CN111046451B - Periodontal ligament stress analysis method and device - Google Patents
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- 210000002379 periodontal ligament Anatomy 0.000 title claims abstract description 208
- 238000004458 analytical method Methods 0.000 title claims abstract description 57
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- 210000000988 bone and bone Anatomy 0.000 claims abstract description 70
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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 periodontal ligament stress analysis device, wherein the method comprises the following steps: the method comprises the steps of obtaining a digital tooth model, a digital periodontal ligament model and a geometric model of a digital alveolar bone model, selecting types of constitutive models of the digital tooth model, the digital periodontal ligament model and the digital alveolar bone model to form a digital dental model, selecting digital dental model boundary conditions to obtain a digital dental finite element model, and carrying out nonlinear finite element calculation to obtain stress distribution data of the digital periodontal ligament model so as to verify consistency between the digital tooth model and an analog correction target when the digital tooth model is rearranged, and accurately judging whether the alveolar bone can be subjected to bone absorption or bone deposition under the conditions of pose change and/or load of the dental jaw to cause the alveolar bone reconstruction; the geometrical model which is closer to the actual condition in the mouth of the patient is utilized, the constitutive model which is closer to the characteristics of periodontal ligament is selected, and the calculated stress distribution data is closer to the actual condition, so that a data basis is provided for the design, preparation and inspection of the follow-up dental appliance.
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
The invisible tooth appliance is more and more accepted by patients because of attractive appearance, comfort and convenience for the patients to pick up and wear by themselves, the invisible tooth appliance is designed according to the intraoral condition of the patients to carry out a virtual appliance scheme, then the invisible tooth appliance capable of repositioning the teeth from a first layout to a second layout is prepared according to the virtual appliance scheme, the prepared invisible tooth appliance is a series of polymer shell-shaped appliances capable of gradually adjusting the tooth layout, and when the patients wear the invisible tooth appliance, the teeth of the patients can be rearranged and gradually changed to the target appliance position. At present, when a 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, as the periodontal ligament is connective tissue positioned between a tooth root and the alveolar bone, the periodontal ligament model is difficult to accurately obtain by the existing intraoral information acquisition means, orthodontic tooth movement is a very complex process, the orthotopic elastic deformation of periodontal tissues is generated, and the long-term displacement caused by reconstruction of the alveolar bone is also generated, so that the generation of osteoblasts and osteoclasts in the alveolar bone can be stimulated by stress/strain generated by the periodontal ligament under the action of orthodontic load. However, due to the structural characteristics of periodontal tissues of a human body and the specificity of biomechanical properties, the biomechanical influence condition of periodontal ligament under the action of orthodontic load cannot be directly measured by an experimental method. Therefore, in the current design of the virtual correction scheme, only the tooth model is considered for simulation arrangement, and the tooth model and the alveolar bone model are combined for simulation arrangement, but the simulation of the two methods has deviation from the actual intraoral structure of the patient. Therefore, it is important to introduce a digitized periodontal ligament model into the virtual appliance while considering the force conditions of the periodontal ligament when performing force analysis during tooth rearrangement.
In the prior art, commercial CAE (Computer Aided Engineering ) software such as Abaqus and Ansys in engineering design is utilized to perform periodontal ligament stress analysis, but the self-contained constitutive model of commercial software is difficult to meet the property of periodontal ligament in orthodontic treatment, and the jacobian matrix representing the stress-strain relationship can be obtained for use after theoretical derivation of the constitutive model of periodontal ligament is needed.
Therefore, the method and the device capable of accurately analyzing the periodontal ligament stress are researched, and have important significance for the subsequent dental instrument design, preparation and inspection.
Disclosure of Invention
The invention aims to provide a periodontal ligament stress analysis method and device, a dental instrument design method, a dental instrument preparation method, a dental instrument design and inspection method, electronic equipment and a computer storage medium, so that periodontal ligament stress analysis in orthodontic treatment can be better performed, a foundation can be provided for dental instrument design, preparation and inspection more accurately, the designed, prepared and inspected dental instrument is closer to an orthodontic treatment plan, and an orthodontic effect of a patient is ensured.
The invention adopts the following technical scheme:
A periodontal ligament stress analysis method comprising: obtaining a geometric model of a digital tooth model, and selecting the type of a constitutive model of the digital tooth model; obtaining a geometric model of a digital periodontal ligament model, and selecting the type of a constitutive model of the digital periodontal ligament model; obtaining 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 geometric model and the type of the constitutive model of the digital dental 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; selecting digital dental model boundary conditions, wherein the digital dental model boundary conditions comprise pose changes and/or received loads of a digital dental model; and obtaining a digital dental finite element model by utilizing the digital dental model and the digital dental model boundary condition, and performing nonlinear finite element calculation to obtain stress distribution data of the digital periodontal ligament model so as to verify the consistency of the digital dental model with a simulated correction target when the digital dental model is rearranged.
In this way, when periodontal ligament stress analysis is carried out, the actual situation of tooth stress in a human body is considered, a digital dental model comprising a digital dental model, a digital alveolar bone model and a digital periodontal ligament model is taken as a whole, the digital dental model and boundary conditions thereof are combined, the obtained digital periodontal ligament stress distribution data is calculated through nonlinear finite elements, and whether the alveolar bone can be subjected to bone absorption or bone deposition under the conditions of pose change of the dental jaw and/or the applied load can be accurately judged through verification of consistency, so that the alveolar bone reconstruction is caused; the geometrical model which is closer to the actual intraoral condition of the patient is utilized, the constitutive model which is closer to the periodontal ligament characteristics is selected, the calculated stress distribution data is closer to the actual intraoral condition of the patient, and a data basis is provided for the design, preparation and inspection of the follow-up dental appliance. In addition, the periodontal ligament stress situation obtained by calculation is more accurate, the stress situations of the teeth and the alveolar bones can be calculated at the same time, the pose change of the teeth or the point load force on the dental crowns can be specified, the corresponding stress situation can be obtained, and the result can effectively guide whether the stress situation can reach the threshold range of the alveolar bone reconstruction in the simulated tooth correction process, so that correction effect is achieved to judge.
Optionally, performing a nonlinear finite element calculation also results in stress distribution data for the digitized tooth model and stress distribution data for the digitized alveolar bone model.
Optionally, the type of constitutive model of the digitized tooth model and the digitized alveolar bone model is a linear elastic model. The linear elastic model has small calculation amount and high calculation efficiency, and compared with the situation that the super elastic model or the viscoelasticity model is selected by the tooth and alveolar bone constitutive model, the calculation amount can be greatly reduced, and the calculation efficiency is improved.
Optionally, the load comprises a point load, a line load, a face load, or a bulk load. Wherein the load is the load to which the dental model is subjected.
Alternatively, an incremental approach is used in performing the nonlinear finite element calculations. The nonlinear problem cannot be solved by equation calculation of a single system, and therefore, can be solved by an incremental method, with a given load applied step by step and solved until a final solution is obtained.
Optionally, the type of constitutive model of the digitized periodontal ligament model is a superelastic V-W model or a superelastic yoh model. Thus, the mechanical behavior of the periodontal ligament can be described using the superelastic V-W model and the superelastic Yeoh model, which are more in line with the actual situation of the periodontal ligament than the linear elastic model.
Optionally, when performing nonlinear finite element calculation, the nonlinear finite element simulation calculation equation is adopted as follows: 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;
taking parameter 0=k 0 <k 1 <…<k N =1, splitting R into n+1 steps for loading, the load at the mth step is k m R, the corresponding displacement is u m The method comprises the steps of carrying out a first treatment on the surface of the N is a positive integer, m is an integer between 0 and N;
wherein when m is<When N, u m The iterative calculation process of (1) comprises:
by u m Calculation (u) m )；(u m ) Is with u m A corresponding strain;
by u m And constitutive relation calculation of superelastic constitutive model (u m )；(u m ) Is with u m A corresponding stress tensor;
by means of (u) m) and (um ) The elastic constitutive relation of the sub-unit fitting line is sigma e ＝D(u m )ε e； wherein D(um ) Is with u m A corresponding elastic matrix; sigma (sigma) e Is the unit stress tensor; epsilon e Is the cell strain;
by means of D (u) m ) Export (u) m )；(u m ) Is with u m A corresponding overall stiffness matrix;
by K (u) m )Δu m ＝(k m+1 -k m ) R calculates Deltau m ；
Calculation u m+1 ：u m+1 ＝u m +Δu m ；
When m=n-1, the final displacement is obtained: u=u N ＝u N-1 +Δu N-1
Therefore, the finite element numerical calculation of the constitutive model is performed by using an incremental method, and the iterative calculation process applied to periodontal ligament stress analysis is optimized.
Alternatively, when m=0, u 0 Is a zero vector;
by means of D (u) 0 ) Export 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 constituted by physical parameters of a constitutive model of the digitized periodontal ligament model;
by K (u) 0 )Δu 0 ＝(k 1 -k 0 ) R calculates Deltau 0 ；
By u 1 ＝Δu 0 +u 0 ＝Δu 0 Calculation u 1 ；
According to said u m And (3) carrying out iterative computation to obtain u and the stress tensor and strain corresponding to u.
Thus, a method of calculating the first step displacement in the initial case where m=0 is given, facilitating the subsequent iterative calculation.
Alternatively, an incremental approach is used in performing the nonlinear finite element calculations.
Optionally, when the type of the constitutive model of the digital periodontal ligament model is a super-elastic V-W model, the obtaining a digital dental finite element model by using the digital dental model and the digital dental model boundary conditions and performing nonlinear finite element calculation to obtain stress distribution data of the digital periodontal ligament model, so as to verify consistency between the digital dental model and a simulated correction target when the digital dental model is rearranged, includes:
the strain energy function W of the super-elastic V-W model is utilized to derive Green strain, and a second class Picola-Kirchhoff stress tensor S is obtained; wherein,
in the formula ,c1 、c 2 and c3 Is a physical property parameter of a constitutive model of the digital periodontal ligament model; e is a natural constant;
and />
Is invariant to the isovolumetric right Cauchy-Green deformation tensor; d (D) 1 Is the reciprocal of the bulk modulus; j is the determinant of deformation gradient tensors;
wherein I is an identity matrix; c is the right Cauchy-Green deformation tensor; c (C) -1 Is the inverse of C;
acquiring a Cauchy stress tensor as stress distribution data of the digital periodontal ligament model by using a second class Picola-Kirchhoff stress tensor S so as to verify consistency of the digital tooth model with a simulated correction target when rearranged; wherein,
wherein F is a deformation gradient tensor; f (F) T Is the transposed matrix of F;
is the isovolumetric left Cauchy-Green deformation tensor.
Thus, a calculation method of stress distribution data of the periodontal ligament is given when the type of constitutive model of the periodontal ligament is a superelastic V-W model.
Alternatively, with periodontal ligament as incompressible material, j=1;
writing the Cauchy stress tensor into a component form of:
in the formula ,i 、 ij is a component of the stress that is present, i and ij is the strain component, i=1, 2, 3, j=1, 2, 3; i 1 Is invariant to the right Cauchy-Green deformation tensor; u (u) i,p Is the displacement component u i For reference configuration position component X p Is a derivative of (2); wherein p, q and k are dummy marks, and the value ranges are 1, 2 and 3 according to Einstein summation convention.
Thus, the periodontal ligament is considered as an incompressible material, simplifying the calculation process of the stress distribution data of the periodontal ligament.
Optionally, when the type of the constitutive model of the digitized periodontal ligament model is a superelastic yoh model, the obtaining a digitized dental finite element model by using the digitized dental model and the digitized dental model boundary condition and performing nonlinear finite element calculation to obtain stress distribution data of the digitized periodontal ligament model so as to verify consistency between the digitized dental model and a simulated correction target when the digitized dental model is rearranged includes:
the strain energy function W of the super-elastic Yeoh model is utilized to derive the Green strain, and the second class Picola-Kirchhoff stress tensor S is obtained; wherein,
W＝c 1 (I 1 -3)+c 2 (I 1 -3) 2 +c 3 (I 1 -3) 3 ；
S＝2[c 1 +2c 2 (I 1 -3)+3c 3 (I 1 -3) 2 ]I；
in the formula ,c1 、c 2 and c3 Is a physical property parameter of a constitutive model of the digital periodontal ligament model; e is a natural constant; i 1 Is invariant to the right Cauchy-Green deformation tensor; i is an identity matrix;
acquiring a Cauchy stress tensor as stress distribution data of the digital periodontal ligament model by using a second class Picola-Kirchhoff stress tensor S so as to verify consistency of the digital tooth model with a simulated correction target when rearranged; wherein,
σ＝FSF T ＝2[c 1 +2c 2 (I 1 -3)+3c 3 (I 1 -3) 2 ]B；
Wherein F is a deformation gradient tensor; f (F) T Is the transposed matrix of F; b is the left Cauchy-Green deformation tensor.
Thus, a calculation method of stress distribution data of the periodontal ligament is given when the type of constitutive model of the periodontal ligament is the superelastic yoh model.
Alternatively, with periodontal ligament as incompressible material, j=1;
writing the Cauchy stress tensor into a component form of:
σ i ＝2(c 1 u i,p u i,p +2c 2 u p,q u p,q +12c 3 ε pp ε qq +4c 2 ε pp +c 1 )+4(c 1 +2c 2 ε pp )ε i ；
σ ij ＝2c 1 u i,p u j,p +4(c 1 +4c 2 ε pp )ε ij ；
where i, ij are stress components, i and ij are strain components, i=1, 2, 3, j=1, 2, 3; u (u) i,p Is the displacement component u i For reference configuration position componentX p Is a derivative of (2); wherein p and q are dummy marks, and the value ranges are 1, 2 and 3 according to Einstein summation convention.
Thus, the periodontal ligament is considered as an incompressible material, simplifying the calculation process of the stress distribution data of the periodontal ligament.
Optionally, the geometric model of the digitized periodontal ligament model is obtained by the digitized tooth model estimation or by simulation. In this way, a digitized periodontal ligament model can be obtained by digitizing the tooth model.
Optionally, the method for obtaining the geometric model of the digitized periodontal ligament model comprises the following steps:
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 includes a root portion wrapped by the geometric model of the digitized periodontal ligament model;
Respectively extending each first layer of datum points outwards to obtain a plurality of second layers of datum points; wherein the direction of the root portion pointing to the alveolar bone around the root portion is outward;
generating a geometric model of the digitized periodontal ligament model outside the geometric model of the digitized tooth model using a plurality of the first layer reference points and a plurality of the second layer reference points.
The geometrical model of the periodontal ligament cannot be automatically generated in the prior art, manual processing is needed, the efficiency is greatly improved by adopting the method for acquiring the geometrical model of the digital periodontal ligament model, the operation amount is small, and the generation speed of the digital periodontal ligament model is high. By combining the above, periodontal ligament stress analysis in orthodontic treatment can be better carried out, and a foundation can be provided for the design, preparation and inspection of dental instruments more accurately, so that the dental instruments after the design, preparation and inspection are closer to an orthodontic plan, and the orthodontic effect of a patient is ensured.
Optionally, the stress distribution data of the digitized periodontal ligament model includes a hydrostatic pressure distribution or a principal stress distribution, which is convenient for 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 the constitutive model of the digital tooth model; obtaining a geometric model of a digital periodontal ligament model, and selecting the type of a constitutive model of the digital periodontal ligament model; obtaining a geometric model of a digital alveolar bone model, and selecting the type of a constitutive model of the digital alveolar bone model;
The composition module is used for composing the digital dental model by utilizing the geometric model and the type of the constitutive model of the digital dental 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 is used for selecting digital dental model boundary conditions, wherein the digital dental model boundary conditions comprise pose changes and/or received loads of the digital dental model;
the computing module is used for obtaining a digital dental finite element model by utilizing the digital dental model and the digital dental model boundary conditions and carrying out nonlinear finite element computation to obtain stress distribution data of the digital periodontal ligament model so as to verify the consistency of the digital dental model with a simulated correction target when the digital dental model is rearranged.
Optionally, the type of 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 surface load, or a bulk load to which the digitized periodontal ligament model is subjected.
Alternatively, an incremental approach is used in performing the nonlinear finite element calculations.
Optionally, the type of constitutive model of the digitized periodontal ligament model is a superelastic V-W model or a superelastic yoh model.
Optionally, the geometric model of the digitized periodontal ligament model is obtained by the digitized tooth model estimation or by simulation.
Optionally, the acquiring 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 includes a root portion wrapped by the geometric model of the digitized periodontal ligament model;
respectively extending each first layer of datum points outwards to obtain a plurality of second layers of datum points; wherein the direction of the root portion pointing to the alveolar bone around the root portion is outward;
generating a geometric model of the digitized periodontal ligament model outside the geometric model of the digitized tooth model using a plurality of the first layer reference points and a plurality of the second layer reference points.
Optionally, the stress distribution data of the digitized periodontal ligament model includes 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, causing 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 dental instrument design method, the dental instrument preparation method, the dental instrument design checking method, the electronic equipment and the computer storage medium can better analyze the periodontal ligament in orthodontic treatment, can provide a basis for the design, preparation and checking of the dental instrument more accurately, and enable the dental instrument after the design, preparation and checking to be closer to a correction plan, thereby ensuring the correction effect of a patient.
Drawings
The invention will be further described with reference to the drawings and examples.
FIG. 1 is a schematic view of the 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 flow chart 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 a schematic diagram of another flow chart of step S4 in FIG. 2;
fig. 7 is a schematic structural diagram of a periodontal ligament stress analysis device according to an embodiment of the present invention.
In the figure: 1. a dental crown; 2. periodontal ligament; 3. alveolar bone; 4. root of tooth; 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 detailed description, wherein it is to be understood that, on the premise of no conflict, the following embodiments or technical features may be arbitrarily combined to form new embodiments.
Referring to fig. 1, according to the structure of a human tooth, a dental model including a crown 1 and a root 4 is shown, a periodontal ligament 2 is wrapped around the root 4, and an alveolar bone 3 is wrapped around the periodontal ligament 2.
Referring to fig. 2, an embodiment of the present invention provides a periodontal ligament stress analysis method, which includes steps S1 to S4.
Step S1: obtaining a geometric model of the digital tooth model, and selecting the type of a constitutive model of the digital tooth model; obtaining a geometric model of a digital periodontal ligament model, and selecting the type of a constitutive model of the digital periodontal ligament model; the method comprises the steps of obtaining a geometric model of a digital alveolar bone model, and selecting the type of a constitutive model of the digital alveolar bone model. In this step, the order of acquiring 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 approximated by digitizing the tooth model. The simulation may be by digitizing the tooth model to generate a digitized periodontal ligament model and performing an analog simulation.
Referring to fig. 3, a 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 reference 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 includes a root portion wrapped by the geometric model of the digitized periodontal ligament model.
Step S12: respectively extending each first layer of datum points outwards to obtain a plurality of second layers of datum points; wherein the direction of the root portion pointing towards the alveolar bone around the root portion is outwards.
Step S13: a geometric model of the digitized periodontal ligament model outside the geometric model of the digitized tooth model is generated using the plurality of first layer reference points and the plurality of second layer reference points. In the generated geometric model of the digital periodontal ligament model, the first layer of reference points and the second layer of reference points can be positioned on the surface of the geometric model of the digital periodontal ligament model. In the geometric model of the digitized periodontal ligament model, a polyhedron such as a tetrahedron may be used as a unit.
Thus, the first layer datum point can be determined according to the digital geometric model of the teeth, the first layer datum point is extended to obtain the second layer datum point, and the two layers of datum points are utilized to generate the digital geometric model of the periodontal ligament.
Referring to fig. 4, step S12 may include steps S121 to S122.
Step S121: and respectively acquiring the outward normal vector of each first layer datum point.
Step S122: and respectively extending each first layer datum point along the outward normal vector of each first layer datum point to obtain a plurality of second layer datum points.
Therefore, the first layer of datum points extend outwards along the normal direction by taking the digital tooth model as a starting point, and the condition that extension routes of different datum points intersect can be avoided as much as possible relative to the condition that the first layer of datum points extend along any direction, so that subsequent calculation is facilitated.
Wherein, step S121 may include: taking a plurality of first layer datum points as vertexes of the digital triangular patch grid, and solving a normal vector v' of the vertexes outwards by utilizing normal vectors of a plurality of digital triangular patches formed by vertex-ring neighborhood points: 
Wherein n is the number of the digital triangular patches taking the first layer datum point as the vertex, and n is a positive integer greater than 1; i is a positive integer not greater than n; a is that i Is the area of the ith triangular patch taking the first layer datum point as the vertex; v i Is the normal vector of the i-th triangular surface patch which takes the first layer datum point as the vertex. In this way, the normal vector of the first layer reference point as the vertex is calculated by using the normal vectors of a plurality of digitized triangular patches composed of a plurality of neighboring points in the digitized triangular patch grid.
The method for automatically generating the periodontal ligament geometric model provided by the embodiment can automatically generate the periodontal ligament geometric model, greatly improves the efficiency, has small operand and has high generation speed of the digital periodontal ligament model. By combining the above, periodontal ligament stress analysis in orthodontic treatment can be better carried out, and a foundation can be provided for the design, preparation and inspection of dental instruments more accurately, so that the dental instruments after the design, preparation and inspection are closer to an orthodontic plan, and the orthodontic effect of a patient is ensured.
The geometric model of the generated digitized periodontal ligament model can be between 0.2 and 0.3 mm thick and split into units for finite element computation, for example tetrahedrons.
The type of constitutive model of the digitized periodontal ligament model can be a superelastic V-W model or a superelastic Yeoh model. The type of the constitutive model is selected to automatically match the corresponding periodontal ligament stress-strain constitutive relation. Thus, the mechanical behavior of the periodontal ligament can be described using the superelastic V-W model and the superelastic Yeoh model, which are more in line with the actual situation of the periodontal ligament than the linear elastic model.
The type of constitutive model of the digitized tooth model may be a linear elastic model. The linear elastic model has small calculation amount and high calculation efficiency, and compared with the situation that the super elastic model or the viscoelasticity model is selected by the tooth and alveolar bone constitutive model, the calculation amount can be greatly reduced, and the calculation efficiency is improved.
In practical applications, the digital tooth model and the geometric model of the digital alveolar bone model in the oral cavity of the patient, or the digital tooth model and the geometric model of the digital alveolar bone model in the standard template, can be given in the format of a digital triangular patch grid. Wherein, patient data can be obtained through in vivo measurement, and a standard template can be obtained through a laser scanning method.
Step S2: the digital dental model is composed by using the type of the geometric model and the constitutive model of the digital dental model, the type of the geometric model and the constitutive model of the digital periodontal ligament model, and the type of the geometric model and the constitutive model of the digital alveolar bone model.
Step S3: and selecting digital dental model boundary conditions, wherein the digital dental model boundary conditions comprise pose changes and/or received loads of the digital dental model. When in use, the user can conveniently modify the boundary conditions acting on the teeth so as to acquire the needed correction experiment 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 for example, the pose change can comprise displacement in the directions of three coordinate axes in a rectangular coordinate system and rotation angles around the three coordinate axes.
The load may include a point load, a line load, a surface load, or a bulk load.
Step S4: and obtaining a digital dental finite element model by utilizing the digital dental model and the digital dental model boundary condition, and performing nonlinear finite element calculation to obtain stress distribution data of the digital periodontal ligament model so as to verify the consistency of the digital dental model with the simulated correction target when the digital dental model is rearranged.
In this step, the stress distribution data of the digitized periodontal ligament model can include a hydrostatic pressure distribution or a principal stress distribution, which is convenient for presentation 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 targets may include a single step movement target of the digitized tooth model and a rotation angle target of the tooth. The verification result of the consistency includes consistency and non-consistency. When the dental alveolar bone meets the consistency, bone absorption or bone deposition occurs under the conditions of pose change of dental jaw and/or load, so as to cause the reconstruction of the dental alveolar bone; if the dental alveolar bone does not conform to the consistency, the alveolar bone cannot be absorbed or deposited under the condition that the dental jaw is changed in pose and/or subjected to load, and the alveolar bone cannot be reconstructed.
Bone resorption of alveolar bone refers to the physiological behavior of gradual decrease in volume and density of bone tissue at lower stress levels. Bone deposition of alveolar bone refers to bone mass deposition.
In this way, when periodontal ligament stress analysis is carried out, the actual situation of tooth stress in a human body is considered, a digital dental model comprising a digital dental model, a digital alveolar bone model and a digital periodontal ligament model is taken as a whole, the digital dental model and boundary conditions thereof are combined, the obtained digital periodontal ligament stress distribution data is calculated through nonlinear finite elements, and whether the alveolar bone can be subjected to bone absorption or bone deposition under the conditions of pose change of the dental jaw and/or the applied load can be accurately judged through verification of consistency, so that the alveolar bone reconstruction is caused; the geometrical model which is closer to the actual intraoral condition of the patient is utilized, the constitutive model which is closer to the periodontal ligament characteristics is selected, the calculated stress distribution data is closer to the actual intraoral condition of the patient, and a data basis is provided for the design, preparation and inspection of the follow-up dental appliance. In addition, the periodontal ligament stress situation obtained by calculation is more accurate, the stress situations of the teeth and the alveolar bones can be calculated at the same time, the pose change of the teeth or the point load force on the dental crowns can be specified, the corresponding stress situation can be obtained, and the result can effectively guide whether the stress situation can reach the threshold range of the alveolar bone reconstruction in the simulated tooth correction process, so that correction effect is achieved to judge.
In this embodiment, the nonlinear finite element calculation may be performed using an incremental method. The nonlinear problem cannot be solved by equation calculation of a single system, and therefore, can be solved by an incremental method, with a given load applied step by step and solved until a final solution is obtained.
Specifically, when nonlinear finite element calculation is performed, the nonlinear finite element simulation calculation equation used may be: k (u) ·u=r, where u is the overall node displacement array, K (u) is the overall stiffness matrix, and R is the overall load array. The equation is solved by a simple integral iteration method, and is not converged, so that the equation can be calculated by adopting an increment method, and the specific construction process is as follows:
taking parameter 0=k 0 <k 1 <…<k N =1, splitting R into n+1 steps for loading, the load at the mth step is k m R, the corresponding displacement is u m The method comprises the steps of carrying out a first treatment on the surface of the N is a positive integer and m is an integer between 0 and N.
Wherein when m is<When N, u m The iterative calculation process of (1) may include:
by u m Calculation (u) m )；(u m ) Is with u m The corresponding strain can be calculated by using an elastomechanical geometric equation;
by u m And constitutive relation calculation of superelastic constitutive model (u m )；(u m ) Is with u m A corresponding stress tensor;
by means of (u) m) and (um ) Sub-unit fitting line elastic constitutive relation sigma e ＝D(u m )ε e； wherein D(um ) Is with u m A corresponding elastic matrix; sigma (sigma) e Is the unit stress tensor; epsilon e Is the cell strain; this step exploits the idea of local linearization;
by means of D (u) m ) Export (u) m )；(u m ) Is with u m A corresponding overall stiffness matrix;
by K (u) m )Δu m ＝(k m+1 -k m ) R calculates Deltau m ；
Calculation u m+1 ：u m+1 ＝u m +Δu m The method comprises the steps of carrying out a first treatment on the surface of the This step yields the next displacement.
The above steps give u 0 ～u N-1 Is an iterative calculation method of (a).
When m=n-1, the final displacement is obtained: u=u N ＝u N-1 +Δu N-1 。u＝u N Is the obtained approximate solution, k is used for meeting the precision requirement m+1 -k m Must be small enough.
Therefore, the finite element numerical calculation of the constitutive model is performed by using an incremental method, and the iterative calculation process applied to periodontal ligament stress analysis is optimized.
In the calculation process, the initial value u 0 The zero vector is typically chosen, but the resulting overall stiffness matrix K (u 0 ) Is a zero matrix, unable to solve for Deltau 0 Thus, the idea of local linearization can be exploited, taking into account k 1 -k 0 The non-linear part of the superelastic model is omitted, and the elastic matrix D (u 0 ) Deriving an overall stiffness matrix K (u 0 ) Then solve for Deltau 0 Further get u 1 ＝Δu 0 . Specifically, when m=0, u 0 Is a zero vector;
by means of D (u) 0 ) Export K (u) 0 ) The method comprises the steps of carrying out a first treatment on the surface of the The process may be represented by D (u 0 ) Deriving a cell stiffness matrix K e (u 0 ) And then assembled into an overall stiffness matrix K (u 0 )。
Wherein, when the type of constitutive model of the digital periodontal ligament model is a superelastic V-W model:
where a is a constant composed of physical parameters of the 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:
by K (u) 0 )Δu 0 ＝(k 1 -k 0 ) R calculates Deltau 0 ；
By u 1 ＝Δu 0 +u 0 ＝Δu 0 Calculation u 1 ；
According to u m And (3) carrying out iterative computation to obtain u and the stress tensor and strain corresponding to u.
Thus, a method of calculating the first step displacement in the initial case where m=0 is given, facilitating the subsequent iterative calculation.
Referring to fig. 5, when the type of constitutive model of the digitized periodontal ligament model is a superelastic V-W model, step S4 may include steps S41 to S42.
Step S41: the strain energy function W of the super-elastic V-W model is utilized to derive Green strain, and a second class Picola-Kirchhoff stress tensor S is obtained; wherein,
in the formula ,c1 、c 2 and c3 The physical parameters of the constitutive model of the digital periodontal ligament model can be obtained through fitting experimental data; e is a natural constant; i 1 and I2 Is invariant to the isovolumetric right Cauchy-Green deformation tensor; d (D) 1 Is the reciprocal of the bulk modulus; j is the determinant of deformation gradient tensors;
Wherein I is an identity matrix; c is the right Cauchy-Green deformation tensor; c (C) -1 Is the inverse of C.
Step S42: acquiring a Cauchy stress tensor as stress distribution data of the digital periodontal ligament model by using a second class Picola-Kirchhoff stress tensor S so as to verify the consistency of the digital tooth model with a simulated correction target when rearranged; wherein,
wherein F is a deformation gradient tensor; f (F) T Is the transposed matrix of F;
is the isovolumetric left Cauchy-Green deformation tensor.
In this embodiment, if periodontal ligament is used as the incompressible material, j=1; since the incompressible material is an ideal material, it is practically nonexistent, and this step discusses an approximation.
The Cauchy stress tensor is written in component form:
where i, ij are stress components, i and ij are strain components, i=1, 2, 3, j=1, 2, 3; i 1 Is invariant to the right Cauchy-Green deformation tensor; u (u) i,p Is the displacement component u i For reference configuration position component X p Is a derivative of (2); wherein p, q and k are dummy marks, and the value ranges are 1, 2 and 3 according to Einstein summation convention.
In vector analysis, a subscript appears among certain single expressions of an expression and only appears 2 times, and the indexes should be subjected to traversal summation in the value range. In vector sum tensor analysis, the dummy index is tied to the einstein summing convention.
Thus, the periodontal ligament is considered as an incompressible material, simplifying the calculation process of the stress distribution data of the periodontal ligament.
Referring to fig. 6, when the type of constitutive model of the digitized periodontal ligament model is a superelastic Yeoh model, step S4 may include steps S43 to S44.
Step S43: the strain energy function W of the super-elastic Yeoh model is utilized to derive the Green strain, and the second class Picola-Kirchhoff stress tensor S is obtained; wherein,
W＝c 1 (I 1 -3)+c 2 (I 1 -3) 2 +c 3 (I 1 -3) 3 ；
S＝2[c 1 +2c 2 (I 1 -3)+3c 3 (I 1 -3) 2 ]I；
in the formula ,c1 、c 2 and c3 Is the physical parameters of the constitutive model of the digital periodontal ligament model; e is a natural constant; i 1 Is invariant to the right Cauchy-Green deformation tensor; i is the identity matrix.
Step S44: acquiring a Cauchy stress tensor as stress distribution data of the digital periodontal ligament model by using a second class Picola-Kirchhoff stress tensor S so as to verify the consistency of the digital tooth model with a simulated correction target when rearranged; wherein,
σ＝FSF T ＝2[c 1 +2c 2 (I 1 -3)+3c 3 (I 1 -3) 2 ]B；
wherein F is a deformation gradient tensor; f (F) T Is the transposed matrix of F; b is the left Cauchy-Green deformation tensor.
In this embodiment, if periodontal ligament is used as the incompressible material, j=1;
the Cauchy stress tensor is written in component form:
σ i ＝2(c 1 u i,p u i,p +2c 2 u p,q u p,q +12c 3 ε pp ε qq +4c 2 ε pp +c 1 )+4(c 1 +2c 2 ε pp )ε i ；
σ ij ＝2c 1 u i,p u j,p +4(c 1 +4c 2 ε pp )ε ij ；
where i, ij are stress components, i and ij are strain components, i=1, 2, 3, j=1, 2, 3; u (u) i,p Is the displacement component u i For reference configuration position component X p Is a derivative of (2); wherein p and q are dummy marks, and the value ranges are 1, 2 and 3 according to Einstein summation convention.
Referring to fig. 7, the embodiment of the invention further provides a periodontal ligament stress analysis device, which comprises a model module 21, a composition module 22, a boundary module 23 and a calculation module 24, wherein the model module 21 is connected with the composition module 22, and the composition module 22 and the boundary module 23 are respectively connected with 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 the constitutive model of the digital tooth model; obtaining a geometric model of a digital periodontal ligament model, and selecting the type of a constitutive model of the digital periodontal ligament model; the method comprises the steps of obtaining a geometric model of a digital alveolar bone model, and selecting the type of a constitutive model of the digital alveolar bone model.
The composition module 22 is configured to compose a digitized dental model using the geometry model and the type of constitutive model of the digitized dental model, the geometry model and the type of constitutive model of the digitized periodontal ligament model, and the geometry model and the type of constitutive model of the digitized alveolar bone model.
The boundary module 23 is configured to select the digital dental model boundary conditions, where the digital dental model boundary conditions include pose changes and/or loads applied to 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 the digital dental model boundary conditions, and perform nonlinear finite element calculation to obtain stress distribution data of the digital periodontal ligament model, so as to verify consistency between the digital dental model and the simulated correction target when the digital dental model is rearranged.
In some embodiments, the model types of the digital tooth model and the digital alveolar bone model may both be linear elastic models.
In some embodiments, the load may include a point load, a line load, a face load, or a bulk load.
In some embodiments, the type of constitutive model of the digitized periodontal ligament model can be a superelastic V-W model or a superelastic Yeoh model.
In some embodiments, the nonlinear finite element computation may be performed using an incremental approach.
In some embodiments, the geometric model of the digitized periodontal ligament model can be obtained by digitized tooth model estimation or analog.
In some embodiments, the model module 21 is further to: generating a plurality of first layer reference 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 includes a root portion wrapped by the geometric model of the digitized periodontal ligament model; respectively extending each first layer of datum points outwards to obtain a plurality of second layers of 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 the geometric model of the digitized tooth model is generated using the plurality of first layer reference points and the plurality of second layer reference points.
In some embodiments, the stress distribution data of the digitized periodontal ligament model includes a hydrostatic pressure distribution or a principal stress distribution.
The embodiment of the invention also provides electronic equipment, which comprises a processor and a memory, wherein the processor executes computer instructions stored in the memory, so that the electronic equipment executes any periodontal ligament stress analysis method.
The embodiment of the invention also provides a computer storage medium, which comprises computer instructions, wherein when the computer instructions are run on the electronic equipment, the electronic equipment is caused to execute any periodontal ligament stress analysis method.
The present invention has been described in terms of its practical advantages, including improved performance, advancement and novelty, which are all aspects of the invention, and the functional improvements and elements of the invention as emphasized by the patent laws, the above description and drawings are not limited to the preferred embodiments of the invention, so that all modifications, equivalents, and modifications, etc. which are similar to or identical to the structures, devices, features, etc. of the invention are included in the scope of the invention.
Claims (26)
1. A periodontal ligament stress analysis method, characterized by further comprising:
Obtaining a geometric model of a digital tooth model, and selecting the type of a constitutive model of the digital tooth model; obtaining a geometric model of a digital periodontal ligament model, and selecting the type of a constitutive model of the digital periodontal ligament model; obtaining 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 geometric model and the type of the constitutive model of the digital dental 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;
selecting digital dental model boundary conditions, wherein the digital dental model boundary conditions comprise pose changes and/or received loads of a digital dental model;
obtaining a digital dental finite element model by utilizing the digital dental model and the digital dental model boundary condition, and performing nonlinear finite element calculation to obtain stress distribution data of the digital periodontal ligament model so as to verify the consistency of the digital dental model with a simulated correction target when the digital dental model is rearranged;
when nonlinear finite element calculation is carried out, the adopted nonlinear finite element simulation calculation equation is as follows: 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;
taking parameter 0=k 0 <k 1 <…<k N =1, splitting R into n+1 steps for loading, the load at the mth step is k m R, the corresponding displacement is u m The method comprises the steps of carrying out a first treatment on the surface of the N is a positive integer, m is an integer between 0 and N;
wherein when m is<When N, u m The iterative calculation process of (1) comprises:
by u m Calculation of ε (u) m )；ε(u m ) Is with u m A corresponding strain;
by u m And constitutive relation calculation sigma (u) m )；σ(u m ) Is with u m A corresponding stress tensor;
using epsilon (u) m) and σ(um ) The elastic constitutive relation of the sub-unit fitting line is sigma e ＝D(u m )ε e； wherein D(um ) Is with u m A corresponding elastic matrix; sigma (sigma) e Is the unit stress tensor; epsilon e Is the cell strain;
by means of D (u) m ) Export K (u) m )；K(u m ) Is with u m A corresponding overall stiffness matrix;
by K (u) m )Δu m ＝(k m+1 -k m ) R calculates Deltau m ；
Calculation u m+1 ：u m+1 ＝u m +Δu m ；
When m=n-1, the final displacement is obtained: u=u N ＝u N-1 +Δu N-1 。
2. The periodontal ligament stress analysis method according to claim 1, wherein the stress distribution data of the digitized tooth model and the stress distribution data of the digitized alveolar bone model are also obtained by performing nonlinear finite element calculations.
3. The periodontal ligament stress analysis method according to claim 1, characterized in that the types of constitutive models of the digitized tooth model and the digitized alveolar bone model are both linear elastic models.
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 bulk load.
5. The periodontal ligament stress analysis method according to claim 1, wherein the nonlinear finite element calculation is performed by an incremental method.
6. The periodontal ligament stress analysis method according to any of claims 1 to 4, characterized in that the type of constitutive model of the digitized periodontal ligament model is a superelastic V-W model or a superelastic yoh model.
7. The periodontal ligament stress analysis method according to claim 6, wherein when m=0, u 0 Is a zero vector;
by means of D (u) 0 ) Export 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 constituted by physical parameters of a constitutive model of the digitized periodontal ligament model;
by K (u) 0 )Δu 0 ＝(k 1 -k 0 ) R calculates Deltau 0 ；
By u 1 ＝Δu 0 +u 0 ＝Δu 0 Calculation u 1 ；
According to said u m And (3) carrying out iterative computation to obtain u and the stress tensor and strain corresponding to u.
8. The periodontal ligament stress analysis method according to claim 6, wherein the nonlinear finite element calculation is performed by an incremental method.
9. The periodontal ligament stress analysis method according to claim 8, wherein when the type of the model of the digital periodontal ligament model is a superelastic V-W model, the obtaining a digital dental finite element model by using the digital dental model and the digital dental model boundary conditions and performing nonlinear finite element computation to obtain stress distribution data of the digital periodontal ligament model to verify consistency with a simulated correction target when the digital dental model is rearranged includes:
the strain energy function W of the super-elastic V-W model is utilized to derive Green strain, and a second class Picola-Kirchhoff stress tensor S is obtained; wherein,
in the formula ,c1 、c 2 and c3 Is a physical property parameter of a constitutive model of the digital periodontal ligament model; e is a natural constant;
and />
Is invariant to the isovolumetric right Cauchy-Green deformation tensor; d (D) 1 Is the reciprocal of the bulk modulus; j is the determinant of deformation gradient tensors;
wherein I is an identity matrix; c is the right Cauchy-Green deformation tensor; c (C) -1 Is the inverse of C;
acquiring a Cauchy stress tensor sigma as stress distribution data of the digital periodontal ligament model by using a second class Picola-Kirchhoff stress tensor S so as to verify consistency of the digital tooth model with a simulated correction target when rearranged; wherein,
Wherein F is a deformation gradient tensor; f (F) T Is the transposed matrix of F;
is the isovolumetric left Cauchy-Green deformation tensor.
10. The periodontal ligament stress analysis method according to claim 9, characterized in that j=1, taking periodontal ligament as an incompressible material;
writing the Cauchy stress tensor sigma into a component form of:
in the formula ,σi and σij Is the stress component, epsilon i and εij Is the strain component, i=1, 2, 3, j=1, 2, 3; i 1 Is invariant to the right Cauchy-Green deformation tensor; u (u) i,p Is the displacement component u i For reference configuration position component X p Is a derivative of (2); wherein p, q and k are dummy marks, and take according to Einstein summation conventionThe value ranges are 1, 2, 3.
11. The periodontal ligament stress analysis method according to claim 8, wherein when the type of the constitutive model of the digitized periodontal ligament model is a superelastic yoh model, the obtaining a digitized dental finite element model using the digitized dental model and the digitized dental model boundary conditions and performing nonlinear finite element computation to obtain stress distribution data of the digitized periodontal ligament model to verify consistency with a simulated correction target when the digitized dental model is rearranged includes:
The strain energy function W of the super-elastic Yeoh model is utilized to derive the Green strain, and the second class Picola-Kirchhoff stress tensor S is obtained; wherein,
W＝c 1 (I 1 -3)+c 2 (I 1 -3) 2 +c 3 (I 1 -3) 3 ；
S＝2[c 1 +2c 2 (I 1 -3)+3c 3 (I 1 -3) 2 ]I；
in the formula ,c1 、c 2 and c3 Is a physical property parameter of a constitutive model of the digital periodontal ligament model; e is a natural constant; i 1 Is invariant to the right Cauchy-Green deformation tensor; i is an identity matrix;
acquiring a Cauchy stress tensor sigma as stress distribution data of the digital periodontal ligament model by using a second class Picola-Kirchhoff stress tensor S so as to verify consistency of the digital tooth model with a simulated correction target when rearranged; wherein,
σ＝FSF T ＝2[c 1 +2c 2 (I 1 -3)+3c 3 (I 1 -3) 2 ]B；
wherein F is a deformation gradient tensor; f (F) T Is the transposed matrix of F; b is the left Cauchy-Green deformation tensor.
12. The periodontal ligament stress analysis method according to claim 11, characterized in that j=1, taking periodontal ligament as an incompressible material;
writing the Cauchy stress tensor sigma into a component form of:
σ i ＝2(c 1 u i,p u i,p +2c 2 u p,q u p,q +12c 3 ε pp ε qq +4c 2 ε pp +c 1 )+4(c 1 +2c 2 ε pp )ε i ；
σ ij ＝2c 1 u i,p u j,p +4(c 1 +4c 2 ε pp )ε ij ；
in the formula ,σi 、σ ij Is the stress component, epsilon i and εij Is the strain component, i=1, 2, 3, j=1, 2, 3; u (u) i,p Is the displacement component u i For reference configuration position component X p Is a derivative of (2); wherein p and q are dummy marks, and the value ranges are 1, 2 and 3 according to Einstein summation convention.
13. The periodontal ligament stress analysis method according to claim 1, characterized in that the geometric model of the digitized periodontal ligament model is obtained by the digitized tooth model estimation or by simulation.
14. The periodontal ligament stress analysis method according to claim 13, characterized in that the acquisition method of 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 includes a root portion wrapped by the geometric model of the digitized periodontal ligament model;
respectively extending each first layer of datum points outwards to obtain a plurality of second layers of datum points; wherein the direction of the root portion pointing to the alveolar bone around the root portion is outward;
generating a geometric model of the digitized periodontal ligament model outside the geometric model of the digitized tooth model using a plurality of the first layer reference points and a plurality of the second layer reference points.
15. The periodontal ligament stress analysis method of claim 1, wherein the stress distribution data of the digitized periodontal ligament model includes a hydrostatic pressure distribution or a principal stress distribution.
16. 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 the constitutive model of the digital tooth model; obtaining a geometric model of a digital periodontal ligament model, and selecting the type of a constitutive model of the digital periodontal ligament model; obtaining a geometric model of a digital alveolar bone model, and selecting the type of a constitutive model of the digital alveolar bone model;
the composition module is used for composing the digital dental model by utilizing the geometric model and the type of the constitutive model of the digital dental 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 is used for selecting digital dental model boundary conditions, wherein the digital dental model boundary conditions comprise pose changes and/or received loads of the digital dental model;
the computing module is used for obtaining a digital dental finite element model by utilizing the digital dental model and the digital dental model boundary condition and carrying out nonlinear finite element computation to obtain stress distribution data of the digital periodontal ligament model so as to verify the consistency of the digital dental model with a simulated correction target when the digital dental model is rearranged;
When the calculation module performs nonlinear finite element calculation, the adopted nonlinear finite element simulation calculation equation 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;
taking parameter 0=k 0 <k 1 <…<k N =1, splitting R into n+1 steps for loading, the load at the mth step is k m R, the corresponding displacement is u m The method comprises the steps of carrying out a first treatment on the surface of the N is a positive integer, m is an integer between 0 and N;
wherein when m is<When N, u m The iterative calculation process of (1) comprises:
by u m Calculation of ε (u) m )；ε(u m ) Is with u m A corresponding strain;
by u m And constitutive relation calculation sigma (u) m )；σ(u m ) Is with u m A corresponding stress tensor;
using epsilon (u) m) and σ(um ) The elastic constitutive relation of the sub-unit fitting line is sigma e ＝D(u m )ε e； wherein D(um ) Is with u m A corresponding elastic matrix; sigma (sigma) e Is the unit stress tensor; epsilon e Is the cell strain;
by means of D (u) m ) Export K (u) m )；K(u m ) Is with u m A corresponding overall stiffness matrix;
by K (u) m )Δu m ＝(k m+1 -k m ) R calculates Deltau m ；
Calculation u m+1 ：u m+1 ＝u m +Δu m ；
When m=n-1, the final displacement is obtained: u=u N ＝u N-1 +Δu N-1 。
17. The periodontal ligament stress analysis device of claim 16, wherein the model types of the digitized tooth model and the digitized alveolar bone model are both linear elastic models.
18. The periodontal ligament stress analysis device of claim 16, wherein 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.
19. The periodontal ligament stress analysis device of claim 16, wherein the nonlinear finite element calculation is performed using an incremental method.
20. Periodontal ligament stress analysis device according to any of the claims 16-18, characterized in that the type of constitutive model of the digitized periodontal ligament model is a superelastic V-W model or a superelastic yoh model.
21. The periodontal ligament stress analysis device of claim 20, wherein the nonlinear finite element calculation is performed using an incremental method.
22. The periodontal ligament stress analysis device of claim 16, wherein the geometric model of the digitized periodontal ligament model is obtained by the digitized tooth model estimation or simulation.
23. The periodontal ligament stress analysis device of claim 22, 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 includes a root portion wrapped by the geometric model of the digitized periodontal ligament model;
Respectively extending each first layer of datum points outwards to obtain a plurality of second layers of datum points; wherein the direction of the root portion pointing to the alveolar bone around the root portion is outward;
generating a geometric model of the digitized periodontal ligament model outside the geometric model of the digitized tooth model using a plurality of the first layer reference points and a plurality of the second layer reference points.
24. The periodontal ligament stress analysis device of claim 16, wherein the stress distribution data of the digitized periodontal ligament model includes a hydrostatic pressure distribution or a principal stress distribution.
25. An electronic device comprising a processor and a memory, the processor executing computer instructions stored in the memory, causing the electronic device to perform the periodontal ligament stress analysis method of any of claims 1 to 15.
26. 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 15.
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| US11229504B1 (en) | 2021-01-07 | 2022-01-25 | Ortho Future Technologies (Pty) Ltd | System and method for determining a target orthodontic force |
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