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D.M. Silver, H.A. Quigley; Iris Structure: Mathematical Model and Analysis . Invest. Ophthalmol. Vis. Sci. 2006;47(13):5619.
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© ARVO (1962-2015); The Authors (2016-present)
To construct a mathematical model to illustrate the mechanical and geometrical behavior of the iris as a function of pupil diameter and anterior segment parameters.
Using geometry, mechanics and the principles of elasticity, a mechanical model of the eye was constructed, consisting of a cornea, sclera, lens, anterior and posterior chambers and an iris. The model of the iris consists of sphincter and dilator zones of variable width and thickness. Literature values of the anatomical parameters of the anterior segment include radii of curvature and relative positions of cornea, lens and sclera, depth of the anterior chamber, and diameter of the limbus. Within this parameter space for numerical experimentation, the pupil diameter and degree of accommodation represent additional degrees of freedom. Conservation of volume of iris tissue with changes in pupil diameter and accommodation requires changes in the size and shape of the iris zones. Stress balance between the two iris muscle systems, sphincter and dilator, is augmented by elastic stresses on iris tissue induced by differential pressure between anterior and posterior chambers accompanying aqueous flow through the iris–lens channel.
One example of the exercise of the model shows that the sphincter zone of the iris can maintain its volume and surface area while maintaining its thickness by decreasing its width from 1.4 to 0.4 mm as the pupil is dilated from 1 to 7 mm diameter. In contrast, the dilator zone of the iris undergoes an increase in thickness of about 50% (420 to 630 microns) and a decrease of surface area of about 66% (240 to 160 mm2) as the pupil is dilated from 1 to 7 mm diameter. These changes in the shape and position of the iris affect the geometry of the iris–lens channel and the anterior chamber angle in the vicinity of the trabecular meshwork.
The flow of aqueous and the maintenance of differential pressure between the posterior and anterior chambers are controlled by the proximity of the iris to the anterior surface of the lens. This control is derived from the mechanics of the sphincter and dilator muscles within the iris and the elastic properties of iris tissues. In addition, dilation or constriction of the pupil or changes in accommodation induce changes in the thickness of the iris that give rise to further constraints on aqueous flow that are potential additional risk factors in glaucoma damage.
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