Refractive development II: Modelling normal and myopic eye growth

During refractive development, eye growth is controlled by a combination of genetically pre-programmed processes and retinal feedback to minimise the refractive error. This work presents a basic differential model of how this process may take place.

The description starts from two bi-exponential descriptions of the axial power P_ax (or dioptric distance) and total refractive power P_eye, the difference between which corresponds with the spherical refractive error S. This description is rewritten as an ordinary differential equation and supplemented by a retinal feedback function that combines retinal blur (closed loop) with a term describing excessive axial growth (open loop). This model is controlled by a total of 18 parameters that allow for a wide variety of developmental behaviours.

The proposed model reproduces refractive development growth curves found in the literature for both healthy and myopic eyes. An early onset of myopisation, a large growth term and a high minimum for the crystalline lens power all lead to higher degrees of myopia. Assigning more importance to the feedback than to the pre-programmed growth makes the model more sensitive to myopogenic influences. Applying refractive corrections to the model, undercorrection is found to produce more myopia. The model compensates for a low-powered imposed lens and can return to (near) emmetropia if that imposed lens is removed quickly thereafter. Finally, simulating the effect of a diffuser leads to high myopia.

Using a series of basic assumptions, the proposed model recreates many well-known experimental and clinical results about refractive development from the literature while placing them in a standardised context. This contributes to a broader understanding of the origins of refractive errors, and future versions may help in the development of solutions for myopia control.