Numerical stress analysis of the iris tissue induced by pupil expansion: Comparison of commercial devices

<div><p>Purpose</p><p>(1) To use finite element (FE) modelling to estimate local iris stresses (i.e. internal forces) as a result of mechanical pupil expansion; and to (2) compare such stresses as generated from several commercially available expanders (Iris hooks, APX dilator and Malyugin ring) to determine which design and deployment method are most likely to cause iris damage.</p><p>Methods</p><p>We used a biofidelic 3-part iris FE model that consisted of the stroma, sphincter and dilator muscles. Our FE model simulated expansion of the pupil from 3 mm to a maximum of 6 mm using the aforementioned pupil expanders, with uniform circular expansion used for baseline comparison. FE-derived stresses, resultant forces and area of final pupil opening were compared across devices for analysis.</p><p>Results</p><p>Our FE models demonstrated that the APX dilator generated the highest stresses on the sphincter muscles, (max: 6.446 MPa; average: 5.112 MPa), followed by the iris hooks (max: 5.680 MPa; average: 5.219 MPa), and the Malyugin ring (max: 2.144 MPa; average: 1.575 MPa). Uniform expansion generated the lowest stresses (max: 0.435MPa; average: 0.377 MPa). For pupil expansion, the APX dilator required the highest force (41.22 mN), followed by iris hooks (40.82 mN) and the Malyugin ring (18.56 mN).</p><p>Conclusion</p><p>Our study predicted that current pupil expanders exert significantly higher amount of stresses and forces than required during pupil expansion. Our work may serve as a guide for the development and design of next-generation pupil expanders.</p></div

Comparison of all results with uniform circular expansion as the baseline.

<p>The sign (+) refers to “greater than” and the sign (-) refers to “smaller than”.</p

Numerical stress analysis of the iris tissue induced by pupil expansion: Comparison of commercial devices - Fig 4

<p><b>A.</b> Initial iris shape with a pupil diameter of 3 mm before pupil expansion. Stress distribution of the iris tissue with the use of <b>B.</b> APX dilator, <b>C.</b> Iris hooks, <b>D.</b> Malyugin ring and <b>E.</b> Uniform circular expansion. The FE models were all deformed to a 6 mm pupil and stress magnitudes adjusted to the same scale. <b>F.</b> Graph of stromal stress along the radial direction starting at the point of greatest stress concentration (marked using solid black lines in <b>B-E</b>) and along the radial direction where a corner is present (marked using dotted black lines in <b>B-E</b>). Note that the starting point of each curve is determined by the size of the pupil and the ends at the iris limbus.</p

Results of FE stroma and muscle stress values, and reaction forces experienced by the iris with the various pupil expanders.

<p>Results of FE stroma and muscle stress values, and reaction forces experienced by the iris with the various pupil expanders.</p

Numerical stress analysis of the iris tissue induced by pupil expansion: Comparison of commercial devices - Fig 1

<p><b>A.</b> Anatomy of the iris tissue. The iris consists of the anterior boundary layer (ABL), the stroma, the sphincter and dilator muscles, and the posterior pigmented epithelium (PE). <b>B.</b> Geometry of the FE model used for simulations. The stroma and the ABL were combined into a single part, and the sphincter and dilator muscles were combined with the PE.</p

Anatomical orientation convention adopted in this study.

<p>The orientation adopted is in Cartesian coordinates in the <i>x</i>, <i>y</i> and <i>z</i> directions. The iris of a left eye is shown in this figure. The direction conventions of the arrows are perpendicular to their respective planes.</p

Numerical stress analysis of the iris tissue induced by pupil expansion: Comparison of commercial devices - Fig 3

<p><b>The FE models and summary of the simulation parameters used in the analyses for A</b>. The iris hooks, <b>B.</b> The APX dilator, <b>C.</b> The Malyugin ring, and for <b>D.</b> Uniform circular expansion. All irides had an initial pupil diameter of 3 mm (initial shape). Following FE analysis, the deformed expanded pupil shapes had diameters of 6 mm (maximum observable diameter, expanded shape).</p

Quantitative trait analysis between <i>ABCC5</i> rs1401999 and anterior chamber depth in SIMES, SINDI, and BES.

<p>SIMES: Singapore Malay Eye Study (typed with Illumina 610K GWAS chip).</p><p>SINDI: Singapore Indian Eye Study (typed with Illumina 610K GWAS chip).</p><p>BES1: Beijing Eye Study typed with Illumina 610K GWAS chip.</p><p>BES2: Beijing Eye Study typed with direct sequencing.</p><p>β: Per-allele effect size of <i>ABCC5</i> rs1401999 on anterior chamber depth.</p><p>SE: Standard error for β.</p><p><i>P</i>gc: Genomic control corrected <i>P</i>-value.</p><p>MAF: Minor allele frequency.</p><p>*: I²-index for heterogeneity = 0%.</p

Association analysis between <i>ABCC5</i> rs1401999 and primary angle closure glaucoma in all chip-typed sample collections (top panel), de-novo genotyped sample collections (middle panel), and PACG cases and clinically certified controls with open angles (bottom panel).

<p>MAF case: Minor allele frequency in PACG cases.</p><p>MAF control: Minor allele frequency in controls.</p><p>OR: Odds ratio.</p><p><i>P</i>: <i>P</i>-value for association with PACG.</p><p>I²: I-squared index for between-collection heterogeneity.</p><p>* Results here are presented based on raw minor allele frequency counts without further adjustment.</p>†<p>PACG patients were recruited from the Beijing Tongren Hospital and controls were recruited from the Handan Eye Study (HES), a population-based study of eye disease in rural Chinese aged 30 years and over.</p

Association analysis between <i>ABCC5</i> rs1401999 and susceptibility to primary angle closure glaucoma (PACG).

<p>The PACG sample collections have been described elsewhere <a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1004089#pgen.1004089-Vithana1" target="_blank">[6]</a>. The vertical line represents a per-allele odds ratio of 1.00. The oblongs represent point estimates (referring to the per-allele odds ratio), with the height of the oblongs inversely proportional to the standard error of the point estimates. Horizontal lines indicate the 95% confidence interval for each point estimate. Meta-analyses of samples are reflected by blue diamonds. The width of the diamonds indicates their 95% confidence intervals. All point estimates in Stage 1 have been adjusted for the top axes of genetic stratification using logistic regression.</p