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
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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. Google Scholar

[2]

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[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. Google Scholar

[4]

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[5]

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[6]

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[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. doi: 10.1111/j.1395-3907.2004.00294.x. Google Scholar

[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. Google Scholar

[9]

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

[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. doi: 10.1076/ceyr.25.6.341.14231. Google Scholar

[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. doi: 10.1076/ceyr.23.3.215.5460. Google Scholar

[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. Google Scholar

[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. doi: 10.1076/ceyr.16.10.1024.9024. Google Scholar

[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. doi: 10.1016/S1350-9462(00)00028-8. Google Scholar

[15]

FreeFem++, version 3.12-0 (2d and 3d), Université Pierre et Marie Curie Laboratoire Jacques-Louis Lions,, , (). Google Scholar

[16]

Y. C. Fung, Biomechanics: Circulatio,, $2^{nd}$ edition, (1997). Google Scholar

[17]

Y. C. Fung, Biomechanics: Mechanical Properties of Living Tissues,, $2^{nd}$ edition, (1993). doi: 10.1115/1.3138285. Google Scholar

[18]

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

[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. doi: 10.1016/j.mvr.2010.02.005. Google Scholar

[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. doi: 10.1016/j.cmpb.2010.12.009. Google Scholar

[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. doi: 10.1016/j.medengphy.2010.10.004. Google Scholar

[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. doi: 10.1167/iovs.02-0792. Google Scholar

[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. doi: 10.1167/iovs.03-0996. Google Scholar

[24]

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