2014, 11(3): 523-546. doi: 10.3934/mbe.2014.11.523

Effect of intraocular pressure on the hemodynamics of the central retinal artery: A mathematical model

1. 

Department of Mathematical Sciences, Indiana University - Purdue University at Indianapolis, Indianapolis, IN, United States, United States

2. 

Department of Ophthalmology, Department of Cellular & Integrative Physiology, Eugene and Marilyn Glick Eye Institute, Indiana University School of Medicine, Indianapolis, IN, United States

3. 

Department of Electro Optics, Jerusalem College of Technology, Jerusalem, Israel

4. 

Department of Ophthalmology, Eugene and Marilyn Glick Eye Institute, Indiana University School of Medicine, Indianapolis, IN, United States

Received  May 2012 Revised  August 2013 Published  January 2014

Retinal hemodynamics plays a crucial role in the pathophysiology of several ocular diseases. There are clear evidences that the hemodynamics of the central retinal artery (CRA) is strongly affected by the level of intraocular pressure (IOP), which is the pressure inside the eye globe. However, the mechanisms through which this occurs are still elusive. The main goal of this paper is to develop a mathematical model that combines the mechanical action of IOP and the blood flow in the CRA to elucidate the mechanisms through which IOP elevation affects the CRA hemodynamics. Our model suggests that the development of radial compressive regions in the lamina cribrosa (a collagen structure in the optic nerve pierced by the CRA approximately in its center) might be responsible for the clinically-observed blood velocity reduction in the CRA following IOP elevation. The predictions of the mathematical model are in very good agreement with experimental and clinical data. Our model also identifies radius and thickness of the lamina cribrosa as major factors affecting the IOP-CRA relationship, suggesting that anatomical differences among individuals might lead to different hemodynamic responses to IOP elevation.
Citation: Giovanna Guidoboni, Alon Harris, Lucia Carichino, Yoel Arieli, Brent A. Siesky. Effect of intraocular pressure on the hemodynamics of the central retinal artery: A mathematical model. Mathematical Biosciences & Engineering, 2014, 11 (3) : 523-546. doi: 10.3934/mbe.2014.11.523
References:
[1]

Y. Aguomi, G. P. Sharpe, D. H. Hutchison, M. T.Nicolela, P. H.Artes and B. C. Chauhan, Laminar and pre laminar tissue displacement during intraocular pressure elevation in glaucoma patients and healthy controls, Ophthalmology, 118 (2011), 52-59.

[2]

R. L. Armentano, J. G. Barra, J. Levenson, A. Simon and R. H. Pichel, Arterial wall mechanics in conscious dogs: Assessment of viscous, inertial, and elastic moduli to characterize aortic wall behavior, Circ. Res., 76 (1995), 468-478. doi: 10.1161/01.RES.76.3.468.

[3]

D. Badeanu, M. Ritt, J. Harazny, J. Heckmann, R. E. Schmieder and G. Michelson, Wall-to-lumen ratio of retinal arterioles and arteriole-to-venule ratio of retinal vessels in patients with cerebrovascular damage, Invest. Ophthalmol. Vis. Sci., 50 (2009), 4351-4359.

[4]

R. R Buhrmann, H. A. Quigley, Y. Barron, S. K. West, M. S. Oliva and B. B. O. Mmbaga, Prevalence of glaucoma in a rural East African population, Invest. Ophthalmol. Vis. Sci., 41 (2000), 40-48.

[5]

C. F. Burgoyne, J. C. Downs, A. J. Bellezza, J. K. F. Suh and R. T. Hart, The optic nerve head as a biomechanical structure: A new paradigm for understanding the role of IOP-related stress and strain in the pathophysiology of glaucomatous optic nerve head damage, Prog. Retin. Eye Res., 24 (2005), 39-73. doi: 10.1016/j.preteyeres.2004.06.001.

[6]

J. Caprioli and A. L. Coleman, Blood pressure, perfusion pressure, and glaucoma, Am. J. Ophthalmol., 149 (2010), 704-712. doi: 10.1016/j.ajo.2010.01.018.

[7]

V. P. Costa, R. Lauande-Pimentel, R. A. Fonseca and L. Magacho, The influence of age, sex, race, refractive error and optic disc parameters on the sensitivity and specificity of scanning laser polarimetry, Acta Ophthalmol. Scand., 82 (2004), 419-425. doi: 10.1111/j.1395-3907.2004.00294.x.

[8]

J. E. De León-Ortega, L. M. Sakata, B. E. Monheit, G. Jr McGwin, S. N Arthur and C. A. Girkin, Comparison of diagnostic accuracy of Heidelberg Retina Tomograph II and Heidelberg Retina Tomograph 3 to discriminate glaucomatous and nonglaucomatous eyes, Am. J. Ophthalmol., 144 (2007), 525-532.

[9]

H. Dongqi and R. Zeqin, A biomathematical model for pressure-dependent lamina cribrosa behavior, J. Biomech., 32 (1999), 579-584. doi: 10.1016/S0021-9290(99)00025-1.

[10]

G. T. Dorner, E. Polska, G. Garhöfer, C. Zawinka, B. Frank and L. Schmetterer, Calculation of the diameter of the central retinal artery from noninvasive measurements in humans, Curr. Eye Res., 25 (2002), 341-345. doi: 10.1076/ceyr.25.6.341.14231.

[11]

M. E. Edwards and T. A. Good, Use of a mathematical model to estimate stress and strain during elevated pressure induced lamina cribrosa deformation, Curr. Eye Res., 23 (2001), 215-225. doi: 10.1076/ceyr.23.3.215.5460.

[12]

R. Ehrlich, A. Harris, N. S. Kheradiya, D. M. Winston, T. A. Ciulla and B. Wirostko, Age-related macular degeneration and the aging eye, Clin. Interv. Aging., 3 (2008), 473-482.

[13]

O. Findl, K. Strenn, M. Wolzt, R. Menapace, C. Vass, H. G. Eichler and L. Schmetterer, Effects of changes in intraocular pressure on human ocular haemodynamics, Curr. Eye Res., 16 (1997), 1024-1029. doi: 10.1076/ceyr.16.10.1024.9024.

[14]

J. Flammer, M. Pache and T. Resink, Vasospasm, its role in the pathogenesis of diseases with particular reference to the eye, Prog. Retin. Eye Res., 20 (2001), 319-349. doi: 10.1016/S1350-9462(00)00028-8.

[15]

FreeFem++, version 3.12-0 (2d and 3d), Université Pierre et Marie Curie Laboratoire Jacques-Louis Lionshttp://www.freefem.org/ff++/.

[16]

Y. C. Fung, Biomechanics: Circulatio, $2^{nd}$ edition, Springer-Verlag, New York, 1997.

[17]

Y. C. Fung, Biomechanics: Mechanical Properties of Living Tissues, $2^{nd}$ edition, Springer-Verlag, New York, 1993. doi: 10.1115/1.3138285.

[18]

P. Ganesan, S. He and H. Xu, Development of an image-based network model of retinal vasculature, Ann. Biomed. Eng., 38 (2010), 1566-1585. doi: 10.1007/s10439-010-9942-4.

[19]

P. Ganesan, S. He and H. Xu, Analysis of retinal circulation using an image-based network model of retinal vasculature, Microvasc. Res., 80 (2010), 99-109. doi: 10.1016/j.mvr.2010.02.005.

[20]

P. Ganesan, S. He and H. Xu, Development of an image-based model for capillary vasculature of retina, Comput. Methods Programs Biomed., 102 (2011), 35-46. doi: 10.1016/j.cmpb.2010.12.009.

[21]

P. Ganesan, S. He and H. Xu, Modelling of pulsatile blood flow in arterial trees of retinal vasculature, Med. Eng. Phys., 33 (2011), 810-823. doi: 10.1016/j.medengphy.2010.10.004.

[22]

C. A. Girkin, G. Jr McGwin, S. F. McNeal and J. DeLeon-Ortega, Racial differences in the association between optic disc topography and early glaucoma, Invest. Ophthalmol. Vis. Sci., 44 (2003), 3382-3387. doi: 10.1167/iovs.02-0792.

[23]

C. A. Girkin, G. Jr McGwin, C. Long, J. DeLeon-Ortega, C. M. Graf and A. W. Everett, Subjective and objective optic nerve assessment in African Americans and whites, Invest. Ophthalmol. Vis. Sci., 45 (2004), 2272-2278. doi: 10.1167/iovs.03-0996.

[24]

C. A. Girkin, G. Jr McGwin, A. Xie and J. E. Deleon-Ortega, Differences in optic disc topography between black and white normal subjects, Ophthalmology, 112 (2005), 33-39. doi: 10.1016/j.ophtha.2004.07.029.

[25]

C. A. Girkin, P. A. Sample, J. M. Liebmann, S. Jain, C. Bowd, L. M. Becerra, F. A. Medeiros, L. Racette, K. A. Dirkes and R. N. Weinreb, African Descent and Glaucoma Evaluation Study (ADAGES): II. Ancestry differences in optic disc, retinal nerve fiber layer, and macular structure in healthy subjects, Arch. Ophthalmol., 128 (2010), 541-550. doi: 10.1001/archophthalmol.2010.49.

[26]

G. Guidoboni, A. Harris, J.C. Arciero, B.A. Siesky, A. Amireskandari, A.L. Gerber, A.H. Huck, N.J. Kim, S. Cassani and L. Carichino, Mathematical modeling approaches in the study of glaucoma disparities among people of African and European Descents, J. Coupled Syst. Multiscale Dyn., 1(1) (2013), 1-21.

[27]

A. Harris, K. Joos, M. Kay, D. Evans, R. Shetty, W. E. Sponsel and B. Martin, Acute IOP elevation with scleral suction: Effects on retrobulbar haemodynamics, Br. J. Ophthalmol., 80 (1996), 1055-1059. doi: 10.1136/bjo.80.12.1055.

[28]

A. Harris, C. P. Jonescu-Cuypers, L. Kagemann, T. A. Ciulla and G. K. Krieglstein, Atlas of Ocular Blood Flow. Vascular Anatomy, Pathophysiology, and Metabolism, Elsevier, Philadelphia, 2003.

[29]

A. Harris, L. Kagemann, R. Ehrlich, C. Rospigliosi, D. Moore and B. Siesky, Measuring and interpreting ocular blood flow and metabolism in glaucoma, Can. J. Ophthalmol., 43 (2008), 328-336. doi: 10.1139/I08-051.

[30]

A. Harris, G. Guidoboni, J.C. Arciero, A. Ameriskandari, L.A. Tobe and B.A. Siesky, Ocular hemodynamics and glaucoma: the role of mathematical modeling, Eur. J. Ophthalmol., 23(2) (2013), 139-146.

[31]

S. S. Hayreh, Blood flow in the optic nerve head and factors that may influence it, Prog. Retin. Eye Res., 20 (2001), 595-624. doi: 10.1016/S1350-9462(01)00005-2.

[32]

E. M. Hoffmann, L. M. Zangwill, J. G. Crowston and R. N. Weinreb, Optic disk size and glaucoma, Surv. Ophthalmol., 52 (2007), 32-49. doi: 10.1016/j.survophthal.2006.10.002.

[33]

I. Januleviciene, R. Ehrlich, B. Siesky, I. Nedzelskiene and A. Harris, Visual function, optic nerve structure, and ocular blood flow parameters after 1 year of glaucoma treatment with fixed combinations, Eur. J. Ophthalmol., 19 (2009), 790-797.

[34]

J. B. Jonas, C. Y. Mardin, U. Schlötzer-Schrehardt and G. O. Naumann, Morphometry of the human lamina cribrosa surface, Invest. Ophthalmol. Vis. Sci., 32 (1991), 401-405.

[35]

J. B. Jonas and L. Holbach, Central corneal thickness and thickness of the lamina cribrosa in human eyes, Invest. Ophthalmol. Vis. Sci., 46 (2005), 1275-1279. doi: 10.1167/iovs.04-0851.

[36]

O. Knight, C. A. Girkin, D. L. Budenz, M. K. Durbin and W. J Feuer, Effect of race, age, and axial length on optic nerve head parameters and retinal nerve fiber layer thickness measured by Cirrus HD-OCT, Arc. Ophthalmol., 130 (2012), 312-318. doi: 10.1001/archopthalmol.2011.1576.

[37]

M. C. Leske, A. M. S. Connell, A. P. Schachat and L. Hyman, The Barbados Eye Study: Prevalence of open angle glaucoma, Arc. Ophthalmol., 112 (1994), 821-829. doi: 10.1001/archopht.1994.01090180121046.

[38]

M. C. Leske, Open-angle glaucoma - an epidemiologic overview, Ophthalmic Epidemiol., 14 (2007), 166-172. doi: 10.1080/09286580701501931.

[39]

M. C. Leske, A. Heijl, L. Hyman, B. Bengtsson, L. Dong and Z. Yang, Predictors of long-term progression in the early manifest glaucoma trial, Ophthalmology, 114 (2007), 1965-1972. doi: 10.1016/j.ophtha.2007.03.016.

[40]

A. Mikelic, G. Guidoboni and S. Canic, Fluid-structure interaction in a pre-stressed tube with thick elastic walls I: the stationary Stokes problem, Netw. Heterog. Media, 2 (2007), 397-423. doi: 10.3934/nhm.2007.2.397.

[41]

D. Moore, A. Harris, D. Wudunn, N. Kheradiya and B. Siesky, Dysfunctional regulation of ocular blood flow: a risk factor for glaucoma? Clin. Ophthalmol., 2 (2008), 849-861.

[42]

W. H Morgan, D. Y. Yu, V. A. Alder, S. J. Cringle, R. L. Cooper, P. H. House and I. J. Constable, The correlation between cerebrospinal fluid pressure and retrolaminar tissue pressure, Invest. Ophthalmol. Vis. Sci., 39 (1998), 3236-3242.

[43]

W. H Morgan, B. C. Chauhan, D. Y. Yu, S. J. Cringle, V. A. Alder and P. H. House, Optic disc movement with variations in intraocular and cerebrospinal fluid pressure, Invest. Ophthalmol. Vis. Sci., 43 (2002), 1419-1428.

[44]

J. Morgan-Davies, N. Taylor, A. R. Hill, P. Aspinall, C. J. O'Brien and A. Azuara-Blanco, Three dimensional analysis of the lamina cribrosa in glaucoma, Br. J. Ophthalmol., 88 (2004), 1299-1304. doi: 10.1136/bjo.2003.036020.

[45]

T. Newson and A. El-Sheikh, Mathematical modeling of the biomechanics of the lamina cribrosa under elevated intraocular pressures, J. Biomech. Eng., 128 (2006), 496-504. doi: 10.1115/1.2205372.

[46]

R. E. Norman, J. G. Flanagan, S. M. K. Rausch, I. A. Sigal, I. Tertinegg, A. Eilaghi, S. Portnoy, J. G. Sled and C. R. Ethier, Dimensions of the human sclera: Thickness measurement and regional changes with axial length, Exp. Eye Res., 90 (2010), 277-284. doi: 10.1016/j.exer.2009.11.001.

[47]

B. Pemp and L. Schmetterer, Ocular blood flow in diabetes and age-related macular degeneration, Can. J. Ophthalmol., 43 (2008), 295-301. doi: 10.1139/I08-049.

[48]

D. Poinoosawmy, L. Fontana, J. X. Wu, F. W. Fitzke and R. A. Hitchings, Variation of nerve fibre layer thickness measurements with age and ethnicity by scanning laser polarimetry, Br. J. Ophthalmol., 81 (1997), 350-354. doi: 10.1136/bjo.81.5.350.

[49]

C. J. Pournaras, E. Rungger-Brändle, C. E. Riva, S. H. Hardarson and E. Stefansson, Regulation of retinal blood flow in health and disease, Prog. Retin. Eye Res., 27 (2008), 284-330. doi: 10.1016/j.preteyeres.2008.02.002.

[50]

A. Quarteroni, M. Tuveri and A. Veneziani, Computational vascular fluid dynamics: Problems, models and methods, Comput. Visual Sci., 2 (2000), 163-197. doi: 10.1007/s007910050039.

[51]

L. Racette, M. R. Wilson, L. M. Zangwill, R. N. Weinreb and P. A. Sample, Primary open-angle glaucoma in blacks: A review, Surv. Ophthalmol., 48 (2003), 295-313. doi: 10.1016/S0039-6257(03)00028-6.

[52]

L. Racette, C. Boden, S. L. Kleinhandler, C. A. Girkin, J. M. Liebmann, L. M. Zangwill, F. A. Medeiros, C. Bowd, R. N. Weinreb and M. R. Wilson, Differences in visual function and optic nerve structure between healthy eyes of blacks and whites, Arch. Ophthalmol., 123 (2005), 1547-1553. doi: 10.1001/archopht.123.11.1547.

[53]

R. Ren, N. Wang, B. Li, L. Li, F. Gao, X. Xu and J. B. Jonas, Lamina cribrosa and peripapillary sclera histomorphometry in normal and advanced glaucomatous Chinese eyes with various axial length, Invest. Ophthalmol. Vis. Sci., 50 (2009), 2175-2184. doi: 10.1167/iovs.07-1429.

[54]

M. I. Seider, R. Y. Lee, D. Wang, M. Pekmezci, T. C. Porco and S. C. Lin, Optic disk size variability between African, Asian, white, Hispanic, and Filipino Americans using Heidelberg retinal tomography, J. Glaucoma, 18 (2009), 595-600. doi: 10.1097/IJG.0b013e3181996f05.

[55]

I. A. Sigal, J. G. Flanagan, I. Tertinegg and C. R. Ethier, Finite element modeling of optic nerve head biomechanics, Invest. Ophthalmol. Vis. Sci., 45 (2004), 4378-4387. doi: 10.1167/iovs.04-0133.

[56]

I. A. Sigal, J. G. Flanagan, I. Tertinegg and C. R. Ethier, Predicted extension, compression and shearing of optic nerve head tissues, Exp. Eye Res., 85 (2007), 312-322. doi: 10.1016/j.exer.2007.05.005.

[57]

I. A. Sigal, J. G. Flanagan, I. Tertinegg and C. R. Ethier, Modeling individual-specific human optic nerve head biomechanics. Part I: IOP-induced deformations and influence of geometry, Biomech. Model. Mechanobiol., 8 (2009), 85-98. doi: 10.1007/s10237-008-0120-7.

[58]

I. A. Sigal, H. Yang, M. D. Roberts, J. L. Grimm, C. F. Burgoyne, S. Demirel and J. C. Downs, IOP-induced lamina cribrosa deformation and scleral canal expansion: Independent or related? Invest. Ophthalmol. Vis. Sci., 52 (2011), 9023-9032. doi: 10.1167/iovs.11-8183.

[59]

I. A. Sigal, R. A. Bilonick, L. Kagemann, G. Wollstein, H. Ishikawa, J. S. Schuman and J. L. Grimm, The optic nerve head as a robust biomechanical system, Invest. Ophthalmol. Vis. Sci., 53 (2012), 2658-2667. doi: 10.1167/iovs.11-9303.

[60]

I. A. Sigal and J. L. Grimm, A few good responses: which mechanical effects of IOP on the ONH to study? Invest. Ophthalmol. Vis. Sci., 53(7) (2012), 4270-4278. doi: 10.1167/iovs.11-8739.

[61]

I. A. Sigal, J. G. Flanagan, K. L. Lathrop, I. Tertinegg and R. Bilonick, Human lamina cribrosa insertion and age, Invest. Ophthalmol. Vis. Sci., 53 (2012), 6870-6879. doi: 10.1167/iovs.12-9890.

[62]

A. Sommer, J. M. Tielsch, J. Katz, H. A. Quigley, J. D. Gottsch, J. C. Javitt, J. F. Martone, R. M. Royall, K. A. Witt and S. Ezrine, Racial differences in the cause-specific prevalence of blindness in east Baltimore, N. Engl. J. Med., 325 (1991), 1412-1417. doi: 10.1056/NEJM199111143252004.

[63]

A. Sommer, Glaucoma risk factors observed in the Baltimore Eye Survey, Curr. Opin. Ophthalmol., 7 (1996), 93-98. doi: 10.1097/00055735-199604000-00016.

[64]

T. Takahashi, T. Nagaoka, H. Yanagida, T. Saitoh, A. Kamiya, T. Hein, L. Kuo and A. Yoshida, A mathematical model for the distribution of hemodynamic parameters in the human retinal microvascular network, J. Biorheol., 23 (2009), 77-86. doi: 10.1007/s12573-009-0012-1.

[65]

J. M. Tielsch, A. Sommer, J. Katz, R. M. Royall, H. A. Quigley and J. Javitt, Racial variations in the prevalence of primary open-angle glaucoma: The Baltimore Eye Survey, JAMA, 266 (1991), 369-374. doi: 10.1001/jama.1991.03470030069026.

[66]

R. Varma, J. M. Tielsch, H. A. Quigley, S. C. Hilton, J. Katz, G. L. Spaeth and A. Sommer, Race-, age-, gender-, and refractive error-related differences in the normal optic disc, Arch. Ophthalmol., 112 (1994), 1068-1076. doi: 10.1001/archopht.1994.01090200074026.

[67]

S. Woo, A. S. Kobayashi, W. A. Schlegel and C. Lawrence, Nonlinear material properties of intact cornea and sclera, Exp. Eye Res., 14 (1972), 29-39. doi: 10.1016/0014-4835(72)90139-X.

[68]

J. R. Zelefsky, N. Harizman, R. Mora, E. Ilitchev, C. Tello, R. Ritch and J. M. Liebmann, Assessment of a race-specific normative HRT-III database to differentiate glaucomatous from normal eyes, J. Glaucoma, 15 (2006), 548-551. doi: 10.1097/01.ijg.0000212289.00917.a8.

show all references

References:
[1]

Y. Aguomi, G. P. Sharpe, D. H. Hutchison, M. T.Nicolela, P. H.Artes and B. C. Chauhan, Laminar and pre laminar tissue displacement during intraocular pressure elevation in glaucoma patients and healthy controls, Ophthalmology, 118 (2011), 52-59.

[2]

R. L. Armentano, J. G. Barra, J. Levenson, A. Simon and R. H. Pichel, Arterial wall mechanics in conscious dogs: Assessment of viscous, inertial, and elastic moduli to characterize aortic wall behavior, Circ. Res., 76 (1995), 468-478. doi: 10.1161/01.RES.76.3.468.

[3]

D. Badeanu, M. Ritt, J. Harazny, J. Heckmann, R. E. Schmieder and G. Michelson, Wall-to-lumen ratio of retinal arterioles and arteriole-to-venule ratio of retinal vessels in patients with cerebrovascular damage, Invest. Ophthalmol. Vis. Sci., 50 (2009), 4351-4359.

[4]

R. R Buhrmann, H. A. Quigley, Y. Barron, S. K. West, M. S. Oliva and B. B. O. Mmbaga, Prevalence of glaucoma in a rural East African population, Invest. Ophthalmol. Vis. Sci., 41 (2000), 40-48.

[5]

C. F. Burgoyne, J. C. Downs, A. J. Bellezza, J. K. F. Suh and R. T. Hart, The optic nerve head as a biomechanical structure: A new paradigm for understanding the role of IOP-related stress and strain in the pathophysiology of glaucomatous optic nerve head damage, Prog. Retin. Eye Res., 24 (2005), 39-73. doi: 10.1016/j.preteyeres.2004.06.001.

[6]

J. Caprioli and A. L. Coleman, Blood pressure, perfusion pressure, and glaucoma, Am. J. Ophthalmol., 149 (2010), 704-712. doi: 10.1016/j.ajo.2010.01.018.

[7]

V. P. Costa, R. Lauande-Pimentel, R. A. Fonseca and L. Magacho, The influence of age, sex, race, refractive error and optic disc parameters on the sensitivity and specificity of scanning laser polarimetry, Acta Ophthalmol. Scand., 82 (2004), 419-425. doi: 10.1111/j.1395-3907.2004.00294.x.

[8]

J. E. De León-Ortega, L. M. Sakata, B. E. Monheit, G. Jr McGwin, S. N Arthur and C. A. Girkin, Comparison of diagnostic accuracy of Heidelberg Retina Tomograph II and Heidelberg Retina Tomograph 3 to discriminate glaucomatous and nonglaucomatous eyes, Am. J. Ophthalmol., 144 (2007), 525-532.

[9]

H. Dongqi and R. Zeqin, A biomathematical model for pressure-dependent lamina cribrosa behavior, J. Biomech., 32 (1999), 579-584. doi: 10.1016/S0021-9290(99)00025-1.

[10]

G. T. Dorner, E. Polska, G. Garhöfer, C. Zawinka, B. Frank and L. Schmetterer, Calculation of the diameter of the central retinal artery from noninvasive measurements in humans, Curr. Eye Res., 25 (2002), 341-345. doi: 10.1076/ceyr.25.6.341.14231.

[11]

M. E. Edwards and T. A. Good, Use of a mathematical model to estimate stress and strain during elevated pressure induced lamina cribrosa deformation, Curr. Eye Res., 23 (2001), 215-225. doi: 10.1076/ceyr.23.3.215.5460.

[12]

R. Ehrlich, A. Harris, N. S. Kheradiya, D. M. Winston, T. A. Ciulla and B. Wirostko, Age-related macular degeneration and the aging eye, Clin. Interv. Aging., 3 (2008), 473-482.

[13]

O. Findl, K. Strenn, M. Wolzt, R. Menapace, C. Vass, H. G. Eichler and L. Schmetterer, Effects of changes in intraocular pressure on human ocular haemodynamics, Curr. Eye Res., 16 (1997), 1024-1029. doi: 10.1076/ceyr.16.10.1024.9024.

[14]

J. Flammer, M. Pache and T. Resink, Vasospasm, its role in the pathogenesis of diseases with particular reference to the eye, Prog. Retin. Eye Res., 20 (2001), 319-349. doi: 10.1016/S1350-9462(00)00028-8.

[15]

FreeFem++, version 3.12-0 (2d and 3d), Université Pierre et Marie Curie Laboratoire Jacques-Louis Lionshttp://www.freefem.org/ff++/.

[16]

Y. C. Fung, Biomechanics: Circulatio, $2^{nd}$ edition, Springer-Verlag, New York, 1997.

[17]

Y. C. Fung, Biomechanics: Mechanical Properties of Living Tissues, $2^{nd}$ edition, Springer-Verlag, New York, 1993. doi: 10.1115/1.3138285.

[18]

P. Ganesan, S. He and H. Xu, Development of an image-based network model of retinal vasculature, Ann. Biomed. Eng., 38 (2010), 1566-1585. doi: 10.1007/s10439-010-9942-4.

[19]

P. Ganesan, S. He and H. Xu, Analysis of retinal circulation using an image-based network model of retinal vasculature, Microvasc. Res., 80 (2010), 99-109. doi: 10.1016/j.mvr.2010.02.005.

[20]

P. Ganesan, S. He and H. Xu, Development of an image-based model for capillary vasculature of retina, Comput. Methods Programs Biomed., 102 (2011), 35-46. doi: 10.1016/j.cmpb.2010.12.009.

[21]

P. Ganesan, S. He and H. Xu, Modelling of pulsatile blood flow in arterial trees of retinal vasculature, Med. Eng. Phys., 33 (2011), 810-823. doi: 10.1016/j.medengphy.2010.10.004.

[22]

C. A. Girkin, G. Jr McGwin, S. F. McNeal and J. DeLeon-Ortega, Racial differences in the association between optic disc topography and early glaucoma, Invest. Ophthalmol. Vis. Sci., 44 (2003), 3382-3387. doi: 10.1167/iovs.02-0792.

[23]

C. A. Girkin, G. Jr McGwin, C. Long, J. DeLeon-Ortega, C. M. Graf and A. W. Everett, Subjective and objective optic nerve assessment in African Americans and whites, Invest. Ophthalmol. Vis. Sci., 45 (2004), 2272-2278. doi: 10.1167/iovs.03-0996.

[24]

C. A. Girkin, G. Jr McGwin, A. Xie and J. E. Deleon-Ortega, Differences in optic disc topography between black and white normal subjects, Ophthalmology, 112 (2005), 33-39. doi: 10.1016/j.ophtha.2004.07.029.

[25]

C. A. Girkin, P. A. Sample, J. M. Liebmann, S. Jain, C. Bowd, L. M. Becerra, F. A. Medeiros, L. Racette, K. A. Dirkes and R. N. Weinreb, African Descent and Glaucoma Evaluation Study (ADAGES): II. Ancestry differences in optic disc, retinal nerve fiber layer, and macular structure in healthy subjects, Arch. Ophthalmol., 128 (2010), 541-550. doi: 10.1001/archophthalmol.2010.49.

[26]

G. Guidoboni, A. Harris, J.C. Arciero, B.A. Siesky, A. Amireskandari, A.L. Gerber, A.H. Huck, N.J. Kim, S. Cassani and L. Carichino, Mathematical modeling approaches in the study of glaucoma disparities among people of African and European Descents, J. Coupled Syst. Multiscale Dyn., 1(1) (2013), 1-21.

[27]

A. Harris, K. Joos, M. Kay, D. Evans, R. Shetty, W. E. Sponsel and B. Martin, Acute IOP elevation with scleral suction: Effects on retrobulbar haemodynamics, Br. J. Ophthalmol., 80 (1996), 1055-1059. doi: 10.1136/bjo.80.12.1055.

[28]

A. Harris, C. P. Jonescu-Cuypers, L. Kagemann, T. A. Ciulla and G. K. Krieglstein, Atlas of Ocular Blood Flow. Vascular Anatomy, Pathophysiology, and Metabolism, Elsevier, Philadelphia, 2003.

[29]

A. Harris, L. Kagemann, R. Ehrlich, C. Rospigliosi, D. Moore and B. Siesky, Measuring and interpreting ocular blood flow and metabolism in glaucoma, Can. J. Ophthalmol., 43 (2008), 328-336. doi: 10.1139/I08-051.

[30]

A. Harris, G. Guidoboni, J.C. Arciero, A. Ameriskandari, L.A. Tobe and B.A. Siesky, Ocular hemodynamics and glaucoma: the role of mathematical modeling, Eur. J. Ophthalmol., 23(2) (2013), 139-146.

[31]

S. S. Hayreh, Blood flow in the optic nerve head and factors that may influence it, Prog. Retin. Eye Res., 20 (2001), 595-624. doi: 10.1016/S1350-9462(01)00005-2.

[32]

E. M. Hoffmann, L. M. Zangwill, J. G. Crowston and R. N. Weinreb, Optic disk size and glaucoma, Surv. Ophthalmol., 52 (2007), 32-49. doi: 10.1016/j.survophthal.2006.10.002.

[33]

I. Januleviciene, R. Ehrlich, B. Siesky, I. Nedzelskiene and A. Harris, Visual function, optic nerve structure, and ocular blood flow parameters after 1 year of glaucoma treatment with fixed combinations, Eur. J. Ophthalmol., 19 (2009), 790-797.

[34]

J. B. Jonas, C. Y. Mardin, U. Schlötzer-Schrehardt and G. O. Naumann, Morphometry of the human lamina cribrosa surface, Invest. Ophthalmol. Vis. Sci., 32 (1991), 401-405.

[35]

J. B. Jonas and L. Holbach, Central corneal thickness and thickness of the lamina cribrosa in human eyes, Invest. Ophthalmol. Vis. Sci., 46 (2005), 1275-1279. doi: 10.1167/iovs.04-0851.

[36]

O. Knight, C. A. Girkin, D. L. Budenz, M. K. Durbin and W. J Feuer, Effect of race, age, and axial length on optic nerve head parameters and retinal nerve fiber layer thickness measured by Cirrus HD-OCT, Arc. Ophthalmol., 130 (2012), 312-318. doi: 10.1001/archopthalmol.2011.1576.

[37]

M. C. Leske, A. M. S. Connell, A. P. Schachat and L. Hyman, The Barbados Eye Study: Prevalence of open angle glaucoma, Arc. Ophthalmol., 112 (1994), 821-829. doi: 10.1001/archopht.1994.01090180121046.

[38]

M. C. Leske, Open-angle glaucoma - an epidemiologic overview, Ophthalmic Epidemiol., 14 (2007), 166-172. doi: 10.1080/09286580701501931.

[39]

M. C. Leske, A. Heijl, L. Hyman, B. Bengtsson, L. Dong and Z. Yang, Predictors of long-term progression in the early manifest glaucoma trial, Ophthalmology, 114 (2007), 1965-1972. doi: 10.1016/j.ophtha.2007.03.016.

[40]

A. Mikelic, G. Guidoboni and S. Canic, Fluid-structure interaction in a pre-stressed tube with thick elastic walls I: the stationary Stokes problem, Netw. Heterog. Media, 2 (2007), 397-423. doi: 10.3934/nhm.2007.2.397.

[41]

D. Moore, A. Harris, D. Wudunn, N. Kheradiya and B. Siesky, Dysfunctional regulation of ocular blood flow: a risk factor for glaucoma? Clin. Ophthalmol., 2 (2008), 849-861.

[42]

W. H Morgan, D. Y. Yu, V. A. Alder, S. J. Cringle, R. L. Cooper, P. H. House and I. J. Constable, The correlation between cerebrospinal fluid pressure and retrolaminar tissue pressure, Invest. Ophthalmol. Vis. Sci., 39 (1998), 3236-3242.

[43]

W. H Morgan, B. C. Chauhan, D. Y. Yu, S. J. Cringle, V. A. Alder and P. H. House, Optic disc movement with variations in intraocular and cerebrospinal fluid pressure, Invest. Ophthalmol. Vis. Sci., 43 (2002), 1419-1428.

[44]

J. Morgan-Davies, N. Taylor, A. R. Hill, P. Aspinall, C. J. O'Brien and A. Azuara-Blanco, Three dimensional analysis of the lamina cribrosa in glaucoma, Br. J. Ophthalmol., 88 (2004), 1299-1304. doi: 10.1136/bjo.2003.036020.

[45]

T. Newson and A. El-Sheikh, Mathematical modeling of the biomechanics of the lamina cribrosa under elevated intraocular pressures, J. Biomech. Eng., 128 (2006), 496-504. doi: 10.1115/1.2205372.

[46]

R. E. Norman, J. G. Flanagan, S. M. K. Rausch, I. A. Sigal, I. Tertinegg, A. Eilaghi, S. Portnoy, J. G. Sled and C. R. Ethier, Dimensions of the human sclera: Thickness measurement and regional changes with axial length, Exp. Eye Res., 90 (2010), 277-284. doi: 10.1016/j.exer.2009.11.001.

[47]

B. Pemp and L. Schmetterer, Ocular blood flow in diabetes and age-related macular degeneration, Can. J. Ophthalmol., 43 (2008), 295-301. doi: 10.1139/I08-049.

[48]

D. Poinoosawmy, L. Fontana, J. X. Wu, F. W. Fitzke and R. A. Hitchings, Variation of nerve fibre layer thickness measurements with age and ethnicity by scanning laser polarimetry, Br. J. Ophthalmol., 81 (1997), 350-354. doi: 10.1136/bjo.81.5.350.

[49]

C. J. Pournaras, E. Rungger-Brändle, C. E. Riva, S. H. Hardarson and E. Stefansson, Regulation of retinal blood flow in health and disease, Prog. Retin. Eye Res., 27 (2008), 284-330. doi: 10.1016/j.preteyeres.2008.02.002.

[50]

A. Quarteroni, M. Tuveri and A. Veneziani, Computational vascular fluid dynamics: Problems, models and methods, Comput. Visual Sci., 2 (2000), 163-197. doi: 10.1007/s007910050039.

[51]

L. Racette, M. R. Wilson, L. M. Zangwill, R. N. Weinreb and P. A. Sample, Primary open-angle glaucoma in blacks: A review, Surv. Ophthalmol., 48 (2003), 295-313. doi: 10.1016/S0039-6257(03)00028-6.

[52]

L. Racette, C. Boden, S. L. Kleinhandler, C. A. Girkin, J. M. Liebmann, L. M. Zangwill, F. A. Medeiros, C. Bowd, R. N. Weinreb and M. R. Wilson, Differences in visual function and optic nerve structure between healthy eyes of blacks and whites, Arch. Ophthalmol., 123 (2005), 1547-1553. doi: 10.1001/archopht.123.11.1547.

[53]

R. Ren, N. Wang, B. Li, L. Li, F. Gao, X. Xu and J. B. Jonas, Lamina cribrosa and peripapillary sclera histomorphometry in normal and advanced glaucomatous Chinese eyes with various axial length, Invest. Ophthalmol. Vis. Sci., 50 (2009), 2175-2184. doi: 10.1167/iovs.07-1429.

[54]

M. I. Seider, R. Y. Lee, D. Wang, M. Pekmezci, T. C. Porco and S. C. Lin, Optic disk size variability between African, Asian, white, Hispanic, and Filipino Americans using Heidelberg retinal tomography, J. Glaucoma, 18 (2009), 595-600. doi: 10.1097/IJG.0b013e3181996f05.

[55]

I. A. Sigal, J. G. Flanagan, I. Tertinegg and C. R. Ethier, Finite element modeling of optic nerve head biomechanics, Invest. Ophthalmol. Vis. Sci., 45 (2004), 4378-4387. doi: 10.1167/iovs.04-0133.

[56]

I. A. Sigal, J. G. Flanagan, I. Tertinegg and C. R. Ethier, Predicted extension, compression and shearing of optic nerve head tissues, Exp. Eye Res., 85 (2007), 312-322. doi: 10.1016/j.exer.2007.05.005.

[57]

I. A. Sigal, J. G. Flanagan, I. Tertinegg and C. R. Ethier, Modeling individual-specific human optic nerve head biomechanics. Part I: IOP-induced deformations and influence of geometry, Biomech. Model. Mechanobiol., 8 (2009), 85-98. doi: 10.1007/s10237-008-0120-7.

[58]

I. A. Sigal, H. Yang, M. D. Roberts, J. L. Grimm, C. F. Burgoyne, S. Demirel and J. C. Downs, IOP-induced lamina cribrosa deformation and scleral canal expansion: Independent or related? Invest. Ophthalmol. Vis. Sci., 52 (2011), 9023-9032. doi: 10.1167/iovs.11-8183.

[59]

I. A. Sigal, R. A. Bilonick, L. Kagemann, G. Wollstein, H. Ishikawa, J. S. Schuman and J. L. Grimm, The optic nerve head as a robust biomechanical system, Invest. Ophthalmol. Vis. Sci., 53 (2012), 2658-2667. doi: 10.1167/iovs.11-9303.

[60]

I. A. Sigal and J. L. Grimm, A few good responses: which mechanical effects of IOP on the ONH to study? Invest. Ophthalmol. Vis. Sci., 53(7) (2012), 4270-4278. doi: 10.1167/iovs.11-8739.

[61]

I. A. Sigal, J. G. Flanagan, K. L. Lathrop, I. Tertinegg and R. Bilonick, Human lamina cribrosa insertion and age, Invest. Ophthalmol. Vis. Sci., 53 (2012), 6870-6879. doi: 10.1167/iovs.12-9890.

[62]

A. Sommer, J. M. Tielsch, J. Katz, H. A. Quigley, J. D. Gottsch, J. C. Javitt, J. F. Martone, R. M. Royall, K. A. Witt and S. Ezrine, Racial differences in the cause-specific prevalence of blindness in east Baltimore, N. Engl. J. Med., 325 (1991), 1412-1417. doi: 10.1056/NEJM199111143252004.

[63]

A. Sommer, Glaucoma risk factors observed in the Baltimore Eye Survey, Curr. Opin. Ophthalmol., 7 (1996), 93-98. doi: 10.1097/00055735-199604000-00016.

[64]

T. Takahashi, T. Nagaoka, H. Yanagida, T. Saitoh, A. Kamiya, T. Hein, L. Kuo and A. Yoshida, A mathematical model for the distribution of hemodynamic parameters in the human retinal microvascular network, J. Biorheol., 23 (2009), 77-86. doi: 10.1007/s12573-009-0012-1.

[65]

J. M. Tielsch, A. Sommer, J. Katz, R. M. Royall, H. A. Quigley and J. Javitt, Racial variations in the prevalence of primary open-angle glaucoma: The Baltimore Eye Survey, JAMA, 266 (1991), 369-374. doi: 10.1001/jama.1991.03470030069026.

[66]

R. Varma, J. M. Tielsch, H. A. Quigley, S. C. Hilton, J. Katz, G. L. Spaeth and A. Sommer, Race-, age-, gender-, and refractive error-related differences in the normal optic disc, Arch. Ophthalmol., 112 (1994), 1068-1076. doi: 10.1001/archopht.1994.01090200074026.

[67]

S. Woo, A. S. Kobayashi, W. A. Schlegel and C. Lawrence, Nonlinear material properties of intact cornea and sclera, Exp. Eye Res., 14 (1972), 29-39. doi: 10.1016/0014-4835(72)90139-X.

[68]

J. R. Zelefsky, N. Harizman, R. Mora, E. Ilitchev, C. Tello, R. Ritch and J. M. Liebmann, Assessment of a race-specific normative HRT-III database to differentiate glaucomatous from normal eyes, J. Glaucoma, 15 (2006), 548-551. doi: 10.1097/01.ijg.0000212289.00917.a8.

[1]

Oualid Kafi, Nader El Khatib, Jorge Tiago, Adélia Sequeira. Numerical simulations of a 3D fluid-structure interaction model for blood flow in an atherosclerotic artery. Mathematical Biosciences & Engineering, 2017, 14 (1) : 179-193. doi: 10.3934/mbe.2017012

[2]

Qiang Du, M. D. Gunzburger, L. S. Hou, J. Lee. Analysis of a linear fluid-structure interaction problem. Discrete and Continuous Dynamical Systems, 2003, 9 (3) : 633-650. doi: 10.3934/dcds.2003.9.633

[3]

Grégoire Allaire, Alessandro Ferriero. Homogenization and long time asymptotic of a fluid-structure interaction problem. Discrete and Continuous Dynamical Systems - B, 2008, 9 (2) : 199-220. doi: 10.3934/dcdsb.2008.9.199

[4]

Serge Nicaise, Cristina Pignotti. Asymptotic analysis of a simple model of fluid-structure interaction. Networks and Heterogeneous Media, 2008, 3 (4) : 787-813. doi: 10.3934/nhm.2008.3.787

[5]

Igor Kukavica, Amjad Tuffaha. Solutions to a fluid-structure interaction free boundary problem. Discrete and Continuous Dynamical Systems, 2012, 32 (4) : 1355-1389. doi: 10.3934/dcds.2012.32.1355

[6]

George Avalos, Roberto Triggiani. Fluid-structure interaction with and without internal dissipation of the structure: A contrast study in stability. Evolution Equations and Control Theory, 2013, 2 (4) : 563-598. doi: 10.3934/eect.2013.2.563

[7]

B. Wiwatanapataphee, D. Poltem, Yong Hong Wu, Y. Lenbury. Simulation of Pulsatile Flow of Blood in Stenosed Coronary Artery Bypass with Graft. Mathematical Biosciences & Engineering, 2006, 3 (2) : 371-383. doi: 10.3934/mbe.2006.3.371

[8]

Daniele Boffi, Lucia Gastaldi, Sebastian Wolf. Higher-order time-stepping schemes for fluid-structure interaction problems. Discrete and Continuous Dynamical Systems - B, 2020, 25 (10) : 3807-3830. doi: 10.3934/dcdsb.2020229

[9]

Andro Mikelić, Giovanna Guidoboni, Sunčica Čanić. Fluid-structure interaction in a pre-stressed tube with thick elastic walls I: the stationary Stokes problem. Networks and Heterogeneous Media, 2007, 2 (3) : 397-423. doi: 10.3934/nhm.2007.2.397

[10]

George Avalos, Roberto Triggiani. Uniform stabilization of a coupled PDE system arising in fluid-structure interaction with boundary dissipation at the interface. Discrete and Continuous Dynamical Systems, 2008, 22 (4) : 817-833. doi: 10.3934/dcds.2008.22.817

[11]

Pavel Eichler, Radek Fučík, Robert Straka. Computational study of immersed boundary - lattice Boltzmann method for fluid-structure interaction. Discrete and Continuous Dynamical Systems - S, 2021, 14 (3) : 819-833. doi: 10.3934/dcdss.2020349

[12]

Salim Meddahi, David Mora. Nonconforming mixed finite element approximation of a fluid-structure interaction spectral problem. Discrete and Continuous Dynamical Systems - S, 2016, 9 (1) : 269-287. doi: 10.3934/dcdss.2016.9.269

[13]

Martina Bukač, Sunčica Čanić. Longitudinal displacement in viscoelastic arteries: A novel fluid-structure interaction computational model, and experimental validation. Mathematical Biosciences & Engineering, 2013, 10 (2) : 295-318. doi: 10.3934/mbe.2013.10.295

[14]

George Avalos, Thomas J. Clark. A mixed variational formulation for the wellposedness and numerical approximation of a PDE model arising in a 3-D fluid-structure interaction. Evolution Equations and Control Theory, 2014, 3 (4) : 557-578. doi: 10.3934/eect.2014.3.557

[15]

Mehdi Badra, Takéo Takahashi. Feedback boundary stabilization of 2d fluid-structure interaction systems. Discrete and Continuous Dynamical Systems, 2017, 37 (5) : 2315-2373. doi: 10.3934/dcds.2017102

[16]

Henry Jacobs, Joris Vankerschaver. Fluid-structure interaction in the Lagrange-Poincaré formalism: The Navier-Stokes and inviscid regimes. Journal of Geometric Mechanics, 2014, 6 (1) : 39-66. doi: 10.3934/jgm.2014.6.39

[17]

George Avalos, Roberto Triggiani. Semigroup well-posedness in the energy space of a parabolic-hyperbolic coupled Stokes-Lamé PDE system of fluid-structure interaction. Discrete and Continuous Dynamical Systems - S, 2009, 2 (3) : 417-447. doi: 10.3934/dcdss.2009.2.417

[18]

Olivier Delestre, Arthur R. Ghigo, José-Maria Fullana, Pierre-Yves Lagrée. A shallow water with variable pressure model for blood flow simulation. Networks and Heterogeneous Media, 2016, 11 (1) : 69-87. doi: 10.3934/nhm.2016.11.69

[19]

Mette S. Olufsen, Ali Nadim. On deriving lumped models for blood flow and pressure in the systemic arteries. Mathematical Biosciences & Engineering, 2004, 1 (1) : 61-80. doi: 10.3934/mbe.2004.1.61

[20]

Derek H. Justice, H. Joel Trussell, Mette S. Olufsen. Analysis of Blood Flow Velocity and Pressure Signals using the Multipulse Method. Mathematical Biosciences & Engineering, 2006, 3 (2) : 419-440. doi: 10.3934/mbe.2006.3.419

2018 Impact Factor: 1.313

Metrics

  • PDF downloads (84)
  • HTML views (0)
  • Cited by (26)

[Back to Top]