1. A modeling method of a periodontal ligament finite element model is characterized by comprising the following steps:

s1: acquiring a tooth surface grid model and a tooth socket bone surface grid model according to the CT image of the dental jaw tissue of the patient;

s2: acquiring an overlapping area between the tooth surface grid model and the alveolar bone surface grid model according to the tooth surface grid model and the alveolar bone surface grid model, and acquiring a periodontal ligament solid model according to the overlapping area;

s3: processing the periodontal ligament solid model through meshing to obtain a periodontal ligament solid mesh model;

s4: elastic mechanical behavior and viscous mechanical behavior of the periodontal ligament are respectively defined through the superelastic model and the relaxation function model, and a periodontal ligament finite element model after the material of the periodontal ligament body mesh model is assigned is obtained.

2. The method of claim 1, wherein step S1 is preceded by the step of:

s0: and acquiring a CT image of the dental jaw tissue of the patient and extracting a thickness value of the periodontal tissue.

3. The method of claim 2, wherein the step S2 comprises the steps of:

s21: expanding the tooth surface grid model along the direction of the external normal line according to the thickness value of the periodontal ligament tissue, and filling and leveling the alveolar fossa in the alveolar bone surface grid model;

s22: acquiring an overlapped area of the expanded tooth surface grid model and the filled alveolar bone surface grid model through Boolean intersection operation;

s23: and successively carrying out Boolean reduction operation and curved surface treatment according to the overlapped region and the tooth surface grid model to obtain the periodontal ligament solid model.

4. The method of claim 1, wherein in step S4, the superelastic model is expressed as:

wherein U is a function of the strain energy density, N is the order of the model, μ_iIs the shear modulus, alpha_iCoefficient of superelastic material, D_iAs an incompressible parameter, λ₁、λ₂And λ₃These three variables are the principal elongations in three directions of the strain energy density function U, J being the volume fraction.

5. The method of claim 1, wherein in step S4, the relaxation function model is expressed as:

where G (t) is a stress relaxation function normalized with respect to time, δⁿAs multipliers of energy functions, lambdaⁿFor the relaxation time constant, t is time.

6. A modeling system for a finite element model of a periodontal ligament, comprising:

the image processing module is used for acquiring a tooth surface mesh model and a tooth socket bone surface mesh model according to the CT image of the dental jaw tissue of the patient;

the model processing module is used for acquiring an overlapping area between the tooth surface grid model and the alveolar bone surface grid model according to the tooth surface grid model and the alveolar bone surface grid model and acquiring a periodontal ligament entity model according to the overlapping area;

the model division module is used for processing the periodontal ligament entity model through grid division to obtain a periodontal ligament entity grid model;

and the finite element construction module is used for respectively defining the elastic mechanical behavior and the viscous mechanical behavior of the periodontal ligament through the superelastic model and the relaxation function model and acquiring the periodontal ligament finite element model after the material of the periodontal ligament body grid model is assigned.

7. The modeling system of a finite element model of periodontal ligament of claim 6, further comprising:

and the image acquisition module is used for acquiring the CT image of the dental jaw tissue of the patient and extracting the thickness value of the periodontal tissue.

8. The modeling system of a periodontal ligament finite element model according to claim 7, wherein the model processing module specifically comprises:

the model processing unit is used for expanding the tooth surface grid model along the direction of the external normal line according to the thickness value of the periodontal tissue and filling and leveling the alveolar fossa in the alveolar bone surface grid model;

the model screening unit is used for acquiring an overlapped area of the expanded tooth surface grid model and the filled alveolar bone surface grid model through Boolean intersection operation;

and the model construction unit is used for successively carrying out Boolean reduction operation and curved surface treatment according to the overlapping region and the tooth surface grid model to obtain the periodontal ligament entity model.

9. The modeling system of a finite element model of periodontal ligament as set forth in claim 6, wherein the superelastic model is expressed as:

wherein U is a function of the strain energy density, N is the order of the model, μ_iIs the shear modulus, alpha_iCoefficient of superelastic material, D_iAs an incompressible parameter, λ₁、λ₂And λ₃These three variables are the principal elongations in three directions of the strain energy density function U, J being the volume fraction.

10. The modeling system of a finite element model of periodontal ligament according to claim 6, wherein the expression of said relaxation function model is:

where G (t) is a stress relaxation function normalized with respect to time, δⁿAs multipliers of energy functions, lambdaⁿFor the relaxation time constant, t is time.

Background

In the oral biomechanical analysis, a finite element analysis method is an important research means, and is widely applied to the fields of orthodontics, jaw restoration, tooth implantation and the like. Before studying the oral biomechanics problem by using a finite element analysis method, firstly, a corresponding dental jaw tissue finite element model including teeth, periodontal ligament, alveolar bone and the like is established according to the actual dental jaw tissue structure of a patient. Among them, periodontal ligament is a layer of connective fiber tissue interposed between the tooth and the alveolar bone, and plays a crucial role in stimulating the reconstruction of periodontal tissue and inducing the movement of the tooth. Therefore, in order to correctly recognize the tooth movement under the action of the orthodontic force, a finite element model close to the actual biological structure and material characteristics of the periodontal tissues of the patient needs to be constructed, so that the analysis result error caused by the inaccuracy of the model is reduced.

For constructing a periodontal ligament finite element model, generally, a method of manual segmentation is adopted according to a CT image of a patient, the CT image of the periodontal ligament is firstly separated from other periodontal tissues, and then a digital model of the periodontal ligament is constructed by using three-dimensional modeling software. However, as for the soft tissue of the oral cavity of the human body, the periodontal ligament has a small size and a thin thickness, and the gray value of the CT image is low compared with the tooth and the alveolar bone, so that it is difficult to distinguish the boundary between the periodontal ligament and other periodontal tissues, and the modeling efficiency and accuracy need to be improved. In addition, the linear elastic model is generally adopted for defining the characteristics of periodontal ligament material, but periodontal ligament has strong super-viscoelastic characteristics, and the accuracy of the periodontal ligament finite element model is greatly reduced due to improper material property definition.

Disclosure of Invention

In order to reduce the operation difficulty in the traditional modeling of a periodontal ligament finite element model, improve the modeling efficiency and precision and establish the periodontal ligament finite element model which accords with the biomechanical characteristics of the periodontal ligament of a human body, the invention refers to a tooth and alveolar bone surface grid model to generate the periodontal ligament surface grid model, and utilizes a superelasticity and viscosity model to define the material characteristics of the periodontal ligament body grid model, and provides a modeling method of the periodontal ligament finite element model, which comprises the following steps:

s1: acquiring a tooth surface grid model and a tooth socket bone surface grid model according to the CT image of the dental jaw tissue of the patient;

s2: acquiring an overlapping area between the tooth surface grid model and the alveolar bone surface grid model according to the tooth surface grid model and the alveolar bone surface grid model, and acquiring a periodontal ligament solid model according to the overlapping area;

s3: processing the periodontal ligament solid model through meshing to obtain a periodontal ligament solid mesh model;

s4: elastic mechanical behavior and viscous mechanical behavior of the periodontal ligament are respectively defined through the superelastic model and the relaxation function model, and a periodontal ligament finite element model after the material of the periodontal ligament body mesh model is assigned is obtained.

Further, the step S1 is preceded by the step of:

s0: and acquiring a CT image of the dental jaw tissue of the patient and extracting a thickness value of the periodontal tissue.

Further, the step S2 specifically includes the steps of:

s21: expanding the tooth surface grid model along the direction of the external normal line according to the thickness value of the periodontal ligament tissue, and filling and leveling the alveolar fossa in the alveolar bone surface grid model;

s22: acquiring an overlapped area of the expanded tooth surface grid model and the filled alveolar bone surface grid model through Boolean intersection operation;

s23: and successively carrying out Boolean reduction operation and curved surface treatment according to the overlapped region and the tooth surface grid model to obtain the periodontal ligament solid model.

Further, in step S4, the expression of the superelastic model is as follows:

wherein U is a function of the strain energy density, N is the order of the model, μ_iIs the shear modulus, alpha_iCoefficient of superelastic material, D_iAs an incompressible parameter, λ₁、λ₂And λ₃These three variables are the principal elongations in three directions of the strain energy density function U, J being the volume fraction.

Further, in step S4, the expression of the relaxation function model is:

where G (t) is a stress relaxation function normalized with respect to time, δⁿAs multipliers of energy functions, lambdaⁿFor the relaxation time constant, t isTime.

The invention also provides a modeling system of the periodontal ligament finite element model, which comprises the following components:

the image processing module is used for acquiring a tooth surface mesh model and a tooth socket bone surface mesh model according to the CT image of the dental jaw tissue of the patient;

the model processing module is used for acquiring an overlapping area between the tooth surface grid model and the alveolar bone surface grid model according to the tooth surface grid model and the alveolar bone surface grid model and acquiring a periodontal ligament entity model according to the overlapping area;

the model division module is used for processing the periodontal ligament entity model through grid division to obtain a periodontal ligament entity grid model;

and the finite element construction module is used for respectively defining the elastic mechanical behavior and the viscous mechanical behavior of the periodontal ligament through the superelastic model and the relaxation function model and acquiring the periodontal ligament finite element model after the material of the periodontal ligament body grid model is assigned.

Further, still include:

and the image acquisition module is used for acquiring the CT image of the dental jaw tissue of the patient and extracting the thickness value of the periodontal tissue.

Further, the model processing module specifically includes:

the model processing unit is used for expanding the tooth surface grid model along the direction of the external normal line according to the thickness value of the periodontal tissue and filling and leveling the alveolar fossa in the alveolar bone surface grid model;

the model screening unit is used for acquiring an overlapped area of the expanded tooth surface grid model and the filled alveolar bone surface grid model through Boolean intersection operation;

and the model construction unit is used for successively carrying out Boolean reduction operation and curved surface treatment according to the overlapping region and the tooth surface grid model to obtain the periodontal ligament entity model.

Further, the expression of the superelastic model is as follows:

wherein U is strain energyDensity function, N is the order of the model, μ_iIs the shear modulus, alpha_iCoefficient of superelastic material, D_iAs an incompressible parameter, λ₁、λ₂And λ₃These three variables are the principal elongations in three directions of the strain energy density function U, J being the volume fraction.

Further, the expression of the relaxation function model is:

where G (t) is a stress relaxation function normalized with respect to time, δⁿAs multipliers of energy functions, lambdaⁿFor the relaxation time constant, t is time.

Compared with the prior art, the invention at least has the following beneficial effects:

(1) according to the modeling method and system of the periodontal ligament finite element model, the tooth surface grid model and the alveolar bone surface grid model are processed, the overlapped area is obtained through Boolean operation, and the periodontal ligament solid model is constructed according to the overlapped area, so that periodontal ligament identification under the condition that periodontal ligament and other periodontal tissues are difficult to distinguish is realized;

(2) the periodontal ligament surface grid model is constructed by utilizing the tooth and alveolar bone surface grid model, so that the modeling efficiency of the periodontal ligament finite element model is effectively improved;

(3) the Ogden model (superelastic model) and the relaxation function model are used for respectively defining the elastic mechanical behavior and the viscous mechanical behavior of the periodontal ligament, and the biomechanical characteristics of the periodontal ligament of the human body are better met.

Drawings

FIG. 1 is a method step diagram of a modeling method and system for a periodontal ligament finite element model;

FIG. 2 is a system diagram of a modeling method and system for a periodontal ligament finite element model.

Detailed Description

The following are specific embodiments of the present invention and are further described with reference to the drawings, but the present invention is not limited to these embodiments.

Example one

In order to reduce the operation difficulty in the traditional modeling of a periodontal ligament finite element model, improve the modeling efficiency and precision and establish the periodontal ligament finite element model which accords with the biomechanical characteristics of the periodontal ligament of a human body, the invention refers to a tooth and alveolar bone surface grid model to generate the periodontal ligament surface grid model, and utilizes a superelasticity and viscosity model to define the material characteristics of the periodontal ligament body grid model, as shown in figure 1, the invention provides a modeling method of the periodontal ligament finite element model, which comprises the following main steps:

s1: acquiring a tooth surface grid model and a tooth socket bone surface grid model according to the CT image of the dental jaw tissue of the patient;

s2: acquiring an overlapping area between the tooth surface grid model and the alveolar bone surface grid model according to the tooth surface grid model and the alveolar bone surface grid model, and acquiring a periodontal ligament solid model according to the overlapping area;

s3: processing the periodontal ligament solid model through meshing to obtain a periodontal ligament solid mesh model;

s4: elastic mechanical behavior and viscous mechanical behavior of the periodontal ligament are respectively defined through the superelastic model and the relaxation function model, and a periodontal ligament finite element model after the material of the periodontal ligament body mesh model is assigned is obtained.

Next, the technical contents of the present invention will be described in detail through a specific flow on the basis of the above-described main steps:

before modeling the periodontal finite element model, the oral cavity of the patient is scanned to obtain a CT image of the dental tissue of the patient, and in consideration of obtaining the periodontal tissue model in the later period, the thickness value of the periodontal tissue (which can be realized by medical image processing software such as miccis 16.0) is extracted according to the oral cavity of the patient, and is denoted as d.

Then, separating the CT images of the teeth and the alveolar bones from other dental tissues by using medical image processing software, and generating a tooth surface mesh model and an alveolar bone surface mesh model.

After the preliminary mesh model is obtained, further processing is needed to be carried out on the preliminary mesh model so that the tooth surface mesh model and the alveolar bone surface mesh model can be covered on the right position of the alveolar bone surface mesh model at the periodontal membrane to avoid covering on the tooth surface mesh model and in the alveolar fossa, therefore, the tooth surface mesh model and the alveolar bone surface mesh model are led into surface model processing software (such as Geomagic12.0), and the tooth surface mesh model is expanded by d width along the direction of the external normal line of the tooth surface mesh model by the software to generate an expanded tooth surface mesh model; and meanwhile, filling the alveolar fossa in the alveolar bone surface grid model to generate the filled alveolar bone surface grid model.

And then, using a face model processing software to solve an overlapping area between the tooth face grid model after expansion and the alveolar bone face grid model after filling the alveolar fossa through Boolean intersection operation to generate an initial periodontal membrane face grid model. Next, the tooth surface mesh model is subtracted from the initial periodontal membrane surface mesh model by boolean subtraction operation to obtain the periodontal membrane surface mesh model. And finally, carrying out NURBS curved surface treatment on the obtained periodontal ligament surface mesh model to generate a periodontal ligament entity model.

The above-described steps for obtaining the periodontal ligament solid model correspond to steps S21 to S23 in fig. 1 as follows:

s21: expanding the tooth surface grid model along the direction of the external normal line according to the thickness value of the periodontal ligament tissue, and filling and leveling the alveolar fossa in the alveolar bone surface grid model;

s22: acquiring an overlapped area of the expanded tooth surface grid model and the filled alveolar bone surface grid model through Boolean intersection operation;

s23: and successively carrying out Boolean reduction operation and curved surface treatment according to the overlapped region and the tooth surface grid model to obtain the periodontal ligament solid model.

In order to ensure the quality of the model, after the periodontal ligament physical model is obtained, the periodontal ligament physical model is further introduced into finite element software (such as Abaqus 13.0) to perform meshing and check the quality of the mesh, so as to generate the periodontal ligament mesh model.

After the periodontal ligament solid model is obtained, in order to enable data obtained through experiments to reflect data in a periodontal ligament super-viscoelastic characteristic state, the precision of the obtained finite element model is improved. After material assignment is carried out on a periodontal ligament entity model, an elastic mechanical behavior and a viscous mechanical behavior of the periodontal ligament are defined by an elastic (Ogden) model and a relaxation function model respectively. Wherein, the expression of the super-elastic model is as follows:

wherein U is a function of the strain energy density, N is the order of the model, μ_iIs the shear modulus, alpha_iCoefficient of superelastic material, D_iFor the incompressible parameter (determining whether the material is compressible), λ₁、λ₂And λ₃These three variables are the principal elongations in three directions of the strain energy density function U, J being the volume fraction.

And the expression of the relaxation function model is:

where G (t) is a stress relaxation function normalized with respect to time, δⁿAs multipliers of energy functions, lambdaⁿFor the relaxation time constant, t is time.

Example two

For better understanding of the present invention, the present embodiment illustrates the present invention by way of a system structure, as shown in fig. 2, a modeling system of finite element model of periodontal ligament, comprising:

the image processing module is used for acquiring a tooth surface mesh model and a tooth socket bone surface mesh model according to the CT image of the dental jaw tissue of the patient;

the model processing module is used for acquiring an overlapping area between the tooth surface grid model and the alveolar bone surface grid model according to the tooth surface grid model and the alveolar bone surface grid model and acquiring a periodontal ligament entity model according to the overlapping area;

the model division module is used for processing the periodontal ligament entity model through grid division to obtain a periodontal ligament entity grid model;

and the finite element construction module is used for respectively defining the elastic mechanical behavior and the viscous mechanical behavior of the periodontal ligament through the superelastic model and the relaxation function model and acquiring the periodontal ligament finite element model after the material of the periodontal ligament body grid model is assigned.

Further, still include:

and the image acquisition module is used for acquiring the CT image of the dental jaw tissue of the patient and extracting the thickness value of the periodontal tissue.

Further, the model processing module specifically includes:

the model processing unit is used for expanding the tooth surface grid model along the direction of the external normal line according to the thickness value of the periodontal tissue and filling and leveling the alveolar fossa in the alveolar bone surface grid model;

the model screening unit is used for acquiring an overlapped area of the expanded tooth surface grid model and the filled alveolar bone surface grid model through Boolean intersection operation;

and the model construction unit is used for successively carrying out Boolean reduction operation and curved surface treatment according to the overlapping region and the tooth surface grid model to obtain the periodontal ligament entity model.

Further, the expression of the superelastic model is as follows:

wherein U is a function of the strain energy density, N is the order of the model, μ_iIs the shear modulus, alpha_iCoefficient of superelastic material, D_iAs an incompressible parameter, λ₁、λ₂And λ₃These three variables are the principal elongations in three directions of the strain energy density function U, J being the volume fraction.

Further, the expression of the relaxation function model is:

wherein G (t) is in respect of timeNormalized stress relaxation function, δⁿAs multipliers of energy functions, lambdaⁿFor the relaxation time constant, t is time.

In summary, according to the modeling method and system of the periodontal ligament finite element model, the tooth surface mesh model and the alveolar bone surface mesh model are processed, the overlapping region is obtained through boolean operations, the periodontal ligament entity model is constructed according to the overlapping region, and periodontal ligament identification under the condition that the periodontal ligament is difficult to distinguish from other periodontal tissues is realized.

The periodontal ligament surface grid model is constructed by utilizing the tooth and alveolar bone surface grid model, so that the modeling efficiency of the periodontal ligament finite element model is effectively improved. The Ogden model (superelastic model) and the relaxation function model are used for respectively defining the elastic mechanical behavior and the viscous mechanical behavior of the periodontal ligament, and the biomechanical characteristics of the periodontal ligament of the human body are better met.

It should be noted that all the directional indicators (such as up, down, left, right, front, and rear … …) in the embodiment of the present invention are only used to explain the relative position relationship between the components, the movement situation, etc. in a specific posture (as shown in the drawing), and if the specific posture is changed, the directional indicator is changed accordingly.

Moreover, descriptions of the present invention as relating to "first," "second," "a," etc. are for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicit ly indicating a number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one such feature. In the description of the present invention, "a plurality" means at least two, e.g., two, three, etc., unless specifically limited otherwise.

In the present invention, unless otherwise expressly stated or limited, the terms "connected," "secured," and the like are to be construed broadly, and for example, "secured" may be a fixed connection, a removable connection, or an integral part; can be mechanically or electrically connected; they may be directly connected or indirectly connected through intervening media, or they may be connected internally or in any other suitable relationship, unless expressly stated otherwise. The specific meanings of the above terms in the present invention can be understood by those skilled in the art according to specific situations.

In addition, the technical solutions in the embodiments of the present invention may be combined with each other, but it must be based on the realization of those skilled in the art, and when the technical solutions are contradictory or cannot be realized, such a combination of technical solutions should not be considered to exist, and is not within the protection scope of the present invention.