### Mathematical Biosciences and Engineering

2014, Issue 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

• Received: 01 May 2012 Accepted: 29 June 2018 Published: 01 January 2014
• MSC : Primary: 76Z05, 74F10, 74L15; Secondary: 76Z05.

• 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[J]. Mathematical Biosciences and Engineering, 2014, 11(3): 523-546. doi: 10.3934/mbe.2014.11.523

### Related Papers:

• 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.

 [1] Ophthalmology, 118 (2011), 52-59. [2] Circ. Res., 76 (1995), 468-478. [3] Invest. Ophthalmol. Vis. Sci., 50 (2009), 4351-4359. [4] Invest. Ophthalmol. Vis. Sci., 41 (2000), 40-48. [5] Prog. Retin. Eye Res., 24 (2005), 39-73. [6] Am. J. Ophthalmol., 149 (2010), 704-712. [7] Acta Ophthalmol. Scand., 82 (2004), 419-425. [8] Am. J. Ophthalmol., 144 (2007), 525-532. [9] J. Biomech., 32 (1999), 579-584. [10] Curr. Eye Res., 25 (2002), 341-345. [11] Curr. Eye Res., 23 (2001), 215-225. [12] Clin. Interv. Aging., 3 (2008), 473-482. [13] Curr. Eye Res., 16 (1997), 1024-1029. [14] Prog. Retin. Eye Res., 20 (2001), 319-349. [15] http://www.freefem.org/ff++/. [16] $2^{nd}$ edition, Springer-Verlag, New York, 1997. [17] $2^{nd}$ edition, Springer-Verlag, New York, 1993. [18] Ann. Biomed. Eng., 38 (2010), 1566-1585. [19] Microvasc. Res., 80 (2010), 99-109. [20] Comput. Methods Programs Biomed., 102 (2011), 35-46. [21] Med. Eng. Phys., 33 (2011), 810-823. [22] Invest. Ophthalmol. Vis. Sci., 44 (2003), 3382-3387. [23] Invest. Ophthalmol. Vis. Sci., 45 (2004), 2272-2278. [24] Ophthalmology, 112 (2005), 33-39. [25] Arch. Ophthalmol., 128 (2010), 541-550. [26] J. Coupled Syst. Multiscale Dyn., 1(1) (2013), 1-21. [27] Br. J. Ophthalmol., 80 (1996), 1055-1059. [28] Elsevier, Philadelphia, 2003. [29] Can. J. Ophthalmol., 43 (2008), 328-336. [30] Eur. J. Ophthalmol., 23(2) (2013), 139-146. [31] Prog. Retin. Eye Res., 20 (2001), 595-624. [32] Surv. Ophthalmol., 52 (2007), 32-49. [33] Eur. J. Ophthalmol., 19 (2009), 790-797. [34] Invest. Ophthalmol. Vis. Sci., 32 (1991), 401-405. [35] Invest. Ophthalmol. Vis. Sci., 46 (2005), 1275-1279. [36] Arc. Ophthalmol., 130 (2012), 312-318. [37] Arc. Ophthalmol., 112 (1994), 821-829. [38] Ophthalmic Epidemiol., 14 (2007), 166-172. [39] Ophthalmology, 114 (2007), 1965-1972. [40] Netw. Heterog. Media, 2 (2007), 397-423. [41] Clin. Ophthalmol., 2 (2008), 849-861. [42] Invest. Ophthalmol. Vis. Sci., 39 (1998), 3236-3242. [43] Invest. Ophthalmol. Vis. Sci., 43 (2002), 1419-1428. [44] Br. J. Ophthalmol., 88 (2004), 1299-1304. [45] J. Biomech. Eng., 128 (2006), 496-504. [46] Exp. Eye Res., 90 (2010), 277-284. [47] Can. J. Ophthalmol., 43 (2008), 295-301. [48] Br. J. Ophthalmol., 81 (1997), 350-354. [49] Prog. Retin. Eye Res., 27 (2008), 284-330. [50] Comput. Visual Sci., 2 (2000), 163-197. [51] Surv. Ophthalmol., 48 (2003), 295-313. [52] Arch. Ophthalmol., 123 (2005), 1547-1553. [53] Invest. Ophthalmol. Vis. Sci., 50 (2009), 2175-2184. [54] J. Glaucoma, 18 (2009), 595-600. [55] Invest. Ophthalmol. Vis. Sci., 45 (2004), 4378-4387. [56] Exp. Eye Res., 85 (2007), 312-322. [57] Biomech. Model. Mechanobiol., 8 (2009), 85-98. [58] Invest. Ophthalmol. Vis. Sci., 52 (2011), 9023-9032. [59] Invest. Ophthalmol. Vis. Sci., 53 (2012), 2658-2667. [60] Invest. Ophthalmol. Vis. Sci., 53(7) (2012), 4270-4278. [61] Invest. Ophthalmol. Vis. Sci., 53 (2012), 6870-6879. [62] N. Engl. J. Med., 325 (1991), 1412-1417. [63] Curr. Opin. Ophthalmol., 7 (1996), 93-98. [64] J. Biorheol., 23 (2009), 77-86. [65] JAMA, 266 (1991), 369-374. [66] Arch. Ophthalmol., 112 (1994), 1068-1076. [67] Exp. Eye Res., 14 (1972), 29-39. [68] J. Glaucoma, 15 (2006), 548-551.
###### 通讯作者: 陈斌, bchen63@163.com
• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142

2.080 2.1