Design, verification analysis and optimization method of the model of the bracket-free invisible aligner

Abstract

The application discloses a design, verification analysis and optimization method of a bracket-free invisible orthodontic appliance model, and belongs to the technical field of oral orthodontics. The design method of the application adopts a cooling method to simulate and adjust the thermal expansion deformation of a local appliance model, restricts the deformation direction and size, and realizes the design deformation of the appliance model. The analysis verification method of the application comprises iterative simulation of the osteogenesis and osteolysis biological effect under orthodontic treatment force based on computer three-dimensional finite element analysis, simulation of wearing of the appliance, reading of simulation results, and analysis and verification. The optimization method of the application is based on the simulation results. The application creatively adopts a "cooling method" with prestress loading to realize the model deformation simulation of the appliance, and can combine the finite element simulation of the periodontal membrane biological effect of the actual clinical treatment time. The application implements the step-by-step design, analysis verification and optimization of the invisible orthodontic appliance model according to the analysis verification results.

Description

Technical Field

[0001] This invention belongs to the field of orthodontic technology, specifically involving the design, verification analysis, and optimization methods of bracketless invisible aligner models. Background Technology

[0002] Clinical studies show that, compared to the initial orthodontic design, current clear aligners only achieve a 30-50% success rate in tooth movement during orthodontics (see references Simon M, Keilig L, Schwarze J, et al. Treatment outcome and efficacy of an aligner technique–regarding incisor torque, premolar derotation and molar distalization[J]. BMC Oral Health, 14, 1(2014-06-11), 2014, 14(1):68. and Kravitz N DA prospective clinical study evaluating the efficacy of tooth movement with Invisalign[J]. Health Sciences Dentistry, 2007.). The main reasons for this are: 1) the sliding contact relationship between the clear aligner and the tooth surface is unclear; 2) the mechanical properties of the materials used to manufacture the aligner are limited.

[0003] Current finite element methodologies for invisible orthodontic treatment are limited to the instantaneous force analysis upon application of force, failing to consider the osteogenic and osteoclastogenic effects within the periodontal ligament in orthodontic biomechanics. This limits their clinical significance, as orthodontics focuses more on tooth movement and force distribution during overall treatment. Existing finite element methods that consider the biomechanical effects of the periodontal ligament are limited to labial fixed orthodontic treatments, simulating these effects through iterative calculations. Furthermore, the number of iterations in existing finite element iterative methods simulating periodontal ligament biological effects does not match the actual clinical treatment time, thus limiting the clinical significance of the analysis results.

[0004] In finite element simulations of fixed orthodontic treatment, the model remains unchanged, facilitating construction and iterative analysis. However, invisible aligners are replaced as teeth move, with different aligners having different shapes, requiring replacement every 7-14 days. This characteristic of invisible orthodontics means the aligner shape is constantly changing, and simulations of the resulting periodontal ligament biological effects have not yet been achieved. Furthermore, current invisible orthodontic techniques involve a step-by-step design, where the initial position of the anterior dentition and the terminal position of the posterior dentition are determined, with the technician and orthodontist collaborating to complete the specific step-by-step design. This method relies solely on clinical experience; its biomechanical considerations depend entirely on the experience level of the technician and orthodontist. The efficiency and treatment results of this step-by-step design have not been analyzed and verified, and cannot be analyzed and verified; moreover, it cannot be optimized based on the results of analysis and verification.

[0005] Therefore, providing a design method for a bracketless invisible aligner model that can realize model deformation of the aligner and automatically generate an aligner model by combining finite element simulation of the periodontal ligament biological effects during actual clinical treatment time has become an urgent problem to be solved by those skilled in the art. Summary of the Invention

[0006] One objective of this invention is to provide a design method for a bracketless clear aligner model. This method employs a pre-stressed "cooling method" to achieve model deformation and incorporates finite element simulation of the periodontal ligament biological effects during actual clinical treatment. This solves the problem of existing technologies that cannot automatically modify the shape of clear aligners. A second objective of this invention is to provide an analysis and verification method for bracketless clear aligner models. This solves the problems of inefficiency in the step-by-step design of clear aligner models and the inability to analyze and verify treatment results in existing technologies, as well as the inability to perform full-process simulation analysis of clear aligner treatment.

[0007] The third objective of this invention is to provide an optimization method for the step-by-step design of a bracketless clear aligner model, thereby solving the problem in the prior art that optimization cannot be performed based on the results of design analysis and verification of the clear aligner model.

[0008] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0009] This invention provides a design method for a bracketless clear aligner model. In the digital model design of the bracketless clear aligner, a cooling method is used to simulate and adjust the thermal expansion deformation of the local aligner model, constrain the direction and magnitude of the deformation, and realize the design deformation of the aligner model.

[0010] The "cooling method" is a common prestressing method in the architectural field of finite element analysis. It can achieve deformation of the object and application of prestress by adjusting the local thermal expansion deformation of the model. This invention creatively introduces the "cooling method" into the design of a bracketless invisible orthodontic appliance model to achieve model deformation of the orthodontic appliance.

[0011] In some embodiments of the present invention, the design method of the bracketless invisible aligner model includes the following steps:

[0012] Step 1: Design the orthodontic appliance model: Based on the patient's clinical data and correction goals, design the orthodontic appliance model for multiple stages using computer technology.

[0013] Step 2: Determine the deformation areas of the orthodontic appliance on the designed appliance model;

[0014] Step 3: Based on the initial position of each crown and the expansion characteristics of the orthodontic appliance in each stage of the appliance model design in Step 1, control the temperature change of the deformation part of the appliance, and use simulation calculation to obtain the displacement and / or rotation of each crown in the dentition in each stage of the appliance model design.

[0015] Step 4: Connect the crown portion and crown connection portion of each orthodontic appliance in each stage of the appliance model design into a whole, and mesh it again to output three-dimensional model data.

[0016] In some embodiments of the present invention, the specific operation of determining the deformation part of the orthodontic appliance in step 2 is as follows: on the occlusal plane view of the orthodontic appliance model designed in step 1, determine the midpoint of the geometric shape of each tooth crown; connect the midpoints Ci and Cj of two adjacent crowns to obtain the connecting line Li, and the intersection points Pi and Pj of Li with the edges of these two crowns, and obtain the midpoint Pc of Pi and Pj; with Pc as the center and Li as the direction, select a certain distance between the front and back of the orthodontic appliance to divide it to obtain the orthodontic appliance model at the connection of the two crowns.

[0017] In some embodiments of the present invention, the displacement in step 3 includes: displacement along the mesiodistal direction, displacement along the buccal-lingual direction, and displacement along the gingiva. The displacement to which the tooth moves; the rotation includes: tooth torsional motion, tooth torque motion, and tooth tilting motion.

[0018] Preferably, the calculation formula for controlling the deformation of the orthodontic appliance by displacement in the mesiodistal direction (Ci-Cj direction) is as follows:

[0019] U y1 =k(d1+∑Δ1)t (1)

[0020] Among them, U y1The deformation amount of the prefabricated orthodontic appliance at each stage in the mesiodistal direction is given by: k is the linear expansion coefficient of the orthodontic appliance; Δ1 is the historical increase in width in the mesiodistal direction; d1 is the width of the deformed part in the mesiodistal direction; t is the temperature change value; based on the deformation results after applying temperature, an orthodontic appliance model is constructed in the mesiodistal direction.

[0021] Preferably, the step of obtaining the buccal-lingual displacement (perpendicular to the Ci-Cj direction) includes: automatically moving the orthodontic appliance portion corresponding to the target tooth to the designed position, and completing the deformation of the deformed portion based on the preset control points at both ends of the deformed portion (i.e., each grid node at the junction of the deformed portion of the orthodontic appliance and the tooth portion) to achieve the effect of keeping the thickness of the orthodontic appliance in the deformed portion unchanged.

[0022] Preferably, obtaining the gingiva The steps of the displacement (perpendicular to the Ci-Cj direction) include: automatically moving the part of the orthodontic appliance corresponding to the target tooth to the designed position, and completing the deformation of the deformed part according to the preset control points at both ends of the deformed part (i.e., each grid node at the junction of the deformed part of the appliance and the tooth part) to achieve the effect of keeping the thickness of the orthodontic appliance in the deformed part unchanged.

[0023] Preferably, obtaining the amount of tooth torsional movement includes the following steps: (rotation about the Z-axis)

[0024] The torque balance in the height direction of the adjustment zone is controlled to reduce tooth torsion. The lower part of the adjustment zone is used as a support point to increase or decrease the temperature of the upper zone and set a vertical temperature gradient to achieve tooth movement with no or little rotation. The temperature load is set in layers according to the height of the upper part of the adjustment zone, while the temperature of the lower part is kept the same.

[0025] In the XY plane, the adjustment area is contracted and stretched by reducing and increasing the wedge size, with the center point (the center point of the adjustment area) as the reference point.

[0026] In the horizontal direction, the orthodontic appliance is divided into n regions, forming n regions with an area of ​​A. spring The spring elements are designed such that each spring element determines the cutting amount of the cavitation along the centerline direction based on the initial shortening amount Δ0 and the wedge load coefficient k, cutting the cavitation in the gap between teeth to form a geometrically broken region. A spring element model is established from the center point to the edge. The internal compression force of each spring element is calculated based on the cutting length using the following formula:

[0027]

[0028] F spring The spring unit's internal compression force is given by Δ0, where Δ0 is the initial shortening amount, and h is the spring unit's internal compression force. spring Where E is the vertical height of the spring unit from the center line, E is the elastic modulus of the orthodontic appliance, and A is the vertical height of the spring unit from the center line. spring Let be the cross-sectional area of ​​the spring unit.

[0029] The determination of the XY plane, X-axis, Y-axis, and Z-axis in this invention is based on existing technology and constitutes a coordinate system for constructing the entire dentition. The XY plane is the plane formed by the X-axis and Y-axis in the coordinate system for constructing the entire dentition. In one embodiment of this invention, the specific operation for constructing the coordinate system for constructing the entire dentition is as follows: First, the occlusal plane is constructed by connecting the midpoints of the incisal edges of the bilateral central incisors with the mesiobuccal cusp of the first molar. The vertical axis (Z-axis) is considered to be perpendicular to the occlusal plane, the line connecting the mesiobuccal cusps of the bilateral first molars is the horizontal axis (X-axis), and the Y-axis is perpendicular to the other two axes.

[0030] The size of the orthodontic appliance is determined based on the preset amount of tooth rotation and formula (2);

[0031] Preferably, the step of obtaining the torque motion (rotation about Ci-Cj direction) includes: subtracting the rotational deformation caused by the stiffness of the adjustment area from the lateral displacement distance of the prefabricated crown to obtain the true rotation angle of the crown area;

[0032] The formula for the prefabrication angle is as follows:

[0033]

[0034] Where Θ y预置 To preset the rotation angle, U y The distance for lateral displacement of the crown is the pre-set distance, and h is the height of the tooth at its typical position.

[0035] Θ y =Θ y预置 -Θ y变形 (4)

[0036] Where, Θ y It is the actual rotation angle, Θ y预置 To preset the rotation angle, Θ y变形 The deformation angle is the characteristic position.

[0037] Preferably, the step of obtaining the amount of tooth tilting movement includes: (rotation around the buccal-lingual axis)

[0038] The preset angle θ is controlled by increasing or decreasing the length of the adjustment zone in the Y direction; the calculation formula for controlling the deformation of the orthodontic appliance is as follows:

[0039] U y2 =k(d2+∑Δ2)t (5)

[0040] θ=atan(U y2 / h) (6)

[0041] Among them, U y2Δ2 represents the initial deformation of the orthodontic appliance at each stage in the Y direction; k represents the linear expansion coefficient of the appliance; Δ2 represents the historical increase in width in the Y direction; d2 represents the width of the deformed part in the Y direction; t represents the temperature change value; θ represents the preset angle; and h represents the height of the tooth at the typical position.

[0042] The method for analyzing and verifying the bracketless invisible aligner model designed by the above-mentioned method provided by the present invention includes the following steps:

[0043] S1. Iterative simulation of osteogenic and osteoclastogenic biological effects under orthodontic force based on computer three-dimensional finite element analysis;

[0044] S2. Simulation of appliance insertion;

[0045] S3. Read the simulation results and analyze and verify the efficiency and results of the step-by-step orthodontic design. The analysis and verification method of this invention achieves automatic simulation of the entire orthodontic process through iterative simulation, insertion simulation, and the above-mentioned automatic modeling of the orthodontic appliance using the cooling method, and verifies the efficiency and results. This solves the problem that existing methods cannot achieve simulation of the entire orthodontic process, but can only simulate a specific step, which has limited clinical significance.

[0046] In some embodiments of the present invention, the specific operation of S1 includes: after simulating the placement of the orthodontic appliance in the i-th stage into the corresponding i-th stage of the dentition, after the calculation converges, a new tooth position is obtained, namely the dentition of ib. Based on the pre-designed wearing time of each set of orthodontic appliances, the number of calculation iterations is determined, and then the simulation calculation is iterated again.

[0047] In some embodiments of the present invention, the simulation of appliance placement in S2 includes: placing the appliance in the dentition of each stage, and releasing it after the inner surface of the appliance has the best fit with the outer surface of the dentition.

[0048] In some embodiments of the present invention, in step S3, the displacement of the marker points, the movement and rotation of the tooth long axis, and the simulation results of stress and strain of each part of the model are read after each iteration calculation, and the efficiency and treatment results of the step-by-step design of orthodontic treatment are analyzed and verified.

[0049] This invention provides an optimization method for the step-by-step design of a bracketless clear aligner model. Based on the simulation results obtained above, the optimization design specifically includes the following steps:

[0050] Step A. Determine the optimization goals; preferably, the optimization goals include total treatment time, treatment efficiency, or reducing undesirable tooth movement;

[0051] Step B. Select an optimization method; preferably, the optimization method includes optimizing the tooth movement sequence and optimizing the size and mode of tooth movement in each stage of the design;

[0052] Step C. Optimize the design according to the selected optimization method.

[0053] In some embodiments of the present invention, the optimization design in step C specifically includes the following steps:

[0054] a. Read the position information of each tooth at the initial position and the designed final position of the dentition: Preferably, the long axis of the tooth and its rotation in three dimensions, and the movement of the tooth in three dimensions at the above points are determined by the preset crown and root landmarks and the calculated tooth impedance center.

[0055] b. Determining the movement path and timing: Read the simulation analysis results data, perform time-based envelope space design, and determine the movement path and timing;

[0056] c. Iterative design of orthodontic appliances

[0057] ① Monitoring and evaluation of effects: Determine the expression rate and monitoring methods for unfavorable tooth movement based on typical tooth positions; optimize the wearing time of orthodontic appliances based on iterative simulation results of osteogenic and osteoclastogenic effects;

[0058] ② Orthodontic appliance design: Based on the optimized sequence of teeth, an orthodontic appliance is designed with adjustments made using calculations and limits;

[0059] ③ Optimization of the orthodontic appliance: Based on the expression rate of the appliance adjustment in step ② and the unfavorable tooth movement, modify the appliance at each stage; preferably, in the appliance adjustment, an appliance with a certain amplification factor is preset for adjustment based on the expression rate; preferably, the translation and rotation of the teeth are adjusted based on the monitoring value of the typical position of the crown of the unfavorable tooth movement, using translation and rotation as indicators.

[0060] ④ Monitoring of periodontal ligament stress: Monitor the stress of the periodontal ligament of each tooth in each step to ensure that it is always within a safe stress range.

[0061] Compared with the prior art, the present invention has the following beneficial effects:

[0062] This invention is scientifically designed and easy to operate. The design method for the bracketless clear aligner model creatively employs a pre-stressed "cooling method" to achieve model deformation of the aligner and can incorporate finite element simulation of the periodontal ligament biological effects during actual clinical treatment. This method requires no manual operation or complex reverse engineering; it can automatically generate the digital model of the clear aligner at each step, resulting in accurate results and patient comfort.

[0063] The method for analyzing and verifying the bracketless clear aligner model of the present invention analyzes the designed bracketless clear aligner model by iterative simulation of the osteogenic and osteoclastogenic biological effects under orthodontic force based on computer three-dimensional finite element analysis and simulation of aligner insertion, evaluates the accuracy of the aligner model design, and provides a basis for further optimization.

[0064] The optimization method for the step-by-step design of the bracketless clear aligner model of the present invention, based on the results of three-dimensional finite element analysis simulation, realizes the automatic optimization of the step-by-step design, thereby shortening the treatment time, reducing unfavorable tooth movement, and optimizing the expression rate of the treatment design within the safe force range of the periodontal ligament. Attached Figure Description

[0065] Appendix Figure 1 This is a schematic diagram showing the deformation location of the orthodontic appliance in this invention. Detailed Implementation

[0066] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below. Where specific conditions are not specified in the embodiments, conventional conditions or conditions recommended by the manufacturer shall apply. Reagents or instruments whose manufacturers are not specified are all conventional products that can be purchased commercially.

[0067] A design method for a bracketless clear aligner model is proposed. In the digital model design of the bracketless clear aligner, a cooling method is used to simulate and adjust the thermal expansion deformation of the local aligner model, constrain the direction and magnitude of the deformation, and realize the design deformation of the aligner model.

[0068] The design method for the bracketless clear aligner model includes the following steps:

[0069] Step 1: Design the orthodontic appliance model: Based on the patient's clinical data and correction goals, design the orthodontic appliance model for multiple stages using computer technology.

[0070] Step 2: Determine the deformation area of ​​the orthodontic appliance on the designed appliance model. Specifically, on the occlusal plane view of the orthodontic appliance model designed in Step 1, determine the midpoint of the geometric shape of each tooth crown; connect the midpoints Ci and Cj of two adjacent crowns to obtain the connecting line Li, and the intersection points Pi and Pj of Li with the edges of these two crowns, and obtain the midpoint Pc of Pi and Pj; with Pc as the center and Li as the direction, select a certain distance in front and behind the appliance to divide it to obtain the appliance model at the connection point of the two crowns;

[0071] Step 3: Based on the initial position of each crown and the expansion characteristics of the orthodontic appliance in each stage of the appliance model design in Step 1, control the temperature change of the deformation part of the appliance, and use simulation calculation to obtain the displacement and / or rotation of each crown in the dentition in each stage of the appliance model design.

[0072] Step 4: Connect the crown portion and crown connection portion of each orthodontic appliance in each stage of the appliance model design into a whole, and mesh it again to output three-dimensional model data.

[0073] In step 3, the fixed and movable ends for tooth movement are set, and simulation calculations are used to obtain the displacement and / or rotation of each crown in each stage of the dentition in the orthodontic appliance model design. The displacement includes: mesiodistal movement, buccal-lingual movement, and gingival movement. The displacement of the tooth movement; the rotation includes: tooth torsional movement, tooth torque movement, and tooth tilting movement.

[0074] Preferably, the calculation formula for controlling the deformation of the orthodontic appliance by displacement in the mesiodistal direction (Ci-Cj direction) is as follows:

[0075] U y1 =k(d1+∑Δ1)t (1)

[0076] Among them, U y1 The deformation amount of the prefabricated orthodontic appliance at each stage in the mesiodistal direction is given by: k is the linear expansion coefficient of the orthodontic appliance; Δ1 is the historical increase in width in the mesiodistal direction; d1 is the width of the deformed part in the mesiodistal direction; t is the temperature change value; based on the deformation results after applying temperature, an orthodontic appliance model is constructed in the mesiodistal direction.

[0077] Preferably, the step of obtaining the buccal-lingual displacement (perpendicular to the Ci-Cj direction) includes: automatically moving the orthodontic appliance portion corresponding to the target tooth to the designed position, and completing the deformation of the deformed portion based on the preset control points at both ends of the deformed portion (i.e., each grid node at the junction of the deformed portion of the orthodontic appliance and the tooth portion) to achieve the effect of keeping the thickness of the orthodontic appliance in the deformed portion unchanged.

[0078] Preferably, obtaining the gingiva The steps of the displacement (perpendicular to the Ci-Cj direction) include: automatically moving the part of the orthodontic appliance corresponding to the target tooth to the designed position, and completing the deformation of the deformed part according to the preset control points at both ends of the deformed part (i.e., each grid node at the junction of the deformed part of the appliance and the tooth part) to achieve the effect of keeping the thickness of the orthodontic appliance in the deformed part unchanged.

[0079] Preferably, obtaining the amount of tooth torsional movement includes the following steps: (rotation about the Z-axis)

[0080] The torque balance in the height direction of the adjustment zone is controlled to reduce tooth torsion. The lower part of the adjustment zone is used as a support point to increase or decrease the temperature of the upper zone and set a vertical temperature gradient to achieve tooth movement with no or little rotation. The temperature load is set in layers according to the height of the upper part of the adjustment zone, while the temperature of the lower part is kept the same.

[0081] In the XY plane, the adjustment area is contracted and stretched by reducing and increasing the wedge size, with the center point (the center point of the adjustment area) as the reference point.

[0082] In the horizontal direction, the orthodontic appliance is divided into n regions, forming n regions with an area of ​​A. spring The spring elements are designed such that each spring element determines the cutting amount of the cavitation along the centerline direction based on the initial shortening amount Δ0 and the wedge load coefficient k, cutting the cavitation in the gap between teeth to form a geometrically broken region. A spring element model is established from the center point to the edge. The internal compression force of each spring element is calculated based on the cutting length using the following formula:

[0083]

[0084] F spring The spring unit's internal compression force is given by Δ0, where Δ0 is the initial shortening amount, and h is the spring unit's internal compression force. spring Where E is the vertical height of the spring unit from the center line, E is the elastic modulus of the orthodontic appliance, and A is the vertical height of the spring unit from the center line. spring Let be the cross-sectional area of ​​the spring unit.

[0085] The size of the orthodontic appliance is determined based on the preset amount of tooth rotation and formula (2).

[0086] Preferably, the step of obtaining the torque motion (rotation about the Ci-Cj direction) includes:

[0087] The true rotation angle of the crown area is obtained by subtracting the rotational deformation caused by the stiffness of the adjustment area from the lateral displacement distance of the prefabricated crown.

[0088] The formula for the prefabrication angle is as follows:

[0089]

[0090] Where Θ y预置 To preset the rotation angle, U y The distance for lateral displacement of the crown is the pre-set distance, and h is the height of the tooth at its typical position.

[0091] Θ y =Θ y预置 -Θ y变形 (4)

[0092] Where, Θ y It is the actual rotation angle, Θ y预置 To preset the rotation angle, Θy变形 The deformation angle is the characteristic position.

[0093] Preferably, the step of obtaining the amount of tooth tilting movement includes: (rotation around the buccal-lingual axis)

[0094] The preset angle is controlled by increasing or decreasing the length of the adjustment zone in the Y direction; the calculation formula for controlling the deformation of the orthodontic appliance is as follows:

[0095] U y2 =k(d2+∑Δ2)t (5)

[0096] θ=atan(U y2 / h) (6)

[0097] Among them, U y2 Δ2 represents the initial deformation of the orthodontic appliance at each stage in the Y direction; k represents the linear expansion coefficient of the appliance; Δ2 represents the historical increase in width in the Y direction; d2 represents the width of the deformed part in the Y direction; t represents the temperature change value; θ represents the preset angle; and h represents the height of the tooth at the typical position.

[0098] An analytical verification method for a bracketless invisible aligner model includes the following steps:

[0099] S1. Iterative simulation of osteogenic and osteoclastogenic biological effects under orthodontic force based on computer three-dimensional finite element analysis; the specific operation includes: simulating the placement of the orthodontic appliance in the i-th stage into the corresponding i-th stage of the dentition, and after the calculation converges, obtaining the new tooth position, i.e. the dentition of ib, and determining the number of calculation iterations based on the pre-designed wearing time of each set of orthodontic appliances, and then iteratively simulating the calculation.

[0100] S2. Orthodontic appliance insertion simulation: The orthodontic appliances for each stage are inserted into the dentition and released after the inner surface of the appliance fits the outer surface of the dentition best.

[0101] S3. Read the simulation results and analyze and verify the efficiency and results of the step-by-step orthodontic design.

[0102] In S3, the simulation results of the displacement of the marker points, the movement and rotation of the tooth long axis, and the stress and strain of each part of the model are read after each iteration calculation. The efficiency of the step-by-step design of the orthodontic treatment and the treatment results are analyzed and verified.

[0103] An optimization method for the step-by-step design of a bracketless clear aligner model, based on the simulation results obtained above, specifically includes the following steps:

[0104] Step A. Determine the optimization goals; preferably, the optimization goals include total treatment time, treatment efficiency, or reducing undesirable tooth movement;

[0105] Step B. Select an optimization method; preferably, the optimization method includes optimizing the tooth movement sequence and optimizing the size and mode of tooth movement in each stage of the design;

[0106] Step C. Optimize the design according to the selected optimization method.

[0107] In some embodiments of the present invention, the optimization design in step C specifically includes the following steps:

[0108] a. Read the position information of each tooth at the initial position and the designed final position of the dentition: Preferably, the long axis of the tooth and its rotation in three dimensions, and the movement of the tooth in three dimensions at the above points are determined by the preset crown and root landmarks and the calculated tooth impedance center.

[0109] b. Determining the movement path and timing: Read the simulation analysis results data, perform time-based envelope space design, and determine the movement path and timing;

[0110] c. Iterative design of orthodontic appliances

[0111] ① Monitoring and evaluation of effects: Determine the expression rate and monitoring methods for unfavorable tooth movement based on typical tooth positions; optimize the wearing time of orthodontic appliances based on iterative simulation results of osteogenic and osteoclastogenic effects;

[0112] ② Orthodontic appliance design: Based on the optimized sequence of teeth, an orthodontic appliance is designed with adjustments made using calculations and limits;

[0113] ③ Optimization of the orthodontic appliance: Based on the expression rate of the appliance adjustment in step ② and the unfavorable tooth movement, modify the appliance at each stage; preferably, in the appliance adjustment, an appliance with a certain amplification factor is preset for adjustment based on the expression rate; preferably, the translation and rotation of the teeth are adjusted based on the monitoring value of the typical position of the crown of the unfavorable tooth movement, using translation and rotation as indicators.

[0114] ④ Monitoring of periodontal ligament stress: Monitor the stress of the periodontal ligament of each tooth in each step to ensure that it is always within a safe stress range.

[0115] Example 1

[0116] This example illustrates a common clinical scenario affecting the posterior displacement of molars during orthodontic treatment. To simplify the model, only the maxillary first and second molars and their periodontal ligaments were used for simulation calculations. The treatment plan was designed as follows: the maxillary second molar was moved distally by 1 mm, with each stage consisting of 0.2 mm increments, for a total of 5 stages.

[0117] First, the digital model of the bracketless clear aligner is automatically generated by computer:

[0118] After completing routine clinical imaging data, dental records, After collecting and uploading facial photographs, a standard computer-based orthodontic procedure is designed.

[0119] The steps related to this invention are as follows:

[0120] 1) Determination of treatment plan: Based on the patient's clinical data, after completing the design of the treatment steps, the initial and final positions of the dentition before and after treatment are determined, and the direction, method and size of tooth movement in each stage are determined. For this case, the plan is designed as follows: the maxillary second molar is moved 1mm distally in parallel, 0.2mm in each stage, for a total of 5 stages.

[0121] 2) Construct a coordinate system for the entire dentition: First, construct an occlusal plane by connecting the midpoints of the incisal edges of the bilateral central incisors with the mesiobuccal cusp of the first molar. Assume that the vertical axis (Z-axis) is perpendicular to the occlusal plane, the line connecting the mesiobuccal cusps of the bilateral first molars is the horizontal axis (X-axis), and the Y-axis is perpendicular to the other two axes.

[0122] 3) Based on the coordinate system of the entire dentition, read the displacement and rotation values ​​of each tooth in three axes at each stage of the orthodontic design. First, identify the long axis and impedance center of each tooth, and then determine the aforementioned displacement and rotation based on the long axis and impedance center; for this case, through... The midpoint and root bifurcation point determine the major axes of the first and second molars, and the impedance center is determined by calculation.

[0123] 4) Building the final orthodontic appliance model based on the terminal position of the dentition: In this case, the initial treatment position, i.e., when the first and second molars are in contact, was used for crown segmentation and shelling. Then, each shelled crown model was subjected to Boolean operations and connected to form a unified appliance model. Finally, the connected appliance model was optimized and meshed to obtain the final final appliance model. Model optimization included removing sharp structures, removing self-intersections, and repairing small holes. In this case, the shell thickness was designed to be 0.7mm.

[0124] 5) Determining the deformation points of the orthodontic appliance: On the occlusal plane view constructed above, determine the midpoint of the geometric shape of the crown of each tooth. For this case, see attached... Figure 1 As shown, connect the midpoints Ci and Cj of the first and second molar crowns to obtain the connecting line Li. Intersect Li with the edges of these two crowns at points Pi and Pj, and obtain the midpoint Pc of Pi and Pj. Using Pc as the center and Li as the direction, select an orthodontic appliance 1mm apart anteriorly and posteriorly to divide the area and obtain the appliance model at the junction of the two crowns.

[0125] 6) Modeling of the orthodontic appliance based on the "cooling method": Based on the initial position of each tooth crown and the expansion characteristics of the appliance in each step of the treatment design, the temperature of the deformation parts of the appliance is controlled, and the displacement and rotation of each tooth crown in the dentition are obtained through simulation calculations. The fixed and moving ends are set during tooth movement. In this case, the first molar is the fixed end, and the second molar is the moving end. Because the movement in this case is a distal parallel movement of the second molar, the following automatic iterative deformation method for the appliance is adopted:

[0126] The formula for calculating the deformation of the orthodontic appliance is:

[0127] U y1 =k(d1+∑Δ1)t (1)

[0128] Among them, U y1 The initial prefabricated appliance deformation amount for each stage in the mesiodistal direction; k is the linear expansion coefficient of the appliance; Δ1 is the historical increase in width in the mesiodistal direction; d1 is the width of the deformed part in the mesiodistal direction; t is the temperature change value; based on the deformation results after applying temperature, the appliance model is constructed.

[0129] 7) Finally, connect the crown portion of each orthodontic appliance and the crown connection portion in each orthodontic design step into a whole, and mesh it again to output three-dimensional model data.

[0130] Example 2

[0131] This embodiment discloses the analysis and verification of the step-by-step design of the bracketless invisible aligner designed in Embodiment 1, specifically as follows:

[0132] After the automatic iterative deformation of the orthodontic appliance is completed:

[0133] 1) An iterative simulation method for osteogenic and osteoclastogenic biological effects under orthodontic force based on computer-aided three-dimensional finite element analysis: After simulating the placement of the orthodontic appliance in the corresponding i-th stage of the dentition, and after the calculation converges, the new tooth position, i.e., the dentition of ib, is obtained. The number of iterations is determined based on the pre-designed wearing time of each appliance (usually 1 or 2 weeks). In this case, the designed appliance wearing time is 1 week, meaning the iteration ratio of appliance deformation to periodontal ligament deformation is 1:1, i.e., one iteration of periodontal ligament followed by one iteration of appliance deformation. Simultaneously, only the strain of the periodontal ligament of the first and second molars, i.e., tooth displacement, in each design step is analyzed.

[0134] 2) Orthodontic appliance insertion simulation: The insertion of the orthodontic appliance into the dentition in each step is completed by releasing the appliance after the inner surface of the appliance fits the outer surface of the dentition best;

[0135] 3) Read the displacement of the landmark points, the movement and rotation of the tooth long axis, and other mechanical simulation results such as stress and strain of each part of the model obtained after each iteration calculation. Analyze and verify the efficiency of the step-by-step orthodontic design and the orthodontic results. The results are presented as a dynamic video display of the orthodontic process, a superimposed deviation diagram of the terminal positions of the dentition in the orthodontic design and the terminal positions obtained from the simulation calculation, and the positional deviation of each landmark point in each iteration step between the simulation calculation and the design.

[0136] In this case, the simulation results of the initial steps show that the second molar did not produce the designed parallel distal movement, but rather distal tilting movement, and the tilting intensified as the steps progressed, resulting in insufficient root movement; at the same time, the second molar produced unfavorable distal tilting movement, and the crown was distally depressurized and mesially raised.

[0137] Example 3

[0138] This embodiment discloses an optimization of the step-by-step design for clear aligner treatment based on the verification analysis results of Embodiment 2. The step-by-step design is automatically optimized to achieve better treatment design expression, reduce treatment time and minimize adverse tooth movement, while ensuring that the designed orthodontic force remains within the safe force range of the periodontal ligament. The specific method is as follows:

[0139] 1) Determining the optimization objective:

[0140] a. Total treatment duration: The total treatment duration is determined by the number of treatment steps and the wearing time of each set of orthodontic appliances. The total treatment duration can be reduced through optimization. In this case, the initial design plan has 5 treatment steps, with each step requiring 1 week of appliance wearing time, for a total of 5 weeks.

[0141] b. Orthodontic efficiency: The achievement rate of the orthodontic design, that is, the ratio of the amount of tooth movement towards the target position after simulation calculation to the designed movement amount. The achievement rate of the orthodontic design can be improved by optimization. In this case, the simulation results of the initial step design show that the second molar did not produce the designed parallel distal movement of the tooth, but rather distal tilted movement, and the tilting intensified as the steps progressed, resulting in insufficient root movement.

[0142] c. Reduction of unfavorable tooth movement: In this case, the simulation results of the initial step design showed that the second molar produced unfavorable distal tilting movement, while the crown was distally depressed and mesially raised;

[0143] 2) Selection of optimization methods: Optimization can be achieved through the following aspects:

[0144] a. Tooth movement sequence: In this case, there is only one tooth movement method, distal movement of the second molar, so it cannot be optimized by the tooth movement sequence;

[0145] b. Design of tooth movement size and method in each step: that is, the direction and size of tooth movement and selection in three-dimensional coordinates in each step of the design;

[0146] 3) Specific optimization methods:

[0147] a. Read the position information of each tooth at the initial position and the designed final position of the dentition: Determine the long axis of the tooth and its rotation in three dimensions by using the preset crown and root landmarks and the calculated tooth impedance center, and the movement of the tooth in three dimensions at the above points.

[0148] b. Determining the movement path and timing: Time-based envelope space design

[0149] For this case, the simulation analysis results of the initial step design were read, including: I. the stress and displacement of each tooth in each step of the simulation results; II. the periodontal ligament stress of each tooth in each step of the simulation results.

[0150] c. Iterative design of orthodontic appliances

[0151] ① Monitoring and evaluation of effects: Based on the typical position of the teeth, the expression rate and the method for monitoring unfavorable tooth movement were determined; based on the iterative simulation results of the osteogenic and osteoclast effects, the wearing time of the orthodontic appliance was optimized; in this case, after extending the wearing time of the orthodontic appliance for each step to 2 weeks, the tilting movement of the second molar was significantly reduced.

[0152] ② Orthodontic appliance design: Based on the optimized sequence of teeth, an orthodontic appliance is designed with adjustments made using calculations and limits;

[0153] ③ Optimization of the orthodontic appliance: Based on the expression rate of appliance adjustment in step ② and the unfavorable tooth movement, modify the appliance in each step. In appliance adjustment, based on the expression rate, preset an appliance with a certain amplification factor for adjustment; based on the monitoring values ​​of the typical crown position of the unfavorable tooth movement, adjust the translation and rotation of the teeth using translation and rotation as indicators.

[0154] ④ Monitoring of periodontal ligament stress: Monitor the stress of the periodontal ligament of each tooth in each step to ensure it remains within a safe stress range. In this case, the maximum stress that the periodontal ligament can withstand is considered to be 26 kPa; exceeding this stress value will cause irreversible necrosis of the periodontal tissues.

[0155] Embodiments 1-3 of this invention provide methods for designing, verifying, analyzing, and optimizing a bracketless clear aligner model that moves along the mesiodistal direction. Based on the concept of this invention, the buccal-lingual displacement, gingival... The method of this invention is used to design, verify, analyze, and optimize the model of the clear aligner, which involves tooth rotation, tooth torque, and tooth tilting. This results in a model of the aligner that achieves deformation. Finally, it should be noted that the above embodiments are merely preferred embodiments used to illustrate the technical solutions of this invention, and are not intended to limit it, much less limit the scope of the patent. Although the invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features. These modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of this invention. That is to say, any changes or refinements made to the main design concept and spirit of this invention that are not substantial in nature, but solve the same technical problem as this invention, should be included within the scope of protection of this invention. Furthermore, the direct or indirect application of the technical solutions of this invention to other related technical fields is similarly included within the scope of patent protection of this invention.

Claims

1. A design method for a bracketless clear aligner model, characterized in that, In the digital model design of bracketless invisible aligners, a cooling method is used to simulate and adjust the thermal expansion deformation of local aligner models, constrain the direction and magnitude of deformation, and realize the design deformation of the aligner model. The design method includes the following steps: Step 1: Design the orthodontic appliance model: Based on the patient's clinical data and correction goals, design the orthodontic appliance model for multiple stages using computer technology. Step 2: Determine the deformation areas of the orthodontic appliance on the designed appliance model; Step 3: Based on the initial position of each crown and the expansion characteristics of the orthodontic appliance in each stage of the appliance model design in Step 1, control the temperature change of the deformation part of the appliance, and use simulation calculation to obtain the displacement and / or rotation of each crown in the dentition in each stage of the appliance model design. Step 4: Connect the crown portion and crown connection portion of each orthodontic appliance in each stage of the appliance model design into a whole, and mesh it again to output three-dimensional model data; The specific operation for determining the deformation location of the orthodontic appliance in step 2 is as follows: On the occlusal plane view of the orthodontic appliance model designed in step 1, determine the midpoint of the geometric shape of each tooth crown; connect the midpoints Ci and Cj of two adjacent tooth crowns to obtain the connecting line Li, and the intersection points Pi and Pj of Li with the edges of these two tooth crowns, and obtain the midpoint Pc of Pi and Pj; with Pc as the center and Li as the direction, select a certain distance between the front and back of the orthodontic appliance to divide it to obtain the orthodontic appliance model at the connection point of the two tooth crowns.

2. The design method of a bracketless invisible aligner model according to claim 1, characterized in that, The displacements mentioned in step 3 include: displacement along the mesiodistal direction, displacement along the buccal-lingual direction, and displacement along the gum line. The displacement of the tooth movement; the rotation includes: tooth torsional movement, tooth torque movement, and tooth tilting movement.

3. The design method of a bracketless invisible aligner model according to claim 2, characterized in that, The formula for calculating the deformation of the orthodontic appliance controlled by displacement in the mesiodistal direction is: U y1 = k ( d 1 +∑Δ 1) t （1） in, U y1 The deformation amount of the initially prefabricated orthodontic appliance at each stage in the mesiodistal direction; k The coefficient of linear expansion of the orthodontic appliance; Δ 1. Increase the width of the history in the near-far-mid direction; d 1 represents the width of the deformation region in the near-to-far direction; t The values ​​represent temperature changes; based on the deformation results after applying temperature, an orthodontic model is constructed in the mesiodistal direction.

4. The design method of a bracketless invisible aligner model according to claim 2, characterized in that, The steps for obtaining the buccal-lingual displacement include: automatically moving the part of the orthodontic appliance corresponding to the target tooth to the designed position, and completing the deformation of the deformed part based on the preset control points at both ends of the deformed part, i.e., the grid nodes at the junction of the deformed part of the appliance and the tooth part, so as to achieve the effect that the thickness of the orthodontic appliance in the deformed part remains unchanged.

5. The design method of a bracketless invisible aligner model according to claim 2, characterized in that, Get gingiva The displacement steps include: automatically moving the part of the orthodontic appliance corresponding to the target tooth to the designed position, and completing the deformation of the deformation part according to the preset control points at both ends of the deformation part, so as to achieve the effect of keeping the thickness of the orthodontic appliance in the deformation part unchanged.

6. The design method of a bracketless invisible aligner model according to claim 2, characterized in that, Obtaining the amount of tooth rotation movement includes the following steps: The torque balance in the height direction of the adjustment zone is controlled to reduce tooth torsion. The lower part of the adjustment zone is used as a support point to increase or decrease the temperature of the upper zone and set a vertical temperature gradient to achieve tooth movement with no or little rotation. The temperature load is set in layers according to the height of the upper part of the adjustment zone, while the temperature of the lower part is kept the same. In the XY plane, the wedge size is reduced or increased around the center point to achieve the purpose of shrinking and stretching the adjustment area respectively; In the horizontal direction, the orthodontic appliance is divided into n regions, forming n regions with an area of A spring The spring units, each spring unit according to the initial shortening amount 0 and wedge load factor k Determine the cutting amount along the centerline of the cavitation bubble, cut the cavitation bubble in the gap between teeth to form a geometrically broken region, and establish spring elements from the center point to the edge as the model. The internal compression force of each spring element is calculated according to the cutting length using the following formula: （2） F spring This is the internal compressive force of the spring unit. 0 represents the initial shortening amount. h spring Where E is the vertical height of the spring unit from the center line, and E is the elastic modulus of the orthodontic appliance. A spring The cross-sectional area of ​​the spring unit; The size of the orthodontic appliance is determined based on the preset amount of tooth rotation and formula (2); The XY plane is the plane formed by the X-axis and Y-axis in the coordinate system for constructing the entire tooth row.

7. The design method of a bracketless invisible aligner model according to claim 2, characterized in that, The design steps for an orthodontic appliance model that realizes the designed tooth torque motion include: The true rotation angle of the crown area is obtained by subtracting the rotational deformation caused by the stiffness of the adjustment area from the lateral displacement distance of the prefabricated crown. The formula for the prefabrication angle is as follows: （3） in To preset the rotation angle, U y To determine the pre-set lateral displacement distance of the crown, h This represents the typical height of a tooth at its position. （4） in, It is the actual rotation angle. To preset the rotation angle, The deformation angle is the characteristic position. Based on the preset rotation angle, the adjustment area is set to 0 near the fixed end boundary and the maximum rotation angle (i.e., the preset angle) is set near the movable end boundary. The crown at the movable end also takes this maximum value. A geometric mesh deformation curve for the orthodontic appliance is then established. This linear deformation curve is used to adjust the gingiva of the appliance in both the adjustment area and the movable end. To construct a model of an orthodontic appliance.

8. The design method of a bracketless invisible aligner model according to claim 2, characterized in that, The steps to obtain the amount of tooth tilting motion include: The preset angle can be controlled by increasing or decreasing the length of the Y-direction length adjustment zone. The formula for calculating the deformation of the orthodontic appliance is: U y2 = k ( d 2 +∑Δ 2) t （5） （6） in, U y2 The deformation amount of the prefabricated orthodontic appliance at each stage in the Y direction; k Δ2 is the linear expansion coefficient of the orthodontic appliance; Δ2 is the historical increase in width in the Y direction. d 2 represents the width of the deformed portion in the Y direction; t represents the temperature change. θ For preset angle, h This represents the typical height of a tooth at its position. Based on the aforementioned preset angles, starting from the boundary near the fixed end of the adjustment area and setting it to 0, and using the boundary near the movable end of the adjustment area as the maximum rotation angle, while also taking this maximum value for the crown at the movable end, a geometric mesh deformation curve for the orthodontic appliance is established. This linear deformation curve is then used to adjust the gingiva of the appliance in both the adjustment area and the movable end. To construct a model of an orthodontic appliance.

9. A method for analyzing and verifying the model of a bracketless invisible aligner designed according to any one of claims 1-8, characterized in that, Includes the following steps: S1. Iterative simulation of osteogenic and osteoclastogenic biological effects under orthodontic force based on computer three-dimensional finite element analysis; S2. Simulation of appliance insertion; S3. Read the simulation results and analyze and verify the efficiency and results of the step-by-step orthodontic design.

10. The analytical verification method according to claim 9, characterized in that, The specific operation of S1 includes: after simulating the placement of the orthodontic appliance in the corresponding i-th stage of the dentition, after the calculation converges, the new tooth position, i.e. the dentition of ib, is obtained. Based on the pre-designed wearing time of each set of orthodontic appliances, the number of calculation iterations is determined, and then the simulation calculation is iterated again.

11. The analytical verification method according to claim 10, characterized in that, The simulation of appliance placement in S2 includes: placing the appliance in the dentition of each stage, and releasing it after the inner surface of the appliance has the best fit with the outer surface of the dentition.

12. The analytical verification method according to claim 10, characterized in that, In S3, the displacement of the marker points, the movement and rotation of the tooth long axis, and the stress and strain of each part of the model are read after each iteration calculation. The efficiency of the step-by-step orthodontic design and the orthodontic results are analyzed and verified.

13. An optimization method for the step-by-step design of a bracketless clear aligner model, characterized in that, The optimization design is based on the simulation results obtained from any one of claims 9-12, specifically including the following steps: Step A. Determine the optimization objective; Step B. Select an optimization method; Step C. Optimize the design according to the selected optimization method.

14. The optimization method according to claim 13, characterized in that, The optimization objectives include total treatment time, treatment efficiency, or reducing undesirable tooth movement.

15. The optimization method according to claim 13, characterized in that, The optimization method includes optimizing the tooth movement sequence and optimizing the size and mode of tooth movement in each stage of the design.

16. The optimization method according to claim 13, characterized in that, The optimization design in step C specifically includes the following steps: a. Read the position information of each tooth at the initial position and the designed final position of the dentition; b. Determining the movement path and timing: Read the simulation analysis results data, perform time-based envelope space design, and determine the movement path and timing; c. Iterative design of orthodontic appliances ① Monitoring and evaluation of effects: Determine the expression rate and monitoring methods for unfavorable tooth movement based on typical tooth positions; optimize the wearing time of orthodontic appliances based on iterative simulation results of osteogenic and osteoclastogenic effects; ② Orthodontic appliance design: Based on the optimized sequence of teeth, an orthodontic appliance is designed with adjustments made using calculations and limits; ③ Optimization of the orthodontic appliance: Based on the expression rate of the appliance adjustment in step ② and the unfavorable tooth movement, modify the appliance at each stage; ④ Monitoring of periodontal ligament stress: Monitor the stress of the periodontal ligament of each tooth in each step to ensure that it is always within a safe stress range.

17. The optimization method according to claim 16, characterized in that, In step a, the long axis of the tooth and its rotation in three dimensions are determined by the preset crown and root landmarks and the calculated tooth impedance center, as well as the movement of the tooth in three dimensions at the above points.

18. The optimization method according to claim 16, characterized in that, In step ③, the optimization of the orthodontic appliance involves adjusting the appliance based on a pre-set amplification factor.

19. The optimization method according to claim 16, characterized in that, In step ③, the optimization of the orthodontic appliance is carried out by adjusting the translation and rotation of the teeth based on the monitoring values ​​of the typical crown positions that are unfavorable to tooth movement, using translation and rotation as indicators.

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