Corneal hyper-viscoelastic model: derivations, experiments, and simulations

• Autorzy: Su P. , Yang Y. , Song Y

Identyfikatory

DOI

10.5277/ABB-00142-2014-03

• Języki publikacji: EN

Abstrakty

EN

Purpose: The aim of this study is to propose a method to construct corneal biomechanical model which is the foundation for simulation of corneal microsurgery. Methods: Corneal material has two significant characteristics: hyperelastic and viscoelastic. Firstly, Mooney–Rivlin hyperelastic model of cornea obtained based on stored-energy function can be simplified as a linear equation with two unknown parameters. Then, modified Maxwell viscoelastic model of the cornea, whose analytical form is consistent with the generalized Prony-series model, is proposed from the perspective of material mechanics. Results: Parameters of the model are determined by the uniaxial tensile tests and the stress-relaxation tests. Corneal material properties are simulated to verify the hyper-viscoelastic model and measure the effectiveness of the model in the finite element simulation. On this basis, an in vivo model of the corneal is built. And the simulation of extrusion in vivo cornea shows that the force is roughly nonlinearly increasing with displacement, and it is consistent with the results obtained by extrusion experiment of in vivo cornea. Conlusions: This paper derives a corneal hyper-viscoelastic model to describe the material properties more accurately, and explains the mathematical method for determination of the model parameters. The model is an effective biomechanical model, which can be directly used for simulation of trephine and suture in keratoplasty. Although the corneal hyper-viscoelastic model is taken as the object of study, the method has certain adaptability in biomechanical research of ophthalmology.

Słowa kluczowe

EN

cornea; biomechanics; constitutive model; hyperelastic; viscoelastic

PL

rogówka; biomechanika; hiperelastyczność; lepkosprężystość

• Wydawca: Oficyna Wydawnicza Politechniki Wrocławskiej
• Czasopismo: Acta of Bioengineering and Biomechanics
• Rocznik: 2015
• Tom: Vol. 17, no. 2
• Strony: 73--84
• Opis fizyczny: Bibliogr. 30 poz., rys., tab., wykr.

Twórcy

autor

Su P.

• School of Mechanical Engineering and Automation, BeiHang University, People’s Republic of China

autor

Yang Y.

• School of Mechanical Engineering and Automation, BeiHang University, People’s Republic of China

autor

Song Y

• School of Mechanical Engineering and Automation, BeiHang University, People’s Republic of China

Bibliografia

• [1] ANDERSON K., EL-SHEIKH A., NEWSON T., Application of structural analysis to the mechanical behaviour of the cornea, J. R. Soc. Interface, 2004, 1(1), 3–15.
• [2] ASEJCZYK-WIDLICKA M., SRODKA W., SCHACHAR R.A., PIERSCIONEK B.K., Material properties of the cornea and sclera: A modelling approach to test experimental analysis, J. Biomech., 2011, 44(3), 543–546.
• [3] BATTAGLIOLI J.L., KAMM R.D., Measurements of the compressive properties of scleral tissue, Invest. Ophth. Vis. Sci., 1984, 25(1), 59–65.
• [4] BERKLEY J., TURKIYYAH G., BERG D., GANTER M., WEGHORST S., Real-time finite element modeling for surgery simulation: An application to virtual suturing, IEEE T Vis. Comput. Gr., 2004, 10(3), 314–325.
• [5] BRYANT M.R., MCDONNELL P.J., Constitutive laws for biomechanical modeling of refractive surgery, J. Biomech. Eng.-T ASME, 1996, 118(4), 473–481.
• [6] CHRISTENSEN R.M., Theory of Viscoelasticity, Academic Press, New York, 1982.
• [7] DOGHRI I., Nonlinear continuum mechanics, Springer, Berlin–Heidelberg, 2000.
• [8] EHLERS N., HJORTDAL J., Corneal thickness: measurement and implications, Exp. Eye Res., 2004, 78(3), 543–548.
• [9] ELSHEIKH A., ALHASSO D., RAMA P., Biomechanical properties of human and porcine corneas, Exp. Eye Res., 2008, 86(5), 783–790.
• [10] ETHIER C.R., JOHNSON M., RUBERTI J., Ocular biomechanics and biotransport, Annu. Rev. Biomed. Eng., 2004, 6, 249– 273.
• [11] FRATZL P., MISOF K., ZIZAK I., Fibrillar structure and mechanical properties of collagen, J. Struct. Biol., 1998, 122(1), 119–122.
• [12] HAMEED-SAYED A.A., SOLOUMA N.H., EL-BERRY A.A., KADAH Y.M., Finite element models for computer simulation of intrastromal photorefractive keratectomy, J. Mech. Med. Biol., 2011, 11(05), 1255–1270.
• [13] HATAMI-MARBINI H., Viscoelastic shear properties of the corneal stroma, J. Biomech., 2014, 47(3), 723–728.
• [14] HATAMI-MARBINI H., ETEBU E., An experimental and theoretical analysis of unconfined compression of corneal stroma, J. Biomech., 2013, 46(10), 1752–1758.
• [15] HENDRIKS F.M., BROKKEN D., OOMENS C.W., BADER D.L., BAAIJENS F.P., The relative contributions of different skin layers to the mechanical behavior of human skin in vivo using suction experiments, Med. Eng. Phys., 2006, 28(3), 259–266.
• [16] HJORTDAL J.O., Regional elastic performance of the human cornea, J. Biomech., 1996, 29(7), 931–942.
• [17] HOLZAPFEL G.A., Nonlinear solid mechanics, Chichester, Wiley, 2000.
• [18] KAMPMEIER J., RADT B., BIRNGRUBER R., BRINKMANN R., Thermal and biomechanical parameters of porcine cornea, Cornea, 2000, 19(3), 355–363.
• [19] KARALIS T.K., A model for corneal swelling, J. Mech. Med. Biol., 2008, 8(04), 473–489.
• [20] KUNTER F.C., SEKER S.S., Web-spline prediction of ocular supface temperature using bioheat equation with external source exposure, J. Mech. Med. Biol., 2013, 14(1), 1450009.
• [21] LI L., TIGHE B., The anisotropic material constitutive models for the human cornea, J. Struct. Biol., 2006, 153(3), 223–230.
• [22] OGDEN R.W., Non-linear elastic deformations, Courier Dover Publications, 1997.
• [23] PANDOLFI A., MANGANIELLO F., A model for the human cornea: constitutive formulation and numerical analysis, Biomech. Model Mechan., 2006, 5(4), 237–246.
• [24] PINSKY P., VAN-DER-HEIDE D., CHERNYAK D., Computational modeling of mechanical anisotropy in the cornea and sclera, J. Cataract. Refract. Surg., 2005, 31(1), 136–145.
• [25] SCHAPERY R.A., Nonlinear viscoelastic solids, Int. J. Solids Struct., 2000, 37(1), 359–366.
• [26] STUDER H., LARREA X., RIEDWYL H., BUCHLER P., Biomechanical model of human cornea based on stromal microstructure, J. Biomech., 2010, 43(5), 836–842.
• [27] THOMASY S.M., RAGHUNATHAN V.K., WINKLERB M., REILLY C.M. et al., Elastic modulus and collagen organization of the rabbit cornea: Epithelium to endothelium, Acta Biomater., 2014, 10(2), 785–791.
• [28] WILDNAUER R.H., BOTHWELL J.W., DOUGLASS A.B., Stratum corneum biomechanical properties I. Influence of relative humidity on normal and extracted human stratum corneum, J. Invest. Dermatol., 1971, 56(1), 72–78.
• [29] WOO S.L., KOBAYASHI A.S., SCHLEGEL W.A., LAWRENCE C., Nonlinear material properties of intact cornea and sclera, Eep. Eye Res., 1972, 14(1), 29–39.
• [30] ZENG Y., YANG J., HUANG K., LEE Z., LEE X., A comparison of biomechanical properties between human and porcine cornea, J. Biomech., 2001, 34(4), 533–537.