Estimation of the full shape of the crystalline lens from OCT: validation using stretched donor lenses.

Quantifying human crystalline lens geometry as a function of age and accommodation is important for improved cataract and presbyopia treatments. In previous works we presented eigenlenses as a basis of 3-D functions to represent the full shape of the crystalline lens ex vivo. Also, we presented the application of eigenlenses to estimate the full shape of the lens in vivo from 3-D optical coherence tomography (OCT) images, where only the central part of the lens -visible through the pupil- is available. The current work presents a validation of the use of eigenlenses to estimate in vivo the full shape of dis-accommodated lenses. We used 14 ex vivo crystalline lenses from donor eyes (11-54 y/o) mounted in a lens stretcher, and measured the geometry and the power of the lenses using a combined OCT and ray tracing aberrometry system. Ex vivo, the full extent of the lens is accessible from OCT because the incident light is not blocked by the iris. We measured in non-stretched (fully accommodated) and stretched (mimicking in vivo dis-accommodated lenses) conditions. Then, we simulated computationally in vivo conditions on the obtained ex vivo lenses geometry (assuming that just the portion of the lens within a given pupil is available), and estimated the full shape using eigenlenses. The mean absolute error (MAE) between estimated and measured lens' diameters and volumes were MAE = 0.26 ± 0.18 mm and MAE = 7.0 ± 4.5 mm3, respectively. Furthermore, we concluded that the estimation error between measured and estimated lenses did not depend on the accommodative state (change in power due to stretching), and thus eigenlenses are also useful for the full shape estimation of in vivo dis-accommodated lenses.

Poster Session: Estimation of scleral biomechanical properties from air-puff-coupled optical coherence tomography.

Progression of myopia is usually accompanied by axial overgrowth of the eyeball, which affects scleral biomechanics (BM). To study scleral biomechanics, we propose the use of air-puff deformation swept-source OCT imaging. Air-puff deformation imaging was performed at different sites of ex vivo porcine (n=5) and rabbit (n=3) eyes, (<24hr postmortem): Nasal/temporal equatorial and posterior sclera (NE, NP, TE, TP), superior (S) and inferior (I) sclera, and cornea (C). Intraocular pressure was kept at 15mmHg. Deformation data were used as input to inverse finite element model (FEM) algorithms to reconstruct BM properties. Experimental deformation amplitudes showed dependence on the animal model, with porcine scleras exhibiting greater inter-site variation (displacement of S, I was up to four times greater than that of N, T), while rabbit scleras exhibited at most 40% of displacement differences between all sites. Both models showed significant (p<.001) differences in the temporal deformation profile between sclera and (C), but similarities in all scleral locations, suggesting that the scleral temporal profile is independent of scleral thickness variations. The FEM estimated an elastic modulus of 1.84 ± 0.30 MPa (I) to 6.04 ± 2.11 MPa (TE) for the porcine sclera. The use of scleral air-puff imaging is promising for noninvasive investigation of structural changes in the sclera associated with myopia and for monitoring possible modulation of scleral stiffness with myopia treatment.

Estimation of Crystalline Lens Material Properties From Patient Accommodation Data and Finite Element Models.

Purpose: The mechanical properties of the crystalline lens are related to its optical function of accommodation, and their changes with age are one of the potential causes for presbyopia. We estimated the mechanical parameters of the crystalline lens using quantitative optical coherence tomography (OCT) imaging and wavefront sensing data from accommodating participants and computer modeling. Methods: Full-lens shape data (from quantitative swept-source OCT and eigenlens representation) and optical power data (from Hartmann-Shack wavefront sensor) were obtained from 11 participants (22-30 years old) for relaxed accommodation at infinity and -4.5 D accommodative demand. Finite element models of lens, capsular bag, zonulae, and ciliary body were constructed using measured lens geometry and literature data, assuming a 60-mN radial force. An inverse modeling scheme was used to determine the shear moduli of the nucleus and cortex of the lens, such that the simulated deformed (maximally stretched) lens matched the participant's lens at -4.5 D. Results: The shear moduli of the nucleus and cortex were 1.62 ± 1.32 and 8.18 ± 5.63 kPa, on average, respectively. The shear modulus of the nucleus was lower than that of the cortex for all participants evaluated. The average of the two moduli per participant was statistically significantly correlated with age (R2 = 0.76, P = 0.0049). Conclusions: In vivo imaging and mechanical modeling of the crystalline lens allow estimations of the crystalline lens' mechanical properties. Differences between nuclear and cortical moduli and their dependency with age appear to be critical in accommodative function and likely in its impairment in presbyopia.

Effect of fixational eye movements in corneal topography measurements with optical coherence tomography.

There is an increasing interest in applying optical coherence tomography (OCT) to quantify the topography of ocular structures. However, in its most usual configuration, OCT data is acquired sequentially while a beam is scanned through the region of interest, and the presence of fixational eye movements can affect the accuracy of the technique. Several scan patterns and motion correction algorithms have been proposed to minimize this effect, but there is no consensus on the ideal parameters to obtain a correct topography. We have acquired corneal OCT images with raster and radial patterns, and modeled the data acquisition in the presence of eye movements. The simulations replicate the experimental variability in shape (radius of curvature and Zernike polynomials), corneal power, astigmatism, and calculated wavefront aberrations. The variability of the Zernike modes is highly dependent on the scan pattern, with higher variability in the direction of the slow scan axis. The model can be a useful tool to design motion correction algorithms and to determine the variability with different scan patterns.

Estimation of the full shape of the crystalline lens in-vivo from OCT images using eigenlenses.

Quantifying the full 3-D shape of the human crystalline lens is important for improving intraocular lens power or sizing calculations in treatments of cataract and presbyopia. In a previous work we described a novel method for the representation of the full shape of the ex vivo crystalline lens called eigenlenses, which proved more compact and accurate than compared state-of-the art methods of crystalline lens shape quantification. Here we demonstrate the use of eigenlenses to estimate the full shape of the crystalline lens in vivo from optical coherence tomography images, where only the information visible through the pupil is available. We compare the performance of eigenlenses with previous methods of full crystalline lens shape estimation, and demonstrate an improvement in repeatability, robustness and use of computational resources. We found that eigenlenses can be used to describe efficiently the crystalline lens full shape changes with accommodation and refractive error.

Estimation of scleral mechanical properties from air-puff optical coherence tomography.

We introduce a method to estimate the biomechanical properties of the porcine sclera in intact eye globes ex vivo, using optical coherence tomography that is coupled with an air-puff excitation source, and inverse optimization techniques based on finite element modeling. Air-puff induced tissue deformation was determined at seven different locations on the ocular globe, and the maximum apex deformation, the deformation velocity, and the arc-length during deformation were quantified. In the sclera, the experimental maximum deformation amplitude and the corresponding arc length were dependent on the location of air-puff excitation. The normalized temporal deformation profile of the sclera was distinct from that in the cornea, but similar in all tested scleral locations, suggesting that this profile is independent of variations in scleral thickness. Inverse optimization techniques showed that the estimated scleral elastic modulus ranged from 1.84 ± 0.30 MPa (equatorial inferior) to 6.04 ± 2.11 MPa (equatorial temporal). The use of scleral air-puff imaging holds promise for non-invasively investigating the structural changes in the sclera associated with myopia and glaucoma, and for monitoring potential modulation of scleral stiffness in disease or treatment.

Simulating Outcomes of Cataract Surgery: Important Advances in Ophthalmology.

As the human eye ages, the crystalline lens stiffens (presbyopia) and opacifies (cataract), requiring its replacement with an artificial lens [intraocular lens (IOL)]. Cataract surgery is the most frequently performed surgical procedure in the world. The increase in IOL designs has not been paralleled in practice by a sophistication in IOL selection methods, which rely on limited anatomical measurements of the eye and the surgeon's interpretation of the patient's needs and expectations. We propose that the future of IOL selection will be guided by 3D quantitative imaging of the crystalline lens to map lens opacities, anticipate IOL position, and develop fully customized eye models for ray-tracing-based IOL selection. Conversely, visual simulators (in which IOL designs are programmed in active elements) allow patients to experience prospective vision before surgery and to make more informed decisions about which IOL to choose. Quantitative imaging and optical and visual simulations of postsurgery outcomes will allow optimal treatments to be selected for a patient undergoing modern cataract surgery.

Isolated human crystalline lens three-dimensional shape: A comparison between Indian and European populations.

There have been many studies on lens properties in specific populations (e.g. in China, Europe, Singapore, etc.) some of which suggest there may be differences between populations. Differences could be caused by ethnic or environmental influences or experimental procedures. The purpose of this study is to evaluate if any differences exist between Indian and European populations in the central geometric and full shape properties of human lenses. Two custom-developed spectral domain optical coherence tomography systems were used to acquire the crystalline lens geometry: one in India (69 lenses from 59 donors) and the other in Spain (24 lenses from 19 donors). The steps for obtaining accurate 3-D models from optical coherence tomography raw images comprised of image segmentation, fan and optical distortion correction, tilt removal and registration. The outcome variables were lens equatorial diameter, lens thickness, anterior and posterior lens thicknesses and their ratio, central radius of curvature of the anterior and posterior lens surfaces, lens volume and lens surface area. A mixed effects model by maximum likelihood estimation was used to evaluate the effect of age, population and their interaction (age*population) on lens parameters. After adjusting for age, there were no population differences observed in anterior and posterior radii of curvature, equatorial diameter, lens thickness, anterior and posterior lens thicknesses and their ratio, volume and surface area (all p ≥ 0.08). There was also no effect of the interaction term on anterior and posterior radii of curvature, equatorial diameter, lens thickness, anterior and posterior lens thicknesses and their ratio, volume and surface area (all p ≥ 0.06). All central geometric and full shape parameters appeared to be comparable between the European and Indian populations. This is the first study to compare geometric and full shape lens parameters between different populations in vitro.

Multi-meridian corneal imaging of air-puff induced deformation for improved detection of biomechanical abnormalities.

Corneal biomechanics play a fundamental role in the genesis and progression of corneal pathologies, such as keratoconus; in corneal remodeling after corneal surgery; and in affecting the measurement accuracy of glaucoma biomarkers, such as the intraocular pressure (IOP). Air-puff induced corneal deformation imaging reveals information highlighting normal and pathological corneal response to a non-contact mechanical excitation. However, current commercial systems are limited to monitoring corneal deformation only on one corneal meridian. Here, we present a novel custom-developed swept-source optical coherence tomography (SSOCT) system, coupled with a collinear air-puff excitation, capable of acquiring dynamic corneal deformation on multiple meridians. Backed by numerical simulations of corneal deformations, we propose two different scan patterns, aided by low coil impedance galvanometric scan mirrors that permit an appropriate compromise between temporal and spatial sampling of the corneal deformation profiles. We customized the air-puff module to provide an unobstructed SSOCT field of view and different peak pressures, air-puff durations, and distances to the eye. We acquired multi-meridian corneal deformation profiles (a) in healthy human eyes in vivo, (b) in porcine eyes ex vivo under varying controlled IOP, and (c) in a keratoconus-mimicking porcine eye ex vivo. We detected deformation asymmetries, as predicted by numerical simulations, otherwise missed on a single meridian that will substantially aid in corneal biomechanics diagnostics and pathology screening.

Eigenlenses: a new model for full crystalline lens shape representation and its applications.

The crystalline lens is an important optical element in the eye, responsible for focusing, and which experiences significant changes throughout life. The shape of the lens is usually studied only in the optical area (central 4 to 6 mm). However, for a great number of applications, a description of the full shape of the crystalline lens is required. We propose a new method for the representation of the full shape of the crystalline lens, constructed from 3-dimensional optical coherence tomography images of 133 isolated crystalline lenses (0-71 y/o), which we have called eigenlenses. The method is shown to be compact and accurate to describe not only the full shape of the crystalline lens, but also the optical zone in comparison with other methods. We also demonstrate its application to the extrapolation of the full shape of the crystalline lens from in-vivo optical images of the anterior segment of the eye, where only the central part of the lens visible through the pupil is available, and in the generation (synthesis) of realistic full lenses of a given age. The method has critical applications, among others, in improving and evaluating myopia and presbyopia treatments.

Crystalline lens gradient refractive index distribution in the guinea pig.

PURPOSE: The crystalline lens undergoes morphological and functional changes with age and may also play a role in eye emmetropisation. Both the geometry and the gradient index of refraction (GRIN) distribution contribute to the lens optical properties. We studied the lens GRIN in the guinea pig, a common animal model to study myopia. METHODS: Lenses were extracted from guinea pigs (Cavia porcellus) at 18 days of age (n = 4, three monolaterally treated with negative lenses and one untreated) and 39 days of age (n = 4, all untreated). Treated eyes were myopic (-2.07 D on average) and untreated eyes hyperopic (+3.3 D), as revealed using streak retinoscopy in the live and cyclopeged animals. A custom 3D spectral domain optical coherence tomography (OCT) system (λ = 840 nm, Δλ = 50 nm) was used to image the enucleated crystalline lens at two orientations. Custom algorithms were used to estimate the lens shape and GRIN was modelled with four variables that were reconstructed using the OCT data and a minimisation algorithm. Ray tracing was used to calculate the optical power and spherical aberration assuming a homogeneous refractive index or the estimated GRIN. RESULTS: Guinea pig lenses exhibited nearly parabolic GRIN profiles. When comparing the two age groups (18- and 39 day-old) there was a significant increase in the central thickness (from 3.61 to 3.74 mm), and in the refractive index of the surface (from 1.362 to 1.366) and the nucleus (from 1.443 to 1.454). The presence of GRIN shifted the spherical aberration (-4.1 µm on average) of the lens towards negative values. CONCLUSIONS: The guinea pig lens exhibits a GRIN profile with surface and nucleus refractive indices that increase slightly during the first days of life. GRIN plays a major role in the lens optical properties and should be incorporated into computational guinea pig eye models to study emmetropisation, myopia development and ageing.

Age-Related Changes to the Three-Dimensional Full Shape of the Isolated Human Crystalline Lens.

Purpose: Studying the full shape crystalline lens geometry is important to understand the changes undergone by the crystalline lens leading to presbyopia, cataract, or failure of emmetropization, and to aid in the design and selection of intraocular lenses and new strategies for correction. We used custom-developed three-dimensional (3-D) quantitative optical coherence tomography (OCT) to study age-related changes in the full shape of the isolated human crystalline lens. Methods: A total of 103 ex vivo human isolated lenses from 87 subjects (age range, 0-56 years) were imaged using a 3-D spectral-domain OCT system. Lens models, constructed after segmentation of the surfaces and distortion correction, were used to automatically quantify central geometric parameters (lens thickness, radii of curvatures, and asphericities of anterior and posterior surfaces) and full shape parameters (lens volume, surface area, diameter, and equatorial plane position). Age-dependencies of these parameters were studied. Results: Most of the measured parameters showed a biphasic behavior, statistically significantly increasing (radii of curvature, lens volume, surface area, diameter) or decreasing (asphericities, lens thickness) very fast in the first two decades of life, followed by a slow but significant increase after age 20 years (for all the parameters except for the posterior surface asphericity and the equatorial plane position, that remained constant). Conclusions: Three-dimensional quantitative OCT allowed us to study the age-dependency of geometric parameters of the full isolated human crystalline lens. We found that most of the lens geometric parameters showed a biphasic behavior, changing rapidly before age 20 years and with a slower linear growth thereafter.

Corneal Collagen Ordering After In Vivo Rose Bengal and Riboflavin Cross-Linking.

Purpose: Photoactivated cornea collagen cross-linking (CXL) increases corneal stiffness by initiating formation of covalent bonds between stromal proteins. Because CXL depends on diffusion to distribute the photoinitiator, a gradient of CXL efficiency with depth is expected that may affect the degree of stromal collagen organization. We used second harmonic generation (SHG) microscopy to investigate the differences in stromal collagen organization in rabbit eyes after corneal CXL in vivo as a function of depth and time after surgery. Methods: Rabbit corneas were treated in vivo with either riboflavin/UV radiation (UVX) or Rose Bengal/green light (RGX) and evaluated 1 and 2 months after CXL. Collagen fibers were imaged with a custom-built SHG scanning microscope through the central cornea (350 µm depth, 225 × 225 µm en face images). The order coefficient (OC), a metric for collagen organization, and total SHG signal were computed for each depth and compared between treatments. Results: OC values of CXL-treated corneas were larger than untreated corneas by 27% and 20% after 1 month and 38% and 33% after 2 months for the RGX and UVX, respectively. RGX OC values were larger than UVX OC values by 3% and 5% at 1 and 2 months. The SHG signal was higher in CXL corneas than untreated corneas, both at 1 and 2 months after surgery, by 18% and 26% and 1% and 10% for RGX and UVX, respectively. Conclusions: Increased OC corresponded with increased collagen fiber organization in CXL corneas. Changes in collagen organization parallel reported temporal changes in cornea stiffness after CXL and also, surprisingly, are detected deeper in the stroma than the regions stiffened by collagen cross-links.

Morphological changes of human crystalline lens in myopia.

Ocular biometric parameters, including full shape crystalline lens, were assessed in myopes and emmetropes using 3-D optical coherence tomography. The anterior chamber depth, the radius of the curvature of the anterior cornea, anterior lens, and posterior lens, lens thickness, lens equatorial diameter, surface area, equatorial position, volume, and power, were evaluated as functions of refractive errors and axial lengths while controlling for age effects. The crystalline lens appears to change with myopia consistent with lens thinning, equatorial, and capsular stretching while keeping constant volume. Axial elongation appears counteracted by a crystalline lens power reduction, while corneal power remains unaffected.

Estimation of intraocular lens position from full crystalline lens geometry: towards a new generation of intraocular lens power calculation formulas.

In a cataract surgery, the opacified crystalline lens is replaced by an artificial intraocular lens (IOL). To optimize the visual quality after surgery, the intraocular lens to be implanted must be selected preoperatively for every individual patient. Different generations of formulas have been proposed for selecting the intraocular lens dioptric power as a function of its estimated postoperative position. However, very few formulas include crystalline lens information, in most cases only one-dimensional. The present study proposes a new formula to preoperatively estimate the postoperative IOL position (ELP) based on information of the 3-dimensional full shape of the crystalline lens, obtained from quantitative eye anterior segment optical coherence tomography imaging. Real patients were measured before and after cataract surgery (IOL implantation). The IOL position and the postoperative refraction estimation errors were calculated by subtracting the preoperative estimations from the actual values measured after surgery. The proposed ELP formula produced lower estimation errors for both parameters -ELP and refraction- than the predictions obtained with standard state-of-the-art methods, and opens new avenues to the development of new generation IOL power calculation formulas that improve refractive and visual outcomes.

Quantization of collagen organization in the stroma with a new order coefficient.

Many optical and biomechanical properties of the cornea, specifically the transparency of the stroma and its stiffness, can be traced to the degree of order and direction of the constituent collagen fibers. To measure the degree of order inside the cornea, a new metric, the order coefficient, was introduced to quantify the organization of the collagen fibers from images of the stroma produced with a custom-developed second harmonic generation microscope. The order coefficient method gave a quantitative assessment of the differences in stromal collagen arrangement across the cornea depths and between untreated stroma and cross-linked stroma.

Three-dimensional OCT based guinea pig eye model: relating morphology and optics.

Custom Spectral Optical Coherence Tomography (SOCT) provided with automatic quantification and distortion correction algorithms was used to measure the 3-D morphology in guinea pig eyes (n = 8, 30 days; n = 5, 40 days). Animals were measured awake in vivo under cyclopegia. Measurements showed low intraocular variability (<4% in corneal and anterior lens radii and <8% in the posterior lens radii, <1% interocular distances). The repeatability of the surface elevation was less than 2 µm. Surface astigmatism was the individual dominant term in all surfaces. Higher-order RMS surface elevation was largest in the posterior lens. Individual surface elevation Zernike terms correlated significantly across corneal and anterior lens surfaces. Higher-order-aberrations (except spherical aberration) were comparable with those predicted by OCT-based eye models.

Evaluation of the True Wavefront Aberrations in Eyes Implanted With a Rotationally Asymmetric Multifocal Intraocular Lens.

PURPOSE: Standard evaluation of aberrations from wavefront slope measurements in patients implanted with a rotationally asymmetric multifocal intraocular lens (IOL), the Lentis Mplus (Oculentis GmbH, Berlin, Germany), results in large magnitude primary vertical coma, which is attributed to the intrinsic IOL design. The new proposed method analyzes aberrometry data, allowing disentangling the IOL power pupillary distribution from the true higher order aberrations of the eye. METHODS: The new method of wavefront reconstruction uses retinal spots obtained at both the near and far foci. The method was tested using ray tracing optical simulations in a computer eye model virtually implanted with the Lentis Mplus IOL, with a generic cornea or with anterior segment geometry obtained from custom quantitative spectral-domain optical coherence tomography in a real patient. The method was applied to laser ray tracing aberrometry data at near and far fixation obtained in a patient implanted with the Lentis Mplus IOL. RESULTS: Higher order aberrations evaluated from simulated and real retinal spot diagrams following the new reconstruction approach matched the nominal aberrations (approximately 98%). Previously reported primary vertical coma in patients implanted with this IOL lost significance with the application of the proposed reconstruction. CONCLUSIONS: Custom analysis of ray tracing-based retinal spot diagrams allowed decoupling of the true higher order aberrations of the patient's eye from the power pupillary distribution of a rotationally asymmetric multifocal IOL, therefore providing the appropriate phase map to accurately evaluate through-focus optical quality. [J Refract Surg. 2017;33(4):257-265.].

OCT-based full crystalline lens shape change during accommodation in vivo.

The full shape of the accommodating crystalline lens was estimated using custom three-dimensional (3-D) spectral OCT and image processing algorithms. Automatic segmentation and distortion correction were used to construct 3-D models of the lens region visible through the pupil. The lens peripheral region was estimated with a trained and validated parametric model. Nineteen young eyes were measured at 0-6 D accommodative demands in 1.5 D steps. Lens volume, surface area, diameter, and equatorial plane position were automatically quantified. Lens diameter & surface area correlated negatively and equatorial plane position positively with accommodation response. Lens volume remained constant and surface area decreased with accommodation, indicating that the lens material is incompressible and the capsular bag elastic.

Optical Coherence Tomography Based Estimates of Crystalline Lens Volume, Equatorial Diameter, and Plane Position.

PURPOSE: Measurement of crystalline lens geometry in vivo is critical to optimize performance of state-of-the-art cataract surgery. We used custom-developed quantitative anterior segment optical coherence tomography (OCT) and developed dedicated algorithms to estimate lens volume (VOL), equatorial diameter (DIA), and equatorial plane position (EPP). METHODS: The method was validated ex vivo in 27 human donor (19-71 years of age) lenses, which were imaged in three-dimensions by OCT. In vivo conditions were simulated assuming that only the information within a given pupil size (PS) was available. A parametric model was used to estimate the whole lens shape from PS-limited data. The accuracy of the estimated lens VOL, DIA, and EPP was evaluated by comparing estimates from the whole lens data and PS-limited data ex vivo. The method was demonstrated in vivo using 2 young eyes during accommodation and 2 cataract eyes. RESULTS: Crystalline lens VOL was estimated within 96% accuracy (average estimation error across lenses ± standard deviation: 9.30 ± 7.49 mm3). Average estimation errors in EPP were below 40 ± 32 µm, and below 0.26 ± 0.22 mm in DIA. Changes in lens VOL with accommodation were not statistically significant (2-way ANOVA, P = 0.35). In young eyes, DIA decreased and EPP increased statistically significantly with accommodation (P < 0.001) by 0.14 mm and 0.13 mm, respectively, on average across subjects. In cataract eyes, VOL = 205.5 mm3, DIA = 9.57 mm, and EPP = 2.15 mm on average. CONCLUSIONS: Quantitative OCT with dedicated image processing algorithms allows estimation of human crystalline lens volume, diameter, and equatorial lens position, as validated from ex vivo measurements, where entire lens images are available.