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G. K. Hung, A. J. Fiedler, J. Liu, K. J. Ciuffreda; Homeomorphic Biomechanical Model of Myopia and Hyperopia. Invest. Ophthalmol. Vis. Sci. 2009;50(13):3946.
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© ARVO (1962-2015); The Authors (2016-present)
To simulate myopic and hyperopic growth in a homeomorphic biomechanical model of the eye based on the Incremental Retinal-Defocus Theory (IRDT) (Hung and Ciuffreda, ARVO, 2001, 2003, 2005) under different optical defocus conditions.
The IRDT is based on earlier experimental work in the areas of: optic nerve section (Wildsoet & Pettigrew, 1988), neurochemical cascade (Wallman, 1997; Troilo et al., 2000), scleral creep (Siegwart and Norton, 1999), form deprivation (Schaeffel and Diether, 1999), and optical defocus (Smith and Hung, 2000). The theory states that the time-integrated reduction in retinal-image defocus magnitude (during an increment of genetically-preprogrammed growth) decreases the rate of retinal neuromodulator release, which in turn decreases the rate of proteoglycan synthesis and reduces scleral structural integrity, thus resulting in axial elongation and myopia development. A homeomorphic biomechanical model of the eye was constructed to test the IRDT theory based only on optical defocus and forces acting on the components of the eye. The model consisted of a distributed assembly of masses and springs that represent the outer shell of the eyeball. Without loss of generality and to simplify calculations, the model was analyzed in 2-dimensions. It has 30 connected nodes forming a circle, where each node consists of a mass that is attached by two springs. The intraocular pressure is represented as an outward force acting on each mass. For a given simulated optical defocus condition, a decrease in blur circle size at a node decreases the spring constant of the adjacent springs. A Matlab program was used to simulate changes in node positions over time.
Relative to the no-lens condition - (1) for a simulated imposed large minus lens, the model eye expanded more in the posterior direction, leading to myopic growth; (2) when the light rays were aimed at an oblique angle, the eye growth occurred more in the oblique direction; (3) for a simulated large imposed plus lens, the model eye expanded less in the posterior direction, leading to hyperopic growth; (4) for form deprivation with progressively increasing graded diffusers, associated with increasing amounts of optical dispersion, there was a progressive increase in the effective amounts of hyperopic defocus, and in turn, increase in myopic growth.
The homeomorphic biomechanical model of the eye was able to simulate the emmetropization mechanism using only the forces acting on the masses at the nodes, where the values of the spring constants were modified by the change in retinal defocus as specified by IRDT.
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