A multi-objective structural optimization design method for porous biomimetic scaffolds

Abstract

The application discloses a kind of multi-objective structure optimization design methods for porous biomimetic stent, the method includes the following steps: step one, by biology constraint, construct the constraint condition of stent structure parameter, and utilize genetic algorithm to obtain the feasible region satisfying constraint condition;Step two, based on feasible region, construct the three-dimensional model of porous biomimetic stent, carry out finite element analysis and fluid dynamics simulation calculation, to obtain the elastic modulus and permeability of stent structure;Step three, based on the mechanical properties and fluid properties of bone tissue, determine the target performance optimization design space consistent with it, to obtain the stent structure parameter design set meeting the performance requirements of bone tissue, determine the structure design scheme capable of simultaneously optimizing the mechanical properties and biological fluid properties of stent according to Pareto optimal solution.This method realizes the high decoupling of elastic modulus and permeability of stent under given porosity while considering multiple performance requirements.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of bone tissue engineering, and relates to a multi-target structure optimization design method of a porous biomimetic scaffold. BACKGROUND

[0002] The porous bone scaffold has interconnected pores, which not only provides a three-dimensional space for the adhesion, growth and proliferation of tissue cells, but also temporarily replaces the damaged bone tissue to play a mechanical support role. In the process of bone tissue repair, if the elastic modulus of the porous scaffold is lower than the mechanical properties required at the implant site, the mechanical support role cannot be played. On the contrary, if the elastic modulus is too high, stress shielding phenomenon will occur, affecting bone tissue growth. In addition, permeability is also a key factor affecting bone tissue repair. High permeability indicates that the structure has strong ability to penetrate tissue fluid, which is conducive to promoting cell migration and nutrient transport, while low permeability hinders cell migration and vascularization. Therefore, designing a porous scaffold with mechanical properties and permeability consistent with actual bone tissue has become a research hotspot.

[0003] In addition, the biological properties of the porous bone scaffold are also a key factor affecting bone tissue repair. For example, the topological parameters such as porosity, pore size, specific surface area, etc. also have important influence on new bone formation and vascularization. Larger pore size is proved to be the best choice for bone growth, which can provide sufficient space for the adhesion, proliferation and vascularization of bone cells. High specific surface area is also conducive to promoting cell adhesion, proliferation and migration. Some biological functions during cell growth, such as ion exchange, oxygen diffusion and nutrient transport, also occur on the surface of the porous scaffold. In addition, the selection of porosity is also one of the key factors to balance the mechanical properties and fluid properties of the scaffold. High porosity cannot guarantee the mechanical properties, and low porosity cannot guarantee the fluid properties.

[0004] At present, scholars mainly focus on one or two properties, such as mechanical properties or fluid properties, when researching the porous biomimetic scaffold, and do not consider the trade-off between multiple properties. However, an ideal scaffold should meet all performance requirements. In addition, since the site of bone tissue defect is not uniform, the performance and geometric structure characteristics of the porous bone scaffold should have high adjustability, which is also not effectively solved at present. SUMMARY

[0005] To effectively address the trade-off between the mechanical and fluid properties of porous scaffolds due to porosity constraints, this invention provides a multi-objective structural optimization design method for porous biomimetic scaffolds. This method derives the feasible region of scaffold structural parameters based on biological constraints, establishes a three-dimensional model, and performs simulation calculations. Based on the simulation results and the performance requirements of bone tissue, a target performance design space is constructed. Pareto optimal solutions are then used to determine the scaffold structural design scheme that simultaneously optimizes both mechanical and biofluidic properties. This method achieves a high degree of decoupling between the elastic modulus and permeability of the scaffold at a given porosity while balancing multiple performance requirements. Furthermore, the structural dimensions and performance of the scaffold are highly adjustable.

[0006] The objective of this invention is achieved through the following technical solution:

[0007] A multi-objective structural optimization design method for porous biomimetic scaffolds includes the following steps:

[0008] Step 1: Construct constraints on the scaffold structure parameters through biological constraints, and use a genetic algorithm to obtain the feasible region that satisfies the constraints;

[0009] Step 2: Construct a three-dimensional model of the porous biomimetic scaffold based on the feasible region, and perform finite element analysis and fluid dynamics simulation calculations to obtain the elastic modulus and permeability of the scaffold structure;

[0010] Step 3: Based on the mechanical and fluid properties of bone tissue, determine the target performance optimization design space that matches it, thereby obtaining the scaffold structure parameter design set that meets the performance requirements of bone tissue. Based on the Pareto optimal solution, determine the structural design scheme that can simultaneously optimize the mechanical and biofluid properties of the scaffold.

[0011] Compared with the prior art, the present invention has the following advantages:

[0012] Based on the design method and process proposed in this invention, the problem of mutual constraints between the mechanical and fluid properties of porous scaffolds can be effectively solved. This method not only takes into account the design requirements of biological constraints on the geometric features of the scaffold, but also achieves a high degree of adjustability of key factors such as pore size, specific surface area, elastic modulus and permeability. This not only provides an effective means to design an ideal scaffold that can completely simulate the real performance of bone tissue, but also provides convenience for the design of multifunctional gradient scaffolds. Attached Figure Description

[0013] Figure 1 The diagram shows a thin-shell TPMS scaffold, with P unit (a) and G unit (c) and their corresponding 3×3×3 array scaffold structures (b, d), where the lattice edge size and aperture size are marked by L and ps, respectively.

[0014] Figure 2 Flow chart of multi-objective structure optimization design method for porous biomimetic scaffold

[0015] Figure 3 For the feasible design space of P unit based on constraint conditions, (a)-(f): region I represents the feasible region, region II represents the maximum design range that the unit size can take when the constant t is constant; (g)-(i) represent the feasible design space that meets all the constraint conditions at the same time;

[0016] Figure 4 For the feasible design space of G unit based on constraint conditions, (a)-(f): region I represents the feasible region, region II represents the maximum design range that the unit size can take when the constant t is constant; (g)-(i) represent the feasible design space that meets all the constraint conditions at the same time;

[0017] Figure 5 Boundary condition setting for finite element simulation calculation

[0018] Figure 6 For the feasible design space of elastic modulus and permeability under different porosities, (a)-(c) P unit; (d)-(f) G unit. Wherein, k i Optimal solution of permeability, E i Optimal solution of elastic modulus, C i Optimal solution of elastic modulus and permeability compromise;

[0019] Figure 7 For the influence of structure parameter optimization on the specific surface area (S / V) and pore size (ps) of P and G units, (a) specific surface area (S / V) of P unit under different porosities, (b) specific surface area (S / V) of G unit under different porosities. (c) Pore size (ps) of P unit under different porosities, (d) Pore size (ps) of G unit under different porosities. R1 and R2 represent the more ideal osteogenic environment shown in the existing literature. DETAILED DESCRIPTION

[0020] The technical solutions of the present application will be further described below in conjunction with the drawings, but are not limited thereto, and any modification or equivalent replacement to the technical solutions of the present application without departing from the spirit and scope of the present application shall be covered in the protection scope of the present application.

[0021] The present application provides a multi-objective structure optimization design method for porous biomimetic scaffold, which is mainly applicable to periodic scaffold structure, including but not limited to three-period minimal surface scaffold, regular geometric scaffold, etc. The optimization design method comprises the following steps:

[0022] Step one, construct the constraint condition of the scaffold structure parameters by biological constraints, and obtain the feasible region satisfying the constraint condition by using genetic algorithm.

[0023] In this step, the scaffold structure parameters include unit size, wall thickness, pore size, specific surface area and porosity, etc. The biological constraint condition considers the structural characteristics of the basic unit of the scaffold, such as the side length, thickness, pore size, specific surface area and porosity, which effectively guarantees the manufacturability and osteoinductivity of the porous scaffold.

[0024] In this step, the feasible region satisfying the constraint condition is obtained by iterative optimization based on genetic algorithm, and other applicable optimization algorithms include but are not limited to particle swarm optimization algorithm, neural network algorithm, etc.

[0025] Step two, construct the three-dimensional model of the porous biomimetic scaffold based on the feasible region, and perform finite element analysis and fluid dynamics simulation calculation, so as to obtain the elastic modulus and permeability of the scaffold structure.

[0026] In this step, the elastic modulus and permeability of the scaffold are obtained by using finite element analysis and fluid dynamics simulation calculation, which are used as the basis for judging the degree of optimization of the mechanical properties and fluid properties of the scaffold.

[0027] Step three, determine the target performance optimization design space that matches the mechanical properties and fluid properties of bone tissue, so as to obtain the scaffold structure parameter design set that meets the performance requirements of bone tissue, and determine the structure design scheme that can optimize the mechanical properties and biological fluid properties of the scaffold at the same time according to the Pareto optimal solution, and finally realize the decoupling and high adjustability of the above two properties by using the target performance optimization design space. The specific surface area and pore size also realize a large adjustment range.

[0028] In this step, the optimization structure that matches the actual performance of bone tissue is considered to establish the target performance design space, and the decoupling and high adjustability of the mechanical properties and fluid properties of the scaffold are realized based on the design space.

[0029] Embodiment

[0030] This embodiment is completed based on a triply periodic minimal surface scaffold structure, and the optimization method is also applicable to other types of periodic scaffold structures. The triply periodic minimal surface unit is as shown in Figure 1 The specific steps are as follows:

[0031] Step 1, establish a typical TPMS thin shell unit according to the expression of triply periodic minimal surface (TPMS).

[0032] The unified expression of TPMS thin shell unit is:

[0033] f(x, y, z) < t 2

[0034] where f(x, y, z) is the implicit expression of a three-periodic minimal surface, and the interval [-t, t] represents the solid boundary of the TPMS shell unit. The expressions of two typical TPMS units are as follows:

[0035] Primitive (P):

[0036] f p (x, y, z) = cos(τ x x) + cos(τ y y) + cos(τ z z)

[0037] Gyroid (G):

[0038] f G (x, y, z) = cos(τ x x) sin(τ y y) + cos(τ y y) sin(τ z z) + cos(τ z z) sin(τ x x)

[0039] where τ i = 2πn i / L i represents the periodicity of the TPMS unit in three directions, and n i represents the number of unit cells along the length L i of the lattice edge. By setting the values of n i and L i , the number of arrangements of the stent unit in each direction and the edge length of the stent are determined, and then the three-dimensional model of the TPMS unit is obtained by parameterized modeling using the above expressions.

[0040] Step 2, obtain the functional relationship between the porosity of the TPMS unit and its functional expression.

[0041]

[0042] Ω = {(x, y, z) | f(x, y, z) < 0, x min ≤ x ≤ x max , y min ≤ y ≤ y max , z min ≤ z ≤ z max}

[0043] where FV and p0 represent the volume fraction and porosity, respectively, and the subscript max-min represents the length of the strut structure. x max -x min represents the length of the strut structure in the x direction, and similarly, the lengths of the strut in the y and z directions are calculated. The function relationship between the constant t in the TPMS expression and the porosity p0 is obtained by substituting the TPMS expression into the above formula, and a function expression is established. The function expression and step 1 are used to establish a three-dimensional model of the TPMS unit with different porosities.

[0044] Step 3, respectively establish the relationship between the pore size and specific surface area of the TPMS unit and the structure parameters.

[0045] Expression of the TPMS thin shell wall thickness:

[0046] h(a, t) = 0.28345 · a · t - 0.00633 · a

[0047] Expression of the pore size:

[0048]

[0049] Expression of the specific surface area:

[0050] S / V _P = 2.347a -1

[0051] S / V _G = 3.097a -1

[0052] where a represents the side length of the strut basic unit, t represents the constant in the TPMS unit expression, h represents the wall thickness of the TPMS unit, ps represents the pore size, and S / V represents the specific surface area. Among them, ps(a*) represents the pore size of the TPMS unit with a side length of a* and a wall thickness of 0.

[0053] Step 4, determine the design variables of the porous scaffold according to the biological constraints of bone tissue growth and establish the constraint conditions.

[0054] Maximum design goal: elastic modulus (E), permeability (k).

[0055] Constraint condition: st1: p(a, t) = 1-FV = p0

[0056] st2: S / V > S / V min

[0057] st3: ps ≥ ps min

[0058] st4: a l≤a≤a u

[0059] st5:t l ≤t≤t u

[0060] In the formula, p0 is the porosity of the designed support structure, and S / V min It is the smallest specific surface area of ​​human bone tissue measured, ps min It is the smallest pore size suitable for new bone and blood vessel formation, a l and t l and a u and t u The lower and upper bounds of the structural design variables were determined.

[0061] Step 5: Based on the constraints in Step 4, set the iteration step size and use the genetic algorithm to iterate continuously to obtain the design variables that satisfy all constraints. Based on this, construct the feasible region of the design variables, and then construct a three-dimensional model of the stent structure based on the feasible region. The elastic modulus and permeability of the stent are obtained through simulation calculation.

[0062] Step 6: Based on the mechanical and fluid properties of actual bone tissue, the simulation results from Step 5 are filtered, and a target performance design space is constructed using structures that meet the performance requirements, thereby obtaining a scaffold structure parameter design set that meets the performance requirements of bone tissue. Finally, the optimal solution for the trade-off between the mechanical and fluid properties of the scaffold is determined based on the Pareto optimal solution.

[0063] The optimization results obtained from the above steps are as follows: Figures 3-7 As shown, the specific conclusions are as follows:

[0064] according to Figure 3 and Figure 4 Feasible solutions for the structural parameters of TPMS units (P units and G units) can be obtained when the constraints are met. That is, the points in the figure represent the structural parameter settings that meet the biological constraints. Based on these points, a preliminary three-dimensional model of the TPMS scaffold can be established.

[0065] according to Figure 5 The boundary conditions set in the simulation are used to analyze the mechanical and fluid properties of the stent model, and the force-displacement curve and pressure drop results are obtained. Then, the elastic modulus and permeability of the stent are obtained according to the slope of the force-displacement curve in the first linear stage and Darcy's law.

[0066] Figure 6 The points in the equation represent the solution set of the elastic modulus and permeability of the support structure. Specifically, point E... i The optimal solution representing the elastic modulus, point k i The optimal solution representing the penetration rate, point C. iThis represents the optimal compromise between permeability and elastic modulus. According to... Figure 6 The results shown demonstrate the ability to decouple and highly adjust the elastic modulus and permeability, achieving a trade-off between these two properties. These results provide an effective solution for designing support structures with superior overall performance.

[0067] Figure 7 The image shows the range of values ​​for the specific surface area and pore size of the optimized support structure. Figure 7 It is known that, for a given porosity, the optimization method based on this invention can achieve a high degree of adjustability in specific surface area and pore size. The larger the specific surface area and pore size, the better the fluid and biological properties of the scaffold, and the more beneficial it is to tissue fluid transport and the proliferation and differentiation of tissue cells. Figure 7 In (a)(b), S / V min It is the minimum specific surface area suitable for bone tissue growth. Figure 7 In (c) and (d), R1 and R2 are the relatively ideal pore size ranges suitable for bone tissue growth obtained from existing research. It can be seen that the results obtained by the present invention effectively cover the above ranges and achieve a wide range of adjustable specific surface area and pore size.

Claims

1. A multi-objective structural optimization design method for porous biomimetic scaffolds, characterized in that... The method includes the following steps: Step 1: Construct constraints on the scaffold structure parameters through biological constraints, and use a genetic algorithm to obtain the feasible region that satisfies the constraints. The scaffold structure is a periodic scaffold structure, and the scaffold structure parameters include unit size, wall thickness, pore size, specific surface area, and porosity. Step 2: Construct a three-dimensional model of the porous biomimetic scaffold based on the feasible region, and perform finite element analysis and fluid dynamics simulation calculations to obtain the elastic modulus and permeability of the scaffold structure; Step 3: Based on the mechanical and fluid properties of bone tissue, determine the target performance optimization design space that matches it, thereby obtaining the scaffold structure parameter design set that meets the performance requirements of bone tissue. Based on the Pareto optimal solution, determine the structural design scheme that can simultaneously optimize the mechanical and biofluid properties of the scaffold.

2. The multi-objective structural optimization design method for porous biomimetic scaffolds according to claim 1, characterized in that... The periodic support structure is a three-period minimal curved surface support.

3. The multi-objective structural optimization design method for porous biomimetic scaffolds according to claim 1, characterized in that... The genetic algorithm is replaced by a particle swarm optimization algorithm or a neural network algorithm.

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