Finite element modeling of the complex anisotropic mechanical behavior of the human sclera and pia mater

Alireza Karimi; Seyed Mohammadali Rahmati; Reza Razaghi; Christopher A Girkin; J Crawford Downs

doi:10.1016/j.cmpb.2022.106618

Finite element modeling of the complex anisotropic mechanical behavior of the human sclera and pia mater

Comput Methods Programs Biomed. 2022 Mar:215:106618. doi: 10.1016/j.cmpb.2022.106618. Epub 2022 Jan 4.

Authors

Alireza Karimi¹, Seyed Mohammadali Rahmati², Reza Razaghi³, Christopher A Girkin⁴, J Crawford Downs⁵

Affiliations

¹ Department of Ophthalmology and Visual Sciences, University of Alabama at Birmingham, Birmingham, AL, USA. Electronic address: akarimi@uabmc.edu.
² School of Biological Sciences, Georgia Institute of Technology, Atlanta, GA, USA.
³ Research Department, Heel of Scene Ltd., Tokyo, Japan.
⁴ Department of Ophthalmology and Visual Sciences, University of Alabama at Birmingham, Birmingham, AL, USA. Electronic address: cgirkin@uabmc.edu.
⁵ Department of Ophthalmology and Visual Sciences, University of Alabama at Birmingham, Birmingham, AL, USA. Electronic address: cdowns@uabmc.edu.

Abstract

Background and objective: Accurate finite element (FE) simulation of the optic nerve head (ONH) depends on accurate mechanical properties of the load-bearing tissues. The peripapillary sclera in the ONH exhibits a depth-dependent, anisotropic, heterogeneous collagen fiber distribution. This study proposes a novel cable-in-solid modeling approach that mimics heterogeneous anisotropic collagen fiber distribution, validates the approach against published experimental biaxial tensile tests of scleral patches, and demonstrates its effectiveness in a complex model of the posterior human eye and ONH.

Methods: A computational pipeline was developed that defines control points in the sclera and pia mater, distributes the depth-dependent circumferential, radial, and isotropic cable elements in the sclera and pia in a pattern that mimics collagen fiber orientation, and couples the cable elements and solid matrix using a mesh-free penalty-based cable-in-solid algorithm. A parameter study was performed on a model of a human scleral patch subjected to biaxial deformation, and computational results were matched to published experimental data. The new approach was incorporated into a previously published eye-specific model to test the method; results were then interpreted in relation to the collagen fibers' (cable elements) role in the resultant ONH deformations, stresses, and strains.

Results: Results show that the cable-in-solid approach can mimic the full range of scleral mechanical behavior measured experimentally. Disregarding the collagen fibers/cable elements in the posterior eye model resulted in ∼20-60% greater tensile and shear stresses and strains, and ∼30% larger posterior deformations in the lamina cribrosa and peripapillary sclera.

Conclusions: The cable-in-solid approach can easily be implemented into commercial FE packages to simulate the heterogeneous and anisotropic mechanical properties of collagenous biological tissues.

Keywords: Finite element; Mesh-free; Ocular Biomechanics; Optic nerve head; Penalty-based cable-in-solid; Pia; Sclera.

MeSH terms

Biomechanical Phenomena
Finite Element Analysis
Humans
Models, Biological
Pia Mater*
Sclera*

Abstract

MeSH terms

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