Mechanical information display method, device and medium for risk prompt of impacted tooth extraction process

Abstract

This invention relates to a method, device, and medium for displaying mechanical information for risk warning during impacted tooth extraction. The method includes: Step S1: Obtaining the three-dimensional modeling results of each tissue unit; Step S2: Obtaining the modeling results of each tooth segment unit; Step S3: Constructing the tooth segment and its contact constraints with surrounding tissues; Step S4: Based on the constructed contact constraints, combined with the overall finite element stiffness matrix and operational load, solving for the displacement response of each finite element mesh; Step S5: Based on the displacement response of each finite element mesh and the shape function, obtaining the displacement matrix of each element, and further obtaining the strain tensor of each element; Step S6: Based on the constitutive matrix of the tissue material corresponding to each element and the strain tensor, obtaining the stress tensor of each element; Step S7: Comparing the stress tensor of each element with its pre-configured threshold and assigning color values ​​to the finite element mesh of each element. Compared with the prior art, this invention has the advantages of real-time performance and high accuracy.

Description

Technical Field

[0001] This invention relates to the field of dental surgical information technology, and in particular to a method, device and medium for displaying mechanical information for risk warning during the extraction of impacted teeth. Background Technology

[0002] Impacted teeth, especially impacted mandibular third molars, are among the most common and complex extraction types in oral and maxillofacial surgery. Their anatomical location is typically adjacent to the medial cortical plate of the mandible, the cancellous alveolar bone, and the mandibular nerve canal. Improper force application during extraction can easily lead to complications such as alveolar bone fracture, damage to adjacent teeth, or damage to the mandibular nerve. Before extracting impacted teeth, clinicians usually need to assess the spatial relationship between the tooth and surrounding important anatomical structures based on CBCT imaging to select an appropriate tooth-cutting method and force direction, in order to reduce surgical risks while improving extraction efficiency. However, current clinical assessment methods mainly rely on the surgeon's experience, lacking quantitative evidence for predicting the biomechanical behavior of complex impacted teeth.

[0003] Current research utilizes CBCT images for automatic segmentation of teeth and surrounding tissues to assist dentists in identifying structures such as enamel, dentin, alveolar bone, and the mandibular nerve canal. However, most of these studies focus on visualizing anatomical structures and verifying segmentation accuracy, failing to provide effective quantitative analysis of the mechanical transmission patterns during tooth extraction, areas of bone stress concentration, and the impact of different segmentation schemes on local tissues. Furthermore, existing finite element analysis of the jawbone is often based on static, single-force conditions, constructing only homogeneous or roughly segmented material models, making it difficult to simulate the actual effects of complex maneuvering forces such as prying, twisting, and traction during impacted tooth extraction. Simultaneously, due to the significant heterogeneity of bone tissue structure, the mechanical properties of cortical bone, cancellous bone, trabeculae, and tissues surrounding the nerve canal differ significantly. Existing models often ignore these microscopic differences, leading to discrepancies between stress and strain calculations and actual conditions.

[0004] In response, while some existing technologies attempt to establish resistance analysis simulations during the extraction of impacted teeth—for example, Chinese patent application CN120874621A discloses a method to assess risk by automatically measuring the minimum spatial distance between the root apex of the wisdom tooth to be extracted and the dental nerve canal, and to select a resistance removal strategy by performing three-dimensional mechanical analysis of the resistance of adjacent teeth, bone resistance, and root resistance of the wisdom tooth to be extracted, and to plan a simulated extraction path based on the risk assessment results and resistance removal strategy—this method aims to analyze complex impacted wisdom teeth, achieve surgical risk assessment and three-dimensional mechanical analysis, and can specifically model, assess, and analyze extraction resistance for high-risk situations such as impacted mandibular wisdom teeth, which are adjacent to the nerve canal, have complex root morphology, and have diverse sources of resistance. It reflects the difficulty of extraction, sources of resistance, and intraoperative risk points, meeting clinical needs. However, its path simulation steps involve iterative collision detection and Fourier transform verification, which are computationally time-consuming, have poor real-time performance, and are not intuitively displayed.

[0005] Furthermore, Chinese patent application CN118806430A mentions using the finite element method to divide the relevant region into multiple finite element meshes and simulating various surgical operations by applying boundary conditions and loads. However, this modeling method using discrete node contact has two drawbacks. First, the number of finite element meshes is enormous, and using microscopic mechanical analysis for modeling will consume a lot of computational resources, which may not meet the real-time requirements of the operation. Second, it is prone to numerical oscillation problems caused by local node contact switching. Summary of the Invention

[0006] The purpose of this invention is to address the deficiencies of the prior art by providing a method, device, and medium for displaying mechanical information to indicate risks during the extraction of impacted teeth.

[0007] The objective of this invention can be achieved through the following technical solutions: A method for displaying biomechanical information for risk warning during impacted tooth extraction, comprising: Step S1: Based on the CBCT data of the area where the impacted tooth is located, perform multi-tissue three-dimensional reconstruction of the surgical area to obtain the three-dimensional modeling results of each tissue unit; Step S2: Perform tooth segmentation modeling on impacted teeth to obtain the modeling results of each tooth segmentation unit; Step S3: Based on the modeling results, construct the tooth segments and their contact constraints with surrounding tissues respectively; Step S4: Based on the constructed contact constraints, combined with the overall finite element stiffness matrix and the operational load, the displacement response of each finite element mesh is obtained; Step S5: Based on the displacement response of each finite element mesh and the shape function, obtain the displacement matrix of each tooth element and the structure element, and further combine the strain displacement matrix of each tooth element and the structure element to obtain the strain tensor of each tooth element and the structure element. Step S6: Obtain the stress tensor of each tooth element and tissue element based on the constitutive matrix and strain tensor of the corresponding tissue material; Step S7: Compare the stress tensor of each tooth element and tissue element with their respective pre-configured thresholds and assign color values ​​to the finite element mesh of each tooth element and tissue element. In step S4, the displacement response of each finite element mesh is obtained by solving the overall equilibrium relationship of the finite element model. The mathematical expression of the overall equilibrium relationship of the finite element model is as follows: ; in: The overall finite element stiffness matrix, For the displacement response of all finite element meshes, For operating force load, The contact reaction force vector is automatically generated from each contact constraint condition; The mathematical expression for the contact reaction force vector automatically generated from each contact constraint condition is: ; in, This represents the normal contact reaction density corresponding to the contact constraint. For the interface normal, Γ k This is the k-th type of contact interface.

[0008] The tissue types in step S1 include enamel, dentin, dental pulp, alveolar cortical bone, cementum, cancellous alveolar bone, medullary cavity, trabecular bone, adipose tissue, and mandibular nerve canal.

[0009] The intersection of any two units is an empty set.

[0010] In step S3, contact constraints are constructed between each tooth segment, between each tooth segment and alveolar bone, between each tooth segment and adjacent teeth, and between each tooth segment and mandibular nerve canal.

[0011] The contact constraint between the tooth segment and the mandibular nerve canal is specifically the contact constraint of the externally expanded safety buffer zone between the tooth segment and the mandibular nerve canal.

[0012] The displacement matrix of each tooth segment and tissue unit is as follows: ; in: Let e ​​be the displacement matrix of element e. Let be the shape function of the i-th finite element mesh. Let i be the displacement response of the i-th finite element mesh. denoted as the number of finite element meshes for element e.

[0013] The strain tensor of each tooth segment and tissue unit is: ; in: Let e ​​be the strain tensor of element e. Let be the strain-displacement matrix of element e; The stress tensor of each tooth segment and tissue unit is: ; in: Let e ​​be the stress tensor of element e. Let e ​​be the constitutive matrix of the material structure corresponding to element e.

[0014] A biomechanical information display device for risk warning during impacted tooth extraction includes a memory, a processor, and a program stored in the memory, wherein the processor executes the program to implement the method described above.

[0015] A storage medium having a program stored thereon, which, when executed, implements the method described above.

[0016] Compared with the prior art, the present invention has the following beneficial effects: 1. By constructing contact constraints and combining the overall finite element stiffness matrix and operational load, the displacement response of each finite element mesh is obtained. The displacement matrix of each tooth element and structure element is obtained by combining shape functions. The stress tensor of each tooth element and structure element is obtained based on the constitutive matrix and strain tensor of the structure material corresponding to each tooth element and structure element. Finally, the information is displayed by using a threshold comparison method, which can realize fast and accurate stress calculation, high real-time performance, and more intuitive display effect.

[0017] 2. By explicitly listing all key tissue types, the comprehensiveness and precision of the 3D reconstruction are ensured. This improves the model's accuracy in reproducing real anatomical structures, makes mechanical analysis more accurate, and enables a more comprehensive assessment of surgical risks, especially the protection of sensitive structures such as the mandibular canal, thereby reducing the possibility of missing key risk points.

[0018] 3. The intersection of any two elements is an empty set, ensuring that each element in the model is independent and non-overlapping, avoiding mesh conflicts and calculation errors. This improves the stability and accuracy of finite element analysis, makes displacement and stress calculations more reliable, reduces numerical instability caused by mesh overlap, and thus enhances the credibility of risk warnings.

[0019] 4. Contact constraints were constructed separately for each tooth segment, between each tooth segment and the alveolar bone, between each tooth segment and adjacent teeth, and between each tooth segment and the mandibular nerve canal. By defining all possible contact constraints in detail, all key mechanical interactions during the operation were covered. This allows the model to more realistically simulate the complex contact behaviors during tooth extraction, improves the completeness of risk analysis, ensures that the impact on structures such as the alveolar bone, adjacent teeth, and nerve canal is fully assessed, and thus provides more comprehensive risk warnings.

[0020] 5. The contact constraint between the tooth segment and the mandibular nerve canal specifically refers to the contact constraint between the tooth segment and the externally expanded safety buffer zone of the mandibular nerve canal. Advantages: Introducing the concept of a safety buffer zone increases the protective layer for the mandibular nerve canal. This reduces the risk of nerve injury because the model considers the safety margin in actual operation, allowing surgeons to be more cautious in surgical planning and improving surgical safety. Simultaneously, this enhances the preventative nature of risk warnings, enabling surgeons to avoid high-risk areas in advance.

[0021] 6. The displacement response is solved based on the overall equilibrium relationship of the finite element model, and a mathematical expression is provided. The mathematical formula clarifies the solution process, ensuring the scientific validity and repeatability of the method. This improves the accuracy and efficiency of displacement response calculation, as the overall equilibrium relationship is the core of finite element analysis, making the solution process more transparent and reliable. This lays a solid foundation for subsequent strain and stress calculations, enhances the real-time performance of the overall model, and the contact-based modeling approach effectively reduces numerical oscillations caused by local node contact switching during the numerical solution process, minimizing instability factors during contact search and constraint application. Simultaneously, interface-level contact modeling helps smooth the spatial distribution of contact forces, improving the convergence and computational stability of the finite element solution under complex geometries.

[0022] 7. A specific method for calculating the displacement matrix is ​​provided, using shape functions and mesh displacement responses to ensure the accuracy and consistency of displacement calculations. This helps to more accurately derive element-level displacements, providing reliable input for strain and stress analysis, thereby improving the accuracy of risk warnings and making the mechanical information display more intuitive.

[0023] 8. Based on the strain-displacement matrix and the material constitutive matrix, the correctness and verifiability of the mechanical quantity calculations are ensured. This makes the risk warning based on solid mechanical principles, improves the reliability of the results, and enables doctors to quickly identify high-stress areas, thereby achieving real-time and accurate risk visualization. Attached Figure Description

[0024] Figure 1 This is a schematic diagram of the main steps of the method of the present invention. Detailed Implementation

[0025] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0026] A method for displaying mechanical information to indicate risks during impacted tooth extraction, such as... Figure 1 As shown, it includes: Step S1: Based on the CBCT data of the area where the impacted tooth is located, perform multi-tissue three-dimensional reconstruction of the surgical area to obtain the three-dimensional modeling results of each tissue unit; The tissue types include enamel, dentin, dental pulp, alveolar cortical bone, cementum, cancellous alveolar bone, medullary cavity, trabecular bone, adipose tissue, and mandibular nerve canal.

[0027] Specifically, CBCT data of the region containing the impacted tooth was first acquired and exported in DICOM format. The surgical area, including the impacted tooth, adjacent teeth, alveolar bone, and mandibular canal, was cropped using image processing software. A unified three-dimensional coordinate system was established to achieve standardized conversion from voxel coordinates to physical coordinates. Multi-tissue segmentation was performed on the surgical area image, identifying enamel, dentin, pulp, cortical bone, cementum, cancellous bone, marrow cavity, trabeculae, fat tissue, mandibular canal, other soft tissues, and air as background, defining their set as TISSUES. Morphological post-processing was then performed on the segmentation results, including small connected component removal, cavity filling, and topological constraints matching anatomical priors to correct misclassified regions. Finally, the voxel center points of each tissue were extracted as point clouds and reconstructed into corresponding three-dimensional surface models. Surface fitting is performed on the critical organizational boundaries.

[0028] Step S2: Perform tooth segmentation modeling on impacted teeth to obtain the modeling results of each tooth segmentation unit; Specifically, after completing the three-dimensional geometric reconstruction of the impacted tooth, a tooth segmentation model is created based on the geometric characteristics of burs commonly used in actual clinical practice. The bur is set as a conical cutting tool with a diameter of approximately 1 mm, and the dentist determines its axial direction and path during cutting. In a computer simulation environment, geometric Boolean operations are performed along the preset path to create a cutting gap with a finite width inside the impacted tooth, simulating the tooth separation effect produced by the bur cutting during actual tooth segmentation. After the above geometric cutting operation, the impacted tooth model is divided into two geometrically independent tooth regions, defined as the first segmentation block and the second segmentation block, respectively.

[0029] In conclusion, regardless of whether it is an organizational unit or a toothed block unit, the intersection between any two units is an empty set.

[0030] Step S3: Based on the modeling results, construct the tooth segments and their contact constraints with surrounding tissues respectively; After completing the CBC-based multi-tissue 3D reconstruction and tooth separation geometry modeling, a unified geometric representation and boundary identification of each anatomical structure within the surgical area were performed to provide a geometric basis for subsequent mechanical modeling.

[0031] The entire technical region used for finite element analysis is defined as a three-dimensional continuum geometric domain. It is composed of impacted teeth, adjacent teeth, alveolar bone, and the mandibular nerve canal, among other anatomical structures. Based on the image segmentation results, the geometric region of the surgical area is... Divided into several non-overlapping subdomains: Impacted tooth geometric domain ; Geometric domain of the first tooth block ; Geometric domain of the second tooth block ; adjacent tooth geometry Alveolar bone geometry Geometric region of the mandibular nerve canal The alveolar bone geometric domain is further divided into cortical bone, cancellous bone, and trabecular bone.

[0032] The aforementioned subdomains are spatially distinct from each other, and their intersection is empty, to ensure the uniqueness of the geometric division.

[0033] Based on the above definition of geometric domains, the boundaries of each geometric subdomain within the surgical area are explicitly identified. For any geometric subdomain... Its outer surface, i.e., the interface with the surrounding space, is defined as: The following types of geometric surface sets should be identified and retained: the outer surface of the first tooth segment. ; outer surface of the second tooth block ; outer surface of adjacent teeth ; Alveolar bone inner wall surface ; outer surface of the mandibular nerve canal The aforementioned surface set is used to describe the geometrical positional relationships between various anatomical structures within the surgical area that may approach or interact in space, and it does not contain any mechanical meaning in itself.

[0034] Because the tooth segment may shift, rotate, and dislocate under surgical forces during extraction, its surface may come into contact with or interact closely with various surrounding anatomical structures. Therefore, it is necessary to identify various candidate contact interfaces before finite element analysis. These candidate contact interfaces are not equivalent to the actual contact areas, but rather are used to limit the scope of contact search and contact constraints during the finite element solution process.

[0035] After determining the candidate contact interfaces between tooth segments, between tooth segments and adjacent teeth, between tooth segments and alveolar bone, and between tooth segments and the mandibular nerve canal, these contact relationships are introduced into the finite element model to establish corresponding contact constraints. These contact constraints describe the mechanical fulcrums and interactions formed between tooth segments and surrounding tissues during surgical procedures, and are used to prevent geometric penetration between tooth segments and between tooth segments and surrounding tissues. Specifically, contact constraints are constructed between each tooth segment, between each tooth segment and alveolar bone, between each tooth segment and adjacent teeth, and between each tooth segment and the mandibular nerve canal.

[0036] First, spatial distance analysis is performed on the outer surfaces of the first and second tooth-splitting blocks. Regions with a distance less than a preset threshold between their surfaces are selected as candidate contact interfaces between the tooth-splitting blocks. This interface is used to simulate potential mutual compression, jamming, or re-contact situations that may occur during prying and traction of the tooth-splitting blocks.

[0037] Define candidate contact interfaces on the first tooth segment. for: ; in: , These represent the boundary surfaces of the two tooth blocks, respectively. This represents the minimum Euclidean distance from a point to a surface. This is the contact determination threshold. The optimal settings are determined by combining the minimum diameter of the conical needle with the finite element mesh size: ; in The diameter of the needle. The characteristic size of the finite element mesh for the contact region.

[0038] Correspondingly, a mating contact interface can be defined on the surface of the second tooth block. .

[0039] Candidate contact interface between the first and second tooth segments and Establish contact constraints between the tooth blocks. For any contact point... The normal gap is defined as: ; in, For point Second tooth block surface The nearest projection point on, The first tooth segment at point The unit outward normal vector at that location.

[0040] By applying non-penetrating constraints: ; To prevent geometric penetration between the two tooth segments during finite element analysis, this method simulates the mutual constraint between the tooth segments after separation due to the limited cutting gap. If necessary, a frictional contact model can be further introduced at this interface to describe the frictional resistance of the tooth segments during relative sliding.

[0041] Modeling the contact constraints between the tooth segment and the alveolar bone For each tooth segment ( ) Analyze its outer surface In the alveolar bone The spatial relationship between them defines the candidate contact interfaces between the tooth segments and the alveolar bone. This term is used to describe the local compression, shearing, or stress concentration effects on the alveolar bone caused by the prying or dislocation of tooth segments.

[0042] ; ; in: The first threshold represents the area on the surface of a toothed block that is within a given threshold range from the surface of another toothed block. It is used to simulate possible contact, squeezing, or jamming between toothed blocks and can be customized by the user using physical distance or finite element mesh size h.

[0043] The contact relationship adopts a non-penetrating contact model, which enables the tooth segment to transfer the load to the alveolar bone structure through the contact interface when subjected to surgical forces, thereby forming a corresponding stress and strain distribution inside the alveolar bone.

[0044] Modeling the contact constraints between the tooth segment and adjacent teeth. In the presence of adjacent teeth In this case, the outer surface of the tooth segment and the surface of the adjacent tooth body are compared. Analyze the spatial distance to determine the area where the two may come into contact. This candidate contact interface is used to simulate the unexpected contact between the tooth segmentation block and adjacent teeth during the operation, thereby assessing the stress state of adjacent teeth and the potential risk of damage.

[0045] ; ; in: The second threshold can be customized by the user using physical distance or finite element mesh size h.

[0046] For the contact constraint modeling between the tooth segment and the mandibular nerve canal, a safety buffer zone is constructed based on the 3D reconstruction model of the mandibular nerve canal region. By analyzing the distance relationship between the outer surface of the tooth segment and the nerve canal and its buffer zone, the risk areas where the tooth segment may cause mechanical disturbance or displacement to the nerve canal during operation are identified. This interface is mainly used for the subsequent display and analysis of mechanical response and displacement contour maps, and is not used as the actual object of contact constraint application.

[0047] Define the geometric domain of the mandibular nerve canal Extended safety buffer : ; Among them, symbols Indicates morphological expansion. The neural safety buffer radius can be defined as a distance value of 0.5-1.0 based on clinical experience regarding "safe distances," or it can be defined based on the local finite element mesh size h. .

[0048] Candidate interface : ; in, The third threshold can be customized by the user using physical distance or finite element mesh size h, with an initial setting of 0.5-1mm.

[0049] Step S4: Based on the constructed contact constraints, combined with the overall finite element stiffness matrix and the operational load, the displacement response of each finite element mesh is obtained; Regarding contact constraints, a surgical force load, defined as F, is applied to a selected area on the surface of the tooth segment, according to the clinical extraction procedure. extThe operating force load is applied in the form of equivalent concentrated force, distributed force, or equivalent torque, and its direction and magnitude are used to simulate common clinical manipulations such as prying, traction, or rotation. At the same time, the distal mandibular region of the surgical area is set as a fixed or semi-fixed boundary condition to simulate the overall stability of the mandible under the constraints of the surrounding muscle and ligament system.

[0050] After completing the contact constraints, external loads, and boundary conditions settings, a complete finite element mechanical model is constructed. In this model, the overall finite element stiffness matrix K is obtained by assembling the stiffness matrices of each finite element element within the surgical area according to the nodal degrees of freedom. Its value is jointly determined by the mechanical properties of multiple tissue materials, the three-dimensional geometric structure, and the topological relationship of the finite element mesh, and is used to describe the overall mechanical response characteristics of the surgical area structure under the combined action of surgical operation loads and contact constraints.

[0051] The finite element nodal displacement vector u is defined as the set of displacement degrees of freedom of all finite element nodes in three-dimensional space, and its specific form is: ; in, , , They represent the first Each finite element node is at , , The actual physical displacement in the direction.

[0052] Under the above definition, the overall equilibrium relationship of the finite element model can be expressed as: ; in: The overall finite element stiffness matrix, For the displacement response of all finite element meshes, For operating force load, This is the contact reaction force vector automatically generated by each contact constraint condition. Mathematically, the contact reaction force can be considered as a Lagrange multiplier introduced by the contact constraint conditions, and its integral result at the contact interface constitutes the overall contact reaction force vector: ; Among them, Γ k This represents the k-th type of contact interface. This represents the normal contact reaction density corresponding to the contact constraint. For interface normals.

[0053] Thus, by integrating the overall contact reaction vector based on each contact surface, the contact is modeled from the discrete node level to the geometric interface level. This allows the contact force to no longer rely on single-point constraints but participate in the overall mechanical equilibrium as a distributed quantity on a continuous interface. Specifically, during impacted tooth extraction, the interaction between the tooth, alveolar bone, and adjacent tissues does not occur at isolated discrete points but is continuously distributed along a contact area with actual physical significance. If contact constraints are applied only at the finite element node level, it is difficult to accurately reflect the contact range, force distribution, and fulcrum formation mechanism between the tooth and surrounding tissues during actual surgery. In this application, since the contact constraints act on a continuous interface rather than isolated nodes, the numerical oscillation problem caused by local node contact switching can be effectively reduced during numerical solution, reducing instability factors in the contact search and constraint application process. At the same time, interface-level contact modeling helps to smooth the spatial distribution of contact forces and improve the convergence and computational stability of finite element solutions under complex geometries. On the one hand, adopting macroscopic contact surface mechanical analysis modeling can save computational resources and satisfactorily meet the real-time requirements during surgery; on the other hand, it can solve the numerical oscillation problem caused by local node contact switching.

[0054] By solving the above equilibrium equations, the displacement response of each node in the surgical area during the surgical procedure can be obtained, providing a basis for subsequent calculations of strain and stress fields.

[0055] Furthermore, in some embodiments, after solving the finite element equilibrium equations, the displacement results of all finite element nodes within the surgical area under the combined action of surgical operation loads and contact constraints are obtained. Based on the node displacement results, strain and stress calculations are performed on each finite element element within the surgical area.

[0056] Step S5: Based on the displacement response of each finite element mesh and the shape function, obtain the displacement matrix of each tooth element and the structure element, and further combine the strain displacement matrix of each tooth element and the structure element to obtain the strain tensor of each tooth element and the structure element. For any finite element, based on its node number, extract the corresponding nodal displacement sub-vector from the global nodal displacement vector. The extracted nodal displacement sub-vector is obtained by interpolating the displacements of each node i of the element using shape functions, and its displacement matrix is: ; in: Let e ​​be the displacement matrix of element e. Let be the shape function of the i-th finite element mesh. Let i be the displacement response of the i-th finite element mesh. denoted as the number of finite element meshes for element e.

[0057] Step S6: Obtain the stress tensor of each tooth element and tissue element based on the constitutive matrix and strain tensor of the corresponding tissue material; Based on the above displacement interpolation relationship, spatial differentiation of the displacement field can map the nodal displacements to the strain state within the element. This mapping relationship is derived from the element's strain-displacement matrix. This indicates that the matrix is ​​composed of the partial derivatives of shape functions with respect to spatial coordinates x, y, z, and its form is uniquely determined by the element geometry and mesh topology. Each term is a shape function Spatial coordinates The combination of partial derivatives of z is shown in the following example: ; The strain tensors of each tooth element and tissue element are: ; in: Let e ​​be the strain tensor of element e. Let be the strain-displacement matrix of element e, used to map nodal displacements to strain components within the element. Through the above calculations, the tensile, compressive, and shear deformations of the element under surgical loading can be obtained.

[0058] The stress tensors of each tooth element and tissue element are:

[0059] in: Let e ​​be the stress tensor of element e. Let be the constitutive matrix of the tissue material corresponding to element e, used to describe the linear elastic mechanical behavior of the tissue under small deformation conditions. By selecting different constitutive matrices for different tissue regions, the differences in the mechanical responses of structures such as enamel, dentin, alveolar bone, and nerve canal can be distinguished and calculated, as follows: ; Where: E is the elastic modulus. It is Poisson's ratio.

[0060] Step S7: Compare the stress tensor of each tooth element and tissue element with their respective pre-configured thresholds and assign color values ​​to the finite element mesh of each tooth element and tissue element.

[0061] After obtaining the element stress tensor, the characteristic mechanical properties of each finite element are further calculated, including but not limited to equivalent stress, principal stress, principal strain, and displacement modulus. These characteristic quantities characterize the stress intensity and deformation of the element during surgical procedures. The strain, stress, and displacement values ​​calculated by each finite element are mapped back to the surgical area geometry model according to their spatial position in the 3D model. By color mapping the discrete element results, corresponding strain, stress, and displacement contour maps are generated, enabling intuitive visualization of the mechanical response of impacted tooth segments, adjacent teeth, alveolar bone, and the area surrounding the mandibular nerve canal.

[0062] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

Claims

1. A method for displaying mechanical information to indicate risks during impacted tooth extraction, characterized in that, include: Step S1: Based on the CBCT data of the area where the impacted tooth is located, perform multi-tissue three-dimensional reconstruction of the surgical area to obtain the three-dimensional modeling results of each tissue unit; Step S2: Perform tooth segmentation modeling on impacted teeth to obtain the modeling results of each tooth segmentation unit; Step S3: Based on the modeling results, construct the tooth segments and their contact constraints with surrounding tissues respectively; Step S4: Based on the constructed contact constraints, combined with the overall finite element stiffness matrix and the operational load, the displacement response of each finite element mesh is obtained; Step S5: Based on the displacement response of each finite element mesh and the shape function, obtain the displacement matrix of each tooth element and the structure element, and further combine the strain displacement matrix of each tooth element and the structure element to obtain the strain tensor of each tooth element and the structure element. Step S6: Obtain the stress tensor of each tooth element and tissue element based on the constitutive matrix and strain tensor of the corresponding tissue material; Step S7: Compare the stress tensor of each tooth element and tissue element with their respective pre-configured thresholds and assign color values ​​to the finite element mesh of each tooth element and tissue element. In step S4, the displacement response of each finite element mesh is obtained by solving the overall equilibrium relationship of the finite element model. The mathematical expression of the overall equilibrium relationship of the finite element model is as follows: ; in: The overall finite element stiffness matrix, For the displacement response of all finite element meshes, For operating force load, The contact reaction force vector is automatically generated from each contact constraint condition; The mathematical expression for the contact reaction force vector automatically generated from each contact constraint condition is: ; in, This represents the normal contact reaction density corresponding to the contact constraint. For the interface normal, Γ k This is the k-th type of contact interface.

2. The method for displaying mechanical information for risk warning during impacted tooth extraction according to claim 1, characterized in that, The tissue types in step S1 include enamel, dentin, dental pulp, alveolar cortical bone, cementum, cancellous alveolar bone, medullary cavity, trabecular bone, adipose tissue, and mandibular nerve canal.

3. The method for displaying mechanical information for risk warning during impacted tooth extraction according to claim 1, characterized in that, The intersection of any two units is an empty set.

4. The method for displaying mechanical information for risk warning during impacted tooth extraction according to claim 1, characterized in that, In step S3, contact constraints are constructed between each tooth segment, between each tooth segment and alveolar bone, between each tooth segment and adjacent teeth, and between each tooth segment and mandibular nerve canal.

5. A method for displaying mechanical information for risk warning during impacted tooth extraction according to claim 4, characterized in that, The contact constraint between the tooth segment and the mandibular nerve canal is specifically the contact constraint of the externally expanded safety buffer zone between the tooth segment and the mandibular nerve canal.

6. The method for displaying mechanical information for risk warning during impacted tooth extraction according to claim 1, characterized in that, The displacement matrix of each tooth segment and tissue unit is as follows: ; in: Let e ​​be the displacement matrix of element e. Let be the shape function of the i-th finite element mesh. Let i be the displacement response of the i-th finite element mesh. denoted as the number of finite element meshes for element e.

7. The method for displaying mechanical information for risk warning during impacted tooth extraction according to claim 1, characterized in that, The strain tensor of each tooth segment and tissue unit is: ; in: Let e ​​be the strain tensor of element e. Let be the strain-displacement matrix of element e; The stress tensor of each tooth segment and tissue unit is: ; in: Let e ​​be the stress tensor of element e. Let e ​​be the constitutive matrix of the material structure corresponding to element e.

8. A biomechanical information display device for risk warning during impacted tooth extraction, comprising a memory, a processor, and a program stored in the memory, characterized in that, When the processor executes the program, it implements the method as described in any one of claims 1-7.

9. A storage medium having a program stored thereon, characterized in that, When the program is executed, it implements the method as described in any one of claims 1-7.

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