Numerical study of aqueous humor flow and iris deformation with pupillary block and the efficacy of laser peripheral iridotomy


      • Detailed simulations of aqueous humor flow inside the eye with pupillary block.
      • Numerical analysis of iris deformation due to an excess of pressure in posterior chamber.
      • Prediction of the orifice size of laser peripheral iridotomy necessary to avoid glaucoma.



      Disclosing the mechanism of primary angle closure glaucoma with pupillary block is important to the diagnosis as well as treatments, such as the laser peripheral iridotomy. Comparing with abundant clinical researches, there have been fewer quantitative studies of the aqueous humor flows with synechia iris configurations, and the efficacy of laser peripheral iridotomy in treating glaucoma.


      Based on the mathematical models of aqueous humor flow and iris deformation, the flow fields were simulated by computational fluid dynamics with normal and synechia iris configurations (iris-lens gap of 30, 5 and 2 μm, respectively), and through one-way fluid-structure coupling technique the deformations of the iris under the flow field pressure were calculated by finite element analysis. The efficacy of glaucoma treatment with different orifice sizes was also investigated.


      Results show that the pressure difference between anterior and posterior chambers and iris deformation increase dramatically with the iris-lens gap distance less than 5 μm, and when further decreasing this gap may lead the iris touch the cornea causing angle closure glaucoma with noticeable iris bombé. Laser peripheral iridotomy simulation results show that iridotomy size of 0.2 mm can effectively decrease the pressure difference across the iris and relieve iris bombé.


      This is a biomechanical numerical study, and the results are reasonable compare to those of published works. It may shed additional light on the diagnosis and treatment of angle closure glaucoma with pupillary block.


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        • Amini R.
        • Barocas V.H.
        Anterior chamber angle opening during corneoscleral indentation: the mechanism of whole eye globe deformation and the importance of the limbus.
        Invest. Ophthalmol. Vis. Sci. 2009; 50: 5288-5294
        • Amini R.
        • Barocas V.H.
        Reverse pupillary block slows iris contour recovery from corneoscleral indentation.
        J. Biomech. Eng. 2010; : 132
        • Amini R.
        • Jouzdani S.
        • Barocas V.H.
        Increased iris–lens contact following spontaneous blinking: mathematical modeling.
        J. Biomech. 2012; 45: 2293-2296
        • Amini R.
        • et al.
        The posterior location of the dilator muscle induces anterior Iris bowing during dilation, even in the absence of pupillary block.
        Investig. Ophthalmol. Visual Sci. 2012; 53: 1188-1194
        • Aptel F.
        • Denis P.
        Optical coherence tomography quantitative analysis of iris volume changes after pharmacologic mydriasis.
        Ophthalmology. 2010; 117: 3-10
        • Beswick J.A.
        • McCulloch C.
        Effect of hyaluronidase on the viscosity of the aqueous humour.
        Br. J. Ophthalmol. 1956; 40: 545-548
        • Cai J.
        • Zhang B.
        • Cao Y.
        • Brazhenko V.
        Numerical study of aqueous humor flow in human eyes.
        Appl. Math. Mech. 2021; 42: 151-161
        • Canning C.R.
        • Greaney M.J.
        • Dewynne J.N.
        • Fitt A.D.
        Fluid flow in the anterior chamber of a human eye.
        Math. Med. Biol. J. IMA. 2002; 19: 31-60
        • Dorairaj S.
        • Oliveira C.
        • Fose A.K.
        • Liebmann J.M.
        • Tello C.
        • Barocas V.H.
        • Ritch R.
        Accommodation-induced changes in iris curvature.
        Exp. Eye Res. 2008; 86: 220-225
        • Dvoriashyna M.
        • Repetto R.
        • Romano M.R.
        • Tweedy J.H.
        Aqueous humour flow in the posterior chamber of the eye and its modifications due to pupillary block and iridotomy.
        Math. Med. Biol. J. IMA. 2018; 35: 447-467
        • Emery A.F.
        • Kramar P.
        • Guy A.W.
        • Lin J.C.
        Microwave induced temperature rises in rabbit eyes in cataract research.
        J. Heat Transf. 1975; 97: 123-128
        • Ethier C.R.
        • Johnson M.
        • Ruberti J.
        Ocular biomechanics and biotransport.
        Annu. Rev. Biomed. Eng. 2004; 6: 249-273
        • Fitt A.D.
        • Gonzalez G.
        Fluid mechanics of the human eye: aqueous humour flow in the anterior chamber.
        Bull. Math. Biol. 2006; 68: 53-71
        • Fleck B.W.
        How large must an iridotomy be?.
        Br. J. Ophthalmol. 1990; 74: 583-588
        • Foster P.J.
        • Johnson G.J.
        Glaucoma in China: how big is the problem?.
        Br. J. Ophthalmol. 2001; 85: 1277-1282
        • He Mingguang
        • et al.
        Laser peripheral iridotomy in primary angle-closure suspects: biometric and gonioscopic outcomes.
        Ophthalmology. 2007; 114: 494-500
        • Heys J.J.
        • Barocas V.H.
        A boussinesq model of natural convection in the human eye and the formation of Krukenberg’s spindle.
        Ann. Biomed. Eng. 2002; 30: 392-401
        • Heys J.J.
        • Barocas V.H.
        • Taravella M.J.
        Modeling passive mechanical interaction between aqueous humor and iris.
        J. Biomech. Eng. 2001; 123: 540-547
        • Huang E.C.
        • Barocas V.H.
        Active iris mechanics and pupillary block: steady-state analysis and comparison with anatomical risk factors.
        Ann. Biomed. Eng. 2004; 32: 1276-1285
        • Huang E.C.
        • Barocas V.H.
        Accommodative microfluctuations and iris contour.
        J. Vis. 2006; 6: 653-660
        • Jouzdani S.
        • Amini R.
        • Barocas V.H.
        Contribution of different anatomical and physiologic factors to iris contour and anterior chamber angle changes during pupil dilation: theoretical analysis.
        Invest. Ophthalmol. Vis. Sci. 2013; 54: 2977-2984
        • Kudsieh B.
        • Fernández-Vigo J.
        • Agujetas R.
        • Montanero J.M.
        • García-Feijóo J.
        Numerical model to predict and compare the hypotensive efficacy and safety of minimally invasive glaucoma surgery devices.
        PLoS ONE. 2020; 15e0239324
        • Kumar S.
        • Acharya S.
        • Beuerman R.
        • Palkama A.
        Numerical solution of ocular fluid dynamics in a rabbit eye: parametric effects.
        Ann. Biomed. Eng. 2006; 34: 530-544
        • Lee C.
        • Li G.
        • Stamer W.D.
        • Ethier C.R.
        In vivo estimation of murine iris stiffness using finite element modeling.
        Exp. Eye Res. 2021; 202108374
        • Liebmann J.M.
        • Tello C.
        • Chew S.-J.
        • Cohen H.
        • Ritch R.
        Prevention of blinking alters Iris configuration in pigment dispersion syndrome and in normal eyes.
        Ophthalmology. 1995; 102: 446-455
        • Mantravadi A.V.
        • Vadhar N.
        Prim. Care. 2015; 42: 437-449
        • Martínez Sánchez G.J.
        • Escobar del Pozo C.
        • Rocha Medina J.A.
        Numerical model of aqueous humor drainage: effects of collector channel position.
        Med. Eng. Phys. 2019; 65: 24-30
        • Millar J.C.
        • Pang I.-H.
        Non-continuous measurement of intraocular pressure in laboratory animals.
        Exp. Eye Res. 2015; 141: 74-90
        • Narayanaswamy A.
        • et al.
        Young’s modulus determination of Normal and glaucomatous human Iris.
        Invest. Ophthalmol. Vis. Sci. 2019; 60: 2690-2695
        • Ooi E.-H.
        • Ng E.Y.-K.
        Simulation of aqueous humor hydrodynamics in human eye heat transfer.
        Comput. Biol. Med. 2008; 38: 252-262
        • Pant A.D.
        • Gogte P.
        • Pathak-Ray V.
        • Dorairaj S.K.
        • Amini R.
        Increased Iris stiffness in patients with a history of angle-closure glaucoma: an image-based inverse modeling analysis.
        Investig. Ophthalmol. Vis. Sci. 2018; 59: 4134-4142
        • Radcliffe N.
        • Thareja T.
        Laser peripheral iridotomy.
        in: Rosenberg E.D. Nattis A.S. Nattis R.J. Operative Dictations in Ophthalmology. Springer International Publishing, Cham2017: 173-176
        • Radhakrishnan S.
        • Chen P.P.
        • Junk A.K.
        • Nouri-Mahdavi K.
        • Chen T.C.
        Laser peripheral iridotomy in primary angle closure: a report by the American Academy of Ophthalmology.
        Ophthalmology. 2018; 125: 1110-1120
        • Repetto R.
        • Pralits J.O.
        • Siggers J.H.
        • Soleri P.
        Phakic iris-fixated intraocular lens placement in the anterior chamber: effects on aqueous FlowPhakic Iris-fixated intraocular lens placement.
        Invest. Ophthalmol. Vis. Sci. 2015; 56: 3061-3068
        • Scott J.A.
        A finite element model of heat transport in the human eye.
        Phys. Med. Biol. 1988; 33: 227-241
        • Siggers J.H.
        • Ethier C.R.
        Fluid mechanics of the eye.
        Annu. Rev. Fluid Mech. 2011; 44: 347-372
        • Silver D.M.
        • Quigley H.A.
        Aqueous flow through the iris-lens channel: estimates of differential pressure between the anterior and posterior chambers.
        J. Glaucoma. 2004; 13: 100-107
        • Tan R.K.Y.
        • Xiaofei W.
        • Perera S.A.
        • Girard M.J.A.
        • Anna P.
        Numerical stress analysis of the iris tissue induced by pupil expansion: comparison of commercial devices.
        PLoS ONE. 2018; 13 (e0194141)
        • Tan R.K.Y.
        • Wang X.
        • Chan A.S.Y.
        • Nongpiur M.E.
        • Boote C.
        • Perera S.A.
        • Girard M.J.A.
        Permeability of the porcine iris stroma.
        Exp. Eye Res. 2019; 181: 190-196
        • Tham Y.C.
        • Li X.
        • Wong T.Y.
        • Quigley H.A.
        • Cheng C.Y.
        Global prevalence of glaucoma and projections of glaucoma burden through 2040: a systematic review and meta-analysis.
        Ophthalmology. 2014; 121: 2081-2090
        • Thomas V.S.
        • Salinas S.D.
        • Pant A.D.
        • Dorairaj S.K.
        • Amini R.
        Biomechanical assessment of the iris in relation to angle-closure glaucoma: a multi-scale computational approach.
        in: Computer Methods, Imaging and Visualization in Biomechanics and Biomedical Engineering. Springer International Publishing, Cham2020: 470-482
        • Villamarin A.
        • Roy S.
        • Hasballa R.
        • Vardoulis O.
        • Reymond P.
        • Stergiopulos N.
        3D simulation of the aqueous flow in the human eye.
        Med. Eng. Phys. 2012; 34: 1462-1470
        • Wang W.
        • Qian X.
        • Song H.
        • Zhang M.
        • Liu Z.
        Fluid and structure coupling analysis of the interaction between aqueous humor and iris.
        Biomed. Eng. Online. 2016; 15: 570-586
        • Wang W.
        • Song H.
        • Liu Z.
        Computational study on the biomechanics of pupil block phenomenon.
        Biomed. Res. Int. 2019; 2019: 4820167
        • Weinreb R.N.
        • Leung C.K.S.
        • Crowston J.G.
        • Medeiros F.A.
        • Friedman D.S.
        • Wiggs J.L.
        • Martin K.R.
        Primary open-angle glaucoma.
        Nat. Rev. Dis. Primers. 2016; 2: 1-19
        • Whitcomb J.E.
        • Barnett V.A.
        • Olsen T.W.
        • Barocas V.H.
        Ex vivo porcine iris stiffening due to drug stimulation.
        Exp. Eye Res. 2009; 89: 456-461
        • Whitcomb J.E.
        • Amini R.
        • Simha N.K.
        • Barocas V.H.
        Anterior–posterior asymmetry in iris mechanics measured by indentation.
        Exp. Eye Res. 2011; 93: 475-481
        • Wyatt H.
        • Ghosh J.
        Behaviour of an iris model and the pupil block hypothesis.
        Br. J. Ophthalmol. 1970; 54: 177-185
        • Yamaji K.
        • Yoshitomi T.
        • Usui S.
        • Ohnishi Y.
        Mechanical properties of the rabbit iris smooth muscles.
        Vis. Res. 2003; 43: 479-487