CN114391986B - 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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- 238000000034 method Methods 0.000 title claims abstract description 21
- 238000013461 design Methods 0.000 title claims abstract description 15
- 238000012937 correction Methods 0.000 claims abstract description 30
- 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
- 210000000214 mouth Anatomy 0.000 claims abstract description 4
- 238000006073 displacement reaction Methods 0.000 claims description 11
- 210000003464 cuspid Anatomy 0.000 claims description 7
- 239000002131 composite material Substances 0.000 claims description 4
- 210000004283 incisor Anatomy 0.000 claims description 4
- 230000008719 thickening Effects 0.000 claims description 4
- 238000004364 calculation method Methods 0.000 claims description 3
- 238000002591 computed tomography Methods 0.000 claims description 3
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- 239000000463 material Substances 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
- 210000004763 bicuspid Anatomy 0.000 claims description 2
- 238000005520 cutting process Methods 0.000 claims description 2
- 230000004927 fusion Effects 0.000 claims description 2
- 210000000332 tooth crown Anatomy 0.000 abstract 1
- 210000001519 tissue Anatomy 0.000 description 3
- 210000003205 muscle Anatomy 0.000 description 2
- 210000002379 periodontal ligament Anatomy 0.000 description 2
- 229910000831 Steel Inorganic materials 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 210000000988 bone and bone Anatomy 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
- 238000003745 diagnosis Methods 0.000 description 1
- 238000000605 extraction Methods 0.000 description 1
- 210000003054 facial bone Anatomy 0.000 description 1
- 210000004195 gingiva Anatomy 0.000 description 1
- 238000003384 imaging method Methods 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 210000005036 nerve Anatomy 0.000 description 1
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- 230000002035 prolonged effect Effects 0.000 description 1
- 230000001737 promoting effect Effects 0.000 description 1
- 238000012772 sequence design Methods 0.000 description 1
- 210000003491 skin Anatomy 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
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- A—HUMAN NECESSITIES
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- 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
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- G—PHYSICS
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- 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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- G06T2207/30004—Biomedical image processing
- G06T2207/30036—Dental; Teeth
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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: obtaining a digital dentition model, intraoral scanning and reconstructing the surface of an oral cavity, marking the position of teeth, calculating the node deformation of the teeth, changing the section shape and section coefficient in a curved beam equation, designing accessories in combination with a specific tooth movement mode, and manufacturing an invisible appliance; compared with the prior art, aiming at the invisible correction cases of serious deformity of a single tooth or a plurality of teeth, the same force is applied to the tooth crown due to the thick tooth root of the molar, the influence on the molar is minimum, the supporting force is dispersed to the molar part, the supporting force is prevented or reduced from being concentrated to the adjacent teeth which do not need to be moved, the correction force of the deformed teeth is more durable and effective, and the treatment period is reduced.
Description
Technical Field
The invention relates to the technical field of orthodontic treatment, in particular to a design method of a non-uniform invisible appliance based on a curved beam deformation differential equation.
Background
In clinical orthodontic treatment, the coordination between facial bones, teeth, and the nerves and muscles of the maxillofacial region is adjusted by various correction devices. The acting force is generated on the teeth through the appliance and then transmitted to the periodontal ligament, and the signals released by the tension and the pressure applied to the periodontal ligament cause a series of reconstruction of the alveolar bone, so that the aims of balancing, stabilizing and beautifying the oral-jaw system are achieved.
Excessive forces applied by the appliance to the teeth can produce related conditions and cause pain to the patient; and the too small correction force can not reach the stress threshold value for promoting the teeth to move, so that the aim of moving the teeth can not be fulfilled. Therefore, in the whole correction process, teeth should be subjected to 50g-150g correction force as much as possible and can be continuously loaded.
The invisible appliance is popular with patients and doctors due to the advantages of beautiful appearance, comfort, easy cleaning, long re-diagnosis period and the like. In order to maintain constant force, a series of appliances are needed in the whole process of the invisible correction, so that the teeth can be moved from the initial malformed position to the target normal position. The whole sequence design process of the invisible appliance is to interpolate the geometric positions of the target tooth position and the initial tooth to manufacture the appliance of each stage. The shape difference of each step of appliance and teeth exists before wearing, the appliance is elastically deformed due to the shape difference of the appliance and the dentition, and the elastic restoring force generated by rebound of the appliance provides the correcting force required by correcting the teeth. The magnitude of the correction force is determined by the preformed variable of the correction device design and the material property of the correction device, and the actual direction of the correction force is determined by the deformation direction of the correction device design, the outline characteristics of the dental crown and the attached accessory. If the correction force is required to be increased only by increasing the correction amount, the difficulty in wearing/picking is increased, and if the correction device is not sleeved in severe cases, the teeth of the patient are required to be subjected to model extraction again, and a subsequent correction sequence is designed.
For the dentition with larger movement amount required by a single tooth, the correction time is prolonged by adopting a mode of adding a sequence due to the limitation of the single-step effective correction amount of a geometric interpolation mode; or forgo the use of invisible appliances, using conventional fixed appliances. The existing optimization mode adopts measures such as local thickening or embedding steel wires to the area with large correction force requirement so as to increase the correction force locally applied to the dentition, but the teeth serving as the anchorage are adjacent to the thickening area, and the adjacent teeth can generate unnecessary movement when the correction force is increased.
Disclosure of Invention
The invention aims to overcome the defects in the prior art, and provides a design method of a non-uniform invisible appliance based on a curved beam deformation differential equation, which has little influence on tooth grinding and aims at invisible correction cases with serious single or a plurality of tooth deformities.
In order to achieve the above object, the present 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:
step A, acquiring a digital dentition model, and obtaining a complete dentition comprising each independent tooth by inputting a medical image scanned by CT into medical image processing and three-dimensional reconstruction software;
and (B) step (B): intraoral scanning and reconstruction of oral surfaces: obtaining oral cavity surface model data by utilizing intraoral scanning to obtain a composite three-dimensional model with complete dentition and periodontal tissues;
step C: marking the position of the teeth: simplifying a geometric model in a 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 the curved beam differential equation:
calculating the total adduction/extrapolation displacement of each tooth node with the maximum bearing force provided by the tooth grinding as the load, wherein +.>For radial displacement of curved beam->For axial displacement of curved beam->Is the curvature radius of the curved beam +.>Is the arc length of the curved beam +.>For the modulus of elasticity of the material>Is the area of the cross section of the curved beam, +.>Is a cross-section parameter of curved beam, +.>For the axial force of the curved beam section determined by the load,/->Is the section bending moment of the curved beam determined by the load;
step E: changing the cross-sectional shape and cross-sectional coefficient in curved beam equation: reducing the section coefficient to increase the displacement of the deformed teeth; increasing the section coefficients of other nodes and reducing the adjacent normal tooth movement;
step F: designing accessories in combination with specific tooth movement modes: the sectional parameters are changed through the sectional design to design an appliance, and the torque is controlled through the offset accessory for the movement form needing to be rotated and translated and needing to be controlled;
step G: manufacturing a concealed correction 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 correction sequence according to the calculated movement amount of the maximum supporting force provided by the molar in the step D, and further completing the whole correction process.
As a preferred scheme of the invention, 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.
As a preferred embodiment of the present invention, the complete dentition in the step a is a complete mandibular dentition or a complete maxillary dentition.
As a preferred embodiment of the present invention, the oral cavity surface model data obtained in the step B is registered and fused with a model reconstructed based on CT images.
As a preferable scheme of the invention, the node in the step C selects a cutting edge midpoint according to incisors, the cuspids and the bicuspids select labial cuspids, and the molars select labial sulcus.
As a preferable scheme of the invention, the step D can obtain the discrete of the curved beam differential equation through a differential formula
As a preferable scheme of the invention, the displacement obtained in the step D is the opening gap or the adduction closing gap of the corresponding teeth.
As a preferred embodiment of the present invention, the offset attachment in the step F is adhered to the corresponding malformed tooth.
As a preferred embodiment of the present invention, said step G, in combination with the attachment design of step F, corrects a single or a few severely malformed dentitions while opening the gap and adducting the closed gap.
Compared with the prior art, the invention has the beneficial effects that: aiming at the invisible correction case of serious deformity of a single tooth or a plurality of teeth, the root of the molar is thick, the same force is applied to the dental crown, the influence on the molar is minimum, the supporting force of the molar is dispersed to the molar part, the supporting force is prevented or reduced from being concentrated to the adjacent teeth which do not need to be moved, the correction force of the deformed teeth is more durable and effective, and the treatment period is reduced.
Drawings
FIG. 1 is a schematic view of a tooth node;
FIG. 2 is a schematic displacement of a tooth node;
FIG. 3 is a schematic representation of a variation of the cross-sectional parameters;
FIG. 4 is a schematic view of a deformed tooth with an offset attachment affixed thereto;
FIG. 5 is a schematic illustration of a partially thickened or thinned invisible appliance;
reference numerals: the anchorage force F1, the node 1, the invisible appliance 2, the section coefficient 3 is increased, the section coefficient 4 is reduced, and the accessory 5 is biased.
Detailed Description
Embodiments of the present invention will be described in detail below with reference to the accompanying drawings.
As shown in fig. 1-5, the method for designing the non-uniform invisible appliance based on the curved beam deformation differential equation comprises the following steps:
and A, acquiring a digital dentition model, and obtaining a complete dentition comprising each independent tooth by inputting a medical image scanned by CT into medical image processing and three-dimensional reconstruction software.
CT scanning ensures that the shape characteristics and the adjacent relation of each independent tooth are accurate, and each tooth is required to be separated independently, so that each tooth is convenient to mark in the subsequent step, 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 requirement of a patient.
And (B) step (B): intraoral scanning and reconstruction of oral surfaces: and (3) carrying out intraoral scanning to obtain intraoral surface model data, carrying out position registration and fusion on the obtained intraoral surface model data and a model based on CT image reconstruction to obtain a composite three-dimensional model with complete dentition and periodontal tissues, thereby avoiding CT image imaging due to density, and obtaining accurate shape characteristics and adjacent relation of each independent tooth when the boundaries of tissues such as low-density gingiva, skin, muscle and the like are blurred.
Step C: marking the position of the teeth: the geometrical model is simplified in the dentition digital model, the coordinate position of each tooth is recorded and is used as a node 1 for calculation, the incisors select the midpoint of the incisors, the cuspids and the double cuspids select the lateral labial cuspids, the labial sulcus are selected by grinding, the node 1 can be marked on the obtained composite three-dimensional model, and each tooth is marked with the corresponding node 1.
Step D: calculating the deformation of the tooth node 1: by the curved beam differential equation:
calculating the total adduction/extrapolation displacement of each tooth node 1 with the maximum bearing force F1 provided by the tooth grinding as load, wherein +.>For radial displacement of curved beam->For axial displacement of curved beam->Is the curvature radius of the curved beam +.>Is the arc length of the curved beam +.>For the modulus of elasticity of the material>Is the area of the cross section of the curved beam,is a cross-section parameter of curved beam, +.>For the axial force of the curved beam section determined by the load,/->Is the cross-sectional bending moment of the curved beam determined by the load.
The curved beam differential equation is obtained by discretizing a differential formula
Thus, by inputting the maximum supporting force F1 provided by the grinding teeth as a load, the displacement of the total internal/external of each tooth node 1 is calculated, which is the displacement of each toothThe movement amount which can be adduced or extrapolated can prevent the damage of teeth or dentition caused by the overlarge movement amount, and the displacement amount of the adduced/extrapolated whole of each tooth node 1 is the opening gap or adduced closing gap of the corresponding teeth.
Step E: changing the cross-sectional shape and cross-sectional coefficient in curved beam equation: reducing the section coefficient to increase the displacement of the deformed teeth; the section coefficients of other nodes 1 are increased, and the adjacent normal tooth movement amount is reduced.
According to the needed dentition, 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 needed dentition model.
Step F: designing accessories in combination with specific tooth movement modes: the sectional parameters are changed through the sectional design to design the appliance 2, for the movement form of needing to rotate and translate and needing to control the torque, the offset accessory 5 is used for controlling the torque, the offset accessory 5 is adhered to the corresponding deformed teeth, the offset accessory 5 can be made of ceramics, porcelain or alloy, and the like, and the offset accessory 5 is a bulge adhered to the corresponding deformed teeth, so that the requirements on rotation, translation and the like of the deformed teeth are met in the collision process of adjacent teeth, and the deformed teeth are conveniently controlled.
Step G: manufacturing the invisible appliance 2: and E, performing non-uniform thickness treatment on the appliance 2, thickening a region needing to increase the section coefficient 3, thinning a region needing to decrease the section coefficient 4, designing accessories in the step F, and correcting a single or a plurality of dental columns with serious deformity while opening a gap and closing the gap.
Specifically, the tooth appliance 2 with small movement is thinner, the tooth appliance 2 with large movement is thicker, the thicker tooth appliance 2 has better stability, and the thinner tooth appliance 2 has better tension, so that the correction of the corresponding tooth is facilitated.
Step H: and D, designing the step length of the correction sequence according to the calculated movement amount of the maximum supporting force F1 provided by the molar in the step D, and further completing the whole correction 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 herein: the terms of anchorage force F1, node 1, invisible appliance 2, increasing section factor 3, decreasing section factor 4, biasing accessory 5, etc., do not exclude the possibility of using other terms. These terms are used merely for convenience in describing and explaining the nature of the invention; they are to be interpreted as any additional limitation that is not inconsistent with 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:
step A, acquiring a digital dentition model, and obtaining a complete dentition comprising each independent tooth by inputting a medical image scanned by CT into medical image processing and three-dimensional reconstruction software;
and (B) step (B): intraoral scanning and reconstruction of oral surfaces: obtaining oral cavity surface model data by utilizing intraoral scanning to obtain a composite three-dimensional model with complete dentition and periodontal tissues;
step C: marking the position of the teeth: simplifying a geometric model in a 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 the curved beam differential equation:
calculating the total adduction/extrapolation displacement of each tooth node (1) with the maximum bearing force (F1) provided by the tooth grinding as load, wherein +.>For radial displacement of curved beam->For axial displacement of curved beam->Is the curvature radius of the curved beam +.>Is the arc length of the curved beam +.>For the modulus of elasticity of the material>Is the area of the cross section of the curved beam, +.>Is a cross-section parameter of curved beam, +.>For the axial force of the curved beam section determined by the load,/->Is the section bending moment of the curved beam determined by the load;
step E: changing the cross-sectional shape and cross-sectional coefficient in curved beam equation: reducing the section coefficient to increase the displacement of the deformed teeth; increasing the section coefficients of other nodes (1) and reducing the adjacent normal tooth movement;
step F: designing accessories in combination with specific tooth movement modes: the section parameters are changed through the section design to design the appliance (2), and the torque is controlled through the offset accessory (5) for the movement form needing to be rotated and translated and needing to be controlled;
step G: manufacturing of the invisible correction device (2): e, performing non-uniform thickness treatment on the appliance (2) according to the calculation result of the section coefficient in the step, thickening the area needing to increase the section coefficient (3), and thinning the area needing to decrease the section coefficient (4);
step H: and D, designing the step length of the correction sequence according to the calculated movement amount of the maximum supporting force (F1) provided by the molar in the step D, so as to complete the whole correction process.
2. The method for designing a non-uniform invisible appliance according to claim 1, wherein the CT scan 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 separately.
3. The method for designing a non-uniform contact appliance based on a curved beam deformation differential equation according to 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 a non-uniform contact appliance based on a curved beam deformation differential equation according to claim 1, wherein the oral surface model data obtained in the step B is subjected to position registration and fusion with a model based on CT image reconstruction.
5. The method for designing a non-uniform contact appliance based on a curved beam deformation differential equation according to claim 1, wherein the node (1) in the step C selects a cutting edge midpoint according to incisors, a cuspid, a bicuspid, a labial cuspid, and a molar labial sulcus.
6. The method for designing a non-uniform contact appliance based on a curved beam deformation differential equation according to claim 1, wherein in the step D, the curved beam differential equation is obtained by discretizing a differential equation
7. The method for designing a non-uniform invisible appliance according to claim 1, wherein the displacement amount of the total adduction/extrapolation of each tooth node (1) obtained in the step D is the opening gap or adduction closing gap of the corresponding tooth.
8. The method of designing a non-uniform contact appliance based on a curved beam deformation differential equation according to claim 1, wherein the offset attachment (5) in step F is adhered to the corresponding deformed tooth.
9. The method of claim 1, wherein the step G, in combination with the attachment design of step F, corrects a single or a few severely malformed dentitions while opening the gap and adducting the closed gap.
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Citations (5)
| 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 |
| 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 |
Family Cites Families (1)
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| EP3547952B1 (en) * | 2016-12-02 | 2020-11-04 | Align Technology, Inc. | Palatal expander |
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Patent Citations (5)
| 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 |
| 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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