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Biomedical Optics Express

Biomedical Optics Express

  • Editor: Joseph A. Izatt
  • Vol. 3, Iss. 10 — Oct. 1, 2012
  • pp: 2471–2488
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In vivo human crystalline lens topography

Sergio Ortiz, Pablo Pérez-Merino, Enrique Gambra, Alberto de Castro, and Susana Marcos  »View Author Affiliations


Biomedical Optics Express, Vol. 3, Issue 10, pp. 2471-2488 (2012)
http://dx.doi.org/10.1364/BOE.3.002471


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Abstract

Custom high-resolution high-speed anterior segment spectral domain optical coherence tomography (OCT) was used to characterize three-dimensionally (3-D) the human crystalline lens in vivo. The system was provided with custom algorithms for denoising and segmentation of the images, as well as for fan (scanning) and optical (refraction) distortion correction, to provide fully quantitative images of the anterior and posterior crystalline lens surfaces. The method was tested on an artificial eye with known surfaces geometry and on a human lens in vitro, and demonstrated on three human lenses in vivo. Not correcting for distortion overestimated the anterior lens radius by 25% and the posterior lens radius by more than 65%. In vivo lens surfaces were fitted by biconicoids and Zernike polynomials after distortion correction. The anterior lens radii of curvature ranged from 10.27 to 14.14 mm, and the posterior lens radii of curvature ranged from 6.12 to 7.54 mm. Surface asphericities ranged from −0.04 to −1.96. The lens surfaces were well fitted by quadrics (with variation smaller than 2%, for 5-mm pupils), with low amounts of high order terms. Surface lens astigmatism was significant, with the anterior lens typically showing horizontal astigmatism ( Z 2 2 ranging from −11 to −1 µm) and the posterior lens showing vertical astigmatism ( Z 2 2 ranging from 6 to 10 µm).

© 2012 OSA

1. Introduction

The optical quality of the human eye is mainly determined by the geometrical and optical properties of two elements, cornea and crystalline lens. The cornea accounts for two-thirds of the optical refractive power, while the crystalline lens provides approximately one third of the total static refractive power of the eye, and it is the responsible for accommodation [1

1. P. Kiely, G. Smith, and L. Carney, “The mean shape of the human cornea,” Opt. Acta (Lond.) 29(8), 1027–1040 (1982). [CrossRef]

10

10. L. F. Garner, “Calculation of the radii of curvature of the crystalline lens surfaces,” Ophthalmic Physiol. Opt. 17(1), 75–80 (1997). [CrossRef] [PubMed]

]. Accurate description of the geometry of the eye’s optical components is critical for understanding their contribution to optical quality. Although the geometrical properties of the cornea have been widely studied due to its accessibility [1

1. P. Kiely, G. Smith, and L. Carney, “The mean shape of the human cornea,” Opt. Acta (Lond.) 29(8), 1027–1040 (1982). [CrossRef]

3

3. M. Dubbelman, H. A. Weeber, R. G. van der Heijde, and H. J. Völker-Dieben, “Radius and asphericity of the posterior corneal surface determined by corrected Scheimpflug photography,” Acta Ophthalmol. Scand. 80(4), 379–383 (2002). [CrossRef] [PubMed]

], accurate quantitative data of the crystalline lens geometry are limited to in vitro studies [11

11. A. Glasser and M. C. W. Campbell, “Biometric, optical and physical changes in the isolated human crystalline lens with age in relation to presbyopia,” Vision Res. 39(11), 1991–2015 (1999). [CrossRef] [PubMed]

13

13. A. M. Rosen, D. B. Denham, V. Fernandez, D. Borja, A. Ho, F. Manns, J. M. Parel, and R. C. Augusteyn, “In vitro dimensions and curvatures of human lenses,” Vision Res. 46(6-7), 1002–1009 (2006). [CrossRef] [PubMed]

], while in vivo data are referred in most cases to axial properties (i.e. thickness) and central areas (i.e. central radius of curvature) [14

14. Y. Sakamoto, K. Sasaki, Y. Nakamura, and N. Watanabe, “Reproducibility of data obtained by a newly developed anterior eye segment analysis system, EAS-1000,” Ophthalmic Res. 24(Suppl 1), 10–20 (1992). [CrossRef] [PubMed]

21

21. P. Rosales and S. Marcos, “Phakometry and lens tilt and decentration using a custom-developed Purkinje imaging apparatus: validation and measurements,” J. Opt. Soc. Am. A 23(3), 509–520 (2006). [CrossRef] [PubMed]

].

The shape and alignment of the crystalline lens have been reported in vivo and in vitro using different imaging techniques. Radii of curvature, tilt and decentration of the lens have been measured using a Purkinje-imaging based method [20

20. P. Rosales, M. Dubbelman, S. Marcos, and R. van der Heijde, “Crystalline lens radii of curvature from Purkinje and Scheimpflug imaging,” J. Vis. 6(10), 5 (2006). [CrossRef] [PubMed]

22

22. P. Rosales, M. Wendt, S. Marcos, and A. Glasser, “Changes in crystalline lens radii of curvature and lens tilt and decentration during dynamic accommodation in rhesus monkeys,” J. Vis. 8(1), 18, 1–12 (2008). [CrossRef] [PubMed]

]. However, although Purkinje-based phakometry is a rapid, systematic, and reliable method, it does not provide the full geometry of the crystalline lens surfaces, nor a direct view of the lens. In contrast, Scheimpflug imaging allows acquisition of cross-sectional images of the crystalline lens, and with proper correction of the geometrical and optical distortions, the radii of curvature and asphericity of the lens surfaces can be obtained [16

16. M. Dubbelman and G. L. Van der Heijde, “The shape of the aging human lens: curvature, equivalent refractive index and the lens paradox,” Vision Res. 41(14), 1867–1877 (2001). [CrossRef] [PubMed]

18

18. M. Dubbelman, G. L. Van der Heijde, and H. A. Weeber, “Change in shape of the aging human crystalline lens with accommodation,” Vision Res. 45(1), 117–132 (2005). [CrossRef] [PubMed]

,23

23. J. E. Koretz, S. A. Strenk, L. M. Strenk, and J. L. Semmlow, “Scheimpflug and high-resolution magnetic resonance imaging of the anterior segment: a comparative study,” J. Opt. Soc. Am. A 21(3), 346–354 (2004). [CrossRef] [PubMed]

,24

24. P. Rosales and S. Marcos, “Pentacam Scheimpflug quantitative imaging of the crystalline lens and intraocular lens,” J. Refract. Surg. 25(5), 421–428 (2009). [CrossRef] [PubMed]

]. The slit-lamp configuration of Scheimpflug imaging-based systems (where the front view of the pupil appears superimposed to the cross-sectional image) frequently limits the view of the posterior lens. Besides, commercial Scheimpflug instruments, although providing images of the lens, are typically not corrected from optical distortion, preventing quantitative evaluation of lens parameters. To our knowledge, custom correction algorithms have only been applied to crystalline lens images in certain Scheimpflug instruments in a laboratory setting, and the reported crystalline lens parameters are restricted to a single cross-section of the lens [16

16. M. Dubbelman and G. L. Van der Heijde, “The shape of the aging human lens: curvature, equivalent refractive index and the lens paradox,” Vision Res. 41(14), 1867–1877 (2001). [CrossRef] [PubMed]

,24

24. P. Rosales and S. Marcos, “Pentacam Scheimpflug quantitative imaging of the crystalline lens and intraocular lens,” J. Refract. Surg. 25(5), 421–428 (2009). [CrossRef] [PubMed]

]. In addition to optical techniques, the anterior chamber of the eye can be imaged through non-optical imaging techniques such as ultrasound [19

19. D. A. Goss, H. G. Van Veen, B. B. Rainey, and B. Feng, “Ocular components measured by keratometry, phakometry, and ultrasonography in emmetropic and myopic optometry students,” Optom. Vis. Sci. 74(7), 489–495 (1997). [CrossRef] [PubMed]

,25

25. A. S. Vilupuru and A. Glasser, “Dynamic accommodative changes in rhesus monkey eyes assessed with A-scan ultrasound biometry,” Optom. Vis. Sci. 80(5), 383–394 (2003). [CrossRef] [PubMed]

] and Magnetic Resonance Imaging (MRI) [26

26. C. E. Jones, D. A. Atchison, R. Meder, and J. M. Pope, “Refractive index distribution and optical properties of the isolated human lens measured using magnetic resonance imaging (MRI),” Vision Res. 45(18), 2352–2366 (2005). [CrossRef] [PubMed]

28

28. S. Kasthurirangan, E. L. Markwell, D. A. Atchison, and J. M. Pope, “MRI study of the changes in crystalline lens shape with accommodation and aging in humans,” J. Vis. 11(3), 19 (2011). [CrossRef] [PubMed]

]. These non-optical techniques allow visualization of the entire crystalline lens and its neighboring ocular structures. However, these are either invasive or time-consuming imaging methods, with significantly lower resolution than optical techniques, which impose major problems (low acquisition speed, motion artifacts or low sampling density) which prevent quantifying the crystalline lens geometry with high accuracy.

To our knowledge, the 3-D structure of the crystalline lens has not been investigated quantitatively with any method, likely as a result of the associated problems of the imaging techniques used to image the crystalline lens. Optical coherence tomography (OCT) is a high-resolution noncontact advanced optical imaging technique capable of providing 3-D evaluation of the anterior segment of the eye [29

29. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991). [CrossRef] [PubMed]

33

33. S. Ortiz, D. Siedlecki, L. Remon, and S. Marcos, “Optical coherence tomography for quantitative surface topography,” Appl. Opt. 48(35), 6708–6715 (2009). [CrossRef] [PubMed]

]. Several geometrical crystalline lens parameters surfaces have been reported previously with OCT, such as lens thickness and anterior and posterior lens radius of curvature in the horizontal meridian [34

34. M. C. M. Dunne, L. N. Davies, and J. S. Wolffsohn, “Accuracy of cornea and lens biometry using anterior segment optical coherence tomography,” J. Biomed. Opt. 12(6), 064023 (2007). [CrossRef] [PubMed]

36

36. M. Shen, M. R. Wang, Y. Yuan, F. Chen, C. L. Karp, S. H. Yoo, and J. Wang, “SD-OCT with prolonged scan depth for imaging the anterior segment of the eye,” Ophthalmic Surg. Lasers Imaging 41(6Suppl), S65–S69 (2010). [CrossRef] [PubMed]

]. In addition, OCT has been used recently to quantify the crystalline lens shape in 2-D in human and primate lenses in vitro [37

37. S. R. Uhlhorn, D. Borja, F. Manns, and J. M. Parel, “Refractive index measurement of the isolated crystalline lens using optical coherence tomography,” Vision Res. 48(27), 2732–2738 (2008). [CrossRef] [PubMed]

39

39. B. M. Maceo, F. Manns, D. Borja, D. Nankivil, S. Uhlhorn, E. Arrieta, A. Ho, R. C. Augusteyn, and J. M. Parel, “Contribution of the crystalline lens gradient refractive index to the accommodation amplitude in non-human primates: in vitro studies,” J. Vis. 11(13), 23 (2011). [CrossRef] [PubMed]

], and to estimate the Gradient Index (GRIN) distribution (from the optical distortion produced by GRIN on the posterior lens surface) in the porcine lens in 3-D and the human lens in 2-D [40

40. A. de Castro, S. Ortiz, E. Gambra, D. Siedlecki, and S. Marcos, “Three-dimensional reconstruction of the crystalline lens gradient index distribution from OCT imaging,” Opt. Express 18(21), 21905–21917 (2010). [CrossRef] [PubMed]

44

44. D. Siedlecki, A. de Castro, E. Gambra, S. Ortiz, D. Borja, S. Uhlhorn, F. Manns, S. Marcos, and J. M. Parel, “Distortion correction of OCT images of the crystalline lens: gradient index approach,” Optom. Vis. Sci. 89(5), E709–E718 (2012). [CrossRef] [PubMed]

].

Imaging the crystalline lens with sOCT poses some challenges: (1) The axial imaging range is limited by the resolution of the spectrometer, and this can be insufficient to image the entire anterior segment (from the anterior cornea to the posterior lens) in a single acquisition [30

30. I. Grulkowski, M. Gora, M. Szkulmowski, I. Gorczynska, D. Szlag, S. Marcos, A. Kowalczyk, and M. Wojtkowski, “Anterior segment imaging with Spectral OCT system using a high-speed CMOS camera,” Opt. Express 17(6), 4842–4858 (2009). [CrossRef] [PubMed]

]. (2) Motion artifacts can limit the repeatability of the measurements, making it necessary to reduce acquisition time [45

45. S. Ortiz, D. Siedlecki, P. Pérez-Merino, N. Chia, A. de Castro, M. Szkulmowski, M. Wojtkowski, and S. Marcos, “Corneal topography from spectral optical coherence tomography (sOCT),” Biomed. Opt. Express 2(12), 3232–3247 (2011). [CrossRef] [PubMed]

]; (3) Fan (arising from the scanning architecture) and optical (refraction) distortions, if left uncorrected, prevent quantitative analysis of the crystalline lens images [45

45. S. Ortiz, D. Siedlecki, P. Pérez-Merino, N. Chia, A. de Castro, M. Szkulmowski, M. Wojtkowski, and S. Marcos, “Corneal topography from spectral optical coherence tomography (sOCT),” Biomed. Opt. Express 2(12), 3232–3247 (2011). [CrossRef] [PubMed]

49

49. S. Ortiz, P. Pérez-Merino, N. Alejandre, E. Gambra, I. Jimenez-Alfaro, and S. Marcos, “Quantitative OCT-based corneal topography in keratoconus with intracorneal ring segments,” Biomed. Opt. Express 3(5), 814–824 (2012). [CrossRef] [PubMed]

].

In this study we measured and quantified the crystalline lens surface in 3-D. Further developments of the methods that we had previously developed and applied to achieve quantitative corneal topography [45

45. S. Ortiz, D. Siedlecki, P. Pérez-Merino, N. Chia, A. de Castro, M. Szkulmowski, M. Wojtkowski, and S. Marcos, “Corneal topography from spectral optical coherence tomography (sOCT),” Biomed. Opt. Express 2(12), 3232–3247 (2011). [CrossRef] [PubMed]

,46

46. S. Ortiz, D. Siedlecki, I. Grulkowski, L. Remon, D. Pascual, M. Wojtkowski, and S. Marcos, “Optical distortion correction in optical coherence tomography for quantitative ocular anterior segment by three-dimensional imaging,” Opt. Express 18(3), 2782–2796 (2010). [CrossRef] [PubMed]

,49

49. S. Ortiz, P. Pérez-Merino, N. Alejandre, E. Gambra, I. Jimenez-Alfaro, and S. Marcos, “Quantitative OCT-based corneal topography in keratoconus with intracorneal ring segments,” Biomed. Opt. Express 3(5), 814–824 (2012). [CrossRef] [PubMed]

] were applied to the quantification of the crystalline lens, overcoming limitations (2) and (3). Newly developed methods for registration and merging of sOCT images at different focus allowed full anterior segment imaging, overcoming limitation (1).

Accurate measurement of the lens geometry is crucial in the understanding of crystalline lens optical properties, and of the physical changes of the lens in accommodation and presbyopia, as well as in the design and evaluation of accommodation-restoration solutions for presbyopia, and to increase the predictability of intraocular lens implantation procedures.

In this study, we present the capability of sOCT imaging to provide 3-D parameters of the anterior and posterior lens surfaces (radii and asphericity) and lens thickness. To our knowledge, this is the first report of 3-D elevation maps of the anterior and posterior lens surfaces of the eye in vivo.

2. Material and Methods

2.1. Experimental sOCT setup

Images were collected using a custom-developed spectral OCT system (from a collaborative effort with Copernicus University, Torun, Poland) [30

30. I. Grulkowski, M. Gora, M. Szkulmowski, I. Gorczynska, D. Szlag, S. Marcos, A. Kowalczyk, and M. Wojtkowski, “Anterior segment imaging with Spectral OCT system using a high-speed CMOS camera,” Opt. Express 17(6), 4842–4858 (2009). [CrossRef] [PubMed]

]. The setup is based on a fiber-optics Michelson interferometer configuration with a superluminescent diode (SLD) (λ0 = 840 nm, Δλ = 50 nm) as a light source, and a spectrometer (volume diffraction grating, and a 12-bit 4096-pixel line-scan CMOS camera) as a detector. The effective acquisition speed is 25000 A-Scans/s, which optimized balance between speed and SNR. The axial range of the instrument is 7 mm, resulting in a theoretical axial pixel resolution of 3.4 µm. The axial resolution predicted by the bandwidth of the SLD laser source is 6.9 µm.

2.2. Validation experiments on samples in vitro

The accuracy of the method to retrieve the shape of the lens was tested on a physical water cell model eye and on a donor lens.

Experiments were also performed on one crystalline lens from a 65-year donor eye, within 24 hours post-mortem (Eye Bank Transplant Services Foundation, Barcelona, Spain). Protocols for human tissue handling followed the guidelines of the Declaration of Helsinki, and had been approved by the Institutional Review Boards. Crystalline lens was extracted immediately before measurements and immersed in preservation medium (DMEM/F-12, D8437, Sigma, St. Louis, MO) at 25°C. The imaging procedure of the crystalline lens in vitro was similar to that described by de Castro et al. [40

40. A. de Castro, S. Ortiz, E. Gambra, D. Siedlecki, and S. Marcos, “Three-dimensional reconstruction of the crystalline lens gradient index distribution from OCT imaging,” Opt. Express 18(21), 21905–21917 (2010). [CrossRef] [PubMed]

]. Images were acquired with the lens in two orientations, first with the anterior surface facing the OCT beam, “anterior up”, and then with the posterior surface facing the OCT beam (“posterior up”), after carefully flipping the lens. A homogeneous lens index of refraction of 1.413 was assumed in the calculations. Each single 3-D collection consisted of 70 B-scans with 1668 A-scans, with a lateral range of 12x12 mm, providing a resolution of 170x7 µm. The acquisition time of a full 3-D image was 4.5 s.

2.3. Experimental protocols for anterior segment image acquisition in vivo

Images were collected on the right eye of 3 young subjects (ages 28-33). The subjects were considered healthy in a clinical ophthalmological examination. Refractions ranged between 0 to −4.75 D sphere and 0 to 1 D of cylinder. All protocols for the measurements in vivo had been approved by Institutional Review Boards. The subjects signed informed consents after the nature of the study had been explained, in accordance to the tenets of the Declaration of Helsinki. Measurements were performed under mydriasis (by Tropicamide 1%). The subjects were stabilized using a bite bar. Alignment of the subject was achieved with respect to the anterior corneal specular reflection, while the subject fixated on a reference maltese cross target projected on a minidisplay at optical infinity.

A total of 15 sets of 3-D data were collected in each eye: 5 repeated images of the cornea, 5 repeated images of the anterior part the lens, and 5 repeated images of the posterior part of the lens. All 3-D sets of data contained also the iris.

The SLD power exposure was fixed at 800 µW [45

45. S. Ortiz, D. Siedlecki, P. Pérez-Merino, N. Chia, A. de Castro, M. Szkulmowski, M. Wojtkowski, and S. Marcos, “Corneal topography from spectral optical coherence tomography (sOCT),” Biomed. Opt. Express 2(12), 3232–3247 (2011). [CrossRef] [PubMed]

]. Focus was changed by an automatic displacement to achieve optimal imaging of the different anterior segment structures (cornea, anterior and posterior lens). Images of each axial region were collected in 0.72 s, in order to minimize the impact of motion artifacts. Measurements were collected on a 10 × 15 mm zone, using 50 B-Scans composed by a collection of 360 A-Scans, providing a resolution of 0.04 mm for horizontal and 0.2 mm for vertical meridian.

2.4. 3-D image analysis: denoising, segmentation, merging, distortion correction and surface fitting

(1) Denoising: A rotational kernel transform was performed for an edge-preserving denoising, using a mask of size 9 pixels [49

49. S. Ortiz, P. Pérez-Merino, N. Alejandre, E. Gambra, I. Jimenez-Alfaro, and S. Marcos, “Quantitative OCT-based corneal topography in keratoconus with intracorneal ring segments,” Biomed. Opt. Express 3(5), 814–824 (2012). [CrossRef] [PubMed]

]. In addition, a wavelet low-pass filtering processing based on log-Gabor wavelet was used for 7 scales and 6 orientations.

(2) Statistical thresholding: An adaptive algorithm based on a multimodal Gaussian fitting of the histogram intensity (in a non-linear least squares sense) was performed on the entire 3-D sets of data, which allowed identifying a noise class from the signal.

(3) Volume clustering: The statistics of the noise and signal are overlapped. As a result, small randomly distributed volumes are mixed with the large volumes representing the objects of interest in 3-D (cornea, iris, lens surfaces, etc.). The number of pixels belonging to certain a volume is obtained by means of the connectivity of points. The volumes of interest are obtained by thresholding the number of elements according to the expected total number. Figure 1(a)
Fig. 1 Illustration of the three acquisitions of an individual data collection in subject S#1. (a) cornea and iris; (b) anterior lens and iris; (c) posterior lens and iris.
shows examples of the volumes clustered in each of the 3-D data set collected at different depths: (a) cornea and iris, (b) anterior lens and iris, (c) posterior lens and iris.

(4) Multilayer segmentation: A new approach for automatic segmentation was developed, based on Canny detection in each A-scan (1-D signals). In an initial step, a Gaussian filter (standard deviation σ = 5 pixels) was convolved with the signal to reduce spurious peaks associated to noise detection in the CMOS line-camera. The first derivatives of the signal were then obtained by convolving the resultant A-Scan with finite-size linear-phase separable kernels for differentiation of the discrete data (A-Scan) [51

51. H. Farid and E. P. Simoncelli, “Differentiation of discrete multidimensional signals,” IEEE Trans. Image Process. 13(4), 496–508 (2004). [CrossRef] [PubMed]

]. The size of the kernels (3-9 pixels) controls the sensitivity of the algorithm to noise (the lower the number of pixels used for the kernel the higher the noise sensitivity). The result of the first derivative calculation provides both local maxima and minima of the A-scan. Maxima are identified by subtraction of the slope sign of two consecutive points (positive values). The number of local maxima is further reduced by thresholding the signal and removing the peaks below a certain value (set to the average of the signal plus a variable amount, in this case, 0.25 times the standard deviation of the signal). The maxima identified in the A-scans are connected in the 2-D cross-sections (B-scans) or in the 3-D data sets using the same neighborhood algorithm used for clustering, therefore allowing to segment layers. Figure 2
Fig. 2 (a) Illustration of the algorithm for maxima detection: Original A-Scan black; Filtered signal by Gaussian filtering, blue; Detected local maxima (red asterisks) by First derivative 9-pixel kernel computation. The anterior and posterior corneal peaks are marked by green and yellow asterisks, respectively. (b) Detection of maxima in corneal B-Scan (in red), and multilayer segmentation of the anterior surface (green line) and posterior surface (yellow line) by the neighborhood algorithm.
shows the application of developed routine to the segmentation of the anterior and posterior surface of the cornea. Figure 2(a) shows a typical raw A-scan (in black), the smoothed signal after application of a Gaussian (σ = 5) filter (in blue), and the identified local maxima (obtained by the application of the first derivative with a kernel of 9 pixels, red asterisks). Figure 2(b) illustrates the estimation of the maxima (red points) in a collection of A-scans in the cornea, and the identified layers for the anterior and posterior cornea surfaces (in green and yellow, respectively), following the application of the neighborhood algorithm.

(6) Merging 3-D volumes: The pupil coordinates are assumed as a common reference for the images of the anterior segment collected at different depths. Variations in the pupil diameter were negligible across images. Images of the cornea, anterior and posterior lens were merged using the pupil center and pupil plane orientation for registration. In a first step prior to merging, the corneal image was inverted, as for efficiency in the focus range shift, the cornea was acquired in the opposite side of the Fourier transform (in comparison with the crystalline lens acquisition). The 3-D volumes of the anterior cornea/iris and posterior lens/iris are shifted to the pupil center reference, and rotated (using a rotation matrix [53

53. T. Möller and J. F. Hughes, “Efficiently building a matrix to rotate one vector to another,” J Graphics Tools 4(4), 1–4 (1999). [CrossRef]

]) in order to superimpose the characteristic vectors of the corresponding pupil plane to those of the anterior lens/iris [53

53. T. Möller and J. F. Hughes, “Efficiently building a matrix to rotate one vector to another,” J Graphics Tools 4(4), 1–4 (1999). [CrossRef]

]. Figure 3
Fig. 3 (Media 1). Illustration of the merging of three volumetric acquisitions to obtain a 3-D full anterior segment image.
(Media 1) illustrates the process to obtain the full anterior segment 3-D image merging from the three volumetric acquisitions. A full overlapping of the iris from the 3 sets of images can be observed.

(9) Surface fitting by quadrics (biconicoid, conicoid), and elevation maps: The surfaces were fitted by quadrics in a 5-mm of diameter optical zone with respect to their apexes. The corneal shape descriptive parameters (radii of curvature Rx and Ry and conic constants Qx and Qy) were obtained by biconic fitting. In addition, surfaces were also fitted by conicoids (defined by the radius of curvature R and conic constants Q). The elevation maps for the anterior and posterior lens after fan distortion correction only, and after full distortion correction and geometrical distances were represented as the difference of elevation data from the reference sphere, where warm colors represent points that are higher than the reference surface and cool colors represent points below the reference. The difference maps between the surfaces obtained with full correction and dividing the optical distances by the refractive indices were calculated by direct subtraction of the elevation maps, fitted to a Zernike expansion (55 terms, 10th order) within the same optical zone. The maps were represented using the so called “jet” color map in Matlab notation, where warm colors depict high differences while cold colors depict low differences. Thickness maps of the lens were obtained by direct subtraction of the anterior elevation map from the posterior, as for the full corrected lens as for the optical distances divided by refractive index one. The maps were represented using the so called “jet” color map in Matlab notation, where warm colors depict a thicker areas while cold colors depict thinner areas All maps were displayed in a square grid of 100x100 points in a 5-mm of diameter, with respect to the pupil center.

3. Results

3.1. In vitro samples

The images obtained from the physical model eye were processed using the developed image analysis and distortion correction algorithms. Table 1

Table 1. Surface radii of curvature from sphere fittings in the model eye: nominal values, values estimated from OCT measurements before and after correction of optical distortion.

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shows the nominal radii of curvature of the cornea and lens surfaces in the model eye, along with the values before and after application of optical distortion correction algorithms. Fan distortion correction was applied in all cases. Discrepancies in the retrieved radii of curvature were 7.5% for the posterior cornea, 9.7% for the anterior lens and as high as 23.5% for the posterior lens. The accuracy in the radius of curvature retrieval increased dramatically after optical distortion correction, with discrepancies of 0.3% for the anterior cornea, 2.0% for the posterior cornea, 1.4% for the anterior lens, and 2.8% for the posterior lens.

The images obtained from the donor lens in vitro were processed using the developed image analysis and distortion correction algorithms. Figure 5
Fig. 5 Quantitative elevation maps of the posterior lens surface for the in vitro 65-year donor lens. Left panel: Measurements with the posterior surface of the lens facing the OCT beam (“posterior up”); Middle panel: Measurement of the posterior surface of the lens viewed through the anterior surface of the lens, and no optical distortion correction (simple division by the index of refraction); Left panel: Measurement of the posterior surface of the lens viewed through the anterior surface of the lens, after application of optical distortion correction Maps are Zernike fits to the elevation maps, relative to the best fitting sphere. R = radii of curvature of the best fitting sphere (from fits to sphere quadrics).
shows the elevation maps obtained of the posterior surface of a donor lens in vitro (direct view of the posterior lens, view of posterior lens distorted by the anterior lens, and posterior lens corrected from optical distortion by the anterior lens). Optical distortion correction decreases the error in the retrieved posterior lens radius of curvature from 8.23% to 0.9%. Correction also decreased the discrepancies in the RMS surface elevation map (referred to the best fitted sphere) from 48.3% (no optical distortion correction) to 4.5% (after optical distortion).

3.2. Cornea shape parameters

Corneal surface quantification is necessary to provide accurate optical distortion correction of the lens surfaces. Table 2

Table 2. Radii of curvature and asphericity (Q-value) of the anterior and posterior cornea from biconicoid and conicoid fittings

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summarizes the anterior and posterior corneal parameters in the 3 subjects of the study after full distortion corrections, obtained from conicoid and biconicoid fittings of corneal surfaces in a 5-mm diameter zone.

3.3. Effects of optical distortion on crystalline lens shape

To quantify the effect of optical distortion from preceding surfaces on the crystalline lens shape, we evaluated difference maps, obtained as the subtraction of the elevation map estimated after full optical correction from the map obtained after fan distortion correction and a simple division of the optical distances by the refractive indices, both for the anterior and posterior lens surface. Not correcting for optical distortion produced discrepancies ranging from 0 μm (in the center of the lens) up to 50 μm in the periphery of the anterior lens surface, and up to 200 μm in the periphery of the posterior lens. The difference maps (Fig. 6
Fig. 6 Difference lens anterior (top) and posterior (bottom) elevation maps after optical distortion correction relative to elevation maps obtained by simple division of the optical distances by their corresponding refractive indices. Data are for 5-mm pupils.
) reveal the progressive overestimation of the lens curvatures in the non-corrected maps. Although dominated by the differences in curvature, slight irregularities in the difference maps indicate the effect of optical distortion in astigmatism and other higher order terms.

3.4. Crystalline lens shape

Lens surfaces radii and asphericities (with and without optical distortion corrections) were obtained from OCT images obtained in vivo in three subjects, from conicoid and biconicoid fits to the retrieved surfaces (within 5-mm diameter zones). Data in Table 3

Table 3. Radii of curvature from biconicoid and conicoid fits of the uncorrected and optical distortion corrected crystalline lens surfaces in vivo

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represent averages (and standard deviations) of 3 repeated measurements on each eye. Not correcting for optical distortion produced a systematic overestimation of the lens radii of curvature (Table 2), between 20.46 and 22.77% for the horizontal meridian, and between 20.96 and 32.81% for the vertical meridian (in the anterior lens), and between 63.40 and 72.70% for the horizontal meridian, and between 68.14 and 80.27% for the vertical meridian (in the posterior lens). For a conic fit, radii were overestimated between 20.20 and 23.56% in the anterior lens, and between 69.28 and 78.72% in the posterior lens.

Lens asphericities (Table 4

Table 4. Asphericity (Q-value) from biconicoid and conicoid fits of the uncorrected and optical distortion corrected crystalline lens surfaces

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) were negative in all eyes, although values differed significantly across subjects. While optical distortion correction modified the asphericity parameter, there was not a consistent trend toward overestimation or understimation without correction.

3.5. Crystalline lens elevation

Lens surfaces were fitted by Zernike polynomial expansions (up to the 10th order) within a 5-mm optical zone. Figure 7
Fig. 7 Representative 2nd and 3rd order Zernike terms from the Zernike fit to full distortion corrected (a) anterior lens surface, and (b) posterior lens surface in 3 human lenses in vivo. Data are average values of 3 repeated measurements on S#1 (red squares), S#2 (green triangles), and S#3 (blue diamonds). Error bars are not represented since the error is smaller than the symbol. Data are for 5-mm pupils.
shows representative 2nd and 3rd order Zernike terms (astigmatism, coma and trefoil). Data are averages of 3 repeated measurements on each eye, and the error bars represent the standard deviation. Only fits corresponding to full distortion corrected surfaces are shown. The most relevant term was astigmatism at 0 and 90 deg (Z22). Not correcting optical distortion produced an underestimation of the magnitude of astigmatism by 33% on average. Interestingly, all eyes showed vertical astigmatism in the anterior lens (negative Z22, i.e. steepest vertical meridian), but a horizontal astigmatism in the posterior lens (positive Z22, i.e. steepest vertical meridian).

Figure 8
Fig. 8 Quantitative anterior (top) and posterior (bottom) crystalline lens elevation maps in 3 eyes in vivo, after full distortion correction. Maps are Zernike fits to the elevation maps, relative to the best fitting sphere. R = radii of curvature of the best fitting sphere (from fits to sphere quadrics). Data are for 5-mm pupils.
shows elevation maps of the anterior and posterior lens surfaces in the 3 subjects of the study, within a 5-mm diameter zone. The elevation maps represent 10th order Zernike fits of the elevation maps relative to the best fitting sphere. The numbers below each map indicate the radii of curvature of best fitting sphere.

Figure 9
Fig. 9 Three repeated anterior and posterior lens surface elevation maps in subject #3. R = radii of curvature of the best fitting sphere (from fits to sphere quadrics). Data are for 5-mm pupils.
shows an illustration of the repeatability of the lens elevation maps in subject S#3, for both the anterior and posterior lens surfaces (5-mm optical zone). The numbers below each map represent the radii of curvature of best fitting sphere in mm. The average anterior lens radius of curvature was 12.02 ± 0.21 mm (1.7% of variability). The average posterior lens radius of curvature was 7.37 ± 0.09 mm, (1.2% variability). The average RMS lens elevation (relative to the best fitting sphere) was 2.08 ± 0.09 mm for the anterior lens (4% variability) and 9.92 ± 0.83 mm for the posterior lens (8% variability).

Additionally, in order to test the overall repeatability, the focal length of the eye was estimated by ray tracing through all reconstructed surfaces (cornea and crystalline lens). The estimated focal length ranged from 25.28 to 25.37 mm across repeated measurements in subject S#3, indicating within 1% repeatability.

3.6. Crystalline lens thickness

Figure 10
Fig. 10 Crystalline lens thickness maps obtained as direct subtraction from anterior to the posterior elevation maps, for uncorrected surfaces (top) and for fully corrected surfaces (bottom). Data are for 5-mm optical zone.
shows lens thickness maps in the three subjects, estimated using uncorrected surfaces (obtained by simple divisions the optical distances by the average lens refractive index, and fan distortion corrections) and fully corrected surfaces (within a 5-mm diameter zone, centered at the pupil center). Central lens thickness was 3.18 ± 0.02mm for S#1, 3.36 ± 0.02mm for S#2, and 3.06 ± 0.04mm for S#3, and did not change with optical distortion correction of the surfaces. However, not correcting for optical distortion overestimated thickness by more than 15% on average in peripheral areas (2.5 mm from the center).

4. Discussion

Correction of optical distortion proved particularly relevant in the crystalline lens imaging, giving the accumulated refraction changes by multiple preceding surfaces, and the ray convergence. In keeping with theoretical predictions [46

46. S. Ortiz, D. Siedlecki, I. Grulkowski, L. Remon, D. Pascual, M. Wojtkowski, and S. Marcos, “Optical distortion correction in optical coherence tomography for quantitative ocular anterior segment by three-dimensional imaging,” Opt. Express 18(3), 2782–2796 (2010). [CrossRef] [PubMed]

], correcting optical distortion improved accuracy in the estimates of the lens radii of curvature by 25% and 65% on average in the anterior and posterior lens respectively.

Our OCT-based crystalline lens elevation maps show minimal amounts of trefoil, coma or other high order aberrations. It is likely that the coma measured by direct subtraction of total minus corneal aberrations arises from the misalignment of the ocular components, including the off-axis position of the fovea [60

60. S. Marcos, P. Rosales, L. Llorente, S. Barbero, and I. Jiménez-Alfaro, “Balance of corneal horizontal coma by internal optics in eyes with intraocular artificial lenses: evidence of a passive mechanism,” Vision Res. 48(1), 70–79 (2008). [CrossRef] [PubMed]

,61

61. E. Berrio, J. Tabernero, and P. Artal, “Optical aberrations and alignment of the eye with age,” J. Vis. 10(14), 34 (2010).

]. Measurements of optical aberrations in isolated lenses using lateral images of the ray tracing in primate lenses [62

62. A. Roorda and A. Glasser, “Wave aberrations of the isolated crystalline lens,” J. Vis. 4(4), 1 (2004). [CrossRef] [PubMed]

], or by diffraction point interferometry [63

63. E. Acosta, J. M. Bueno, C. Schwarz, and P. Artal, “Relationship between wave aberrations and histological features in ex vivo porcine crystalline lenses,” J. Biomed. Opt. 15(5), 055001 (2010). [CrossRef] [PubMed]

] indicate presence of trefoil and other high order aberrations. The fact that the lens surface topographies are relative smooth suggests a contribution of the internal lens structure (likely line sutures) to the reported lens optical irregularities.

5. Conclusions

Anterior segment OCT provided with full distortion correction and automatic analysis tools allowed quantification of the human crystalline lens in vivo in 3-D. Correction of optical distortion is critical as simple division of the OCT optical distances by the refractive index produces an overestimation of the crystalline lens anterior and posterior radii of curvature by 25% and 65% respectively. The retrieved lens radii of curvature from OCT agree with phakometric data previously reported using Scheimpflug and Purkinke image along one meridian. We found slight negative lens surface asphericities, crossed astigmatism in the anterior and posterior lens surface, and low high order irregularities in the lens surfaces. OCT-based lens topography is a promising tool to investigate the lens optical properties, the contribution of the lens to the overall retinal image quality, and understanding the change of the physical properties of the lens with accommodation and aging.

Acknowledgments

The authors acknowledge funding from MICINN FIS2008-02065 and FIS2011-25637, EURHORCs-ESF EURYI-05-102-ES, ERC-2011-AdG-294099 and CEN-2091021 to S. Marcos.

References and links

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A. Glasser and P. L. Kaufman, “The mechanism of accommodation in primates,” Ophthalmology 106(5), 863–872 (1999). [CrossRef] [PubMed]

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F. Manns, V. Fernandez, S. Zipper, S. Sandadi, M. Hamaoui, A. Ho, and J. M. Parel, “Radius of curvature and asphericity of the anterior and posterior surface of human cadaver crystalline lenses,” Exp. Eye Res. 78(1), 39–51 (2004). [CrossRef] [PubMed]

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17.

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18.

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41.

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42.

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43.

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44.

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45.

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46.

S. Ortiz, D. Siedlecki, I. Grulkowski, L. Remon, D. Pascual, M. Wojtkowski, and S. Marcos, “Optical distortion correction in optical coherence tomography for quantitative ocular anterior segment by three-dimensional imaging,” Opt. Express 18(3), 2782–2796 (2010). [CrossRef] [PubMed]

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49.

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50.

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55.

A. Pérez-Escudero, C. Dorronsoro, and S. Marcos, “Correlation between radius and asphericity in surfaces fitted by conics,” J. Opt. Soc. Am. A 27(7), 1541–1548 (2010). [CrossRef] [PubMed]

56.

J. Birkenfeld, A. de Castro, S. Ortiz, P. Pérez-Merino, E. Gambra, and S. Marcos, “Three-dimensional reconstruction of the isolated human crystalline lens gradient index distribution,” Invest. Ophthalmol. Vis. Sci. 52, E-Abstract 3404 (2011).

57.

P. Artal, E. Berrio, A. Guirao, and P. Piers, “Contribution of the cornea and internal surfaces to the change of ocular aberrations with age,” J. Opt. Soc. Am. A 19(1), 137–143 (2002). [CrossRef] [PubMed]

58.

S. Barbero, S. Marcos, and J. Merayo-Lloves, “Corneal and total optical aberrations in a unilateral aphakic patient,” J. Cataract Refract. Surg. 28(9), 1594–1600 (2002). [CrossRef] [PubMed]

59.

J. E. Kelly, T. Mihashi, and H. C. Howland, “Compensation of corneal horizontal/vertical astigmatism, lateral coma, and spherical aberration by internal optics of the eye,” J. Vis. 4(4), 2 (2004). [CrossRef] [PubMed]

60.

S. Marcos, P. Rosales, L. Llorente, S. Barbero, and I. Jiménez-Alfaro, “Balance of corneal horizontal coma by internal optics in eyes with intraocular artificial lenses: evidence of a passive mechanism,” Vision Res. 48(1), 70–79 (2008). [CrossRef] [PubMed]

61.

E. Berrio, J. Tabernero, and P. Artal, “Optical aberrations and alignment of the eye with age,” J. Vis. 10(14), 34 (2010).

62.

A. Roorda and A. Glasser, “Wave aberrations of the isolated crystalline lens,” J. Vis. 4(4), 1 (2004). [CrossRef] [PubMed]

63.

E. Acosta, J. M. Bueno, C. Schwarz, and P. Artal, “Relationship between wave aberrations and histological features in ex vivo porcine crystalline lenses,” J. Biomed. Opt. 15(5), 055001 (2010). [CrossRef] [PubMed]

OCIS Codes
(110.4500) Imaging systems : Optical coherence tomography
(110.6880) Imaging systems : Three-dimensional image acquisition
(120.4640) Instrumentation, measurement, and metrology : Optical instruments
(120.4800) Instrumentation, measurement, and metrology : Optical standards and testing
(120.6650) Instrumentation, measurement, and metrology : Surface measurements, figure
(330.7327) Vision, color, and visual optics : Visual optics, ophthalmic instrumentation

ToC Category:
Ophthalmology Applications

History
Original Manuscript: June 7, 2012
Revised Manuscript: July 26, 2012
Manuscript Accepted: August 24, 2012
Published: September 12, 2012

Citation
Sergio Ortiz, Pablo Pérez-Merino, Enrique Gambra, Alberto de Castro, and Susana Marcos, "In vivo human crystalline lens topography," Biomed. Opt. Express 3, 2471-2488 (2012)
http://www.opticsinfobase.org/boe/abstract.cfm?URI=boe-3-10-2471


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References

  1. P. Kiely, G. Smith, and L. Carney, “The mean shape of the human cornea,” Opt. Acta (Lond.)29(8), 1027–1040 (1982). [CrossRef]
  2. J. Schwiegerling, J. E. Greivenkamp, and J. M. Miller, “Representation of videokeratoscopic height data with Zernike polynomials,” J. Opt. Soc. Am. A12(10), 2105–2113 (1995). [CrossRef] [PubMed]
  3. M. Dubbelman, H. A. Weeber, R. G. van der Heijde, and H. J. Völker-Dieben, “Radius and asphericity of the posterior corneal surface determined by corrected Scheimpflug photography,” Acta Ophthalmol. Scand.80(4), 379–383 (2002). [CrossRef] [PubMed]
  4. A. Gullstrand, “Appendices to Part I,” in Helmholtz's Treatise on Physiological Optics (Optical Society of America, Rochester, NY, 1924), pp. 350–358.
  5. H. Helmholtz, “Ueber die accommodation des auges,” Arch. Ophthal.1, 1–74 (1855).
  6. A. Glasser and M. C. W. Campbell, “Presbyopia and the optical changes in the human crystalline lens with age,” Vision Res.38(2), 209–229 (1998). [CrossRef] [PubMed]
  7. A. Glasser and P. L. Kaufman, “The mechanism of accommodation in primates,” Ophthalmology106(5), 863–872 (1999). [CrossRef] [PubMed]
  8. G. Smith, B. K. Pierscionek, and D. A. Atchison, “The optical modelling of the human lens,” Ophthalmic Physiol. Opt.11(4), 359–369 (1991). [CrossRef] [PubMed]
  9. L. F. Garner and M. K. Yap, “Changes in ocular dimensions and refraction with accommodation,” Ophthalmic Physiol. Opt.17(1), 12–17 (1997). [CrossRef] [PubMed]
  10. L. F. Garner, “Calculation of the radii of curvature of the crystalline lens surfaces,” Ophthalmic Physiol. Opt.17(1), 75–80 (1997). [CrossRef] [PubMed]
  11. A. Glasser and M. C. W. Campbell, “Biometric, optical and physical changes in the isolated human crystalline lens with age in relation to presbyopia,” Vision Res.39(11), 1991–2015 (1999). [CrossRef] [PubMed]
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  13. A. M. Rosen, D. B. Denham, V. Fernandez, D. Borja, A. Ho, F. Manns, J. M. Parel, and R. C. Augusteyn, “In vitro dimensions and curvatures of human lenses,” Vision Res.46(6-7), 1002–1009 (2006). [CrossRef] [PubMed]
  14. Y. Sakamoto, K. Sasaki, Y. Nakamura, and N. Watanabe, “Reproducibility of data obtained by a newly developed anterior eye segment analysis system, EAS-1000,” Ophthalmic Res.24(Suppl 1), 10–20 (1992). [CrossRef] [PubMed]
  15. C. A. Cook and J. F. Koretz, “Methods to obtain quantitative parametric descriptions of the optical surfaces of the human crystalline lens from Scheimpflug slit-lamp images. I. Image processing methods,” J. Opt. Soc. Am. A15(6), 1473–1485 (1998). [CrossRef] [PubMed]
  16. M. Dubbelman and G. L. Van der Heijde, “The shape of the aging human lens: curvature, equivalent refractive index and the lens paradox,” Vision Res.41(14), 1867–1877 (2001). [CrossRef] [PubMed]
  17. M. Dubbelman, G. L. van der Heijde, and H. A. Weeber, “The thickness of the aging human lens obtained from corrected Scheimpflug images,” Optom. Vis. Sci.78(6), 411–416 (2001). [CrossRef] [PubMed]
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