Research Papers

Finite Element Biomechanics of Optic Nerve Sheath Traction in Adduction

[+] Author and Article Information
Andrew Shin

Department of Ophthalmology,
Stein Eye Institute,
Los Angeles, CA 90095

Lawrence Yoo

Department of Ophthalmology,
Stein Eye Institute,
Los Angeles, CA 90095;
Intelon Optics Inc.,
Cambridge, MA 02138-4430

Joseph Park

Department of Ophthalmology,
Stein Eye Institute,
Los Angeles, CA 90095;
Department of Mechanical Engineering,
University of California,
Los Angeles, CA 90095

Joseph L. Demer

Arthur L. Rosenbaum Professor of Pediatric Ophthalmology Department of Ophthalmology, Stein Eye Institute, Los Angeles, CA 90095 e-mail: jld@jsei.ucla.edu; Biomedical Engineering Interdepartmental Program, University of California, Los Angeles, CA 90095;Neuroscience Interdepartmental Program, University of California, Los Angeles, CA 90095; Department of Neurology, University of California, Los Angeles, CA 90095

1Corresponding author.

Manuscript received March 28, 2017; final manuscript received July 28, 2017; published online August 25, 2017. Assoc. Editor: Thao (Vicky) Nguyen.

J Biomech Eng 139(10), 101010 (Aug 25, 2017) (10 pages) Paper No: BIO-17-1133; doi: 10.1115/1.4037562 History: Received March 28, 2017; Revised July 28, 2017

Historical emphasis on increased intraocular pressure (IOP) in the pathogenesis of glaucoma has been challenged by the recognition that many patients lack abnormally elevated IOP. We employed finite element analysis (FEA) to infer contribution to optic neuropathy from tractional deformation of the optic nerve head (ONH) and lamina cribrosa (LC) by extraocular muscle (EOM) counterforce exerted when optic nerve (ON) redundancy becomes exhausted in adduction. We characterized assumed isotropic Young's modulus of fresh adult bovine ON, ON sheath, and peripapillary and peripheral sclera by tensile elongation in arbitrary orientations of five specimens of each tissue to failure under physiological temperature and humidity. Physical dimensions of the FEA were scaled to human histological and magnetic resonance imaging (MRI) data and used to predict stress and strain during adduction 6 deg beyond ON straightening at multiple levels of IOP. Young's modulus of ON sheath of 44.6 ± 5.6 MPa (standard error of mean) greatly exceeded that of ON at 5.2 ± 0.4 MPa, peripapillary sclera at 5.5 ± 0.8 MPa, and peripheral sclera at 14.0 ± 2.3 MPa. FEA indicated that adduction induced maximum stress and strain in the temporal ONH. In the temporal LC, the maximum stress was 180 kPa, and the maximum strain was ninefold larger than produced by IOP elevation to 45 mm Hg. The simulation suggests that ON sheath traction by adduction concentrates far greater mechanical stress and strain in the ONH region than does elevated IOP, supporting the novel concept that glaucomatous optic neuropathy may result at least partly from external traction on the ON, rather than exclusively on pressure on the ON exerted from within the eye.

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Fig. 1

Previously unpublished T2-weighted axial (left) and quasi-coronal (right) MRI of a normal right adult orbit from the study of Demer [5] showing that the sinuous ON in abduction (a) straightens in adduction (c). Quasi-coronal images obtained in the same eye positions show that in adduction, the ON shifts temporally as the CSF (bright ring surrounding the dark ON) within the ON sheath (dark ring) shifts nasally. LR—lateral rectus muscle and MR—medial rectus muscle.

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Fig. 2

Tensile loading apparatus and specimen clamping. (a) The Linear motor on the left was connected to a strain gauge transmitting its measured tensile force through a frictionless air bearing and cylindrical shaft to the moveable specimen clamp to which one end of the specimen was affixed in an environmentally controlled chamber at right. The other clamp at right was rigidly anchored at the opposite end of the specimen. ON (b), ON sheath (c), and sclera (d) were similarly clamped at each end.

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Fig. 3

Representative preconditioning curves for human sclera and ON sheath. Cyclic loading was up to 5% of the initial length. Dotted lines illustrate the elastic stiffness of each loading cycle; slopes of these lines did not change significantly during cyclic loading.

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Fig. 4

Hemisected axial view of FEM. The sclera is divided into peripheral (①) and peripapillary regions (②), with LC (③) attached to the ON (④) and posterior sclera attached to the ON sheath (⑤) that also contains CSF (⑥).

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Fig. 5

Masson's trichrome-stained transverse histological section of retrobulbar ON from a 57-year-old human 1.84 mm posterior to the globe. Collagen stains blue, nerve tissue purple, and acellular protein in the cerebrospinal space pink. (a) The ON sheath is the external blue ring surrounding the light pink of the CSF space that bathes the ON within it. (b) Magnified view of red circle area illustrating the intimate connection between pia and the dense blue network of connective tissue within the ON. It is thus reasonable to model the ON and its incorporated pia and connective tissue as one composite structure.

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Fig. 6

Mesh convergence. Strain simulations for LC and ON sheath were plotted from small (30 and 80 μm) to large (70 and 110 μm) mesh size by 10 μm increment. Appropriate mesh size was determined to be 50 μm for LC and 100 μm for ON sheath by balancing simulation accuracy against the computational load.

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Fig. 7

Mean tensile behavior of five samples of each of ON sheath (a), ON (b), peripapillary sclera (c), and peripheral sclera (d). Young's moduli were calculated from each linear regions as 44.6 ± 5.6 (standard error of mean) MPa for ON sheath, 5.2 ± 0.4 MPa for ON, 5.5 ± 0.8 MPa for peripapillary sclera, and 14.0 ± 2.3 MPa for peripheral sclera.

Grahic Jump Location
Fig. 8

FEA of von Mises stress ((a) and (c)) and strain ((b) and (d)) in ON sheath and posterior sclera in adduction 6 deg past the point of ON straightening, assuming 15 mm Hg IOP and 136 mm H2O ICP. For visualization, a hemisected view is shown with the temporal side oriented upward. (c) Magnified view showing maximum stress generated at the junction of ON, ON sheath, and sclera, propagating widely from the temporal peripapillary region to a wide zone of the temporal inner sclera, including the macular region. (d) Magnified view showing maximum strain is induced in two areas: temporal peripapillary sclera adjacent to the stiff ON sheath and temporal LC.

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Fig. 9

FEA of posterior globe before and after adduction 6 deg past the point of ON straightening. (a) Before adduction rendered in green. (b) After adduction, rendered in red, the temporal peripapillary sclera was deformed. (c) Overlay of (a) and (b), so that overlapping area is yellowish. The ONH tilted temporally in adduction.

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Fig. 10

FEA of strain in the LC during adduction from the point of ON straightening (top) to an additional 6 deg adduction (bottom) assuming 15 mm Hg IOP and 136 mm H2O ICP. While there is a little deformation of the nasal LC, the temporal side exhibits shear with compression anteriorly and elongation posteriorly.

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Fig. 11

Sensitivity analysis of LC strain to variation in IOP, ICP, and adduction. (a) IOP was increased from 5 to 45 mm Hg with constant 136 mm H2O ICP, without adduction. For the 45 mm Hg IOP, approximately 2% strain was induced around the inner LC rim. (b) ICP was increased from 68 to 408 mm H2O while maintaining 15 mm Hg IOP, without adduction. There was no significant strain. (c) IOP was increased from 5 to 45 mm Hg with constant 136 mm H2O ICP, and with 6 deg adduction past the point of ON straightening, inducing strain exceeding 10% in temporal LC that increased only slightly with increasing IOP.

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Fig. 12

Hemisected axial rendering of the sensitivity of peripapillary and LC strain to variation in Young's elastic modulus of tissues in 6 deg adduction. Simulation input was 15 mm Hg IOP and 136 mm H2O ICP. (a) Magnified strain distribution assuming identical 3 MPa elastic modulus for all tissues. (b) Magnified strain distribution with measured individual bovine parameters for various tissues. Note that the strain distributions in (a) and (b) localize in qualitatively similar temporal regions, implying that the general phenomenon of temporal peripapillary strain is independent of precise local biomechanical properties. However, in (b) there is a greater strain in the temporal LC.

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Fig. 13

FEA of adduction 6 deg past the point of ON straightening, assuming mechanically distinguishable rather than composite ON pia and neural tissue. (a) Modified ON model with soft neural tissue surrounded by separable pia. Neural tissues enclosed by 0.06-mm thick pia are rendered as green. Stress (b) and strain (c) distributions are qualitatively similar to those in Figs. 7(c) and 7(d) that assumed ON and pia to be composite, except for greater strain in the temporal ONH in the mechanically distinguishable model due to the low elastic modulus of neural tissue when assumed to lack internal connective tissue support.

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Fig. 14

Tensile data compared with Mooney–Rivlin fits. Peripheral sclera, ON, and peripapillary sclera fitted experimental data reasonably, but the relatively linear Mooney–Rivlin model did not fit the ON sheath data well in the nonlinear, low-strain region.

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Fig. 15

FEA using Mooney–Rivlin hyperelastic model. (a) Magnified view of stress distribution showing maximum stress at the temporal junction of ON, ON sheath, and sclera, which is similar to the linear FEA stress result in Fig. 8(c). (b) Magnified view showing maximum strain at the temporal sclera–ON sheath junction and outer rim of LC that is also similar to the linear FEA strain result in Fig. 8(d).



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