CN111046451A - Periodontal ligament stress analysis method and device - Google Patents
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- 210000002379 periodontal ligament Anatomy 0.000 title claims abstract description 206
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- 210000000988 bone and bone Anatomy 0.000 claims abstract description 71
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- 230000003239 periodontal effect Effects 0.000 description 2
- 210000001519 tissue Anatomy 0.000 description 2
- 208000006386 Bone Resorption Diseases 0.000 description 1
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- 230000024279 bone resorption Effects 0.000 description 1
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- 238000002474 experimental method Methods 0.000 description 1
- 230000001632 homeopathic effect Effects 0.000 description 1
- 238000012623 in vivo measurement Methods 0.000 description 1
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- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 210000000963 osteoblast Anatomy 0.000 description 1
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- A61C7/00—Orthodontics, i.e. obtaining or maintaining the desired position of teeth, e.g. by straightening, evening, regulating, separating, or by correcting malocclusions
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- A61C19/00—Dental auxiliary appliances
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Abstract
The invention discloses a periodontal ligament stress analysis method and a device, wherein the method comprises the following steps: the method comprises the steps of obtaining geometric models of a digital tooth model, a digital periodontal ligament model and a digital alveolar bone model, selecting the types of constitutive models of the digital tooth model, the digital dental jaw model and the digital alveolar bone model to form the digital dental jaw model, selecting boundary conditions of the digital dental jaw model, obtaining a digital dental finite element model, performing nonlinear finite element calculation to obtain stress distribution data of the digital periodontal ligament model, verifying consistency between the digital dental model and a simulated correction target during rearrangement, and accurately judging whether the alveolar bone can be subjected to bone absorption or bone deposition under the condition that the dental jaw is subjected to pose change and/or load to cause alveolar bone reconstruction; the geometric model closer to the actual condition in the mouth of the patient is utilized, the constitutive model closer to the periodontal ligament characteristic is selected, the calculated stress distribution data is closer to the actual condition, and a data basis is provided for the design, preparation and inspection of subsequent dental instruments.
Description
Technical Field
The invention relates to the technical field of medical instruments, in particular to a periodontal ligament stress analysis method and device, electronic equipment and a computer storage medium.
Background
Use stealthy tooth to rescue the ware and rescue more and more accepted by the patient to the tooth, because it is pleasing to the eye, comfortable and make things convenient for the patient to take by oneself and wear, stealthy tooth is rescued the ware and is carried out the design of virtual scheme of correcting according to patient's intraoral condition, prepare according to virtual scheme of correcting again and to make the tooth reposition to the stealthy tooth of second overall arrangement from first overall arrangement and rescue the ware, the ware is rescued to the stealthy tooth of preparation and is a series of macromolecular shell form apparatus that adjust the tooth overall arrangement gradually, can make patient's tooth carry out layout again when the patient wears stealthy tooth and rescue the ware, change gradually to the target and rescue the position. At present, when the virtual correction scheme is designed, teeth are rearranged according to intraoral data of a patient, but an alveolar bone and a periodontal ligament model are not used for arrangement analysis in the design process, because the periodontal ligament is a connective tissue between a tooth root and the alveolar bone, the periodontal ligament model is difficult to accurately obtain through the existing intraoral information acquisition means, orthodontic tooth movement is a very complicated process, the homeopathic elastic deformation of the periodontal tissue is realized, and the stress/strain generated by the periodontal ligament can stimulate the generation of osteoblasts and osteoclasts in the alveolar bone under the action of orthodontic load because the alveolar bone is subjected to long-term displacement caused by reconstruction. However, due to the structural characteristics of human periodontal tissues and the particularity of biomechanical properties, the biomechanical influence of periodontal ligament under orthodontic load cannot be directly measured by an experimental method. Therefore, the existing virtual correction scheme is designed only by considering the simulated arrangement of the tooth models, and the simulated arrangement of the tooth models and the alveolar bone models is combined, but the simulation of the two methods has deviation due to different actual intraoral structures of patients. Therefore, it is important to introduce the digitized periodontal ligament model into virtual correction and to consider the stress condition of the periodontal ligament during the stress analysis in the tooth rearrangement process.
In the prior art, stress analysis of periodontal ligament is performed by using commercial CAE (Computer Aided Engineering) software such as Abaqus and Ansys, but a constitutive model carried by the commercial software is difficult to meet the properties of periodontal ligament in orthodontic treatment, and a jacobian matrix representing a stress-strain relationship is obtained after theoretical derivation of the constitutive model of periodontal ligament and can be used.
Therefore, the method and the device for accurately analyzing the periodontal ligament stress have great significance for subsequent design, preparation and inspection of dental instruments.
Disclosure of Invention
The invention aims to provide a periodontal ligament stress analysis method and device, a dental appliance design method, a dental appliance preparation method, a dental appliance design inspection method, electronic equipment and a computer storage medium, which can better analyze periodontal ligament stress in orthodontic treatment and provide a basis for design, preparation and inspection of the dental appliance more accurately, so that the designed, prepared and inspected dental appliance is closer to an orthodontic plan, and the orthodontic effect of a patient is ensured.
The purpose of the invention is realized by adopting the following technical scheme:
a periodontal ligament stress analysis method comprising: acquiring a geometric model of a digital tooth model, and selecting the type of a constitutive model of the digital tooth model; acquiring a geometric model of a digital periodontal ligament model, and selecting the type of a constitutive model of the digital periodontal ligament model; acquiring a geometric model of a digital alveolar bone model, and selecting the type of a constitutive model of the digital alveolar bone model; forming a digital dental model by using the types of the geometric model and the constitutive model of the digital tooth model, the types of the geometric model and the constitutive model of the digital periodontal ligament model, and the types of the geometric model and the constitutive model of the digital alveolar bone model; selecting boundary conditions of a digital dental model, wherein the boundary conditions of the digital dental model comprise pose changes and/or loads of the digital dental model; and obtaining a digital dental finite element model by using the digital dental model and the boundary conditions of the digital dental model, performing nonlinear finite element calculation to obtain stress distribution data of the digital periodontal ligament model, and verifying the consistency of the digital dental model and a simulated orthodontic target when the digital dental model is rearranged.
Therefore, when periodontal ligament stress analysis is carried out, the actual situation of stress on teeth in a human body is considered, the digital jaw model comprising the digital tooth model, the digital alveolar bone model and the digital periodontal ligament model is taken as a whole, the digital jaw model and boundary conditions thereof are combined, nonlinear finite element calculation is carried out to obtain digital periodontal ligament stress distribution data, and whether bone absorption or bone deposition occurs to the alveolar bone under the condition that the position and posture of the alveolar bone are changed and/or the load is applied to the jaw can be accurately judged by verifying consistency, so that alveolar bone reconstruction is caused; the geometric model closer to the actual condition in the mouth of the patient is utilized, the constitutive model closer to the periodontal ligament characteristic is selected, the calculated stress distribution data is closer to the actual condition in the mouth of the patient, and a data basis is provided for the design, preparation and inspection of subsequent dental instruments. In addition, the stress condition of the periodontal ligament obtained by calculation is more accurate, the stress conditions of the tooth and the alveolar bone can be calculated simultaneously, the posture change of the tooth or the point load force on the dental crown can be specified to obtain the corresponding stress condition, and the result can effectively guide whether the stress condition can reach the threshold range of alveolar bone reconstruction in the process of simulating tooth correction, so that the correction effect is achieved for judgment.
Optionally, performing nonlinear finite element calculation further obtains stress distribution data of the digital tooth model and stress distribution data of the digital alveolar bone model.
Optionally, the type of the constitutive model of the digitized tooth model and the digitized alveolar bone model is a linear elastic model. The linear elastic model has small computation amount and high computation efficiency, and compared with the situation that the tooth and alveolar bone constitutive model selects the super-elastic model or the visco-elastic model, the computation amount can be greatly reduced, and the computation efficiency is improved.
Optionally, the load comprises a point load, a line load, a face load or a body load. Wherein the load is a load to which the dental model is subjected.
Optionally, the nonlinear finite element calculation is performed by an incremental method. The nonlinear problem cannot be solved by equation calculation of a single system, and therefore, it can be solved by an incremental method, applying a given load step by step and solving until a final solution is obtained.
Optionally, the constitutive model of the digitized periodontal ligament model is of the type of superelastic V-W model or superelastic Yeoh model. Thus, the superelasticity V-W model and the superelasticity Yeoh model can be used to describe the mechanical behavior of the periodontal ligament, and the superelasticity model is more consistent with the actual behavior of the periodontal ligament than the linear elasticity model.
Optionally, when performing nonlinear finite element calculation, the nonlinear finite element simulation calculation equation used is: k (u) u ═ R;
wherein u is an integral node displacement array, K (u) is an integral stiffness matrix, and R is an integral load array;
take the parameter 0 ═ k0<k1<…<kNSplitting R into N +1 steps to load, wherein the load of the mth step is kmR, corresponding to a displacement of um(ii) a N is a positive integer, m is an integer between 0 and N;
wherein, when m<When N is, umThe iterative calculation process of (a) includes:
using umCalculating (u)m)；(um) Is and umThe corresponding strain;
using umAnd constitutive relation calculation of superelasticity constitutive model (u)m)；(um) Is and umThe corresponding stress tensor;
utilizing (u)m) and (um) The elastic constitutive relation of the unit-divided fit line is sigmae＝D(um)εe； wherein D(um) Is and umA corresponding elasticity matrix; sigmaeIs the cell stress tensor; epsiloneIs the cell strain;
by usingD(um) Derivation (u)m)；(um) Is and umA corresponding global stiffness matrix;
using K (u)m)Δum＝(km+1-km) R calculation of Δ um；
Calculating um+1：um+1＝um+Δum；
When m ═ N-1, the final shift is obtained: u-uN＝uN-1+ΔuN-1
In this way, the incremental method is used for finite element numerical calculation of the constitutive model, and the iterative calculation process applied to periodontal ligament stress analysis is optimized.
Optionally, when m is 0, u0Is a zero vector;
using D (u)0) Derivation of K (u)0)；
Wherein when the type of constitutive model of the digitized periodontal ligament model is a superelastic V-W model:
when the type of constitutive model of the digitized periodontal ligament model is a superelastic Yeoh model:
wherein a is a constant consisting of physical parameters of a constitutive model of the digitized periodontal ligament model;
using K (u)0)Δu0＝(k1-k0) R calculation of Δ u0；
Using u1＝Δu0+u0＝Δu0Calculating u1；
According to umAnd carrying out iterative computation in the iterative computation process to obtain u, and stress tensor and strain corresponding to u.
Thus, a method for calculating the displacement of the first step in the initial case when m is 0 is provided, and the subsequent iterative calculation is convenient.
Optionally, the nonlinear finite element calculation is performed by an incremental method.
Optionally, when the type of the constitutive model of the digitized periodontal ligament model is a superelasticity V-W model, obtaining a finite element model of the digitized tooth jaw by using the boundary conditions of the digitized tooth jaw model and performing nonlinear finite element calculation to obtain stress distribution data of the digitized periodontal ligament model so as to verify the consistency of the rearranged digitized tooth model with a simulated orthodontic target, including:
deriving the Green strain by using a strain energy function W of the superelasticity V-W model to obtain a second Piola-Kirchoff stress tensor S; wherein,
in the formula ,c1、c2 and c3Is a physical property parameter of a constitutive model of the digital periodontal ligament model; e is a natural constant;
and
is the invariant of the deformation tensor of the equal volume of the right Cauchy-Green; d1Is the inverse of the bulk modulus; j is the determinant of the deformation gradient tensor;
wherein I is an identity matrix; c is the right Cauchy-Green deformation tensor; c-1Is the inverse matrix of C;
acquiring Cauchy stress tensor by utilizing a second-class Piola-Kirchoff stress tensor S as stress distribution data of the digital periodontal ligament model so as to verify the consistency between the digital tooth model and a simulated correction target during rearrangement; wherein,
wherein F is the deformation gradient tensor; fTIs the transposed matrix of F;
is the isometric left Cauchy-Green deformation tensor.
Thus, a method of calculating stress distribution data of the periodontal ligament when the type of the constitutive model of the periodontal ligament is the superelastic V-W model is given.
Alternatively, with periodontal ligament as the incompressible material, J ═ 1;
writing the Cauchy stress tensor into a component form of:
in the formula ,i、ijis the component of the stress that is,iandijis the strain component, i 1, 2, 3, j 1, 2, 3; i is1Is the invariant of the right Cauchy-Green deformation tensor; u. ofi,pIs the displacement component uiFor reference configuration position component XpA derivative of (a); in the formula, p, q and k are dumb marks, the Einstein summation convention is followed, and the value ranges are 1, 2 and 3.
Thus, the periodontal ligament is regarded as an incompressible material, and the calculation process of the stress distribution data of the periodontal ligament is simplified.
Optionally, when the constitutive model of the digitized periodontal ligament model is a superelasticity Yeoh model, obtaining a digitized dental finite element model by using the digitized dental model and boundary conditions of the digitized dental model and performing nonlinear finite element calculation to obtain stress distribution data of the digitized periodontal ligament model so as to verify consistency of the digitized dental model with a simulated orthodontic target when the digitized dental model is rearranged, the method includes:
deriving the Green strain by using a strain energy function W of the superelasticity Yeoh model to obtain a second Piola-Kirchoff stress tensor S; wherein,
W＝c1(I1-3)+c2(I1-3)2+c3(I1-3)3；
S＝2[c1+2c2(I1-3)+3c3(I1-3)2]I；
in the formula ,c1、c2 and c3Is a physical property parameter of a constitutive model of the digital periodontal ligament model; e is a natural constant; i is1Is the invariant of the right Cauchy-Green deformation tensor; i is an identity matrix;
acquiring Cauchy stress tensor by utilizing a second-class Piola-Kirchoff stress tensor S as stress distribution data of the digital periodontal ligament model so as to verify the consistency between the digital tooth model and a simulated correction target during rearrangement; wherein,
σ＝FSFT＝2[c1+2c2(I1-3)+3c3(I1-3)2]B；
wherein F is the deformation gradient tensor; fTIs the transposed matrix of F; b is the left Cauchy-Green deformation tensor.
Thus, a method of calculating stress distribution data of the periodontal ligament when the constitutive model of the periodontal ligament is the superelastic Yeoh model is given.
Alternatively, with periodontal ligament as the incompressible material, J ═ 1;
writing the Cauchy stress tensor into a component form of:
σi＝2(c1ui,pui,p+2c2up,qup,q+12c3εppεqq+4c2εpp+c1)+4(c1+2c2εpp)εi；
σij＝2c1ui,puj,p+4(c1+4c2εpp)εij；
wherein i and ij are stress components, i and ij are strain components, i is 1, 2, and 3, and j is 1, 2, and 3; u. ofi,pIs the displacement component uiFor reference configuration position component XpA derivative of (a); in the formula, p and q are dumb marks, the Einstein summation convention is followed, and the value range is 1, 2 and 3.
Thus, the periodontal ligament is regarded as an incompressible material, and the calculation process of the stress distribution data of the periodontal ligament is simplified.
Optionally, the geometric model of the digitized periodontal ligament model is obtained by the digitized tooth model estimation or simulation. In this way, a digitized periodontal ligament model can be obtained from the digitized tooth model.
Optionally, the method for obtaining the geometric model of the digitized periodontal ligament model comprises:
generating a plurality of first layer fiducial points of a geometric model of the digitized periodontal ligament model from the geometric model of the digitized tooth model; wherein the geometric model of the digitized tooth model comprises a root portion encapsulated by the geometric model of the digitized periodontal ligament model;
respectively extending each first-layer datum point outwards to obtain a plurality of second-layer datum points; wherein the direction from the root portion to the alveolar bone around the root portion is outward;
generating a geometric model of the digitized periodontal ligament model outside of the geometric model of the digitized tooth model using the plurality of first layer fiducial points and the plurality of second layer fiducial points.
The method for acquiring the geometric model of the digital periodontal ligament model has the advantages that the efficiency is greatly improved, the calculation amount is small, and the generation speed of the digital periodontal ligament model is high. The periodontal ligament stress analysis in orthodontic treatment can be better combined, a foundation can be more accurately provided for the design, preparation and inspection of the dental appliance, the dental appliance after the design, preparation and inspection is closer to the correction plan, and the correction effect of a patient is ensured.
Optionally, the stress distribution data of the digitized periodontal ligament model comprises a hydrostatic pressure distribution or a principal stress distribution for easy presentation and analysis.
A periodontal ligament stress analysis device comprising:
the model module is used for acquiring a geometric model of the digital tooth model and selecting the type of a constitutive model of the digital tooth model; acquiring a geometric model of a digital periodontal ligament model, and selecting the type of a constitutive model of the digital periodontal ligament model; acquiring a geometric model of a digital alveolar bone model, and selecting the type of a constitutive model of the digital alveolar bone model;
a composition module for composing a digital dental model by using the types of the geometric model and the constitutive model of the digital dental model, the types of the geometric model and the constitutive model of the digital periodontal ligament model, and the types of the geometric model and the constitutive model of the digital alveolar bone model;
the boundary module is used for selecting boundary conditions of the digital dental model, and the boundary conditions of the digital dental model comprise pose changes and/or loads of the digital dental model;
and the calculation module is used for obtaining a digital dental finite element model by utilizing the digital dental model and the boundary conditions of the digital dental model, performing nonlinear finite element calculation to obtain stress distribution data of the digital periodontal ligament model, and verifying the consistency between the digital dental model and a simulated orthodontic target when the digital dental model is rearranged.
Optionally, the type of the constitutive model of the digitized tooth model and the digitized alveolar bone model is a linear elastic model.
Optionally, the load comprises a point load, a line load, a face load, or a body load to which the digitized periodontal ligament model is subjected.
Optionally, the nonlinear finite element calculation is performed by an incremental method.
Optionally, the constitutive model of the digitized periodontal ligament model is of the type of superelastic V-W model or superelastic Yeoh model.
Optionally, the geometric model of the digitized periodontal ligament model is obtained by the digitized tooth model estimation or simulation.
Optionally, the obtaining module is further configured to:
generating a plurality of first layer fiducial points of a geometric model of the digitized periodontal ligament model from the geometric model of the digitized tooth model; wherein the geometric model of the digitized tooth model comprises a root portion encapsulated by the geometric model of the digitized periodontal ligament model;
respectively extending each first-layer datum point outwards to obtain a plurality of second-layer datum points; wherein the direction from the root portion to the alveolar bone around the root portion is outward;
generating a geometric model of the digitized periodontal ligament model outside of the geometric model of the digitized tooth model using the plurality of first layer fiducial points and the plurality of second layer fiducial points.
Optionally, the stress distribution data of the digitized periodontal ligament model comprises a hydrostatic pressure distribution or a principal stress distribution.
An electronic device comprising a processor and a memory, the processor executing computer instructions stored by the memory to cause the electronic device to perform any of the periodontal ligament stress analysis methods described above.
A computer storage medium comprising computer instructions which, when run on an electronic device, cause the electronic device to perform any of the periodontal ligament stress analysis methods described above.
The periodontal ligament stress analysis method and device, the design method of the dental appliance, the preparation method of the dental appliance, the design and inspection method of the dental appliance, the electronic equipment and the computer storage medium provided by the invention can better perform stress analysis on the periodontal ligament in orthodontic treatment, can provide a basis for design, preparation and inspection of the dental appliance more accurately, so that the designed, prepared and inspected dental appliance is closer to an orthodontic plan, and the orthodontic effect of a patient is ensured.
Drawings
The invention is further illustrated with reference to the following figures and examples.
FIG. 1 is a schematic view of an overall structure of a dental model according to an embodiment of the present invention;
FIG. 2 is a schematic flow chart of a periodontal ligament stress analysis method according to an embodiment of the present invention;
FIG. 3 is a schematic flow diagram of a method of obtaining a geometric model of a digitized periodontal ligament model;
FIG. 4 is a schematic flow chart of step S12 in FIG. 3;
FIG. 5 is a schematic flow chart of step S4 in FIG. 2;
FIG. 6 is another schematic flow chart of step S4 in FIG. 2;
fig. 7 is a schematic structural diagram of a periodontal ligament stress analysis apparatus according to an embodiment of the present invention.
In the figure: 1. a crown of a tooth; 2. periodontal ligament; 3. alveolar bone; 4. a tooth root; 21. a model module; 22. forming a module; 23. a boundary module; 24. and a calculation module.
Detailed Description
The present invention will be further described with reference to the accompanying drawings and the detailed description, and it should be noted that any combination of the embodiments or technical features described below can be used to form a new embodiment without conflict.
Referring to fig. 1, according to the structure of a human tooth, the illustrated dental model includes a crown 1 and a root 4, a periodontal ligament 2 is wrapped outside the root 4, and an alveolar bone 3 is wrapped outside the periodontal ligament 2.
Referring to fig. 2, an embodiment of the present invention provides a periodontal ligament stress analysis method, including steps S1 to S4.
Step S1: acquiring a geometric model of the digital tooth model, and selecting the type of a constitutive model of the digital tooth model; acquiring a geometric model of the digital periodontal ligament model, and selecting the type of a constitutive model of the digital periodontal ligament model; and acquiring a geometric model of the digital alveolar bone model, and selecting the type of a constitutive model of the digital alveolar bone model. In this step, the order of obtaining the plurality of geometric models and selecting the types of the plurality of constitutive models may be adjusted.
Wherein the geometric model of the digitized periodontal ligament model can be obtained by digitized tooth model estimation or simulation. The estimation may be a rough estimation by digitizing the tooth model. The simulation may be a digital periodontal ligament model generated by digitizing a tooth model and performing an analog simulation.
Referring to fig. 3, the method of acquiring a geometric model of a digitized periodontal ligament model may include steps S11 to S13.
Step S11: generating a plurality of first layer fiducials of a geometric model of the digitized periodontal ligament model from the geometric model of the digitized tooth model; wherein the geometric model of the digitized tooth model includes a root portion encapsulated by the geometric model of the digitized periodontal ligament model.
Step S12: respectively extending each first-layer datum point outwards to obtain a plurality of second-layer datum points; wherein the direction in which the root portion is directed to the alveolar bone around the root portion is outward.
Step S13: a geometric model of the digitized periodontal ligament model outside of the geometric model of the digitized tooth model is generated using the plurality of first layer fiducial points and the plurality of second layer fiducial points. In the generated geometric model of the digital periodontal ligament model, the first layer reference point and the second layer reference point can be positioned on the surface of the geometric model of the digital periodontal ligament model. The geometric model of the digitized periodontal ligament model may be a polyhedron, such as a tetrahedron.
Thus, by inputting a digitized geometric model of a tooth, a first-layer reference point can be determined based on the first-layer reference point, a second-layer reference point can be obtained by extending the first-layer reference point, and a digitized geometric model of periodontal ligament can be generated using the two-layer reference points.
Referring to fig. 4, step S12 may include steps S121 to S122.
Step S121: and respectively acquiring outward normal vectors of each first-layer reference point.
Step S122: and respectively extending each first layer reference point along the outward normal vector of each first layer reference point to obtain a plurality of second layer reference points.
Therefore, the first layer of reference points extend outwards along the respective normal directions by taking the digital tooth model as a starting point, and the condition that extension paths of different reference points intersect can be avoided as much as possible relative to the condition that the first layer of reference points extend along any directions, so that subsequent calculation is facilitated.
Wherein, step S121 may include: taking a plurality of first-layer reference points as vertexes of the digital triangular patch mesh, and solving a normal vector v' with outward vertexes by using normal vectors of a plurality of digital triangular patches formed by vertex-ring neighborhood points:
the number n is the number of the digital triangular patches with the first layer of reference points as vertexes, and the number n is a positive integer greater than 1; i is a positive integer no greater than n; a. theiThe area of the ith triangular patch taking the first layer of reference point as a vertex; v. ofiAnd the outward normal vector of the ith triangular patch taking the first layer reference point as a vertex. In this way, the normal vectors of the first-layer reference points as vertices are calculated by using the normal vectors of the plurality of digitized triangular patches composed of one ring of neighborhood points in the digitized triangular patch mesh.
The method for automatically generating the geometric model of the periodontal ligament can automatically generate the geometric model of the periodontal ligament, greatly improves the efficiency, has small calculation amount and high generation speed of a digital periodontal ligament model. The periodontal ligament stress analysis in orthodontic treatment can be better combined, a foundation can be more accurately provided for the design, preparation and inspection of the dental appliance, the dental appliance after the design, preparation and inspection is closer to the correction plan, and the correction effect of a patient is ensured.
The resulting geometric model of the digitized periodontal ligament model may be between 0.2 and 0.3 mm thick and split into elements for finite element calculations, such as tetrahedrons.
The constitutive model of the digitized periodontal ligament model may be a superelastic V-W model or a superelastic Yeoh model. The corresponding periodontal ligament stress-strain constitutive relation can be automatically matched by selecting the type of the constitutive model. Thus, the superelasticity V-W model and the superelasticity Yeoh model can be used to describe the mechanical behavior of the periodontal ligament, and the superelasticity model is more consistent with the actual behavior of the periodontal ligament than the linear elasticity model.
The type of constitutive model of the digitized tooth model may be a linear elastic model. The linear elastic model has small computation amount and high computation efficiency, and compared with the situation that the tooth and alveolar bone constitutive model selects the super-elastic model or the visco-elastic model, the computation amount can be greatly reduced, and the computation efficiency is improved.
In practical applications, the geometric models of the digitized tooth model and the digitized alveolar bone model inside the oral cavity of the patient, or the geometric models of the digitized tooth model and the digitized alveolar bone model in the standard template, can be provided in the format of a digitized triangular patch mesh. Wherein, the patient data can be obtained by in vivo measurement, and the standard template can be obtained by a laser scanning method.
Step S2: and forming the digital dental model by using the geometric model and the constitutive model of the digital tooth model, the geometric model and the constitutive model of the digital periodontal ligament model, and the geometric model and the constitutive model of the digital alveolar bone model.
Step S3: and selecting boundary conditions of the digital dental model, wherein the boundary conditions of the digital dental model comprise pose changes and/or loads of the digital dental model. In use, the user can conveniently modify the boundary conditions applied to the teeth to obtain the required orthodontic experimental data. The pose change of the digital dental model can be given according to 6 degrees of freedom of the rigid body in space, and can comprise displacement in three coordinate axis directions and rotation angles around three coordinate axes under a rectangular coordinate system.
The load may include a point load, a line load, a face load, or a body load.
Step S4: and obtaining a digital dental finite element model by utilizing the boundary conditions of the digital dental model and the digital dental model, performing nonlinear finite element calculation to obtain stress distribution data of the digital periodontal ligament model, and verifying the consistency between the digital dental model and the simulated orthodontic target when the digital dental model is rearranged.
In this step, the stress distribution data of the digitized periodontal ligament model may include a hydrostatic pressure distribution or a principal stress distribution for easy display and analysis.
Step S4 may also obtain stress distribution data of the digitized tooth model and stress distribution data of the digitized alveolar bone model simultaneously.
The simulated orthodontic objectives may include a single step movement amount objective for the digitized tooth model and a rotation angle objective for the teeth. The verification result of the consistency includes consistency and non-consistency. If the consistency is met, the alveolar bone is subjected to bone absorption or bone deposition under the condition that the position and/or the load of the jaw of the tooth are changed, so that the alveolar bone is reconstructed; if the consistency is not met, the alveolar bone does not have bone absorption or bone deposition under the condition that the position and/or the load of the jaw of the tooth are changed, and the alveolar bone cannot be reconstructed.
Bone resorption of alveolar bone refers to the physiological behavior of gradually decreasing volume and density of bone tissue at lower stress levels. The bone deposition of alveolar bone refers to bone deposition.
Therefore, when periodontal ligament stress analysis is carried out, the actual situation of stress on teeth in a human body is considered, the digital jaw model comprising the digital tooth model, the digital alveolar bone model and the digital periodontal ligament model is taken as a whole, the digital jaw model and boundary conditions thereof are combined, nonlinear finite element calculation is carried out to obtain digital periodontal ligament stress distribution data, and whether bone absorption or bone deposition occurs to the alveolar bone under the condition that the position and posture of the alveolar bone are changed and/or the load is applied to the jaw can be accurately judged by verifying consistency, so that alveolar bone reconstruction is caused; the geometric model closer to the actual condition in the mouth of the patient is utilized, the constitutive model closer to the periodontal ligament characteristic is selected, the calculated stress distribution data is closer to the actual condition in the mouth of the patient, and a data basis is provided for the design, preparation and inspection of subsequent dental instruments. In addition, the stress condition of the periodontal ligament obtained by calculation is more accurate, the stress conditions of the tooth and the alveolar bone can be calculated simultaneously, the posture change of the tooth or the point load force on the dental crown can be specified to obtain the corresponding stress condition, and the result can effectively guide whether the stress condition can reach the threshold range of alveolar bone reconstruction in the process of simulating tooth correction, so that the correction effect is achieved for judgment.
In this embodiment, an incremental method may be used for the nonlinear finite element calculation. The nonlinear problem cannot be solved by equation calculation of a single system, and therefore, it can be solved by an incremental method, applying a given load step by step and solving until a final solution is obtained.
Specifically, when performing nonlinear finite element calculation, the nonlinear finite element simulation calculation equation used may be: k (u) u ═ R, where u is the global nodal displacement array, k (u) is the global stiffness matrix, and R is the global loading array. The equation is solved by a simple integral iteration method and is not converged, so an increment method can be adopted for calculation, and the specific construction process is as follows:
take the parameter 0 ═ k0<k1<…<kNSplitting R into N +1 steps to load, wherein the load of the mth step is kmR, corresponding to a displacement of um(ii) a N is a positive integer, and m is an integer between 0 and N.
Wherein, when m<When N is, umThe iterative calculation process of (a) may include:
using umCalculating (u)m)；(um) Is and umThe corresponding strain can be calculated by using an elastic mechanical geometrical equation;
using umAnd constitutive relation calculation of superelasticity constitutive model (u)m)；(um) Is and umThe corresponding stress tensor;
utilizing (u)m) and (um) Elastic constitutive switch of unit-by-unit fitting lineSystem sigmae＝D(um)εe； wherein D(um) Is and umA corresponding elasticity matrix; sigmaeIs the cell stress tensor; epsiloneIs the cell strain; this step utilizes the idea of local linearization;
using D (u)m) Derivation (u)m)；(um) Is and umA corresponding global stiffness matrix;
using K (u)m)Δum＝(km+1-km) R calculation of Δ um；
Calculating um+1：um+1＝um+Δum(ii) a This step yields the next step of displacement.
The above steps give u0～uN-1The iterative computation method of (1).
When m ═ N-1, the final shift is obtained: u-uN＝uN-1+ΔuN-1。u＝uNIs an approximate solution to be solved, k to meet the accuracy requirementm+1-kmMust be sufficiently small.
In this way, the incremental method is used for finite element numerical calculation of the constitutive model, and the iterative calculation process applied to periodontal ligament stress analysis is optimized.
In the calculation process, the initial value u0The zero vector is generally chosen, but the overall stiffness matrix K (u) is generated therefrom0) Is a zero matrix and cannot solve for Δ u0Therefore, the idea of local linearization can be utilized, taking into account k1-k0Very small, omitting the non-linear part of the superelastic model, using the elastic matrix D (u) of the linear part0) Deriving a global stiffness matrix K (u)0) Then solve for Δ u0And further obtain u1＝Δu0. Specifically, when m is 0, u0Is a zero vector;
using D (u)0) Derivation of K (u)0) (ii) a The process may be represented by D (u)0) Deriving a cell stiffness matrix Ke(u0) Reassembling into a global stiffness matrix K (u)0)。
Wherein, when the type of constitutive model of the digitized periodontal ligament model is a superelasticity V-W model:
wherein a is a constant composed of physical parameters of a constitutive model of the digitized periodontal ligament model.
When the type of constitutive model of the digitized periodontal ligament model is the superelastic Yeoh model:
using K (u)0)Δu0＝(k1-k0) R calculation of Δ u0；
Using u1＝Δu0+u0＝Δu0Calculating u1；
According to umAnd carrying out iterative computation in the iterative computation process to obtain u, and stress tensor and strain corresponding to u.
Thus, a method for calculating the displacement of the first step in the initial case when m is 0 is provided, and the subsequent iterative calculation is convenient.
Referring to fig. 5, when the type of the constitutive model of the digitized periodontal ligament model is the superelastic V-W model, step S4 may include steps S41 to S42.
Step S41: deriving the Green strain by using a strain energy function W of the superelasticity V-W model to obtain a second Piola-Kirchoff stress tensor S; wherein,
in the formula ,c1、c2 and c3The physical property parameters of the constitutive model of the digital periodontal ligament model can be obtained by fitting experimental data; e is a natural constant; i is1 and I2Is the invariant of the deformation tensor of the equal volume of the right Cauchy-Green; d1Is the inverse of the bulk modulus; j is the determinant of the deformation gradient tensor;
wherein I is an identity matrix; c is the right Cauchy-Green deformation tensor; c-1Is the inverse matrix of C.
Step S42: acquiring Cauchy stress tensor as stress distribution data of the digital periodontal ligament model by utilizing a second Piola-Kirchoff stress tensor S so as to verify the consistency of the digital tooth model and a simulated correction target during rearrangement; wherein,
wherein F is the deformation gradient tensor; fTIs the transposed matrix of F;
is the isometric left Cauchy-Green deformation tensor.
In this example, if the periodontal ligament is made of incompressible material, J ═ 1; since incompressible material is an ideal material and does not exist in practice, this step discusses an approximation.
The Cauchy stress tensor is written as a component form:
wherein i and ij are stress components, i and ij are strain components, i is 1, 2, and 3, and j is 1, 2, and 3; i is1Is the invariant of the right Cauchy-Green deformation tensor; u. ofi,pIs the displacement component uiFor reference configuration position component XpA derivative of (a); in the formula, p, q and k are dumb marks, the Einstein summation convention is followed, and the value ranges are 1, 2 and 3.
The dummy index is a subscript which appears only 2 times in a certain monomial expression in vector analysis, and the index is subjected to traversal summation in the value range of the index. In the vector and tensor analysis, the dumb index is tied to the einstein summation convention.
Thus, the periodontal ligament is regarded as an incompressible material, and the calculation process of the stress distribution data of the periodontal ligament is simplified.
Referring to fig. 6, when the type of the constitutive model of the digitized periodontal ligament model is the superelastic Yeoh model, step S4 may include steps S43 to S44.
Step S43: deriving the Green strain by using a strain energy function W of the superelasticity Yeoh model to obtain a second Piola-Kirchoff stress tensor S; wherein,
W＝c1(I1-3)+c2(I1-3)2+c3(I1-3)3；
S＝2[c1+2c2(I1-3)+3c3(I1-3)2]I；
in the formula ,c1、c2 and c3Is a physical property parameter of a constitutive model of the digital periodontal ligament model; e is a natural constant; i is1Is the invariant of the right Cauchy-Green deformation tensor; i is the identity matrix.
Step S44: acquiring Cauchy stress tensor as stress distribution data of the digital periodontal ligament model by utilizing a second Piola-Kirchoff stress tensor S so as to verify the consistency of the digital tooth model and a simulated correction target during rearrangement; wherein,
σ＝FSFT＝2[c1+2c2(I1-3)+3c3(I1-3)2]B；
wherein F is the deformation gradient tensor; fTIs the transposed matrix of F; b is the left Cauchy-Green deformation tensor.
In this example, if the periodontal ligament is made of incompressible material, J ═ 1;
the Cauchy stress tensor is written as a component form:
σi＝2(c1ui,pui,p+2c2up,qup,q+12c3εppεqq+4c2εpp+c1)+4(c1+2c2εpp)εi；
σij＝2c1ui,puj,p+4(c1+4c2εpp)εij；
wherein i and ij are stress components, i and ij are strain components, i is 1, 2, and 3, and j is 1, 2, and 3; u. ofi,pIs the displacement component uiFor reference configuration position component XpA derivative of (a); in the formula, p and q are dumb marks, the Einstein summation convention is followed, and the value range is 1, 2 and 3.
Referring to fig. 7, an embodiment of the present invention further provides a periodontal ligament stress analysis apparatus, including a model module 21, a composition module 22, a boundary module 23, and a calculation module 24, where the model module 21 is connected to the composition module 22, and the composition module 22 and the boundary module 23 are respectively connected to the calculation module 24.
The model module 21 is used for obtaining a geometric model of the digital tooth model and selecting the type of a constitutive model of the digital tooth model; acquiring a geometric model of the digital periodontal ligament model, and selecting the type of a constitutive model of the digital periodontal ligament model; and acquiring a geometric model of the digital alveolar bone model, and selecting the type of a constitutive model of the digital alveolar bone model.
The composition module 22 is used for composing the digital dental model by using the geometric model and the type of the constitutive model of the digital tooth model, the geometric model and the type of the constitutive model of the digital periodontal ligament model, and the geometric model and the type of the constitutive model of the digital alveolar bone model.
The boundary module 23 is used for selecting boundary conditions of the digital dental model, and the boundary conditions of the digital dental model include pose changes and/or loads of the digital dental model.
The calculation module 24 is configured to obtain a digital dental finite element model by using the digital dental model and boundary conditions of the digital dental model, perform nonlinear finite element calculation to obtain stress distribution data of the digital periodontal ligament model, and verify consistency between the digital dental model and the simulated orthodontic target when the digital dental model is rearranged.
In some embodiments, the type of constitutive model of the digitized tooth model and the digitized alveolar bone model may both be a linear elastic model.
In some embodiments, the load may include a point load, a line load, a face load, or a body load.
In some embodiments, the constitutive model of the digitized periodontal ligament model may be of the type of superelastic V-W model or superelastic Yeoh model.
In some embodiments, incremental methods may be used in performing the nonlinear finite element calculations.
In some embodiments, the geometric model of the digitized periodontal ligament model may be obtained by digitized tooth model estimation or simulation.
In some embodiments, model module 21 is further configured to: generating a plurality of first layer fiducials of a geometric model of the digitized periodontal ligament model from the geometric model of the digitized tooth model; wherein the geometric model of the digitized tooth model comprises a root portion encapsulated by the geometric model of the digitized periodontal ligament model; respectively extending each first-layer datum point outwards to obtain a plurality of second-layer datum points; wherein the direction of the tooth root part pointing to the alveolar bone around the tooth root part is outward; a geometric model of the digitized periodontal ligament model outside of the geometric model of the digitized tooth model is generated using the plurality of first layer fiducial points and the plurality of second layer fiducial points.
In some embodiments, the stress distribution data of the digitized periodontal ligament model includes a hydrostatic pressure distribution or a principal stress distribution.
Embodiments of the present invention further provide an electronic device, which includes a processor and a memory, and the processor executes computer instructions stored in the memory, so that the electronic device executes any one of the periodontal ligament stress analysis methods described above.
Embodiments of the present invention also provide a computer storage medium comprising computer instructions that, when run on an electronic device, cause the electronic device to perform any one of the above methods of periodontal ligament stress analysis.
The invention has been described in terms of its several purposes, including but not limited to, specific embodiments, examples, and applications, and it is to be understood that such modifications are intended to cover such departures from the present disclosure as come within known or customary practice in the art to which this invention pertains and which fall within the limits of the appended claims.
Claims (27)
1. A periodontal ligament stress analysis method is characterized by further comprising:
acquiring a geometric model of a digital tooth model, and selecting the type of a constitutive model of the digital tooth model; acquiring a geometric model of a digital periodontal ligament model, and selecting the type of a constitutive model of the digital periodontal ligament model; acquiring a geometric model of a digital alveolar bone model, and selecting the type of a constitutive model of the digital alveolar bone model;
forming a digital dental model by using the types of the geometric model and the constitutive model of the digital tooth model, the types of the geometric model and the constitutive model of the digital periodontal ligament model, and the types of the geometric model and the constitutive model of the digital alveolar bone model;
selecting boundary conditions of a digital dental model, wherein the boundary conditions of the digital dental model comprise pose changes and/or loads of the digital dental model;
and obtaining a digital dental finite element model by using the digital dental model and the boundary conditions of the digital dental model, performing nonlinear finite element calculation to obtain stress distribution data of the digital periodontal ligament model, and verifying the consistency of the digital dental model and a simulated orthodontic target when the digital dental model is rearranged.
2. The periodontal ligament stress analysis method according to claim 1, wherein performing nonlinear finite element calculation further obtains stress distribution data of the digitized tooth model and stress distribution data of the digitized alveolar bone model.
3. The periodontal ligament stress analysis method according to claim 1, wherein the type of the constitutive model of the digitized tooth model and the digitized alveolar bone model is a linear elastic model.
4. The periodontal ligament stress analysis method of claim 1, wherein the load comprises a point load, a line load, a face load, or a body load.
5. The periodontal ligament stress analysis method according to claim 1, wherein an incremental method is used for the nonlinear finite element calculation.
6. The periodontal ligament stress analysis method according to any one of claims 1 to 5, wherein the constitutive model of the digitized periodontal ligament model is a superelastic V-W model or a superelastic Yeoh model.
7. The periodontal ligament stress analysis method according to claim 6, wherein the nonlinear finite element simulation calculation equation used in the nonlinear finite element calculation is:K(u)·u＝R；
wherein u is an integral node displacement array, K (u) is an integral stiffness matrix, and R is an integral load array;
take the parameter 0 ═ k0<k1<…<kNSplitting R into N +1 steps to load, wherein the load of the mth step is kmR, corresponding to a displacement of um(ii) a N is a positive integer, m is an integer between 0 and N;
wherein, when m<When N is, umThe iterative calculation process of (a) includes:
using umCalculating (u)m)；(um) Is and umThe corresponding strain;
using umAnd constitutive relation calculation of superelasticity constitutive model (u)m)；(um) Is and umThe corresponding stress tensor;
utilizing (u)m) and (um) The elastic constitutive relation of the unit-divided fit line is sigmae＝D(um)εe； wherein D(um) Is and umA corresponding elasticity matrix; sigmaeIs the cell stress tensor; epsiloneIs the cell strain;
using D (u)m) Derivation (u)m)；(um) Is and umA corresponding global stiffness matrix;
using K (u)m)Δum＝(km+1-km) R calculation of Δ um；
Calculating um+1：um+1＝um+Δum；
When m ═ N-1, the final shift is obtained: u-uN＝uN-1+ΔuN-1。
8. The periodontal ligament stress analysis method according to claim 7, wherein u is 0 when m is 00Is a zero vector;
using D (u)0) Derivation of K (u)0)；
Wherein when the type of constitutive model of the digitized periodontal ligament model is a superelastic V-W model:
when the type of constitutive model of the digitized periodontal ligament model is a superelastic Yeoh model:
wherein a is a constant consisting of physical parameters of a constitutive model of the digitized periodontal ligament model;
using K (u)0)Δu0＝(k1-k0) R calculation of Δ u0；
Using u1＝Δu0+u0＝Δu0Calculating u1；
According to umAnd carrying out iterative computation in the iterative computation process to obtain u, and stress tensor and strain corresponding to u.
9. The periodontal ligament stress analysis method according to claim 6, wherein an incremental method is used for the nonlinear finite element calculation.
10. The periodontal ligament stress analysis method according to claim 9, wherein when the type of the constitutive model of the digitized periodontal ligament model is a superelasticity V-W model, obtaining a finite element model of the digitized jaw by using the boundary conditions of the digitized jaw model and the digitized jaw model, and performing nonlinear finite element calculation to obtain stress distribution data of the digitized periodontal ligament model so as to verify consistency of the rearranged digitized tooth model with a simulated orthodontic target comprises:
deriving the Green strain by using a strain energy function W of the superelasticity V-W model to obtain a second Piola-Kirchoff stress tensor S; wherein,
in the formula ,c1、c2 and c3Is a physical property parameter of a constitutive model of the digital periodontal ligament model; e is a natural constant;
and
is the invariant of the deformation tensor of the equal volume of the right Cauchy-Green; d1Is the inverse of the bulk modulus; j is the determinant of the deformation gradient tensor;
wherein I is an identity matrix; c is the right Cauchy-Green deformation tensor; c-1Is the inverse matrix of C;
acquiring Cauchy stress tensor by utilizing a second-class Piola-Kirchoff stress tensor S as stress distribution data of the digital periodontal ligament model so as to verify the consistency between the digital tooth model and a simulated correction target during rearrangement; wherein,
wherein F is the deformation gradient tensor; fTIs the transposed matrix of F;
is the isometric left Cauchy-Green deformation tensor.
11. The periodontal ligament stress analysis method according to claim 10, wherein when the periodontal ligament is made of an incompressible material, J ═ 1;
writing the Cauchy stress tensor into a component form of:
wherein i and ij are stress components, i and ij are strain components, i is 1, 2, 3, and j is 1, 2, 3; i is1Is the invariant of the right Cauchy-Green deformation tensor; u. ofi,pIs the displacement component uiFor reference configuration position component XpA derivative of (a); in the formula, p, q and k are dumb marks, the Einstein summation convention is followed, and the value ranges are 1, 2 and 3.
12. The periodontal ligament stress analysis method according to claim 9, wherein when the constitutive model of the digitized periodontal ligament model is a superelasticity Yeoh model, the obtaining of the digitized dental finite element model by using the boundary conditions of the digitized dental model and the nonlinear finite element calculation to obtain the stress distribution data of the digitized periodontal ligament model to verify the consistency of the digitized dental model with the simulated orthodontic target when the digitized dental model is rearranged comprises:
deriving the Green strain by using a strain energy function W of the superelasticity Yeoh model to obtain a second Piola-Kirchoff stress tensor S; wherein,
W＝c1(I1-3)+c2(I1-3)2+c3(I1-3)3；
S＝2[c1+2c2(I1-3)+3c3(I1-3)2]I；
in the formula ,c1、c2 and c3Is a physical property parameter of a constitutive model of the digital periodontal ligament model; e is a natural constant; i is1Is the invariant of the right Cauchy-Green deformation tensor; i is an identity matrix;
acquiring Cauchy stress tensor by utilizing a second-class Piola-Kirchoff stress tensor S as stress distribution data of the digital periodontal ligament model so as to verify the consistency between the digital tooth model and a simulated correction target during rearrangement; wherein,
σ＝FSFT＝2[c1+2c2(I1-3)+3c3(I1-3)2]B；
wherein F is the deformation gradient tensor; fTIs the transposed matrix of F; b is the left Cauchy-Green deformation tensor.
13. The periodontal ligament stress analysis method according to claim 12, wherein when the periodontal ligament is made of an incompressible material, J ═ 1;
writing the Cauchy stress tensor into a component form of:
σi＝2(c1ui,pui,p+2c2up,qup,q+12c3εppεqq+4c2εpp+c1)+4(c1+2c2εpp)εi；
σij＝2c1ui,puj,p+4(c1+4c2εpp)εij；
wherein i and ij are stress components, i and ij are strain components, i is 1, 2, and 3, and j is 1, 2, and 3; u. ofi,pIs the displacement component uiFor reference configuration position component XpA derivative of (a); in the formula, p and q are dumb marks, the Einstein summation convention is followed, and the value range is 1, 2 and 3.
14. The periodontal ligament stress analysis method according to claim 1, wherein the geometric model of the digitized periodontal ligament model is obtained by the digitized tooth model estimation or simulation.
15. The periodontal ligament stress analysis method according to claim 14, wherein the method for obtaining the geometric model of the digitized periodontal ligament model includes:
generating a plurality of first layer fiducial points of a geometric model of the digitized periodontal ligament model from the geometric model of the digitized tooth model; wherein the geometric model of the digitized tooth model comprises a root portion encapsulated by the geometric model of the digitized periodontal ligament model;
respectively extending each first-layer datum point outwards to obtain a plurality of second-layer datum points; wherein the direction from the root portion to the alveolar bone around the root portion is outward;
generating a geometric model of the digitized periodontal ligament model outside of the geometric model of the digitized tooth model using the plurality of first layer fiducial points and the plurality of second layer fiducial points.
16. The periodontal ligament stress analysis method according to claim 1, wherein the stress distribution data of the digitized periodontal ligament model includes a hydrostatic pressure distribution or a principal stress distribution.
17. A periodontal ligament stress analysis device comprising:
the model module is used for acquiring a geometric model of the digital tooth model and selecting the type of a constitutive model of the digital tooth model; acquiring a geometric model of a digital periodontal ligament model, and selecting the type of a constitutive model of the digital periodontal ligament model; acquiring a geometric model of a digital alveolar bone model, and selecting the type of a constitutive model of the digital alveolar bone model;
a composition module for composing a digital dental model by using the types of the geometric model and the constitutive model of the digital dental model, the types of the geometric model and the constitutive model of the digital periodontal ligament model, and the types of the geometric model and the constitutive model of the digital alveolar bone model;
the boundary module is used for selecting boundary conditions of the digital dental model, and the boundary conditions of the digital dental model comprise pose changes and/or loads of the digital dental model;
and the calculation module is used for obtaining a digital dental finite element model by utilizing the digital dental model and the boundary conditions of the digital dental model, performing nonlinear finite element calculation to obtain stress distribution data of the digital periodontal ligament model, and verifying the consistency between the digital dental model and a simulated orthodontic target when the digital dental model is rearranged.
18. The periodontal ligament stress analysis device according to claim 17, wherein the type of the constitutive model of the digitized tooth model and the digitized alveolar bone model is a linear elastic model.
19. The periodontal ligament stress analysis device of claim 17, wherein the load comprises a point load, a line load, a surface load, or a body load to which the digitized periodontal ligament model is subjected.
20. The periodontal ligament stress analysis device according to claim 17, wherein an incremental method is used for performing the nonlinear finite element calculation.
21. Periodontal ligament stress analysis device according to any one of claims 17 to 20, wherein the constitutive model of the digitized periodontal ligament model is of the superelastic V-W model or superelastic Yeoh model.
22. The periodontal ligament stress analysis device according to claim 21, wherein an incremental method is used for performing the nonlinear finite element calculation.
23. The periodontal ligament stress analysis device according to claim 17, wherein the geometric model of the digitized periodontal ligament model is obtained by the digitized tooth model estimation or simulation.
24. The periodontal ligament stress analysis device of claim 23, wherein the acquisition module is further configured to:
generating a plurality of first layer fiducial points of a geometric model of the digitized periodontal ligament model from the geometric model of the digitized tooth model; wherein the geometric model of the digitized tooth model comprises a root portion encapsulated by the geometric model of the digitized periodontal ligament model;
respectively extending each first-layer datum point outwards to obtain a plurality of second-layer datum points; wherein the direction from the root portion to the alveolar bone around the root portion is outward;
generating a geometric model of the digitized periodontal ligament model outside of the geometric model of the digitized tooth model using the plurality of first layer fiducial points and the plurality of second layer fiducial points.
25. The periodontal ligament stress analysis device according to claim 17, wherein the stress distribution data of the digitized periodontal ligament model includes a hydrostatic pressure distribution or a principal stress distribution.
26. An electronic device comprising a processor and a memory, the processor executing computer instructions stored by the memory to cause the electronic device to perform the periodontal ligament stress analysis method of any of claims 1 to 16.
27. A computer storage medium comprising computer instructions which, when run on an electronic device, cause the electronic device to perform the periodontal ligament stress analysis method of any of claims 1 to 16.
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US11229504B1 (en) | 2021-01-07 | 2022-01-25 | Ortho Future Technologies (Pty) Ltd | System and method for determining a target orthodontic force |
| US11241301B1 (en) | 2021-01-07 | 2022-02-08 | Ortho Future Technologies (Pty) Ltd | Measurement device |
| US11278376B1 (en) | 2021-01-07 | 2022-03-22 | Ortho Future Technologies (Pty) Ltd | Orthodontic treatment staging |
| US11291524B1 (en) | 2021-01-07 | 2022-04-05 | Ortho Future Technologies (Pty) Ltd | Orthodontic appliance configuration |
Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20030059736A1 (en) * | 2001-09-26 | 2003-03-27 | 3M Innovative Properties Company | Use of finite element analysis for orthodontic mechanics and appliance selection |
| US20100280798A1 (en) * | 2007-12-21 | 2010-11-04 | Materialise Dental N.V. | Tooth movement system and method |
| CN102415916A (en) * | 2011-07-29 | 2012-04-18 | 首都医科大学附属北京口腔医院 | Correction method for preventing excessive stress concentration of teeth roots and jaws in process of orthodontic treatment |
| CN108242267A (en) * | 2018-04-11 | 2018-07-03 | 大连市口腔医院 | A kind of dentognathic system finite element modeling method based on DICM data |
| CN108268673A (en) * | 2016-12-30 | 2018-07-10 | 无锡时代天使医疗器械科技有限公司 | The method of emulation is digitized for the rectifying effect to dental appliance |
| CN108831551A (en) * | 2017-04-27 | 2018-11-16 | 无锡时代天使医疗器械科技有限公司 | Area of computer aided dental orthodontic rescues the method for inspection of instrument |
| CN109002635A (en) * | 2018-08-02 | 2018-12-14 | 东南大学 | A kind of bolt connection considering connected nonlinearity |
-
2019
- 2019-12-06 CN CN201911245262.3A patent/CN111046451B/en active Active
Patent Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20030059736A1 (en) * | 2001-09-26 | 2003-03-27 | 3M Innovative Properties Company | Use of finite element analysis for orthodontic mechanics and appliance selection |
| US20100280798A1 (en) * | 2007-12-21 | 2010-11-04 | Materialise Dental N.V. | Tooth movement system and method |
| CN102415916A (en) * | 2011-07-29 | 2012-04-18 | 首都医科大学附属北京口腔医院 | Correction method for preventing excessive stress concentration of teeth roots and jaws in process of orthodontic treatment |
| CN108268673A (en) * | 2016-12-30 | 2018-07-10 | 无锡时代天使医疗器械科技有限公司 | The method of emulation is digitized for the rectifying effect to dental appliance |
| CN108831551A (en) * | 2017-04-27 | 2018-11-16 | 无锡时代天使医疗器械科技有限公司 | Area of computer aided dental orthodontic rescues the method for inspection of instrument |
| CN108242267A (en) * | 2018-04-11 | 2018-07-03 | 大连市口腔医院 | A kind of dentognathic system finite element modeling method based on DICM data |
| CN109002635A (en) * | 2018-08-02 | 2018-12-14 | 东南大学 | A kind of bolt connection considering connected nonlinearity |
Non-Patent Citations (3)
| Title |
|---|
| 魏志刚;汤文成;严斌;杨宝宽;: "基于有限元法的牙周膜本构模型研究" * |
| 魏志刚;汤文成;严斌;杨宝宽;: "基于次弹性模型的三维牙周膜建模仿真研究" * |
| 黄建龙;解广娟;刘正伟;: "基于Mooney-Rivlin和Yeoh模型的超弹性橡胶材料有限元分析" * |
Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US11229504B1 (en) | 2021-01-07 | 2022-01-25 | Ortho Future Technologies (Pty) Ltd | System and method for determining a target orthodontic force |
| US11241301B1 (en) | 2021-01-07 | 2022-02-08 | Ortho Future Technologies (Pty) Ltd | Measurement device |
| US11278376B1 (en) | 2021-01-07 | 2022-03-22 | Ortho Future Technologies (Pty) Ltd | Orthodontic treatment staging |
| US11291524B1 (en) | 2021-01-07 | 2022-04-05 | Ortho Future Technologies (Pty) Ltd | Orthodontic appliance configuration |
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