A method for establishing a corneal endothelial cell finite element model

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 in particular to a method for establishing a corneal endothelial cell finite element model. [Background technology]

[0002] Corneal endothelial cells, the innermost layer of cells in the cornea, are single-layered hexagonal cells that play an important role in maintaining corneal transparency and normal visual function. Corneal endothelial cell density slowly declines at a rate of 0.3% to 0.6% per year, and significant endothelial cell loss occurs following wounds and intraocular surgery. After injury, endothelial cells repair themselves by migrating and expanding. Excessive corneal endothelial cell loss can lead to decompensation of the endothelial metabolic pump function, resulting in corneal edema, loss or loss of tight intercellular connections, loss and fusion of cell edges, and reduced barrier function, which clinically manifests as corneal endothelial dysfunction. Corneal endothelial cell morphology and number are often important reference indicators in the diagnosis and treatment of corneal diseases.

[0003] Currently, most studies focus on corneal endothelial cell density and hexagonal cell occupancy. However, clinical studies have found that there are cases where the cornea is clear despite a high cell density, or where the cornea is transparent despite a low cell density. This indicates that current methods for examining corneal endothelial cell morphology cannot accurately reflect cell function. Summary of the Invention [Problem to be solved by the invention]

[0004] To overcome the deficiencies of the prior art, the present invention aims to provide a method for establishing a corneal endothelial cell finite element model. [Means for solving the problem]

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

[0006] A method for establishing a corneal endothelial cell finite element model, comprising: Importing the standard corneal model into finite element pre-processing software and generating a 2D grid to obtain a base grid model; Importing a detailed geometric model of the corneal endothelium and determining a complete corneal endothelial cell model based on the base grid model and the detailed geometric model; and calculating based on the complete corneal endothelial cell model.

[0007] Preferably, generating the 2D grid comprises: 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 model intermediate grid size is 2 μm, and gradually increases in the radial direction. The transition grid scribe method is used, and all the holding units are square units; This involves removing the intermediate grid and leaving a 469 μm x 324 μm space as the base mesh to replace the detailed cell model.

[0008] Preferably, after importing a detailed geometric model of the corneal endothelium, The method further includes generating a 2D grid having a grid size of 2 μm based on the detailed geometric model.

[0009] Preferably, determining a complete corneal endothelial cell model based on the base grid model and the detailed geometric model comprises: Simulating intercellular connexins using beam elements; projecting a grid generated by the detailed geometric model onto the surface of the corneal endothelium, and closely fitting the detailed geometric model to the surface of the corneal endothelium; Connecting the basic grid model and the detailed grid model to construct a complete corneal endothelial cell model; This involves projecting all grids onto the corneal endothelial surface and fitting the complete grid model to the corneal endothelial cell surface.

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

[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, 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. [Brief explanation of the drawings]

[0013] In order to more clearly explain the embodiments of the present invention or the technical solutions in the prior art, the following will briefly introduce the drawings that need to be used in the embodiments. It is obvious that the drawings in the following description are only some embodiments of the present invention, and those skilled in the art can also obtain other drawings based on these drawings without exerting any creative efforts. [Figure 1] 2 is a flowchart of a method according to an embodiment of the present invention. [Figure 2] 1 is a schematic diagram of the inner surface of a standard corneal geometric model according to an embodiment of the present invention. [Figure 3] FIG. 2 is a schematic diagram of grid size transition according to an embodiment of the present invention. [Figure 4] FIG. 2 is a schematic diagram of a basic grid model according to an embodiment of the present invention. [Figure 5] FIG. 2 is a schematic diagram of a detailed geometric model of corneal endothelial cells in the compensatory stage after PKP surgery according to an embodiment of the present invention. [Figure 6] FIG. 1 is a schematic diagram of a detailed grid model of corneal endothelial cells in a decompensated stage after PKP surgery according to an embodiment of the present invention. [Figure 7] 1 is a schematic diagram of a beam element connection according to an embodiment of the present invention. [Figure 8] 1 is a schematic diagram of a complete corneal endothelial cell model according to an embodiment of the present invention. [Figure 9] FIG. 2 is a schematic diagram of a basic model and a detailed grid model connection according to an embodiment of the present invention. [Figure 10] 1 is a schematic diagram of a corneal restraint according to an embodiment of the present invention. [Figure 11] FIG. 1 is a pressure schematic diagram according to an embodiment of the present invention. [Figure 12] 1 is a schematic diagram of a normal corneal endothelial cell grid model according to an embodiment of the present invention. FIG. [Figure 13] 1 is a first principal stress nephogram (MPa) of a normal human corneal single endothelial cell according to an embodiment of the present invention. [Figure 14] FIG. 1 is a schematic diagram of an example cell edge element according to an embodiment of the present invention. [Figure 15] FIG. 1 is a schematic diagram of a corneal endothelial cell grid model in a decompensation stage after PKP surgery according to an embodiment of the present invention. [Figure 16] 1 shows a first principal stress nephogram (MPa) of a single human corneal endothelial cell in the decompensation stage after PKP according to an embodiment of the present invention. [Figure 17] FIG. 1 is a schematic diagram of an example cell edge element according to an embodiment of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0014] The following clearly and completely describes the technical solutions in the embodiments of the present invention in conjunction with the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only some embodiments of the present invention, and not all embodiments, and all other embodiments obtained by those skilled in the art based on the embodiments of the present invention without any creative efforts are all within the protection scope of the present invention.

[0015] In order to make the above objects, features and advantages of the present invention more clearly comprehensible, the present invention will be described in more detail below in conjunction with the drawings and specific embodiments.

[0016] In this example, the applicable cases or disease ranges are not distinguished or limited, that is, any disease related to the endothelium, such as glaucoma, is applicable to the method according to this example.

[0017] FIG. 1 is a flowchart of a method according to an embodiment of the present invention. As shown in FIG. 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 cornea model into the finite element pre-processing software and generate a 2D grid to obtain a base grid model.

[0019] Step 200: Import a detailed geometric model of the corneal endothelium.

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

[0021] Step 400: Calculation is performed based on the complete corneal endothelial cell model.

[0022] Specifically, the cornea of ​​the eye includes an endothelial cell layer, connexins, a posterior elastic layer, a stromal layer, an anterior elastic layer, and an epithelial cell layer. Considering factors such as verification method, calculation accuracy, and calculation efficiency, there are multiple methods for establishing a corneal endothelial cell finite element model, with different expressions for the model level and area. The model in this embodiment includes a corneal endothelial cell layer and connexins, 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, as shown in Figure 2.

[0024] 2. Select the corneal endothelial surface to generate a 2D grid. The minimum grid size is 2 μm, and the maximum grid size is 368 μm. The base grid model is a model with an intermediate grid size of 2 μm, gradually increasing in the radial direction. Using the transition grid scribing method, the holding units are all square (see Figure 3). The middle grid is removed, leaving a 469 μm x 324 μm space as the base mesh to replace the detailed cell model (see Figure 4).

[0025] 3. After importing penetrating keratoplasty (PKP), a detailed geometric model of the compensatory corneal endothelial cells (see Figure 5), a 2D grid was generated with a grid size of 2 μm (see Figure 6).

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

[0027] 5. The grid generated by the detailed model is projected onto the corneal endothelial surface, and the detailed model is fitted to 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. The connection between the basic model and the detailed grid model is shown in Figure 9.

[0029] 7. All grids are projected onto the corneal endothelial surface, and the complete grid model is fitted perfectly to the corneal endothelial cell surface.

[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, the material configuration is selected as Neo-Hooke, the material parameter C10 is set to 173 Pa, the material parameter D1 is set to 0.0006 1 / Pa, and the thickness of the endothelial cell is defined as 5 μm.

[0033] 11. The connections between cells are beam elements, which have a circular cross section and a radius of 1 μm.

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

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

[0036] 14. You can submit your calculations and view the results once they are complete.

[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 in this solution are performed. The model is as shown in Figure 12. A calculation is submitted and the results are obtained. 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 163.98 MPa. The axial forces of the beam elements on the cell edge are taken as the force per unit length on the cell edge to obtain the sum (F), which is then divided by the edge length (L) to represent the edge length and force-bearing situation, as shown in Figure 14. The result is used to calculate F / L to be 7.14E-10 N / μm. The cell edge length and the average stress value on the edge were taken to represent the difference in stress on the cell edge, as shown in Figure 13. The average value of the first principal stress on one of the 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 a decompensated state after PKP surgery. A detailed geometric model of a human corneal endothelial cell in a decompensated state after PKP surgery is imported into Hypermesh, and the subsequent steps in this solution are performed. The model is shown in Figure 15. A calculation is submitted and the results are obtained. The cell apex angles are different, and the first principal stresses of the apex angles are different. Referring to Figure 16, the angle and first principal stress of one of the angles are taken, and the results are 131.624° and 164.40 MPa. The axial forces of the beam elements on the cell edge are calculated as the force per unit length to obtain the sum (F), which is then divided by the edge length (L) to represent the edge length and force-bearing situation on the cell edge. Referring to Figure 17, the result is obtained and F / L is calculated to be 7.96E-10 N / μm. The cell edge length and the stress value on the edge are taken to represent the difference in stress on the cell edge. Referring to Figure 16, the average value of the first principal stress on one of the edges is taken, and the result is 162.289 Pa.

[0039] Each embodiment in this specification is described recursively, and each embodiment is described focusing on the differences from other embodiments, and similar parts between embodiments may be referred to mutually.

[0040] In this specification, the principles and embodiments of the present invention are described using specific examples, and the explanation of the above examples is only intended to help understand the method of the present invention and its core idea, and those skilled in the art may make any changes to the specific embodiments and application scope based on the idea 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 corneal endothelial cell finite element model, comprising: Importing the standard corneal model into finite element pre-processing software and generating a 2D grid to obtain a base grid model; Importing a detailed geometric model of the corneal endothelium and 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.

2. Said generating a 2D grid comprises: 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 model intermediate grid size is 2 μm, and gradually increases in the radial direction; The transition grid scribe method is used, and all the holding units are square units; The method for establishing a corneal endothelial cell finite element model according to claim 1, further comprising: deleting the intermediate grid, leaving a 469 μm x 324 μm space as a base mesh, and replacing the detailed cell model therewith.

3. After importing a detailed geometric model of the corneal endothelium, The 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 the detailed geometric model.

4. determining a complete corneal endothelial cell model based on the base grid model and the detailed geometric model, Simulating intercellular connexins using beam elements; Projecting a grid generated by the detailed geometric model onto the corneal endothelial surface, and fitting the detailed geometric model to the corneal endothelial surface; Connecting the basic grid model and the detailed grid model to construct a complete corneal endothelial cell model; 2. The method for establishing a corneal endothelial cell finite element model according to claim 1, further comprising projecting all grids onto the corneal endothelial surface and fitting the complete grid model to the corneal endothelial cell surface.

5. Calculating based on the complete corneal endothelial cell model Assigning material and cross-sectional attributes to the corneal endothelial cell model using finite element simulation software, selecting Neo-Hooke as the material configuration, setting the material parameter C10 to 173 Pa, setting the material parameter D1 to 0.0006 1 / Pa, and defining the thickness of the endothelial cell to 5 μm; The connections between the cells are beam elements, and the beam elements are given a circular cross section with a radius of 1 μm; Fixing the complete corneal endothelial cell model by constraining the translational degrees of freedom in the X, Y, and Z directions at the outermost peripheral nodes of the corneal endothelial cell; Selecting a corneal endothelial cell model and applying a pressure of 2E-07 MPa to simulate intraocular pressure; 2. The method for establishing a corneal endothelial cell finite element model according to claim 1, further comprising: submitting a calculation to the finite element simulation software and obtaining a calculation result.

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