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Effect of intraocular pressure on the hemodynamics of the central retinal artery: a mathematical model. (English) Zbl 1298.76245

Summary: 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.

MSC:

76Z05 Physiological flows
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74L15 Biomechanical solid mechanics

Software:

FreeFem++

References:

[1] Y. Aguomi, Laminar and pre laminar tissue displacement during intraocular pressure elevation in glaucoma patients and healthy controls,, Ophthalmology, 118, 52 (2011)
[2] R. L. Armentano, Arterial wall mechanics in conscious dogs: Assessment of viscous, inertial, and elastic moduli to characterize aortic wall behavior,, Circ. Res., 76, 468 (1995) · doi:10.1161/01.RES.76.3.468
[3] D. Badeanu, 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, 4351 (2009)
[4] R. R. Buhrmann, Prevalence of glaucoma in a rural East African population,, Invest. Ophthalmol. Vis. Sci., 41, 40 (2000)
[5] C. F. Burgoyne, 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, 39 (2005) · doi:10.1016/j.preteyeres.2004.06.001
[6] J. Caprioli, Blood pressure, perfusion pressure, and glaucoma,, Am. J. Ophthalmol., 149, 704 (2010) · doi:10.1016/j.ajo.2010.01.018
[7] V. P. Costa, 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, 419 (2004) · doi:10.1111/j.1395-3907.2004.00294.x
[8] J. E. De León-Ortega, Comparison of diagnostic accuracy of Heidelberg Retina Tomograph II and Heidelberg Retina Tomograph 3 to discriminate glaucomatous and nonglaucomatous eyes,, Am. J. Ophthalmol., 144, 525 (2007)
[9] H. Dongqi, A biomathematical model for pressure-dependent lamina cribrosa behavior,, J. Biomech., 32, 579 (1999) · doi:10.1016/S0021-9290(99)00025-1
[10] G. T. Dorner, Calculation of the diameter of the central retinal artery from noninvasive measurements in humans,, Curr. Eye Res., 25, 341 (2002) · doi:10.1076/ceyr.25.6.341.14231
[11] M. E. Edwards, Use of a mathematical model to estimate stress and strain during elevated pressure induced lamina cribrosa deformation,, Curr. Eye Res., 23, 215 (2001) · doi:10.1076/ceyr.23.3.215.5460
[12] R. Ehrlich, Age-related macular degeneration and the aging eye,, Clin. Interv. Aging., 3, 473 (2008)
[13] O. Findl, <em><em>Effects of changes in intraocular pressure on human ocular haemodynamics</em></em>,, Curr. Eye Res., 16, 1024 (1997) · doi:10.1076/ceyr.16.10.1024.9024
[14] J. Flammer, Vasospasm, its role in the pathogenesis of diseases with particular reference to the eye,, Prog. Retin. Eye Res., 20, 319 (2001) · doi:10.1016/S1350-9462(00)00028-8
[15] FreeFem++, <em>Université Pierre et Marie Curie Laboratoire Jacques-Louis Lions</em>,, <a href=
[16] Y. C. Fung, <em>Biomechanics: Circulatio</em>,, \(2^{nd}\) edition (1997)
[17] Y. C. Fung, <em>Biomechanics: Mechanical Properties of Living Tissues</em>,, \(2^{nd}\) edition (1993) · doi:10.1115/1.3138285
[18] P. Ganesan, Development of an image-based network model of retinal vasculature,, Ann. Biomed. Eng., 38, 1566 (2010) · doi:10.1007/s10439-010-9942-4
[19] P. Ganesan, Analysis of retinal circulation using an image-based network model of retinal vasculature,, Microvasc. Res., 80, 99 (2010) · doi:10.1016/j.mvr.2010.02.005
[20] P. Ganesan, Development of an image-based model for capillary vasculature of retina,, Comput. Methods Programs Biomed., 102, 35 (2011) · doi:10.1016/j.cmpb.2010.12.009
[21] P. Ganesan, Modelling of pulsatile blood flow in arterial trees of retinal vasculature,, Med. Eng. Phys., 33, 810 (2011) · doi:10.1016/j.medengphy.2010.10.004
[22] C. A. Girkin, Racial differences in the association between optic disc topography and early glaucoma,, Invest. Ophthalmol. Vis. Sci., 44, 3382 (2003) · doi:10.1167/iovs.02-0792
[23] C. A. Girkin, Subjective and objective optic nerve assessment in African Americans and whites,, Invest. Ophthalmol. Vis. Sci., 45, 2272 (2004) · doi:10.1167/iovs.03-0996
[24] C. A. Girkin, Differences in optic disc topography between black and white normal subjects,, Ophthalmology, 112, 33 (2005) · doi:10.1016/j.ophtha.2004.07.029
[25] C. A. Girkin, 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, 541 (2010) · doi:10.1001/archophthalmol.2010.49
[26] G. Guidoboni, <em>Mathematical modeling approaches in the study of glaucoma disparities among people of African and European Descents</em>,, J. Coupled Syst. Multiscale Dyn., 1, 1 (2013)
[27] A. Harris, Acute IOP elevation with scleral suction: Effects on retrobulbar haemodynamics,, Br. J. Ophthalmol., 80, 1055 (1996) · doi:10.1136/bjo.80.12.1055
[28] A. Harris, <em>Atlas of Ocular Blood Flow. Vascular Anatomy, Pathophysiology, and Metabolism</em>,, Elsevier (2003)
[29] A. Harris, Measuring and interpreting ocular blood flow and metabolism in glaucoma,, Can. J. Ophthalmol., 43, 328 (2008) · doi:10.1139/I08-051
[30] A. Harris, <em>Ocular hemodynamics and glaucoma: the role of mathematical modeling</em>,, Eur. J. Ophthalmol., 23, 139 (2013)
[31] S. S. Hayreh, Blood flow in the optic nerve head and factors that may influence it,, Prog. Retin. Eye Res., 20, 595 (2001) · doi:10.1016/S1350-9462(01)00005-2
[32] E. M. Hoffmann, Optic disk size and glaucoma,, Surv. Ophthalmol., 52, 32 (2007) · doi:10.1016/j.survophthal.2006.10.002
[33] I. Januleviciene, Visual function, optic nerve structure, and ocular blood flow parameters after 1 year of glaucoma treatment with fixed combinations,, Eur. J. Ophthalmol., 19, 790 (2009)
[34] J. B. Jonas, Morphometry of the human lamina cribrosa surface,, Invest. Ophthalmol. Vis. Sci., 32, 401 (1991)
[35] J. B. Jonas, Central corneal thickness and thickness of the lamina cribrosa in human eyes,, Invest. Ophthalmol. Vis. Sci., 46, 1275 (2005) · doi:10.1167/iovs.04-0851
[36] O. Knight, 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, 312 (2012) · doi:10.1001/archopthalmol.2011.1576
[37] M. C. Leske, The Barbados Eye Study: Prevalence of open angle glaucoma,, Arc. Ophthalmol., 112, 821 (1994) · doi:10.1001/archopht.1994.01090180121046
[38] M. C. Leske, Open-angle glaucoma - an epidemiologic overview,, Ophthalmic Epidemiol., 14, 166 (2007) · doi:10.1080/09286580701501931
[39] M. C. Leske, Predictors of long-term progression in the early manifest glaucoma trial,, Ophthalmology, 114, 1965 (2007) · doi:10.1016/j.ophtha.2007.03.016
[40] A. Mikelic, Fluid-structure interaction in a pre-stressed tube with thick elastic walls I: the stationary Stokes problem,, Netw. Heterog. Media, 2, 397 (2007) · Zbl 1260.35147 · doi:10.3934/nhm.2007.2.397
[41] D. Moore, Dysfunctional regulation of ocular blood flow: a risk factor for glaucoma?, Clin. Ophthalmol., 2, 849 (2008)
[42] W. H. Morgan, The correlation between cerebrospinal fluid pressure and retrolaminar tissue pressure,, Invest. Ophthalmol. Vis. Sci., 39, 3236 (1998)
[43] W. H. Morgan, Optic disc movement with variations in intraocular and cerebrospinal fluid pressure,, Invest. Ophthalmol. Vis. Sci., 43, 1419 (2002)
[44] J. Morgan-Davies, Three dimensional analysis of the lamina cribrosa in glaucoma,, Br. J. Ophthalmol., 88, 1299 (2004) · doi:10.1136/bjo.2003.036020
[45] T. Newson, Mathematical modeling of the biomechanics of the lamina cribrosa under elevated intraocular pressures,, J. Biomech. Eng., 128, 496 (2006) · doi:10.1115/1.2205372
[46] R. E. Norman, Dimensions of the human sclera: Thickness measurement and regional changes with axial length,, Exp. Eye Res., 90, 277 (2010) · doi:10.1016/j.exer.2009.11.001
[47] B. Pemp, Ocular blood flow in diabetes and age-related macular degeneration,, Can. J. Ophthalmol., 43, 295 (2008) · doi:10.1139/I08-049
[48] D. Poinoosawmy, Variation of nerve fibre layer thickness measurements with age and ethnicity by scanning laser polarimetry,, Br. J. Ophthalmol., 81, 350 (1997) · doi:10.1136/bjo.81.5.350
[49] C. J. Pournaras, Regulation of retinal blood flow in health and disease,, Prog. Retin. Eye Res., 27, 284 (2008) · doi:10.1016/j.preteyeres.2008.02.002
[50] A. Quarteroni, Computational vascular fluid dynamics: Problems, models and methods,, Comput. Visual Sci., 2, 163 (2000) · Zbl 1096.76042 · doi:10.1007/s007910050039
[51] L. Racette, Primary open-angle glaucoma in blacks: A review,, Surv. Ophthalmol., 48, 295 (2003) · doi:10.1016/S0039-6257(03)00028-6
[52] L. Racette, Differences in visual function and optic nerve structure between healthy eyes of blacks and whites,, Arch. Ophthalmol., 123, 1547 (2005) · doi:10.1001/archopht.123.11.1547
[53] R. Ren, Lamina cribrosa and peripapillary sclera histomorphometry in normal and advanced glaucomatous Chinese eyes with various axial length,, Invest. Ophthalmol. Vis. Sci., 50, 2175 (2009) · doi:10.1167/iovs.07-1429
[54] M. I. Seider, Optic disk size variability between African, Asian, white, Hispanic, and Filipino Americans using Heidelberg retinal tomography,, J. Glaucoma, 18, 595 (2009) · doi:10.1097/IJG.0b013e3181996f05
[55] I. A. Sigal, Finite element modeling of optic nerve head biomechanics,, Invest. Ophthalmol. Vis. Sci., 45, 4378 (2004) · doi:10.1167/iovs.04-0133
[56] I. A. Sigal, Predicted extension, compression and shearing of optic nerve head tissues,, Exp. Eye Res., 85, 312 (2007) · doi:10.1016/j.exer.2007.05.005
[57] I. A. Sigal, Modeling individual-specific human optic nerve head biomechanics. Part I: IOP-induced deformations and influence of geometry,, Biomech. Model. Mechanobiol., 8, 85 (2009) · doi:10.1007/s10237-008-0120-7
[58] I. A. Sigal, IOP-induced lamina cribrosa deformation and scleral canal expansion: Independent or related?, Invest. Ophthalmol. Vis. Sci., 52, 9023 (2011) · doi:10.1167/iovs.11-8183
[59] I. A. Sigal, The optic nerve head as a robust biomechanical system,, Invest. Ophthalmol. Vis. Sci., 53, 2658 (2012) · doi:10.1167/iovs.11-9303
[60] I. A. Sigal, A few good responses: which mechanical effects of IOP on the ONH to study?, Invest. Ophthalmol. Vis. Sci., 53, 4270 (2012) · doi:10.1167/iovs.11-8739
[61] I. A. Sigal, Human lamina cribrosa insertion and age,, Invest. Ophthalmol. Vis. Sci., 53, 6870 (2012) · doi:10.1167/iovs.12-9890
[62] A. Sommer, Racial differences in the cause-specific prevalence of blindness in east Baltimore,, N. Engl. J. Med., 325, 1412 (1991) · doi:10.1056/NEJM199111143252004
[63] A. Sommer, Glaucoma risk factors observed in the Baltimore Eye Survey,, Curr. Opin. Ophthalmol., 7, 93 (1996) · doi:10.1097/00055735-199604000-00016
[64] T. Takahashi, A mathematical model for the distribution of hemodynamic parameters in the human retinal microvascular network,, J. Biorheol., 23, 77 (2009) · doi:10.1007/s12573-009-0012-1
[65] J. M. Tielsch, Racial variations in the prevalence of primary open-angle glaucoma: The Baltimore Eye Survey,, JAMA, 266, 369 (1991) · doi:10.1001/jama.1991.03470030069026
[66] R. Varma, Race-, age-, gender-, and refractive error-related differences in the normal optic disc,, Arch. Ophthalmol., 112, 1068 (1994) · doi:10.1001/archopht.1994.01090200074026
[67] S. Woo, Nonlinear material properties of intact cornea and sclera,, Exp. Eye Res., 14, 29 (1972) · doi:10.1016/0014-4835(72)90139-X
[68] J. R. Zelefsky, Assessment of a race-specific normative HRT-III database to differentiate glaucomatous from normal eyes,, J. Glaucoma, 15, 548 (2006) · doi:10.1097/01.ijg.0000212289.00917.a8
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