Customized crown design method based on template matching and mechanical property simulation optimization

Abstract

The application belongs to the technical field of digital medical treatment, image processing and digital modeling, and discloses a customized dental crown design method based on template matching and mechanical property simulation optimization. Specifically, the method comprises six steps of data preprocessing, statistical shape model construction, conditional shape model construction, template matching, neck margin line adhesion and dental crown internal hollow design. The existing adjacent teeth of the dental site to be designed are used as shape references to solve the problem of missing dental crown design. The application is based on a dental template library scanned by an oral cavity, adopts a conditional shape model to learn the shape correlation between the target dental crown and the surrounding teeth, so that the dental crown and the surrounding teeth are optimally shape-fitted, and the dental crown is further sutured with the patient's abutment through the neck margin line. The application also designs the internal structure of the dental crown prosthesis to be hollow, uses mechanical simulation as a means to optimize the porosity of the hollow and the distribution direction of the support structure, and avoids shortening the service life of the dental crown due to excessive local stress concentration.

Description

Technical Field

[0001] This invention relates to the fields of digital healthcare, image processing technology, and digital modeling technology, and in particular to a customized dental crown design method based on template matching and mechanical performance simulation optimization. Background Technology

[0002] With the growing awareness of health and the improvement of medical standards, the global demand for dental restoration is rapidly expanding. As big data, artificial intelligence, and other technologies continue to integrate with dental care, the digitalization of dental care is accelerating, and computer-aided design (CAD) and computer-aided manufacturing (CAM) technologies are increasingly being applied to the field of digital dental restoration.

[0003] Currently, clinical practice mainly relies on manual software operation for the design of dental crown restorations. This involves adjusting standard crowns to suit the patient's dentition morphology and occlusal relationship, a time-consuming and labor-intensive process with poor objectivity. To further improve the efficiency and accuracy of digital dental crown restoration design, some studies on automated digital design of dental crown restorations based on traditional algorithms or deep learning have been proposed, such as "Zhang C., Statistical Reconstruction Algorithm for Restoring Broken Tooth Surface Based on Occupation Spatial Constraint, JME.52(2016)165. https: / / doi.org / 10.3901 / JME.2016.01.165." and "X.Jiang, N.Dai, X.Cheng, J.Wang, Q.Peng, H.Liu, C.Cheng, Robust tooth surface reconstruction by iterative deformation, Computers in Biologics and Medicine.68(2016)90–100.https: / / doi.org / 10.1016 / j.compbiomed.2015.11.001.","F.Yuan,N.Dai,S.Tian,B.Zhang,Y.Sun,Q.Yu,H.Liu,Personalized design technique for the dental occlusalsurface based on conditional gene rative adversarial networks,Int J NumerMeth Biomed Engng.36(2020).https: / / doi.org / 10.1002 / cnm.3321.","S.Tian,M.Wang,N.Dai,H.Ma,L.Li,L.Fior enza,Y.Sun,Y.Li,DCPR-GAN: Dental Crown ProsthesisRestoration Using Two-Stage Generative Adversarial Networks,IEEEJ.Biomed.Health Inform.26(2022)151–160.https: / / doi.org / 10.1109 / JBHI.2021.3119394.”However, preserving anatomical features such as developmental grooves and ridges during automated crown design remains a highly challenging task. While some current algorithms have achieved occlusal surface reconstruction of crowns with anatomical features, they have not solved the problem of matching the crown with adjacent teeth and prepared parts, resulting in an incomplete restoration design process that cannot be readily applied in clinical practice. Summary of the Invention

[0004] This invention proposes a customized crown design method based on template matching and mechanical performance simulation optimization. It is an automatic design algorithm for full-crown restorations, utilizing a tooth template library from oral scans. A conditional shape model is used to learn the shape correlation between the target crown and surrounding teeth, thereby achieving optimal shape fit between the crown and the surrounding teeth. Further deformation is employed to ensure the crown aligns with the cervical margin of the patient's abutment teeth. This invention also incorporates a hollow design for the internal structure of the crown restoration, using mechanical simulation to optimize the porosity of the hollow design and the distribution direction of the support structure, preventing the crown from experiencing shortened lifespan due to excessive localized stress concentration.

[0005] The technical solution of the present invention is as follows: a customized crown design method based on template matching and mechanical performance simulation optimization, comprising the following steps;

[0006] S1, Data Preprocessing;

[0007] Individual tooth models are manually segmented from the oral cavity scanning model to serve as oral cavity scanning sample data. Calibration points are added to the locations of significant anatomical feature points on the occlusal surface of the tooth crown in the tooth model, and the calibration point data is added to the oral cavity scanning sample data to form complete oral cavity scanning sample data. The significant anatomical feature points include cusps and pits / fissures.

[0008] S2. Construct a statistical shape model of the teeth;

[0009] Based on complete oral scan sample data, a statistical shape model is constructed to create a dental template library with natural anatomical morphological features of teeth. The dental template library includes tooth models with different deformation coefficients and different natural anatomical morphological features.

[0010] S21. Using the Thin Plate Spline Robust Point Matching Method (TPS-RPM), a set of complete oral scan sample data is used as a standard tooth template and registered to other oral scan sample data to establish the surface vertex correspondence between the crowns of different individuals. The standard tooth template is deformed by calibration points to ensure that all sample mesh models obtained after registration have the same number of vertices, and the corresponding vertices are located in the same anatomical position in different sample mesh models. The n vertices of each sample mesh model form a sample vector s. The sample mesh model is a tooth model formed based on different sets of complete oral scan sample data.

[0011] s = [x1, y1, z1, ..., x n ,y n ,z n ] T

[0012] Among them, (x j ,y j ,z j (j) represents the coordinates of the j-th vertex in the sample mesh model;

[0013] S22. The sample vectors are aligned using Generalized Protodyakonov Analysis (GPA) to obtain the average model of all sample mesh models. This model is used to cancel the effects of similarity transformations, i.e., translation, rotation, and scaling, on the SSM construction.

[0014]

[0015] Where m is the number of sample grid models;

[0016] S23. Statistical modeling of the sample vectors after generalized Protodyakonov analysis is performed using principal component analysis (PCA), and the eigenvectors Φ are calculated. i and the corresponding eigenvalue λ i eigenvector Φ i For different deformation modes, the largest eigenvalue corresponds to the most significant deformation mode; changing the coefficients of a series of changing modes can cause different deformations in the average model; the statistical shape model of a tooth is represented as:

[0017]

[0018] Where S is the statistical shape model. For the average model, Φ i This represents the different deformation modes obtained from principal component analysis, a i The deformation coefficients represent the deformation modes; the range of variation of the deformation coefficients is...

[0019] S3. Construct a conditional shape model of the teeth;

[0020] In an ideal tooth morphology, adjacent teeth should have good contact relationships. In the task of designing a missing crown, the size and position of the missing tooth largely depend on its adjacent teeth. Therefore, there is a high correlation between the SSM deformation coefficients of the tooth to be designed (hereinafter referred to as the "sub-model") and its five adjacent teeth as a whole (hereinafter referred to as the "parent model"). The tooth to be designed is used as the sub-model, and the five adjacent teeth are used as the parent model. Given the deformation coefficients of the parent model, the distribution of the deformation coefficients of the sub-model is modeled as a conditional Gaussian distribution. This conditional Gaussian distribution is described by establishing a conditional shape model (CSM) parameterization.

[0021] P(S|F)=N(μ,Σ)

[0022]

[0023]

[0024] Where μ is the conditional mean, Σ is the conditional covariance, and μ S μ is the mean of the shape coefficient S of the sub-model; F Σ is the mean of the shape coefficient F of the parent model. S Σ represents the variance of the shape coefficient S of the sub-model; F Σ is the variance of the shape coefficient F of the parent model. SF and Σ FS It is the covariance matrix of the sub-model shape coefficient S and the parent model shape coefficient F;

[0025] Given any set of parent model SSM shape coefficients, the statistical shape model modal distribution coefficients of a set of child models can be obtained according to the above conditional Gaussian distribution probability model, that is, the child models that match the shape of the parent models are obtained.

[0026] S4, Template Matching;

[0027] The statistical shape model of the parent model is registered to the adjacent teeth of the tooth to be designed, and the deformation coefficient of the parent model is obtained. The matching sub-model is then calculated through the conditional shape model.

[0028] S41. Use iterative ICP and TPS-RPM methods to register the parent model with the oral cavity scanning model of the tooth to be designed, and calculate the shape coefficient of the parent model corresponding to the oral cavity scanning model through least squares approximation.

[0029] S42. Based on the conditional shape model constructed in S3, obtain a set of sub-model shape coefficients and apply them to the average model of the sub-model to generate a sub-model that matches the shape and position of the parent model; the sub-model is the designed crown model.

[0030] S43. Use the cross-crossing algorithm to detect the cross-crossing between the crown and the adjacent teeth of the tooth to be designed, and make adjustments to ensure that there is no unreasonable cross-crossing between the designed crown and the adjacent teeth of the tooth to be designed.

[0031] S5, neckline is closely closed;

[0032] In clinical use, the fit between the crown and the abutment tooth must be considered to ensure sufficient retention of the crown. The cervical margin is a ridge-like protrusion formed on the abutment tooth after grinding and polishing before the crown restoration is designed; the bottom edge of the designed crown fits snugly with the cervical margin.

[0033] S51. Curvature represents the curvature of a surface. The protrusions of the surface represent the maximum curvature. The maximum curvature is calculated based on the abutment tooth, thereby automatically identifying the cervical margin line of the abutment tooth and fitting the surface where the cervical margin line is located.

[0034] S52. Use the Signed Distance Function (SDF) to control the deformation of the bottom of the crown model. SDF is defined as the distance from a point in space to a surface, with the inside being positive and the outside being negative. The surface is the 0 isosurface of SDF. Diffusion filtering is applied to the SDF array to make the crown model and the junction of the abutment tooth change uniformly, and to ensure that the SDF below the fitting plane of the cervical margin of the abutment tooth and at the occlusal surface is fixed. That is, in the process of continuous filtering iteration, the outer surface of the bottom of the crown model gradually and smoothly shrinks to the cervical margin.

[0035] S53. Set the SDF of the points located inside the abutment tooth to 0, and use the marching cube algorithm to extract the 0 isosurface, thus obtaining a closed crown model that matches the shape of the abutment tooth.

[0036] Based on the closed crown model, the internal hollow design of the crown is carried out; the internal hollow design of the crown is used to give the crown restoration good mechanical properties, and at the same time, it can effectively save materials in additive manufacturing.

[0037] First, an initial porous structure is randomly obtained based on the designed closed crown model. By optimizing the pore repetition period and wall thickness of the porous structure inside the crown, the stress distribution under given boundary conditions is minimized, and finally a porous structure with good biomechanical properties is obtained.

[0038] The oral scanning model includes complete clinical oral scanning model data of the missing tooth side, the opposing tooth side, the prepared tooth body, and the artificially designed crown.

[0039] The Statistical Shape Models (SSM) can represent the average shape and deformation of a class of three-dimensional models.

[0040] The beneficial effects of this invention are: a customized crown design method based on template matching and mechanical performance simulation optimization. Based on a dental template library obtained from oral scans, a conditional shape model is used to learn the shape correlation between the target crown and surrounding teeth, thereby achieving optimal shape fit between the crown and surrounding teeth. Furthermore, the crown is sutured along the cervical margin to ensure proper fit with the patient's abutment teeth. This method efficiently achieves personalized automated design of crown restorations, with a complete design process, facilitating its transfer to clinical applications, and effectively reducing material consumption in additive manufacturing. Attached Figure Description

[0041] Figure 1 This is a flowchart of a customized dental crown design method based on template matching and mechanical performance simulation optimization.

[0042] Figures 2(a)-2(f) This is a schematic diagram of the anatomical landmarks of different occlusal surfaces of teeth.

[0043] Figures 3(a)-3(f) for Figures 2(a)-2(f) The average statistical shape model is constructed for each individual tooth.

[0044] Figure 4 This shows the deformation effect of the right maxillary second premolar under different modalities. The six modalities are characteristic values. The deformation effects corresponding to different modes.

[0045] Figure 5 It is based on Figure 4 The system constructs conditional shape models under different modalities, changes the shape of the parent model, and automatically designs a matching child model.

[0046] Figure 6 This is a flowchart of the neckline sealing process.

[0047] Figure 7(a) shows the effect before the neckline is closed; Figure 7(b) shows the effect after the neckline is closed. Detailed Implementation

[0048] The following uses an oral cavity scanning model of a missing right mandibular first molar as an example to further illustrate the invention in conjunction with specific implementation steps, such as... Figure 1 As shown, the customized crown design method based on template matching and mechanical performance simulation optimization includes the following steps:

[0049] Step 1: Data preprocessing;

[0050] S11. In order to build a statistical shape model of a single tooth, it is necessary to separate the single tooth from the complete oral cavity scan model. For this example task, the second premolar, first molar and second molar of the right upper and lower jaws need to be segmented separately.

[0051] S12. Add calibration points at the anatomical feature points on the occlusal surface, as shown in Figure 2.

[0052] Step 2: Construct a statistical shape model of the teeth;

[0053] S21. Guided by the marker points, the standard tooth model is registered onto the clinical oral scan data using the TPS-RPM method, resulting in a set of sample mesh models with consistent vertex counts and topological relationships. The n vertices of each sample mesh model can form a sample vector s:

[0054]

[0055] Among them, (xj ,y j ,z j ) represents the coordinates of the j-th vertex in the grid.

[0056] S22. The 3D model features of the object should not be affected by similarity transformations such as translation, rotation, and scaling. Generalized Procrustes analysis (GPA) is used to process the sample vectors to obtain the average model of the tooth model.

[0057]

[0058] The average model of the second premolar, first molar, and second molar of the right maxilla and mandible is shown in Figure 3.

[0059] S23. Statistical modeling is performed on the sample vectors after generalized Protodyakonov analysis using principal component analysis (PCA), and the eigenvectors Φ are calculated. i and the corresponding eigenvalue λ i That is, different modes of variation and their corresponding variances, with the largest eigenvalue corresponding to the most significant mode of variation. Therefore, the statistical shape model of teeth can be expressed as:

[0060]

[0061] Where S is the statistical shape model, S is the average model, and Φ i This represents the different deformation modes obtained from principal component analysis, a i This represents the deformation coefficient for different deformation modes. Changing a series of values ​​for the shape coefficient allows the model to undergo different deformations. To ensure the deformation is reasonable, its range of variation is usually controlled within a certain range.

[0062] Figure 4 The deformation effect of the right maxillary second premolar SSM is shown in the three modalities with the largest eigenvalues.

[0063] Step 3: Construct a conditional shape model of the teeth;

[0064] S3. For this example task, the lower right first molar to be designed is used as the sub-model, and the five adjacent teeth around it are used as the parent model. SSMs of the two are constructed respectively.

[0065] Given the shape coefficient F of the parent model SSM, the distribution P(S|F) of the statistical shape model modal distribution coefficient S of the child model can be modeled as a conditional Gaussian distribution:

[0066] P(S|F)=N(μ,Σ)

[0067]

[0068]

[0069] Where μ is the conditional mean, Σ is the conditional covariance, and μ S and μ F Let Σ be the mean of S and F, respectively. S and Σ F The variances of S and F are Σ, respectively. SF and Σ FS It is the covariance matrix of the two.

[0070] Figure 5 The results show that by changing the deformation coefficient of the parent model under two different modalities, the deformation coefficient of the child model is predicted by the conditional shape model. It can be seen that the child model exhibits a good adaptation relationship with the parent model.

[0071] Step 4: Template matching;

[0072] S4. In clinical applications, in order to personalize the design of a patient's missing teeth, it is necessary to match the already constructed parent model SSM with the adjacent teeth of the tooth to be designed in order to obtain the deformation coefficient of the parent model.

[0073] Using ICP and TPS-RPM algorithms for overall coarse and fine registration respectively, the average model of the parent model SSM is deformed into a mesh surface consistent with the shape of the adjacent teeth of the tooth to be designed, and the corresponding shape coefficients of the parent model are calculated using least squares approximation. The shape coefficients of the child model are then calculated using the established conditional shape model, thus obtaining the child model that matches the shape of the parent model.

[0074] To ensure that the designed crown matches the position of the adjacent teeth, further fine adjustments are needed to remove any unreasonable overlaps between the crown and the adjacent teeth.

[0075] Step 5: Ensure the neckline is tightly closed;

[0076] S5. The above steps ensure that the occlusal anatomical features of the crown restoration are clear and the external surface is coordinated with the morphology of adjacent teeth. However, in clinical use, the fit between the crown and the prepared body must be considered to ensure that the crown has sufficient retention force.

[0077] Figure 6 The flowchart for cervical margin fitting is shown, and the specific steps are as follows: extract the cervical margin of the abutment tooth; fit the cervical margin surface; calculate SDF; perform SDF filtering and diffusion; set the SDF inside the abutment tooth to 0; and construct the crown surface using marching cubes. The position of the crown and abutment tooth before and after cervical margin fitting is shown in Figure 7.

[0078] Step Six: Hollowing out the interior of the crown;

[0079] S6. Considering the close relationship between crown morphology and the mechanical properties of teeth, unreasonable stress can significantly shorten the lifespan of restorations. Therefore, it is necessary to design an internal support structure optimized for the internal stress distribution of the crown. Furthermore, the internal hollow design of the crown can effectively save materials during additive manufacturing.

[0080] Specifically, an initial porous structure is first obtained randomly based on the input crown model. Under specific mechanical loading conditions, two parameters—the repetition period of the pores and the pore wall thickness—are continuously adjusted to optimize the stress distribution throughout the crown, ultimately resulting in a smooth porous structure with good biomechanical properties. Mechanical simulation experiments verify the biomechanical performance of the crown model with the internal hollow structure.

Claims

1. A customized dental crown design method based on template matching and mechanical performance simulation optimization, characterized in that, The steps are as follows; S1, Data Preprocessing; Individual tooth models are manually segmented from the oral cavity scanning model to serve as oral cavity scanning sample data. Calibration points are added to the locations of significant anatomical feature points on the occlusal surface of the tooth crown in the tooth model, and the calibration point data is added to the oral cavity scanning sample data to form complete oral cavity scanning sample data. The significant anatomical feature points include cusps and pits / fissures. S2. Construct a statistical shape model of the teeth; Based on complete oral scan sample data, a statistical shape model is constructed to create a dental template library with natural anatomical morphological features of teeth. The dental template library includes tooth models with different deformation coefficients and different natural anatomical morphological features. S21. Using the Thin Plate Spline Robust Point Matching Method (TPS-RPM), a set of complete oral scan sample data is used as a standard tooth template and registered to other oral scan sample data to establish the surface vertex correspondence between the crowns of different individuals. The standard tooth template is deformed by calibration points to ensure that all sample mesh models obtained after registration have the same number of vertices, and the corresponding vertices are located in the same anatomical position in different sample mesh models. The n vertices of each sample mesh model form a sample vector s. The sample mesh model is a tooth model formed based on different sets of complete oral scan sample data. s=[x1,y1,z1,…,x n ,y n ,z n ] T Among them, (x j ,y j ,z j (j) represents the coordinates of the j-th vertex in the sample mesh model; S22. Align the sample vectors using generalized Protodyakonov analysis (GPA) to obtain the average model of all sample grid models: Where m is the number of sample grid models; S23. Statistical modeling of the sample vectors after generalized Protodyakonov analysis is performed using principal component analysis (PCA), and the eigenvectors Φ are calculated. i and the corresponding eigenvalue λ i eigenvector Φ i For different deformation modes, the largest eigenvalue corresponds to the most significant deformation mode; the statistical shape model of a tooth is represented as: Where S is the statistical shape model. For the average model, Φ i This represents the different deformation modes obtained from principal component analysis, a i The deformation coefficients represent the deformation modes; the range of variation of the deformation coefficients is... S3. Construct a conditional shape model of the teeth; The tooth to be designed is used as the sub-model, and the five adjacent teeth at the same position are used as the parent model. Given the deformation coefficients of the parent model, the distribution of the deformation coefficients of the sub-model is modeled as a conditional Gaussian distribution. This conditional Gaussian distribution is then described parametrically using a Conditional Shape Model (CSM). P(S|F)=N(μ,∑) Where μ is the conditional mean, ∑ is the conditional covariance, and μ S μ is the mean of the shape coefficient S of the sub-model; F The mean of the shape coefficient F of the parent model, ∑ S The variance of the shape coefficient S of the sub-model; ∑ F Let ∑ be the variance of the shape coefficient F of the parent model. SF and ∑ FS It is the covariance matrix of the sub-model shape coefficient S and the parent model shape coefficient F; S4, Template Matching; The statistical shape model of the parent model is registered to the adjacent teeth of the tooth to be designed, and the deformation coefficient of the parent model is obtained. The matching sub-model is then calculated through the conditional shape model. S41. Use iterative ICP and TPS-RPM methods to register the parent model with the oral cavity scanning model of the tooth to be designed, and calculate the shape coefficient of the parent model corresponding to the oral cavity scanning model through least squares approximation. S42. Based on the conditional shape model constructed in S3, obtain a set of sub-model shape coefficients and apply them to the average model of the sub-model to generate a sub-model that matches the shape and position of the parent model; the sub-model is the designed crown model. S43. Use the cross-crossing algorithm to detect the cross-crossing between the crown and the adjacent teeth of the tooth to be designed, and make adjustments to ensure that there is no unreasonable cross-crossing between the designed crown and the adjacent teeth of the tooth to be designed. S5, neckline is closely closed; The cervical margin is a ridge-shaped protrusion on the abutment tooth that has been ground down before the crown restoration is designed. The bottom edge of the designed crown fits closely with the cervical margin. S51. Curvature represents the curvature of a surface. The protrusions of the surface represent the maximum curvature. The maximum curvature is calculated based on the abutment tooth, thereby automatically identifying the cervical margin line of the abutment tooth and fitting the surface where the cervical margin line is located. S52. Use the Signed Distance Function (SDF) to control the deformation of the bottom of the crown model. SDF is defined as the distance from a point in space to a surface, with the inside being positive and the outside being negative. The surface is the 0 isosurface of SDF. Diffusion filtering is applied to the SDF array to make the crown model and the junction of the abutment tooth change uniformly, and to ensure that the SDF below the fitting plane of the cervical margin of the abutment tooth and at the occlusal surface is fixed. That is, in the process of continuous filtering iteration, the outer surface of the bottom of the crown model gradually and smoothly shrinks to the cervical margin. S53. Set the SDF of the points located inside the abutment tooth to 0, and use the marching cube algorithm to extract the 0 isosurface, thus obtaining a closed crown model that matches the shape of the abutment tooth.

2. The customized crown design method based on template matching and mechanical performance simulation optimization according to claim 1, characterized in that, The internal hollow design of the crown is carried out based on the closed crown model; The interior of the crown is hollowed out to give the crown restoration good mechanical properties, while also effectively saving materials in additive manufacturing; First, an initial porous structure is randomly obtained based on the designed closed crown model. By optimizing the pore repetition period and wall thickness of the porous structure inside the crown, the stress distribution under given boundary conditions is minimized, and finally a porous structure with good biomechanical properties is obtained.

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