Eigenlenses: an eigenvectors-based model for full crystalline lens shape description

Abstract

Purpose : Accurate quantification of the full shape of the crystalline lens is essential for understanding accommodation and age-related disorders such as cataract and presbyopia. We propose a new method for the representation of the full crystalline lens geometry.

Methods : Isolated human crystalline lenses (n=76; 0-71y/o) immersed in preservation media were imaged using two custom-developed 3-D Optical Coherence Tomography (OCT) systems (OCT1, India, n=49; OCT2, Spain, n=27) with the anterior and the posterior surfaces facing the beam. Full shape 3-D models were obtained after automatic segmentation of the images, fan and optical distortion correction, tilt removal and registration. A laser ray tracing system was used to measure the lens spherical aberration (SA) in OCT1. Principal component analysis was applied to the lens models, previously normalized by their equatorial diameters (DIA), obtaining a new set of orthogonal basis (eigenlenses) allowing any 3-D lens to be expressed as a linear combination of eigenlenses. Root mean square (RMS) error between the actual lens full shape and its representation with eigenlenses was compared with the RMS using radii (Rs) of the best sphere fitting and radii (Rq) and asphericity (Q) of the best conicoid fitting of anterior (AL) and posterior (PL) surfaces.

Results : Mean RMS of eigenlenses representation (0.062±0.009 mm) was significantly lower than those using sphere (0.085±0.013 mm; p<0.01) and conicoid (0.082±0.016 mm; p<0.01) fittings with the same number of parameters. 1^st, 4^th & 5^th eigenlenses mainly represent symmetric variations of the shape, while 2^nd & 3^rd represent non-symmetric variations. Age was modeled from 1^st & 4^th eigenlenses coefficients and DIA (multiple linear regression, R²=0.79, p<0.01), while R² was lower when modeling with RqAL, RqPL and DIA (R²=0.60, p<0.01). Spherical aberration (6 mm pupil) was modeled from 1^st, 3^rd, 4^th, 5^th & 7^th eigenlenses coefficients and DIA (R²=0.62, p<0.01) resulting in a higher R² than with RqAL, RqPL, QAL, QPL, lens thickness and DIA (R²=0.53, p<0.01).

Conclusions : The new eigenlenses provide a more compact and accurate representation of the full shape of the lens than the classical models using radii of curvature and conic constants. Eigenlenses represent the crystalline lens as a whole, facilitating intuitive conclusions on geometrical changes of the lens, e.g., as a function of age, accommodation or refractive error.

This abstract was presented at the 2019 ARVO Annual Meeting, held in Vancouver, Canada, April 28 - May 2, 2019.