An imaged-based inverse finite element method to determine in-vivo mechanical properties of the human trabecular meshwork

Anup D. Pant, Larry Kagemann, Joel S. Schuman, Ian A. Sigal, Rouzbeh Amini

Abstract


Aim/Purpose: Previous studies have shown that the trabecular meshwork (TM) is mechanically stiffer in glaucomatous eyes as compared to normal eyes. It is believed that elevated TM stiffness increases resistance to the aqueous humor outflow, producing increased intraocular pressure (IOP).It would be advantageous to measure TM mechanical properties in vivo, as these properties are believed to play an important role in the pathophysiology of glaucoma and could be useful for identifying potential risk factors.  The purpose of this study was to develop a method to estimate in-vivo TM mechanical properties using clinically available exams and computer simulations.

Design: Inverse finite element simulation

Methods: A finite element model of the TM was constructed from optical coherence tomography (OCT) images of a healthy volunteer before and during IOP elevation. An axisymmetric model of the TM was then constructed. Images of the TM at a baseline IOP level of 11, and elevated level of 23 mmHg were treated as the undeformed and deformed configurations, respectively. An inverse modeling technique was subsequently used to estimate the TM shear modulus (G). An optimization technique was used to find the shear modulus that minimized the difference between Schlemm’s canal area in the in-vivo images and simulations.

Results: Upon completion of inverse finite element modeling, the simulated area of the Schlemm’s canal changed from 8,889 μm2 to 2,088 μm2, similar to the experimentally measured areal change of the canal (from 8,889 μm2 to 2,100 μm2). The calculated value of shear modulus was found to be 1.93 kPa,  (implying an approximate Young’s modulus of 5.75 kPa), which is consistent with previous ex-vivo measurements.

Conclusion: The combined imaging and computational simulation technique provides a unique approach to calculate the mechanical properties of the TM in vivo without any surgical intervention. Quantification of such mechanical properties will help us examine the mechanistic role of TM biomechanics in the regulation of IOP in healthy and glaucomatous eyes.

 


Keywords


inverse algorithm, glaucoma, intraocular pressure (IOP), Schlemm’s canal, trabecular Meshwork

Full Text:

PDF

References


Tham Y, Li X, Wong TY, Quigley HA, Aung T, Cheng C. Global Prevalence of Glaucoma and Projections of Glaucoma Burden through 2040: A Systematic Review and Meta-Analysis. Ophthalmology 2014 11;121(11):2081-2090.

Grant WM, Burke JF. Why do some people go blind from glaucoma? Ophthalmology 1982;89(9):991-998.

Quigley HA, Broman AT. The number of people with glaucoma worldwide in 2010 and 2020. Br J Ophthalmol 2006 Mar;90(3):262-267.

Congdon N, O'Colmain B, Klaver CC, Klein R, Munoz B, Friedman DS, et al. Causes and prevalence of visual impairment among adults in the United States. Arch Ophthalmol 2004 Apr;122(4):477-485.

Alm A, Nilsson SF. Uveoscleral outflow–a review. Exp Eye Res 2009;88(4):760-768.

Kaufman PL, Adler FH, Levin LA, Alm A. Adler's Physiology of the Eye. New York: Elsevier Health Sciences; 2011:274.

Kahook MY, Schuman JS, Epstein DL. Chandler and Grant's Glaucoma. Thorofare, N.J.: SLACK Incorporated; 2013:8.

Rohen J, Witmer R. Electron microscopic studies on the trabecular meshwork in glaucoma simplex. Albrecht von Graefes Archiv für klinische und experimentelle Ophthalmologie 1972;183(4):251-266.

Mäepea O, Bill A. The pressures in the episcleral veins, Schlemm's canal and the trabecular meshwork in monkeys: effects of changes in intraocular pressure. Exp Eye Res 1989;49(4):645-663.

Acott TS, Kelley MJ. Extracellular matrix in the trabecular meshwork. Exp Eye Res 2008;86(4):543-561.

Gottanka J, Johnson DH, Martus P, Lütjen-Drecoll E. Severity of optic nerve damage in eyes with POAG is correlated with changes in the trabecular meshwork. J Glaucoma 1997;6(2):123-132.

Johnson D, Flügel C, Hoffmann F, Futa R, Lütjen-Drecoll E. Ultrastructural changes in the trabecular meshwork of human eyes treated with corticosteroids. Arch Ophthalmol 1997;115(3):375-383.

Gottanka J, Johnson DH, Grehn F, Lütjen-Drecoll E. Histologic findings in pigment dispersion syndrome and pigmentary glaucoma. J Glaucoma 2006;15(2):142-151.

Murphy CG, Johnson M, Alvarado JA. Juxtacanalicular tissue in pigmentary and primary open angle glaucoma the hydrodynamic role of pigment and other constituents. Arch Ophthalmol 1992;110(12):1779-1785.

Camras LJ, Stamer WD, Epstein D, Gonzalez P, Yuan F. Circumferential tensile stiffness of glaucomatous trabecular meshwork. Invest Ophthalmol Vis Sci 2014;55(2):814-823.

Alvarado J, Murphy C, Polansky J, Juster R. Age-related changes in trabecular meshwork cellularity. Invest Ophthalmol Vis Sci 1981;21(5):714-727.

Last JA, Pan T, Ding Y, Reilly CM, Keller K, Acott TS, et al. Elastic modulus determination of normal and glaucomatous human trabecular meshwork. Invest Ophthalmol Vis Sci 2011;52(5):2147-2152.

Russell P, Last J, Ding Y, Pan T, Acott T, Keller K, et al. Compliance and the human trabecular meshwork: implications about glaucoma. Invest Ophthalmol Vis Sci 2010;51(13):3205-3205.

Brouwer I, Ustin J, Bentley L, Sherman A, Dhruv N, Tendick. Measuring in vivo animal soft tissue properties for haptic modeling in surgical. Medicine meets virtual reality; 2001:69-74.

Kagemann L, Wang B, Wollstein G, Ishikawa H, Nevins JE, Nadler Z, et al. IOP elevation reduces Schlemm's canal cross-sectional area. Invest Ophthalmol Vis Sci 2014;55(3):1805-1809.

Amini R, Whitcomb JE, Al-Qaisi MK, Akkin T, Jouzdani S, Dorairaj S, et al. The posterior location of the dilator muscle induces anterior iris bowing during dilation, even in the absence of pupillary block. Invest Ophthalmol Vis Sci 2012;53(3):1188-1194.

Amini R, Jouzdani S, Barocas VH. Increased iris–lens contact following spontaneous blinking: Mathematical modeling. J Biomech 2012;45(13):2293-2296.

Amini R, Barocas VH. Reverse pupillary block slows iris contour recovery from corneoscleral indentation. J Biomech Eng 2010;132:071010.

Jouzdani S, Amini R, Barocas VH. Contribution of different anatomical and physiologic factors to iris contour and anterior chamber angle changes during pupil dilation: theoretical analysis. Invest Ophthalmol Vis Sci 2013;54(4):2977-2984.

Storn R, Price K. Differential evolution–a simple and efficient heuristic for global optimization over continuous spaces. J Global Optimiz 1997;11(4):341-359.

Ohio Supercomputer Center. Oakley supercomputer (Columbus, OH). 2012.

Johnson M, Schuman JS, Kagemann L. Trabecular meshwork stiffness in the living human eye. Invest Ophthalmol Vis Sci 2015;56(7):3541-3541.

Camras LJ, Stamer WD, Epstein D, Gonzalez P, Yuan F. Effects of trabecular meshwork stiffness on outflow. Invest Ophthalmol Vis Sci 2012;53(9):5242-5250.

Wang K, Read AT, Sulchek T, Ethier CR. Trabecular meshwork stiffness in glaucoma. Experimental Eye Research Volume 158, May 2017, Pages 3–12

Simon B, Kaufmann M, McAfee M, Baldwin A. Finite element models for arterial wall mechanics. J Biomech Eng-T ASME 1993;115:489-489.

Soltz MA, Ateshian GA. A conewise linear elasticity mixture model for the analysis of tension-compression nonlinearity in articular cartilage. J Biomech Eng-T ASME 2000;122(6):576-586.

Powell TA, Amini R, Oltean A, Barnett VA, Dorfman KD, Segal Y, et al. Elasticity of the porcine lens capsule as measured by osmotic swelling. J Biomech Eng 2010 Sep;132(9):091008.

Nagel TM, Hadi MF, Claeson AA, Nuckley DJ, Barocas VH. Combining displacement field and grip force information to determine mechanical properties of planar tissue with complicated geometry. J Biomech Eng 2014;136(11):114501.


Refbacks

  • There are currently no refbacks.


Copyright (c) 2017 Journal for Modeling in Ophthalmology