Method for establishing corneal endothelial cell finite element model

Abstract

Provided in the present invention is a method for establishing a corneal endothelial cell finite element model, the method comprising: importing a standard corneal model into finite element pre-processing software, and generating 2D grids, so as to obtain a basic grid model; importing a corneal endothelial cell detailed geometric model; determining a complete corneal endothelial cell model on the basis of the basic grid model and the detailed geometric model; and performing calculation on the basis of the complete corneal endothelial cell model. The present invention can improve the efficiency and effect of establishing a corneal endothelial cell finite element model.

Description

A method for establishing a finite element model of corneal endothelial cells Technical Field

[0001] The present invention relates to the field of model design, and in particular to a method for establishing a finite element model of corneal endothelial cells. Background Art

[0002] Corneal endothelial cells, a single layer of hexagonal cells, are the innermost cells of the cornea. They play an important role in maintaining corneal transparency and normal visual function. The density of corneal endothelial cells slowly decreases at a rate of 0.3% to 0.6% per year. Trauma, intraocular surgery, and other conditions can lead to greater endothelial cell loss. Damaged endothelial cells repair themselves by expanding and migrating. Excessive loss of corneal endothelial cells and decompensated metabolic pump function can cause corneal edema, rupture or loss of tight junctions between cells, partial loss and fusion of cell boundaries, and reduced barrier function, clinically manifesting as corneal endothelial decompensation. The morphology and number of corneal endothelial cells are often important indicators in the diagnosis and treatment of corneal diseases.

[0003] Currently, a large number of studies have focused on corneal endothelial cell density and the proportion of hexagonal cells. However, clinical findings indicate that there are many cases where the cornea is edematous despite high cell density or transparent despite low cell density, indicating that current methods of examining corneal endothelial cell morphology cannot accurately reflect cell function.

[0004] Summary of the Invention

[0005] In order to overcome the deficiencies of the prior art, the present invention aims to provide a method for establishing a finite element model of corneal endothelial cells.

[0006] To achieve the above object, the present invention provides the following solutions:

[0007] A method for establishing a finite element model of corneal endothelial cells, comprising:

[0008] Import the standard cornea model into the finite element pre-processing software and generate a 2D mesh to obtain a basic mesh model;

[0009] Import detailed geometric model of corneal endothelial cells;

[0010] determining a complete corneal endothelial cell model based on the basic mesh model and the detailed geometric model;

[0011] Calculations were performed based on the intact corneal endothelial cell model.

[0012] Preferably, generating a 2D grid comprises:

[0013] The corneal endothelial surface was selected to generate a 2D grid with a minimum grid size of 2 μm and a maximum grid size of 368 μm as the basic grid model. The grid size in the middle of the model was 2 μm and gradually increased in the radial direction.

[0014] Use transition meshing method to keep all elements as quadrilateral elements;

[0015] Delete the middle grid as the base grid, leaving a 469 μm x 324 μm space for replacing the detailed cell model.

[0016] Preferably, after importing the detailed geometric model of corneal endothelial cells, the method further comprises:

[0017] A 2D mesh was generated based on the detailed geometric model; the mesh size was 2 μm.

[0018] Preferably, determining a complete corneal endothelial cell model according to the basic mesh model and the detailed geometric model comprises:

[0019] Use beam elements to simulate the junction proteins between cells;

[0020] Projecting the mesh generated by the detailed geometric model onto the corneal endothelial surface so that the detailed geometric model fits the corneal endothelial surface;

[0021] Connect the basic mesh model and the detailed mesh model to form a complete corneal endothelial cell model;

[0022] All meshes are projected onto the corneal endothelial surface, and the complete mesh model fits the surface of the corneal endothelial cells.

[0023] Preferably, the calculation is performed based on the complete corneal endothelial cell model, including:

[0024] In the finite element simulation software, the corneal endothelial cell model was assigned material and cross-sectional properties. The material constitutive model was Neo-Hooke, the material parameter C10 was set to 173Pa, the material parameter D1 was set to 0.00061 / Pa, and the thickness of the endothelial cells was defined as 5μm.

[0025] The connection between cells is a beam unit, and the beam unit is given a circular cross-section; the radius of the circular cross-section is 1 μm;

[0026] The outermost nodes of the corneal endothelial cells are constrained to move in the X, Y and Z directions to fix the complete corneal endothelial cell model;

[0027] The corneal endothelial cell model was selected and a pressure of 2E-07 MPa was applied to simulate intraocular pressure;

[0028] Submit calculations in the finite element simulation software to obtain calculation results.

[0029] According to the specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0030] The present invention provides a method for establishing a finite element model of corneal endothelial cells, comprising: importing a standard corneal model into finite element pre-processing software and generating a 2D mesh to obtain a base mesh model; importing a detailed geometric model of corneal endothelial cells; determining a complete corneal endothelial cell model based on the base mesh model and the detailed geometric model; and performing calculations based on the complete corneal endothelial cell model. The present invention can improve the efficiency and effectiveness of establishing a finite element model of corneal endothelial cells. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0032] FIG1 is a flow chart of a method provided by an embodiment of the present invention;

[0033] FIG2 is a schematic diagram of the inner surface of a standard corneal geometric model provided by an embodiment of the present invention;

[0034] FIG3 is a schematic diagram of a grid size transition according to an embodiment of the present invention;

[0035] FIG4 is a schematic diagram of a basic grid model provided by an embodiment of the present invention;

[0036] FIG5 is a schematic diagram of a detailed geometric model of corneal endothelial cells in the compensatory stage after PKP surgery provided by an embodiment of the present invention;

[0037] FIG6 is a schematic diagram of a detailed grid model of corneal endothelial cells in the decompensated stage after PKP surgery provided by an embodiment of the present invention;

[0038] FIG7 is a schematic diagram of beam unit connection according to an embodiment of the present invention;

[0039] FIG8 is a schematic diagram of a complete model of corneal endothelial cells provided by an embodiment of the present invention;

[0040] FIG9 is a schematic diagram showing the connection between the basic model and the detailed grid model provided by an embodiment of the present invention;

[0041] FIG10 is a schematic diagram of corneal constraint provided by an embodiment of the present invention;

[0042] FIG11 is a schematic diagram of pressure provided by an embodiment of the present invention;

[0043] FIG12 is a schematic diagram of a normal corneal endothelial cell grid model provided by an embodiment of the present invention;

[0044] FIG13 is a cloud diagram of the first principal stress (MPa) of a single endothelial cell of a normal human cornea provided by an embodiment of the present invention;

[0045] FIG14 is a schematic diagram of a cell edge beam unit according to an embodiment of the present invention;

[0046] FIG15 is a schematic diagram of a corneal endothelial cell grid model in the decompensated stage after PKP surgery according to an embodiment of the present invention;

[0047] FIG16 is a cloud diagram of the first principal stress (MPa) of a single endothelial cell of a human cornea in the decompensated stage after PKP surgery according to an embodiment of the present invention;

[0048] FIG17 is a schematic diagram of a cell edge beam unit according to an embodiment of the present invention. DETAILED DESCRIPTION

[0049] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0050] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0051] In this embodiment, there is no distinction or limitation on the scope of applicable cases or diseases, that is, diseases such as glaucoma involving the endothelium are all applicable to the method involved in this embodiment.

[0052] FIG1 is a flow chart of a method provided by an embodiment of the present invention. As shown in FIG1 , the present invention provides a method for establishing a finite element model of corneal endothelial cells, comprising:

[0053] Step 100: Import the standard cornea model into the finite element pre-processing software and generate a 2D mesh to obtain a basic mesh model;

[0054] Step 200: importing a detailed geometric model of corneal endothelial cells;

[0055] Step 300: determining a complete corneal endothelial cell model based on the basic mesh model and the detailed geometric model;

[0056] Step 400: performing calculations based on the complete corneal endothelial cell model.

[0057] Specifically, the cornea comprises an endothelial cell layer, connexins, Descemet's membrane, stroma, Descemet's membrane, and epithelial cell layer. Considering factors such as calibration methods, computational accuracy, and computational efficiency, there are various methods for establishing a finite element model of the corneal endothelial cell layer, each with different model layers and areas. The model in this embodiment includes the corneal endothelial cell layer and connexins, and the model area is the same as that of a complete endothelial cell layer. The specific implementation process is as follows:

[0058] 1. Import the standard corneal model into the finite element pre-processing software Hypermesh. See Figure 2.

[0059] 2. Select the corneal endothelial surface to generate a 2D grid with a minimum grid size of 2 μm and a maximum grid size of 368 μm as the basic grid model. The grid size in the middle of the model is 2 μm and gradually increases in the radial direction. Use the transition meshing method to keep all units as quadrilaterals, as shown in Figure 3. Delete the middle grid as the basic grid, leaving a space of 469 μm x 324 μm to replace the detailed cell model, as shown in Figure 4.

[0060] 3. After penetrating keratoplasty (PKP), a detailed geometric model of corneal endothelial cells in the compensatory phase is shown in Figure 5 ; and a 2D mesh is generated with a mesh size of 2 μm, as shown in Figure 6 .

[0061] 4. The connecting proteins between cells are simulated using beam elements. The black connections in Figure 7 are beam elements.

[0062] 5. Project the mesh generated by the detailed model onto the surface of the corneal endothelium so that the detailed model fits the corneal endothelium surface, as shown in Figure 8.

[0063] 6. Connect the basic mesh model and the detailed mesh model to form a complete corneal endothelial cell model, as shown in Figure 7. The connection between the basic model and the detailed mesh model is shown in Figure 9.

[0064] 7. Project all meshes onto the surface of the corneal endothelium. The complete mesh model fits the surface of the corneal endothelial cells.

[0065] 8. Export the complete corneal endothelial cell model as an inp file.

[0066] 9. Import the inp file into the simulation software Abaqus.

[0067] 10. In Abaqus, assign material and cross-sectional properties to the endothelial cell mesh model. Select Neo-Hooke as the material constitutive model, set the material parameter C10 to 173 Pa, the material parameter D1 to 0.00061 / Pa, and define the thickness of the endothelial cells as 5 μm.

[0068] 11. The connection between cells is a beam element, and the beam element is given a circular cross-section with a radius of 1 μm.

[0069] 12. Constrain the outermost nodes of the corneal endothelial cells to the translational degrees of freedom in the X, Y, and Z directions, as shown in Figure 10, to fix the complete corneal endothelial cell model.

[0070] 13. Select the corneal endothelial cell model and apply a pressure of 2E-07 MPa (see Figure 11) to simulate intraocular pressure.

[0071] 14. Submit the calculation and you can view the results after the calculation is completed.

[0072] In this embodiment, the model can be a normal human corneal endothelial cell model. The detailed geometric model of normal human corneal endothelial cells is imported into Hypermesh. The subsequent steps are carried out according to the steps in this scheme. The model is shown in Figure 12. Submit the calculation and view the results. The cell apex angle is different, and the first principal stress of the apex angle is different (see Figure 13). The angle and first principal stress of one of the angles are extracted, and the results are 120.212° and 163.98MPa. The axial force (F) of the beam unit on the cell edge is extracted and divided by the side length (L) as the force per unit length on the cell edge, reflecting the side length and force situation, see Figure 14, extract the results, and calculate F / L to be 7.14E-10N / μm. Extract the cell side length and the average stress value on the edge to reflect the difference in stress on the cell edge, see Figure 13, extract the average value of the first principal stress on one of the edges, and the result is 158.330Pa.

[0073] In this embodiment, the model can also be a model of human corneal endothelial cells in the decompensated stage after PKP surgery. The detailed geometric model of human corneal endothelial cells in the decompensated stage after PKP surgery is imported into Hypermesh. The subsequent steps are carried out according to the steps in this scheme. The model is shown in Figure 15. Submit the calculation and view the results. The cell vertex angle is different, and the first principal stress of the vertex angle is different. See Figure 16. The angle and first principal stress of one of the angles are extracted, and the results are 131.624° and 164.40MPa. The axial force (F) of the beam unit on the cell edge is extracted and divided by the side length (L) as the force per unit length on the cell edge, reflecting the side length and force situation, see Figure 17, extract the results, and calculate F / L to be 7.96E-10N / μm. Extract the cell side length and stress value on the edge to reflect the difference in stress on the cell edge, see Figure 16. Extract the average value of the first principal stress on one of the edges, and the result is 162.289Pa.

[0074] The various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be referenced to each other.

[0075] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The above examples are only intended to help understand the method and core concept of the present invention. At the same time, those skilled in the art will find that the specific implementation methods and application scopes may vary based on the concept of the present invention. In summary, the contents of this specification should not be construed as limiting the present invention.

Claims

1. A method for establishing a finite element model of corneal endothelial cells, characterized in that: include: Import the standard cornea model into the finite element pre-processing software and generate a 2D mesh to obtain a basic mesh model; Import detailed geometric model of corneal endothelial cells; Determine a complete corneal endothelial cell model based on the basic mesh model and the detailed geometric model; Calculations were performed based on the intact corneal endothelial cell model.

2. The method for establishing a finite element model of corneal endothelial cells according to claim 1, characterized in that: The generating of 2D grid comprises: The corneal endothelial surface was selected to generate a 2D grid with a minimum grid size of 2 μm and a maximum grid size of 368 μm as the basic grid model. The grid size in the middle of the model was 2 μm and gradually increased in the radial direction. Use transition meshing method to keep all elements as quadrilateral elements; Delete the middle grid as the base grid, leaving 469 μm x 324 μm space to replace the detailed cell model.

3. The method for establishing a finite element model of corneal endothelial cells according to claim 1, characterized in that: After importing the detailed geometry model of corneal endothelial cells, it also includes: A 2D mesh was generated based on the detailed geometric model; the mesh size was 2 μm.

4. The method for establishing a finite element model of corneal endothelial cells according to claim 1, characterized in that: A complete corneal endothelial cell model is determined according to the basic mesh model and the detailed geometric model, including: Use beam elements to simulate junction proteins between cells; Projecting the mesh generated by the detailed geometric model onto the surface of the corneal endothelium so that the detailed geometric model fits the surface of the corneal endothelium; Connect the basic mesh model and the detailed mesh model to form a complete corneal endothelial cell model; All meshes are projected onto the corneal endothelial surface, and the complete mesh model fits the surface of corneal endothelial cells.

5. The method for establishing a finite element model of corneal endothelial cells according to claim 1, characterized in that: Calculations were performed based on the complete corneal endothelial cell model, including: In the finite element simulation software, the corneal endothelial cell model was given material and cross-sectional properties. The material constitutive model was selected as Neo-Hooke, the material parameter C10 was set to 173Pa, the material parameter D1 was set to 0.00061 / Pa, and the thickness of the endothelial cells was defined as 5μm. The connection between cells is a beam unit, and the beam unit is given a circular cross section; the radius of the circular cross section is 1 μm; The outermost nodes of the corneal endothelial cells are constrained to move in the X, Y and Z directions to fix the complete corneal endothelial cell model; The corneal endothelial cell model was selected and a pressure of 2E-07MPa was applied to simulate intraocular pressure; Submit calculations in the finite element simulation software to obtain calculation results.

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