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Three-dimensional biomechanical modeling and simulation of trephine cutting cornea for keratoplasty

Su P., Lu D., Deng S., Zhang L., Hao Y., Yang Y.

Acta of Bioengineering and Biomechanics

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2018

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Vol. 20, no. 2

23--33

EN

Trephination is one of the basic operations of keratoplasty, and the biomechanical mechanism of the operation can be revealed based on three-dimensional modeling and simulation of trephine cutting cornea. Methods: Based on the analysis of the physical and biomechanical characteristics of corneal trephination, a three-dimensional numerical model of corneal trephination is built, where the cornea can be simplified to two layers structure including stroma and epithelium, and the trephine cuts the cornea under the vertical motion load and the rotational motion load. A three-dimensional failure criterion of corneal material is proposed based on the yield strength theory. On this basis, trephination simulation is carried out, and the units of corneal material are removed from the model when they meet the defined failure criterion. Results: Under the given parameters including the velocity, the angle and the angular velocity, the trephine force curves, include the linear cutting force and the rotary cutting force are obtained, and show the change of the forces with displacement during the process of trephination simulation. The maps of the equivalent stress show the destruction and deformation of the cornea. Then, the experiment of robotic trephination is carried out under the same parameters and the effectiveness of the simulation is evaluated. Conclusions: Based on mechanics theory and finite element method, the process of trephine cutting cornea has been reproduced, and the interaction mechanism is revealed, which lays the foundation for the development of real-time simulation and virtual system of the corneal surgery.

2

Biomechanical simulation of needle insertion into cornea based on distortion energy failure criterion

Su P., Yang Y., Huang L.

Acta of Bioengineering and Biomechanics

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2016

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Vol. 18, no. 1

65--75

EN

Purpose: This paper is mainly about biomechanical behavior of needle insertion into cornea, and proposes a failure criterion to simulate the insertion process which has attracted considerable attention due to its importance for the minimally invasive treatment. Methods: In the process of needle insertion into cornea, tiny and complex insertion force is generated due to contact between needle and soft tissue. Based on the distortion energy theory, there is proposed a failure criterion of corneal material that can solve contact problem between rigid body and biological tissue in insertion simulation, where Cauchy stress of corneal material is the key to numerical calculation. A finite element model of in vivo cornea is built, and the cornea constrained by sclera is simplified to two layers containing epithelium and stroma. Considering the hyper-viscoelastic property of corneal material, insertion simulation is carried out. Results: By insertion experiment, the insertion force increases with insertion depth accompanying obvious fluctuations. Different insertion forces are generated at different speeds. The punctured locations are obvious in the force-displacement curves. The results of insertion simulation are generally consistent with experimental data. Maps of von Mises stress reflect the tissue injury of the cornea during insertion process, and punctured status corresponds to the point in the curves. Conclusions: The ability of this study to reproduce the behavior of needle insertion into cornea opens a promising perspective for the control of robotic surgery operation as well as the real-time simulation of corneal suture surgery.

3

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

Su P., Yang Y., Song Y

Acta of Bioengineering and Biomechanics

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2015

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Vol. 17, no. 2

73--84

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.