Reverse design method for obtaining concave superstructure with specific mechanical property

Abstract

The invention discloses a reverse design method for obtaining a concave superstructure with specific mechanical properties. The reverse design method comprises the following steps: constructing concave lattice structures with different configurations; obtaining a stress-strain curve and a Poisson ratio value of each lattice structure; dividing all samples of the lattice structure into a training set and a test set; the stress value and the Poisson's ratio value serve as input parameters, theta, t and the loading direction serve as output parameters, the back-propagation neural network model is trained and verified, and the mapping relation between the mechanical property of the inwards-concave type superstructure and the configuration parameters of the inwards-concave type superstructure is obtained; and inputting a mechanical property curve of the host bone tissue, and matching configuration parameters of the concave superstructure based on the mapping relation. According to the method, the machine learning algorithm and the reverse design are combined, and the multivariate nonlinear mapping relation between the mechanical properties of the lattice structure and the configuration parameters of the lattice structure is established, so that the implant structure with specific mechanical properties is quickly obtained, and personalized design for different patients is realized.

Description

Technical Field

[0001] The present invention relates to the technical field of medical devices, and particularly to a reverse design method for an inwardly concave superstructure with specific mechanical properties. Background Art

[0002] With the increasing maturity of 3D printing technology, a class of mechanical metamaterial structures with novel structural forms and unique properties has emerged. Among them, the negative Poisson's ratio structure (auxetic structure) is widely used in the design of orthopedic implant structures due to its mechanical properties of expanding under tension and contracting under compression, as well as its superior fracture toughness, indentation resistance, impact resistance, and crack propagation resistance. The inwardly concave structure is a typical auxetic structure. Due to its property of expanding under tension, it is often used in bone implants at the tension position to prevent the bone implant from slipping out of the host bone after being subjected to tensile loads, such as bone nails, femoral stems, etc.; due to its property of contracting under compression, it is often used in bone implants at the compression position to minimize the deformation of the bone implant and prevent its deformation from interfering with the surrounding bone, soft tissue, nerves, etc., such as intervertebral disc implants, etc.

[0003] Currently, the mechanical properties of commonly used metal implants in clinics are usually greater than those of the host bone, which is likely to cause stress concentration and stress shielding effects, and thus become an important inducement for implant failure or postoperative refracture. In order to obtain an implant with mechanical properties matching those of the host bone tissue, traditional implant configuration design methods often rely on theoretical analysis, exhaustive iteration, and topology optimization. These methods highly depend on the prior knowledge of the designer, have a long design cycle, and the structural properties designed are often suboptimal, making it difficult to quickly obtain the configuration parameters of an implant with specific mechanical properties, which is not conducive to formulating personalized diagnosis and treatment strategies for different patients.

[0004] Therefore, for the currently advanced metamaterial structure - the inwardly concave structure, it is very necessary to provide a reverse design method for an inwardly concave superstructure with specific mechanical properties. Summary of the Invention

[0005] The purpose of the present invention is to provide a reverse design method for an inwardly concave superstructure with specific mechanical properties, which combines a machine learning algorithm and reverse design to establish a multi - variable non - linear mapping relationship between the mechanical properties of the lattice structure and its configuration parameters, so as to quickly obtain an implant structure with specific mechanical properties to achieve personalized design for different patients.

[0006] To achieve the above purpose, the present invention provides a reverse design method for an inwardly concave superstructure with specific mechanical properties, and the steps include:

[0007] S1. Generate corresponding three - dimensional unit cell structures (4×4×4mm) based on two - dimensional inwardly concave superstructures with different configurations 3) Generate concave lattice structures with different configurations from the three-dimensional unit cell structure array (16×16×16mm 3 ).

[0008] S2. Use the finite element method to simulate the quasi-static compression process of lattice structures with different configurations, obtain the stress-strain curve corresponding to each lattice structure, and calculate the Poisson's ratio value;

[0009] S3. Divide the established lattice structure samples with different configurations into a training set and a test set;

[0010] S4. Build a backpropagation neural network model, use the stress value and Poisson's ratio value under a fixed strain as input parameters, and use θ, t, and the loading direction as output parameters. Train and validate the backpropagation neural network model to obtain the mapping relationship between the mechanical properties of the concave superstructure and its configuration parameters;

[0011] S5. Input the mechanical property curve of the host bone tissue, and match the concave superstructure with the mechanical properties of the host bone based on the mapping relationship between the mechanical properties of the concave superstructure and its configuration parameters.

[0012] Preferably, the parameters describing the concave superstructure in step S1 include the length l of the diagonal strut, the length h of the vertical strut, the concave angle θ, and the strut width t. Among them, l = 2 / sinθ, h = 2 + l×cosθ. Therefore, the decisive parameters of the concave superstructure configuration are the concave angle θ and the strut width t.

[0013] Preferably, the design range of the concave angle θ of the concave superstructure in step S1 is 50° to 90°, and the design range of the strut width t is 0.36mm to 1.09mm. The Latin hypercube method is used to establish the sample space to obtain multiple concave lattice structures with different configurations covering the value ranges of θ and t.

[0014] Preferably, step S2 specifically includes:

[0015] S21. Mesh the finite element model using tetrahedral elements;

[0016] S22. Establish two rigid planes in the loading direction of the lattice structure, set the bonded contact, and apply boundary conditions to the lattice structure, that is, completely constrain the lower plane of the finite element model and apply a displacement of 30% of the compression height to the upper plane. Among them, the loading directions are the Y and Z directions;

[0017] S23. After the displacement loading is completed, obtain the stress-strain curve of each finite element model and calculate the Poisson's ratio value.

[0018] Preferably, in step S23, starting from the origin in the stress-strain curve, 31 stress values corresponding to strains are selected based on a strain interval of 0.5%.

[0019] Preferably, in step S3, the lattice structure samples with two loading directions are divided into a training set and a test set.

[0020] Preferably, in step S4, the performance of the backpropagation neural network model is evaluated by the coefficient of determination and the root mean square error.

[0021] Therefore, the present invention adopts the above-mentioned reverse design method for obtaining an inwardly concave superstructure with specific mechanical properties, and has the following beneficial effects:

[0022] (1) Compared with the traditional forward design method of obtaining a stent structure with specific mechanical properties by continuously adjusting the configuration parameters of the stent, the reverse design method proposed by the present invention, based on the mapping relationship between the mechanical properties of the obtained inwardly concave superstructure and its configuration parameters, can quickly obtain the configuration parameters of the inwardly concave superstructure with matching mechanical properties at one time by inputting the mechanical property curve of the host bone tissue, so as to meet the personalized needs of different patients, thereby improving the postoperative bone integration effect of patients and accelerating the rehabilitation process;

[0023] (2) The present invention combines machine learning algorithms with reverse design, breaks through the limitations of traditional methods, and can quickly obtain the configuration parameters of an inwardly concave superstructure with specific mechanical properties on the premise of ensuring calculation accuracy, providing a theoretical basis and technical support for the design of related orthopedic implants and the formulation of personalized diagnosis and treatment strategies in clinical practice;

[0024] (3) It is applicable to the structural design of different porous bone scaffolds and has strong practicability.

[0025] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 is a flowchart of the method according to an embodiment of the present invention;

[0027] Figure 2 is a design diagram of an inwardly concave lattice structure according to an embodiment of the present invention;

[0028] Figure 3 is a schematic diagram of simulating quasi-static compression loading of a finite element model of an inwardly concave lattice structure according to an embodiment of the present invention;

[0029] Figure 4 is a graph of the predicted performance of the BPNN model according to an embodiment of the present invention;

[0030] Figure 5Reverse design method for concave superstructure and configuration design flow chart of porous femoral stem according to embodiments of the present invention;

[0031] Figure 6 Structural schematic diagrams of healthy femur and femur after implanting femoral stem according to embodiments of the present invention;

[0032] Figure 7 Schematic diagram of 7 Gruen regions of femur according to embodiments of the present invention;

[0033] Figure 8 Average stress diagram of each Gruen region of femur according to embodiments of the present invention. Detailed implementation manners

[0034] To make the objectives, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some but not all of the embodiments of the present invention. Components of the embodiments of the present invention usually described and illustrated in the accompanying drawings here can be arranged and designed in various different configurations. In the description of the present invention, it should be noted that the orientation or positional relationship indicated by terms such as "upper", "lower", "inner", "outer", etc. is based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship when the product of this invention is usually placed. It is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation to the present invention.

[0035] Embodiment

[0036] As Figure 1 shown, the present invention provides a reverse design method for a concave superstructure to obtain specific mechanical properties. The steps include:

[0037] S1. Establish a finite element model of a concave superstructure with different configuration parameters, generate corresponding three-dimensional unit cell structures (4×4×4 mm 3 ) based on two-dimensional concave superstructures with different configurations, and generate concave lattice structures with different configurations (16×16×16 mm 3 ) by arraying the three-dimensional unit cell structures.

[0038] The configuration of the concave superstructure can be described by 4 parameters, such as Figure 2As shown, they are the length \(l\) of the diagonal strut, the length \(h\) of the vertical strut, the concave angle \(\theta\), and the strut width \(t\), where \(l = \frac{2}{\sin\theta}\), \(h = 2 + l\times\cos\theta\). Therefore, the decisive parameters of the concave superstructure configuration are the concave angle \(\theta\) and the strut width \(t\). Considering the 3D printing manufacturing accuracy and the porosity requirements (50% - 90%) beneficial to bone tissue ingrowth, the design range of \(\theta\) is determined to be \(50^{\circ}\) to \(90^{\circ}\), and the design range of \(t\) is \(0.36\mathrm{mm}\) to \(1.09\mathrm{mm}\). In order to enable the established structure to cover the value ranges of \(\theta\) and \(t\), the Latin hypercube method is used to establish the sample space to obtain 150 concave lattice structures with different configurations.

[0039] S2. Use the finite element method to simulate the quasi-static compression process of lattice structures with different configurations, obtain the stress-strain curve corresponding to each lattice structure, and calculate the Poisson's ratio value. The finite element model is meshed using tetrahedral elements with a mesh size of \(0.1\mathrm{mm}\), and the material is set as Ti6Al4V. Two rigid planes are established in the loading direction of the lattice structure, and a bonded contact is set. Boundary conditions are applied to the lattice structure, the lower plane of the finite element model is fully constrained, and a compressive displacement of \(4.8\mathrm{mm}\) is applied to the upper plane (simulating that the lattice structure is compressed by 30% of the overall height). Among them, the loading directions are the \(Y\) and \(Z\) directions, as Figure 3 shown, and the loading rate is \(1\mathrm{mm / min}\). General contact is set inside the lattice structure, a penalty function friction is set tangentially, the friction coefficient is \(0.2\), and a hard contact is set normally. After the displacement loading is completed, the stress-strain curve of each finite element model is obtained and the Poisson's ratio value is calculated. Starting from the origin in the stress-strain curve, with a strain interval of \(0.5\%\) as the benchmark, 31 stress values corresponding to the strains are selected to standardize and describe the stress-strain curve of each finite element model.

[0040] S3. Divide the established lattice structure samples with different configurations into a training set and a test set. Among the 150 lattice structures with different configurations, since two loading directions (\(Y\) direction and \(Z\) direction) are involved, the sample space is 300 lattice structures. Randomly select 240 of them as training set samples and 60 as test set samples.

[0041] S4. Build a backpropagation neural network (BPNN) model, with the stress value and the Poisson's ratio value as input parameters, and \(\theta\), \(t\), and the loading direction (0 represents the loading direction is the \(Y\) direction, 1 represents the loading direction is the \(Z\) direction) as output parameters. Train and verify the BPNN model to obtain the mapping relationship between the mechanical properties of the concave superstructure and its configuration parameters. The performance of the BPNN model is determined by the coefficient of determination (\(R\) 2) and the root mean square error (RMSE). The number of neurons in the input layer of the established BPNN model is 32, the hidden layer has 3 layers, the number of neurons is 29, 7, and 5 respectively, the number of neurons in the output layer is 3, the learning rate is set to 0.003, and the number of iterations is 300. The prediction performance of the established BPNN model is as Figure 4 shown, where the prediction performance of t is: R 2 ≥0.976, RMSE ≤ 0.032 mm; the prediction performance of θ is: R 2 ≥0.945, RMSE ≤ 2.573; the prediction accuracy of the loading direction is 100%. Figure 4 Among them, (a) in it represents the prediction performance of the training set t, (b) represents the prediction performance of the test set t, (c) represents the prediction performance of the training set θ, (d) represents the prediction performance of the test set θ, (e) represents the prediction performance of the training set loading direction, and (f) represents the prediction performance of the test set loading direction.

[0042] S5. Input the mechanical property curve of the host bone tissue, and match the concave-shaped superstructure with the mechanical properties of the host bone based on the mapping relationship between the mechanical properties of the concave-shaped superstructure and its configuration parameters.

[0043] To further evaluate the effectiveness of the proposed design method, taking the design of a personalized femoral stem as an example, the process is as Figure 5 shown. After the femoral stem is implanted into the femur, the outer side is subjected to tensile force and the inner side is subjected to compressive force. To prevent the femoral implant from detaching from the host bone under tensile force, the outer part of the femoral stem should be designed as a concave-shaped superstructure.

[0044] In this embodiment, the overall configuration design parameters of the femoral stem are based on the femur of a 66-year-old healthy male. The CT images of the subject are imported into Mimics software for three-dimensional reconstruction. To determine the configuration parameters of the concave-shaped superstructure required for the design of the femoral stem, a cancellous bone block is intercepted from the corresponding bone position of the subject, meshed in Hypermesh software, and a finite element simulation compression experiment is carried out on this bone block in Abaqus software to obtain its stress-strain curve. Similarly, 31 stress values are obtained at intervals of 0.5% strain. The Poisson's ratio is set to -0.3. The 31 stress values and Poisson's ratio of the cancellous bone block are input into the machine learning model of the mechanical properties and configuration relationship of the concave-shaped superstructure established to obtain the concave-shaped superstructure that matches the mechanical properties of the cancellous bone block. The obtained matching concave-shaped configuration parameters are: t = 0.474 mm, θ = 73.157 m, and the compression direction is the Y direction.

[0045] Apply the determined concave-shaped superstructure (t = 0.474 mm, θ = 73.157°, compression direction is the Y direction) to the design of the femoral stem. Establish a finite element model of a healthy femur (Figure 6 a), the finite element model of the solid femoral stem implant and the finite element model of the concave porous femoral stem implant Figure 6 b). A vertical downward load of 750 N was applied to the three finite element models to simulate the human standing posture. According to the commonly used Gruen zoning method in clinical practice, each femoral finite element model was divided into 7 regions, as Figure 7 shown. By comparing the average stresses in the same Gruen region of the three models, the average stress diagrams of each Gruen region are as Figure 8 and Table 1 shown. Compared with the solid femoral stem implant model, the average stress in each Gruen region of the concave porous femoral stem implant model has been significantly improved, indicating that the stress shielding effect can be effectively reduced. In addition, for the regions involved in the concave superstructure (1, 2, 6, 7), the average stress of the concave porous femoral stem implant model in the above regions almost reaches the level consistent with that of the healthy femur, Region 1 (healthy femur: 0.815 MPa vs. porous femoral stem: 0.734 MPa), Region 2 (healthy femur: 2.654 MPa vs. porous femoral stem: 2.817 MPa), Region 6 (healthy femur: 4.499 MPa vs. porous femoral stem: 3.667 MPa), Region 7 (healthy femur: 1.776 MPa vs. porous femoral stem: 1.428 MPa), indicating that it is beneficial to postoperative bone healing.

[0046] Table 1 Average stress values (MPa) in each Gruen region of the three finite element models

[0047] Region Healthy femur model Solid stem implant model Porous stem implant model 1 0.815 0.309 0.734 2 2.654 1.963 2.817 3 4.189 4.66 5.031 4 5.616 6.245 6.356 5 8.211 6.998 7.371 6 4.499 2.792 3.667 7 1.776 0.686 1.428

[0048] Therefore, the present invention adopts the above-mentioned reverse design method for obtaining a concave superstructure with specific mechanical properties. Based on the mapping relationship between the mechanical properties of the obtained concave superstructure and its configuration parameters, by inputting the mechanical property curve of the host bone tissue, the configuration parameters of the concave superstructure with matching mechanical properties can be quickly obtained, which can meet the personalized needs of different patients.

[0049] 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 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 they can still modify or equivalently replace the technical solutions of the present invention, and these modifications or equivalent replacements cannot make the modified technical solutions deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A reverse design method for obtaining an inwardly concave superstructure with specific mechanical properties, characterized by the steps Including: S1. Generate corresponding three-dimensional unit cell structures based on two-dimensional concave superstructures with different configurations, and generate concave lattice structures with different configurations by arraying the three-dimensional unit cell structures; S2. Use the finite element method to simulate the quasi-static compression process of lattice structures with different configurations, obtain the stress-strain curves corresponding to each lattice structure, and calculate the Poisson's ratio values; S3. Divide the established lattice structure samples with different configurations into a training set and a test set; S4. Build a backpropagation neural network model, use the stress values and Poisson's ratio values at a fixed strain as input parameters, and use θ, t, and the loading direction as output parameters. Train and validate the backpropagation neural network model to obtain the mapping relationship between the mechanical properties of the concave superstructure and its configuration parameters; S5. Input the mechanical property curve of the host bone tissue, and match the concave superstructure with the mechanical properties of the host bone based on the mapping relationship between the mechanical properties of the concave superstructure and its configuration parameters.

2. The reverse design method of a concave superstructure for obtaining specific mechanical properties according to claim 1, characterized in that: The parameters describing the concave superstructure in step S1 include the length l of the diagonal strut, the length h of the vertical strut, the concave angle θ, and the strut width t. Among them, l = 2 / sinθ, h = 2 + l×cosθ. Therefore, the decisive parameters of the concave superstructure configuration are the concave angle θ and the strut width t.

3. The reverse design method of a concave superstructure for obtaining specific mechanical properties according to claim 2, characterized in that: In step S1, the range of the concave angle θ of the concave superstructure is 50° to 90°, and the design range of the strut width t is 0.36 mm to 1.09 mm. The Latin hypercube method is used to establish the sample space to obtain multiple concave lattice structures with different configurations covering the value ranges of θ and t.

4. The reverse design method of a concave superstructure for obtaining specific mechanical properties according to claim 1, characterized in that Step S2 specifically includes: S21. Mesh the finite element model using tetrahedral elements; S22. Establish two rigid planes in the loading direction of the lattice structure, set bonded contacts, fully constrain the lower plane of the finite element model, and apply a displacement of 30% of the compression height to the upper plane. Among them, the loading directions are the Y and Z directions; S23. After the displacement loading is completed, obtain the stress-strain curve of each finite element model and calculate the Poisson's ratio value.

5. The reverse design method of a concave superstructure for obtaining specific mechanical properties according to claim 4, characterized in that: In step S23, starting from the origin in the stress-strain curve, select the stress values corresponding to 31 strains based on a strain interval of 0.5%.

6. The inverse design method of a concave superstructure for obtaining specific mechanical properties according to claim 4, characterized in that: In step S3, the lattice structure samples subjected to two loading directions are divided into a training set and a test set.

7. The reverse design method of a concave superstructure for obtaining specific mechanical properties according to claim 1, characterized in that: In step S4, the performance of the backpropagation neural network model is evaluated by the coefficient of determination and the root mean square error.

Images