 and A3 meet the requirements and can avoid stress shielding problems after implantation into the femur. A2 can increase the porosity by further reducing the wall thickness to meet the mechanical performance requirements of the implant.

[0038] Table 2

[0039] type A1 A2 A3 Yield strength (MPa) 159.3 457.6 144.42 Elastic modulus (GPa) 12.06 34.67 10.94

[0040] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit the scope of protection of the present invention. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention may be modified or replaced by equivalents without departing from the essence and scope of the technical solutions of the present invention.

Claims

1. A method for designing a bionic bone scaffold based on a gradient change in unit cell size, characterized in that: The specific steps include: (1) Calculate the overall wall thickness of the FCC, TH, and G unit cell size gradient models based on the required porosity; (2) Create a cube CAD model in the Create module of the Ntopology software, then use the Graph Unite Cell command to select the FCC unit cell and the TH unit cell, and then use the Rectangular Volume Lattice command to set the initial wall thickness parameters of each unit to generate the FCC and TH homogeneous unit porous structure models respectively; use the TPMS Unite cell with Offset command to select the G unit cell, and use the Rectangular Volume Lattice command to set the initial Midsurface Offset parameter to 0 to generate the G homogeneous porous structure model; (3) Then, the Ramp and Remap Field commands in the Ntopology software were called out as innovation commands and relevant parameters were set. The two commands were used to generate the initial FCC, TH and G cubic cell size gradient CAD models. The relevant parameters in the Ramp command are as follows: the In Max parameter of 2mm acts on the original cubic model to grow symmetrically outward by 1mm in the x and y directions in the three-dimensional Cartesian space coordinate system while the z direction remains unchanged, forming a new cubic model, and the 1mm expanded outward acts as the outer layer; the Out parameter of 0.5 controls the cell size ratio, that is, the outer cell size / inner cell size = 0.

5.

2. The method for designing a bionic bone scaffold based on a gradient change in unit cell size according to claim 1, characterized in that: When generating the FCC unit cell size gradient porous structure model, the relationship between the overall wall thickness B1 and the porosity P1 of the FCC unit cell size gradient model is as follows: P1 = (1.151298-1.9014B1) × 100%.

3. The method for designing a bionic bone scaffold based on a gradient change in unit cell size according to claim 1, characterized in that: When generating a porous structure model with a TH cell size gradient change, the relationship between the overall wall thickness B2 and the porosity P2 of the TH cell size gradient model is as follows: P2 = (0.79606-2.4998B2) × 100%.

4. The method for designing a bionic bone scaffold based on a gradient change in unit cell size according to claim 1, characterized in that: When generating a G cell size gradient porous structure model, the relationship between the overall wall thickness B3 and the porosity P3 of the G cell size gradient model is as follows: P3 = (0.998205-1.9929B3) × 100%.

5. The method for designing a bionic bone scaffold based on a gradient change in unit cell size according to claim 1, characterized in that: Preparation of a cylindrical porous structure model: Based on step (3), a cylindrical CAD model was created in the Create module of the Ntopology software, and the initial FCC, TH and G unit cell size gradient models were merged with the cylinder using the Boolean Intersect command to form a final overall morphology of a cylindrical FCC, TH and G unit cell size gradient CAD model with a diameter and height of 7 mm × 10 mm.

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