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Aqueous Humor Flow in the Posterior Chamber of the Eye with iridotomy Mariia Dvoriashyna 1 Rodolfo Repetto Jennifer H. Tweedy 1 2 1 Department of Civil, Chemical and Environmental Engineering, University of Genoa, Italy 2 (ne

  1. Aqueous Humor Flow in the Posterior Chamber of the Eye with iridotomy Mariia Dvoriashyna 1 Rodolfo Repetto Jennifer H. Tweedy 1 2 1 Department of Civil, Chemical and Environmental Engineering, University of Genoa, Italy 2 (née Siggers) Department of Bioengineering, Imperial College London, UK WIAM16 September 1 st , 2016

  2. Introduction Figure 1. Sketch of the cross section of the human eye September 1 st , 2016 Mariia Dvoriashyna (University of Genoa) WIAM16 2/11

  3. Introduction Motivation: • Investigate the effects of the iridotomy procedure on aqueous flow and find optimal iridotomy size and location Aims: • Find pressure difference between anterior and the posterior chambers – indicates risk of angle closure glaucoma • Find shear stress on the surrounding tissues – indicates risk of tissue damage Figure 1. Sketch of the cross section of the human eye September 1 st , 2016 Mariia Dvoriashyna (University of Genoa) WIAM16 3/11

  4. Introduction Motivation: • Investigate the effects of the iridotomy procedure on aqueous flow and find optimal iridotomy size and location Aims: • Find pressure difference between anterior and the posterior chambers – indicates risk of angle closure glaucoma • Find shear stress on the surrounding tissues – indicates risk of tissue damage Figure 1. Sketch of the cross section of the human eye September 1 st , 2016 Mariia Dvoriashyna (University of Genoa) WIAM16 3/11

  5. Model (1) (2) Where p is independent of r and the subscript Figure 1. Considered domain and Coordinate system ‘h’ indicates that only 𝜄, 𝜒 − components are considered. Mechanisms that drive aqueous flow: aqueous production in We assume that the iris is moving with the the ciliary body and miosis (i.e. iris motion due to the pupil velocity distribution v . The, from (1) we get the contraction) dependence of the fluid velocity on the We use Lubrication theory to simplify Navier-Stokes pressure gradient: equations for incompressible flow in a long and thin domain. integrating (2) with this velocity we get the governing equation September 1 st , 2016 Mariia Dvoriashyna (University of Genoa) WIAM16 4/11

  6. Model We model iridotomy as a point sink. 𝑄 𝑗 − pressure related to the sink, 𝜖𝜄 ′ ~ 𝑅 𝑗 𝜖𝑄 𝑗 𝑏 → ∞, 𝑏 → 0. where 𝑅 𝑗 - flux through the iridotomy and 𝑏 is radius of iridotomy. Figure 1. Considered domain and Coordinate system To avoid singularity at the point of the sink, we introduce regularised pressure: 𝑞 𝑠𝑓𝑕 = 𝑞 − 𝑄 𝑗 . Governing equations: To close the problem, we assume that the flux through the iridotomy is proportional to the pressure drop across the hole (Dagan et al, 1982): inlet flux F at ciliary body 𝑅 𝑗 8𝑚𝜈+3𝑏𝜌𝜈 𝑄 𝑗 = , 𝑏 4 𝜌 imposed pressure at the pupil where l is the thickness of the iris. September 1 st , 2016 Mariia Dvoriashyna (University of Genoa) WIAM16 5/11

  7. Considered Geometry Figure 1. Ultrasound scan image of the human eye Figure 2. Interpolated height of the Posterior chamber (distance between posterior iris and anterior lens) September 1 st , 2016 Mariia Dvoriashyna (University of Genoa) WIAM16 6/11

  8. Flow due to aqueous production Pressure distribution and normalized velocity vectors Figure 1. No iridotomy Figure 2. Iridotomy with diameter 50 um Figure 3. Iridotomy with diameter 100 um September 1 st , 2016 Mariia Dvoriashyna (University of Genoa) WIAM16 7/11

  9. Flow due to aqueous production Figure 1. Flux through the iridotomy out of the total flux for different Figure 2. Maximum pressure in the posterior chamber with locations of the iridotomy: blue line – halfway along the posterior blocked pupil (i.e. the iridotomy is the only outlet) chamber, red line – 5/6 of the way from pupil to ciliary body September 1 st , 2016 Mariia Dvoriashyna (University of Genoa) WIAM16 8/11

  10. Flow due to miosis Figure 1. Schematic velocity distribution at the iris during miosis 𝑤 is chosen to satisfy the given volume change Ԧ of the posterior chamber after miosis: 𝑊 𝑜𝑓𝑥 = 1 − 𝑄 𝑊, 𝑄 − percentage of PC volume change, V – initial volume of the PC Figure 2. Volumetric flux (as a multiple of that produced by ciliary body) passing through the iridotomy at the start of the miosis. P – percentage of the volume change in the posterior chamber during miosis. September 1 st , 2016 Mariia Dvoriashyna (University of Genoa) WIAM16 9/11

  11. Flow due to miosis Figure 1. Maximum wall shear stress on the cornea Figure 2. Maximum wall shear stress on the cornea for the iridotomy diameter 80 um, for different located at the distance 0.2 mm from the iridotomy, percentage of PC volume change for different percentage of PC volume change September 1 st , 2016 Mariia Dvoriashyna (University of Genoa) WIAM16 10/11

  12. Conclusions • The geometry of the posterior chamber and the presence or absence of pupillary block have a strong influence on the choice of an iridotomy size • Iridotomy diameters of at least 40 um are required in case of pupillary block • Even a small variation of the volume of the posterior chamber produced during miosis can generate velocities that are much bigger than those with a fixed iris. • During miosis, a jet through the iridotomy is produced. The resulting jet velocity and wall shear stress on the cornea are strongly dependent on the radius of the iridotomy and on the volume change of the posterior chamber. Our results suggest that there could be a risk of corneal endothelial cell detachment if the cornea is too close to the iridotomy and/or the volume change of the posterior chamber is sufficiently large. September 1 st , 2016 Mariia Dvoriashyna (University of Genoa) WIAM16 11/11

  13. Conclusions • The geometry of the posterior chamber and the presence or absence of pupillary block have a strong influence on the choice of an iridotomy size • Iridotomy diameters of at least 40 um are required in case of pupillary block • Even a small variation of the volume of the posterior chamber produced during miosis can generate velocities that are much bigger than those with a fixed iris. • During miosis, a jet through the iridotomy is produced. The resulting jet velocity and wall shear stress on the cornea are strongly dependent on the radius of the iridotomy and on the volume change of the posterior chamber. Our results suggest that there could be a risk of corneal endothelial cell detachment if the cornea is too close to the iridotomy and/or the volume change of the posterior chamber is sufficiently large. Thank you for your attention! September 1 st , 2016 Mariia Dvoriashyna (University of Genoa) WIAM16 11/11

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