CN114391986A - Design method of non-uniform invisible appliance based on curved beam deformation differential equation - Google Patents
Design method of non-uniform invisible appliance based on curved beam deformation differential equation Download PDFInfo
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- CN114391986A CN114391986A CN202210171351.3A CN202210171351A CN114391986A CN 114391986 A CN114391986 A CN 114391986A CN 202210171351 A CN202210171351 A CN 202210171351A CN 114391986 A CN114391986 A CN 114391986A
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- 238000000034 method Methods 0.000 title claims abstract description 22
- 238000013461 design Methods 0.000 title claims abstract description 17
- 210000004513 dentition Anatomy 0.000 claims abstract description 29
- 230000036346 tooth eruption Effects 0.000 claims abstract description 29
- 238000004519 manufacturing process Methods 0.000 claims abstract description 4
- 238000006073 displacement reaction Methods 0.000 claims description 11
- 239000002131 composite material Substances 0.000 claims description 4
- 238000002591 computed tomography Methods 0.000 claims description 4
- 210000003464 cuspid Anatomy 0.000 claims description 4
- 238000013213 extrapolation Methods 0.000 claims description 4
- 210000004283 incisor Anatomy 0.000 claims description 4
- 239000000463 material Substances 0.000 claims description 4
- 210000004763 bicuspid Anatomy 0.000 claims description 3
- 230000004927 fusion Effects 0.000 claims description 3
- 230000003239 periodontal effect Effects 0.000 claims description 3
- 238000012545 processing Methods 0.000 claims description 3
- 238000005452 bending Methods 0.000 claims description 2
- 238000004364 calculation method Methods 0.000 claims description 2
- 238000012937 correction Methods 0.000 abstract description 16
- 239000012141 concentrate Substances 0.000 abstract description 2
- 230000002045 lasting effect Effects 0.000 abstract description 2
- 239000006185 dispersion Substances 0.000 abstract 1
- 210000001519 tissue Anatomy 0.000 description 3
- 230000003796 beauty Effects 0.000 description 2
- 210000000988 bone and bone Anatomy 0.000 description 2
- 210000000214 mouth Anatomy 0.000 description 2
- 210000003205 muscle Anatomy 0.000 description 2
- 210000002379 periodontal ligament Anatomy 0.000 description 2
- 230000008719 thickening Effects 0.000 description 2
- 229910000831 Steel Inorganic materials 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 238000004140 cleaning Methods 0.000 description 1
- 230000003247 decreasing effect Effects 0.000 description 1
- 230000007547 defect Effects 0.000 description 1
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- 201000010099 disease Diseases 0.000 description 1
- 208000037265 diseases, disorders, signs and symptoms Diseases 0.000 description 1
- 210000004195 gingiva Anatomy 0.000 description 1
- 238000003384 imaging method Methods 0.000 description 1
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- 239000010959 steel Substances 0.000 description 1
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- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61C—DENTISTRY; APPARATUS OR METHODS FOR ORAL OR DENTAL HYGIENE
- A61C7/00—Orthodontics, i.e. obtaining or maintaining the desired position of teeth, e.g. by straightening, evening, regulating, separating, or by correcting malocclusions
- A61C7/002—Orthodontic computer assisted systems
-
- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61C—DENTISTRY; APPARATUS OR METHODS FOR ORAL OR DENTAL HYGIENE
- A61C7/00—Orthodontics, i.e. obtaining or maintaining the desired position of teeth, e.g. by straightening, evening, regulating, separating, or by correcting malocclusions
- A61C7/08—Mouthpiece-type retainers or positioners, e.g. for both the lower and upper arch
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
- G06F17/13—Differential equations
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T17/00—Three dimensional [3D] modelling, e.g. data description of 3D objects
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T19/00—Manipulating 3D models or images for computer graphics
- G06T19/20—Editing of 3D images, e.g. changing shapes or colours, aligning objects or positioning parts
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- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T7/00—Image analysis
- G06T7/0002—Inspection of images, e.g. flaw detection
- G06T7/0012—Biomedical image inspection
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- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61C—DENTISTRY; APPARATUS OR METHODS FOR ORAL OR DENTAL HYGIENE
- A61C7/00—Orthodontics, i.e. obtaining or maintaining the desired position of teeth, e.g. by straightening, evening, regulating, separating, or by correcting malocclusions
- A61C7/002—Orthodontic computer assisted systems
- A61C2007/004—Automatic construction of a set of axes for a tooth or a plurality of teeth
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T2207/00—Indexing scheme for image analysis or image enhancement
- G06T2207/10—Image acquisition modality
- G06T2207/10072—Tomographic images
- G06T2207/10081—Computed x-ray tomography [CT]
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- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T2207/00—Indexing scheme for image analysis or image enhancement
- G06T2207/30—Subject of image; Context of image processing
- G06T2207/30004—Biomedical image processing
- G06T2207/30036—Dental; Teeth
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
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- G06T2210/00—Indexing scheme for image generation or computer graphics
- G06T2210/41—Medical
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Abstract
The design method of the non-uniform invisible appliance based on the curved beam deformation differential equation comprises the following steps: acquiring a digital dentition model, scanning in the mouth, reconstructing the surface of the mouth, marking the position of teeth, calculating the deformation of tooth nodes, changing the section shape and section coefficient in a curved beam equation, designing an accessory by combining a specific tooth moving mode, and manufacturing an invisible appliance; compared with the prior art, to the comparatively serious stealthy case of correcting of single or several tooth deformities, because the root of tooth of grinding is big, exert the same power at the dental crown, the influence to the grinding is minimum, with anchorage force dispersion to the grinding position, avoid or reduce anchorage force and concentrate on the tooth that does not need to remove that closes on to make the correction power of deformity tooth more lasting effective, reduce treatment cycle.
Description
Technical Field
The invention relates to the technical field of orthodontic correction, in particular to a design method of a nonuniform invisible corrector based on a curved beam deformation differential equation.
Background
In clinical orthodontic treatment, coordination among bones of the face, nerves and muscles of the teeth and the maxillofacial region is adjusted by various correction devices. The appliance generates acting force on teeth and then transmits the acting force to periodontal ligament, and signals released by tension and pressure applied to the periodontal ligament cause a series of reconstruction of alveolar bone, thereby achieving the purposes of balance, stability and beauty of the oromandibular system.
The related diseases can be caused by the excessive correction force applied to the teeth by the corrector, and the pain is caused to the patient; if the orthodontic force is too small, the stress threshold for promoting the tooth to move cannot be reached, and the purpose of moving the tooth cannot be realized. Therefore, the teeth should be subjected to the correction force of 50g-150g and can be continuously loaded as much as possible in the whole correction process.
The invisible appliance is gradually favored by patients and doctors due to the advantages of beauty, comfort, easy cleaning, long period of the return visit and the like. In order to make the correction force continuously constant, a series of invisible correction devices are needed in the whole process of invisible correction, so that teeth move from an initial deformed position to a target normal position. The design process of the whole sequence of the invisible orthodontic appliance is to interpolate the geometric positions of the target teeth and the initial teeth to manufacture the orthodontic appliance at each stage. The shape difference of the appliance and the teeth exists before the appliance is worn, the appliance is elastically deformed due to the shape difference of the appliance and the dentition, and the elastic restoring force generated by the resilience of the appliance provides the correcting force needed by correcting the teeth. The size of the correcting force is determined by the designed pre-deformation amount of the correcting device and the material property of the correcting device material, and the actual direction of the correcting force is determined by the designed deformation direction of the correcting device, the external shape characteristic of the dental crown and the pasted accessory. If the correction force is increased by increasing the correction amount, the difficulty in wearing/taking can be increased, and in severe cases, the correction device is separated from the sleeve, so that the patient teeth need to be subjected to mold taking again and subsequent correction sequences are designed.
For dentition with a single tooth needing a large movement amount, due to the limitation of single-step effective correcting amount in a geometric interpolation mode, a sequence increasing mode is adopted, and correcting time is prolonged; or abandon the invisible appliance and use the traditional fixed appliance. The existing optimization mode adopts measures such as local thickening or embedding steel wires in a region with large demand on the correction force so as to increase the local correction force on dentition, but teeth serving as anchorage are adjacent to the thickened region, and the adjacent teeth are caused to generate unnecessary movement while the increased correction force is exerted.
Disclosure of Invention
The invention aims to overcome the defects in the prior art and provides a design method of a nonuniform invisible appliance based on a curved beam deformation differential equation, which has small influence on molar and aims at the invisible appliance cases with serious single or a plurality of tooth deformities.
In order to achieve the purpose, the invention adopts the following technical scheme: the design method of the non-uniform invisible appliance based on the curved beam deformation differential equation is characterized by comprising the following steps of:
a, acquiring a digital dentition model, and inputting a medical image scanned by CT into medical image processing and three-dimensional reconstruction software to obtain a complete dentition comprising each independent tooth;
and B: intraoral scanning and reconstruction of oral surfaces: obtaining oral surface model data by utilizing intraoral scanning to obtain a composite three-dimensional model with complete dentition and periodontal tissues;
and C: marking the position of the teeth: simplifying a geometric model in the dentition digital model, recording the coordinate position of each tooth, and calculating as a node;
step D: calculating the deformation of the tooth nodes: by curved beam differential equation:
calculating the integral adduction/extrapolation displacement of each tooth node by taking the maximum anchorage force provided by the molar as a load, wherein v is the radial displacement of the curved beam, u is the axial displacement of the curved beam, R is the curvature radius of the curved beam, s is the arc length of the curved beam, E is the elastic modulus of the material, A is the area of the section of the curved beam, and J is the area of the section of the curved beamzThe section parameters of the curved beam are shown, N is the axial force of the section of the curved beam determined by load, and M is the section bending moment of the curved beam determined by load;
step E: changing the cross-sectional shape and cross-sectional coefficient J in the curved beam equationz: the section coefficient is reduced, so that the displacement of the malformed teeth is increased; increasing the section coefficients of other nodes and reducing the adjacent normal tooth movement amount;
step F: designing an accessory according to a specific tooth moving mode: the design of the appliance is carried out by changing section parameters through section design, and the control of the torque is achieved through a bias accessory for a moving form which needs to rotate and translate and needs to control the torque;
step G: manufacturing the invisible orthodontic appliance: e, performing non-uniform thickness treatment on the appliance according to the calculation result of the section coefficient in the step E, thickening the area needing to increase the section coefficient, and thinning the area needing to decrease the section coefficient;
step H: and D, designing the step length of the correcting sequence by the movement amount calculated by the maximum support force which can be provided by the molar in the step D, and further finishing the whole correcting process.
As a preferred embodiment of the present invention, the CT scanning in step a ensures that the shape characteristics and the adjacent relationship of each individual tooth are accurate, and each tooth needs to be separated individually.
In a preferred embodiment of the present invention, the complete dentition in step a is a complete mandibular dentition or a complete maxillary dentition.
As a preferred embodiment of the present invention, the oral surface model data obtained in step B is subjected to position registration and fusion with a model reconstructed based on CT images.
As a preferred scheme of the present invention, the node in step C selects a midpoint of an incisal edge according to incisors, a labial cusp is selected for cuspid teeth and bicuspid teeth, and a labial sulcus is selected for molar teeth.
As a preferred embodiment of the present invention, in the step D, the curved beam differential equation can be obtained by dispersing through a difference formula
As a preferable embodiment of the present invention, the total adduction/extrapolation displacement of each tooth node obtained in step D is an opening gap or adduction closing gap of the corresponding tooth.
In a preferred embodiment of the present invention, the offset attachment of step F is adhered to the corresponding deformed tooth.
As a preferred embodiment of the present invention, step G is combined with the attachment design of step F to correct a single or several severely misshapen dentition while opening the gap and adducting the closed gap.
Compared with the prior art, the invention has the beneficial effects that: to single or the comparatively serious stealthy case of correcting of a few tooth deformities, because the root of a tooth of grinding is big, exert the same power at the dental crown, the influence to the grinding is minimum, and the anchorage force of grinding disperses to the grinding position, avoids or reduces anchorage force and concentrates on the tooth that does not need to remove that closes on to make the power of correcting of deformity tooth more lasting effective, reduce treatment cycle.
Drawings
FIG. 1 is a schematic structural view of a dental node;
FIG. 2 is a schematic representation of the displacement of a tooth node;
FIG. 3 is a schematic illustration of a variation of varying cross-sectional parameters;
FIG. 4 is a schematic view of a deformed tooth with an offset attachment affixed thereto;
FIG. 5 is a schematic view of a partially thickened or thinned invisible appliance;
reference numerals: abutment force F1, node 1, invisible appliance 2, increase section factor 3, decrease section factor 4, bias appendage 5.
Detailed Description
The following describes embodiments of the present invention in detail with reference to the accompanying drawings.
As shown in fig. 1 to 5, the design method of the non-uniform invisible appliance based on the differential equation of the deformation of the curved beam comprises the following steps:
a, acquiring a digital dentition model, and inputting medical images of CT scanning into medical image processing and three-dimensional reconstruction software to obtain complete dentition comprising each independent tooth.
The CT scanning ensures that the shape characteristics and the adjacent relation of each independent tooth are accurate, and each tooth needs to be separated independently, so that the teeth can be conveniently marked in the subsequent process, the complete dentition is a complete mandibular dentition or a complete maxillary dentition, and the actually required mandibular dentition or maxillary dentition is selected according to the actual requirements of the patient.
And B: intraoral scanning and reconstruction of oral surfaces: the method comprises the steps of obtaining oral cavity surface model data by utilizing intraoral scanning, and carrying out position registration and fusion on the obtained oral cavity surface model data and a model reconstructed based on a CT image to obtain a composite three-dimensional model with complete dentition and periodontal tissues, so that the fuzzy boundary of low-density tissues such as gingiva, skin and muscles due to density imaging of the CT image is avoided, and the shape characteristics and the adjacent relation of each independent tooth are accurate.
And C: marking the position of the teeth: simplifying a geometric model in the dentition digital model, recording the coordinate position of each tooth, calculating as a node 1, selecting the middle point of an incisor edge of an incisor, selecting the cuspid of the labial side of the cuspid and the bicuspid, selecting the sulcus of the labial side of the molar, marking the node 1 on the obtained composite three-dimensional model, and marking the corresponding node 1 on each tooth.
Step D: calculating the deformation of the tooth node 1: by curved beam differential equation:
calculating the total adduction/extrapolation displacement of each tooth node 1 by taking the maximum support force F1 provided by the molar as a load, wherein v is the radial displacement of the curved beam, u is the axial displacement of the curved beam, R is the curvature radius of the curved beam, s is the arc length of the curved beam, E is the elastic modulus of the material, A is the area of the section of the curved beam, and J is the section area of the curved beamzThe section parameter of the curved beam is N is the axial force of the section of the curved beam determined by the load, and M is the section bending moment of the curved beam determined by the load.
The differential equation of the curved beam is dispersed through a differential formula to obtain
Therefore, the maximum support force F1 provided by the molar is input as a load, the adduction/extrapolation displacement of each tooth node 1 as a whole is calculated, the displacement is the adduction or extrapolation displacement of each tooth, the damage of the tooth or dentition caused by the overlarge displacement is prevented, and the adduction/extrapolation displacement of each tooth node 1 as a whole is the opening gap or the adduction closing gap of the corresponding tooth.
Step E: changing the cross-sectional shape and cross-sectional coefficient J in the curved beam equationz: the section coefficient is reduced, so that the displacement of the malformed teeth is increased; the section coefficients of the other nodes 1 are increased, and the amount of the adjacent normal tooth movement is decreased.
According to the dentition required to be obtained, the existing dentition composite three-dimensional model is designed, and the section coefficient is reduced or increased at the proper position of the existing dentition composite three-dimensional model, so that the finally obtained dentition accords with the required dentition model.
Step F: designing an accessory according to a specific tooth moving mode: the design of the appliance 2 is carried out by changing section parameters through section design, for a moving form needing to rotate and translate to control torque, the torque is controlled through the offset attachment 5, the offset attachment 5 is adhered to the corresponding malformed teeth, the offset attachment 5 can be made of ceramic, porcelain or alloy and the like, and the offset attachment 5 is a protrusion adhered to the corresponding malformed teeth, so that the requirements of rotating, translating and the like on the malformed teeth are met in the collision process of adjacent teeth, and the control on the malformed teeth is facilitated.
Step G: manufacturing the invisible orthodontic appliance 2: and D, performing non-uniform thickness treatment on the appliance 2 according to the calculation result of the section coefficient in the step E, thickening the area needing to increase the section coefficient by 3, thinning the area needing to decrease the section coefficient by 4, and correcting single or several seriously-deformed dentitions while opening the gap and closing the gap by the accessory design in the step F.
Specifically, the appliance 2 is thinly rescued at the tooth with small movement amount, the appliance 2 is thickly rescued at the tooth with large movement amount, the thicker appliance 2 has better stability, and the thinner part of the appliance 2 has better tension, which is convenient for correcting the corresponding tooth.
Step H: and D, designing the step length of the correcting sequence according to the movement amount calculated by the maximum support force F1 provided by the molar teeth in the step D, and further finishing the whole correcting process.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention; thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Although the reference numerals in the figures are used more here: abutment force F1, node 1, invisible appliance 2, increasing section factor 3, decreasing section factor 4, biasing attachment 5, etc., but does not exclude the possibility of using other terms. These terms are used merely to more conveniently describe and explain the nature of the present invention; they are to be construed as being without limitation to any additional limitations that may be imposed by the spirit of the present invention.
Claims (9)
1. The design method of the non-uniform invisible appliance based on the curved beam deformation differential equation is characterized by comprising the following steps of:
a, acquiring a digital dentition model, and inputting a medical image scanned by CT into medical image processing and three-dimensional reconstruction software to obtain a complete dentition comprising each independent tooth;
and B: intraoral scanning and reconstruction of oral surfaces: obtaining oral surface model data by utilizing intraoral scanning to obtain a composite three-dimensional model with complete dentition and periodontal tissues;
and C: marking the position of the teeth: simplifying a geometric model in the dentition digital model, recording the coordinate position of each tooth, and calculating as a node (1);
step D: calculating the deformation of the tooth node (1): by curved beam differential equation:
calculating the total adduction/extrapolation displacement of each tooth node (1) by taking the maximum support force (F1) provided by the molar as a load, wherein v is the radial displacement of the curved beam, u is the axial displacement of the curved beam, R is the curvature radius of the curved beam, s is the arc length of the curved beam, E is the elastic modulus of the material, A is the area of the section of the curved beam, and J is the section area of the curved beamzThe section parameters of the curved beam are shown, N is the axial force of the section of the curved beam determined by load, and M is the section bending moment of the curved beam determined by load;
step E: changing the cross-sectional shape and cross-sectional coefficient J in the curved beam equationz: the section coefficient is reduced, so that the displacement of the malformed teeth is increased; increasing the section coefficients of other nodes (1) and reducing the adjacent normal tooth movement amount;
step F: designing an accessory according to a specific tooth moving mode: the design of the appliance (2) is carried out by changing section parameters through section design, and the control of the torque is achieved through a bias attachment (5) for the moving form which needs to rotate and translate and needs to control the torque;
step G: manufacturing the invisible appliance (2): according to the calculation result of the section coefficient in the step E, the appliance (2) is subjected to non-uniform thickness treatment, the area needing to increase the section coefficient (3) is thickened, and the area needing to decrease the section coefficient (4) is thinned;
step H: and D, designing the step length of the correcting sequence by the movement amount calculated by the maximum support force (F1) provided by the molar in the step D, and further finishing the whole correcting process.
2. The design method of the non-uniform invisible appliance based on the differential equation of the deformation of the curved beam as claimed in claim 1, wherein the CT scanning in the step A ensures that the shape characteristics and the adjacent relation of each independent tooth are accurate, and each tooth needs to be separated independently.
3. The method for designing a non-uniform invisible appliance based on the differential equation of the deformation of the curved beam as claimed in claim 2, wherein the complete dentition in the step A is a complete mandibular dentition or a complete maxillary dentition.
4. The method for designing the nonuniform invisible appliance based on the differential equation of the deformation of the curved beam as claimed in claim 1, wherein the model data of the oral surface obtained in step B is subjected to position registration and fusion with a model based on CT image reconstruction.
5. The design method of the nonuniform invisible appliance based on the curved beam deformation differential equation as claimed in claim 1, wherein the node (1) in the step C selects the incisal edge midpoint according to incisors, cuspids and bicuspids select labial cusps, and molars select labial sulci.
6. The method for designing the non-uniform invisible orthodontic appliance based on the differential equation of the deformation of the curved beam as claimed in claim 1, wherein in the step D, the differential equation of the curved beam can be dispersed through a differential formula to obtain the non-uniform invisible orthodontic appliance
7. The design method of the non-uniform invisible appliance based on the differential equation of the deformation of the curved beam as set forth in the claim 1, wherein the total adduction/extrapolation displacement of each tooth node (1) obtained in the step D is the opening gap or the adduction closing gap of the corresponding tooth.
8. The method for designing a non-uniform invisible appliance based on the differential equation of deformation of the curved beam as claimed in claim 1, wherein the offset attachments (5) in the step F are adhered to the corresponding deformed teeth.
9. The method for designing non-uniform invisible appliances based on the differential equation of deformation of curved beams as claimed in claim 1, wherein the step G is combined with the accessory design of the step F to correct single or several seriously malformed dentitions while opening the gap and adducting the closed gap.
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| CN202210171351.3A CN114391986B (en) | 2022-02-24 | 2022-02-24 | Design method of non-uniform invisible appliance based on curved beam deformation differential equation |
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|---|---|---|---|---|
| KR20020072318A (en) * | 2001-03-08 | 2002-09-14 | 김정만 | Method for forming orthodontic brace |
| CN103405276A (en) * | 2013-07-10 | 2013-11-27 | 浙江工业大学 | Digitalized making method of dental orthodontic appliance and fixed appliance |
| US20180153648A1 (en) * | 2016-12-02 | 2018-06-07 | Align Technology, Inc. | Palatal expanders and methods of expanding a palate |
| CN110013329A (en) * | 2019-05-20 | 2019-07-16 | 哈尔滨理工大学 | A kind of T shape song dynamic Orthodontic force effect lower teeth mobility model establishing method |
| CN110916820A (en) * | 2019-11-21 | 2020-03-27 | 西安博恩生物科技有限公司 | Optimization method of invisible orthodontic appliance |
| CN111475946A (en) * | 2020-04-04 | 2020-07-31 | 哈尔滨理工大学 | Method for establishing positive axis action box-shaped curve orthodontic force prediction model |
-
2022
- 2022-02-24 CN CN202210171351.3A patent/CN114391986B/en active Active
Patent Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| KR20020072318A (en) * | 2001-03-08 | 2002-09-14 | 김정만 | Method for forming orthodontic brace |
| CN103405276A (en) * | 2013-07-10 | 2013-11-27 | 浙江工业大学 | Digitalized making method of dental orthodontic appliance and fixed appliance |
| US20180153648A1 (en) * | 2016-12-02 | 2018-06-07 | Align Technology, Inc. | Palatal expanders and methods of expanding a palate |
| CN110013329A (en) * | 2019-05-20 | 2019-07-16 | 哈尔滨理工大学 | A kind of T shape song dynamic Orthodontic force effect lower teeth mobility model establishing method |
| CN110916820A (en) * | 2019-11-21 | 2020-03-27 | 西安博恩生物科技有限公司 | Optimization method of invisible orthodontic appliance |
| CN111475946A (en) * | 2020-04-04 | 2020-07-31 | 哈尔滨理工大学 | Method for establishing positive axis action box-shaped curve orthodontic force prediction model |
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