Personalized jaw repair implant parameter optimization method based on approximation model

Abstract

The invention relates to an approximation model-based personalized jaw repair implant parameter optimization method, which comprises the following steps of: determining a design variable which has a great influence on a design target by applying a screening experiment, and establishing a second-order polynomial approximation model function of a mapping relationship among the corresponding implant thickness, an included angle and a maximum stress value; determining test arrangement by applying center composite experiment design, and generating sample points; performing finite element analysis according to the test arrangement, and calculating target function values corresponding to the sample points; solving an approximate model coefficient; carrying out significance test on the obtained coefficients, removing non-significant items, and solving again until all the coefficients are significant; constructing a satisfaction function according to the problem characteristics; and solving the satisfaction function by adopting an intelligent optimization algorithm to obtain an optimal parameter value enabling the stress value to be minimum. According to the method, the approximate model of the design variable and the target function is constructed, and the maxima stress value is minimum as the target, so that the parameter optimization of the jaw repair implant can be quickly realized.

Description

Technical Field

[0001] The present invention relates to the field of digital design of personalized jaw repair implants, and mainly relates to a method for optimizing parameters of personalized jaw repair implants based on an approximate model. Background Art

[0002] The optimization of the structural parameters of mandibular repair implants is an important part of the digital design of personalized implants. It is a nonlinear optimization problem that requires the stress value of the structure to be as small as possible while meeting the repair requirements. When using traditional design methods, it is often difficult to use strict mathematical formulas to express the functional relationship between the objective function, constraints and design variables for personalized implant structures, which can easily lead to problems such as conservative performance parameters. The present invention uses an approximate model and a satisfaction function method to reduce the computational complexity while ensuring accuracy, and obtains optimized personalized implant structural parameters, providing a basis for the design of clinical mandibular repair implants. Summary of the Invention

[0003] The present invention addresses the shortcomings of the prior art by proposing a method for optimizing the parameters of personalized mandibular prosthetic implants based on an approximate model. This method minimizes stress while ensuring the structure meets the required restoration. An approximate model for maximum stress and various design factors is established. By applying a satisfaction function to the approximate model, the optimization process is reduced in computational complexity and accelerated.

[0004] The method for optimizing parameters of a personalized implant for jaw repair based on an approximate model according to the present invention comprises the following steps: Step 1: Taking into account the requirements of manufacturing process standardization, reduce design variables, apply screening experiments to determine the main structural parameters that affect stress magnitude, and determine the design factors and their level numbers; Step 2: Based on the optimization design problem, the central composite experimental design is used to generate the initial sample points; Step 3: Call the finite element simulation program to obtain the response index corresponding to each set of experimental designs; Step 4: Apply the least square method to solve the coefficients of the approximate model expression; Step 5: Perform a significance test on the obtained coefficients through variance analysis. If there are insignificant items, remove them and solve again until all coefficients are significant. Step 6: Construct a satisfaction function based on the characteristics of the problem; Step 7: Taking the maximum satisfaction function as the goal, apply the simulated annealing algorithm to solve and obtain the optimal parameter value; In the above scheme, in step 1, the approximate model adopts a second-order polynomial approximate model. The approximate model is a functional relationship between the design variables and the response quantity established on the basis of the experimental design. In the second-order polynomial approximate model, there are n independent experimental factors x i ( i = 1,2,…,n), obtain the corresponding sample points through experimental design, calculate the corresponding sample values, and the fitting approximate model is:

[0005] Where, β 0 is the unknown coefficient of the constant term, β i is the undetermined coefficient of the linear term, β ii is the coefficient of the quadratic term to be determined, β ij is the interaction term coefficient to be determined.

[0006] The above models can replace complex real models for analysis and optimization.

[0007] In the above scheme, in step 2, the central composite design includes CCF (face-centered cubic central composite design), CCC (circumscribed central composite design) and CCI (nested central composite design). The experimental point distribution of two-factor CCC, CCF and CCI is as follows: Figure 3 As shown, from left to right they are CCC, CCF, and CCI. The design variables are expressed in coded units. The distance from the center point of the design matrix to the high and low levels of the factor is ±1, and the distance from the axial point to the center is ±a. When a = (k) 1 / 2 When a = 1, the axial point is generally on the sphere. When a = 1, the axial point is on the cube. k is the number of design variables. The experimental design of this method uses CCF, and each factor requires three levels: ±1, 0.

[0008] In the above scheme, in step 6, when the target value is expected to be as small as possible, the satisfaction function is

[0009] Where, y i is the estimated value of the ith response, h i is the maximum value, l i is the minimum value, q i is any positive constant, which can be 1.

[0010] The beneficial effects of the present invention are: The present invention determines the sample points through face-centered cubic center composite design, establishes an approximate model between the maximum stress and the implant thickness and angle, and optimizes the implant parameters based on the approximate model. Compared with complete biomechanical calculation simulation, it reduces the calculation complexity and shortens the calculation time while ensuring accuracy. It can find the optimal solution more quickly, reduce the maximum stress of the implant, and avoid the subjectivity brought about by previous design relying on experience. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Figure 1 It is a design flow chart of the present invention.

[0012] Figure 2 1 is a diagram defining implant design variables in an embodiment of the present invention.

[0013] Figure 3 is a distribution diagram of sample points in a central composite design in an embodiment of the present invention.

[0014] Figure 4 This is the finite element simulation model of the implant in the embodiment of the present invention.

[0015] Figure 5 2 is a variance analysis diagram in an embodiment of the present invention.

[0016] Figure 6 1 is a diagram showing the relationship between maximum stress and design variables in an embodiment of the present invention. DETAILED DESCRIPTION

[0017] In order to explain the technical features of the present invention more clearly, the following description will be made of a customized personalized mandibular repair implant as a research object with reference to the accompanying drawings to specifically explain a parameter optimization method of a personalized mandibular repair implant based on an approximate model proposed by the present invention.

[0018] Step 1: Taking into account the requirements of manufacturing process standardization, reduce design variables, apply screening experiments to determine the structural parameters that mainly affect the stress magnitude, and determine the design factors and their level numbers.

[0019] The mandible is the only movable bone in the face. It is arched and participates in bite, chewing, and swallowing. When partial mandibular resection is necessary due to deformity, trauma, or oral cancer, it directly impacts the patient's oral function and appearance. Mandibular reconstruction is an effective way to restore mandibular function and correct deformities. Ideal mandibular reconstruction aims to restore the mandibular's normal shape and structure, along with proper dentition and occlusion, and to restore normal function.

[0020] In the clinical treatment of jaw injuries, titanium plates can be used for long-term repair or temporary replacement. When selecting a titanium plate for implantation, the shape of the plate should be considered. Customizing a titanium plate to perfectly match the patient's jaw shape is more conducive to fixation of the injured jaw, while meeting structural requirements while minimizing maximum stress.

[0021] The main parameters of the personalized implant titanium plate include the thickness, angle, length and width of each side. Considering the standardization of process parameters, the length and width of each side are taken as fixed values. By applying the screening experiment, it is determined that the experimental factors in the optimization are angle (x1) and thickness (x2), such as Figure 2 shown.

[0022] The objective function is the maximum stress (y1). The thickness of medical titanium plates is usually 0.5-2.0 mm, and the angle parameter of personalized titanium plates is generally between 20-40 degrees.

[0023] Based on the above situation, the experimental factors and their levels are determined, as shown in the following table Step 2: Based on the optimization design problem, the central composite experimental design is used to generate the initial sample points.

[0024] A two-factor central composite design is used, requiring a total of 13 experiments. The experimental arrangement is shown in the following table No. x1 x2 y1 1 30 1.0 33.07 2 30 1.0 33.07 3 35 1.0 31.72 4 30 1.5 20.03 5 30 0.5 64.75 6 30 1.0 33.07 7 25 1.0 34.40 8 25 0.5 79.40 9 35 1.0 25.83 10 30 1.0 33.07 11 30 1.0 33.07 12 35 0.5 61.73 13 25 1.5 24.90

[0025] The left end of the titanium plate is simplified as a fixed constraint, and the right end bears the load to simulate the stress condition of the titanium plate during occlusion.

[0026] The magnitude and direction of mandibular muscle force vary under different occlusal modes, with the maximum resultant force generally being approximately 47.5 N. A 50 N vertical load was applied to the right end to simulate the force on the titanium plate.

[0027] Step 3: Call the finite element simulation program to obtain the response index corresponding to each set of experimental designs.

[0028] The elastic modulus of the material is 110 MPa and the Poisson's ratio is 0.3. The finite element simulation program is called to calculate the stress value of each experiment. Under the conditions of experiment 1, the Von Mises stress distribution is as follows: Figure 4 shown.

[0029] According to the experimental arrangement, obtain the stress distribution under each test condition and record the maximum stress value y1. The results are listed in the last column of the experimental arrangement table.

[0030] Step 4: Apply the least squares method to solve the coefficients of the approximate model expression.

[0031] Apply the least squares method to find the coefficient of y1 and obtain the approximate model equation under non-coding units.

[0032] Step 5: Perform a significance test on the obtained coefficients through variance analysis. If there are insignificant items, remove them and solve again until all coefficients are significant.

[0033] ANOVA Figure 5 As shown in Figure 2, the results of the variance analysis show that the model itself, the constant term, the linear term, the quadratic term and the interaction term are all significant.

[0034] Step 6: Construct a satisfaction function based on the characteristics of the problem.

[0035] The smaller the stress value of the implanted titanium plate, the better. The optimization goal is to minimize the stress. Therefore, in the satisfaction function, the maximum and minimum values ​​are obtained based on the maximum and minimum stress values ​​obtained in each experiment.

[0036] Step 7: Taking the maximum satisfaction function as the goal, use the simulated annealing algorithm to solve and obtain the optimal parameter value.

[0037] Substitute each value into the satisfaction function formula, find the parameter value that maximizes the satisfaction function, and obtain the optimization result and satisfaction value. The relationship between stress and design variables is as follows: Figure 6 According to the results of theoretical analysis, the optimized angle and thickness values ​​are obtained.

[0038] The advantages of the method of the present invention are as follows: 1. Analyze the design variables through screening experiments and select the variables that have a greater impact on the optimization target, thereby reducing the difficulty of the optimization problem; 2. Taking into account the requirements of individualization and strength of jaw repair implants, the stress value is minimized while meeting the performance requirements, reducing the risk of implant fracture and extending the service life of the implant; 3. By constructing an approximate model of the personalized implant instead of the real implant biomechanical model, the optimization process is accelerated and the computational complexity is reduced.

[0039] The above content further illustrates the present invention in conjunction with specific optimized implementation methods, but the present invention is not limited to the above specific implementation methods. For those skilled in the art to which the present invention belongs, many alternative forms can be made without departing from the scope of protection of the present invention and the claims, and these all fall within the scope of protection of the present invention.

Claims

1. A method for optimizing parameters of a personalized jaw restoration implant based on an approximate model, characterized by: First, a screening experiment is applied to determine the design variables that have a greater impact on the design objectives, and a second-order polynomial approximate model function of the mapping relationship between the corresponding implant thickness, angle and maximum stress value is established; then the central composite experimental design is applied to determine the experimental arrangement and generate sample points; finite element analysis is performed according to the experimental arrangement, and the objective function value corresponding to each sample point is calculated; the approximate model coefficients are solved; a significance test is performed on the obtained coefficients, and after removing the insignificant items, the solution is re-solved until all coefficients are significant; finally, a satisfaction function is constructed according to the characteristics of the problem; an intelligent optimization algorithm is used to solve the satisfaction function to obtain the optimal parameter value that minimizes stress. The method for optimizing the parameters of personalized mandibular repair implants based on an approximate model specifically includes the following steps: Step 1: Taking into account the requirements of manufacturing process standardization, reduce design variables, apply screening experiments to determine the main structural parameters that affect stress magnitude, and determine the design factors and their level numbers; Step 2: Based on the optimization design problem, the central composite experimental design is used to generate the initial sample points; Step 3: Call the finite element simulation program to obtain the response index corresponding to each set of experimental designs; Step 4: Apply the least square method to solve the coefficients of the approximate model expression; Step 5: Perform a significance test on the obtained coefficients through variance analysis. If there are insignificant items, remove them and solve again until all coefficients are significant. Step 6: Construct a satisfaction function based on the characteristics of the problem; Step 7: With the goal of maximizing the satisfaction function, the simulated annealing algorithm in the intelligent optimization algorithm is used to solve the problem and obtain the optimal parameter value that minimizes the stress.

2. The method for optimizing parameters of a personalized jaw repair implant based on an approximate model according to claim 1, characterized in that: In step 1, the approximate model adopts a second-order polynomial approximate model. The approximate model is a functional relationship between the design variables and the response quantity established on the basis of the experimental design. In the second-order polynomial approximate model, there are n independent experimental factors x i ( i = 1,2,…,n), obtain the corresponding sample points through experimental design, calculate the corresponding sample values, and the fitting approximate model is ； In the formula, β0 is the constant term to be determined, β i is the undetermined coefficient of the linear term, β ii is the coefficient of the quadratic term to be determined, β ij is the unknown coefficient of the interaction term. This model can replace the complex real model for analysis and optimization.

3. The method for optimizing parameters of a personalized jaw repair implant based on an approximate model according to claim 1, characterized in that: In step 2, the central composite design includes CCF (face-centered cubic central composite design), CCC (circumscribed central composite design), and CCI (nested central composite design). The experimental point distribution of the two factors CCC, CCF, and CCI is shown in Figure 3, from left to right: CCC, CCF, and CCI. The design variables are expressed in coded units. The distance from the center point of the design matrix to the high and low levels of the factor is ±1, and the distance from the axial point to the center is ±a. When a = (k) 1 / 2 When a = 1, the axial point is generally on the sphere. When a = 1, the axial point is on the cube. k is the number of design variables. The experimental design of this method uses CCF, and each factor requires three levels: ±1, 0.

4. The method for optimizing parameters of a personalized jaw repair implant based on an approximate model according to claim 1, characterized in that: In step 6, we hope that the target value is as small as possible, and the satisfaction function is ； Where, y i is the estimated value of the ith response, h i is the maximum value, l i is the minimum value, q i is any positive constant, which can be 1.

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