A method for optimizing retention of a dental implant titanium alloy bridge for edentulous jaws

Abstract

The application relates to the technical field of dental bridge construction, in particular to a retention optimization method for a dental implant titanium alloy bridge for an edentulous jaw. The method comprises the following steps: constructing a digital model of the bridge; constructing a three-dimensional graph structure based on the point cloud density and position corresponding to the initial point position in the digital model; obtaining a stress coefficient according to the position offset of a vertex in the three-dimensional graph structure before and after simulation, the distance between the vertex and adjacent vertices of the vertex and the position offset of the adjacent nodes of the vertex before and after simulation, screening the offset vertex, adjusting the position of the offset vertex according to the position of the offset vertex before and after simulation and the stress coefficient to obtain a new graph structure; iteratively adjusting the corresponding positions in the graph structure according to the stress coefficient of the offset vertex in the new graph structure, and establishing an iteration function in the adjustment process; obtaining a target model based on the distribution characteristics of the iteration function value, and then manufacturing the dental implant titanium alloy bridge. The application improves the rationality of the structure design of the dental implant titanium alloy bridge and improves the wearing experience of the patient.

Description

Technical Field

[0001] This invention relates to the field of dental implant bridge technology, and specifically to a retention optimization method for titanium alloy bridges for edentulous dental implants. Background Technology

[0002] Dental implants for edentulous jaws are a dental functional restoration technique that uses artificial implants to replace missing teeth. During the restoration process, titanium alloy bridges are usually required for fixation, connecting the implant with adjacent teeth or other implants to form a mechanically unified structure. This reduces the burden on individual implants and extends their lifespan. In order to design implant bridges that conform to the patient's anatomy more precisely, digital modeling and computer-aided design technologies are currently used to structurally design and optimize the titanium alloy bridge fixation components to meet the patient's needs as much as possible.

[0003] However, when designing the structure of titanium alloy bridge fixation components for dental implants using computer-aided design (CAD), the focus is more on the patient's facial features and the restoration of dental function. This may result in unreasonable bridge structure, leading to uneven stress distribution and consequently, problems such as loosening or falling out of the dental implant. Summary of the Invention

[0004] To address the problem of unreasonable structural design in existing methods for designing titanium alloy bridges for dental implants, the present invention aims to provide a retention optimization method for titanium alloy bridges for edentulous jaw implants. The specific technical solution adopted is as follows: This invention provides a retention optimization method for titanium alloy bridges used in edentulous dental implants, the method comprising the following steps: Constructing a digital model of the patient's dental implant titanium alloy bridge; Based on the point cloud density characteristics and spatial location corresponding to the initial points in the digital model, a three-dimensional graph structure is constructed; according to the positional offset of each vertex before and after the simulation, the distance between each vertex and its neighboring vertices, and the positional offset of each vertex's neighboring nodes before and after the simulation, the force coefficient of each vertex is obtained. Based on the force coefficient, offset vertices are selected. According to the relative positions of the offset vertices before and after the simulation and the force coefficient, the positions of the offset vertices in the 3D graph structure are adjusted to obtain a new graph structure. The corresponding positions in the graph structure are iteratively adjusted according to the force coefficient of the offset vertices in the new graph structure, and an iterative function is established during the adjustment process. The target model of the dental implant bridge is obtained based on the distribution characteristics of the function values ​​of the iterative function; the titanium alloy dental implant bridge is then fabricated based on the target model.

[0005] Preferably, the step of constructing a three-dimensional graph structure based on the point cloud density features and spatial locations corresponding to the initial points in the digital model includes: Obtain the Gaussian curvature of each initial point in the digital model; The point cloud density corresponding to each initial point is determined based on the Gaussian curvature, and the Gaussian curvature is positively correlated with the point cloud density. Target points are selected based on the Gaussian curvature and spatial location of each initial point; The target points are used as vertices, and the spatial connection relationship between the target points is constructed based on the triangulation algorithm to obtain the connecting edges between the vertices. All vertices are connected using the connecting edges to obtain the three-dimensional graph structure.

[0006] Preferably, the step of filtering target points based on the Gaussian curvature and spatial location of each initial point includes: The ratio between the absolute value of the Gaussian curvature of each initial point and the maximum value of the absolute value of the Gaussian curvature of all initial points is denoted as the first ratio of each initial point; the structure coefficient of each initial point is obtained by combining the first ratio and the degree centrality of each initial point in its nearest neighbor graph. Based on the structural coefficients and the spatial positions of each initial point in the digital model, it is determined whether each initial point is a target point.

[0007] Preferably, determining whether each initial point is a target point based on the structural coefficients and the spatial positions of each initial point in the digital model includes: Clustering is performed on all initial points based on the Euclidean distance between the attribute arrays of the initial points, resulting in several clusters and discrete initial points; the attribute arrays consist of structural coefficients and spatial coordinates. The initial points within clusters with an average structure coefficient greater than the structure threshold, along with the discrete initial points, are used as target points.

[0008] Preferably, the step of obtaining the force coefficient of each vertex based on the positional offset of each vertex in the three-dimensional graph structure before and after the simulation, the distance between each vertex and its neighboring vertices, and the positional offset of each vertex's neighboring nodes before and after the simulation includes: For any vertex in the aforementioned three-dimensional graph structure: By combining the Euclidean distance between any vertex and each of its neighboring vertices, the displacement of each neighboring node of any vertex before and after the simulation, and the displacement of any vertex, the force coefficient of any vertex is obtained. The Euclidean distance, the displacement of each neighboring node before and after the simulation, and the displacement of any vertex are all positively correlated with the force coefficient.

[0009] Preferably, the step of filtering offset vertices based on the force coefficient includes: Vertices in the three-dimensional structure diagram whose force coefficient is greater than a preset force threshold are designated as offset vertices.

[0010] Preferably, adjusting the position of the offset vertex in the 3D graph structure according to the relative position of the offset vertex before and after the simulation and the force coefficient to obtain a new graph structure includes: Obtain the 3D coordinates of the offset vertex before and after the simulation, and combine them with the 3D coordinates to obtain the offset vector of the offset vertex in the direction from before to after the simulation. The product of the force coefficient of the offset vertex and the offset vector is used as the adjustment vector of the offset vertex; the three-dimensional coordinates of the endpoint of the offset vertex in the direction corresponding to the adjustment vector are obtained and denoted as the migration coordinates; the migration coordinates are used as the new three-dimensional coordinates of the offset vertex to obtain a new graph structure.

[0011] Preferably, establishing the iterative function during the adjustment process includes: For any iteration: Obtain the degree of dispersion of the force coefficients of all vertices in the new graph structure obtained after any one iteration; An iterative function is constructed by combining the number of vertices in the new graph structure obtained after any iteration, the average force coefficient of all vertices in the new graph structure obtained after any iteration, and the degree of dispersion.

[0012] Preferably, the method of obtaining the target model of the cable tray based on the distribution characteristics of the function values ​​of the iterative function includes: The elbow method is used to obtain the inflection points of the function values ​​of all iterative functions, and the new graph structure obtained by the number of iterations corresponding to the inflection points is taken as the final graph structure. The target model of the cable tray is obtained based on the final graph structure.

[0013] Preferably, obtaining the dispersion of the force coefficients of all vertices in the new graph structure obtained after any iteration includes: using the standard deviation of the force coefficients of all vertices in the new graph structure obtained after any iteration as the dispersion.

[0014] The present invention has at least the following beneficial effects: This invention first constructs a digital model of a titanium alloy dental implant framework for the patient. To ensure accurate stress analysis of the framework structure while simplifying the analysis of the stress structure of the digital model, the invention extracts the structure of the digital model to form a corresponding three-dimensional graph. Then, based on the positional offset of vertices before and after simulation, the distance between vertices and their neighboring vertices, and the positional offset of neighboring nodes of vertices before and after simulation, the stress situation of each vertex is analyzed, and the stress coefficient of each vertex is obtained. Subsequently, offset vertices are screened, and the digital model of the dental implant framework is iteratively adjusted according to the stress coefficient of the offset vertices. This ensures that after multiple adjustments, the dental implant framework maintains a certain degree of stress uniformity under different stress environments, thereby avoiding problems such as loosening and falling out of dental implants due to unreasonable structure during use. This improves the fixation effect of the dental implant framework on the dental implant and the uniformity of stress during use, thus enhancing the patient experience. Attached Figure Description

[0015] To more clearly illustrate the technical solutions and advantages in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0016] Figure 1 A flowchart illustrating a retention optimization method for a titanium alloy bridge for edentulous dental implants provided in an embodiment of the present invention; Figure 2 This is a distribution diagram of the iterative function values ​​provided in an embodiment of the present invention. Detailed Implementation

[0017] To further illustrate the technical means and effects adopted by the present invention to achieve the intended purpose, the following detailed description, in conjunction with the accompanying drawings and preferred embodiments, provides a method for optimizing the retention of titanium alloy bridges for edentulous dental implants based on the present invention.

[0018] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0019] The following description, in conjunction with the accompanying drawings, details the specific scheme of the retention optimization method for titanium alloy bridges used in edentulous dental implants provided by this invention.

[0020] An example of a retention optimization method for titanium alloy bridges used in edentulous dental implants: This embodiment proposes a retention optimization method for titanium alloy bridges used in edentulous dental implants, such as... Figure 1 As shown, the retention optimization method for a titanium alloy bridge for edentulous dental implants in this embodiment includes the following steps: Step S1: Construct a digital model of the patient's dental implant titanium alloy bridge.

[0021] Titanium alloy bridges for edentulous dental implants typically require CAD design. In general, when performing dental implants, in order to ensure the proper function of the teeth and eliminate the impact of tooth loss on facial aesthetics, the focus is often on meeting these conditions. This can lead to insufficient consideration of the stress structure of the bridge, resulting in problems such as insufficient connection and easy loosening, which affects the long-term effect of the implant restoration and the patient's comfort.

[0022] In order to ensure that the dental implant framework structure is reasonable and to avoid structural problems caused by uneven stress distribution, the framework structure needs to be optimized. However, since the dental implant framework is designed according to the actual needs of the patient, the patient's oral cavity must first be scanned to create a corresponding digital model of the dental implant framework.

[0023] First, an intraoral scanner is used to perform a three-dimensional scan of the patient's edentulous alveolar ridge and surrounding soft tissues to obtain oral surface morphology data. At the same time, a cone-beam computed tomography (CBCT) device is used to perform a tomographic scan of the patient's jawbone to obtain three-dimensional data on bone tissue structure, bone density distribution, and the location of important anatomical structures. The intraoral scan data and CBCT scan data are then imported into professional oral medical image processing software (such as OsiriX). Image registration and fusion are performed through feature point matching and iterative nearest point algorithms to establish a three-dimensional digital model of the jawbone-alveolar ridge that includes information on both soft and hard tissues.

[0024] Then, based on the three-dimensional digital model of the jawbone and alveolar ridge, the implant placement was planned in CAD design software. According to the jawbone bone mass distribution, bone density characteristics and biomechanical requirements, the number of implants and the optimal implantation position, angle and depth parameters were determined. The patient's jawbone CT scan data was processed using reverse engineering technology to establish a virtual implantation model that conforms to the patient's anatomical characteristics, and the rationality of the positional relationship between the implants was verified. On this basis, the basic geometric contour of the titanium alloy bridge was designed to ensure that the connection interface between the bridge and each implant abutment is precisely matched to achieve passive placement of the bridge. At the same time, the gingival contour and tooth arrangement of the bridge were optimized according to the patient's occlusal relationship, facial morphology and aesthetic needs.

[0025] Thus, this embodiment has constructed a digital model of the patient's dental implant titanium alloy bridge.

[0026] Step S2: Based on the point cloud density features and spatial positions corresponding to the initial points in the digital model, construct a three-dimensional graph structure; according to the positional offset of each vertex before and after the simulation, the distance between each vertex and its neighboring vertices, and the positional offset of each vertex's neighboring nodes before and after the simulation, obtain the force coefficient of each vertex.

[0027] Because the location of dental implants varies from patient to patient, the designed bridge structure will differ. Therefore, due to the influence of the bridge structure differences, it is necessary to establish a corresponding stress simulation strategy for the stress analysis of the bridge structure during the digital model design and optimization process, based on the specific bridge structure characteristics of different patients. This will allow for the optimization and adjustment of the implant bridge structure in the digital model to ensure uniform stress distribution.

[0028] Since the cable tray digital model is a complex three-dimensional structure with multiple supports and complex force paths, it is not easy to directly and accurately simulate the complex forces during chewing using the cable tray digital model. In this embodiment, in order to ensure accurate stress analysis of the cable tray structure while realizing simple analysis of the stress structure of the cable tray digital model, thereby identifying stress concentration areas and discovering potential weak points, and providing a basis for subsequent structural optimization, the structure of the cable tray digital model is extracted to form the corresponding three-dimensional structure.

[0029] First, points are selected in the digital model of the cable tray, and the spatial structure of these points is used to form a three-dimensional graph structure. Some points in the digital model of the cable tray are more advantageous for stress analysis than others, and these points are spatially related, forming a three-dimensional mechanical structure. Therefore, in this embodiment, these points are extracted from the digital model of the cable tray, and the corresponding three-dimensional graph structure is constructed based on their spatial location and structural relationships within the digital model.

[0030] Specifically, an adaptive mesh generation algorithm is used to generate an initial point cloud on the surface of the digital model of the cable tray. The point cloud density is automatically adjusted according to the local curvature of the cable tray. Uniform sampling is performed in the initial point cloud to obtain several initial points.

[0031] Then, the Gaussian curvature of each initial point in the digital model is obtained; and the point cloud density corresponding to each initial point is determined based on the Gaussian curvature. The Gaussian curvature and the point cloud density are positively correlated. The positive correlation means that the dependent variable increases as the independent variable increases and decreases as the independent variable decreases. It can be an additive relationship, a multiplicative relationship, etc., which is determined by the actual application.

[0032] As a concrete example, for any initial point, As the point cloud density corresponding to this initial point, This represents the Gaussian curvature at the initial point. The preset base point cloud density, This represents the normalization function, and 2 is a preset scaling factor. In this embodiment... The value is 10, and in specific applications, implementers can set it according to the specific circumstances. Using this method, the point cloud density corresponding to each initial point can be obtained.

[0033] Then, based on the spatial location and structural characteristics of the initial point, the structural coefficient of the initial point will be obtained.

[0034] Specifically, the absolute value of the Gaussian curvature of each initial point is calculated; the degree centrality of each initial point in its nearest neighbor graph is obtained; the ratio between the absolute value of the Gaussian curvature of each initial point and the maximum value of the absolute values ​​of the Gaussian curvature of all initial points is denoted as the first ratio of each initial point; and the structure coefficient of each initial point is obtained by combining the first ratio and the degree centrality of each initial point in its nearest neighbor graph.

[0035] As a concrete example, the specific calculation method for the structure coefficient is given. The structure coefficient of the i-th initial point can be expressed as: in, This represents the structural coefficient of the i-th initial point. Represents the Gaussian curvature of the i-th initial point; This represents the Gaussian curvature of the j-th initial point; Represents the initial set of points; Indicate the degree centrality of the i-th initial point in its k-nearest neighbor graph; Represents the normalization function. Indicates the absolute value sign. This represents the function for finding the maximum value.

[0036] The structural coefficient describes the degree to which the corresponding initial point represents the stress structure of the dental implant bridge in the digital model. A larger structural coefficient indicates a better representation of the stress characteristics at the corresponding location on the implant bridge, resulting in a more accurate representation of the stress situation during subsequent stress simulations and providing greater reference value for bridge structure optimization. In force transmission, the topological location of the point (e.g., whether it is located on the main force flow path) directly affects the force distribution. It should be noted that the value of k in the k-nearest neighbor graph is set by the implementer according to specific circumstances; this embodiment will not elaborate further.

[0037] This represents the absolute value of the Gaussian curvature at the j-th initial point, used to eliminate the influence of the sign of the Gaussian curvature. A positive Gaussian curvature indicates a convex surface, and a negative one indicates a concave surface, but the degree of stress concentration depends on the bending amplitude.

[0038] The first ratio represents the initial point i, reflecting the local curvature of the surface at that point. The greater the curvature, the more drastic the surface change. In dental implant bridge structures, high-curvature areas (such as bridge corners and connections) are prone to stress concentration points, leading to uneven stress distribution and potentially causing loosening or detachment. Degree centrality reflects the point's ability to act as a hub connecting other points; the higher the value, the more critical the point is in the local network and the more likely it is to bear the main force transmission path. It should be noted that, as with bridge structures, there will not be a situation where the Gaussian curvature of all initial points is zero; therefore, the denominator in the formula for calculating the structural coefficients will not be zero.

[0039] An array of structural coefficients and spatial coordinates of the initial points is used as the attribute array of the initial points, with each initial point having its own corresponding attribute array. The Euclidean distance between the attribute arrays of the initial points is used as the distance metric for the DBSCAN algorithm. The DBSCAN clustering algorithm is then used to cluster all the initial points, resulting in several clusters and discrete initial points. The average structural coefficient of all initial points in each cluster is obtained. Clusters with an average structural coefficient greater than a structural threshold are designated as target clusters, and the initial points in these target clusters are designated as target points. Additionally, for discrete initial points, those with a structural coefficient greater than the structural threshold are also designated as target points. In this embodiment, the structural threshold is 0.7; however, in specific applications, the implementer can set this threshold according to the specific circumstances.

[0040] Using the above method, multiple target points were selected, and these target points were used as vertices. Based on the triangulation algorithm, the spatial connection relationship between the target points was constructed to obtain the connecting edges between the vertices. Then, all the target points used as vertices were connected using all the connecting edges to obtain a three-dimensional graph structure.

[0041] Under different stress environments, the specific response of dental implant bridges to the forces generated by teeth chewing varies. Consequently, the degree of stress concentration at different locations of the dental implant bridge also differs under different stress responses. Therefore, in order to ensure that the dental implant bridge maintains a certain degree of stress uniformity under various stress environments and avoids a large degree of stress concentration, it is necessary to conduct stress simulation analysis based on the stress environment when optimizing the bridge structure.

[0042] First, a three-dimensional graph structure and a three-dimensional digital model of the jawbone-alveolar ridge are established in Ansys software (an existing modeling and simulation software). Then, a three-dimensional simulation is performed using Ansys software. During the three-dimensional simulation, the spatial position changes of the vertices in the three-dimensional graph structure are obtained during the stress simulation analysis of the three-dimensional graph structure, and the stress coefficient of each vertex is calculated.

[0043] Specifically, when performing a 3D simulation in Ansys software, the Euclidean distance between the 3D coordinates of each vertex before and after the simulation is obtained, and this Euclidean distance is used as the displacement of each vertex.

[0044] For any vertex in the constructed 3D graph structure: First, in the 3D graph structure, starting from the given vertex, a depth-first search algorithm is used to traverse along the edges between vertices in the 3D graph structure to obtain the shortest search path from the given vertex to other vertices. Vertices whose shortest search path contains no more than a preset threshold number of edges are considered as the vertex's neighboring vertices. In this embodiment, the preset threshold number is 10; in specific applications, the implementer can set it according to the specific circumstances.

[0045] Then, by combining the Euclidean distance between the vertex and each of its neighboring vertices, the displacement of each neighboring node before and after the simulation, and the displacement of the vertex, the stress coefficient of the vertex is obtained. The Euclidean distance, the displacement of each neighboring node before and after the simulation, and the displacement of the vertex are all positively correlated with the stress coefficient.

[0046] Among them, a positive correlation means that the dependent variable increases as the independent variable increases, and the dependent variable decreases as the independent variable decreases. It can be an additive relationship, a multiplicative relationship, etc., which is determined by the actual application.

[0047] In this embodiment, a specific formula for calculating the force coefficient is given. The force coefficients at each vertex can be expressed as: in, Indicates the first The force coefficient at each vertex; Indicates the first The displacement of each vertex; Indicates the first The number of neighboring vertices of a vertex; Indicates the first The vertex and its first vertex Euclidean distance between neighboring vertices; Indicates the first The vertex of the first vertex The displacement of the nearest vertex; This represents the normalization function.

[0048] The force coefficient is used to describe the degree of displacement change of the local area of ​​the corresponding vertex under periodic pressure. The larger the value of the force coefficient, the greater the degree of displacement of the corresponding position under periodic pressure. This indicates that the vertex has a serious positional conflict with the patient's jawbone-alveolar ridge three-dimensional digital model. In actual use, the bridge may loosen due to the long-term uneven pressure on the vertex. Therefore, the position of the vertex needs to be adjusted in the future to reduce the degree of displacement.

[0049] Step S3: Based on the force coefficient, filter the offset vertices; according to the relative positions of the offset vertices before and after the simulation and the force coefficient, adjust the positions of the offset vertices in the three-dimensional graph structure to obtain a new graph structure; according to the force coefficient of the offset vertices in the new graph structure, iteratively adjust the corresponding positions in the graph structure, and establish an iterative function during the adjustment process.

[0050] Next, based on the stress coefficients of each vertex, the corresponding regions in the digital model of the cable tray corresponding to the 3D graph structure are iteratively adjusted, and an iterative function is established, with the numerical change of the iterative function used as the termination condition for the iteration.

[0051] Specifically, vertices in the 3D structure diagram whose force coefficient is greater than a preset force threshold are designated as offset vertices. In this embodiment, the preset force threshold is 0.7; however, in specific applications, the implementer can set it according to the specific circumstances.

[0052] For any offset vertex, obtain its 3D coordinates before and after the simulation. Following the direction from before to after the simulation, and combining this with the 3D coordinates, obtain the offset vector of the offset vertex. That is, the direction of the offset vector is from its position before the simulation to its position after the simulation, and the magnitude of the offset vector is the displacement of the offset vertex. The product of the force coefficient of the offset vertex and its offset vector is used as the adjustment vector for that offset vertex. Using the 3D coordinates of the offset vertex before the simulation as the starting point of the adjustment vector, obtain the 3D coordinates of the endpoint of the offset vertex in the direction corresponding to the adjustment vector, and record this as the migration coordinates. Use the migration coordinates as the new 3D coordinates of the offset vertex. Using the above method, adjust the positions of all offset vertices to obtain a new graph structure.

[0053] Furthermore, the new graph structure was used in Ansys software to simulate the jawbone-alveolar ridge three-dimensional digital model again, and the three-dimensional coordinate adjustment process described above was repeated, with an iterative function established during the adjustment process.

[0054] For any given iteration: the standard deviation of the force coefficients of all vertices in the new graph structure obtained after that iteration. This standard deviation characterizes the dispersion of the force coefficients of the vertices; the larger the value, the more dispersed the distribution of the force coefficients of the vertices. Combining the number of vertices in the new graph structure obtained after that iteration, the average force coefficient of all vertices in the new graph structure obtained after that iteration, and the aforementioned standard deviation, an iterative function is constructed.

[0055] As a concrete example, the specific expression for the iteration function is given, the first... The iteration function after the nth iteration can be expressed as: in, Indicates the first The function value of the iterative function after the nth iteration; Indicates the first The number of offset vertices in the new 3D graph structure obtained after the iteration; Indicates the first The average force coefficient of all vertices in the new graph structure obtained after the next iteration; Indicates the first The standard deviation of the force coefficients of all vertices in the new graph structure obtained after the next iteration; This indicates the preset first adjustment parameter.

[0056] In this embodiment, a preset first adjustment parameter is introduced into the iteration function to prevent the denominator from being 0. In this embodiment, the preset first adjustment parameter is 0.01. In specific applications, the implementer can set it according to the specific situation.

[0057] The iteration function value reflects the degree of structural inconsistency that may exist in the new 3D graph structure after each iteration. The lower the value of the iteration function, the smaller the degree of vertex offset in the new 3D graph structure. In this case, the dental implant bridge corresponding to the 3D graph structure fits the jawbone-alveolar ridge 3D digital model more closely. During the patient's use, the force on each position of the dental implant bridge can be more uniform, thereby reducing the probability of dental implant loosening and falling out.

[0058] Using the above method, the value of the iterative function for each iteration can be obtained.

[0059] Step S4: Obtain the target model of the dental implant based on the distribution characteristics of the function values ​​of the iterative function; fabricate the titanium alloy dental implant bridge according to the target model.

[0060] In this embodiment, the iterative function value for each iteration is obtained in step S3. Next, the best digital model will be selected based on the iterative function value, and the corresponding titanium alloy cable tray will be obtained using 3D printing technology.

[0061] Specifically, a two-dimensional Cartesian coordinate system is established, with the iteration number as the horizontal axis and the iteration function value as the vertical axis. The iteration function value obtained after each iteration is input into the two-dimensional Cartesian coordinate system to obtain a scatter plot of the iteration function, as shown below. Figure 2 As shown.

[0062] Then, the elbow method is used to obtain the inflection points of the iterative function values ​​in a two-dimensional Cartesian coordinate system. The new graph structure corresponding to the iteration number at the inflection point is taken as the final graph structure. It should be noted that if there are multiple inflection points, the new graph structure obtained at the iteration number corresponding to the first inflection point is taken as the final graph structure.

[0063] Finally, the final graphic structure is restored to the corresponding digital model of the dental implant, which is the target model. The target model is then used as input to the 3D printing equipment, which produces the corresponding titanium alloy dental implant bridge.

[0064] Thus, the method provided in this embodiment has been used to optimize the titanium alloy bridge for dental implants in patients.

[0065] This embodiment first constructs a digital model of the patient's titanium alloy dental implant framework. To ensure accurate stress analysis of the framework structure while simplifying the analysis of the stress structure of the digital model, this embodiment extracts the structure of the digital model to form a corresponding three-dimensional graph. Then, based on the positional offset of vertices before and after simulation, the distance between vertices and their neighboring vertices, and the positional offset of neighboring nodes of vertices before and after simulation, the stress situation of each vertex is analyzed, and the stress coefficient of each vertex is obtained. Subsequently, offset vertices are screened, and the digital model of the dental implant framework is iteratively adjusted according to the stress coefficient of the offset vertices. This ensures that after multiple adjustments, the dental implant framework maintains a certain degree of stress uniformity under different stress environments, thereby avoiding problems such as loosening and falling out of dental implants due to unreasonable structure during use. This improves the fixation effect of the dental implant framework on the dental implant and the uniformity of stress during use, thus enhancing the patient experience.

[0066] It should be noted that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for optimizing the retention of titanium alloy bridges for edentulous dental implants, characterized in that, include: Constructing a digital model of the patient's dental implant titanium alloy bridge; Obtain the Gaussian curvature of each initial point in the digital model; determine the point cloud density corresponding to each initial point based on the Gaussian curvature, as Gaussian curvature and point cloud density are positively correlated; denote the ratio between the absolute value of the Gaussian curvature of each initial point and the maximum absolute value of the Gaussian curvature of all initial points as the first ratio of each initial point; combine the first ratio and the degree centrality of each initial point in its nearest neighbor graph to obtain the structure coefficient of each initial point; cluster all initial points based on the Euclidean distance between the attribute arrays of the initial points to obtain several clusters and discrete initial points; the attribute array consists of the structure coefficient and spatial coordinates; and select the initial points with an average structure coefficient greater than the specified value. Initial points within the clusters with thresholds and discrete initial points are used as target points. These target points are then used as vertices, and a spatial connection relationship between them is constructed based on a triangulation algorithm to obtain connecting edges between vertices. All vertices are then connected using these connecting edges to obtain a 3D graph structure. For any vertex in the 3D graph structure: the force coefficient of any vertex is obtained by combining the Euclidean distance between any vertex and each of its neighboring vertices, the displacement of each neighboring node before and after the simulation, and the displacement of any vertex. The Euclidean distance, the displacement of each neighboring node before and after the simulation, and the displacement of any vertex are all positively correlated with the force coefficient. The process involves selecting offset vertices based on their stress coefficients, obtaining their 3D coordinates before and after the simulation, and then using these coordinates to determine their offset vectors. The product of the stress coefficient and the offset vector is used as the adjustment vector. The 3D coordinates of the endpoint of the offset vertex in the direction corresponding to the adjustment vector are then obtained and denoted as the migration coordinates. These migration coordinates are used as the new 3D coordinates of the offset vertex, resulting in a new graph structure. The corresponding positions in the graph structure are iteratively adjusted based on the stress coefficients of the offset vertices in the new graph structure. For any given iteration, the dispersion of the stress coefficients of all vertices in the new graph structure obtained after any iteration is obtained. Finally, an iterative function is constructed by combining the number of vertices in the new graph structure obtained after any iteration, the average stress coefficient of all vertices in the new graph structure obtained after any iteration, and the dispersion. The target model of the dental implant bridge is obtained based on the distribution characteristics of the function values ​​of the iterative function; the titanium alloy dental implant bridge is then fabricated based on the target model. An adaptive mesh generation algorithm is used to generate an initial point cloud on the surface of the digital model of the cable tray. The point cloud density is automatically adjusted according to the local curvature of the cable tray. Uniform sampling is performed in the initial point cloud to obtain several initial points.

2. The retention optimization method for a titanium alloy bridge for edentulous dental implants according to claim 1, characterized in that, Offset vertices are selected based on stress coefficients, including: Vertices in the 3D structure diagram whose stress coefficient is greater than a preset stress threshold are used as offset vertices.

3. The retention optimization method for a titanium alloy bridge for edentulous dental implants according to claim 1, characterized in that, The target model of the cable tray is obtained based on the distribution characteristics of the function values ​​of the iterative function, including: The elbow method is used to obtain the inflection points of the function values ​​of all iterative functions, and the new graph structure obtained by the number of iterations corresponding to the inflection points is taken as the final graph structure. The target model of the cable tray is obtained based on the final graph structure.

4. The retention optimization method for a titanium alloy bridge for edentulous dental implants according to claim 3, characterized in that, Obtain the dispersion of the force coefficients of all vertices in the new graph structure obtained after any iteration, including: using the standard deviation of the force coefficients of all vertices in the new graph structure obtained after any iteration as the dispersion.

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