Method for designing bionic bone scaffold based on unit cell size gradient change

Abstract

The invention discloses a method for designing a bionic bone scaffold based on unit cell size gradient change, and belongs to the field of biological material design. The method comprises the following steps: calculating the overall wall thickness of FCC, TH and G cell size gradient models according to the required porosity; a unit is selected as a unit cell size radial gradient, in order to better simulate a natural bone structure, the overall porous structure morphology is designed as a cylinder model, and the unit cell sizes of the outer layer and the inner layer of each model are designed as required; the overall porosity of the three novel porous structure scaffolds reaches 55% by changing the wall thickness; carrying out mechanical property testing on the novel porous structure; observing the compression deformation behavior of each model and recording the numerical results of the elastic modulus and the yield strength after simulation; the designed novel porous scaffold has different functional gradients in the radial direction, and the application range of the energy absorption material unit in bionic bone scaffold design is expanded.

Description

Technical Field

[0001] The invention relates to a method for designing a bionic bone scaffold based on the gradient change of 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] The existing bionic bone scaffold structure design mostly focuses on the three-periodic minimal surface (TPMS) material unit structure because the TPMS structure itself can be expressed by a mathematical formula composed of trigonometric functions. Researchers can use this feature to develop and apply porous structures in various styles, 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 structure design is mostly homogeneous porous structure, which is inconsistent with the heterogeneity and anisotropy of natural bone. In addition, due to the lack of relevant mathematical formulas for the expression of lattice material units and plate lattice material units, the design method of porous structures generated by using such structures as bionic bone scaffolds is relatively simple, and usually focuses on the design of homogeneous porous structures or performs a certain gradient design in the axial direction, such as the wall thickness and unit cell density gradually increasing from top to bottom. The actual structure of the human femur can be seen as consisting of an outer ring part of cortical bone and an inner part of cancellous bone in the radial direction. The cortical bone has a lower porosity and mainly bears the load, while the cancellous bone (bone marrow) has a porosity of 50% to 90%. Its higher porosity is mainly used to transport nutrients and provide growth space and landing points for the proliferation and differentiation of bone cells. Therefore, the above-mentioned porous structure designs based on TPMS, lattice and plate lattice structures are very inconsistent with the actual femoral structure and fail to fully reflect this hierarchical structural characteristic.

[0004] In summary, in the existing research, especially the use of lattice and plate lattice material structural units based on changing the radial unit cell size to make a gradient porous structure as a bionic bone scaffold to reflect the natural bone hierarchical structure, this feature has not been designed yet, so a general method is proposed to design the three common energy-absorbing material unit structures of TPMS unit structure, lattice unit structure and plate lattice unit structure into a radial unit cell size gradient model. In the example of the present invention, the porous structure with a functional gradient change in the radial direction is designed using G unit, FCC unit and TH unit respectively 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 the 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 according to the required porosity;

[0007] (2) Create a cubic 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 their respective initial wall thickness parameters 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, call out Ramp and Remap Field in Ntopology software as innovation commands and set relevant parameters. These two commands are used to generate three initial cubic unit cell size gradient CAD models: FCC, TH and G. The relevant parameters in the Ramp command are as follows: the In Max parameter of 2 mm acts on the original cubic model to grow symmetrically outward by 1 mm in the x and y directions in the three-dimensional Cartesian space coordinate system while keeping the z direction unchanged, forming a new cubic model, and the 1 mm expanded outward acts as the outer layer; the Out parameter of 0.5 controls the unit cell size ratio, that is, the outer unit cell size / inner unit cell size = 0.5.

[0009] Preferably, when generating a porous structure model with a FCC unit cell size gradient change, 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%.

[0010] Preferably, when generating a TH cell size gradient porous structure model, 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 a G cell size gradient porous structure model is generated, 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 based on the gradient change of the unit cell size designed by the present invention has the following advantages:

[0015] Mechanical properties: good energy absorption characteristics, the selected energy-absorbing material units can effectively absorb energy when subjected to external forces, providing for the internal structure; whether it is the three-period minimal surface G unit, the lattice material FCC unit or the plate lattice material triangular honeycomb TH structure, they all have unique mechanical properties and can disperse and absorb impact forces in different directions; high structural stability: the overall structure is a cylindrical structure, and the outer ring adopts 1mm×1mm×1mm unit cells. 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 in the unit cell size of 2mm×2mm×2mm, 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, honeycombs, etc.; 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 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 center 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, and 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 diagram of the finite element models of A1, A2 and A3 porous structures under different strains in the elastic stage;

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

[0021] The present invention is further described in detail below in conjunction with 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 5 mm × 5 mm × 10 mm 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 initial wall thickness parameters (Thickness) to 0.4 mm and 0.2 mm respectively (the initial wall thickness value can be set arbitrarily, as long as the wall thickness can generate a 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 1 mm × 1 mm × 1 mm, and the Trim command that is checked by default by the system is cancelled, while the Frame is set to the default.

[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 unit cell size gradient CAD models, namely, FCC, TH and G. The relevant parameters in the Ramp command are as follows: the In Max parameter of 2mm acts on the original 5mm×5mm×10mm cubic unit cell 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 unit cell model with a length, width and height of 7mm×7mm×10mm, and the 1mm expanded outward acts as the outer layer; the Out parameter of 0.5 controls the unit cell size ratio, that is, the outer unit cell size / inner unit cell size = 0.5. Since the initial unit cell size is 1mm×1mm×1mm, the inner unit 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 bears the load, 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 the proliferation and differentiation of bone cells and transports nutrients, and its porosity is relatively high, so the inner unit cell size 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 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 size 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[Unit G B3 (mm)]]> 0.05 0.15 0.25 0.35 0.45 <![CDATA[G Pore Rate P3 (%)]]> 90.09 69.46 50.00 30.53 9.91

[0029] According to the above data, the linear fitting results 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 unit 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 is then adjusted to 55%, respectively, with P1 = (1.151298-1.9014B1) × 100%, P2 = (0.79606-2.4998B2) × 100% and P3 = (0.998205-1.9929B3) × 100%. The wall thickness parameters are B1 = 0.32065 mm, B2 = 0.10686 mm and B3 = 2.4741 mm. After readjusting the wall thickness parameters, three unit cell size gradient models are generated and named A1, A2 and A3, respectively. The models are shown in Figure 2. Figure 3 shown.

[0031] When generating cylindrical FCC and TH 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 cell size gradient CAD models, 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 cell size gradient CAD model have a porosity of 55%; this is because Midsurface Offset means that the wall thickness can be increased or decreased, and the initial cell size is 1mm×1mm×1mm, so in Midsurface Offset, When the value of Offset 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 the 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 cell. When the parameter is set to -0.0259, the actual wall thickness of the G 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 55% porosity cylindrical FCC, TH and G unit cell size gradient CAD model files. Then, the Export FE Mesh command was used to generate the inp form CAD model file and imported 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 to the inp form CAD model file again. 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 are set, and the mesh unit is set to yield failure when the maximum deformation ratio is 1.5; the compression boundary conditions are set: a 60% displacement load is applied to the top surface, and only the Z direction is free to move in the X, Y, and Z directions, and the X, Y, and Z rotations and X, Y movements are completely restricted; the top surface and the bottom surface are set as rigid surfaces, the friction coefficient is 0.2, and the total simulation time is 0.006 seconds.

[0033] like Figure 4 The deformation behaviors of three new porous structures were analyzed by 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 when compressed, 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; a larger unit cell size will provide a higher bearing capacity, but at the same time, it will also begin to deform significantly in the later stage of compression; the radial gradient change enables the entire inner layer of small cylinders 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 bear the compression load together; 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 show 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 simulation. In terms of yield strength, A1 and A3 are both within the range of cortical bone (33-193 MPa), but A2 is greater than the yield strength of cortical bone. In addition, in terms of elastic modulus, only A1 and A3 are within the range of cortical bone (3-20 GPa), and A2 also exceeds the range of cortical bone elastic modulus. The data show that the mechanical properties (yield strength and elastic modulus) of the TH cell size gradient porous structure under the same porosity of 55% are almost 3 times that of the FCC and G cell size gradients, and the mechanical properties are superior. However, as porous scaffold bone implants, only A1 and A3 meet the requirements and can avoid stress shielding problems after implantation into the femur. A2 can increase the porosity by reducing the wall thickness again 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 solution of the present invention rather than to limit the scope of protection of the present invention. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solution of the present invention can be modified or replaced by equivalents without departing from the essence and scope of the technical solution 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 according to the required porosity; (2) Create a cubic 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 their respective initial wall thickness parameters 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, call out Ramp and Remap Field in Ntopology software as innovation commands and set relevant parameters. These two commands are used to generate three initial cubic unit cell size gradient CAD models: FCC, TH and G. The relevant parameters in the Ramp command are as follows: the In Max parameter of 2 mm acts on the original cubic model to grow symmetrically outward by 1 mm in the x and y directions in the three-dimensional Cartesian space coordinate system while keeping the z direction unchanged, forming a new cubic model, and the 1 mm expanded outward acts as the outer layer; the Out parameter of 0.5 controls the unit cell size ratio, that is, the outer unit cell size / inner unit cell size = 0.

5.

2. The method for designing a bionic bone scaffold based on the gradient change of unit cell size according to claim 1, characterized in that: When generating the FCC unit cell size gradient change 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 the gradient change of unit cell size according to claim 1, characterized in that: When generating a TH cell size gradient porous structure model, 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 the gradient change of unit cell size according to claim 1, characterized in that: When the G cell size gradient porous structure model is generated, 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 the gradient change of 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 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.

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