A method for locating a dynamic center of resistance of a tooth

Abstract

The application discloses a positioning method of a tooth dynamic resistance center. The method comprises the following steps: firstly, modeling teeth and periodontal membranes according to CBCT data of a patient's oral cavity to obtain an independent three-dimensional model of each tooth and a three-dimensional model of the periodontal membranes; then, calculating the resistance of different regions of each tooth according to the independent three-dimensional model of each tooth and the three-dimensional model of the periodontal membranes; and finally, positioning the resistance center of each tooth according to the resistance of different regions of each tooth. The application uses the actual model of the teeth and the periodontal membranes of the patient as calculation data, and combines the actual movement type of the teeth, so that the three-dimensional position of the accurate resistance center is determined, and the more personalized positioning of the resistance center is determined according to the real situation of the patient and the tooth movement direction. The method has high automation, high accuracy and good repeatability.

Description

Technical Field

[0001] This invention relates to a method for locating the center of tooth resistance in the field of dentistry, specifically a method for locating the center of dynamic tooth resistance. Background Technology

[0002] Resistance Center (Cen) t er of Resis t The center of resistance (CFR) is an important concept in tooth movement mechanics, referring to the simplified center of resistance of a tooth to the constraints imposed by surrounding tissues during tooth movement. In free space, the center of resistance of an object is its center of mass. The root of a tooth is surrounded by the periodontal ligament and alveolar bone, so its movement is subject to the constraint forces of the periodontal tissues. Therefore, the center of resistance of a tooth is the equilibrium point of the constrained portion during tooth movement.

[0003] When the line of force applied to a tooth passes through the center of resistance, the tooth will move as a whole; when the line of force applied to a tooth does not pass through the center of resistance, the tooth will tilt. Therefore, in orthodontic treatment, the accurate location of the center of resistance will affect the final form of tooth movement, and thus affect the orthodontic treatment effect.

[0004] Studies have found that the resistance center for single-rooted teeth is located on the long axis of the tooth, approximately at the junction of the upper and middle thirds of the root neck, while the resistance center for multi-rooted teeth is located near the root bifurcation. However, in practical applications, the distribution of periodontal tissue resistance to the tooth varies due to different types and directions of movement. Therefore, the location of the resistance center is affected by different types of tooth movement. Consequently, traditional positioning methods do not take into account the actual type of tooth movement, thus increasing the error in the positioning of the resistance center.

[0005] CBCT data contains information about the patient's tooth roots and alveolar bone. Through CBCT data processing and reconstruction technology, the patient's real tooth root and alveolar bone data can be obtained. Based on this, combined with the type of tooth movement and the force conditions of the tooth root, the location of the resistance center can be obtained more accurately, thereby enabling better control of tooth movement. Summary of the Invention

[0006] To address the problems existing in the background technology, this invention proposes a method for locating the center of tooth resistance. First, a three-dimensional model of the periodontal ligament of the tooth is obtained through the input and processing of CBCT data. Second, the distribution of resistance experienced by the tooth is calculated and analyzed by inputting the type of tooth movement or rotation. Finally, the location of the center of tooth resistance is located by weighted averaging of the resistance steps.

[0007] The technical solution adopted in this invention is as follows:

[0008] 1) Based on the patient's oral CBCT data, model the teeth and periodontal ligament to obtain an independent three-dimensional model of each tooth and a three-dimensional model of the periodontal ligament.

[0009] 2) Based on the independent 3D model of each tooth, the 3D model of the periodontal ligament, and the tooth movement information, calculate the resistance before movement in different areas of each tooth;

[0010] 3) Locate the resistance center of each tooth based on the resistance in different areas of each tooth.

[0011] Specifically, 2) refers to:

[0012] 2.1) Divide the independent 3D model of each tooth and the 3D model of the periodontal ligament into regions to obtain several tooth sub-regions and several periodontal ligament sub-regions.

[0013] 2.2) Calculate the area and center of each of the tooth sub-regions and the periodontal ligament sub-regions to obtain the initial tooth region information set A. t Information set A of periodontal ligament regions p ;

[0014] 2.3) Based on the periodontal ligament region information set A p Remove the initial tooth region information set A t In the region not covered by the periodontal ligament, obtain a precise set of tooth region information A. t ';

[0015] 2.4) Based on the tooth space transformation matrix, the precise tooth region information set A t 'Perform a center position update to obtain the spatially transformed region information set A' t ”;

[0016] 2.5) Based on the precise tooth region information set A t 'and the spatially transformed region information set A t "Calculate the resistance in different areas before tooth movement."

[0017] In section 2.2), the area of ​​each tooth sub-region or periodontal ligament sub-region is the sum of the areas of all triangular meshes in the current sub-region. The center of the sub-region is obtained by calculating the geometric center of each triangular mesh in the current sub-region and then calculating the average of the geometric centers of all triangular meshes.

[0018] In section 2.3), the information set A of each tooth sub-region and the periodontal ligament region is... p The closest spatial distance between the periodontal ligament sub-regions in the diagram is denoted as the periodontal ligament wrapping distance. If the periodontal ligament wrapping distance of each tooth sub-region is greater than the limit distance ε between the tooth and the periodontal ligament, then the tooth sub-region is removed.

[0019] In section 2.5), for the precise tooth region information set A t For each tooth sub-region in ', calculate the displacement vector of each tooth sub-region. Where A ti ".C represents the spatially transformed region information set A." t "The center C', A of the tooth sub-region" ti '.C represents the set of precise tooth region information A' t 'The center C of the tooth sub-region;

[0020] If the displacement vector If the product of this product and the tooth translation vector T is greater than 0, then the resistance of this sub-region of the tooth to the tooth is equal to... A ti ".A represents the set of regional information after spatial transformation. t "The area of ​​the tooth sub-region, e2 is the periodontal ligament compressive elastic modulus, if the displacement vector is moved..." If the product of this product and the tooth translation vector T is less than 0, then the resistance Ati'.F of this sub-region on the tooth is equal to... e1 is the tensile elastic modulus of the periodontal ligament.

[0021] Specifically, 3) refers to:

[0022] 3.1) After summing the resistances of different regions of each tooth, the total resistance F of each tooth is obtained, and then the resistance weights of different regions of each tooth are obtained.

[0023] 3.2) After weighted summation of the centers of different regions of each tooth according to the resistance weight of different regions of each tooth, the resistance center of each tooth is obtained.

[0024] The beneficial effects of this invention are:

[0025] This invention combines the patient's CBCT data to obtain accurate tooth and periodontal ligament data. Using the tooth movement type as input, it can determine and analyze the resistance distribution during tooth movement. Furthermore, it can accurately determine the three-dimensional location of the resistance center, enabling more personalized resistance center localization based on the patient's actual periodontal condition and tooth movement type. The algorithm is highly automated, accurate, and repeatable. Attached Figure Description

[0026] Figure 1 This is a flowchart of the present invention.

[0027] Figure 2 A flowchart for determining the resistance distribution of teeth.

[0028] Figure 3 A class diagram illustrating the characteristics of the sub-regions. Detailed Implementation

[0029] The present invention will now be described in further detail with reference to the accompanying drawings.

[0030] like Figure 1 As shown, the present invention includes the following steps:

[0031] 1) Based on the patient's oral CBCT data, model the teeth and periodontal ligament to obtain an independent 3D model of each tooth and a 3D model of the periodontal ligament; both the 3D model of the teeth and the 3D model of the periodontal ligament are surface triangular mesh models composed of points and surfaces.

[0032] 2) Based on the independent 3D model of each tooth, the 3D model of the periodontal ligament, and the tooth movement information, calculate the resistance in different areas before the movement of each tooth;

[0033] like Figure 2 As shown, 2) specifically refers to:

[0034] 2.1) Divide the independent 3D model of each tooth and the 3D model of the periodontal ligament into regions to obtain several tooth sub-regions {T}. a1 ,T a2 ,...,T ai ,...,T aI} and several periodontal ligament subregions {T p1 ,T p2 ,...,T pj ,...,T pJ}, T ai T represents the i-th tooth sub-region. pj This represents the i-th periodontal ligament subregion. Each subregion consists of at least one triangular mesh. The number of teeth and periodontal ligament subregions is controlled by parameters and can be adjusted in specific implementations.

[0035] 2.2) Calculate the area and center of each of the tooth sub-regions and the periodontal ligament sub-regions to obtain the initial tooth region information set A. t Information set A of periodontal ligament regions p ;

[0036] In section 2.2), the area of ​​each tooth subregion or periodontal ligament subregion is the sum of the areas of all triangular meshes within the current subregion. The center C of the subregion is obtained by calculating the geometric center of each triangular mesh within the current subregion separately, and then calculating the average of the geometric centers of all triangular meshes. Figure 3 It displays the characteristic descriptions of each sub-region in the set;

[0037] 2.3) Based on the periodontal ligament region information set Ap Remove the initial tooth region information set A t In the region not covered by the periodontal ligament, obtain a precise set of tooth region information A. t ';

[0038] In 2.3), the information set A of each tooth sub-region and the periodontal ligament region is combined. p The closest spatial distance between the periodontal ligament subregions is denoted as the periodontal ligament wrapping distance. The spatial distance is the distance between the center of the tooth subregion and the center of the periodontal ligament subregion. If the periodontal ligament wrapping distance of each tooth subregion is greater than the limit distance ε between the tooth and the periodontal ligament, then the tooth subregion is removed.

[0039] 2.4) Based on the tooth space transformation matrix, the precise tooth region information set A t 'Perform a center position update to obtain the spatially transformed region information set A' t ”;

[0040] The tooth spatial transformation matrix contains the type and data of tooth movement. In the field of invisible orthodontics, it originates from the transformation matrix of a predicted step in an orthodontic plan compared to the current step. The matrix format is generally a single 4x4 matrix M, or a 3x3 tooth rotation matrix R and a 3x1 tooth translation vector T. Taking the latter as an example, the calculation method for obtaining the updated center C' after updating the position of the center C of each sub-region is as follows:

[0041] C′=C*R+T

[0042] 2.5) Based on the precise tooth region information set A t 'and the spatially transformed region information set A t , calculate the resistance in different areas before tooth movement;

[0043] In 2.5), for the precise tooth region information set A t For each tooth sub-region in ', calculate the displacement vector of each tooth sub-region. Where A ti ".C represents the spatially transformed region information set A." t "The center C', A of the tooth sub-region" ti '.C represents the set of precise tooth region information A' t 'The center C of the tooth sub-region;

[0044] If the displacement vector If the product of the product with the tooth translation vector T is greater than 0, it indicates that the displacement of this sub-region of the tooth has caused compression of the periodontal ligament, and the resistance of this sub-region to the tooth is equal to... A ti".A represents the set of regional information after spatial transformation. t "The area of ​​the tooth sub-region, e2 is the periodontal ligament compressive elastic modulus, if the displacement vector is moved..." If the product of the displacement vector T and the tooth translation vector is less than 0, it indicates that the displacement of this sub-region of the tooth has caused stretching of the periodontal ligament, and the resistance A of this sub-region to the tooth is... ti '.F equals e1 is the tensile elastic modulus of the periodontal ligament.

[0045] 3) Locate the resistance center of each tooth based on the resistance in different areas of each tooth.

[0046] 3.1) After summing the resistances of different regions of each tooth, the total resistance F of each tooth is obtained, and then the resistance weights of different regions of each tooth are obtained.

[0047] 3.2) After weighted summation of the centers of different regions of each tooth according to the resistance weight of different regions of each tooth, the resistance center (CenterResistant) of each tooth under the current movement type is obtained.

[0048] The calculation formula is as follows:

[0049]

[0050] In practice, the three-dimensional models of teeth and periodontal ligaments, as well as the tooth movement type, can be updated to dynamically locate the resistance center of each tooth.

Claims

1. A method for locating the center of dynamic resistance in a tooth, characterized in that, Includes the following steps: 1) Based on the patient's oral CBCT data, model the teeth and periodontal ligament to obtain an independent three-dimensional model of each tooth and a three-dimensional model of the periodontal ligament; 2) Based on the independent 3D model of each tooth, the 3D model of the periodontal ligament, and the tooth movement information, calculate the resistance before movement in different areas of each tooth; 3) Locate the resistance center of each tooth based on the resistance in different areas of each tooth; Specifically, 3) refers to: 3.1) After summing the resistances of different regions of each tooth, the total resistance F of each tooth is obtained, and then the resistance weights of different regions of each tooth are obtained. 3.2) After weighted summation of the centers of different regions of each tooth according to the resistance weight of different regions, the resistance center of each tooth is obtained. The calculation formula is as follows: in, Let n be the resistance center of each tooth; n is the number of regions for each tooth. For precise tooth region information set A t The center of the i-th tooth sub-region; Let be the resistance of the i-th tooth sub-region to the tooth.

2. The method for locating the dynamic resistance center of a tooth according to claim 1, characterized in that, Specifically, 2) refers to: 2.1) Divide the independent 3D model of each tooth and the 3D model of the periodontal ligament into regions to obtain several tooth sub-regions and several periodontal ligament sub-regions. 2.2) Calculate the area and center of each tooth sub-region and each periodontal membrane sub-region respectively, and obtain the initial tooth region information set A t and the periodontal membrane region information set A p ; 2.3) Obtaining the precise tooth region information set A p from the initial tooth region information set A t by removing the region not surrounded by the periodontal membrane from the initial tooth region information set A t ’; 2.4) performing center position update on the precise tooth region information set A t to obtain the spatial transformed region information set A t ’’; 2.5) According to the precise tooth region information set A t and the spatially transformed region information set A t '', the resistance of different regions before tooth movement is calculated.

3. The method for locating the center of dynamic resistance in a tooth according to claim 2, characterized in that, In section 2.2), the area of ​​each tooth sub-region or periodontal ligament sub-region is the sum of the areas of all triangular meshes in the current sub-region. The center of the sub-region is obtained by calculating the geometric center of each triangular mesh in the current sub-region and then calculating the average of the geometric centers of all triangular meshes.

4. The method for locating the center of dynamic resistance in a tooth according to claim 2, characterized in that, In section 2.3), the information set A of each tooth sub-region and the periodontal ligament region is... p The closest spatial distance between the periodontal ligament sub-regions in the diagram is denoted as the periodontal ligament wrapping distance. If the periodontal ligament wrapping distance of each tooth sub-region is greater than the limit distance ε between the tooth and the periodontal ligament, then the tooth sub-region is removed.

5. The method for locating the center of dynamic resistance in a tooth according to claim 2, characterized in that, In section 2.5), for the precise tooth region information set A t For each tooth sub-region in ', calculate the displacement vector of each tooth sub-region. , = A ti ''.C - A ti '.C, where A ti ''.C represents the set of regional information A after spatial transformation. t 'Center C' of the tooth sub-region, A ti '.C represents the set of precise tooth region information A' t 'The center C of the tooth sub-region; If the displacement vector If the product of this product and the tooth translation vector T is greater than 0, then the resistance of this sub-region of the tooth to the tooth is equal to... * A ti ''.A * e2,A ti ''.A is the set of regional information after spatial transformation. t The area of ​​the tooth sub-region in '', e2 is the compressive elastic modulus of the periodontal ligament, if the displacement vector is moved If the product of this product and the tooth translation vector T is less than 0, then the resistance of that sub-region of the tooth to the tooth is... equal * A ti ''.A * e1, where e1 is the tensile elastic modulus of the periodontal ligament.

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