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Glaucoma
The aqueous humour dynamics in primary angle closure disease: a computational study
  1. Lin Fu1,2,3,
  2. Xinyi Liu4,
  3. Longqian Zhang5,
  4. Jiangtao Lou1,2,3,
  5. Xiaobo Zheng1,2,3,
  6. Xiaojue Wang1,
  7. Haishuang Lin1,
  8. Liang Guo6,
  9. Kezhao Wang6,
  10. Yan Wang6,
  11. Min Kan6,
  12. Yuanbo Liang1,2,3
  1. 1National Clinical Research Center for Ocular Diseases, EyeHospital, Wenzhou Medical University Eye Hospital, Wenzhou, 325027, China
  2. 2National Engineering Research Center of Ophthalmologyand Optometry, Eye Hospital, Wenzhou Medical University, Wenzhou, 325027, China
  3. 3State Key Laboratory of Ophthalmology, Optometry andVisual Science, Eye Hospital, Wenzhou Medical University, Wenzhou, 325027, China
  4. 4Department of Ophthalmology, People’s Hospital of Yichun, Yichun, Jiangxi, China
  5. 5Faculty of Engineering and Applied Science, Ontario Tech University, Oshawa, Ontario, Canada
  6. 6Suzhou Purevision Medical Technology Co., LTD, Suzhou, China
  1. Correspondence to Dr Yuanbo Liang; yuanboliang{at}wmu.edu.cn

Abstract

Purpose To create a computational fluid dynamics (CFD) model of ocular anterior segment for primary angle closure diseases (PACD) and assess the aqueous humour (AH) dynamics in different angle closure ranges (ACRs).

Methods The ocular anterior segment geometry was obtained from an optical coherence tomography image by SOLIDWORKS. Three different angle opening distance at 750 µm from the scleral spur (AOD750) values were established to mimic three widths of anterior chamber angle. The AH dynamics were modelled using the Navier-Stokes equation. The 3D CFD model of the ocular anterior segment was created in COMSOL Multiphysics. The major outcome was the maximum flow velocity (MFV) and pressure in the ocular anterior segment. An in vitro simulation model was used to validate the computational results of the pressure and ACRs.

Results The MFV and pressure both showed a non-linear association with ACR in the CFD models of PACD. The MFV and pressure started to elevate when ACR was larger than 180°, and increased dramatically when the ACR was larger than 270°. The in vitro experiment of the pressure changes was consistent with the CFD model. No significant differences of the MFV and pressure among the three AOD750 models.

Conclusions The association among the ACR, MFV and pressure is an ascending curve in PACD, and ACR of 180° and 270° are two critical turning points. Our results are consistent with clinical phenomenon and may be used to provide better guidances for the clinical management of PACD in different stages.

  • Aqueous humour
  • Glaucoma

Data availability statement

Data are available upon reasonable request. Data can be acquired from the corresponding author upon reasonable request.

http://creativecommons.org/licenses/by-nc/4.0/

This is an open access article distributed in accordance with the Creative Commons Attribution Non Commercial (CC BY-NC 4.0) license, which permits others to distribute, remix, adapt, build upon this work non-commercially, and license their derivative works on different terms, provided the original work is properly cited, appropriate credit is given, any changes made indicated, and the use is non-commercial. See: http://creativecommons.org/licenses/by-nc/4.0/.

https://doi.org/10.1136/bjo-2023-325109

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    WHAT IS ALREADY KNOWN ON THIS TOPIC

    • Intraocular pressure elevates when angle closure range increases in primary angle closure disease, which means the aqueous humour outflow was obstructed. However, the exact relationship between the angle closure range, aqueous humour outflow and intraocular pressure is unclear.

    WHAT THIS STUDY ADDS

    • This study found the relationship among the maximum flow velocity, pressure and angle closure range showed an ascending curve, and 180° and 270° of angle closure range are two important change points.

    HOW THIS STUDY MIGHT AFFECT RESEARCH, PRACTICE OR POLICY

    • The findings of this study can explain the clinical outcomes of different glaucoma surgeries and may also provide references for the clinical interventions of glaucoma patients.

    Introduction

    Glaucoma is the leading irreversible blindness all over the world, and primary angle closure disease (PACD) is the major type of glaucoma in Asia, especially, in China.1–3 PACD is divided into several subtypes including primary angle closure suspect (PACS), primary angle closure (PAC) and primary angle closure glaucoma (PACG) according to anterior chamber angle morphology, intraocular pressure (IOP) and optic nerve damage.4 IOP is the only modifiable factor of the glaucoma management, and its balance is maintained through the production of aqueous humour (AH) and its drainage through the outflow pathway. In PACD, IOP elevation is induced by the AH outflow obstruction due to angle closure. However, few studies have quantitatively assessed the influence of the AH dynamics on the PACD severity and progression.

    The anterior chamber angle (ACA) is the major channel for the AH outflow, and the ACA width is the critical parameter to predict the PACD progression.5 IOP elevation would occur when the ACA is narrowed or closed. The glaucomatous optic neuropathy (GON) will develop after persistent IOP elevation. In PACD, peripheral anterior synechia (PAS) is defined by the observation of synechial contact of the iris and the trabecular meshwork (TM).6 PAS is the pathological basis of PACD and stands for the angle closure in the dynamic gonioscopy. The angle closure restricts AH outflow and theoretically, larger range of angle closure leads to a greater reduction in AH outflow and higher IOP. From our previous investigation, PAS range is associated with GON development and predicts higher IOP.7 Nonetheless, IOP is not simply linear related with the range of PAS, and the exact relationship of angle closure with IOP is not clear.

    In recent years, several mathematical models have been designed to explain the AH flow in the eye drainage system. Rocha Medina JA et al.8 modelled the motion of aqueous humour through the anterior chamber and the trabecular drainage system using a 3D computational model to analyse the flow characteristics and the heat transfer in the anterior chamber. Guo JM et al9 studied on the AH flow dynamic features under various Schlemm’s canal (SC) morphological parameters by numerical simulations of 3D models and revealed the relationship between SC morphological parameters and the dynamic features of AH drainage. However, the quantitative relationship between the flow state of AH and the anterior chamber angle remains unclear. Therefore, to assess the outflow rate of the AH in different angle width and various ranges of angle closure, we tried to build a 3D computational fluid dynamics (CFD) model of the ocular anterior segment to analyse the fluid dynamics of AH.

    Materials and methods

    To create a fully functional CFD model of the AH according to the different angle widths and angle closure ranges and to assess the AH dynamics in different angle closure ranges.

    Establishing realistic 3D ocular anterior segment geometry

    In order to establish anatomically accurate pathway of the aqueous humour, an image of the anterior segment was drawn by the SOLIDWORKS (SolidWorks Corporation, Concord, MA, USA) referring to several previous literature to build 2D geometric models of the ocular anterior segment and aqueous production and outflow. In order to simulate the natural human eye, the internal structural features of the eye are shown, including the scleral spur, ciliary body, iris and angle opening distance at 750 µm from the scleral spur (AOD750). The AOD750 is a critical biometric parameter related to the angle width in PACG.10 11 The reason that we chose the AOD750 for the modelling of different anterior chamber angle widths is that AOD750 was reported to have the highest receiver operating characteristic curves (AUCs) for the detection of gonioscopic angle closure,12 and in this study of computational modelling, the angle was set to be closed gradually to test the changes of fluid dynamics. Therefore, we chose the AOD750 in this study. Referring to the value of AOD750 in previous clinical reports in human, three different values of 0.05 mm, 0.15 mm and 0.40 mm were used to represent three angle widths of PACD in this study for computational modelling (figure 1a–d).10 11 13 14

    Figure 1
    Figure 1

    Ocular anterior segment geometry and computational fluid model. (a) Cross-sectional view of the human ocular anterior segment. (b–d) Partial view at anterior chamber angle AOD750 0.4 mm, 0.15 mm and AOD750 0.05 mm. (e) Computational fluid model of the aqueous humour production and outflow.

    The angle closure ranges (ACRs) of 0°, 90°, 180° and 345° were tested in the models of three different AOD750 values. In clinical practice, the diagnosis of PACD is based on the gonioscopic examination.15 PACS is determined if more than 180° of iridotrabecular contact was observed under static gonioscopy without the presence of PAS under dynamic gonioscopy, and the IOP is lower than 21 mm Hg. PAC is diagnosed if PAS was observed or IOP was higher than 21 mm Hg without the glaucomatous optic neuropathy. PACG is defined in the eyes with gonioscopic PAS and glaucomatous optic neuropathy. As in this computational study, the angle was set closed to represent the PAS formation in clinical phenomenon, and ACR of 0° represents PACS in the three different AOD750 models. Since the glaucomatous optic disc changes could not be modelled in this study, the models with ACRs of 90°, 180° and 345° represent both PAC and PACG.

    In this study, we focused on the effect of ACA narrowing and closure on the AH dynamics; the iris deformation caused by IOP elevation was not considered. Hence, the iris was simply assumed as a rigid integrity that was not affected by the AH flow. Because the average width of TM in human eyes of different age groups is 0.4769 to 1.2188 mm, and the functional TM with the ability of AH drainage accounts for about two-thirds of the whole TM, this study assumed that the width of the outflow area of ACA is 0.5 mm.16

    Aqueous Humor Dynamics simulation

    COMSOL Multiphysics (COMSOL, Inc., Palo Alto, CA, USA) was used to perform fluid dynamic analysis of aqueous humour. In the simulation, we adjusted the liquid density at 997 kg/m3 and a consistent temperature of 37° so that the inside of the model closely resembles the liquid environment in the natural human eye. Additionally, the ciliary process was set as the inlet of the aqueous humour and the aqueous production rate of 5-8 kg/s was used in this simulation.17–19 Furthermore, the aqueous humour dynamics were conducted by using the Darcy law; the equations are provided by:

    Embedded Image(1)

    Embedded Image(2)

    Where μ is dynamic viscosity 0.001 Pa*s, p is pressure (Pa) and u represents the fluid velocity (m·s−1). The κ (m2) stands for the trabecular meshwork permeability, and it was supposed to be in a pathological situation of glaucoma with the value of 2.3-15 m2.20 The eyeball wall was as the outlet the pressure was set as 15 mmHg.21 In this study, we derived the relationship among the maximum intraocular pressure, flow rate and the ACR by varying the AOD750 and angle closure ranges. Here, we used a hyperfine mixed mesh for mesh construction to obtain steady-state maps of angular closure vs flow velocity. The number of meshes for each model is about two million (figure 1e).

    In vitro simulation model

    In order to validate the computational results from finite element analysis of the aqueous humour dynamics, an in vitro model was established in a simplified eye model (Ophthalmic Surgical Training Models, SimulEYE, Westlake Village, CA). In this experiment, 12 drainage tubes with an inner diameter of 0.1 mm were evenly distributed around the simplified eyeball limbus to simulate the actual human eye drainage (figure 2a). Each quadrant has 3 tubes and 3, 6, 9 and 11 tubes were closed sequentially to simulate the angle closure range of 90°, 180°, 270° and 330°. The intraocular fluid was injected by a syringe pump (R462, RWD Life Science Co., LTD), the posterior chamber which was set as the inlet with a 3 µL/min flow velocity (figure 2b), and the pressure was measured and translated by a pressure transducer (PX419, OMRON).

    Figure 2
    Figure 2

    In vitro simulation model of the aqueous outflow. (a) A simplified eye model with 12 find tubes inserted at the limbus evenly. (b) A syringe pump which injected fluid into the posterior chamber of the simplified eye model with a flow velocity of 3 µL/min.

    Consideration of the influence of gravity and different quadrants

    Based on the previous description of the aqueous outflow in different quadrants, the nasal quadrant had the greatest outflow signal intensity of 45.1%±4.6%, followed by the superior of 22.7%±9.0%, inferior of 23.0%±6.7%, and the temporal quadrant of 9.1%±1.3%.22 These indicate that the outflow of the nasal quadrant possesses 50% of the whole ocular aqueous outflow, temporal quadrant possesses only 10%, superior and inferior quadrants drained 20% respectively. Therefore, different trabecular meshwork permeability was set referring to the outflow differences in the four quadrants. The nasal quadrant had the greatest permeability of 4.6-15 m2, the superior and inferior had similar permeability of 1.84-15 m2 and the temporal quadrant had the least permeability of 9.2-16 m2. Moreover, in our clinical observation, angle closure is mostly located in the superior quadrant, followed by nasal, inferior and finally temporal quadrant.6 Herein, when considering the outflow differences in the four quadrants, we tested the results in the following four conditions, all open angle status, angle closure of superior quadrant, superior plus nasal quadrant angle closure, and superior, nasal and inferior quadrant angle closure in the model of AOD750=0.4 mm.

    When considering the impact of posture, we add the influence of gravity based on equation (2) in this computational model, a modified equation (4) was as follows:

    Embedded Image(4)

    Where u represents the fluid velocity (m·s−1), κ (m2) stands for the trabecular meshwork permeability, μ is dynamic viscosity 0.001 Pa*s, p is pressure (Pa), ρ is the liquid density and g is gravitational acceleration vector.

    Statistical analysis

    All data were analysed using IBM SPSS V.23.0 (IBM, Chicago, IL). The Kruskal-Wallis test was used to compare the maximum flow velocity (MFV) and pressure among the three AOD750 models. The correlations between average flow velocity and pressure gradient of each group were analysed with Spearman correlation test. Statistical significance was set at a p value <0.05.

    Results

    For different widths of AOD750, the MFV and pressure both showed no significant differences among the three models (p=0.852 and p=0.811 respectively). Figure 3a illustrated the partial flow at the open ACA with different ACRs in the model of AOD750=0.05 mm. The flow velocity increased as the ACR increased. The flow pattern of the aqueous humour was that the AH flow passed through the pupil, reaching the maximum flow velocity at the ACA. Moreover, the flow velocity on both sides of the closed angle showed a symmetric pattern. Similarly, the anterior chamber pressure demonstrated an increasing pattern as the ACR increased (figure 3b).

    Figure 3
    Figure 3

    The computational fluid modelling results of the maximum flow velocity and pressure. (a) The representative computational partial velocity figure for the aqueous humour outflow in the model of AOD750=0.05 mm. (b) The representative computational pressure figure for the aqueous humour outflow in the three models. (c) The relationships among the MFV, pressure and ACR. AOD750, angle opening distance at 750 µm from the scleral spur; ACR, angle closure range; MFV, maximum flow velocity.

    Figure 3c illustrated the quantitative relationship among the MFV, pressure and ACR. Both MFV and pressure increased exponentially with the increase of the ACR. MFV and pressure gradually elevated when ACR was larger than 180° and became obviously larger when ACR was 270° than those of 90° in all the three different AOD750 models.

    In the in vitro simulation model, the maximum pressure was retrieved in each angle closure range, and the ascending curve was similar with the result in the computational model. The pressure showed very minor elevation when ACR was less than 180°, and increased sharply when ACR was larger than 270° (figure 4).

    Figure 4
    Figure 4

    In vitro simulation model showing the maximum pressure in different angle closure ranges.

    Figure 5 showed that after considering the different aqueous outflow properties in the four quadrants, and closing sequence in clinical investigation, the maximum flow velocity and pressure both increased obviously when three quadrants closed (270°). When the gravity impact was added, it showed no differences on the maximum flow velocity and pressure (p=0.058 and p=0.586 respectively).

    Figure 5
    Figure 5

    The maximum flow velocity and maximum pressure in different quadrant closure with and without the impact of gravity. (a) The flow velocity pattern and pressure in different quadrant closure. (b) The association between the maximum flow velocity and closed quadrant, maximum pressure and closed quadrant. ACR, angle closure range; None, none quadrant closed; S, superior quadrant; SN, superior and inferior quadrants; SNI, superior, nasal and inferior quadrants. Maximum Flow Velocity_g, maximum flow velocity when consideration of the impact of gravity; Maximum Pressure_ g, maximum pressure when consideration of the impact of gravity.

    Discussion

    In the present study, we created a CFD model of primary angle closure disease for the analysis of aqueous humour dynamics. We pioneeringly found a non-linear association between the MFV and ACR, pressure and ACR in this PACD model. Both the MFV and pressure showed an exponential ascending curve in the numerical models of PACD, in which the MFV and pressure started to increase when the ACR was larger than 180° and increased obviously when the ACR was larger than 270° in the CFD model of PACD. These results may explain the underlying mechanism of how PACD progresses and provide the possible references on the management of PACD patients in different stages.

    The results from this CFD analysis are consistent with the clinical phenomenon that the IOP cannot be controlled by medication when the PAS is greater than 270°.23 Therefore, in clinical practices, when the ACR is greater than 180°, clinical intervention such as laser peripheral iridotomy or Argon laser peripheral iridotomy may be required for patients to avoid the PAS progress to larger extent and closer to 270°. For patients with ACR greater than 270°, a prompt management such as lens extraction may be guaranteed to prevent the acute angle-closure crisis. Furthermore, the current aqueous humour dynamics from this study may provide an explanation that the postoperative IOP after combined goniosynechialysis with phacoemulsification for PACD was similar to the phacoemulsification alone.24 25 As the figure 4 showed that the pressure and MFV only increased dramatically when angle closure was larger than 270°. As phacoemulsification procedure itself could open certain degree of PAS, the reported PACD eyes underwent combined goniosynechialysis with phacoemulsification may not differ largely in the ACR when compared with the eyes received phacoemulsification alone either before or after surgery.24 25 Thereafter, the little ACR differences may not be large enough to trigger apparent differences of the IOP and glaucoma medication usage.

    Moreover, the results from this study may also apply to explain the surgical outcomes for primary open angle glaucoma (POAG). It is reported that the efficacy of 120° goniotomy is similar to 240° and 360° goniotomy.26 27 From the exponential curve in figure 4, when functioning anterior chamber angle was 120°, the pressure and MFV did not differ largely from those with 240° and 360° functioning.26 27 Unlike PACD, the gonioscopy can examine the anterior chamber angle to investigate whether the ACA is open or closed. In clinical, there is no procedure to assess the function of the aqueous humour outflow pathway for POAG eyes. Since the ACA is open in POAG eyes and the dysfunction of the aqueous humour outflow occurs at trabecular meshwork or other microstructures of the aqueous outflow pathway. For eyes underwent 120° goniotomy, the left 240° may not be totally non-functioning. Therefore, the functioning aqueous outflow range may be larger than 120° for those eyes after 120° goniotomy. This is why in clinical practice, the surgical outcomes of the 120° goniotomy could persist for a relative long-term follow-up (6.0–48.0 months).26

    So far as we know, this is the first CFD model simulated different stages of PACD. A number of clinical studies have used tonographic aqueous outflow facility (TOF) which shows the AH outflow outside the anterior chamber to calculate the AH dynamics in glaucoma patients. PACD patients underwent goniosynechialysis combined with phacoemulsification were reported to have increased TOF and reduced glaucoma medications compared with eyes only underwent phacoemulsification.28 However, TOF only roughly measures overall AH velocity outside the eye without analysing the relationship between the AH dynamics and the parameters of the anterior segment. And in several clinical studies, the IOP and medication reduction effect was similar between the phacoemulsification with or without goniosynechialysis. The model in this study better explained the underlying reason that if a surgery can keep a certain degree of angle open, it may be enough to maintain low IOP and additional goniosynechialysis is not necessary.

    Compared with other studies, the present 3D CFD model is more realistic to the natural outflow pathway of the human eye. In other studies, the flow inlet was set at the trabecular meshwork9 or in the boundary between the posterior chamber and anterior vitreous.21 In our study, the fluid inlet was positioned at the location of the ciliary process that produces AH, which flows out through the posterior chamber, pupil, central anterior chamber, anterior chamber angle and trabecular network. This pathway is similar to the natural AH outflow pathway in the human eye, which improves the structure of outflow pathway of aqueous humour and makes the numerical results more accurate. The resistance coefficient test showed the AH dynamics were dominated by the viscous resistance rather than the inertia resistance (online supplemental material section 1). As the ocular anterior segment is a small lumen with various tiny pores, this further proves our model is accessible to evaluate the AH dynamics in the human eye.

    Supplemental material

    This study has a number of limitations. First, the human eye is a complicated and accurate chamber; it is difficult to perfectly consider all the morphological parameters of ocular anterior segment, such as the axial length and anterior chamber depth, were not considered in this study, while these were important risk factors for the development of angle closure glaucoma. However, when shallowing the anterior chamber depth to the half, the relationships among the maximum flow velocity, pressure and ACR were similar (online supplemental material section 2). Second, this geometry is a robust simulation of the outflow and did not include the microstructures of the TM; a study found that aqueous flow was more turbulent in models with higher TM microstructure stiffness.29 Finally, the contacts between the iris with trabecular meshwork and iris with lens are also important in the development of PACD.30 31 However, the iris was set as a rigid tissue in this model; the dynamic contacts could not be simulated. A model with elastic iris may be able to find out the impact of the contacts. Therefore, our further studies may introduce these factors based on the current computational model to better simulate the intraocular fluid dynamics for PACD.

    In conclusion, the study proposes the possibility for quantitatively evaluating AH flow in various angle width and ACRs. The relationship among pressure, MFV and ACR in this study well explains the underlying mechanism of similar surgical outcomes after phacoemulsification with or without goniosynechialysis and the comparative effect of IOP reduction after 120°, 240° and 360° of goniotomy. This CFD model also illustrates the reason that is why the ACR of 180° and 270° are important in clinical practice and may provide a theoretical basis for the clinical intervention of PACD.

    Data availability statement

    Data are available upon reasonable request. Data can be acquired from the corresponding author upon reasonable request.

    Ethics statements

    Patient consent for publication

    Ethics approval

    Not applicable.

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    Supplementary materials

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    Footnotes

    • LF and XL contributed equally.

    • Contributors YL is responsibel for the overall content. XL and YL contributed to the design of the manuscript. LZ, XZ, XW and HL created the model, run the software and analysed the data. LG, KW, YW and MK carried out the in vitro experiment and analysed the data. XL, LZ and JL reviewed papers and drafted the manuscript; LF, XZ and YL revised the manuscript. All authors read and approved the final manuscript.

    • Funding This work was supported by the Program for Zhejiang Leading Talent of S&T Innovation (2021R52012), National Natural Science Foundation of China Youth Science Foundation Project (grant no. 82201176), the Foundation of Wenzhou City Science & Technology Bureau (Y20210972) and Zhejiang Provincial Medical and Health Science Technology Program (2022KY905).

    • Competing interests None declared.

    • Provenance and peer review Not commissioned; externally peer reviewed.

    • Supplemental material This content has been supplied by the author(s). It has not been vetted by BMJ Publishing Group Limited (BMJ) and may not have been peer-reviewed. Any opinions or recommendations discussed are solely those of the author(s) and are not endorsed by BMJ. BMJ disclaims all liability and responsibility arising from any reliance placed on the content. Where the content includes any translated material, BMJ does not warrant the accuracy and reliability of the translations (including but not limited to local regulations, clinical guidelines, terminology, drug names and drug dosages), and is not responsible for any error and/or omissions arising from translation and adaptation or otherwise.