Mathematical modeling and glaucoma: the need for an individualized approach to risk assessment
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Verticchio Vercellin AC, Harris A, Cordell JV, Do T, Moroney J, Belamkar A, Siesky B. Mathematical modeling and glaucoma: the need for an individualized approach to risk assessment. MAIO [Internet]. 2016 Feb. 24 [cited 2024 Jun. 16];1(1):6-20. Available from:

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blood flow; disease progression; mathematical modeling; primary open-angle glaucoma; risk factors


Primary open-angle glaucoma is a chronic optic neuropathy characterized by retinal ganglion cell loss and subsequent visual field impairment. Elevated intraocular pressure remains the only treatable and modifiable risk factor and vascular impairment has been demonstrated in glaucomatous patients. New research has uncovered varying and often contradictory data suggesting more than just a casual correlation with ethnicity, diabetes, gender, obesity and age. Little is known about each variables’ contribution to the etiology of glaucoma and how their presence or absence with other risk factors potentiate or reduce an individual’s overall risk. The realization that glaucoma is more than a simple, binary disease necessitates a next-generation mathematical model with the capability to integrate individual patient characteristics and clinical risk factors to predict its formation and progression.
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Leske MC. Open-angle glaucoma: an epidemiological overview. Ophthalmic Epidemiol 2007Jul-Aug;14(4):166-72.

Kingman S. Glaucoma is second leading cause of blindness globally. Bull World Health Organ. 2004 Nov; 82(11):887-8.

Cook C, Foster P. Epidemiology of glaucoma: What's new? Can J Ophthalmol. 2012 Jun; 47(3):223-6. doi: 10.1016/j.jcjo.2012.02.003

Grewe R. The history of glaucoma. Klin Monbl Augenheilkd. 1986 Feb;188(2):167-9.

Leske CM, Heijl A, Hyman L et al. Predictors of long-term progression in the early manifest glaucoma trial. Ophthalmology. 2007 Nov;114(11):1965-72.

Caprioli J, Coleman AL. Intraocular pressure fluctuation a risk factor for visual field progression at low intraocular pressures in the advanced glaucoma intervention study. Ophthalmology. 2008 Jul; 115(7):1123-29.

Caprioli J, Coleman AL. Blood flow in glaucoma discussion; blood pressure, perfusion pressure, and glaucoma. Am J Ophthalmol. 2010 May; 149(5):704-12. doi: 10.1016/j.ajo.2010.01.018.

Danias J, Podos SM. Comparison of glaucomatous progression between untreated patients with normal-tension glaucoma and patients with therapeutically reduced intraocular pressures. The effectiveness of intraocular pressure reduction in the treatment of normal-tension glaucoma. Am J Ophthalmol. 1999 May; 127(5):623-5.

Ehrnrooth P, Puska P, Lehto I et al. Progression of visual field defects and visual loss in trabeculectomized eyes. Graefes Arch Clin Exp Ophthalmol. 2005 Aug; 243(8):741-7.

Tielsch JM, Sommer A, Katz J et al. Racial variations in the prevalence of primary open angle glaucoma, the baltimore eye survey. JAMA. 1991 Jul 17; 266(3):369-74.

Chung HS, Harris A, Kagemann L et al. Peripapillary retinal blood flow in normal tension glaucoma. Br J Ophthalmol. 1999;83(4), 466-9.

Harris A, Sergott RC, Spaeth GL et al. Color Doppler analysis of ocular vessel blood velocity in normal-tension glaucoma. Am J Ophthalmol. 1994; 118(5), 642-9.

Coleman AL, Caprioli J. The logic behind target intraocular pressure. Am J Ophthalmol. 2009 Mar;147(3):379-80. doi: 10.1016/j.ajo.2008.10.027

Snell RS, Lemp MA. Clinical anatomy of the eye. Second edition. Blackwell Science Ltd, 1998.

Karpinich NO, Caron KM. Schlemm’s canal: more than meets the eye, lymphatics in disguise. The Journal of Clinical Investigation. 2014; 124(9), 3701-3703.

Truong TN, Li H, Hong Y-K, Chen L. Novel Characterization and Live Imaging of Schlemm's Canal Expressing Prox-1. PLoS ONE. 2014;9(5): e98245.

Kansky JJ. Clinical ophthalmology: a systemic approach. Seventh edition. Elsevier, 2011.

Harris A, Guidoboni G, Arciero JC et al. Ocular hemodynamics and glaucoma: The role of mathematical modeling. Eur J Ophthalmol. 2013 Mar-Apr;23(2):139-46. doi: 10.5301/ejo.5000255.

19. Norman RE, Flanagan JG, Sigal IA et al. Finite element modeling of the human sclera: influence on optic nerve head biomechanics and connections with glaucoma. Exp Eye Res;2011 Jul;93(1):4-12. doi: 10.1016/j.exer.2010.09.014

Donqqi H, Zegin R. A biomathematical model for pressure-dependent lamina cribrosa behavior. J Biomech. 1999 Jun;32(6):579-84.

Bellezza A, Hart R, Burgoyne C. The optic nerve head as a biomechanical structure: initial finite element modeling. Invest Ophthalmol Vis Sci. 2000 Sept;41(10):2991-3000.

Sigal I, Flanagan J, Tertinegg I et al. Finite element modeling of optic nerve head biomechanics. Invest Ophthalmol Vis Sci. 2004 Dec;45(12):4378-87.

Yousefi S, Goldbaumn M, Balasubramanian M et al. Glaucoma progression detection using structural retinal nerve fiber layer measurements and functional visual field points. IEEE Trans Biomed Eng. 2014;61(4):1143-54.

Newson T, El-Sheikh A. “Mathematical modeling of the biomechanic of the laimina cribrosa under elevated intraocular pressures.” J Biomech Eng. 2006;128(4):496-504.

Leske MC, Connell AM, Schachat AP et al. The Barbados eye study, prevalence of open angle glaucoma. Arch Ophthalmol. 1994 Jun;112(6):821-9.

Mason RP, Kosoko O, Wilson MR et al. National survey of the prevalence and risk factors of glaucoma in St. Lucia, West Indies. Part I. Prevalence findings. Ophthalmology. 1989; 96:1363.

Rotchford AP, Kirwan JF, Muller MA et al. Temba glaucoma study: A population-based crosssectional survey in urban South Africa. Ophthalmology. 2003 Feb; 110(2):376-82.

Gordon MO, Beiser JA, Brandt JD et al. The ocular hypertension treatment study: Baseline factors that predict the onset of primary open-angle glaucoma. Arch Ophthalmol. 2002 Jun; 120(6):714-20;discussion 829–30.

Martin MJ, Sommer A, Gold EB et al. Race and primary open-angle glaucoma. Am J Ophthalmol. 1985 April; 99(4):383-7.

Racette L, Liebmann JM, Girkin CA, et al. African Descent and Glaucoma Evaluation Study (ADAGES): III. Ancestry differences in visual function in healthy eyes. Arch Ophthalmol. 2010 May;128(5):551-9. doi: 10.1001/archophthalmol.2010.58

Racette L, Wilson MR, Zangwill LM et al. Primary open-angle glaucoma in blacks: A review. Surv Ophthalmol. 2003 May-Jun; 48(3):295-313.

Girkin CA, Nievergelt CM, Kuo JZ, et al. Biogeographic Ancestry in the African Descent and Glaucoma Evaluation Study (ADAGES): Association with corneal and optic nerve structure. Invest Ophthalmol Vis Sci. 2015 Mar;56(3):2043-9. doi: 10.1167/iovs.14-15719.

Girkin CA, Sample PA, Liebmann JM et al. 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 May; 128(5):541-50. doi: 10.1001/archophthalmol.2010.49.

Moore GH, Bowd C, Medeiros FA, et al. African Descent and Glaucoma Evaluation Study (ADAGES): Asymmetry of structural measures in normal participants. J Glaucoma. 2013 Feb;22(2);65-72. doi: 10.1097/IJG.0b013e31822e8e51.

Sample PA, Girkin CA, Zangwill LM et al. The African Descent and Glaucoma Evaluation Study (ADAGES): Design and baseline data. Arch Ophthamol. 2009 Sep;127(9):1136-45. doi: 10.1001/archophthalmol.2009.187.

Siesky B, Harris A, Racette L, et al. Differences in ocular blood flow in glaucoma between patients of African and European descent. J Glaucoma. 2015 Feb;24(2):117-21. doi: 10.1097/IJG.0b013e31829d9bb0.

Kanakamedala P, Harris A, Siesky B, et al. Optic nerve head morphology in glaucoma patients of African descent is strongly correlated to retinal blood flow. Br J Ophthalmol. 2014 Nov;98(11):1551-4. doi: 10.1136/bjophthalmol-2013-304393

Sayin N, Kara N, and Pekel G. Ocular complications of Diabetes Mellitus. World J Diabetes. 2015 Feb 15;6(1):92-108. doi:10.4239/wjd.v6.i1.92.

Newman-Casey PA, Talwar N, Nan B et al. The relationship between components of metabolic syndrome and open-angle glaucoma. Ophthalmology . 2011 July;118(7): 1318–26. doi:10.1016/j.ophtha.2010.11.022.

Chopra V, Varma R, Francis BA et al. Type 2 Diabetes Mellitus and the risk of open-angle glaucoma the Los Angeles Latino Eye Study. Ophthalmology. 2008 Feb;115(2):227-32.

Halilovic EA, Ljaljevic S, Alimanovic I et al. Analysis of the Influence of Type of Diabetes Mellitus on the Development and Type of Glaucoma. Medical Archives. 2015 Feb;69(1):34-7. doi: 10.5455/medarh.2015.69.34-37.

Shoshani Y, Harris A, Shoja MM et al. Impaired ocular blood flow regulation in patients with open-angle glaucoma and diabetes. Clin Experiment Ophthalmol. 2012 Sep-Oct;40(7):697-705. doi:10.1111/j.1442-9071.2012.02778.x.

Mitchell P, Smith W, Attebo K, Healey PR. Prevalence of open-angle glaucoma in Australia. The Blue Mountains Eye Study. Ophthalmology. 1996 Oct;103(10):1661–9.

Zhou M, Wang W, Huang W et al. Diabetes Mellitus as a risk factor for open-angle glaucoma: A Systematic Review and Meta-Analysis. PloS One. 2014 Aug 19;9(8):e102972. doi: 10.1371/journal.pone.0102972.

de Voogd S, Ikram MK, Wolfs RC et al. Is Diabetes Mellitus a risk factor for open-angle glaucoma? The Rotterdam Study. Ophthalmology. 2006 Oct;113(10):1827-31.

Ozdamar Y, Cankaya B, Ozalp S et al. Is There a correlation between Diabetes Mellitus and central corneal thickness? J Glaucoma. 2010 Dec;19(9);613-6. doi:10.1097/IJG.0b013e3181ca7c62.

Kanamori A, Nakamura M, Mukuno H et al. Diabetes has an additive effect on neural apoptosis in rat retina with chronically elevated intraocular pressure. Curr Eye Res. 2004 Jan;28(1): 47-54. doi:10.1076/ceyr.

Halilovic EA, Ljaljevic S, Alimanovic I et al. Analysis of the Influence of Type of Diabetes Mellitus on the Development and Type of Glaucoma. Medical Archives. 2015 Feb;69(1):34-7. doi: 10.5455/medarh.2015.69.34-37.

Shoshani Y, Harris A, Shoja MM et al. Impaired ocular blood flow regulation in patients with openangle glaucoma and diabetes. Clin Experiment Ophthalmol. 2012 Sep-Oct;40(7):697-705. doi:10.1111/j.1442-9071.2012.02778.x.

Mitchell P, Smith W, Attebo K, Healey PR. Prevalence of open-angle glaucoma in Australia. The Blue Mountains Eye Study. Ophthalmology. 1996 Oct;103(10):1661–9.

Rudnicka AR, Mt-Isa S, Owen CG et al. Variations in primary open-angle glaucoma prevalence by age, gender, and race: a Bayesian meta-analysis. Invest Ophthalmol Vis Sci. 2006 Oct;47(10):4254–61.

Khan HA, Leibowitz HM, Ganley JP et al. The Framingham Eye Study. II. Association of ophthalmic pathology with single variables previously measured in the Framingham Heart Study. Am J Epidemiol. 1977;106:33-41.

Klein BE, Klein R, Sponsel WE et al. Prevalence of glaucoma. The Beaver Dam Eye Study. Ophthalmology. 1992;99:1499-1504.

Ustymowicz A, Mariak Z, Weigele J et al. Normal reference intervals and ranges of side-to-side and day-to-day variability of ocular blood flow Doppler parameters. Ultrasound Med Biol 2005 Jul;31(7):895–903.

Marjanovic I, Marjanovic M, Gvozdenovic R et al. Retrobulbar heodynamic parameters in men and women with open angle glaucoma. Voinosanit Pregl. 2014 Dec; 71(12):1128-31

Harris-Yitzhak M, Harris A, Ben-Refael Z et al. Estrogen-replacement therapy: effects on retrobulbar hemodynamics. Am J Ophthalmol 2000;129(5):623–8.

Siesky B, Harris A, Kheradiya N et al. The effects of raloxifene hydrochloride on ocular hemodynamics and visual function. Int Ophthalmol. 2009 Aug;29(4):225–30. doi: 10.1007/s10792-008-9224-4.

Wang S, Xu L, Wang Y et al. Retinal vessel diameter in normal and glaucomatous eyes: the Beijing eye study. Clin Experiment Ophthalmol. 2007 Dec;35(9):800–7. doi: 10.1111/j.14429071.2007.01627.x

Wong TY, Klein R, Klein BE et al. Retinal vessel diameters and their associations with age and blood pressure. Invest Ophthalmol Vis Sci. 2003 Nov;44(11): 4644–50.

Ogden C, Carroll M, Kit B et al. Prevalence of childhood and adult obesity in the United States, 2011-2012. JAMA. 2014 Feb 26;311(8):806-14. doi: 10.1001/jama.2014.732

Finkelstein EA, Khavjou OA, Thompson H et al. Obesity and severe obesity forecasts through 2030. Am J Prev Med. 2012 Jun;42(6):563-70. doi: 10.1016/j.amepre.2011.10.026.

Yoshida M, Ishikawa M, Karita K et al. Association of blood pressure and body mass index with intraocular pressure in middle-aged and older Japanese residents: a cross-sectional and longitudinal study. Acta Med Okayama. 2015;68(1):27-34.

Geloneck MM, Crowell EL, Wilson EB, et al. Correlation between intraocular pressure and body mass index in the seated and supine positions. J Glaucoma. 2015 Feb;24(2):130-4. doi: 10.1097/01.ijg.0000435775.05032.87.

OH SW, Lee S, Park C et al. Elevated intraocular pressure is associated with insulin resistance and metabolic syndrome. Diabetes Metab Res Rev. 2005 Sep-Oct;21(5):434-40.

Gasser P, Stumpfig D, Schozau A et al. Body mass index in glaucoma. J Glaucoma. 1999 Feb;8(1):8-11.

Asrani S, Samuels B, Thakur M et al. Clinical profiles of primary open angle glaucoma versus normal tension glaucoma patients: a pilot study. Curr Eye Res. 2011 May;36(5):429-35. doi: 10.3109/02713683.2011.559563.

Kang JH, Loomis SJ, Rosner BA et al. Comparison of risk factor profiles for primary open-angle glaucoma subtypes defined by pattern of visual field loss: a prospective study. Invest Ophthalmolmol Vis Sci. 2015 April;56(4):2439-48. doi: 10.1167/iovs.14-16088.

Berdahl JP, Allingham RR, Johnson DH. Cerebrospinal fluid pressure is decreased in primary open-angle glaucoma. Ophthalmology. 2008 May;115:763-8. doi: 10.1016/j.ophtha.2008.01.013.

Berdahl JP, Fautsch MP, Stinnet SS et al. Intracranial pressure in primary open angle glaucoma, normal tension glaucoma, and ocular hypertension: a case-control study. Invest Ophthalmol Vis Sci. 2008 Dec;49(12):5412-8. doi: 10.1167/iovs.08-2228.

Ngo S, Harris A, Sieksy BA et al. Blood pressure, ocular perfusion pressure, and body mass index in glaucoma patients. Eur J Ophthal. 2013 Sept-Oct;23(5):664-9.

Pedro-Egbe C and Awoyesuku E. The relationship between vertical cup-disc ratio and body mass index in Port Harcourt, Nigeria. Niger J Clin Pract. 2013 Oct-Dec;16(4):517-20.

69. Leske MC, Wu SY, Hennis A et al. Risk factors for incident open-angle glaucoma: The Barbados Eye Studies. Ophthalmology. 2008 Jan;115(1):85-93.

Müskens RP, de Voogd S, Wolfs RC et al. Systemic antihypertensive medication and incident open angle glaucoma. Ophthalmology. 2007 Dec;114(12):2221-6.

Le A, Mukesh BN, McCarty CA et al. Risk factors associated with the incidence of open-angle glaucoma: the visual impairment project. Invest Ophthalmol Vis Sci. 2003 Sep;44(9):3783-9.

Kass MA, Heuer DK, Higginbotham EJ et al. The Ocular Hypertension Treatment Study: a randomized trial determines that topical ocular hypotensive medication delays or prevents the onset of primary open-angle glaucoma. Arch Ophthalmol. 2002 Jun;120(6):701-13; discussion 829-30.

Miglior S, Zeyen T, Pfeiffer N et al. Results of the European Glaucoma Prevention Study, Ophthalmology. 2005 Mar;112(3):366-75.

Heijl A, Leske MC, Bengtsson B et al. Reduction of intraocular pressure and glaucoma progression: results from the Early Manifest Glaucoma Trial. Arch Ophthalmol. 2002 Oct;120(10):1268-79.

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