with iridotomy Mariia Dvoriashyna 1 Rodolfo Repetto - - PowerPoint PPT Presentation
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
Department of Civil, Chemical and Environmental Engineering, University of Genoa, Italy (née Siggers) Department of Bioengineering, Imperial College London, UK WIAM16
September 1st , 2016
1 1 2 1 2
Mariia Dvoriashyna (University of Genoa) WIAM16 September 1st , 2016 2/11
Figure 1. Sketch of the cross section of the human eye
Mariia Dvoriashyna (University of Genoa) WIAM16
Figure 1. Sketch of the cross section of the human eye
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Mariia Dvoriashyna (University of Genoa)
Figure 1. Sketch of the cross section of the human eye WIAM16 September 1st , 2016 3/11
Mariia Dvoriashyna (University of Genoa)
Figure 1. Considered domain and Coordinate system
Mechanisms that drive aqueous flow: aqueous production in the ciliary body and miosis (i.e. iris motion due to the pupil contraction) We use Lubrication theory to simplify Navier-Stokes equations for incompressible flow in a long and thin domain. (1) (2) Where p is independent of r and the subscript ‘h’ indicates that only 𝜄, 𝜒 − components are considered. We assume that the iris is moving with the velocity distribution v. The, from (1) we get the dependence of the fluid velocity on the pressure gradient: integrating (2) with this velocity we get the governing equation
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Mariia Dvoriashyna (University of Genoa)
Figure 1. Considered domain and Coordinate system
inlet flux F at ciliary body imposed pressure at the pupil
We model iridotomy as a point sink. 𝑄𝑗 − pressure related to the sink, 𝜖𝑄𝑗 𝜖𝜄′ ~ 𝑅𝑗 𝑏 → ∞, 𝑏 → 0. where 𝑅𝑗 - flux through the iridotomy and 𝑏 is radius of iridotomy. To avoid singularity at the point of the sink, we introduce regularised pressure: 𝑞𝑠𝑓 = 𝑞 − 𝑄𝑗. 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): 𝑄𝑗 =
𝑅𝑗 8𝑚𝜈+3𝑏𝜌𝜈 𝑏4𝜌
, where l is the thickness of the iris.
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Mariia Dvoriashyna (University of Genoa)
Figure 1. Ultrasound scan image of the human eye Figure 2. Interpolated height of the Posterior chamber (distance between posterior iris and anterior lens) WIAM16 September 1st , 2016 6/11
Mariia Dvoriashyna (University of Genoa)
Figure 1. No iridotomy Figure 2. Iridotomy with diameter 50 um Figure 3. Iridotomy with diameter 100 um
Pressure distribution and normalized velocity vectors
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Mariia Dvoriashyna (University of Genoa)
Figure 1. Flux through the iridotomy out of the total flux for different locations of the iridotomy: blue line – halfway along the posterior chamber, red line – 5/6 of the way from pupil to ciliary body Figure 2. Maximum pressure in the posterior chamber with blocked pupil (i.e. the iridotomy is the only outlet) WIAM16 September 1st , 2016 8/11
Mariia Dvoriashyna (University of Genoa)
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. Figure 1. Schematic velocity distribution at the iris during miosis Ԧ 𝑤 is chosen to satisfy the given volume change
𝑊
𝑜𝑓𝑥= 1 − 𝑄 𝑊, 𝑄 − percentage of PC
volume change, V – initial volume of the PC WIAM16 September 1st , 2016 9/11
Mariia Dvoriashyna (University of Genoa)
Figure 1. Maximum wall shear stress on the cornea located at the distance 0.2 mm from the iridotomy, for different percentage of PC volume change Figure 2. Maximum wall shear stress on the cornea for the iridotomy diameter 80 um, for different percentage of PC volume change WIAM16 September 1st , 2016 10/11
Mariia Dvoriashyna (University of Genoa)
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Mariia Dvoriashyna (University of Genoa)
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