Method for establishing a finite element model of corneal endothelial cells

Abstract

The present invention provides a method for establishing a corneal endothelial cell finite element model, which includes importing a standard corneal model into finite element preprocessing software and generating a 2D grid to obtain a base grid model, importing a detailed geometric model of the corneal endothelial cell, determining a complete corneal endothelial cell model based on the base grid 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 corneal endothelial cell finite element model.

Description

Technical Field

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

Background Art

[0002] Corneal endothelial cells are the innermost layer cells of the cornea and are single-layer hexagonal cells, which play an important role in maintaining corneal transparency and normal visual function. The corneal endothelial cell density decreases slowly at a rate of 0.3% - 0.6% per year, and when encountering trauma, intraocular surgery, etc., the loss of endothelial cells increases. The damaged endothelial cells are repaired by expanding migration. If the loss of corneal endothelial cells is too much, the compensation failure of the endothelial metabolic pump function can cause corneal edema, the close connection between cells is broken or missing, the partial cell edge is missing, fused, the barrier function is reduced, and clinically it appears as corneal endothelial dysfunction compensation failure. In the diagnosis and treatment of corneal diseases, the morphology and number of corneal endothelial cells are often important reference indicators.

[0003] Currently, many studies mainly focus on corneal endothelial cell density and hexagonal cell occupancy rate. However, it has been discovered clinically that there are phenomena where a large number of cells have a high density but there is obvious corneal edema, or the cell density is low but the cornea is in a transparent state, indicating that the current method for examining corneal endothelial cell morphology cannot accurately reflect cell function.

Summary of the Invention

Problems to be Solved by the Invention

[0004] 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.

Means for Solving the Problems

[0005] To achieve the above object, the present invention provides the following solutions.

[0006] A method for establishing a finite element model of corneal endothelial cells, Import a standard corneal model into finite element preprocessing software, generate a 2D grid, and obtain a basic grid model. Importing a detailed geometric model of corneal endothelial cells, To determine a complete corneal endothelial cell model based on the aforementioned basic grid model and the aforementioned detailed geometric model, This includes performing calculations based on the complete corneal endothelial cell model described above.

[0007] Preferably, generating the 2D grid is A 2D grid was generated by selecting the corneal endothelial surface, with a minimum grid size of 2 μm and a maximum grid size of 368 μm. The basic grid model had an intermediate grid size of 2 μm, gradually increasing in the radial direction. Using the transition grid scribe method, all retained units are quadrilateral units, This involves removing the intermediate grid, leaving a 469 μm × 324 μm space as the base mesh, and replacing it with a more detailed cell model.

[0008] Preferably, after importing a detailed geometric model of corneal endothelial cells, The method further includes generating a 2d grid with a grid size of 2 μm based on the detailed geometric model described above.

[0009] Preferably, determining a complete corneal endothelial cell model based on the basic grid model and the detailed geometric model is Using tension elements to simulate intercellular connexins, The grid generated by the detailed geometric model is projected onto the corneal endothelial surface, and the detailed geometric model is precisely aligned with the corneal endothelial surface. To connect the basic grid model and the detailed grid model to construct a complete corneal endothelial cell model, This includes projecting all grids onto the corneal endothelial surface and precisely aligning the complete grid model with the surface of corneal endothelial cells.

[0010] Preferably, the calculation is based on the complete corneal endothelial cell model. In finite element simulation software, material and cross-sectional attributes are assigned to the corneal endothelial cell model, Neo-Hooke material composition is selected, material parameter C10 is set to 173 Pa, material parameter D1 is set to 0.0006 1 / Pa, and the thickness of the endothelial cells is defined as 5 μm. The connections between cells are tension elements, and these tension elements are given a circular cross-section with a radius of 1 μm. The complete corneal endothelial cell model is fixed by constraining the translational degrees of freedom in the X, Y, and Z directions at the outermost nodes of the corneal endothelial cells, Select a corneal endothelial cell model and apply a pressure of 2E-07MPa to simulate intraocular pressure. This includes submitting calculations to the aforementioned finite element simulation software and obtaining the calculation results.

[0011] According to specific embodiments of the present invention, the present invention discloses the following technical effects. [Effects of the Invention]

[0012] The present invention provides a method for establishing a corneal endothelial cell finite element model, comprising: importing a standard corneal model into finite element preprocessing software to generate a 2D grid and obtain a basic grid model; importing a detailed geometric model of corneal endothelial cells; determining a complete corneal endothelial cell model based on the basic grid 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 corneal endothelial cell finite element model. [Brief explanation of the drawing]

[0013] To more clearly explain the technical solutions in the embodiments of the present invention or the prior art, the following briefly introduces the drawings that need to be used in the embodiments. It is self-evident that the drawings in the following description are only some embodiments of the present invention. For those skilled in the art, based on these drawings and without creative efforts, other drawings can also be obtained. [Figure 1] It is a flowchart of the method according to the embodiment of the present invention. [Figure 2] It is a schematic diagram of the inner surface of the standard corneal geometric model according to the embodiment of the present invention. [Figure 3] It is a schematic diagram of the grid size transition according to the embodiment of the present invention. [Figure 4] It is a schematic diagram of the basic grid model according to the embodiment of the present invention. [Figure 5] It is a schematic diagram of the detailed geometric model of corneal endothelial cells during the compensatory period after PKP according to the embodiment of the present invention. [Figure 6] It is a schematic diagram of the detailed grid model of corneal endothelial cells during the decompensated period after PKP according to the embodiment of the present invention. [Figure 7] It is a schematic diagram of the connection of bar elements according to the embodiment of the present invention. [Figure 8] It is a schematic diagram of the complete model of corneal endothelial cells according to the embodiment of the present invention. [Figure 9] It is a schematic diagram of the connection between the basic model and the detailed grid model according to the embodiment of the present invention. [Figure 10] It is a schematic diagram of corneal restraint according to the embodiment of the present invention. [Figure 11] It is a schematic diagram of pressure according to the embodiment of the present invention. [Figure 12] It is a schematic diagram of the grid model of normal corneal endothelial cells according to the embodiment of the present invention. [Figure 13] It is the first principal stress nephogram (MPa) of a single normal human corneal endothelial cell according to the embodiment of the present invention. [Figure 14] It is a schematic diagram of the edge bar elements of the example cells according to the embodiment of the present invention. [Figure 15] It is a schematic diagram of the grid model of corneal endothelial cells during the decompensated period after PKP in the example according to the embodiment of the present invention. [Figure 16] This is an example of the present invention, showing the first principal stress nephogram (MPa) of a single human corneal endothelial cell in the decompensated phase after PKP surgery. [Figure 17] This is a schematic diagram of the edge element of an example cell according to an embodiment of the present invention. [Modes for carrying out the invention]

[0014] The following clearly and completely describes the technical concepts in the embodiments of the present invention, linking them with drawings. Clearly, the described embodiments represent only a portion of the embodiments of the present invention, not all of them. All other embodiments obtained based on the embodiments of the present invention without the creative effort of a person skilled in the art are all within the scope of the protection of the present invention.

[0015] To make the above-mentioned objectives, features, and advantages of the present invention clearer and easier to understand, the present invention will be described in more detail below, linking the drawings with specific embodiments.

[0016] In this embodiment, there is no distinction or limitation regarding the range of applicable cases or disease types; that is, any disease relating to the endothelium, such as glaucoma, is applicable to the method according to this embodiment.

[0017] Figure 1 is a flowchart of a method according to an embodiment of the present invention, and as shown in Figure 1, the present invention provides a method for establishing a corneal endothelial cell finite element model, which includes the following steps.

[0018] Step 100: Import the standard corneal model into finite element preprocessing software to generate a 2D grid and obtain the base grid model.

[0019] Step 200: Import a detailed geometric model of corneal endothelial cells.

[0020] Step 300: Determine the complete corneal endothelial cell model based on the basic grid model and the detailed geometric model.

[0021] Step 400: Calculate based on the complete corneal endothelial cell model described above.

[0022] Specifically, the cornea includes the endothelial cell layer, connexin, post-elastic layer, matrix layer, pre-elastic layer, and epithelial cell layer. Considering factors such as verification methods, computational accuracy, and computational efficiency, there are multiple methods for establishing a finite element model of corneal endothelial cells, and they can be represented differently in terms of model level and area. In this example, the model includes the corneal endothelial cell layer and connexin, and the model area is the same as the area of ​​the complete endothelial cell layer. The specific implementation process is as follows.

[0023] 1. Import the standard corneal model into the finite element preprocessing software Hypermesh. This is shown in Figure 2.

[0024] 2. Select the corneal endothelial surface and generate a 2D grid with a minimum grid size of 2 μm and a maximum grid size of 368 μm. As the base grid model, the intermediate grid size of the model is 2 μm, gradually increasing radially. The transition grid scribe method is used, and all retaining units are square. See Figure 3. Remove the intermediate grid and replace it with a detailed cell model, leaving a 469 μm × 324 μm space as the base mesh. See Figure 4.

[0025] 3. After importing penetrating keratoplasty (PKP), which will be abbreviated as PKP below, a detailed geometric model of compensatory corneal endothelial cells is generated, as shown in Figure 5, with a 2D grid size of 2 μm, as shown in Figure 6.

[0026] 4. Intercellular connexins are simulated using beam elements, and the black connections in Figure 7 are the beam elements.

[0027] 5. The grid generated by the detailed model is projected onto the corneal endothelial surface, and the detailed model is precisely aligned with the corneal endothelial surface, as shown in Figure 8.

[0028] 6. The basic grid model and the detailed grid model are connected to form a complete corneal endothelial cell model, as shown in Figure 7. For the connection between the basic model and the detailed grid model, see Figure 9.

[0029] 7. All grids are projected onto the corneal endothelial surface, so that the complete grid model fits perfectly onto the surface of the corneal endothelial cells.

[0030] 8. Export the complete corneal endothelial cell model as an inp file.

[0031] 9. Import the .inp file into the emulation software Abaqus.

[0032] 10. In Abaqus, material and cross-sectional attributes are assigned to the endothelial cell grid model. Neo-Hooke is selected for the material composition, material parameter C10 is set to 173 Pa, material parameter D1 is set to 0.0006 1 / Pa, and the thickness of the endothelial cells is defined as 5 μm.

[0033] 11. Intercellular connections are provided by beam elements, each beam element having a circular cross-section with a radius of 1 μm.

[0034] 12. The translational degrees of freedom in the X, Y, and Z directions are constrained at the outermost nodes of the corneal endothelial cells, as shown in Figure 10, thereby fixing the complete model of the corneal endothelial cells.

[0035] 13. Select a corneal endothelial cell model and apply a pressure of 2E-07MPa, as shown in Figure 11, to simulate intraocular pressure.

[0036] 14. Submit your calculations, and once the calculations are complete, you can view the results.

[0037] The model in this embodiment may be a normal human corneal endothelial cell model. A detailed geometric model of a normal human corneal endothelial cell is imported into Hypermesh, and the subsequent steps are carried out according to the steps in this solution. The model is as shown in Figure 12, and the calculation is submitted to view the results. The cell apex angles are different, and the first principal stress at the apex angle is different (see Figure 13). The angle and first principal stress of one of these angles are extracted, and the results are 120.212° and 163.98 MPa. The axial force of the beam element on the cell edge is taken as the force per unit length on the cell edge, its sum (F) is calculated, and it is divided by the edge length (L) to represent the edge length and the force bearing situation, as shown in Figure 14. The result is taken, and F / L is calculated to be 7.14E-10 N / μm. The cell edge length and the average stress value along the edge were taken to represent the difference in stress along the cell edge, as shown in Figure 13. The average value of the first principal stress of one of these edges was taken, and the result was 158.330 Pa.

[0038] The model in this embodiment may be a human corneal endothelial cell model in the decompensated phase after PKP surgery. A detailed geometric model of human corneal endothelial cells in the decompensated phase after PKP surgery is imported into Hypermesh, and the subsequent steps are carried out in the steps of this solution. The model is as shown in Figure 15, and the calculations are submitted and the results are viewed. The angles of the cell apex angles differ, and the first principal stress of the apex angles differs. Refer to Figure 16, and take the angle and first principal stress of one of these angles. The results are 131.624° and 164.40 MPa. As the force per unit length, take the axial force of the beam element on the cell edge and calculate the sum (F), divide by the edge length (L), and refer to Figure 17 to represent the edge length and force bearing situation on the cell edge. Take the result and calculate F / L to 7.96E-10 N / μm. The cell edge length and edge stress values ​​were taken to represent the differences in stress along the cell edges. Referring to Figure 16, the average value of the first principal stress along one of these edges was taken, and the result was 162.289 Pa.

[0039] Each example in this specification is described recursively, with each example focusing on its differences from the others, and any similar parts between examples should be referenced to one another.

[0040] This specification describes the principles and embodiments of the present invention using specific examples. The above description of the examples is intended only to aid in understanding the methods and core ideas of the present invention, and those skilled in the art will likely modify the specific embodiments and scope of application based on the ideas of the present invention. In summary, the contents of this specification should not be understood as limitations on the present invention.

Claims

1. A method for establishing a finite element model of corneal endothelial cells, Computers The process involves generating a 2D grid consisting of nodes and elements used in finite element analysis based on shape data of a standard corneal model, thereby generating a basic grid model representing the corneal endothelial surface. The steps include: constructing a complete corneal endothelial cell model as a finite element model representing the corneal endothelial cell layer, based on the aforementioned basic grid model and a detailed geometric model representing the shape and arrangement of corneal endothelial cells; The process includes setting material properties and boundary conditions for the complete corneal endothelial cell model, and calculating the stress generated in the corneal endothelial cells using the finite element method. The above-mentioned generation of a 2D grid is A 2d grid is generated in the region corresponding to the corneal endothelial surface, with a minimum grid size of 2 μm and a maximum grid size of 368 μm. The basic grid model has an intermediate grid size of 2 μm, which gradually increases in the radial direction. The transition grid scribe method constructs the grid such that all retained units are quadrilateral units, A method for establishing a finite element model of corneal endothelial cells, characterized by removing intermediate grids, leaving a 469 μm × 324 μm space as a base mesh, and replacing this space with a detailed cell model.

2. A method for establishing a corneal endothelial cell finite element model according to claim 1, further comprising generating a 2d grid with a grid size of 2 μm based on a detailed geometric model of corneal endothelial cells.

3. Constructing a complete corneal endothelial cell model based on the aforementioned basic grid model and the aforementioned detailed geometric model is possible. Modeling intercellular connection structures using tension elements that represent intercellular connexins, The grid generated by the detailed geometric model described above is projected onto the corneal endothelial surface, and the grid is made to correspond to the corneal endothelial surface. Connecting the basic grid model and the detailed grid model to construct a complete corneal endothelial cell model representing the corneal endothelial cell layer, A method for establishing a corneal endothelial cell finite element model according to claim 1, characterized by comprising projecting all the grids constituting the complete corneal endothelial cell model onto the corneal endothelial surface and corresponding them to the corneal endothelial cell surface.

4. The calculation based on the complete corneal endothelial cell model is: The corneal endothelial cell model is configured with material properties and cross-sectional attributes, using the Neo-Hook model as the material composition, setting the material parameter C10 to 173 Pa, the material parameter D1 to 0.0006 1 / Pa, and the endothelial cell thickness to 5 μm. The connections between cells are represented by beam elements, and a circular cross-section with a radius of 1 μm is set for each beam element, The translational degrees of freedom in the X, Y, and Z directions are constrained at the outermost nodes of the corneal endothelial cells, thereby fixing the complete corneal endothelial cell model. Applying a pressure of 2E-07 MPa to a corneal endothelial cell model and setting a load condition that represents intraocular pressure, A method for establishing a corneal endothelial cell finite element model according to claim 1, characterized by comprising calculating the stress generated in the complete corneal endothelial cell model using the finite element method.

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