[Simulation par éléments finis visant à déterminer la vitesse des ondes de cisaillement dans la cornée féline et comparaison avec la vitesse des ondes de cisaillement dans la cornée humaine, canine et dans le cas du kératocône]
This study presents a finite element (FE) simulation framework for determining the shear wave velocity of the feline cornea and comparing it with human, canine, and keratoconic corneas. A hyper-viscoelastic material model was implemented in ABAQUS, combining a Neo-Hookean hyperelastic formulation with a generalized Maxwell viscoelastic model represented by a Prony series. The corneal geometry incorporated species-specific thickness, curvature, and diameter parameters under physiological intraocular pressure (15 mmHg). Shear wave propagation was simulated using excitation pressures of 15 000–30 000 Pa. The calculated shear wave velocity in the feline cornea ranged from 5.26 m/s to 5.43 m/s, showing an increasing trend with excitation pressure. Comparative results indicated the following interspecies relationship: cs,keratoconus < cs,human < cs,feline < cs,canine.
These findings demonstrate that the feline cornea exhibits biomechanical characteristics closer to the canine cornea, reflecting similar hyper-viscoelastic responses. The model provides a validated computational basis for evaluating corneal stiffness and supports future shear wave elastography studies in comparative and veterinary ophthalmology.
Cette étude présente un cadre de simulation par éléments finis (EF) permettant de déterminer la vitesse des ondes de cisaillement de la cornée féline et de la comparer à celle des cornées humaines, canines et atteintes de kératocône. Un modèle de matériau hype-rviscoélastique a été mis en œuvre dans ABAQUS, combinant une formulation hyperélastique de type Neo-Hookeen avec un modèle viscoélastique généralisé de Maxwell représenté par une série de Prony. La géométrie cornéenne intégrait des paramètres spécifiques à chaque espèce, notamment l’épaisseur, la courbure et le diamètre, sous une pression intraoculaire physiologique (15 mmHg). La propagation des ondes de cisaillement a été simulée à l’aide de pressions d’excitation comprises entre 15 000 et 30 000 Pa. La vitesse des ondes de cisaillement calculée dans la cornée féline variait de 5,26 m/s à 5,43 m/s, affichant une tendance à l’augmentation avec la pression d’excitation. Les résultats comparatifs ont mis en évidence la relation interespèces suivante : cs,kératocône < cs,humain < cs,félin < cs,canin.
Ces résultats démontrent que la cornée féline présente des caractéristiques biomécaniques plus proches de celles de la cornée canine, reflétant des réponses hyper-viscoélastiques similaires. Le modèle fournit une base de calcul validée pour l’évaluation de la rigidité cornéenne et soutient les futures études d’élastographie par ondes de cisaillement en ophtalmologie comparative et vétérinaire.
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Mots-clés : Cornée féline, Modélisation par éléments finis, Élastographie par ondes de cisaillement, Hyper-viscoélasticité, Biomécanique comparative, Simulation numérique
Pouria Mazinani 1
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Pouria Mazinani. Finite element simulation for finding shear wave velocity on the Feline cornea and Comparison with shear wave velocity on human cornea, canine, and keratoconus. Comptes Rendus. Mécanique, Volume 354 (2026), pp. 527-541. doi: 10.5802/crmeca.359
@article{CRMECA_2026__354_G1_527_0,
author = {Pouria Mazinani},
title = {Finite element simulation for finding shear wave velocity on the {Feline} cornea and {Comparison} with shear wave velocity on human cornea, canine, and keratoconus},
journal = {Comptes Rendus. M\'ecanique},
pages = {527--541},
year = {2026},
publisher = {Acad\'emie des sciences, Paris},
volume = {354},
doi = {10.5802/crmeca.359},
language = {en},
}
TY - JOUR AU - Pouria Mazinani TI - Finite element simulation for finding shear wave velocity on the Feline cornea and Comparison with shear wave velocity on human cornea, canine, and keratoconus JO - Comptes Rendus. Mécanique PY - 2026 SP - 527 EP - 541 VL - 354 PB - Académie des sciences, Paris DO - 10.5802/crmeca.359 LA - en ID - CRMECA_2026__354_G1_527_0 ER -
%0 Journal Article %A Pouria Mazinani %T Finite element simulation for finding shear wave velocity on the Feline cornea and Comparison with shear wave velocity on human cornea, canine, and keratoconus %J Comptes Rendus. Mécanique %D 2026 %P 527-541 %V 354 %I Académie des sciences, Paris %R 10.5802/crmeca.359 %G en %F CRMECA_2026__354_G1_527_0
[1] Animal models in eye research: focus on corneal pathologies, Int. J. Mol. Sci., Volume 24 (2023), 16661 | DOI
[2] In vivo biomechanical measurements of the cornea, Bioengineering, Volume 10 (2023) no. 1, 120 | DOI
[3] A generalised plate with kinematically independent thickness for modelling shapes of corneas affected by keratoconus before and after penetrating keratoplasty, Math. Mech. Solids (2025) | DOI
[4] A numerical comparison of the uniformly valid asymptotic plate equations with a 3D model: clamped rectangular incompressible elastic plates, Math. Mech. Solids, Volume 27 (2022) no. 8, pp. 1370-1396 | DOI | MR
[5] Wrinkling of twisted thin films, Int. J. Solids Struct., Volume 262 (2023), 112075
[6] A continuum model based on Rayleigh dissipation functions to describe a Coulomb-type constitutive law for internal friction in woven fabrics, Z. Angew. Math. Phys., Volume 73 (2022) no. 5, 209 | DOI | MR
[7] A Biot–Cosserat two-dimensional elastic nonlinear model for a micromorphic medium, Contin. Mech. Thermodyn., Volume 32 (2020) no. 5, pp. 1357-1369 | DOI | MR
[8] Material characterization and computations of a polymeric metamaterial with a pantographic substructure, Z. Angew. Math. Phys., Volume 69 (2018) no. 4, 105 | DOI | MR
[9] Second-gradient continua: From Lagrangian to Eulerian and back, Math. Mech. Solids, Volume 27 (2022) no. 12, pp. 2715-2750 | DOI
[10] Piola transformations in second-gradient continua, Mech. Res. Commun., Volume 120 (2022), 103836 | DOI
[11] Analytical continuum mechanics à la Hamilton–Piola least action principle for second gradient continua and capillary fluids, Math. Mech. Solids, Volume 20 (2015) no. 4, pp. 375-417 | DOI
[12] Lagrangian and Eulerian formulations of second-grade elasticity via convected coordinates, Math. Mech. Complex Syst., Volume 13 (2025) no. 3, pp. 377-389 | DOI | MR
[13] Deformation of an elastic second gradient spherical body under equatorial line density of dead forces, Eur. J. Mech. A Solids, Volume 103 (2024), 105153 | DOI | MR
[14] A comparison between the finite element method and a kinematic model derived from robot swarms for first and second gradient continua, Contin. Mech. Thermodyn., Volume 35 (2023) no. 4, pp. 1769-1786 | DOI
[15] A kinematic swarm-based approach for simulating stress-strain curves, Math. Mech. Complex Syst., Volume 13 (2025) no. 2, pp. 99-125 | DOI
[16] Viscous second gradient porous materials for bones reconstructed with bio-resorbable grafts, Extreme Mech. Lett., Volume 13 (2017), pp. 141-147 | DOI
[17] Simplified analysis of a generalized bias test for fabrics with two families of inextensible fibres, Z. Angew. Math. Phys., Volume 67 (2016) no. 3, 61 | DOI
[18] Towards the synthesis of planar beams whose deformation energy depends on the third gradient of displacement, Math. Mech. Complex Syst., Volume 12 (2024) no. 4, pp. 573-597 | DOI
[19] Planar one-dimensional continua whose energy depends on the gradient of curvature: an overview of their applications in metamaterials design, Math. Mech. Complex Syst., Volume 13 (2025) no. 2, pp. 127-166 | DOI | MR
[20] A study about the impact of the topological arrangement of fibers on fiber-reinforced composites: some guidelines aiming at the development of new ultra-stiff and ultra-soft metamaterials, Int. J. Solids Struct., Volume 203 (2020), pp. 73-83 | DOI
[21] Deformation patterns in a second-gradient lattice annular plate composed of “spira mirabilis” fibers, Contin. Mech. Thermodyn., Volume 35 (2023) no. 4, pp. 1561-1580 | MR | DOI
[22] Lattice shells composed of two families of curved Kirchhoff rods: an archetypal example, topology optimization of a cycloidal metamaterial, Contin. Mech. Thermodyn., Volume 33 (2021) no. 4, pp. 1063-1082 | DOI | MR
[23] A Green operator-based elastic modeling for two-phase pantographic-inspired bi-continuous materials, Int. J. Solids Struct., Volume 188 (2020), pp. 282-308 | DOI
[24] Symmetrization of mechanical response in fibrous metamaterials through micro-shear deformability, Symmetry, Volume 14 (2022) no. 12, 2660 | DOI
[25] Synthesis of fibrous complex structures: designing microstructure to deliver targeted macroscale response, Appl. Mech. Rev., Volume 67 (2015) no. 6, 060804
[26] A mixed Cosserat and higher gradient formulation for fibrous tissues and biomaterials, Int. J. Solids Struct., Volume 324 (2026), 113671 | DOI
[27] Chirality in 2D Cosserat media related to stretch-micro-rotation coupling with links to granular micromechanics, Int. J. Solids Struct., Volume 202 (2020), pp. 28-38 | DOI
[28] Experimental verification of 2D cosserat chirality with stretch-micro-rotation coupling in orthotropic metamaterials with granular motif, Mech. Res. Commun., Volume 126 (2022), 104020 | DOI
[29] On rotational instability within the nonlinear six-parameter shell theory, Int. J. Solids Struct., Volume 196 (2020), pp. 179-189 | DOI
[30] A new deformation measure for the nonlinear micropolar continuum, Z. Angew. Math. Phys., Volume 73 (2022) no. 2, 78 | MR | DOI
[31] A Biot–Cosserat two-dimensional elastic nonlinear model for a micromorphic medium, Contin. Mech. Thermodyn., Volume 32 (2020) no. 5, pp. 1357-1369 | MR | DOI
[32] At the origins and in the vanguard of peridynamics, non-local and higher-gradient continuum mechanics: an underestimated and still topical contribution of Gabrio Piola, Math. Mech. Solids, Volume 20 (2015) no. 8, pp. 887-928 | DOI | MR
[33] Nonlocal strain gradient elastic beam models with two-step differential approach and decoupling of standard and extra boundary conditions, I, Math. Mech. Complex Syst., Volume 10 (2022) no. 3, pp. 205-231 | DOI | MR
[34] Microscopic, kinetic and hydrodynamic hybrid models of collective motions with chemotaxis: a numerical study, Math. Mech. Complex Syst., Volume 12 (2023) no. 1, pp. 47-83 | DOI | MR
[35] On mechanically driven biological stimulus for bone remodeling as a diffusive phenomenon, Biomech. Model. Mechanobiol., Volume 18 (2019) no. 6, pp. 1639-1663 | DOI
[36] Modeling of a non-local stimulus for bone remodeling process under cyclic load: application to a dental implant using a bioresorbable porous material, Math. Mech. Solids, Volume 22 (2017) no. 9, pp. 1790-1805 | DOI | MR
[37] A bone remodeling approach encoding the effect of damage and a diffusive bio-mechanical stimulus, Contin. Mech. Thermodyn., Volume 36 (2024) no. 4, pp. 993-1012 | DOI | MR
[38] An orthotropic continuum model with substructure evolution for describing bone remodeling: an interpretation of the primary mechanism behind Wolff’s law, Biomech. Model. Mechanobiol., Volume 22 (2023) no. 6, pp. 2135-2152 | DOI
[39] Wave motions in unbounded poroelastic solids infused with compressible fluids, Z. Angew. Math. Phys., Volume 53 (2002) no. 6, pp. 1110-1138 | DOI
[40] A continuum model for deformable, second gradient porous media partially saturated with compressible fluids, J. Mech. Phys. Solids, Volume 61 (2013) no. 11, pp. 2196-2211 | DOI
[41] Boundary conditions at fluid-permeable interfaces in porous media: a variational approach, Int. J. Solids Struct., Volume 46 (2009) no. 17, pp. 3150-3164 | DOI
[42] Fluid diffusion related aging effect in a concrete dam modeled as a Timoshenko beam, Math. Mech. Complex Syst., Volume 11 (2023) no. 2, pp. 313-334 | DOI | MR
[43] Bio-inspired design of a porous resorbable scaffold for bone reconstruction: a preliminary study, Biomimetics, Volume 6 (2021) no. 1, 18 | DOI
[44] A proposal for a novel formulation based on the hyperbolic Cattaneo’s equation to describe the mechano-transduction process occurring in bone remodeling, Symmetry, Volume 14 (2022) no. 11, 2436 | DOI
[45] Comparative morphological evaluation of domestic animal cornea, Vet. Ophthalmol., Volume 19 (2015) no. 4, pp. 297-304 | DOI
[46] Veterinary Ophthalmology, Wiley-Blackwell, Ames, IA, 2013
[47] The organization of collagen in the corneal stroma, Exp. Eye Res., Volume 78 (2004) no. 3, pp. 503-512 | DOI
[48] A comparison of the intrarectal and intramuscular effects of a dexmedetomidine, ketamine and midazolam mixture on tear production in cats: a randomized controlled trial, Animals, Volume 14 (2024) no. 1, 145 | DOI
[49] Veterinary Ocular Pathology: A Comparative Review, Saunders (Elsevier), Edinburgh, New York, 2010
[50] Essentials of Veterinary Ophthalmology, John Wiley & Sons, New York, 2022 (ISBN 978-1119801320) | DOI
[51] Through the cat-map gateway: a brief history of cataract genetics, Genes, Volume 15 (2024) no. 6, 785 | DOI
[52] Corneal biomechanical stiffness and histopathological changes after in vivo repeated accelerated corneal cross-linking in cat eyes, Exp. Eye Res., Volume 227 (2023), 109363 | DOI
[53] The influence of hydration on different mechanical moduli of the cornea, Graefes Arch. Clin. Exp. Ophthalmol., Volume 256 (2018) no. 9, pp. 1653-1660 | DOI
[54] An inverse finite element method for determining the anisotropic properties of the cornea, Biomech. Model. Mechanobiol., Volume 10 (2011) no. 3, pp. 323-337 | DOI
[55] Photorefractive keratectomy in the cat eye: biological and optical outcomes, J. Cataract Refract. Surg., Volume 33 (2007) no. 6, pp. 1051-1064 | DOI
[56] Characterization of non-linear mechanical behavior of the cornea, Sci. Rep., Volume 10 (2020) no. 1, 11549 | DOI
[57] Shear wave elastography in ophthalmic diagnosis, J. Fr. Ophtalmol., Volume 42 (2019) no. 1, pp. 73-80 | DOI
[58] Relationship between corneal sensitivity, corneal thickness, corneal diameter, and intraocular pressure in normal cats and cats with congenital glaucoma, Vet. Ophthalmol., Volume 22 (2019) no. 1, pp. 4-12 | DOI
[59] In vivo human corneal shear-wave optical coherence elastography, Optom. Vis. Sci., Volume 98 (2021) no. 1, pp. 58-63 | DOI
[60] Effect of body position, eyelid manipulation, and manual jugular compression on intraocular pressure in clinically normal cats, Vet. Ophthalmol., Volume 21 (2018) no. 2, pp. 140-143 | DOI
[61] Hydration-Dependent Structuring in the Cornea: A Model for Bound Water in Collagenous Tissues, McGill University, Canada, 2023
[62] Assessment of corneal viscoelasticity using elastic wave optical coherence elastography, J. Biophotonics, Volume 13 (2020) no. 1, e201960074
[63] Finite element model of cornea deformation, International Conference on Medical Image Computing and Computer-Assisted Intervention, Springer, Berlin, Heidelberg (2005), pp. 591-598
[64] Finite element modeling of corneal biomechanical behavior, J. Refract. Surg., Volume 26 (2010) no. 4, pp. 289-300 | DOI
[65] A review of human cornea finite element modeling: geometry modeling, constitutive modeling, and outlooks, Front. Bioeng. Biotechnol., Volume 12 (2024), 1455027 | DOI
[66] Evaluating corneal biomechanics using shear wave elastography and finite element modeling: sensitivity analysis and parametric optimization, Continuum. Mech. Thermodyn., Volume 37 (2025), 12 | DOI
[67] Multiple optical elastography techniques reveal the regulation of corneal stiffness by collagen XII, Invest. Ophthalmol. Vis. Sci., Volume 63 (2022) no. 12, 24 | DOI
[68] Advances in corneal imaging: current applications and beyond, Asia-Pac. J. Ophthalmol., Volume 8 (2019) no. 2, pp. 105-114
[69] Ophthalmology of felidae: cats, Wild and Exotic Animal Ophthalmology: Volume 2: Mammals, Springer, Cham (2022), pp. 155-180 | DOI
[70] Characterization of plaque components with intravascular ultrasound elastography in human femoral and coronary arteries in vitro, Circulation, Volume 102 (2000) no. 6, pp. 617-623 | DOI
[71] Biomechanical properties of human and porcine corneas, Exp. Eye Res., Volume 86 (2008) no. 5, pp. 783-790 | DOI
[72] Ocular biomechanics and biotransport, Annu. Rev. Biomed. Eng., Volume 6 (2004), pp. 249-273 | DOI
[73] Corneal hyper-viscoelastic model: Derivations, experiments, and simulations, Acta Bioeng. Biomech., Volume 17 (2015) no. 2, pp. 73-84
[74] Liver fibrosis in viral hepatitis: Noninvasive assessment with acoustic radiation force impulse imaging versus transient elastography, Radiology, Volume 252 (2009) no. 2, pp. 595-604 | DOI
[75] Constitutive laws for biomechanical modeling of refractive surgery, J. Biomech. Eng., Volume 118 (1996) no. 4, pp. 473-481 | DOI
[76] Corneal thickness and diameter in the domestic cat, Ophthalmic Physiol. Opt., Volume 6 (1986) no. 4, pp. 385-389 | DOI
[77] Corneal hyper-viscoelastic model: derivations, experiments, and simulations, Acta Bioeng. Biomech., Volume 17 (2015) no. 2, pp. 73-84
[78] Corneal viscoelastic properties from finite-element analysis of in vivo air-puff deformation, PLoS One, Volume 9 (2014) no. 8, e104904 | DOI
[79] High-resolution shear wave imaging of the human cornea using a dual-element transducer, Sensors, Volume 18 (2018) no. 12, 4244 | DOI
[80] Correlation of corneal acoustic and elastic properties in a canine eye model, Invest. Ophthalmol. Vis. Sci., Volume 52 (2011) no. 2, pp. 731-736 | DOI
[81] Evaluating corneal biomechanics using intraocular pressure methods and finite element modeling: parameters study and parametric optimization, Z. Angew. Math. Phys., Volume 76 (2025), 220 | MR | DOI
[82] Finite element simulation for finding shear wave velocity on the canine cornea and sensitivity analysis for IOP parameter, Mech. Res. Commun., Volume 150 (2025), 104558 | DOI
[83] Shear wave velocity and finite element modeling for understanding keratoconus biomechanics: comparison with healthy cornea, Math. Mech. Solids (2025) | DOI
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