Ocular Hemodynamics and Glaucoma: The Role of Mathematical Modeling

Hollows R.C. , Graham P.A. . Intraocular pressure, glaucoma, and glaucoma suspects in a defined population. Br J Ophthalmol 1966; 50: 570–86.

Shah R. , Wormald R.P. . Glaucoma. Clin Evid (Online) 2011; pii: 0703.

Leske M.C. . Open-angle glaucoma: an epidemiologic overview. Ophthalmic Epidemiol 2007; 14: 166–72.

Bonomi L. , Marchini G. , Marraffa M. , Bernardi P. , Morbio R. , Varotto A. . Vascular risk factors for primary open angle glaucoma: the Egna-Neumarkt Study. Ophthalmology 2000; 107: 1287–93.

Harris A. , Kagemann L. , Ehrlich R. , Rospigliosi C. , Moore D. , Siesky B. . Measuring and interpreting ocular blood flow and metabolism in glaucoma. Can J Ophthalmol 2008; 43: 328–36.

Hayreh S.S. . Blood flow in the optic nerve head and factors that may influence it. Prog Retin Eye Res 2001; 20: 595–624.

Hulsman C.A. , Vingerling J.R. , Hofman A. , Witteman J.C. , de Jong P.T. . Blood pressure, arterial stiffness, and open-angle glaucoma: the Rotterdam study. Arch Ophthalmol 2007; 125: 805–12.

Leske M.C. , Heijl A. , Hyman L. . Predictors of long-term progression in the early manifest glaucoma trial. Ophthalmology 2007; 114: 1965–72.

Moore D. , Harris A. , Wudunn D. , Kheradiya N. , Siesky B. . Dysfunctional regulation of ocular blood flow: a risk factor for glaucoma? Clin Ophthalmol 2008; 2: 849–61.

Galassi F. , Giambene B. , Varriale R. . Systemic vascular dysregulation and retrobulbar hemodynamics in normal-tension glaucoma. Invest Ophthalmol Vis Sci 2011; 52: 4467–71.

Sines D. , Harris A. , Siesky B. The response of retrobulbar vasculature to hypercapnia in primary open-angle glaucoma and ocular hypertension. Ophthalmic Res 2007; 39: 76–80.

Leighton D.A. , Phillips C.I. . Systemic blood pressure in open-angle glaucoma, low tension glaucoma, and the normal eye. Br J Ophthalmol 1972; 56: 447–53.

Hayreh S.S. , Zimmerman M.B. , Podhajsky P. , Alward W.L. . Nocturnal arterial hypotension and its role in optic nerve head and ocular ischemic disorders. Am J Ophthalmol 1994; 117: 603–24.

Drance S. , Anderson D.R. , Schulzer M ; Collaborative Normal-Tension Glaucoma Study Group. Risk factors for progression of visual field abnormalities in normal-tension glaucoma. Am J Ophthalmol 2001; 131: 699–708.

Harris A. , Harris M. , Biller J. Aging affects the retrobulbar circulation differently in women and men. Arch Ophthalmol 2000; 118: 1076–80.

Caprioli J. , Coleman AL ; Blood Flow in Glaucoma Discussion. Blood pressure, perfusion pressure, and glaucoma. Am J Ophthalmol 2010; 149: 704–12.

Osborne N.N. , Melena J. , Chidlow G. , Wood J.P.M. . A hypothesis to explain ganglion cell death caused by vascular insults at the optic nerve head: possible implication for the treatment of glaucoma. Br J Ophthalmol 2001; 85: 1252–9.

Galassi F. , Sodi A. , Ucci F. , Renieri G. , Pieri B. , Baccini M. . Ocular hemodynamics and glaucoma prognosis: a color Doppler imaging study. Arch Ophthalmol 2003; 121: 1711–5.

Hesse R.J. . The relationship between progression of visual field defects and retrobulbar circulation in patients with glaucoma. Am J Ophthalmol 1998; 125: 566–7.

Satilmis M. , Orgül S. , Doubler B. , Flammer J. . Rate of progression of glaucoma correlates with retrobulbar circulation and intraocular pressure. Am J Ophthalmol 2003; 135: 664–9.

Schumann J. , Orgül S. , Gugleta K. , Dubler B. , Flammer J. . Interocular difference in progression of glaucoma correlates with interocular differences in retrobulbar circulation. Am J Ophthalmol 2000; 129: 728–33.

Yamazaki Y. , Drance S.M. . The relationship between progression of visual field defects and retrobulbar circulation in patients with glaucoma. Am J Ophthalmol 1997; 124: 287–95.

Zeitz O. , Galambos P. , Wagenfeld L. Glaucoma progression is associated with decreased blood flow velocities in the short posterior ciliary artery. Br J Ophthalmol 2006; 90: 1245–8.

Tielsch J.M. , Katz J. , Sommer A. , Quigley H.A. , Javitt J.C. . Hypertension, perfusion pressure, and primary open-angle glaucoma. A population-based assessment. Arch Ophthalmol 1995; 113: 216–21.

Quigley H.A. , West S.K. , Rodriguez J. , Munoz B. , Klein R. , Snyder R. . The prevalence of glaucoma in a population-based study of Hispanic subjects: Proyecto VER. Arch Ophthalmol 2001; 119: 1819–26.

Bonomi L. , Marchini G. , Marraffa M. , Bernardi P. , Morbio R. , Varotto A. . Vascular risk factors for primary open angle glaucoma: the Egna-Neumarkt Study. Ophthalmology 2000; 107: 1287–93.

Leske M.C. , Wu S.Y. , Nemesure B. , Hennis A. . Incident open-angle glaucoma and blood pressure. Arch Ophthalmol 2002; 120: 954–59.

Medeiros F.A. , Weinreb R.N. , Zangwill L.M. Long-term intraocular pressure fluctuations and risk of conversion from ocular hypertension to glaucoma. Ophthalmology 2008; 115: 934–40.

Sehi M. , Flanagan J.G. , Zeng L. , Cook R.J. , Trope G.E. . The association between diurnal variation of optic nerve head topography and intraocular pressure and ocular perfusion pressure in untreated primary open-angle glaucoma. J Glaucoma 2011; 20: 44–50.

Jonas J.B. . Role of cerebrospinal fluid pressure in the pathogenesis of glaucoma. Acta Ophthalmol 2011; 89: 505–14.

Downs J.C. , Roberts M.D. , Burgoyne C F. . Mechanical environment of the optic nerve head in glaucoma. Optom Vis Sci 2008; 85: 425–35.

Burgoyne C.F. , Downs J.C. , Bellezza A.J. , Suh J.K. , Hart R.T. . 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 2005; 24: 39–73.

Sigal I.A. , Ethier C.R. . Biomechanics of the optic nerve head. Exp Eye Res 2009; 88: 799–807.

Dongqi H. , Zeqin R. . A biomathematical model for pressure-dependent lamina cribrosa behavior. J Biomech 1999; 32: 579–84.

Edwards M.E. , Good T.A. . Use of a mathematical model to estimate stress and strain during elevated pressure induced lamina cribrosa deformation. Curr Eye Res 2001; 23: 215–25.

Newson T. , El-Sheikh A. . Mathematical modeling of the biomechanics of the lamina cribrosa under elevated intraocular pressures. J Biomech Eng 2006; 128: 496–504.

Norman R.E. , Flanagan J.G. , Sigal I.A. , Rausch S.M. , Tertinegg I. , Ethier C.R. . Finite element modeling of the human sclera: influence on optic nerve head biomechanics and connections with glaucoma. Exp Eye Res 2011; 93: 4–12.

Sigal I.A. , Flanagan J.G. , Ethier C.R. . Factors influencing optic nerve head biomechanics. Invest Ophthalmol Vis Sci 2005; 46: 4189–99.

Sigal I.A. , Yang H. , Roberts M.D. , Burgoyne C.F. , Downs J.C. . IOP-induced lamina cribrosa displacement and scleral canal expansion: an analysis of factor interactions using parameterized eye-specific models. Invest Ophthalmol Vis Sci 2011; 52: 1896–907.

Sigal I.A. , Yang H. , Roberts M.D. IOP-induced lamina cribrosa deformation and scleral canal expansion: independent or related? Invest Ophthalmol Vis Sci 2011; 52: 9023–32.

Sigal I.A. , Bilonick R.A. , Kagemann L. The optic nerve head as a robust biomechanical system. Invest Ophthalmol Vis Sci 2012; 53: 2658–67.

Takahashi T. , Nagaoka T. , Yanagida H. A mathematical model for the distribution of hemodynamic parameters in the human retinal microvascular network. J Biorheol 2009; 23: 77–86.

Ganesan P. , He S. , Xu H. . Analysis of retinal circulation using an image-based network model of retinal vasculature. Microvasc Res 2010; 80: 99–109.

Guidoboni G. , Harris A. , Carichino L. , Arieli Y. , Siesky B.A. . Effect of lamina cribrosa deformation on the hemodynamics of the central retinal artery: a mathematical model. Math Biosci Eng (in press 2013).

Birinci H. , Danaci M. , Oge I. , Erkan N.D. . Ocular blood flow in healthy and primary open-angle glaucomatous eyes. Ophthalmologica 2002; 216: 434–7.

Joos K.M. , Kay M.D. , Pillunat L.E. Effect of acute intraocular pressure changes on short posterior ciliary artery haemodynamics. Br J Ophthalmol 1999; 83: 33–8.

Anderson D.R. . Glaucoma, capillaries and pericytes. 1. Blood flow regulation. Ophthalmologica 1996; 210: 257–62.

Anderson D.R. . Introductory comments on blood flow autoregulation in the optic nerve head and vascular risk factors in glaucoma. Surv Ophthalmol 1999; 43(Suppl 1): S5–S9.

Harris A. , Jonescu-Cuypers C. , Martin B. , Kagemann L. , Zalish M. , Garzozi H.J. . Simultaneous management of blood flow and IOP in glaucoma. Acta Ophthalmol Scand 2001; 79: 336–41.

Ursino M. , Lodi C.A. . Interaction among autoregulation, CO2 reactivity, and intracranial pressure: a mathematical model. Am J Physiol Heart Circ 1998; 274: H1715–28.

Cornelissen A.J.M. , Dankelman J. , VanBavel E. , Spaan J.A.E. . Balance between myogenic, flow-dependent, and metabolic flow control in coronary arterial tree: a model study. Am J Physiol Heart Circ 2002; 282: H2224–37.

Holstein-Rathlou N.H. , Marsh D.J. . A dynamic model of renal blood flow autoregulation. Bull Math Biol 1994; 56: 411–29.

Carlson B.C. , Arciero J.C. , Secomb T.W. . Theoretical model of blood flow autoregulation: roles of myogenic, shear-dependent, and metabolic responses. Am J Physiol Heart Circ 2008; 295: H1572–9.

Jeppesen P. , Aalkjaer C. , Bek T. . Myogenic response in isolated porcine retinal arterioles. Curr Eye Res 2003; 27: 217–22.

Schmidl D. , Garhofer G. . Schmetterer L. The complex interaction between ocular perfusion pressure and ocular blood flow: relevance for glaucoma. Exp Eye Res 2011; 93: 141–55.

Aubert M. , Chaplain M.A. , McDougall S.R. , Devlin A. , Mitchell C.A. . A continuum mathematical model of the developing murine retinal vasculature. Bull Math Biol 2011; 73: 2430–51.

Watson M.G. , McDougall S.R. , Chaplain M.A. , Devlin A.H. , Mitchell C.A. . Dynamics of angiogenesis during murine retinal development: a coupled in vivo and in silico study. J R Soc Interface 2012; 9: 2351–64.

Shirinifard A. , Glazier J.A. , Swat M. Adhesion failures determine the pattern of choroidal neovascularization in the eye: a computer simulation study. PLoS Comput Biol 2012; 8: e1002440.

Racette L. , Wilson M.R. , Zangwill L.M. , Weinreb R.N. , Sample P.A. . Primary open-angle glaucoma in blacks: a review. Surv Ophthalmol 2003; 48: 295–313.

Costa V.P. , Lauande-Pimentel R. , Fonseca R.A. , Magacho L. . The influence of age, sex, race, refractive error and optic disc parameters on the sensitivity and specificity of scanning laser polarimetry. Acta Ophthalmol Scand 2004; 82: 419–25.

De León-Ortega J.E. , Sakata L.M. , Monheit B.E. , McGwin G Jr. , Arthur S.N. , Girkin C.A. . Comparison of diagnostic accuracy of Heidelberg Retina Tomograph II and Heidelberg Retina Tomograph 3 to discriminate glaucomatous and nonglaucomatous eyes. Am J Ophthalmol 2007; 144: 525–32.

Girkin C.A. , McGwin G Jr. , McNeal S.F. , DeLeon-Ortega J. . Racial differences in the association between optic disc topography and early glaucoma. Invest Ophthalmol Vis Sci 2003; 44: 3382–7.

Girkin C.A. , McGwin G Jr. , Long C. , DeLeon-Ortega J. , Graf C.M. , Everett A.W. . Subjective and objective optic nerve assessment in African Americans and whites. Invest Ophthalmol Vis Sci 2004; 45: 2272–8.

Girkin C.A. , McGwin G Jr. , Xie A. , Deleon-Ortega J.E. . Differences in optic disc topography between black and white normal subjects. Ophthalmology 2005; 112: 33–9.

Girkin C.A. , Sample P.A. , Liebmann J.M. ; ADAGES Group. 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 2010; 128: 541–50.

Knight O.J. , Girkin C.A. , Budenz D.L. , Durbin M.K. , Feuer WJ ; Cirrus OCT Normative Database Study Group. Effect of race, age, and axial length on optic nerve head parameters and retinal nerve fiber layer thickness measured by Cirrus HD-OCT. Arch Ophthalmol 2012; 130: 312–8.

Poinoosawmy D. , Fontana L. , Wu J.X. , Fitzke F.W. , Hitchings R.A. . Variation of nerve fibre layer thickness measurements with age and ethnicity by scanning laser polarimetry. Br J Ophthalmol 1997; 81: 350–4.

Racette L. , Boden C. , Kleinhandler S.L. Differences in visual function and optic nerve structure between healthy eyes of blacks and whites. Arch Ophthalmol 2005; 123: 1547–53.

Seider M.I. , Lee R.Y. , Wang D. , Pekmezci M. , Porco T.C. , Lin S.C. . Optic disk size variability between African, Asian, white, Hispanic, and Filipino Americans using Heidelberg retinal tomography. J Glaucoma 2009; 18: 595–600.

Zelefsky J.R. , Harizman N. , Mora R. Assessment of a race-specific normative HRT-III database to differentiate glaucomatous from normal eyes. J Glaucoma 2006; 15: 548–51.