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

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

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

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

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

Factors influencing the mean LC depth.

<p>Factors influencing the mean LC depth.</p

Demographics and baseline characteristics.

<p>Demographics and baseline characteristics.</p

Correlation between the mean anterior lamina cribrosa surface depth (LCD) and age (A), untreated intraocular pressure (IOP; B), and retinal nerve fiber layer (RNFL) thickness (C), according to the location of the central retinal vessel trunk (CRVT).

<p>Note that the correlations between age and mean LCD (<b>A</b>), and between untreated IOP and mean LCD (<b>B</b>) were more prominent in the peripheral CRVT group than in the central CRVT group.</p