Biological bone scaffold design method of tetragonal symmetric lattice structure based on extremely small curved surface

Abstract

According to the method for designing the biological bone scaffold of the tetragonal symmetric lattice structure based on the minimal curved surface, reconstruction is performed based on a classic three-period minimal curved surface lattice structure implicit function for the biological bone scaffold, and a novel implicit function of the three-period minimal curved surface lattice structure is obtained; and judging whether a lattice structure obtained on the basis of the reconstructed implicit function meets a set constraint condition or not, and if so, designing and preparing the biological bone scaffold by using the reconstructed implicit function. Therefore, the biological bone scaffold prepared from the tetragonal symmetrical lattice structure has good mechanical properties and material transport performance on the premise of light weight.

Description

Technical Field

[0001] The present invention relates to a 3D printing design method, and particularly to a design method of a biological bone scaffold with a tetragonal symmetric lattice structure based on minimal surfaces. Background Art

[0002] A biological bone scaffold is a medical material used for corresponding treatments of patients. When producing a biological bone scaffold, the prior art often adopts 3D printing, because 3D printing has high precision and can produce biological bone scaffolds with complex structural designs.

[0003] In the prior art, a TPMS implicit function is used to generate the structure of a biological bone scaffold during 3D printing. When conducting structural design, the designs of biological bone scaffolds prepared by additive manufacturing all focus on balancing the performance of light weight and high strength and mass transport. Since there are mutually restrictive relationships among these performances, an improvement in one performance caused by geometric optimization may weaken another performance. For example, reducing the porosity of the lattice material of the bone scaffold will improve its mechanical properties, but also increase the weight and weaken the permeability, thus affecting the transport of nutrients and metabolites.

[0004] Therefore, in order to solve the above technical problems, it is urgent to propose a new technical means. Summary of the Invention

[0005] In view of this, the purpose of the present invention is to provide a design method of a biological bone scaffold with a tetragonal symmetric lattice structure based on minimal surfaces, reconstruct the TPMS lattice implicit function for the design of biological bone scaffolds, and satisfy corresponding constraint conditions during reconstruction, so that the biological bone scaffold prepared from the tetragonal symmetric lattice structure has good mechanical properties and mass transport performance while having the premise of light weight.

[0006] A design method of a biological bone scaffold with a tetragonal symmetric lattice structure based on minimal surfaces provided by the present invention includes the following steps:

[0007] S1. Reconstruct based on the implicit function of the classical triply periodic minimal surface lattice structure for biological bone scaffolds to obtain an implicit function of a new triply periodic minimal surface lattice structure;

[0008] S2. Based on the implicit function of the new triply periodic minimal surface lattice, fit the relationship between its relative density and the median surface offset control parameter to obtain the relationship ρ * = f(t), and generate a lattice structure model with an arbitrary relative density based on this relationship, and perform a representative volume element simulation calculation on this lattice structure to obtain the stiffness matrix of this lattice structure;

[0009] S3. Determine whether the stiffness matrix is a characteristic of a tetragonally symmetric stiffness matrix. If not, return to step S1. If so, determine whether the simulated lattice structure has three-periodic arrayability. If not, return to step S1. If so, determine whether the inclination angle of the median surface generated by the implicit function of the new three-periodic minimal surface lattice structure with respect to the horizontal direction satisfies the inclination angle condition. If not, return to step S1. If so, output the implicit function of the new three-periodic minimal surface lattice structure;

[0010] S4. Design and fabricate a biological bone scaffold based on the output implicit function of the new three-periodic minimal surface lattice structure.

[0011] Furthermore, the implicit function of the classical three-periodic minimal surface lattice structure specifically includes any one of the Gyroid implicit function, the Diamond implicit function, the Primitive implicit function, and the IWP implicit function, where:

[0012] The Gyroid implicit function is:

[0013]

[0014] The Diamond implicit function is:

[0015]

[0016] The Primitive implicit function is:

[0017]

[0018] The IWP implicit function is:

[0019]

[0020] Furthermore, the implicit function of the new three-periodic minimal surface lattice structure specifically includes:

[0021] The Gyroid implicit function is reconstructed as:

[0022] Or:

[0023]

[0024] The Diamond implicit function is reconstructed as:

[0025] Or:

[0026]

[0027] The Primitive implicit function is reconstructed as:

[0028] Or it is:

[0029]

[0030] The IWP implicit function is reconstructed as:

[0031] Or it is:

[0032] Furthermore, the stiffness matrix of tetragonal symmetry is characterized by having 6 independent and unequal elastic tensors C ij , where i, j = 1, 2, 3, 4, 5, 6, and the stiffness matrix of tetragonal symmetry is:

[0033] Where: σ ij and ε ij represent the macroscopic stress tensor and strain tensor respectively.

[0034] Furthermore, the inclination angle condition specifically includes:

[0035] Calculate the inclination angle θ of each point on the median surface of the reconstructed implicit function of the simulated lattice structure relative to the horizontal plane:

[0036] Where, represents the first derivative of the reconstructed implicit function, i = x, y, z;

[0037] Determine the ratio of the number of points with the inclination angle θ greater than the set angle threshold to the total number of calculation points. When this ratio is greater than the set value, the inclination angle condition of the median surface of the implicit function of the tetragonal symmetry lattice structure for biologic scaffold design is satisfied.

[0038] The beneficial effects of the present invention: Through the present invention, the TPMS lattice implicit function for biologic bone scaffold design is reconstructed, and corresponding constraint conditions are satisfied during the reconstruction, so that the biologic bone scaffold prepared from the tetragonal symmetry lattice structure has good mechanical properties and mass transfer properties while having the premise of light weight. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] The present invention will be further described below in conjunction with the drawings and embodiments:

[0040] Figure 1 is the flowchart of the present invention.

[0041] Figure 2 is the schematic diagram of the median surface of the tetragonal symmetry TPMS of the TPMS implicit function reconstruction of the present invention.

[0042] Figure 3 is the comparison of the design processes of strut - type and sheet - type cubic symmetry and tetragonal symmetry lattices.

[0043] Figure 4 It is a schematic diagram of a sample part.

[0044] Figure 5 It is a schematic diagram of the inclination angles of the tetragonal symmetric and cubic symmetric lattices and the surface of the three-dimensional elastic modulus.

[0045] Figure 6 It is a schematic diagram for comparing the mechanical properties of the tetragonal symmetric lattice and the cubic symmetric lattice.

[0046] Figure 7 It is a schematic diagram for comparing the permeability of the tetragonal symmetric and cubic symmetric lattices of the patch type and the strut type.

[0047] Figure 8 It is a graph showing the relationship between the relative density of the tetragonal symmetric and cubic symmetric lattice structures and the median plane offset control parameter. Specific implementation manners

[0048] The following further details the present invention:

[0049] As Figure 1 shown, a method for designing a bio-bone scaffold with a tetragonal symmetric lattice structure based on minimal surfaces provided by the present invention includes the following steps:

[0050] S1. Reconstruct based on the implicit function of the classical triply periodic minimal surface lattice structure for bio-bone scaffolds to obtain an implicit function of a new triply periodic minimal surface lattice structure; wherein, the implicit function of the triply periodic minimal surface lattice structure is abbreviated as the TPMS implicit function in English;

[0051] S2. Based on the implicit function of the new triply periodic minimal surface lattice, fit its relative density and the median plane offset control parameter to obtain a relational expression ρ * = f(t), and generate a lattice structure model with an arbitrary relative density based on this relational expression, and perform a representative volume element simulation calculation on this lattice structure to obtain the stiffness matrix of this lattice structure; that is to say: the implicit function of the new triply periodic minimal surface lattice generates the median plane of the lattice, and this median plane has no thickness and is not a three-dimensional lattice structure. It is necessary to set different median plane offset control parameters to obtain a three-dimensional lattice structure with an arbitrary relative density, as Figure 3 shown;

[0052] S3. Determine whether the stiffness matrix is a characteristic of a tetragonal symmetric stiffness matrix. If not, return to step S1. If so, determine whether the simulated lattice structure has triply periodic arrayability. If not, return to step S1. If so, determine whether the inclination angle between the median plane generated by the implicit function of the new triply periodic minimal surface lattice structure and the horizontal direction satisfies the inclination angle condition. If not, return to step S1. If so, output the implicit function of the new triply periodic minimal surface lattice structure;

[0053] S4. Design and preparation of a biological bone scaffold based on the implicit function of a new three-period minimal surface lattice structure of the output, that is, input the implicit function into the 3D printing controller, and then print the biological bone scaffold according to the implicit function. Through the above method, the TPMS lattice implicit function for biological bone scaffold design is reconstructed, and corresponding constraint conditions are satisfied during the reconstruction, so that the biological bone scaffold prepared from the tetragonal symmetric lattice structure has good mechanical properties and mass transfer properties while having the premise of light weight.

[0054] In this embodiment, the implicit function of the classical three-period minimal surface lattice structure specifically includes any one of the Gyroid implicit function, the Diamond implicit function, the Primitive implicit function, and the IWP implicit function, where:

[0055] The Gyroid implicit function is:

[0056]

[0057] The Diamond implicit function is:

[0058]

[0059] The Primitive implicit function is:

[0060]

[0061] The IWP implicit function is:

[0062]

[0063] The implicit function of the new three-period minimal surface lattice structure specifically includes:

[0064] The Gyroid implicit function is reconstructed as:

[0065] Or:

[0066]

[0067] The Diamond implicit function is reconstructed as:

[0068] Or:

[0069]

[0070] The Primitive implicit function is reconstructed as:

[0071] Or:

[0072]

[0073] The IWP implicit function is reconstructed as:

[0074] Or it is:

[0075] In this embodiment, the characteristics of the tetragonal symmetric stiffness matrix are that it has 6 independent elastic tensors C that are not equal to each other ij , where i, j = 1, 2, 3, 4, 5, 6, and the characteristics of the tetragonal symmetric stiffness matrix are:

[0076] Where: σ ij and ε ij respectively represent the macroscopic stress tensor and the strain tensor.

[0077] In this embodiment, the inclination angle condition specifically includes:

[0078] Calculating the inclination angle θ of each point on the median surface of the reconstructed simulated lattice structure implicit function with respect to the horizontal plane:

[0079] Where, represents the first-order derivative of the reconstructed implicit function, i = x, y, z;

[0080] Determining the ratio of the number of points where the inclination angle θ is greater than the set angle threshold to the total number of calculation points. When this ratio is greater than the set value, the inclination angle condition of the median surface of the implicit function of the tetragonal symmetric lattice structure for biocompatible scaffold design is satisfied.

[0081] The tetragonal symmetric TPMS median surface formed by reconstructing the TPMS implicit function using the present invention is as Figure 2 shown. Select the Gyroid (G) and Diamond (D) lattice structures with richer topological configurations and larger design spaces, as well as their newly designed Gyroid (NG) and Diamond (ND) types after tetragonal symmetric reconstruction, for the next step of design, so as to further verify the improvement of mechanical properties and mass transfer properties by tetragonal symmetric reconstruction design. As Figure 3 shown, through two-way offset and one-way offset, the lattice structure is further formed into a sheet-type (sl) and a strut-type (st) lattice structure respectively. The solid regions of the lattice structure are respectively defined by

[0082] and inequalities, where t is the control parameter for controlling the offset of the median surface of the lattice structure. The relative densities of the sheet-type and strut-type lattice structures are calculated using the triple integral method, as follows respectively:

[0083]

[0084] In the formula, L, W, and H respectively represent the length, width, and height of the lattice unit. As Figure 8 shown, 8 lattice structures with predefined relative densities can be generated using the linear fitting equation. = is the relative density of the sheet-like lattice structure. is the relative density of the strut-like lattice structure. and = is namely ρ * = f(LtW)HL's specific expression of WH.

[0085] By generating 8 lattice structures with a relative density of 25%, they are prepared by L-PBF and DLP respectively for the verification of mechanical experiments and mass transfer experiments. The cell unit size of the L-PBF prepared model is 5×5×5mm, and the total size of the model is 20×20×20mm, as Figure 4 (a). The unit size of the DLP prepared model is 2.5×2.5×2.5mm, and the total size of the model is 7.5×7.5×25mm, as Figure 4 (b).

[0086] The median surface inclination, three-dimensional elastic modulus surface, and experimental analysis are carried out on these 8 structures. The results show that the overall inclination of the tetragonal symmetric lattice is larger ( Figure 5 (a) shown), so the material distributed along the load direction is more than that in other directions, thus providing a more solid support for the structure to resist deformation and making it more advantageous in elastic properties. The tetragonal symmetric lattice significantly changes the three-dimensional elastic modulus surface of the lattice (as Figure 5 (b) shown), making its strongest modulus distributed on the upper and lower surfaces of the axis to enhance the stiffness of the structure. As Figure 6 (a) shown, both the sheet-like and strut-like lattices with tetragonal symmetry exhibit a stronger elastic-plastic stage, so their elastic modulus and higher strength. As Figure 6 (b) and (c) shown, the elastic modulus and yield strength are increased by up to 98% and 120% respectively. In addition, the mass transfer experimental analysis of these 8 structures is carried out as Figure 6 shown. The results are as Figure 7 shown. The permeability of the tetragonal symmetric lattice can be increased by up to 165% compared with the traditional cubic symmetric lattice. This proves that the tetragonal symmetric design method proposed by the present invention based on the crystal system theory can synergistically enhance the mechanical properties and mass transfer properties of the lattice structure bone scaffold.

[0087] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that the technical solutions of the present invention can be modified or equivalently replaced without departing from the spirit and scope of the technical solutions of the present invention, and they should all be covered within the scope of the claims of the present invention.

Claims

1. A design method of a biological bone scaffold with a tetragonal symmetric lattice structure based on minimal surface, characterized in that: It includes the following steps: S1. Reconstruct based on the implicit function of the classic triply periodic minimal surface lattice structure for the bio-bone scaffold to obtain the implicit function of the new triply periodic minimal surface lattice structure; S2. Based on the implicit function of the new three - periodic minimal surface lattice, fit the relationship between its relative density and the median surface offset control parameter to obtain the relation ρ * = f(t), and generate a lattice structure model with arbitrary relative density based on this relation, and perform representative volume element simulation calculations on this lattice structure to obtain the stiffness matrix of this lattice structure; S3. Determine whether the stiffness matrix is a characteristic of the tetragonal symmetric stiffness matrix. If not, return to step S1. If so, determine whether the simulated lattice structure has triply periodic arrayability. If not, return to step S1. If so, determine whether the inclination angle of the median surface generated by the implicit function of the new triply periodic minimal surface lattice structure with respect to the horizontal direction meets the inclination angle condition. If not, return to step S1. If so, output the implicit function of the new triply periodic minimal surface lattice structure; S4. Design and prepare the bio-bone scaffold based on the output implicit function of the new triply periodic minimal surface lattice structure.

2. The method for designing a biological bone scaffold with a tetragonal symmetric lattice structure based on minimal surface according to claim 1, characterized in that: The implicit function of the classic triply periodic minimal surface lattice structure specifically includes any one of the Gyroid implicit function, Diamond implicit function, Primitive implicit function, and IWP implicit function, where: The Gyroid implicit function is: The Diamond implicit function is: The Primitive implicit function is: The IWP implicit function is:

3. The method for designing a biological bone scaffold with a tetragonal symmetric lattice structure based on minimal surface according to claim 2, wherein: The implicit function of the new triply periodic minimal surface lattice structure specifically includes: The reconstructed Gyroid implicit function is: Or it is: The reconstructed Diamond implicit function is: Or it is: The reconstructed Primitive implicit function is: Or it is: The reconstructed IWP implicit function is: Or it is:

4. The method for designing a biological bone scaffold with a tetragonal symmetric lattice structure based on minimal surfaces according to claim 1, characterized in that: The characteristics of the tetragonal symmetric stiffness matrix are that there are 6 independent elastic tensors C that are not equal to each other ij , where i, j = 1, 2, 3, 4, 5, 6, and the characteristics of the tetragonal symmetric stiffness matrix are as follows: where: σ ij and ε ij represent the macroscopic stress tensor and strain tensor, respectively.

5. The method for designing a biological bone scaffold with a tetragonal symmetric lattice structure based on minimal surface according to claim 1, characterized in that: The inclination angle condition specifically includes: Calculate the inclination angle θ of each point on the surface of the median surface of the reconstructed implicit function of the simulated lattice structure with respect to the horizontal plane: Among them, represents the first-order derivative of the reconstructed implicit function, where i = x, y, z; Determine the ratio of the number of points with the inclination angle θ greater than the set angle threshold to the total number of calculated points. When this ratio is greater than the set value, the inclination angle condition of the median surface of the implicit function of the tetragonal symmetric lattice structure for bio-scaffold design is met.

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