A method and system for pre-extraction planning of a maxillary first molar

Abstract

The application provides a maxillary first molar pre-extraction planning method and system; the maxillary first molar pre-extraction planning method comprises the following steps: constructing a three-dimensional model of the diseased tooth based on CBCT data and oral scanning data of a patient; obtaining an optimal tooth separation depth based on the three-dimensional model of the diseased tooth; constructing a finite element model according to the CBCT data to obtain an optimal force direction of the tooth extraction instrument based on the finite element model; obtaining an optimal luxation direction of each tooth block according to the three-dimensional model of the diseased tooth; and combining the optimal tooth separation depth, the optimal force direction and the optimal luxation direction to evaluate the intraoperative risk level, so as to generate a risk evaluation and planning report. The application deeply integrates digital technology with the clinical needs of tooth extraction surgery, significantly improves the accuracy, predictability and safety of preoperative evaluation of maxillary first molar extraction, especially high-difficulty cases, and helps to systematically reduce surgical complications and improve surgical success rate.

Description

Technical Field

[0001] This application relates to the field of digital technology in oral medicine, and in particular to a method and system for preoperative planning of maxillary first molar extraction. Background Technology

[0002] The maxillary first molar is one of the permanent teeth with the heaviest functional load in the oral cavity. The root of the maxillary first molar is closely related to the floor of the maxillary sinus; in a significant proportion of cases, only a thin layer of bone separates the root from the sinus floor, or the root even protrudes directly into the maxillary sinus. Improper surgical technique during extraction of the maxillary first molar can easily lead to serious complications such as root fracture, perforation of the maxillary sinus floor, and accidental entry of the root into the maxillary sinus. This is especially true for teeth that have undergone root canal treatment, where the fragility of the tooth structure is significantly increased, resulting in a higher risk of root fracture during extraction.

[0003] Traditional preoperative assessment for maxillary first molar extraction relies primarily on two-dimensional panoramic radiographs and clinical experience. However, two-dimensional images cannot accurately represent the true three-dimensional morphology of the tooth root, its bifurcation angle, and its spatial relationship with adjacent anatomical structures (such as the maxillary sinus floor and adjacent tooth roots), making it difficult to accurately assess the extraction difficulty and predict intraoperative risks. In recent years, cone-beam computed tomography (CBCT) has been increasingly used for preoperative assessment of oral surgery due to its high spatial resolution and three-dimensional imaging capabilities. CBCT can clearly display key information such as tooth root morphology, variations in the number of roots, the relationship between the tooth root and the maxillary sinus floor, and resistance from adjacent teeth. Meanwhile, intraoral scanners (IOS) can acquire high-precision three-dimensional models of the tooth crown surface through optical scanning technology, with an accuracy of up to 20 μm. However, single CBCT images suffer from high noise and low resolution in the crown portion, while intraoral scan data cannot obtain tooth root information; both have their limitations. Summary of the Invention

[0004] This application provides a method and system for preoperative planning of maxillary first molar extraction to solve the above-mentioned technical problems.

[0005] Specifically, this application provides a preoperative planning method for the extraction of the maxillary first molar, comprising the following steps: constructing a three-dimensional model of the affected tooth based on the patient's CBCT data and intraoral scan data; obtaining the optimal tooth separation depth based on the three-dimensional model of the affected tooth; constructing a finite element model based on the CBCT data to obtain the optimal force direction of the extraction instrument based on the finite element model; obtaining the optimal detachment direction of each tooth segment based on the three-dimensional model of the affected tooth; and assessing the intraoperative risk level by combining the optimal tooth separation depth, optimal force direction, and optimal detachment direction to generate a risk assessment and planning report.

[0006] The above technical solution deeply integrates advanced digital technologies (multi-source data fusion, 3D modeling, finite element biomechanical simulation) with the clinical needs of tooth extraction surgery, realizing a leap from the traditional experience-dependent, two-dimensional assessment mode to a data-driven, three-dimensional quantitative, and personalized simulation planning mode. It significantly improves the accuracy, predictability, and safety of preoperative assessment for maxillary first molar extraction, especially in high-difficulty cases (such as after root canal treatment or adjacent to the maxillary sinus), and helps to systematically reduce surgical complications and improve the success rate of surgery.

[0007] Furthermore, the construction of a three-dimensional model of the affected tooth based on the patient's CBCT data and intraoral scan data includes: simultaneously solving the spatial rigid transformation matrix and the latent code of tooth morphology by jointly optimizing the objective function, so as to fuse the CBCT data and intraoral scan data to generate a three-dimensional model of the affected tooth.

[0008] Furthermore, the joint optimization objective function is specifically as follows: In the formula, This represents CBCT data or oral scan data. This represents the set of points on the crown surface in the oral scan data. This represents the set of tooth root and crown points in CBCT data. and Let represent the rotation matrix and translation vector that unify the point set to the standard anatomical coordinate system, respectively. This represents the confidence weighting coefficient; denoted as the regularization term, and z represents the latent encoding of tooth morphology.

[0009] The above technical solution overcomes the shortcomings of a single data source; it jointly optimizes registration (through R,t) and shape completion / correction (through latent encoding z) within a unified framework. This means that while searching for the best alignment, it also utilizes the complementary information of CBCT and intraoral scan data to correct each other's defects (such as noise in CBCT crowns) to obtain an optimal and complete three-dimensional morphological representation; the introduction of regularization terms can prevent overfitting.

[0010] Furthermore, obtaining the optimal tooth separation depth based on the three-dimensional model of the affected tooth includes: extracting the bifurcation points of the mesobuccal root, distal buccal root, and palatal root based on the three-dimensional model of the affected tooth; calculating the cervical stenosis at the bifurcation points; and using a dynamic programming algorithm to obtain the optimal tooth separation depth with the goal of balancing the risk of root fracture, the cost of bone loss, and the gain of root independence.

[0011] Furthermore, the formula for extracting the bifurcation point location is as follows: , ; In the formula, This represents the z-axis height coordinate of the crown tip. This represents the z-axis height coordinate of the root tip. This indicates the three-dimensional space occupied by the affected tooth. Indicates height as The cross section; where, when When the height changes abruptly from 1 to 3, the corresponding height represents the location of the bifurcation point.

[0012] In the above technical solution, by analyzing the number of connected components of different height sections and the space occupied by teeth, the precise bifurcation height of the tooth root separating from the whole can be detected objectively and automatically. This is the anatomical basis for determining the tooth separation depth.

[0013] Furthermore, the formula for calculating the stenosis of the neck at the bifurcation point is as follows: In the formula, This represents the cross-sectional boundary of the three-dimensional model of the affected tooth at height z. Denotes any boundary point of the cross-section boundary. Indicates height as The geometric centroid of the cross section, z, is based on the bifurcation center point P. furc Confirmed; where z < z furc , z furc Let P be the center point of the bifurcation. furc The height coordinates.

[0014] The above technical solution quantifies the degree of narrowing of the tooth root at the bifurcation point. The higher the narrowing, the more concentrated the stress at that point, and the greater the risk of root fracture, providing a key quantitative indicator for risk assessment.

[0015] Furthermore, the dynamic programming algorithm can systematically search all possible tooth separation depth schemes and find the global optimum rather than the local optimum, ensuring that the optimal tooth separation depth is the best clinical decision point after comprehensively balancing all factors.

[0016] Furthermore, obtaining the optimal force direction of the extraction instrument includes: simulating the force applied by the extraction instrument at different loading angles based on a finite element model, calculating the stress distribution and root fracture threshold at each loading angle; and outputting the optimal loading angle vector with the peak stress of the root being less than the root fracture threshold at the current loading angle, using minimizing the peak stress of the root as the objective function, to determine the optimal force direction.

[0017] In the above technical solution, finite element analysis can visualize and quantify the stress distribution of extraction force in the tooth and periodontal tissues. By comparing the simulated peak root stress with the pre-set root material fracture threshold, the probability of root fracture under different operating angles can be directly and objectively predicted. The optimal loading angle vector output by searching with minimizing the peak root stress as the clear objective is a data-driven and personalized operating guide. It tells doctors which direction to apply force to maximize the uniform distribution of force, reduce the risk of root fracture, and protect weak structures such as the maxillary sinus floor.

[0018] Furthermore, obtaining the optimal dislocation direction for each tooth block includes: marking the resistance boundary based on the three-dimensional model of the affected tooth; using the dislocation of each tooth block along its long axis as the reference path, iteratively optimizing the dislocation trajectory using a collision detection algorithm, and finally outputting the optimal dislocation direction vector that minimizes the dislocation journey and avoids the floor of the maxillary sinus as the optimal dislocation direction; wherein, the tooth block includes the mesial buccal root block, the distal buccal root block, and the palatal root block.

[0019] In the above technical solution, the collision detection algorithm is used for iterative optimization, which can automatically adjust the trajectory to ensure the dislocation path, so as to avoid key structures (such as the maxillary sinus floor), minimize the dislocation distance, and avoid collision with adjacent teeth.

[0020] Furthermore, a risk assessment and planning report is generated, including: obtaining the minimum three-dimensional distance between the root apex of each tooth and the floor of the maxillary sinus based on the three-dimensional model of the affected tooth, and obtaining the risk level according to the distance threshold; predicting the fracture risk score of each tooth root based on the optimal tooth separation depth and the optimal force direction; calculating the minimum gap between each tooth fragment and adjacent teeth in the extraction path based on the optimal dislocation direction and predicting the collision probability; and generating a risk assessment and planning report by combining the risk level, fracture risk score and collision probability.

[0021] The above technical solution integrates and analyzes all the aforementioned quantitative results to generate multi-level, visualized reports, reducing the operational threshold for young doctors and improving medical safety.

[0022] Based on the same concept, this application also provides a system for preoperative planning of maxillary first molar extraction, comprising: a data acquisition module for acquiring the patient's CBCT data and intraoral scan data; a three-dimensional reconstruction module for constructing a three-dimensional model of the affected tooth based on the CBCT data and intraoral scan data; a tooth separation depth calculation module for obtaining the optimal tooth separation depth based on the three-dimensional model of the affected tooth; a force direction calculation module for constructing a finite element model based on the CBCT data to obtain the optimal force direction of the extraction instrument based on the finite element model; a luxation direction calculation module for obtaining the optimal luxation direction of each tooth segment based on the three-dimensional model of the affected tooth; and a risk assessment module for assessing the intraoperative risk level by combining the optimal tooth separation depth, optimal force direction, and optimal luxation direction to generate a risk assessment and planning report.

[0023] Compared with the prior art, the beneficial effects of this application are as follows: This application deeply integrates digital technology with the clinical needs of tooth extraction surgery, significantly improving the accuracy, predictability, and safety of preoperative assessment for maxillary first molar extraction, especially in high-difficulty cases. It helps to systematically reduce surgical complications and increase the success rate of surgery. Attached Figure Description

[0024] Figure 1 This is a flowchart of the preoperative planning method for the extraction of the maxillary first molar described in this application.

[0025] Figure 2 This is a schematic diagram showing the location of the bifurcation point, the bifurcation center point, and the geometric centroid as described in the embodiments of this application.

[0026] Figure 3 This is a schematic diagram of the local coordinate system described in an embodiment of this application.

[0027] Figure 4 This is a schematic diagram of the minimum three-dimensional distance described in the embodiments of this application.

[0028] Figure 5 This is a block diagram of the preoperative planning system for the extraction of the maxillary first molar described in this application. Detailed Implementation

[0029] The following describes in further detail a preoperative planning method and system for the extraction of the maxillary first molar, in conjunction with specific embodiments and accompanying drawings.

[0030] Please see Figure 1 This application provides a preoperative planning method for the extraction of the maxillary first molar, including the following steps S100-S500.

[0031] Step S100: Construct a three-dimensional model of the affected tooth based on the patient's CBCT data and intraoral scan data.

[0032] The step of constructing a three-dimensional model of the affected tooth based on the patient's CBCT data and intraoral scan data includes: simultaneously solving the spatial rigid transformation matrix and the latent code of tooth morphology by jointly optimizing the objective function, so as to fuse the CBCT data and intraoral scan data to generate a three-dimensional model of the affected tooth.

[0033] In some embodiments, CBCT data refers to cone-beam computed tomography (CBCT) data used to acquire three-dimensional oral images; intraoral scan data refers to three-dimensional surface data of the teeth acquired by an intraoral scanner; a deep implicit representation network (DeepSDF) is used to fuse CBCT data and intraoral scan data. Specifically, the three-dimensional morphology of the affected tooth is implicitly expressed as a continuous signed distance function, defining any point in space... The shortest distance to the three-dimensional shape surface is , Let represent the set of real numbers. Its neural network mapping relationship is expressed as: ; In the formula, These are the learnable parameters of the neural network. This is a potential code characterizing the anatomical morphology of the affected tooth. When At that time, the set of points constitutes the zero level set of the affected tooth, that is, the three-dimensional surface.

[0034] In the fusion and registration stage, in order to solve the spatial misalignment and morphological stitching problems between intraoral scan data (containing only high-precision crowns) and CBCT data (containing noisy crowns and complete roots), a joint optimization objective function was constructed to simultaneously solve the spatial rigid transformation matrix and the optimal tooth morphology code (i.e., the tooth morphology latent code).

[0035] Furthermore, the joint optimization objective function is specifically as follows: ; In the formula, This represents CBCT data or oral scan data. This represents the set of points on the crown surface in the oral scan data. This represents the set of tooth root and crown points in CBCT data. and Let represent the rotation matrix and translation vector that unify the point set to the standard anatomical coordinate system, respectively. This represents the confidence weighting coefficient; denoted as the regularization term, and z represents the latent encoding of tooth morphology.

[0036] It should be noted that, because the accuracy of intraoral scanning of crowns is significantly higher than that of CBCT, it is usually set to... (e.g., a value of 0.3-0.5) to reduce interference from noise in the crown portion of CBCT; the regularization term is used to constrain the generated shape latent encoding. Within the prior distribution space, ensure that the generated teeth conform to the actual anatomical rules.

[0037] Through gradient descent backpropagation optimization of the above objective function, the system simultaneously completes robust registration and morphological interpolation of high-precision crowns and complete roots in a unified implicit space. Finally, the zero-level set is extracted by the Marching Cubes algorithm to generate a seamless, watertight, and anatomically consistent 3D model of the affected tooth.

[0038] The above technical solution overcomes the shortcomings of a single data source; it jointly optimizes registration (through R, t) and shape completion / correction (through latent encoding z) within a unified framework. This means that while searching for the best alignment, it also utilizes the complementary information of CBCT and intraoral scan data to correct each other's defects (such as noise in CBCT crowns) to obtain an optimal and complete three-dimensional morphological representation; the introduction of regularization terms can prevent overfitting.

[0039] Step S200: Obtain the optimal tooth separation depth based on the three-dimensional model of the affected tooth.

[0040] The process of obtaining the optimal tooth separation depth based on the three-dimensional model of the affected tooth includes: extracting the bifurcation points of the mesobuccal root, distal buccal root, and palatal root based on the three-dimensional model of the affected tooth; calculating the cervical stenosis at the bifurcation points; and using a dynamic programming algorithm to obtain the optimal tooth separation depth with the goal of balancing the risk of root fracture, the cost of bone loss, and the gain of root independence.

[0041] Among them, the optimal tooth separation depth refers to the best cutting depth calculated by the algorithm, so that each root block is independent during extraction and the risk of root fracture is minimized; the bifurcation point location refers to the position where the tooth root separates into multiple independent roots from the common root trunk; the cervical stenosis refers to the minimum radial distance of the tooth root cross section below the bifurcation point, reflecting the "waist" degree of the tooth root at that point. The higher the stenosis, the greater the risk of root fracture.

[0042] In some embodiments, spatial geometric topology analysis and multi-constraint optimization algorithms are employed. Specifically, based on the fused three-dimensional network model, the critical points for the transition from a single root trunk to the mesubungal root (MB), distal buccal root (DB), and palatal root (P) are identified by calculating the change in the number of connected domains in the cross-section along the long axis (z-axis) of the tooth. The geometric centroid at the bottom of the pulp chamber is defined as the bifurcation center point P. furc (like Figure 2 (As shown).

[0043] Furthermore, extract the location of the bifurcation point (e.g.) Figure 2 The formula shown is as follows: , ; In the formula, This represents the z-axis height coordinate of the crown tip. This represents the z-axis height coordinate of the root tip. This indicates the three-dimensional space occupied by the affected tooth. Indicates height as The cross section; where, when When the height changes abruptly from 1 to 3, the corresponding height represents the location of the bifurcation point.

[0044] In the above technical solution, by analyzing the number of connected components of different height sections and the space occupied by teeth, the precise bifurcation height of the tooth root separating from the whole can be detected objectively and automatically. This is the anatomical basis for determining the tooth separation depth.

[0045] Furthermore, to ensure that the root blocks after tooth splitting have sufficient resistance shape, the radial contraction ratio is calculated on each root section below the bifurcation point, and the minimum radial distance of the section is defined as the neck stenosis. The formula for calculating the stenosis of the neck at the bifurcation point is as follows: ; In the formula, This represents the cross-sectional boundary of the three-dimensional model of the affected tooth at height z. Denotes any boundary point of the cross-section boundary. Indicates height as The geometric centroid of the cross section, z, is based on the bifurcation center point P. furc (like Figure 2 (As shown) confirmed; where z < z furc , z furc Let P be the center point of the bifurcation. furc The height coordinates; the bifurcation center point refers to the geometric centroid of the bottom of the pulp chamber, which is usually located in the center of the three root bifurcation regions and serves as a reference point for the tooth division depth.

[0046] Below the bifurcation point, the tooth root begins to taper and contract inwards; this area is the cervical stenosis zone. The rate of change in stenosis is used to identify "dangerous sections" to prevent excessive tooth separation that could lead to insufficient root strength and intraoperative root fracture. The system models the tooth separation process as a state transition problem to find the optimal tooth separation plane height. The state is defined as depth. : ; in, The risk cost of root fracture is calculated based on the neck stenosis and finite element stress distribution. The cost of bone removal is directly related to the depth of tooth separation; is the root independence gain, defined as the probability that all roots below the dividing plane are completely physically separated.

[0047] A dynamic programming algorithm is used to recursively calculate the local optimal solution of the subproblem while satisfying the interdental spacing. and the distance from the root apex to the floor of the maxillary sinus Under the constraints, the globally optimal tooth separation depth value is output.

[0048] The above technical solution quantifies the degree of narrowing of the tooth root at the bifurcation point. The higher the degree of narrowing, the more concentrated the stress at that point, and the greater the risk of root fracture, providing a key quantitative indicator for risk assessment.

[0049] Furthermore, the dynamic programming algorithm can systematically search all possible tooth separation depth schemes and find the global optimum rather than the local optimum, ensuring that the optimal tooth separation depth is the best clinical decision point after comprehensively balancing all factors.

[0050] Step S300: Construct a finite element model based on the CBCT data to obtain the optimal force direction of the extraction instrument based on the finite element model.

[0051] The process of obtaining the optimal force direction of the tooth extraction instrument includes: simulating the force applied by the tooth extraction instrument at different loading angles based on a finite element model, calculating the stress distribution and root fracture threshold at each loading angle; and outputting the optimal loading angle vector with the peak stress of the tooth root being less than the root fracture threshold at the current loading angle, using the minimization of the peak stress of the tooth root as the objective function, in order to determine the optimal force direction.

[0052] The optimal force direction refers to the loading angle vector that minimizes the peak stress inside the tooth root and keeps it below the dynamic fracture threshold, guiding the doctor in the direction of force application.

[0053] In some embodiments, considering the directionality of fiber distribution within the alveolar bone and dental tissues, the relevant anatomical tissues are defined as orthotropic materials whose mechanical response follows the generalized Hooke's law. In the local coordinate system, the stress vector... With strain vector The mapping relationship is represented as follows: ; ; ; .

[0054] In the formula, , and These represent the elastic modulus, shear modulus, and Poisson's ratio along the main anatomical directions (mesiodistal, buccal-lingual, and long axis), respectively. Coupled with the Young's modulus field extracted by CBCT voxel density and this constitutive matrix, a non-homogeneous and accurate simulation of the force response of the affected tooth was achieved. Studies have shown that the risk of root fracture during tooth extraction depends not only on the absolute load magnitude but also on the amplification angle. The contribution of the angle between the cutting edge and the tooth's long axis to the local stress concentration factor. Define the dynamic fracture threshold function. as follows: ; in, The quasi-static compressive / tensile strength of the material. The coefficient of friction between the cutting edge and the tooth surface is denoted as . This is a geometric correction factor based on the root curvature characteristics. The formula quantifies the impact of the amplification angle on the root structure's load-bearing limit by altering the proportion of the lateral force component, reflecting the angle-dependent nature of stress distribution. To find the optimal extraction path, an optimization model is constructed with the core objective of reducing the probability of root fracture.

[0055] make Root region Any voxel point within To load angle The equivalent (Von Mises) stress calculated below, and its optimization objective function. Expressed as: ; .

[0056] By traversing and searching the massive stress vector field generated by the finite element simulation, the optimal loading angle vector that minimizes the peak stress inside the tooth root and is below the dynamic fracture threshold is output, thereby establishing the recommended instrument force direction, i.e. the optimal force direction.

[0057] In the above technical solution, finite element analysis can visualize and quantify the stress distribution of extraction force in the tooth and periodontal tissues. By comparing the simulated peak root stress with the pre-set root material fracture threshold, the probability of root fracture under different operating angles can be directly and objectively predicted. The optimal loading angle vector output by searching with minimizing the peak root stress as the clear objective is a data-driven and personalized operating guide. It tells doctors which direction to apply force to maximize the uniform distribution of force, reduce the risk of root fracture, and protect weak structures such as the maxillary sinus floor.

[0058] Step S400: Obtain the optimal dislocation direction of each tooth segment based on the three-dimensional model of the affected tooth.

[0059] The process of obtaining the optimal detachment direction for each tooth block includes: marking resistance boundaries based on the three-dimensional model of the affected tooth; using the detachment of each tooth block along its long axis as the reference path, iteratively optimizing the detachment trajectory using a collision detection algorithm, and finally outputting the optimal detachment direction vector that minimizes the detachment distance and avoids the floor of the maxillary sinus as the optimal detachment direction; wherein, the tooth block includes the mesial buccal root block, the distal buccal root block, and the palatal root block; the optimal detachment direction refers to the best removal direction vector that minimizes the detachment distance, avoids the floor of the maxillary sinus, and does not collide with adjacent teeth or bone walls.

[0060] In some embodiments, this is achieved by establishing a local anatomical coordinate system and a discrete trajectory optimization algorithm: to accurately describe the motion vectors of each tooth block (such as the mesiobuccal root block, palatal root block, etc.), firstly, for each independent tooth block... Constructing a local coordinate system .

[0061] like Figure 3 As shown, the geometric centroid of the tooth block is set as the origin. Using its root long axis (or the direction of the first principal axis in principal component analysis of the root canal centerline) as... The axis (i.e., the direction of the dislocation reference path) is defined based on its adjacent contact point and the normal of the cortical bone surface. and Axis. In this coordinate system, any displacement transformation of the tooth block can be expressed as an operator. ,in and These are the rotation matrix and translation vector, respectively. The dislocation process is discretized as the movement from the bottom of the extraction socket. To the safe evacuation point of A sequence of pose nodes The total dislocation distance S is defined as the sum of the Euclidean distances of each segment of the path, and its calculation formula is as follows: ; During the iterative optimization process, a collision detection algorithm is used to monitor the tooth blocks in real time. With resistance boundary region The overlapping state; if in pose Detected at the location Then, the path vector is adjusted using the local gradient descent method to make... In satisfying And distance from the floor of the maxillary sinus It obtains a minimum value under the constraint of .

[0062] The final output is the optimal dislocation direction vector. The unit direction vectors for the first and last nodes of the sequence: ; This vector guides the surgeon in clinical practice to achieve successful tooth dislocation using the shortest path while avoiding key structures such as the maxillary sinus.

[0063] In the above technical solution, the collision detection algorithm is used for iterative optimization, which can automatically adjust the trajectory to ensure the dislocation path, so as to avoid key structures (such as the maxillary sinus floor), minimize the dislocation distance, and avoid collision with adjacent teeth.

[0064] Step S500: Assess the intraoperative risk level by combining the optimal tooth separation depth, optimal force direction, and optimal detachment direction to generate a risk assessment and planning report.

[0065] The process of generating a risk assessment and planning report includes: obtaining the minimum three-dimensional distance between the root apex of each tooth and the floor of the maxillary sinus based on a three-dimensional model of the affected tooth, and obtaining the risk level based on the distance threshold; predicting the fracture risk score of each tooth root based on the optimal tooth separation depth and the optimal force direction; calculating the minimum gap between each tooth fragment and adjacent teeth in the extraction path based on the optimal dislocation direction and predicting the collision probability; and generating a risk assessment and planning report by combining the risk level, fracture risk score and collision probability.

[0066] In some embodiments, a multi-criteria quantitative analysis algorithm is used to automatically grade and evaluate the safety of the surgical procedure by calculating the point set on each root surface of the affected tooth. To the bony wall of the maxillary sinus floor minimum three-dimensional distance (like Figure 4 As shown in the figure, spatial risk quantification is achieved; its calculation formula is as follows: ; In the formula, and These are the three-dimensional coordinates of the corresponding point cloud. The system, based on... The value of is combined with the continuity of the maxillary sinus floor bone plate in CBCT (i.e., whether there is an anatomical defect) to output high, medium, and low risk warnings, providing mechanical boundary constraints for clinical decisions on whether to perform root segmentation. Based on the aforementioned finite element analysis results, the stress intensity ratio is introduced. As a core indicator for fracture risk scoring, it is defined as the current loading angle. Lower root region The ratio of the peak equivalent stress within the range to the dynamic fracture threshold at that angle: ; In the formula, The calculated Von Mises equivalent stress. When At that time, it was determined to be of high risk of fracture; the system evaluates different combinations of tooth separation depth and force direction. Values ​​that automatically filter out those that meet the safety factor The optimal removal path. In the discretized dislocation trajectory Every time step Above, real-time calculation of tooth blocks With adjacent tooth surfaces The dynamic minimum gap between : ; Based on the recommended force direction vector, through evaluation Calculate the collision probability function based on the rate of change and minimum value during the motion. If the path contains If the interval is within a certain range, it is marked as a high risk of adjacent tooth damage, and it is suggested to increase the amount of bone removed or adjust the dislocation vector.

[0067] Furthermore, based on the above risk analysis, a visual report can be generated and output to a digital navigation system or a 3D-printed surgical guide manufacturing system to achieve intraoperative visual guidance.

[0068] The above technical solution integrates and analyzes all the aforementioned quantitative results to generate multi-level, visualized reports, reducing the operational threshold for young doctors and improving medical safety.

[0069] In summary, the preoperative planning method for maxillary first molar extraction described in this application deeply integrates advanced digital technologies (multi-source data fusion, 3D modeling, and finite element biomechanical simulation) with the clinical needs of tooth extraction surgery. It achieves a leap from the traditional experience-dependent, two-dimensional assessment model to a data-driven, three-dimensional quantitative, and personalized simulation planning model. It significantly improves the accuracy, predictability, and safety of preoperative assessment for maxillary first molar extraction, especially in high-difficulty cases (such as after root canal treatment or adjacent to the maxillary sinus), and helps to systematically reduce surgical complications and improve the success rate of surgery.

[0070] Based on the same concept, please refer to Figure 5 This application also provides a system for preoperative planning of maxillary first molar extraction, including a data acquisition module, a three-dimensional reconstruction module, a tooth separation depth calculation module, a force direction calculation module, a dislocation direction calculation module, and a risk assessment module.

[0071] The data acquisition module is used to acquire the patient's CBCT data and oral scan data.

[0072] In some embodiments, taking a patient requiring extraction of the right maxillary first molar as an example; firstly, the patient's maxillofacial region is scanned using a cone-beam CT scanner to obtain DICOM format CBCT image data, with a slice thickness set to 0.2 mm, covering the maxilla, maxillary sinus, affected tooth, and adjacent tooth area; simultaneously, the patient's dentition is optically scanned using an intraoral scanner to obtain STL format intraoral scan data, with the scanning range covering the crown of the affected tooth and at least two adjacent teeth and part of the gingival surface; the above two sets of data are then imported into the three-dimensional reconstruction module.

[0073] The three-dimensional reconstruction module is used to construct a three-dimensional model of the affected tooth based on the CBCT data and intraoral scan data.

[0074] In some embodiments, a fusion algorithm based on deep implicit representation is used. First, the CBCT data is segmented in three dimensions to extract the complete root contour of the affected tooth. At the same time, the crown surface is reconstructed from the intraoral scan data. The two sets of data are precisely registered in space by the iterative nearest point algorithm and fused to generate a three-dimensional model that includes both the high-precision crown at the intraoral scan level and the complete tooth root at the CBCT level. This model is further extended to reconstruct anatomical structures such as adjacent teeth, the floor of the maxillary sinus, and alveolar bone, laying the foundation for subsequent analysis.

[0075] The tooth separation depth calculation module is used to obtain the optimal tooth separation depth based on the three-dimensional model of the affected tooth.

[0076] In some embodiments, based on the constructed 3D model, the spatial location information of the three roots of the maxillary first molar—the mesobuccal root, the distal buccal root, and the palatal root—is extracted, and the bifurcation point position of each root (i.e., the starting position where the three roots branch off from the common root trunk) is calculated. The bifurcation angle and neck stenosis of each root are analyzed to identify the bifurcation structures that are most likely to cause extraction difficulties. In accordance with the minimally invasive principle of "bifurcation first, then extraction one by one," the optimal tooth separation depth is calculated: usually, the tooth separation plane is set 1-2 mm below the root bifurcation, so that after tooth separation, each root block is independent of each other and retains sufficient clamping length.

[0077] In special cases of large and curved palatal roots, the algorithm automatically adjusts the tooth separation position based on the direction and radius of curvature to avoid the separation plane coinciding with the highest point of the root curvature, which could lead to root fracture during surgery. The algorithm outputs the tooth separation depth value (accurate to 0.1 mm) and a visual annotation of the separation plane on the 3D model, which can be used for 3D printing of surgical guides or imported into navigation systems.

[0078] The force direction calculation module is used to construct a finite element model based on the CBCT data, so as to obtain the optimal force direction of the tooth extraction instrument based on the finite element model.

[0079] In some embodiments, to determine the optimal instrument force direction when extracting each tooth fragment, this embodiment employs a three-dimensional finite element analysis method. A three-dimensional finite element model including the affected tooth, periodontal ligament, alveolar bone, adjacent teeth, and maxillary sinus floor is constructed based on CBCT data. Anisotropic properties (elastic modulus, Poisson's ratio, fracture strength, etc.) are assigned to the tooth tissue according to reported material parameters, and a hyperelastic constitutive model is used to simulate the nonlinear mechanical behavior of the periodontal ligament.

[0080] The extraction process using both dental elevators and forceps at different loading angles was simulated. The loading angles were set to vary from 0° to 45° in the buccal-lingual and mesiodistal directions, with a step size of 5°. Stress distribution contour maps were calculated for each loading angle, with a focus on monitoring peak stresses in the apical and furcation regions. Using the fracture threshold of the tooth material (according to literature, dentin tensile strength is approximately 50-100 MPa, and compressive strength is approximately 250-350 MPa) as a safety boundary, a set of loading angles with peak stresses below the threshold was selected. Then, with the goal of minimizing the stress value, the optimal force direction and its allowable safe angle range were output.

[0081] For dental elevators, simulation results show that when a wedge force is applied to the root bifurcation region, the larger the force amplification angle (i.e., the larger the angle between the elevator blade and the long axis of the tooth), the lower the stress on the surrounding tissues. However, the root fracture threshold exhibits an angle-dependent change, requiring an optimal balance between the two. This algorithm uses finite element calculation results as a benchmark and outputs a specific direction vector, for example: "It is recommended that the dental elevator be inserted into the bifurcation space at a 20° angle from the buccal mesial direction."

[0082] The dislocation direction calculation module is used to obtain the optimal dislocation direction of each tooth segment based on the three-dimensional model of the affected tooth.

[0083] In some embodiments, after tooth separation, the evoked direction of each tooth block needs to be planned. Taking the mesial buccal root block as an example, the evoked direction calculation module first marks all resistance boundaries in the 3D model: buccal cortical bone plate, palatal hard palate bone plate, maxillary sinus floor, and contact points with adjacent teeth. The evoked starting point is set as the centroid of the current tooth block, and the target point is the safe area outside the extraction socket. Using the evoked path along the root longitudinal axis in the apical direction as the reference, collision detection iterative optimization is performed in 3D space. In each iteration, if a collision with a resistance boundary is detected, the evoked direction vector is adjusted at the collision point to deviate from the collision normal, and the length of the new evoked path is calculated. The optimization objectives are: minimizing the evoked distance, avoiding contact with the maxillary sinus floor, and avoiding adjacent tooth areas.

[0084] After iterative optimization, the optimal dislocation direction vector for each tooth block is output. For example, "the mesiobuccal root block dislocates towards the buccal side, at a 15° angle to the long axis of the tooth; the palatal root block dislocates towards the palatal side, in a straight line along the long axis of the palatal root." This result can be converted into a visual arrow guide on the surgical navigation interface.

[0085] The risk assessment module is used to assess the intraoperative risk level by combining the optimal tooth separation depth, optimal force direction, and optimal detachment direction, in order to generate a risk assessment and planning report.

[0086] In some embodiments, by combining the analysis results of the above modules, the risk assessment module outputs a multi-dimensional risk report: Risk of maxillary sinus floor perforation: Measure the minimum three-dimensional distance between the root apex of each tooth and the floor of the maxillary sinus. If the affected tooth has a root protrusion into the maxillary sinus (negative distance), it is marked as high risk, and it is suggested that maxillary sinus repair material be prepared during the operation; if the distance is between 1-3 mm, it is marked as medium risk, and it is recommended to operate gently during the operation and avoid applying force to the root apex towards the maxillary sinus.

[0087] Root fracture risk: Based on finite element analysis results, the ratio of peak stress to material fracture threshold (stress ratio) is calculated for each tooth segment under the recommended force direction. A stress ratio <0.5 indicates low risk, 0.5-0.8 indicates medium risk, and >0.8 indicates high risk. For teeth that have undergone root canal treatment, the algorithm automatically reduces the fracture threshold (by 20%-30% based on the brittleness increase factor) to improve the sensitivity of risk warning.

[0088] Risk of damage to adjacent teeth: Calculate the minimum dynamic gap between each tooth fragment and adjacent teeth along the avulsion path. If the minimum gap is <1mm, it is marked as high risk, indicating the need to expand the bone removal area or adjust the avulsion direction.

[0089] The risk report is presented visually on the 3D model, with risk areas marked with heat maps, and also provides textual clinical advice and intraoperative precautions.

[0090] Although exemplary embodiments have been described herein with reference to the accompanying drawings, it should be understood that the above exemplary embodiments are merely illustrative and are not intended to limit the scope of this application. Various changes and modifications can be made therein by those skilled in the art without departing from the scope and spirit of this application. All such changes and modifications are intended to be included within the scope of this application as claimed in the appended claims.

[0091] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0092] Although the description of this application has been made in conjunction with the specific embodiments described above, it will be apparent to those skilled in the art that many substitutions, modifications, and variations can be made based on the foregoing. Therefore, all such substitutions, modifications, and variations are included within the spirit and scope of the appended claims.

Claims

1. A preoperative planning method for the extraction of the maxillary first molar, characterized in that, Includes the following steps: A three-dimensional model of the affected tooth was constructed based on the patient's CBCT and intraoral scan data; The optimal tooth separation depth is obtained based on the three-dimensional model of the affected tooth. A finite element model is constructed based on the CBCT data to obtain the optimal force direction of the extraction instrument. The optimal avulsion direction of each tooth segment is obtained based on the three-dimensional model of the affected tooth; Furthermore, the intraoperative risk level is assessed by combining the optimal tooth separation depth, optimal force direction, and optimal detachment direction to generate a risk assessment and planning report.

2. The preoperative planning method for maxillary first molar extraction according to claim 1, characterized in that, The construction of a three-dimensional model of the affected tooth based on the patient's CBCT and intraoral scan data includes: By jointly optimizing the objective function, the spatial rigid transformation matrix and the latent code of tooth morphology are solved simultaneously, so as to fuse the CBCT data and intraoral scan data and generate a three-dimensional model of the affected tooth.

3. The preoperative planning method for maxillary first molar extraction according to claim 2, characterized in that, The joint optimization objective function is specifically as follows: ； In the formula, This represents CBCT data or oral scan data. This represents the set of points on the crown surface in the oral scan data. This represents the set of tooth root and crown points in CBCT data. and Let represent the rotation matrix and translation vector that unify the point set to the standard anatomical coordinate system, respectively. This represents the confidence weighting coefficient; denoted as the regularization term, and z represents the latent encoding of tooth morphology.

4. The preoperative planning method for maxillary first molar extraction according to claim 2, characterized in that, The optimal tooth separation depth is obtained based on the three-dimensional model of the affected tooth, including: Based on the three-dimensional model of the affected tooth, the bifurcation points of the mes buccal root, distal buccal root, and palatal root were extracted. Calculate the neck stenosis at the bifurcation point; To balance the risks of root fracture, the costs of bone loss, and the gains of root independence, a dynamic programming algorithm is used to obtain the optimal tooth separation depth.

5. The preoperative planning method for maxillary first molar extraction according to claim 4, characterized in that, The formula for extracting the location of the bifurcation point is as follows: ， ； In the formula, This represents the z-axis height coordinate of the crown tip. This represents the z-axis height coordinate of the root tip. This indicates the three-dimensional space occupied by the affected tooth. Indicates height as The cross section; Among them, when When the height changes abruptly from 1 to 3, the corresponding height represents the location of the bifurcation point.

6. The preoperative planning method for maxillary first molar extraction according to claim 4, characterized in that, The formula for calculating the stenosis of the neck at the bifurcation point is as follows: ； In the formula, This represents the cross-sectional boundary of the three-dimensional model of the affected tooth at height z. Denotes any boundary point of the cross-section boundary. Indicates height as The geometric centroid of the cross section, z, is based on the bifurcation center point P. furc Confirmed; where z < z furc , z furc Let P be the center point of the bifurcation. furc The height coordinates.

7. The preoperative planning method for maxillary first molar extraction according to claim 1, characterized in that, To obtain the optimal force direction of the extraction instruments, including: Based on the finite element model, the force applied by the tooth extraction instrument under different loading angles is simulated, and the stress distribution and root fracture threshold under each loading angle are calculated. Using minimizing the peak stress at the tooth root as the objective function, the optimal loading angle vector is output when the peak stress is less than the tooth root fracture threshold at the current loading angle, in order to determine the optimal force direction.

8. The preoperative planning method for maxillary first molar extraction according to claim 2, characterized in that, Obtain the optimal dislocation direction for each tooth block, including: The resistance boundary was marked based on the three-dimensional model of the affected tooth; Using the dislocation of each tooth block along its long axis as the baseline path, a collision detection algorithm is used to iteratively optimize the dislocation trajectory. Finally, the optimal dislocation direction vector that minimizes the dislocation distance and avoids the floor of the maxillary sinus is output as the optimal dislocation direction. The tooth blocks include the mesial buccal root block, the distal buccal root block, and the palatal root block.

9. The preoperative planning method for maxillary first molar extraction according to claim 1, characterized in that, Generate risk assessment and planning reports, including: The minimum three-dimensional distance between the root apex of each tooth and the floor of the maxillary sinus is obtained based on the three-dimensional model of the affected tooth, and the risk level is obtained based on the distance threshold. The fracture risk score of each tooth root is predicted based on the optimal tooth separation depth and optimal force direction; The minimum gap between each tooth block and adjacent teeth in the extraction path is calculated based on the optimal dislocation direction, and the collision probability is predicted. A risk assessment and planning report is generated by combining the aforementioned risk level, breakage risk score, and collision probability.

10. A system employing the preoperative planning method for maxillary first molar extraction as described in any one of claims 1-9, characterized in that, include: The data acquisition module is used to acquire the patient's CBCT data and oral scan data; A three-dimensional reconstruction module is used to construct a three-dimensional model of the affected tooth based on the CBCT data and intraoral scan data; The tooth separation depth calculation module is used to obtain the optimal tooth separation depth based on the three-dimensional model of the affected tooth. The force direction calculation module is used to construct a finite element model based on the CBCT data, so as to obtain the optimal force direction of the tooth extraction instrument based on the finite element model; The dislocation direction calculation module is used to obtain the optimal dislocation direction of each tooth segment based on the three-dimensional model of the affected tooth; In addition, a risk assessment module is used to assess the intraoperative risk level by combining the optimal tooth separation depth, optimal force direction, and optimal detachment direction, in order to generate a risk assessment and planning report.

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