Optical coherence tomography quantifies gradient refractive index and mechanical stiffness gradient across the human lens

Abstract

Background: As a key element of ocular accommodation, the inherent mechanical stiffness gradient and the gradient refractive index (GRIN) of the crystalline lens determine its deformability and optical functionality. Quantifying the GRIN profile and deformation characteristics in the lens has the potential to improve the diagnosis and follow-up of lenticular disorders and guide refractive interventions in the future.

Methods: Here, we present a type of optical coherence elastography able to examine the mechanical characteristics of the human crystalline lens and the GRIN distribution in vivo. The concept is demonstrated in a case series of 12 persons through lens displacement and strain measurements in an age-mixed group of human subjects in response to an external (ambient pressure modulation) and an intrinsic (micro-fluctuations of accommodation) mechanical deformation stimulus.

Results: Here we show an excellent agreement between the high-resolution strain map retrieved during steady-state micro-fluctuations and earlier reports on lens stiffness in the cortex and nucleus suggesting a 2.0 to 2.3 times stiffer cortex than the nucleus in young lenses and a 1.0 to 7.0 times stiffer nucleus than the cortex in the old lenses.

Conclusions: Optical coherence tomography is suitable to quantify the internal stiffness and refractive index distribution of the crystalline lens in vivo and thus might contribute to reveal its inner working mechanism. Our methodology provides new routes for ophthalmic pre-surgical examinations and basic research.

Fig. 1. Overview of the data post-processing pipeline, illustrated at a representative case.

a Temporal and b cross-sectional views of the motion-correction structural raw OCT data. c Structural reflectivity profile. d Axial, e lateral and f, g cross-sectional phase difference tracking. j Temporal strain fluctuation. Mathematical operations and correspondingly derived parameters: h refractive index distribution, i axial displacement, k frequency assessment.

Fig. 2. Refractive and mechanical profiles averaged across the optical zone.

a Structural reflectivity profile of the human crystalline lens as a function of depth. The gray shaded area indicates the region, which was considered as the nucleus at all ages. b Corresponding gradient refractive index distribution. c Corresponding displacement and d the smoothed strain profile corresponding to the deformation in response to an ambient pressure change by −10 mmHg recorded during ~ 0.6 s. In panels a–c, error bars represent standard error across the full data set (n = 12 biologically independent samples).

Fig. 3. Cross-sectional structural and mechanical images.

a, c, e, g, i Representative cross-sectional views of the crystalline lens in structural and elastographic OCT images. b, d, f, h, j Elastographic images show the strain distribution at maximal strain amplitude during micro-accommodation (left half) and micro-dis-accommodation (right half). From top to bottom in each image there is the anterior lens cortex, lens nucleus and posterior lens cortex. In lenses ≤45 years the lens nucleus deformed most (presented largest strains) demonstrating a softer behavior compared to the cortex.

Fig. 4. Strain assessment from micro-fluctuations.

a–f Average axial strain profiles of the human crystalline lens during a micro-fluctuation obtained with OCT elastography. With increasing age, the strain amplitude in the nucleus decreases drastically and strains in the cortical region slightly increase. Gray dots represent the mean strain profile of an individual participant (n = 2 independent samples per panel). The black line shows the average strain profile for the respective age range. g Correlation between age range and the axial strain (n = 12 independent samples) induced in the nucleus and cortex, respectively. Gray markers represent single data points, the black continuous and dashed lines represent the average trend lines, respectively in the nucleus and cortex. h Strain ratio of cortex: nucleus as a function of age (n = 12 independent samples). A substantial change is observed between the age of 45 and 55, which corresponds to the onset of presbyopia. Gray markers represent single data points, the black line represents the average curve.

Fig. 5. Simulation results.

a Axial displacement profile in response to an ambient pressure decrease of 10 mmHg. For comparison with the experimental data, see Fig. 2c. b Axial strain profile during a micro-fluctuation with a ciliary force of 39 μN. For comparison with the experimental data, see Fig. 4a–f.