Universal model of the bilenticular eye

Abstract

Purpose : To present a paraxial eye model capable of describing any ocular configuration consisting of two thin lenses without prior assumptions. This model consists of 5 equations that instantly provide values for the corneal power P_c, lens power P_l, interlenticular distance d (from corneal apex to the lenticular principal point), axial length AL or refractive error S, provided the other values are known.

Methods : The model starts by defining refractive error as S = P_ax – P_eye, or the difference between axial power P_ax (or dioptric distance) and the total refractive power of the entire eye P_eye. Next, the axial and total powers in this equation are expanded as P_ax = n/(AL–pp₂) and P_eye = P_c + P_l – P_c×P_l×d/n, with n the refractive index of the aqueous and vitreous humors and pp₂ the position of the second principal point of the eye with respect to the corneal apex. Although usually pp₂ is considered constant, this assumption was not made here. By fully expanding the resulting equation, one can derive equations as a function of P_c, P_l, d, AL, or S. Together, the solutions to these 5 equations form the model. This model is exceedingly robust, providing solutions for a wide range of biometric values, both physiological (e.g., for various animal species, Figure 1) and unrealistic (e.g., negative lens powers). Hence, the Gullstrand-Emsley model was used as a reference, and the following restrictions were used: AL between 20 -30 mm, d between 2 -9 mm, P_c between 30 - 55D, P_l between 15 - 35D, and S between -10 – +10D.

Results : Figure 2 shows examples of how the model provide the correct parameter value in a single step by either choosing fixed values for two parameters and varying two other parameters (Figure 2a&b), or by choosing a single fixed parameter and varying three other parameters (Figure 2c&d).

Conclusions : As it does not make any assumptions, the universal model provides the most mathematical accurate description available for any eye configuration, both within the physiological range and beyond. Moreover, the proposed equations improve on typical vergence calculations by allowing to solve for any parameter in a single step.

This abstract was presented at the 2024 ARVO Annual Meeting, held in Seattle, WA, May 5-9, 2024.

 

Figure 1: Model applied to the biometry of various species.

 

Figure 2: Results for a) fixed lens power of 21.76D and position d of 6.08 mm; b) emmetropic eye of 23.89 mm long; c) emmetropic eyes of various lengths; d) 23.89 mm long eye with various refractive errors.