Fluid and structure coupling analysis of the interaction between aqueous humor and iris
© The Author(s) 2016
Published: 28 December 2016
The Erratum to this article has been published in BioMedical Engineering OnLine 2017 16:22
Glaucoma is the primary cause of irreversible blindness worldwide associated with high intraocular pressure (IOP). Elevated intraocular pressure will affect the normal aqueous humor outflow, resulting in deformation of iris. However, the deformation ability of iris is closely related to its material properties. Meanwhile, the passive deformation of the iris aggravates the pupillary block and angle closure. The nature of the interaction mechanism of iris deformation and aqueous humor fluid flow has not been fully understood and has been somewhat a controversial issue. The purpose here was to study the effect of IOP, localization, and temperature on the flow of the aqueous humor and the deformation of iris interacted by aqueous humor fluid flow.
Based on mechanisms of aqueous physiology and fluid dynamics, 3D model of anterior chamber (AC) was constructed with the human anatomical parameters as a reference. A 3D idealized standard geometry of anterior segment of human eye was performed. Enlarge the size of the idealization geometry model 5 times to create a simulation device by using 3D printing technology. In this paper, particle image velocimetry technology is applied to measure the characteristic of fluid outflow in different inlet velocity based on the device. Numerically calculations were made by using ANSYS 14.0 Finite Element Analysis. Compare of the velocity distributions to confirm the validity of the model. The fluid structure interaction (FSI) analysis was carried out in the valid geometry model to study the aqueous flow and iris change.
In this paper, the validity of the model is verified through computation and comparison. The results indicated that changes of gravity direction of model significantly affected the fluid dynamics parameters and the temperature distribution in anterior chamber. Increased pressure and the vertical position increase the velocity of the aqueous humor fluid flow, with the value increased of 0.015 and 0.035 mm/s. The results act on the iris showed that, gravity direction from horizontal to vertical decrease the equivalent stress in the normal IOP model, while almost invariably in the high IOP model. With the increased of the iris elasticity modulus, the equivalent strain and the total deformation of iris is decreased. The maximal value of equivalent strain of iris in high IOP model is higher than that of in normal IOP model. The maximum deformation of iris is lower in the high IOP model than in the normal IOP model.
The valid model of idealization geometry of human eye could be helpful to study the relationship between localization, iris deformation and IOP. So far the FSI analysis was carried out in that idealization geometry model of anterior segment to study aqueous flow and iris change.
Glaucoma is the primary cause of incurable blindness in the world . It generally develops from a resistance of aqueous humor outflow, leading to an increase in IOP . The retina ganglion cells progressively damages, as a consequence of this, visual field reduced and finally grows blind . In primary angle-closure glaucoma (PACG), the iris is abnormally positioned and physically impedes aqueous humor outflow through the trabecular meshwork. PACG derives its name from the narrow anterior chamber angel, defined by the iris anterior surface and the posterior surface of the corneoscleral shell.
The interest in comprehensive the iris mechanics develops from the influence of abnormal iris morphology on specific ocular disorders. For instance, in angle closure, the iris bows anteriorly, and the passively deformed shape and position of the iris restrict aqueous humor outflow, leading to a high intraocular pressure . A recent study suggested that biomechanical properties of the iris may play an important role in the development of acute angle closure attacks . Therefore, it is necessary to understand the changes of the mechanical properties of iris in the course of glaucoma. However, the fluid dynamics of aqueous humor in the anterior chamber and the change of the iris passive deformation have not been fully understood. Consequently, numerical simulation of fluid structure interaction in anterior chamber could present enlightening information on ocular diseases such as glaucoma where the outflow of AH is obstructed.
Previous report carried out several simulations and mathematical models to research the mechanism of aqueous humor fluid flow in anterior chamber, such as the distribution of temperature and velocity [8–13]. Heys et al.  created a numerical model of anterior segment to research on the mechanical mechanism interaction between aqueous humor and iris. Considering the miosis and blinking, etc., they analyzed the aqueous flow in anterior chamber. Repetto et al.  used a numerical model to study aqueous flow in anterior chamber whether the presence of a phakic intraocular lenses. However, the lack of verification to the validity and reliability of the finite-element analysis models might limit their accuracy. In addition, none of these simulations used fluid–structure coupling method to analysis the relationship between iris deformation and IOP in human eyes.
The goal of this research was to develop a 3D eye model based on idealization geometry of human eye and to establish the characteristics of aqueous humor flow under physiological and pathological conditions such as primary angle-closure glaucoma. This device will make a foundation for further simulations and evaluations of different influence factors of glaucoma.
Parameter values applied in the simulations
Volumetric flux Q
3 µl/min = 5 · 10−8 kg s−1
Dynamic viscosity v
0.001 kg m−1 K−1
Specific heat Cp
4.178 · 103 J kg−1 K−1
Thermal expansion coefficient α
Thermal conductivity k
0.578 W m−1 K−1
0.001 kg−1 s−1
Geometric characteristics of the domain
Diameter of the anterior chamber DC
Maximum height of chamber hC
Minimum radius of curvature of the posterior cornea RC
Radius of curvature of the natural lens RL
Height of the iris–lens channel
Angle between cornea and iris
Young’s modulus of cornea
Poisson’s ratio of cornea
Density of cornea
Young’s modulus of iris
Poisson’s ratio of iris
Simulation device production
Compared with the idealization geometry, a cylindrical water sink with a 78 mm diameter was created outside the cornea of the simulation device to reduce the laser reflection on cornea surface. We also designed an inlet and an outlet channel to simulate the inflow and the outflow of aqueous humor. In order to make the fluid flow balance and uniform through the simulation device, outside of the inlet buffer space and the outlet buffer space are designed with many small holes. A column below the lens plays a supporting role, engendering a 10 µm gap between lens and iris. A silicon wafer, which to prevent the downward leakage of fluid flow, is provided substantially entirely on the back surface of the lens, connected under the holes of inlet.
The simulation device of anterior segment is used to simulate the physiological environment of aqueous humor fluid flow. The flow field in anterior chamber is measured by particle image velocimetry technology. The pivotal device in our study is image velocimetry system, provided by Beijing Institute of Technology, which can be found in Yang et al. .
Compared with the velocity calculated by ANSYS Fluent14.0, utilized the 5 times geometry model, to verify the validity of the finite element model.
The cornea limbus, iris root, and lens are modeled as stationary boundaries, and impased no-slip boundary condition on the surfaces. The front and back surface of iris and the corneal endothelium are set as FSI surfaces. Set the plane XY to a plane of symmetry. The temperature at the cornea is assumed along the outer surface, generally considered to lie between 33 and 35 °C , and was defined to be 34 °C in this study. The buoyant force mechanism provided by temperature difference between iris (37 °C) and cornea drives aqueous humor in the anterior chamber.
Aqueous humor is simulated inflows from the ciliary body area at a rate of 10 e−8 kg/s (3 µl/min). The working IOP condition was defined by an IOP of 13.5 mmHg to represent the healthy model while the glaucomatous case was set of 27 mmHg of IOP. Thus, the static pressure forced at the trabecular meshwork was estimated 13.5 mmHg and 27 mmHg to simulate the healthy and the glaucomatous models. In our study, aqueous humor secreted from the ciliary body and the trabecular meshwork was assumed to be at 37 °C. The boundary conditions are presented in Fig. 2a. The model consisted of two elastic isotropic segments—iris and cornea, structure properties are given in Table 1.
A volumetric mesh was developed by ICEM CFD software (ANSYS Inc., Canomsburg, PA, USA) and exported to ANSYS Fluent (ANSYS Inc., Canonsburg, PA, USA) for the fluid simulation. The 3D model of fluid structure and solid structures (iris and cornea) are depicted in Fig. 2b, c. A group of 20 s was performed to simulate the process with a time step of 0.5 s. There is no need to set a too small time step, because the aqueous humor flow in human eye is relatively low. Since the time step of 0.5 s was small enough, it allowed us to have a better assessment of the pattern of stress and deformations at iris and cornea of the simulation. The distributions of stress, velocity and temperature in each region when the velocity inlet at a speed of 10e−8 kg/s and the IOP of 13.5 or 27 mmHg were modeled and compared by the post-processing software(ANSYS Inc., Canonsburg, PA, USA).
Flow field induced by different velocity of inlet in simulation device
Velocity values on the transverse plan at a distance of 10 mm from the XZ plane in the supine position of anterior chamber
(a) PIV measurement
(b) FEA calculation
Min velocity (m/s)
Max velocity (m/s)
Min velocity (m/s)
Max velocity (m/s)
Flows induced by high and normal IOP
Values of aqueous humor obtained by the simulation of high and normal IOP with the gravity in horizontal and vertical directions
Maximum velocity (m/s)
Average velocity (m/s)
In the horizontal position
In the vertical direction
Distributions of velocities in the anterior chamber are similar in healthy and glaucomatous simulation calculations.
Distributions on cornea and iris
Values of iris obtained by the simulation of high and normal IOP with the gravity in −Y and −X directions
Iris elasticity modulus (Pa)
Equivalent stress (MPa)
Total deformations (mm)
(a) In the horizontal position
IOP = 27 mmHg
IOP = 13.5 mmHg
(b) In the vertical direction
IOP = 27 mmHg
IOP = 13.5 mmHg
We also show the corresponding equivalent strain values in Table 4, and this reveals significant changes due to iris elasticity modulus. The maximum equivalent strain is at the middle of cornea. However, while the equivalent strain of iris achieved the peak at the thicker part of the anterior surface of the iris. Compared the results of various situations, we found that the equivalent strain was higher in horizontal orientation than that of in vertical position. With the increase of elasticity modulus of iris, the equivalent strain of iris decreased at almost the same rate.
Through the analysis of fluid–structure interaction, we can also see the presence of IOP makes some difference to the total deformation of iris. The maximum deformation with a value of 0.33917 mm (Fig. 9c) is in peripheral iridotomy, whereas the peak is reached to the iridocorneal angle of cornea in horizontal orientation. We also note that the deformation of iris varies from the changes of the iris elasticity modulus. However, the deformation of the iris in high IOP is lower than that of in normal.
Due to the low rate of aqueous humor fluid flow, the difference in v m and v could be neglect in Eq. (5). The similarity of the flow in model and human eye could be proved, when using the inlet volumetric flow rate Q m (15 µl/min) in PIV experiment. And we will achieve this low speed measurement in the following experiments.
The study on the visualization of the flow field distribution, the experimental model will be amplified to a certain degree based on the Reynolds number similarity principle. Because the human eye is small, and the fluid flow rate of aqueous humor is relatively low, there is very little experimental method to verify the validity of the model. 5 times amplified model is more easily carried out PIV experiment for the rate of infusing is larger than the secreted rate of aqueous humor in real eye, while we are trying to validate under a real scale model. To verify, we focus on the fluid streamlines, and the flow field distribution. The measured fluid distributions are similar to the results obtained by finite element method, so it can be explained that this method is valuable, and it is feasible to continue to improve in the verification experiment. We plan to improve the simulation model and use the advanced experimental equipment to complete the measurement of the flow field in low speeds.
The values of velocity and pressure of aqueous humor formulated in steady state makes no difference in horizontal position or vertical orientation. Therefore, under the rapid eye movement, the study of the mixing aqueous humor in the anterior chamber becomes more meaningful. Modarreszadeh  carried out a detailed simulation study on this issue. The importance of the driving mechanism for aqueous flows was considered in our study. We find that environmental temperature could increase the maximum velocity of aqueous humor, while produce no significant increase in pressure difference.
Our study provides a means to verify the validity and reliability of the finite-element analysis model. Through PIV experiment, we have captured the flow field in anterior chamber in the simulation device and calculated the corresponding velocity distributions. The valid model of idealization geometry of human eye can be helpful to investigate the relationship among localization, the changes of iris elasticity modulus and high IOP, so as to make further exploration in the pathogenesis of glaucoma.
WW, XQ, HS, MZ, ZL were responsible for the design, data collection and overall investigation. WW and XQ were responsible for computational modeling, performed the statistical analysis part. WW, HS and MZ were responsible for PIV experiment and data processing. All authors (1) have made substantial contributions to conception and design, or acquisition of data, or analysis and interpretation of data; (2) have been involved in drafting the manuscript or revising it critically for important intellectual content; and (3) have given final approval of the version to be published. Each author has participated sufficiently in the work to take public responsibility for appropriate portions of the content. All authors read and approved the final manuscript.
The authors declare that they have no competing interests.
About this supplement
This article has been published as part of BioMedical Engineering OnLine Volume 15 Supplement 2, 2016. Computational and experimental methods for biological research: cardiovascular diseases and beyond. The full contents of the supplement are available online http://biomedical-engineering-online.biomedcentral.com/articles/supplements/volume-15-supplement-2.
Availability of data and materials
Data available upon request.
Publication charges for this article were funded by National Naturel Science Foundation of China (51711805). This work was funded by the National Natural Science Foundation of China (No. 31070840), National Natural Science Foundation of China (No. 10802053), National Natural Science Foundation of China (No. 7152022), and the Natural Science Foundation of Beijing (No. 3122010), and by the Funding Project for Academic Human Resources Development in Institutions of Higher Learning Under the Jurisdiction of Beijing Municipality (No. PHR 201110506).
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.
- Eye Diseases Prevalence Research Group. Causes and prevalence of visual impairment among adults in the United States. Arch Ophthalmol. 2004;122(4):477.View ArticleGoogle Scholar
- Ethier CR, Johnson M, Ruberti J. Ocular biomechanics and biotransport. Annu Rev Biomed Eng. 2004;6:249–73.View ArticleGoogle Scholar
- Kwon YH, Fingert JH, Kuehn MH, Alward WLM. Primary open-angle glaucoma. N Engl J Med. 2009;360(11):1113–24.View ArticleGoogle Scholar
- Caprioli J. The ciliary epithelia and aqueous humor. In: Hart WM, editor. Adler’s physiology of the eye: clinical application. St. Louis: C.V. Mosby Year-book; 1992. p. 228–47.Google Scholar
- Fontana ST, Brubaker RF. Volume and depth of the anterior chamber in the normal aging human eye. Arch Ophthalmol. 1980;98(10):1803–8.View ArticleGoogle Scholar
- Epstein DL, Allingham RR, Schuman J, Liebmann JM. Chandler and Grant’s glaucoma. Am J Ophthalmol. 1997;123(6):863.View ArticleGoogle Scholar
- He M. Histologic changes of the iris in the development of angle closure in Chinese eyes. J Glaucoma. 2008;17(5):386–92.View ArticleGoogle Scholar
- Canning CR, Greaney MJ, Dewynne JN, Fitt AD. Fluid flow in the anterior chamber of a human eye. Math Med Biol. 2002;19(1):31–60.View ArticleMATHGoogle Scholar
- Ethier CR, Kamm RD, Palaszewski BA, Johnson MC, Richardson TM. Calculations of flow resistance in the juxtacanalicular meshwork. Invest Ophthalmol Vis Sci. 1986;27(12):1741–50.Google Scholar
- Heys JJ, Barocas VH. A boussinesq model of natural convection in the human eye and the formation of Krukenberg’s spindle. Ann Biomed Eng. 2002;30(3):392–401.View ArticleGoogle Scholar
- Johnson MC, Kamm RD. The role of Schlemm’s canal in aqueous outflow from the human eye. Invest Ophthalmol Vis Sci. 1983;24(3):320–5.Google Scholar
- Scott JA. The computation of temperature rises in the human eye induced by infrared radiation. Phys Med Biol. 1988;33(2):243.View ArticleGoogle Scholar
- Scott JA. A finite element model of heat transport in the human eye. Phys Med Biol. 1988;33(2):227.View ArticleGoogle Scholar
- Heys JJ, Barocas VH, Taravella MJ. Modeling passive mechanical interaction between aqueous humor and iris. J Biomech Eng. 2001;123(6):540–7.View ArticleGoogle Scholar
- Repetto R, Pralits JO, Siggers JH, Soleri P. Phakic iris-fixated intraocular lens placement in the anterior chamber: effects on aqueous flow phakic iris-fixated intraocular lens placement. Invest Ophthalmol Vis Sci. 2015;56(5):3061–8.View ArticleGoogle Scholar
- Wollensak G, Spoerl E, Seiler T. Stress-strain measurements of human and porcine corneas after riboflavin–ultraviolet-A-induced cross-linking. J Cataract Refract Surg. 2003;29(9):1780–5.View ArticleGoogle Scholar
- Wang ZH, Chen D, Zeng YF, Wang YD, Liang XW, Liu X. Comparison of anterior segment optical coherence tomography and ultrasound biomicroscopy for iris parameter measurements in patients with primary angle closure glaucoma. Eye Sci. 2013;28:1–6.Google Scholar
- Cohen A, Laviv A, Berman P, Nashef R, Abu-Tair J. Mandibular reconstruction using stereolithographic 3-dimensional printing modeling technology. Oral Surg Oral Med Oral Pathol Oral Radiol Endod 2009;108(5):661–6.View ArticleGoogle Scholar
- Leukers B, Gülkan H, Irsen SH, Milz S, Tille C, Schieker M, Seitz H. Hydroxyapatite scaffolds for bone tissue engineering made by 3D printing. J Mater Sci Mater Med. 2005;16(12):1121–4.View ArticleGoogle Scholar
- Yang HY, Song HF, Mei X, Li L, Fu XN, Zhang MD, Liu ZC. Experimental research on intraocular aqueous flow by PIV method. Biomed Eng Online. 2013;12(1):108.View ArticleGoogle Scholar
- Ruan C, Sun CD, Bai YL, Wang YS, Ren KH, Feng S. The characteristics of the tracer particles used in water flow field for PIV system. J Exper Fluid Mech. 2006;20(2):72–6.Google Scholar
- Koçak I, Orgül S, Flammer J. Variability in the measurement of corneal temperature using a noncontact infrared thermometer. Ophthalmologica. 1999;213(6):345–9.View ArticleGoogle Scholar
- White FM. Chapter 5 dimensional analysis and similarity. Fluid Mech. 2009.Google Scholar
- Camras LJ, Stamer WD, Epstein D, Gonzalez P, Yuan F. Differential effects of trabecular meshwork stiffness on outflow facility in normal human and porcine eyes effects of trabecular meshwork stiffness on outflow. Investig Ophthalmol Visual Sci. 2012;53(9):5242–50.View ArticleGoogle Scholar
- Modarreszadeh SA, Abouali O, Ghaffarieh A, Ahmadi G. Physiology of aqueous humor dynamic in the anterior chamber due to rapid eye movement. Physiol Behav. 2014;135:112–8.View ArticleGoogle Scholar
- Ritch R. Angle-closure glaucoma: mechanism and epidemiology. Glaucomas Clin Sci. 1996:801–19.Google Scholar
- Mapstone R. Mechanics of pupil block. Br J Ophthalmol. 1968;52:19–25.View ArticleGoogle Scholar
- Brubaker RF. Measurement of aqueous flow by fluorophotometry. In: The Glaucoma. St. Louis: Mosby; 1989.Google Scholar
- Brubaker RF. Flow of aqueous humor in humans [the Friedenwald Lecture]. Invest Ophthalmol Vis Sci. 1991;32:3145–66.Google Scholar
- Kumar S, Acharya S, Beuerman R, Palkama A. Numerical solution of ocular fluid dynamics in a rabbit eye: parametric effects. Ann Biomed Eng. 2006;34:530–44.View ArticleGoogle Scholar
- Batchelor GK. An introduction to fluid dynamics. Cambridge: Cambridge University Press; 1967. p. 596.MATHGoogle Scholar
- Poppendiek HF, Randall R, Breeden JA, Chambers JE, Murphy JR. Thermal conductivity measurements and predictions for biological fluids and tissues. Cryobiology. 1967;3:318–27.View ArticleGoogle Scholar
- Hjortdal JO. Regional elastic performance of the human cornea. J Biomech. 1996;29(7):931–42.View ArticleGoogle Scholar
- Bryant MR, Szerenyi K, Schmotzer H, McDonnell PJ. Corneal tensile strength in fully healed radial keratotomy wounds. Invest Ophthalmol Vis Sci. 1994;35(7):3022–31.Google Scholar
- Buzard KA. Introduction to biomechanics of the cornea. J Refract Surg. 1992;8(2):127–38.Google Scholar
- Stitzel JD, Duma SM, Cormier JM, Herring IP. A nonlinear finite element model of the eye with experimental validation for the prediction of globe rupture. Stapp Car Crash J. 2002;46:81–102.Google Scholar
- Heys J, Barocas VH. Mechanical characterization of the bovine iris. J Biomech. 1999;32(9):999–1003.View ArticleGoogle Scholar