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Howard F. Fine, Jonathan L. Prenner, Peter L. Bishay, Daniel B. Roth, William J. Bottega; A Mechanics Based Model Of A Detaching Retina. Invest. Ophthalmol. Vis. Sci. 2012;53(14):6362.
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© ARVO (1962-2015); The Authors (2016-present)
To advance the current technical view of retinal detachment and develop a rigorous mechanics based model of the process.
The mathematical model (Fig. 1a) incorporates elements of structural and detachment mechanics (spherical shell theory and Griffith type detachment criterion) in an energy formulation. The calculus of variations is employed, with the propagating boundary of the detached region of the retina allowed to vary as well as the displacements. This yields the self-consistent energy release per unit detached area of retina as the "driver" of the detachment process, and formulae for critical stress and critical radial deflection that provide a basis for measuring critical parameters (Fig.1b).
Results are presented in the form of threshold curves for the detaching structure, and reveal characteristic behavior, including threshold levels and stability for detachment, and the influence of the presence and size of a retinal tear on detachment propagation. The model predicts that once detachment ensues it does so in an unstable manner and is extensive in scope. Results also suggest that, under appropriate conditions, the presence and size of a retinal tear or hole can have a stabilizing effect with regard to detachment propagation. "Dimpling" of the retina is predicted for detachment angles ≥ 0.3 radians. The influence of altering material parameters such as fibril stiffness, Poisson's ratio (between 0.1 and 0.49), and thickness ratio, as well as the tear size are presented. The latter shows that, under appropriate circumstances, the presence and size of a retinal tear can have a stabilizing effect on detachment propagation.
A mathematical model to describe the mechanics of a detaching retina was devised incorporating an energy based criterion for detachment propagation. The model describes under what conditions a detachment will progress, predicts "dimpling" phenomenon of the retina under specific circumstances, and indicates that once propagation ensues it will be extensive.
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