A 3D geometrical model and meshing procedures for the human eyeball

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GitHub Information

Vincent Chabannes

Affiliation: Cemosis, IRMA UMR 7501, Université de Strasbourg, CNRS, France
Email: vincent.chabannes@cemosis.fr
Orcid:

Christophe Prud’homme

Affiliation: Cemosis, IRMA UMR 7501, Université de Strasbourg, CNRS, France
Email: christophe.prudhomme@cemosis.fr
Orcid:

Thomas Saigre

Affiliation: Cemosis, IRMA UMR 7501, Université de Strasbourg, CNRS, France
Email: thomas.saigre@math.unistra.fr
Orcid:

Lorenzo Sala

Affiliation: Université Paris-Saclay, INRAE, MaIAGE, 78350, Jouy-en-Josas, France
Email: lorenzo.sala@inrae.fr
Orcid:

Marcela Szopos

Affiliation: Université Paris Cité, CNRS, MAP5, F-75006 Paris, France
Email: marcela.szopos@u-paris.fr
Orcid:

Christophe Trophime

Affiliation: LNCMI, CNRS
Email: trophime@lncmi.cnrs.fr
Orcid:

This document describes the procedure to generate the geometry and the meshes of the 3D model of the human eyeball. To generate the geometry and the meshes, the following tools are needed:

• Salome [Ribes17] (v9.12.0) www.salome-platform.org/,

• Feel++ [Prudhomme24] (0.111.0) docs.feelpp.org/home/index.html.

Generate the geometry and the initial mesh

Generate the geometry of the human eyeball with the following command:

salome [-t] construct-eye-STP.py [--geometrical_args...]

More details on the gemetrical arguments can be found in [Sala24].

Note	For newer version of Salome, the script construct-eye-STP.py may no longer be working, still the STEP file generate by this script is present in the repository, Eye.step.

And generate the meshes with the following command:

salome [-t] eye.py

To be utilized with Feel++, the mesh must be converted to the Gmsh format with the following command:

gmsh -0 Eye_Mesh3D.med -o Eye_Mesh3D.msh

Generate the uniform family mesh M.

To generate the uniform family mesh M., run the following command:

python3 generate_family.py

It will generate the meshes M0, M1, M2, M3, M4 and M5 of various refinement levels.

To east the usage of the meshed in parallel with Feel++, the meshes need to be partitionned. This can be performed with the following command:

./partition_mesh_M.sh

Generate the adapted mesh Mr

The mesh Mr is generated by adapting M with a tinier refinement level around the aqueous humor part. At this point, the pipeline to perform the mesh refinement with the tools of Feel++ is quite tricky, but the script generate_Mr.sh permit to do it:

./generate_mesh_Mr.sh

Generate the adapted family mesh Mr.

The adapted family mesh Mr. is generated by remeshing the mesh Mr with the following command:

python3 generate_family.py Mr

Partition the adapted family mesh Mr.

To partition the adapted family mesh Mr., run the following command:

./partition_mesh_Mr.sh

Note	With this partitionnement, the parts where the physics are considered are split: namely the AqueousHumor on the one hand where the coupled model is considered, and the remaining regions on the other hand, where the sole heat transfer is considered, see [Saigre24] for more details.

Mesh description

Figure 1. 3D geometry of the human eyeball.

The markers of all the meshes are identical.

• The volume markers are: "Cornea", "Sclera", "AqueousHumor", "Lens", "VitreousHumor", "Iris", "Lamina", "Choroid", "Retina", "OpticNerve".

• The interfaces markers are defined when two volumes are in contact, and follow the convention "Volume1_Volume2", where "Volume1" and "Volume2" are in lexicographic order. For example, the interface between the "Cornea" and the "AqueousHumor" is "AqueousHumor_Cornea".

• The is one exception to the previous rule: the boudary surfaces around the lamina crobrosa are names "Lamina_In", "Lamina_Out", Lamina_Lateral" and "Lamina_Hole".

• The external surfaces are: "BC_Cornea", "BC_Sclera" and "BC_OpticNerve".

2D extraction

The mesh can be extracted in 2D, making a vertical cut of the eyeball, using the command:

python3 eye2d.py [--add-syringe]

The --add-syringe (which is by default True) adds a small domain that represents the syringe used to inject cell in the eye in the context of cell sedimentation therapy. Two 2D meshes are generated:

• EyeMesh_2d.med

• EyeMesh_AH.med with the sole domain of the aqueous humor.

These MED meshes can be converted to GMSH format, as above.

In the case --add-syringe is set to True, a marker Syringe is added to the mesh, wich is a small rectangular domain. A marker BC_Injection is also added to represent the boundary of the syringe where the injection is performed.

Figure 2. Domain of injection.

Bibliography

• Alejandro Ribes, Adrien Bruneton, Anthony Geay. SALOME: an Open-Source simulation platform integrating ParaView. (2017) doi.org/10.13140/RG.2.2.12107.08485.

• Christophe Prud’homme, Vincent Chabannes, Thomas Saigre, Christophe Trophime, Luca Berti, Abdoulaye Samaké, Céline Van Landeghem, et al. « Feelpp/feelpp: Feel++ Release V111 Preview.10 ». Zenodo, 15 juillet 2024. doi.org/10.5281/zenodo.12742155.

• Sala L, Prud’homme C, Guidoboni G, Szopos M, Harris A. The ocular mathematical virtual simulator: A validated multiscale model for hemodynamics and biomechanics in the human eye. Int J Numer Meth Biomed Engng. 2024; 40(2):e3791. doi.org/10.1002/cnm.3791.

• Thomas Saigre, Vincent Chabannes, Christophe Prud’homme, Marcela Szopos. A coupled model of heat transfer and fluid flow in the human eye. (2024). hal.science/hal-04918559.