Porous implant design-oriented truss structure parametric modeling method based on hierarchical features

Abstract

The invention discloses a hierarchical feature-based porous implant design-oriented truss structure parameterization modeling method, which is characterized by comprising the following steps of: 1, representing hierarchical features of truss unit cells, respectively describing relative positions of nodes and a connection relationship between the nodes by adopting a normalized coordinate matrix and an edge set, representing a topological structure; geometric characteristic parameters including the size of a unit cell and the diameter of a rod piece are defined; 2, a truss unit cell parameterized modeling process is carried out, a truss unit cell topological framework and a three-dimensional entity model are generated in sequence based on hierarchical features, and topological feature and geometric feature parameters are supported and regulated. And 3, defining a periodic expansion coefficient of the porous structure in a three-dimensional space, and performing periodic expansion on the unit cells according to the expansion coefficient to obtain a truss porous structure model with a macrostructure. And 4, performing Boolean operation on the generated truss porous structure model and the implant model to finally obtain the porous implant. According to the method, independent regulation and control of topological configuration and geometric parameters are realized through hierarchical characteristic decomposition, and the design flexibility is improved. Meanwhile, the parametric modeling process is packaged into an automatic tool, rapid generation and parameter adjustment of the truss porous structure are supported, efficient porous implant design is achieved, and the method has important significance on large-scale popularization and clinical conversion of porous implants.

Description

Technical Field

[0001] The present invention relates to the intersection of computer-aided design and biomedical engineering, and in particular to a parameterized modeling method of a truss structure for porous implant design based on hierarchical features. Background Art

[0002] Porous implants are important medical devices for repairing or replacing bone defects. They play an irreplaceable role in orthopedic clinical treatment and are widely used in fracture fixation, joint replacement, spinal fusion, and bone defect repair after bone tumor resection. The comprehensive performance of porous implants depends to a large extent on the precise design of their internal structural parameters, including porosity (pore volume fraction), pore size (pore diameter), pore shape (such as sphere, cube, rhombus, etc.), pore gradient distribution, and pore connectivity. Among them, porosity directly affects the overall mechanical properties of the implant. Properly increasing the porosity can effectively reduce the elastic modulus and alleviate the stress shielding effect caused by excessively high elastic modulus. The pore size must meet the biological requirements of bone cell migration and angiogenesis to promote bone tissue regeneration.

[0003] Truss structures are a type of porous structure commonly used in the design of porous implants. They are usually composed of a periodically repetitive network of rods and can be modeled using CAD software. However, traditional CAD methods have many inconveniences when modeling such complex porous structures. The modeling process is highly dependent on manual operation, which is not only cumbersome and inefficient, but also difficult to achieve efficient regulation of key structural parameters such as porosity and pore size, and lacks design flexibility and scalability. With the continuous development of computer-aided design technology, parametric modeling methods have provided a powerful tool for the design of porous implants. This method makes the modeling process of porous structures more efficient, automated and controllable by establishing a mathematical relationship between geometric shape and structural parameters. Designers can flexibly adjust key parameters such as porosity, pore size, rod size and topology type according to biomechanical performance requirements, greatly improving design efficiency and accuracy. Summary of the Invention

[0004] A parametric modeling method for truss structures for porous implant design based on hierarchical features can solve the problems of traditional methods such as cumbersome operation, low design efficiency, high parameter coupling and difficulty in control, and poor design flexibility. To achieve the above goals, the present invention adopts the following technical solutions:

[0005] A parametric modeling method for truss structures for porous implant design based on hierarchical features includes the following steps:

[0006] Step 1: Hierarchical feature representation of truss cells. The connection relationship between truss cell nodes is established through the graph structure. The normalized coordinate matrix N and edge set E are used to describe the topological characteristics of the cell. The topological characteristic parameters are quantified using mathematical methods to make them independent of the geometric characteristic parameters. The geometric characteristic parameters of the top layer are defined, including the unit cell size c and the rod diameter d, and a quantitative relationship between the porosity and the geometric characteristic parameters is established.

[0007] Step 2: parametric modeling of truss unit cells;

[0008] Step 2a. Based on the topological feature parameters, traverse the edge set in the topological feature parameters, connect the corresponding node pairs, and obtain the topological skeleton of the truss unit cell in the unit design space.

[0009] Step 2b. Based on the geometric feature parameters, the nodes are scaled and transformed according to the unit cell size parameters to obtain the actual physical coordinates of each node, and the topological skeleton is mapped to the actual size; based on the rod diameter parameters, a cylindrical rod is generated to replace the topological skeleton.

[0010] Step 2c. Use Boolean operations to assemble the rods to obtain a three-dimensional solid model of the truss unit cell.

[0011] Step 2d. Adjust specific parameters as needed. If you modify topological feature parameters, return to step 2a; if you modify geometric feature parameters, return to step 2b.

[0012] Step 3: Establish macroscopic structural parameters based on the bounding box of the implant and define the periodic expansion coefficient (N) of the porous structure in three-dimensional space. x ,N y ,N z ), the unit cell is periodically expanded based on the expansion coefficient to obtain a truss porous structure model with a macroscopic structure.

[0013] Step 4: Perform Boolean operation on the generated truss porous structure model and the implant model to finally obtain the porous implant.

[0014] The present invention is beneficial in that it utilizes computer-aided design technology to achieve parametric design of porous implants in the field of biomedical engineering. Hierarchical feature decomposition enables independent control of topological configuration and geometric parameters, enhancing design flexibility. Furthermore, the parametric modeling process is encapsulated as an automated tool, supporting the rapid generation and parameter adjustment of truss porous structures, enabling efficient porous implant design. This is of great significance for the large-scale promotion and clinical translation of porous implants. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 This is a flow chart of the parametric modeling method of truss structure for porous implant design based on hierarchical features.

[0016] Figure 2 It is a schematic diagram of the topological characteristic parameters and geometric characteristic parameters of the truss unit cell (body-centered cubic).

[0017] Figure 3 It is a schematic diagram of macro-structural parameters. DETAILED DESCRIPTION

[0018] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0019] like Figure 1 As shown in FIG, a parametric modeling method of a truss structure for porous implant design based on hierarchical features includes the following steps:

[0020] Step 1: Hierarchical feature representation of truss cells, mathematically describe the topological features of truss cells through graph structure, such as Figure 2 As shown. The normalized coordinate matrix N is used to describe the relative position relationship of the nodes in space, and the edge set E is used to describe the connection relationship between the nodes. The normalized coordinate matrix and edge set are expressed as the following formula:

[0021]

[0022] E={(i,j)|1≤i<j≤k}

[0023] Define the geometric characteristic parameters of the top layer, such as Figure 2 As shown, it includes the unit cell size c and the rod diameter d, and establishes a quantitative relationship between porosity and geometric characteristic parameters. The truss unit cell is composed of cylindrical rods, and its solid volume is the sum of the volumes of all rods. The porosity calculation formula can be expressed as the following formula:

[0024]

[0025] Step 2: parametric modeling of truss unit cells;

[0026] Step 2a. Based on the topological feature parameters, traverse the edge set E. For each node pair (i, j), the corresponding node coordinate n can be extracted from the normalized matrix N. i and n j , connecting node pairs with straight line segments in three-dimensional space, and obtaining the topological skeleton of the truss unit cell in the unit design space.

[0027] Step 2b. Based on the geometric characteristic parameters, the actual coordinates of the nodes are determined by the coordinate matrix P after mapping the unit cell size c. For each node i∈{1,2,K,k}, its physical coordinate calculation formula is as follows:

[0028] p i =c·n i =(c·xi ,c·y i ,c·z i )

[0029] The edge set E describes the connection relationship of the rods. Each node pair (i, j) represents the two endpoints of a rod. The number of node pairs is the number of rods. The length and axial vector of the rod are determined by the two endpoints. Traverse the edge set E, and for each node pair (i, j), obtain the actual coordinates p of the two endpoints from the coordinate matrix P. i (x i ,y i ,z i ) and p j (x j ,y j ,z j ), the axial vector of the member Calculated as:

[0030]

[0031] Then take endpoint p i Starting from the axial direction Generate a cylindrical member with radius r = d / 2.

[0032] Step 2c. Use Boolean operations to assemble the rods to obtain a three-dimensional solid model of the truss unit cell.

[0033] Step 2d. Adjust specific parameters as needed. If you modify topological feature parameters, return to step 2a; if you modify geometric feature parameters, return to step 2b.

[0034] Step 3: Establish macroscopic structural parameters based on the bounding box of the implant and define the periodic expansion coefficient (N) of the porous structure in three-dimensional space. x ,N y ,N z ), based on the expansion coefficient, the unit cell is periodically expanded to obtain a truss porous structure model with a macroscopic structure. Figure 3 As shown in the figure, the spatial configuration of the truss porous structure usually adopts a three-dimensional orthogonal array as the basic arrangement paradigm. Its macroscopic parameter system is composed of structural dimension parameters and geometric control parameters: at the structural dimension level, the periodic expansion coefficients (N) of the three orthogonal axes x, y, and z in the Cartesian coordinate system are used. x ,N y ,N z ) defines the number of unit cell replications, thereby determining the spatial size of the porous structure; at the geometric control level, the unit cell characteristic size coefficient c is introduced m The scale parameters of all unit cells are uniformly controlled, and the rod diameter coefficient d is used. m The cross-sectional dimensions of the globally coordinated structural members. Size coefficient cm It has dual engineering semantics: one is to characterize the reference geometric scale of a single unit cell, and the other is to define the periodic step parameters of the unit cell array. m In essence, it constitutes the displacement increment modulus when the unit cell is extended along the Cartesian coordinate axis. Figure 2-3 As shown, when the three-dimensional unit cell array is in the rectangular enveloping domain [L x ,L y ,L z ], the spacing of the unit cells along the i-th axis is strictly equal to c m The mathematical expression of value can be described as:

[0035]

[0036] Among them, δ i Characterizes the distance between the centroids of the unit cell, that is, the periodic step parameter of the spatial array. The expansion coefficient is derived from this formula.

[0037] Step 4: The truss porous structure model generated based on the implant bounding box can be filled into the implant, and a porous implant is obtained by performing Boolean operations with the implant model.

Claims

1. A parametric modeling method for truss structures based on hierarchical features for porous implant design, characterized in that: The steps include: Step 1: Hierarchical feature representation of truss unit cells. Node connection relationships are established through a graph structure. The normalized coordinate matrix N and edge set E are used to describe the topological features. Geometric feature parameters including the unit cell size c and the rod diameter d are defined. Step 2: Parametric modeling of truss unit cells, including: Step 2a. Based on the topological feature parameters, traverse the edge set E to connect the normalized node pairs to generate a topological skeleton. Step 2b. Based on the geometric feature parameters, the nodes are scaled and transformed according to the unit cell size c to obtain physical coordinates; based on the rod diameter d, a cylindrical rod is generated to replace the topological skeleton. Step 2c. Assemble the rods through Boolean operations to form a unit cell solid model. Step 2d. Adjust specific parameters as needed. If you modify topological feature parameters, return to step 2a; if you modify geometric feature parameters, return to step 2b. Step 3: Define the three-dimensional periodic expansion coefficient according to the implant bounding box, and perform periodic array expansion on the unit cell to generate a macroscopic truss structure; Step 4: Perform Boolean operation on the truss structure and the implant model to obtain the porous implant.

2. The parameterized modeling method of truss structure for porous implant design based on hierarchical features according to claim 1, characterized in that: The topological feature parameters are independent of the geometric feature parameters. The normalized coordinate matrix N stores the relative positions of nodes in the unit design space, and the edge set E stores the connection relationship between node pairs.

3. The method according to claim 2, characterized in that The mathematical expressions of the normalized coordinate matrix N and edge set E are: E={(i,j)|1≤i<j≤k} 4. The method according to claim 1, wherein The calculation formula for the node physical coordinates in step 2 is: P=c·N Where N is the normalized coordinate and c is the unit cell size.

5. The method according to claim 1, wherein The porosity calculation formula is:

6. The method according to claim 1, characterized in that The three-dimensional period expansion coefficient in step 3 is determined by the following formula: Among them L i is the size of the implant bounding box, c m is the unit cell characteristic size coefficient, δ i is the array step size in each direction.

7. The method according to claim 6, characterized in that The unit cell characteristic size coefficient controls both the unit cell geometric size and the periodic step parameters of the unit cell array.

8. The method according to claim 1, characterized in that In step three, the periodic array expansion adopts a three-dimensional orthogonal arrangement paradigm, and the layout spacing of the unit cells along the Cartesian coordinate axis is equal to the unit cell characteristic size coefficient.

9. The method according to claim 1, characterized in that The rod generation method in step 2 includes: calculating the axial vector of the rod; generating a cylinder of a specified diameter along the axial direction based on the end point; and batch generating all rod entities through a parametric modeling tool.

10. The method according to claim 1, characterized in that The parametric modeling process is encapsulated as an automated design module, which supports independent adjustment and real-time update of topological parameters and geometric parameters.

Images