November 2015
Volume 56, Issue 12
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Lens  |   November 2015
Active Maintenance of the Gradient of Refractive Index Is Required to Sustain the Optical Properties of the Lens
Author Affiliations & Notes
  • Ehsan Vaghefi
    School of Optometry and Vision Science School of Medical Sciences, New Zealand National Eye Center, University of Auckland, Aukland, New Zealand
    Auckland Bioengineering Institute, University of Auckland, Auckland, New Zealand
  • Andy Kim
    School of Optometry and Vision Science School of Medical Sciences, New Zealand National Eye Center, University of Auckland, Aukland, New Zealand
  • Paul J. Donaldson
    School of Optometry and Vision Science School of Medical Sciences, New Zealand National Eye Center, University of Auckland, Aukland, New Zealand
    Auckland Bioengineering Institute, University of Auckland, Auckland, New Zealand
    Department of Physiology, School of Medical Sciences, New Zealand National Eye Center, University of Auckland, Auckland, New Zealand
  • Correspondence: Ehsan Vaghefi, Building 502, Level 4, 85 Park Road, Grafton, Auckland, New Zealand; e.vaghefi@auckland.ac.nz
Investigative Ophthalmology & Visual Science November 2015, Vol.56, 7195-7208. doi:10.1167/iovs.15-17861
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      Ehsan Vaghefi, Andy Kim, Paul J. Donaldson; Active Maintenance of the Gradient of Refractive Index Is Required to Sustain the Optical Properties of the Lens. Invest. Ophthalmol. Vis. Sci. 2015;56(12):7195-7208. doi: 10.1167/iovs.15-17861.

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      © ARVO (1962-2015); The Authors (2016-present)

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Abstract

Purpose: To determine whether the cellular physiology of the lens actively maintains the optical properties of the lens and whether inhibition of lens transport affects overall visual quality.

Methods: One lens from a pair of bovine lenses was cultured in artificial aqueous humor (AAH), while the other was cultured in either AAH-High-K+ or AAH + 0.1 mM ouabain for 4 hours. Lens pairs or whole enucleated eyes were then imaged in 4.7 Tesla (T) high-field small animal magnet. Lens surface curvatures, T1 measurements of water content, and T2 measurements of water/protein ratios were extracted from cultured lenses, while the geometrical parameters that define the optical pathway were obtained from whole eyes. Gradients of refractive index (GRIN), calculated from T2 measurements, and the extracted geometric parameters were inputted into optical models of the isolated lens and the whole bovine eye.

Results: Inhibiting circulating fluxes by inhibiting the Na/K-ATPase with ouabain or depolarization of the lens potential by High K+ caused changes to lens water content, the water/protein ratio (GRIN) and surface geometry that manifested as an increase in optical power and a decrease in negative spherical aberration in cultured lenses. Changes to optical properties of the lens resulted in a myopic shift that impaired vision quality in the optical model of the bovine eye.

Conclusions: The cellular physiology of the lens actively maintains its optical properties and inhibiting the Na/K/ATPase induces a myopic shift in vision similar to that observed clinically in patients who go on to develop cataract.

Our sense of sight is critically dependent on the optical properties of the ocular lens that enables light to be focused onto the retina.1 Like a glass window, the lens allows light rays that enter the eye to pass through it with minimal scattering. However, the lens is more than a simple pane of glass, because its curved surfaces enable it to focus light. In addition, the lens needs to correct for positive spherical aberration introduced to the optical pathway via the cornea. This spherical aberration is an optical error caused by the increased refraction of light rays that strike the periphery of the cornea relative to those that strike its center.2 The lens compensates for this optical error by imposing and maintaining a compensating negative spherical aberration through the establishment an inherent gradient of refractive index (GRIN).3 Being a biological tissue, this gradient is generated by over expressing different subtypes of crystallin proteins with varying refractive indices,4 thereby ensuring that incoming light is accurately focussed on the retina. While the biophysical properties of the crystallins that generate the GRIN have been extensively studied5 and the fundamental importance of the GRIN to the overall optical properties of the lens at the tissue level is well known,6,7 how the actual gradient in protein concentration is established and maintained at the cellular level is currently unknown. 
In this regard, it is important to note that the lens is not a passive optical element, but is a dynamic living biological tissue with a unique cellular structure and function. Structurally the lens consists of an anterior layer of epithelial cells that at the lens equator differentiate into fiber cells in a process that is characterized by extensive cellular elongation, the loss of cellular organelles and nuclei, and the expression of fiber-specific proteins, including the crystallins.8,9 Fiber cell elongation continues until differentiating fibers from opposite hemispheres meet at the poles and interdigitate to form the lens sutures.10 Because this process continues throughout life, a gradient of fiber cells at different stages of differentiation is established around an internalized core (nucleus) of anucleate mature fiber cells11 that were laid down in the embryo and are maintained for the lifetime of the organism. Recently, it has been shown that the lens consists of a series of discrete growth rings that contain fiber cells, which at specific stages of fiber cell differentiation, become metabolically linked by membrane fusions.12 These fusions permit the exchange of large proteins within, but not between adjacent growth rings. Because gap junction channels functionally couple all fiber cells13 they provide a pathway for ion and water movement from the lens center to periphery that crosses these discrete growth rings. Imposed upon this structural framework is the GRIN, which is primarily generated by the differentiation-dependent over expression of the lens crystallins. These proteins possess extraordinary stability and solubility, constitute a greater than 90% of lens dry weight and exhibit a concentration that ranges from 240 mg mL−1 in the lens cortex to 400 to 600 mg mL−1 in the core of the lens.14 Indeed the failure to maintain crystallin solubility, results in protein aggregation, increased light scattering, and eventually cataract. 
To maintain its cellular architecture and crystallin solubility, it has been proposed that in the absence of a blood supply the lens operates an internal microcirculation system.1517 Briefly, in this model a circulating current of Na+ ions primarily enters at the poles and travels into the lens via the extracellular clefts between fiber cells. Na+ crosses fiber cell membranes, and returns toward the surface via an intercellular pathway mediated by gap junction channels, where it is actively removed by Na+ pumps concentrated at the lens equator. This circulating ionic current in turn generates an isotonic flux of fluid through the lens that convects nutrients and antioxidants via an extracellular route toward the core of the lens faster than would occur via passive diffusion alone. This accumulated fluid and associated metabolic wastes are removed from the lens core by a hydrostatic pressure gradient that drives fluid to the surface via the gap junctions.18 Thus, active pumping of Na+ by surface cells is thought to regulate extracellular and intercellular fluid fluxes17 that deliver nutrients and antioxidants to the lens core, thereby protecting crystallin thiol groups from the oxidation effectively preventing protein aggregation and maintaining crystallin solubility.19 
Recently, using T1 magnetic resonance imaging (MRI) in combination with D2O tracer experiments20 to spatially map lens water content, we have shown that reducing Na+ pump activity or depolarizing lens potential, two perturbations known to inhibit measured circulating ionic currents in the lens,16 not only inhibited fluid fluxes driven by the circulation system, but also abolished the steady state water gradient known to exist in the lens. These experiments showed for the first time that fluid circulates through the lens and that at steady state these fluxes act to maintain a lower water content in the lens core relative to the cortex. It follows, therefore, that the removal of water from the lens core driven by the microcirculation system would act to increase the concentration of crystallin proteins in that inner region, thereby simultaneously steepening and smoothening the GRIN profile produced by regional differences in crystallin subtype expression. 
In this paper, we have used T1 and T2 MRI imaging modalities to obtain accurate information on the geometry, water content, and water to protein ratios (from which we can calculate the GRIN) in bovine lenses organ cultured under conditions in which the lens microcirculation system is inhibited by either depolarization of the lens potential, or inhibition of the Na+ pumps. Using this approach we show that the cellular physiology of the lens actively contributes to the maintenance of lens surface geometry and the GRIN. Furthermore, we have used optical modeling software to assess the effects these alterations in lens physiology have on the optical properties of the lens and its resultant contribution to overall vision quality of the bovine eye. Our results show that perturbing ionic and fluid fluxes in the lens induces changes to the optical properties of the lens that in turn distort image formation in our model of the bovine eye. Taken together our results suggest that the lens microcirculation system by actively maintaining the optical properties of the lens indirectly contributes to the overall vision quality. 
Methods
Preparation of Bovine Eyes
Fresh bovine eyes were obtained from a local abattoir (Auckland Meat Processing, Auckland, New Zealand) and immediately transferred into PBS for transfer to the laboratory (4.3 mM NaH2PO4; 137 mM NaCl; 2.7 mM KCl; 1.4 mM KH2PO4). Bovine eyes were either imaged intact to extract geometrical information on the tissues that comprise the optical pathway, or were dissected to obtain isolated lenses for organ culture experiments. Dissected lenses were incubated in artificial aqueous humor (AAH; NaCl 125 mM; KC1 4.5 mM; MgCl2 0.5 mM; CaCl2 2 mM; NaHCO3 10 mM; glucose 5 mM; Sucrose 20mM; buffered with 10 mM HEPES to pH 7.1), or either High-K+ (NaCl 25 mM; KC1 100 mM; MgCl2 0.5 mM; CaCl2 2 mM; NaHCO3 10 mM; glucose 5 mM; Sucrose 20 mM; buffered with 10 mM HEPES to pH 7.1) to depolarize the lens20 or AAH plus 0.1 mM ouabain to block Na+ pump activity21 for 4 hours prior to being placed in the scanner. One bovine eye or two isolated lenses with their anterior surfaces facing up were placed in sample holders, the temperature of which was monitored and controlled at 37°C by a MR compatible temperature control unit (SAII, Stony Brook, NY, USA). Because only two isolated lenses could be imaged at once, a control lens incubated in AAH was always compared with an experimental lens to determine the effect of lens depolarization (AAH-High K+) or Na+ pump inhibition (AAH + ouabain) on the geometrical and optical properties of the lens. 
Magnetic Resonance Imaging
A Varian Unity Inova 4.7 Tesla (T) horizontal bore MRI system (Varian, Inc., Palo Alto, CA, USA), equipped with a 65-mm internal diameter (ID) and a 100 G/cm gradient system was used in all experiments. 
T1-Weighted Imaging of Whole Bovine Eyes.
To image whole bovine eyes, a 60-mm ID radio frequency (RF) probe based on the Varian's Millipede design was used with a custom spin echo pulse sequence (TR = 1 s, TE = 15 ms, TI = 100 ms, flip angle = 90°, slice thickness = 2 mm, field of view = 5.5 × 5.5 cm, and acquisition matrix = 512 × 512). The resultant MRI image stacks of the whole bovine eye were then volume rendered using custom-written routines (MATLAB; The MathWorks, Inc., Natick, MA, USA) to produce an accurate three-dimensional (3D) reconstruction of the bovine eye. A subsample of this 3D structural model was taken to extract a 2D projection through the optical axis. This 2D slice was subsequently subjected to thresholding in order to remove background noise and highlight the tissue margins. The thickness of the cornea and the depths of the anterior and posterior chambers were obtained directly from this 2D projection; while the radii of curvature and conic constants were obtained indirectly by curve fitting the front and inner surfaces of the cornea and retina, respectively. The curve fitting was performed using the Image Processing Toolbox of MATLAB (in the public domain, www.mathworks.com/products/image) and used the equation  where Ra is the radius of the fitted surface, Rm is the semidiameter and Q is the conic factor of the fitted ellipsoid to the lenticular surface. Using a freely available MATLAB function (FITELLIPSE: in the public domain, www.mathworks.com/matlabcentral/fileexchange/3215-fitellipse) this equation was fitted to the threshold ocular geometry and their radii of curvature and conic factors were calculated.  
T1 Measurements of the Organ Cultured Bovine Lenses.
Generally in biological tissue, MR-measured T1 values are directly proportional to the water content of the imaged tissue. To facilitate comparisons to existing data on the water content of lenses incubated in AAH-High K+ incubation,20 T1 measurements were performed on lenses incubated for 4 hours in AAH + ouabain using a gradient echo sequence of TR = 1.5 s, TE = 3.4 ms, slice thickness = 4 mm, field of view = 23.4 × 23.4 mm, and matrix size = 256 × 256. The T1 signal from the resultant images was extracted using Equation 2,22  where S is the obtained signal, S0 is the maximum signal and TI is the inversion time. In the above equation, T1 values are extracted by applying a train of TI values (20, 50, 80, 100, 150, 200, 250, 300, 350, and 400 ms) to obtain 10 data points which were then fitted with a monoexponential curve using a nonlinear curve fitting routine (EZYFIT, in the public domain, http://www.fast.u-psud.fr/ezyfit/). EZYFIT uses a recursive process and unconstrained nonlinear minimization of the sum of squared residuals, to find the optimum fit.23 T1 values were obtained from six lenses incubated in AAH + ouabain.  
T2-Weighted Imaging of Organ Cultured Bovine Lenses.
The dissected lenses of different groups were imaged using a 40-mm ID RF probe and a spin-echo pulse sequence of TR = 2 s, TE = 6.7 ms, TI = 200 ms, slice thickness = 1 mm, field of view = 24 × 24 mm, matrix size = 256 × 256, in-plane resolution = 93 μm. Using these parameters, MRI scans took less than 100 minutes to complete. The geometric parameters of the lens (front and back radii of curvature, and conic constants, axial length, and equatorial radius) were extracted from the MRI T2-weighted images (Fig. 1A) using the common filtering and masking methods (MATLAB Image Processing Toolbox) and (Equation 1). After the calculation of geometrical features of these lenses, the T2 constants were extracted from the T2-weighted image series using equation 3,24 where M is the magnitude of signal at given time and M0 is the initial magnitude. By performing the spin-echo sequence using a train of TE values (7.5, 8, 10, 12, 15, 18, 22, 30, 40, and 45 ms) (Fig. 2A), this imaging protocol created a dataset of 10 T2-weighted signal points for each pixel within the image. The data set for each pixel was then fitted with a monoexponential curve using the EZYFIT (Fig. 2B). This process allowed a T2 constant to be calculated for each pixel within the image,25,26 and by repeating the process for all pixels within an image a 2D map of T2 values for each lens and experimental condition could be constructed (Fig. 2C). Because T2 constants are inversely proportional to refractive index (n ∼Image not available ),26 T2 values for each pixel were then converted to refractive indices using Equation 4,  where n is the unitless refractive index and the T2 values are in milliseconds. Geometrical and T2 constant measurements were performed on six lenses (n = 6) from each experimental group (AAH, AAH-High K+, and AAH + ouabain) in order to ensure the statistical significance (verified by unpaired t-test, confidence interval 95%) of the results.  
Figure 1
 
Inhibition of lens physiology alters the geometry of organ-cultured bovine lenses. (A) High resolution T2-weighted image of the bovine lens captured with MRI showing the anterior pole (AP), posterior pole (PP), equator (EQ), front (Ra) and back (Rp) radii of curvature, the equatorial radius (Re), and axial thickness (TA-P) are extracted from the image using MATLAB custom-written code. (B) Table summarizing the average values extracted for geometrical parameters defined in (A) plus the conic factors extracted from MRI images of lenses organ cultured in either AHH, AAH-High K+, or AAH + ouabain. Numbers in brackets represent the percent change in these parameters in relative to the AAH control group with statistical significance indicated (*P > 0.05). (C) The average values for these lens surface radii, conic factor and thicknesses listed in (B) have been used to draw representative profiles for lenses cultured in either AAH control, AAH-High K+, or AAH + ouabain.
Figure 1
 
Inhibition of lens physiology alters the geometry of organ-cultured bovine lenses. (A) High resolution T2-weighted image of the bovine lens captured with MRI showing the anterior pole (AP), posterior pole (PP), equator (EQ), front (Ra) and back (Rp) radii of curvature, the equatorial radius (Re), and axial thickness (TA-P) are extracted from the image using MATLAB custom-written code. (B) Table summarizing the average values extracted for geometrical parameters defined in (A) plus the conic factors extracted from MRI images of lenses organ cultured in either AHH, AAH-High K+, or AAH + ouabain. Numbers in brackets represent the percent change in these parameters in relative to the AAH control group with statistical significance indicated (*P > 0.05). (C) The average values for these lens surface radii, conic factor and thicknesses listed in (B) have been used to draw representative profiles for lenses cultured in either AAH control, AAH-High K+, or AAH + ouabain.
Figure 2
 
Calculation of the lens T2 constant maps in organ-cultured bovine lenses. (A) A series of T2-weighted images collected from a single lens using varying echo time (TE) values shows that longer TE values produce lower T2 weighted signals from the inner regions of the lens. (B) An exponential curve (Equation 3) was fitted to the T2-weighted data series in order to calculate the T2 constant of a single pixel from a MRI image. (C) Maps of T2 constants calculated from lenses organ cultured in AAH, AAH-High K+, or AAH + ouabain. The numbers on the color bar represent T2 values in seconds. Axial (D) and equatorial (E) T2 value plots are extracted for all the conditions and superimposed.
Figure 2
 
Calculation of the lens T2 constant maps in organ-cultured bovine lenses. (A) A series of T2-weighted images collected from a single lens using varying echo time (TE) values shows that longer TE values produce lower T2 weighted signals from the inner regions of the lens. (B) An exponential curve (Equation 3) was fitted to the T2-weighted data series in order to calculate the T2 constant of a single pixel from a MRI image. (C) Maps of T2 constants calculated from lenses organ cultured in AAH, AAH-High K+, or AAH + ouabain. The numbers on the color bar represent T2 values in seconds. Axial (D) and equatorial (E) T2 value plots are extracted for all the conditions and superimposed.
Optical Modeling
The commercial optical modeling software package ZEMAX (Development Corp., San Diego, CA, USA) which uses Snell's law27 to simulate light rays propagation through optical devices and calculates first and higher order aberrations of an optical system was used to assess the optical properties of lenses cultured under different conditions and to simulate the effect changing the optical properties of the lens have on overall vision quality. 
Measurement of the Optical Properties of Organ Cultured Lenses.
The average geometric parameters (front and back radii of curvature, conic constants, axial length, and equatorial radius) and the GRIN calculated from T2 imaging, using Equation 4, of bovine lenses cultured in either AAH, AAH-High K+, or AAH + ouabain were used by ZEMAX to calculate the optical power (D) and Seidel (spherical, coma, astigmatism, distortion, field curvature, longitudinal chromatic, and transverse chromatic) aberrations23,28,29 of lenses in the three different conditions. To determine the contribution of GRIN to overall optical power and spherical aberration in lenses incubated under the different conditions the model was solved in the absence of a gradient in refractive index using a constant value for refractive index. This homogenous refractive index was chosen to be the median value between the periphery and core indices values for each perturbation category (i.e., AAH = 1.41, AAH-High K+ = 1.395, and AAH + ouabain = 1.41).3032 
Modeling Vision Quality of the Bovine Eye.
To simulate what effect changes to the optical properties of the lens induced by changes in lens physiology could be having on overall vision quality, T1 measurements of the geometry of the isolated bovine eye (see Fig. 6) were combined with average refractive indices for the cornea, aqueous humor, and vitreous humor33 to create a ZEMAX model of the optical pathway of the bovine eye. This model was solved using the average optical properties calculated for lenses incubated in either AAH, AAH-High K+, or AAH + ouabain and using a fixed pupil diameter of 2 mm and a polychromatic (wavelengths = 0.486, 0.587, and 0.656 μm) light source.34 These parameters were used to calculate the optical parameters of the bovine eye and their effect on image quality for each experimental condition at two different focal lengths: an optimum focal length of the optical pathway formed by the eye that results in the formation of the sharpest final image; or with the focal length set to the vitreous chamber thickness (VT), to assess the quality of the image formed on the retina. 
Results
Physiological Perturbation of Optical Parameters in Isolated Bovine Lenses
Magnetic resonance imaging uses the resonance of the protons, called spins, to generate images. Protons, such as hydrogen nuclei, are excited by a radiofrequency pulse generated by MRI and then re-emit the absorbed energy as signal while returning to their original energy level. Because the lens consist of mainly proteins and water, which magnetize to different energy states, their relaxation precess can be distinguished by two distinct time constants defined as T1 and T2. The T1 time constant is related to the dispersion of the protons' excess energy to the surrounding environment, and in the lens it is dominated by the signal from the water molecules. Hence, T1-weighted imaging is used for looking at the water content of the lens. The T2 time constant is related to the dispersion of the protons' excess energy due to their interatomic interactions. This time constant is effected by both the water and protein signals, and hence been used to look at the water/protein ratio in the lens. 
In a previous study using T1 weighted imaging we showed that inhibiting the circulation system in the bovine lenses by either incubating them in AAH-High K+, or low temperature, abolished the inherent water gradient and increased the water content in the lens core.20 In this study, we have complemented our existing T1 imaging results and introduced T2 imaging to determine whether the observed increase in water content induced by inhibiting the lens microcirculation changes overall lens geometry and the GRIN, both key determinants of the optical properties of the lens. In the current study, in addition to inhibiting the circulation system by incubating lenses in AAH-High K+ to depolarize the lens potential, we have incubated lenses in ouabain to specifically block Na+ pump activity, which is known to drive the microcirculation system.21 
Effects of Physiological Perturbation on Lens Geometry.
Like other ocular lenses, the bovine lens is an asymmetrical oblate spheroid by virtue of having an axial diameter that is less than its equatorial diameter, and having anterior and posterior surfaces with different radii of curvature.35 The key parameters that determine lens geometry, namely axial thicknesses (TA-P), equatorial radius (Re), and the radii and conic factors of the anterior (Ra, Qa) and posterior (Rp, Qp) surfaces were extracted from high resolution T2-weighted image datasets (Fig. 1A), obtained from imaging lenses organ cultured for 4 hours in AAH, or either AAH-High K+, or AAH + ouabain to perturb lens physiology. The extracted parameters of each culture condition were then averaged (Fig. 1B) and used to reconstruct the shape of the lens (Fig. 1C) in order to visually compare the changes in lens geometry induced by the either depolarizing the lens potential (AAH-High K+) or inhibiting the Na+ pump (AAH + ouabain). Both perturbations significantly increased the axial thickness of the lens, but had no significant effect on the equatorial diameter. This change in axial thickness changes the aspect ratio (TA-P/Re) of the lens and shows that inhibiting lens physiology is causing it to become more spherical in shape relative to control lenses organ cultured in AAH alone. Furthermore, this trend toward a more spherical lens was predominately driven by changes to the shape of the anterior surface of the lens relative to the posterior surface (Fig. 1B). Lenses incubated in AAH-High K+ (ΔRa = 16%, ΔRp = 8%) or AAH + ouabain (ΔRa = 11%, ΔRp = 2%) showed 2- and 5-fold, respectively, larger increases in Ra relative to Rp. This coupled with similar relative changes in conic factor of the anterior and posterior surfaces in treated lenses (AAH-High K+, ΔQa = 12%, ΔQp = 7%; AAH + ouabain, ΔQa = 11%, ΔQp = 2%) indicates that the curvature of the anterior surface has become more curved in response to inhibition of the lens physiology. 
Effects of Physiological Perturbation on Lens GRIN.
The refractive index of a tissue is directly related to its water content and percentage of solid material, which in the lens is due primarily to its protein concentration.6,26,36 Accurate measurements of the water to protein ratio can be obtained from T2 constants measured by MRI imaging protocols (Fig. 2). T2 constants were extracted for each pixel from a series of MRI images collected from an individual lens (Figs. 2A, 2B) and used to compile a spatial map of T2 values for each lens organ cultured under the different experimental conditions (Fig. 2C). Because refractive index is inversely proportional to T2, the T2 maps collected from lenses organ cultured maps in AAH, or either AAH-High K+, or AAH + ouabain to perturb lens physiology (Fig. 2C) were then converted to GRIN maps using Equation 4 (Fig. 3A). To facilitate comparison between the different treatment groups axial (Fig. 3B) and equatorial (Fig. 3C) refractive index profiles were extracted from individual lenses and averaged to produce representative plots of the GRIN for lens cultured in AAH, AAH-High K+, or AAH + ouabain. 
Figure 3
 
Inhibition of lens physiology alters the GRIN in organ-cultured bovine lenses. (A) The T2 constant maps obtained for lens organ cultured in either AAH, AAH-High K+, and AAH + ouabain shown in Figure 2C have been converted using Equation 4 into color coded maps of refractive index (n) to visualize the GRIN. (B, C) Line profiles of refractive index extracted through the anterior (AP) and posterior (PP) poles (B) or equatorial (C) axis of lenses cultured in AAH (green), AAH-High K+ (red), or AAH + ouabain (blue) are plotted against the relative distance into the lens (r/a), where 0 and 1 represent the lens center and periphery, respectively. Arrows in (B) show that changes to the GRIN induced by inhibiting lens physiology are more apparent on the anterior side (blue arrow) of the lens rather than the posterior surface (purple arrow). (D, E) Comparison of regional differences in the average RI from the outer cortex (OC), inner cortex (IC), and nucleus (N) obtained from for the anterior (AP) and posterior (PP) poles (B) or equatorial (C) axes of lenses cultured in AAH (green), AAH-High K+ (red), or AAH + ouabain (blue). Brackets indicate the regions where a statistically significant difference (P < 0.01) between the RI of control lenses (AAH) and the two experimental groups (AAH-High K+ or AAH + ouabain) were obtained.
Figure 3
 
Inhibition of lens physiology alters the GRIN in organ-cultured bovine lenses. (A) The T2 constant maps obtained for lens organ cultured in either AAH, AAH-High K+, and AAH + ouabain shown in Figure 2C have been converted using Equation 4 into color coded maps of refractive index (n) to visualize the GRIN. (B, C) Line profiles of refractive index extracted through the anterior (AP) and posterior (PP) poles (B) or equatorial (C) axis of lenses cultured in AAH (green), AAH-High K+ (red), or AAH + ouabain (blue) are plotted against the relative distance into the lens (r/a), where 0 and 1 represent the lens center and periphery, respectively. Arrows in (B) show that changes to the GRIN induced by inhibiting lens physiology are more apparent on the anterior side (blue arrow) of the lens rather than the posterior surface (purple arrow). (D, E) Comparison of regional differences in the average RI from the outer cortex (OC), inner cortex (IC), and nucleus (N) obtained from for the anterior (AP) and posterior (PP) poles (B) or equatorial (C) axes of lenses cultured in AAH (green), AAH-High K+ (red), or AAH + ouabain (blue). Brackets indicate the regions where a statistically significant difference (P < 0.01) between the RI of control lenses (AAH) and the two experimental groups (AAH-High K+ or AAH + ouabain) were obtained.
Consistent with previous reports37,38 refractive index profiles for control bovine lenses organ cultured in AAH had a refractive index of approximately 1.38 at the periphery of the lens which increased, smoothly to reach approximately 1.44 in the center (Figs. 3B, 3C). Incubating lenses in AAH-High K+ to depolarizing the lens potential, and therefore inhibit the lens microcirculation system, caused a global reduction in refractive index in all regions of the lens. Although in axial profiles, the difference in refractive index was more pronounced at the anterior surface than the posterior surface (Fig. 3B, arrows). In contrast, abolishing circulating fluxes by incubating lenses in AAH + ouabain to block the Na+ pump had the effect of decreasing the refractive index in the lens periphery, but increasing it in the lens nucleus (Figs. 3B, 3C). Again the observed decrease in refractive index induced in the periphery by ouabain was more pronounced at the anterior surface of the lenses (Fig. 3B, arrows). These regional differences in the GRIN can be better visualized by extracting the mean refractive index in the outer cortex (r/a 1–0.75), inner cortex (r/a 0.75–0.5), and central nucleus (r/a 0.5–0) for axial (Fig. 3D) and equatorial (Fig. 3E) profiles. We found these values to be 1.391, 1.411, and 1.429 in the AAH control group for outer cortex, inner cortex, and the core, respectively. For the AAH-High K+ these values were 1.373, 1.392, and 1.414. As for the AAH + ouabain subgroup, the mean refractive indices were 1.381, 1.413, and 1.440 for outer cortex, inner cortex, and the core, respectively. This analysis clearly shows that while the two perturbations significantly reduce the refractive index of the outer cortex, they have opposite effects on the refractive index of the lens nucleus. Inhibiting ion and water fluxes with ouabain increases the refractive index in the nucleus while their inhibition by high extracellular K+ decreases the index. 
Because refractive index is determined by the local water to protein ratio in the lens, the different effects of the two physiological perturbations on the refractive index in the lens nucleus could be explained by differential effects of the two treatments on either the overall water content of the lens, or its protein content. With regard to lens depolarization, in a previous study we used T1 measurements of water content to show that incubating lenses in AAH-High K+ caused a flattening of the steady-state water gradient in the lens due to an accumulation of water in the lens nucleus.20 Consistent with this finding, we show in the present study that incubating lenses in AAH-High K+ decreases the refractive index in all regions of the lens due to an increase in the water content of the lens. Here, we have performed a similar T1 analysis of lens water content on lenses incubated in AAH + ouabain (Fig. 4A) and compared the overall profiles (Fig. 4B) and mean refractive indices in specific regions of the lens (Fig. 4C) obtained from our previous data20 collected on lens incubated in AAH-High K+. This analysis shows that although the two treatments have both been shown to inhibit ion and water fluxes at the lens surface,39,40 they have different effects on the water content in the lens nucleus. This suggests that relative to the AAH control, the AAH + ouabain condition has led to higher water content, and hence higher T1 values at the periphery and in the core of these lenses.41 
Figure 4
 
Effect of ouabain on the water content of bovine lenses. Color maps of calculated T1 constants that are directly proportional to free water content, obtained from bovine lenses organ cultured in either AAH (A) or AAH + ouabain (B). (C) Line profiles of T1 values extracted through the equatorial axis of lenses cultured in AAH (green), AAH-High K+ (red), or AAH + ouabain (blue) plotted against the relative distance into the lens (r/a), where 0 and 1 represent the lens center and periphery, respectively. (D) Comparison of regional differences in the average T1 values from the outer cortex (OC), inner cortex (IC), and nucleus (N) extracted from the equatorial (C) axis of lenses cultured in either AAH, AAH-High K+, and AAH + ouabain. Brackets indicate the regions where a statistically significant difference (P < 0.01) between the average T1 values of control lenses (AAH) and the two experimental groups (AAH-High K+ or AAH + ouabain) were obtained.
Figure 4
 
Effect of ouabain on the water content of bovine lenses. Color maps of calculated T1 constants that are directly proportional to free water content, obtained from bovine lenses organ cultured in either AAH (A) or AAH + ouabain (B). (C) Line profiles of T1 values extracted through the equatorial axis of lenses cultured in AAH (green), AAH-High K+ (red), or AAH + ouabain (blue) plotted against the relative distance into the lens (r/a), where 0 and 1 represent the lens center and periphery, respectively. (D) Comparison of regional differences in the average T1 values from the outer cortex (OC), inner cortex (IC), and nucleus (N) extracted from the equatorial (C) axis of lenses cultured in either AAH, AAH-High K+, and AAH + ouabain. Brackets indicate the regions where a statistically significant difference (P < 0.01) between the average T1 values of control lenses (AAH) and the two experimental groups (AAH-High K+ or AAH + ouabain) were obtained.
In summary, it appears that the inhibition of the ion and water fluxes by either incubation in high extracellular K+ to depolarize the lens potential, or ouabain to inhibit the Na+ pump produces distinct changes to not only to the shape of the lens, but also its GRIN, which we would predict would alter the optical properties of the lens. 
Modeling of the Contribution of the Optical Properties of the Lens to Vision Quality
To test whether perturbing lens physiology affects not only its optical properties, but overall vision quality, we used a commercial optical modeling software package, ZEMAX. This software package simulates the propagation of light rays through an optical pathway and provides measures of the optical properties of the individual elements in the pathway and the overall optical pathway. We have used ZEMAX to first assess what effects perturbing lens physiology has on the optical properties of the lens and then how these changes in optical properties impact on the overall vision quality of a model bovine eye. 
Effects of Physiological Perturbation of the Optical Properties of the Lens.
Using the average geometric parameters (Fig. 1) and the GRIN (Fig. 3) obtained by T2 imaging we have used ZEMAX to calculate the optical power and spherical aberration of bovine lenses organ cultured in either AAH, AAH-High K+, or AAH + ouabain (Fig. 5). The optical power of any lens or curved mirror is expressed in diopters (D), which is equal to the reciprocal of the focal length measured in meters. Relative to lenses incubated in AAH (30.21 ± 3.07 D), depolarizing the lens potential by incubating lens in high extracellular K+ (34.88 ± 3.45 D) or inhibiting the Na+ pump by the addition of ouabain (84.19 ± 9.98 D) increased the optical power of the bovine lens (Fig. 5A). Furthermore, this change in power was driven primarily by a change in the surface curvature of the lens rather than changes to the GRIN. In addition to measurements of optical power, the ZEMAX software quantifies the Seidel aberrations42 that are associated with the passage of light through an optical system. While the majority of Seidel (coma, astigmatism, distortion, field curvature, longitudinal chromatic, and transverse chromatic) aberrations calculated for the bovine lenses were either minimal or unaffected by the imposed physiological perturbations (data not shown), a significant effect on spherical aberration was observed (Fig. 5B). Consistent with previous data43,44 lenses incubated in AAH exhibited a substantial (−3.69E-04 ± 2.33E-05 mm) negative spherical aberration. This intrinsic negative spherical aberration is believed to correct for the positive spherical aberration introduced by the cornea.45 Incubating lenses in either AAH-High K+ (−2.28E-04 ± 6.84E-05), or AAH + ouabain (−1.89E-04 ± 6.00E-05 mm) both significantly decreased this intrinsic spherical aberration. Unlike the change in optical power, the effect of physiological perturbation on spherical aberration was predominately driven by changes in GRIN rather than changes to lens surface curvature. Thus, it appears that altering lens physiology through depolarizing the lens potential and inhibiting the Na+ pump induces changes to the surface curvatures and the GRIN that increase the optical power and reduces the degree of negative spherical aberration in the bovine lens. 
Figure 5
 
Inhibition of lens physiology alters the optical properties of organ-cultured bovine lenses. The average geometric parameters (Fig. 2B) and the GRIN (Fig. 4) obtained from T2 imaging of bovine lenses cultured in either AAH, AAH-High K+, or AAH + ouabain we used by ZEMAX to calculate the optical power (A) and spherical aberration (B) of lenses in each condition. The relative contribution of the GRIN (light gray) to overall optical power and spherical aberration in lenses incubated under the different conditions was determined by re-solving the model in absence of a gradient in refractive index using a constant value for refractive index. *P < 0.01.
Figure 5
 
Inhibition of lens physiology alters the optical properties of organ-cultured bovine lenses. The average geometric parameters (Fig. 2B) and the GRIN (Fig. 4) obtained from T2 imaging of bovine lenses cultured in either AAH, AAH-High K+, or AAH + ouabain we used by ZEMAX to calculate the optical power (A) and spherical aberration (B) of lenses in each condition. The relative contribution of the GRIN (light gray) to overall optical power and spherical aberration in lenses incubated under the different conditions was determined by re-solving the model in absence of a gradient in refractive index using a constant value for refractive index. *P < 0.01.
Figure 6
 
Extraction of anatomical measures of the bovine eye for optical modeling. (A) A single T1-weighted MRI image splice from a 3D data set of the bovine eye showing the cornea (C) vitreous, (V), lens (L) and retina (R). (B) Same T1-weighted MRI dataset processed using MATLAB to allow accurate measurement of the 3D surfaces of the cornea, lens, and retina that shows the corneal thickness, (CT), corneal radius of curvature (CR), aqueous chamber thickness (AT), vitreous chamber thickness (VT), and retinal radius of curvature (RR). (C) Table showing the average values of the parameters defined above extracted from 10 bovine eyes. The values for the refractive index of the cornea, aqueous, and vitreous were obtained from the literature.66,67
Figure 6
 
Extraction of anatomical measures of the bovine eye for optical modeling. (A) A single T1-weighted MRI image splice from a 3D data set of the bovine eye showing the cornea (C) vitreous, (V), lens (L) and retina (R). (B) Same T1-weighted MRI dataset processed using MATLAB to allow accurate measurement of the 3D surfaces of the cornea, lens, and retina that shows the corneal thickness, (CT), corneal radius of curvature (CR), aqueous chamber thickness (AT), vitreous chamber thickness (VT), and retinal radius of curvature (RR). (C) Table showing the average values of the parameters defined above extracted from 10 bovine eyes. The values for the refractive index of the cornea, aqueous, and vitreous were obtained from the literature.66,67
Effects of Physiological Perturbation of the Optical Properties of the Lens on Overall Vision Quality.
The ocular lens is of course only one element in the optical pathway, used by the eye to focusing light on the retina, thereby enabling image formation to occur. In order to assess the how changes to the cellular physiology of the lens specifically impacts on overall vision quality we created an anatomically accurate ZEMAX model of the bovine eye (Fig. 6). To obtain the data to input into this model enucleated bovine eyes were subjected to an MRI to produce a data stack of T1 images (Fig. 6A) that were volume rendered to produce a 3D reconstruction of the bovine eye. From this reconstruction a 2D volume slice through the optical axis was extracted and thresholded to highlight tissue margins in order to facilitate the extraction of measurements of the thickness, radius and conic factors of the cornea and retina, plus the depths of anterior and posterior chambers (Fig. 6B). These measurements (Fig. 6C) were found to be in broad agreement with those available in the literature.35,46,47 To this dataset values for the refractive indices of the cornea, aqueous, and vitreous humors obtained from the literature were added.48,49 Finally values for optical power (Fig. 5A) and spherical aberration (Fig. 5B) obtained from lenses incubated under the different experimental conditions were added to produce ZEMAX models of the bovine eye that could be used to assess the effect depolarizing lens potential or inhibiting the Na+ pump have on overall vision quality. 
To determine how changes to the optical properties of the lens impact on the overall optical properties (Fig. 7) and image quality (Fig. 8) of the bovine eye, model simulations were initially performed to calculate the optimal focal length and the extent of total spherical aberration of the model eye. In these simulations the vitreous chamber length (VT = 12.8 mm) was allowed to vary between incubation conditions to determine the focal length of the model eye, which provides the optimal focus. Using this approach it is apparent that lenses incubated in both AAH (13.315 ± 0.4797 mm), and AAH-High K+ (12.645 ± 0.5707 mm) have an optimal focal length that was not significantly different to the vitreous chamber length (12.8 mm) measured in the bovine eye (Fig. 7A). However, lenses incubated in AAH + ouabain (8.5375 ± 0.7551 mm) exhibited a dramatic shortening of the optimal focal length that would result in images being focused in front of the retina. Next we used the model to assess what effect changing lens physiology has on the total spherical aberration of the bovine eye (Fig. 7B). The total spherical aberration of the bovine eye is given by the sum of the positive and negative contributions of the cornea and the lens, respectively. In our model the contribution of the cornea to total spherical aberration of the eye remains constant, but the negative spherical aberration from the lens is reduced by alterations to lens physiology that change the GRIN (Fig. 5B). The result of this reduction on the negative spherical aberration of the lens is a net increase in total positive spherical aberration (Fig. 7B), which has the potential to blur image formation. 
Figure 7
 
Inhibition of lens physiology alters the optical properties of a model bovine eye. The average optical properties obtained for bovine lenses cultured in either AAH, AAH-High K+, or AAH + ouabain (Fig. 5) were implemented in a ZEMAX model of the bovine eye that used the geometrical parameters and refractive indices defined in Figure 6C to calculate the optimal focal length (A), and spherical aberration (B) of the bovine eye for each condition. (A) The optimal focal length is calculated using the “best focus” feature of the ZEMAX modeling platform which calculates for each lens dataset the ideal focal length of the model bovine eye. The dotted line represents the vitreous chamber thickness (VT), which acts as a reference for comparison of the in situ of focal length of the bovine eye to focal lengths calculated by the model eye. (B) Contribution of the cornea (positive) and lens (negative) to total spherical aberration of the bovine model eye. While the contribution of the cornea to total spherical aberration is constant, the negative contribution of the lens decreases in AAH-High K+ and AAH + ouabain, resulting in an overall increase in total positive spherical aberration. *P < 0.01.
Figure 7
 
Inhibition of lens physiology alters the optical properties of a model bovine eye. The average optical properties obtained for bovine lenses cultured in either AAH, AAH-High K+, or AAH + ouabain (Fig. 5) were implemented in a ZEMAX model of the bovine eye that used the geometrical parameters and refractive indices defined in Figure 6C to calculate the optimal focal length (A), and spherical aberration (B) of the bovine eye for each condition. (A) The optimal focal length is calculated using the “best focus” feature of the ZEMAX modeling platform which calculates for each lens dataset the ideal focal length of the model bovine eye. The dotted line represents the vitreous chamber thickness (VT), which acts as a reference for comparison of the in situ of focal length of the bovine eye to focal lengths calculated by the model eye. (B) Contribution of the cornea (positive) and lens (negative) to total spherical aberration of the bovine model eye. While the contribution of the cornea to total spherical aberration is constant, the negative contribution of the lens decreases in AAH-High K+ and AAH + ouabain, resulting in an overall increase in total positive spherical aberration. *P < 0.01.
Figure 8
 
Inhibition of lens physiology alters image quality of a model bovine eye. The ability of the model bovine eye to reproduce an input image of a young child was tested using the image simulation capability of ZEMAX. This analysis was performed using either the calculated optimal focal length for the model eye (A, C, E) or a fixed-focal length given by the vitreous chamber depth (B, D, F), which more closely represents the situation in the bovine eye. Images at the optimal and fixed focal lengths are shown for models in which the optical properties of the lens were extracted from lenses organ cultured in either AAH (A, B), AAH-High K+ (C, D), or AAH + ouabain (E, F). Used with permission from Singapore Laser Pte LTD.
Figure 8
 
Inhibition of lens physiology alters image quality of a model bovine eye. The ability of the model bovine eye to reproduce an input image of a young child was tested using the image simulation capability of ZEMAX. This analysis was performed using either the calculated optimal focal length for the model eye (A, C, E) or a fixed-focal length given by the vitreous chamber depth (B, D, F), which more closely represents the situation in the bovine eye. Images at the optimal and fixed focal lengths are shown for models in which the optical properties of the lens were extracted from lenses organ cultured in either AAH (A, B), AAH-High K+ (C, D), or AAH + ouabain (E, F). Used with permission from Singapore Laser Pte LTD.
Finally to visually assess what effects the changes in the optical power and spherical aberration induced by alterations to lens physiology have on overall image quality we used the image simulation capability of ZEMAX to determine the ability of the model eye to reproduce an input image (Fig. 8). This analysis was performed using either the calculated optimal focal length for the model eye (Figs. 8A, 8C, 8E), or a fixed focal length given by the vitreous chamber depth (Figs. 8B, 8D, 8F), which more closely represents the situation in the bovine eye. Under the conditions of optimal focal length any distortion to the image output from the model would primarily be due to changes in spherical aberration correction caused by an inability of the lens to compensate for the positive spherical aberration imposed by the cornea. While under conditions where the focal length is fixed to that of the vitreous chamber any visual distortion to the output image is the sum of both out of focus blur and the increase in uncorrected spherical aberration. Relative to the input image the model eye was able to produce a clear image on the retina with minimal distortions under conditions of optimal (Fig. 8A) and fixed-focal (Fig. 8B) length using the optical properties calculated for lenses incubated in AAH. In the absence of a clinical examination of the visual acuity of the living bovine eye this comparison of the actual and optimal focal length provides us with some measure of the accuracy of our model eye. Inputting the optical properties of lenses incubated in AAH-High K+ introduced peripheral distortions to the shape of the output image at a the optimal focal length (Fig. 8C) and significantly blurring of the image when the fixed-focal length was used (Fig. 8D). While the use of the optical properties obtained from lenses incubated in AAH + ouabain introduced substantially image distortion at the optimal focal length (Fig. 8E), and this distortion was further exacerbated at the fixed-focal length (Fig. 8F). In summary, our results show that inhibiting the cellular physiology of the lens not only changes the optical properties of the lens, but also its contribution to overall vision quality in the bovine eye. 
Discussion
In this study, we have used two different experimental perturbations known to inhibit the lens internal microcirculation system50 and have employed MRI and optical modeling to evaluate how the induced changes to the cellular physiology of the lens alter not only lens optical power, but also what impact these changes have on overall vision quality. Depolarizing the lens potential with high extracellular K+, or blocking the Na+ pump with ouabain are two perturbations known to inhibit circulating ion and water fluxes20,21,51 at the lens surface. While these two treatments had no immediate effects on lens transparency over the 4-hour incubation period, they had quite different effects on lens geometry (Fig. 1) and GRIN (Fig. 3), which in turn altered the optical properties of the lens (Fig. 5). Using optical modeling we were then able to quantify (Fig. 7) and visualize (Fig. 8) the effects inhibiting the lens circulation system had on overall vision quality. These results raise the possibility that changes to the underlying cellular physiology of the lens may be responsible for the clinically observed shifts in optical power associated with the onset of lens cataract. 
The lens microcirculation system is established by differences in the membrane transport properties of cells in different regions of the lens. The concentration of Na+ pumps in epithelial and peripheral fiber cells at the lens equator generate a circulating Na+ current that enters the lens at both poles via an extracellular pathway, with Na+ moving into deeper fiber cells by diffusion down its electrochemical gradient, before exiting the lens at the equator via an intercellular pathway mediated by gap junction channels. An isotonic fluid flow accompanies this circulating Na+ gradient and delivers nutrients to the lens core. Because this fluid flux also exits the lens via a gap junction mediated pathway, the outflow pathway acts to restrict fluid flow that generates a substantial hydrostatic pressure gradient that ranges from 0 mm Hg in the lens periphery to approximately 32 mm Hg in the lens core. Thus, it is the integrated activity of multiple spatially distinct transport processes that generate the lens circulation, a system which is increasingly seen to be vital for maintaining lens transparency, and as shown in this study the refractive properties of the lens. 
Previous studies using a variety of experimental techniques such as vibrating probe,16,52,53 Using chambers,21 MRI,20 and computational modeling54 have all shown that incubating lenses in high extracellular K+ is an experimental intervention that inhibits20,21,51 and can actually reverse the circulating fluxes. High extracellular K+ by depolarizing the negative transmembrane potential gradient54,55 abolishes the electrochemical gradients for Na+ and K+21 to produce a cation-shift phenomenon in which the concentration of Na+ and K+ increase and decrease, respectively, in the lens.56 More recently, it has been shown that incubating lenses in high extracellular K+ effectively eliminates the hydrostatic pressure gradient in the lens18 that is proposed to drive water removal from the lens core. Consistent with this finding our previous T1-weighed MRI results20 showed that incubating lenses in AAH-High K+ reduces the inherent water gradient in the lens by increasing the water content in the core (Fig. 4). In this present study T2 mapping of water to protein ratios in lenses incubated in AAH-High K+ have shown that the observed increase in water content observed with T1 imaging results in changes to lens geometry (Fig. 1) and GRIN (Fig. 3) relative to lenses maintained in AAH. As an asymmetrical oblate spheroid the axial diameter of the lens is less than its equatorial diameter, and its anterior and posterior surfaces have different radii of curvature.35 Incubation in AAH-High K+ caused a significant increase in only the axial diameter of the lens due predominantly to a decrease in the radii of the anterior surface, which effectively increased the curvature of the anterior surface of the lens (Fig. 1). Subsequent analysis of the T2 maps (Fig. 2C) showed a preferential increase in T2 signal in the anterior relative to the posterior pole of the lens, indicating that a local increase in water content is the underlying cause of the increase in the curvature of the anterior surface. Conversion of T2 values to refractive index enabled GRIN profiles to be extracted (Fig. 3). This analysis revealed that incubating lenses in AAH-High K+ reduced refractive index values in all regions of the lens producing a homogenous flattening of the GRIN a result that is consistent with the observed increase in water content obtained by T1 measurements. Because AAH-High K+ is inhibiting the circulating water fluxes into and out of the lens by depolarizing the lens potential we proposed that this homogenous increase in water content is due to the passive diffusion of water into the lens that is driven by osmotic forces that are accentuated by Cl diffusion into the lens in response to the loss of a negative membrane potential. This water influx by increasing the curvature of the anterior surface of the lens and globally reducing the GRIN changes the optical properties of the lens causing a small increase in optical power (Fig. 5A) and a significant reduction in negative spherical aberration (Fig. 5B) that affects overall vision quality (Fig. 8). 
Like high extracellular K+, ouabain has also been shown to inhibit ion and water fluxes measured at the surface of the lens,21,57,58 and to increase the Na+ content of the lens, but unlike high extracellular K+ it does not, at least initially, reduce to zero either the lens potential,59 or hydrostatic pressure gradients.18 In this present study, we show that blocking the circulation system with ouabain also has a different effect on the water gradient than that observed for lenses incubated in AAH-High K+ (Fig. 4). In ouabain-treated lenses the water content increased more in the core relative to other regions, a result that cannot be solely explained by the passive radial diffusion of water into the lens as proposed for AAH-High K+. Furthermore, in ouabain-treated lenses this preferential increase in the water content of the core paradoxically resulted in an increase of refractive index in this region (Fig. 3). One possible explanation for this paradox maybe due to the fact that in a tissue with such short T1 and T2 constants, the MRI is much more sensitive to the free water content and not the water bound to proteins.60 Hence, the increase in water content induced by inhibiting the circulation system with ouabain could be explained by an abrupt and localized release of water that is normally bound to proteins in the lens core. This idea is supported by the observation that the ratio of free to bound water gradually increases in human lenses with advancing age and this change is more pronounced in cataractic lenses.61,62 Altering the hydration state of lens proteins either progressively as seen in aging human lenses, or experimentally by the pharmacologic manipulation of the Na+ pumps, will change the refraction of light by altering the homogenous composition of the cytoplasm. In our study, this localized change in protein hydration manifests itself as an increase in refractive index specifically in the core of ouabain treated lenses. This localized change in refractive index differs from that observed in AAH-High K+ where a more global change in total hydration occurred. 
Ouabain also had more dramatic effects on the optical properties of the lens than those observed when AAH-High K+ was used to inhibit ion and water fluxes. The increase in water content induced by ouabain produced a greater change in the geometry of the lens causing it to swell and lose its asymmetrical oblate spheroid shape and resemble a sphere with very similar anterior and posterior surface curvatures (Fig. 1). These changes dramatically increased the power of the ouabain treated lenses relative to lenses incubated in AAH or AAH-High K+ (Fig. 5A), but had a similar reduction in negative spherical as that observed by AAH-High K+ (Fig. 5B). These ouabain induced alterations to the optical properties of the lens manifest themselves primarily as a shorting of the focal length of our model bovine eye such that images are formed in front of the retina. 
Our findings that we can alter overall vision through the alterations to the optical properties of the lens induced by acutely perturbing the cellular physiology of lens offers new insights into the cellular origins of the clinically observed refractive changes that precede the initiation of cataract. The overall refractive properties of the eye are the sum of the optical properties of the cornea, lens, and axial length of the vitreous chamber. During the rapid growth phases of early and late childhood the optical properties of all three tissues change and failure to coordinate these changes can result in the development of refractive errors. However, in adulthood only the lens continues to grow and the aging of the lens has been associated with a gradual shift toward hyperopia in unaccommodated lenses that occurs over many decades.63 This hyperopic shift is due to a gradual loss of lens power, which is due primarily to a flattening of the GRIN that has been attributed by some research groups to a compaction of deeper lying fiber cells by the continued addition of new fiber cells at the lens equator.63 In some individual this age-dependent loss of lens power is abruptly disrupted by a rapid myopic shift often referred to as second sight as the resultant increase in lens power restores near vision. Unfortunately, in these individuals this period of improved “second sight” is closely followed by the onset of nuclear cataract64 Our ouabain experiments suggest a physiological explanation for this phenomenon. An abrupt failure of the lens circulation system, as induced in our study by the inhibition of the Na+ pumps with ouabain, would be expected to produce an accumulation of water in the core of the lens resulting in lens swelling, disruption of the GRIN and an increase in the optical power of the lens that restore near vision in presbyopic individuals. Unfortunately, this improvement in the optical power of the lens is only transient, as the inhibition of the circulation system also reduces the delivery nutrients and antioxidants to the lens core so that the myopic shift is rapidly followed by the oxidation, cross linking and aggregation of crystallin proteins in the lens core. 
In conclusion, our work on cultured bovine lenses show that the optical properties of the lens are actively maintain by circulating ionic and fluid fluxes whose modulation can alter the surface curvature and GRIN of the lens. These findings in turn offer functional explanations for the refractive changes observed in humans that precede the onset of cataract in some individuals.65 
Acknowledgments
The authors thank the Royal Society of New Zealand's Marsden Fund for funding this research. 
Disclosure: E. Vaghefi, None; A. Kim, None; P.J. Donaldson, None 
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Figure 1
 
Inhibition of lens physiology alters the geometry of organ-cultured bovine lenses. (A) High resolution T2-weighted image of the bovine lens captured with MRI showing the anterior pole (AP), posterior pole (PP), equator (EQ), front (Ra) and back (Rp) radii of curvature, the equatorial radius (Re), and axial thickness (TA-P) are extracted from the image using MATLAB custom-written code. (B) Table summarizing the average values extracted for geometrical parameters defined in (A) plus the conic factors extracted from MRI images of lenses organ cultured in either AHH, AAH-High K+, or AAH + ouabain. Numbers in brackets represent the percent change in these parameters in relative to the AAH control group with statistical significance indicated (*P > 0.05). (C) The average values for these lens surface radii, conic factor and thicknesses listed in (B) have been used to draw representative profiles for lenses cultured in either AAH control, AAH-High K+, or AAH + ouabain.
Figure 1
 
Inhibition of lens physiology alters the geometry of organ-cultured bovine lenses. (A) High resolution T2-weighted image of the bovine lens captured with MRI showing the anterior pole (AP), posterior pole (PP), equator (EQ), front (Ra) and back (Rp) radii of curvature, the equatorial radius (Re), and axial thickness (TA-P) are extracted from the image using MATLAB custom-written code. (B) Table summarizing the average values extracted for geometrical parameters defined in (A) plus the conic factors extracted from MRI images of lenses organ cultured in either AHH, AAH-High K+, or AAH + ouabain. Numbers in brackets represent the percent change in these parameters in relative to the AAH control group with statistical significance indicated (*P > 0.05). (C) The average values for these lens surface radii, conic factor and thicknesses listed in (B) have been used to draw representative profiles for lenses cultured in either AAH control, AAH-High K+, or AAH + ouabain.
Figure 2
 
Calculation of the lens T2 constant maps in organ-cultured bovine lenses. (A) A series of T2-weighted images collected from a single lens using varying echo time (TE) values shows that longer TE values produce lower T2 weighted signals from the inner regions of the lens. (B) An exponential curve (Equation 3) was fitted to the T2-weighted data series in order to calculate the T2 constant of a single pixel from a MRI image. (C) Maps of T2 constants calculated from lenses organ cultured in AAH, AAH-High K+, or AAH + ouabain. The numbers on the color bar represent T2 values in seconds. Axial (D) and equatorial (E) T2 value plots are extracted for all the conditions and superimposed.
Figure 2
 
Calculation of the lens T2 constant maps in organ-cultured bovine lenses. (A) A series of T2-weighted images collected from a single lens using varying echo time (TE) values shows that longer TE values produce lower T2 weighted signals from the inner regions of the lens. (B) An exponential curve (Equation 3) was fitted to the T2-weighted data series in order to calculate the T2 constant of a single pixel from a MRI image. (C) Maps of T2 constants calculated from lenses organ cultured in AAH, AAH-High K+, or AAH + ouabain. The numbers on the color bar represent T2 values in seconds. Axial (D) and equatorial (E) T2 value plots are extracted for all the conditions and superimposed.
Figure 3
 
Inhibition of lens physiology alters the GRIN in organ-cultured bovine lenses. (A) The T2 constant maps obtained for lens organ cultured in either AAH, AAH-High K+, and AAH + ouabain shown in Figure 2C have been converted using Equation 4 into color coded maps of refractive index (n) to visualize the GRIN. (B, C) Line profiles of refractive index extracted through the anterior (AP) and posterior (PP) poles (B) or equatorial (C) axis of lenses cultured in AAH (green), AAH-High K+ (red), or AAH + ouabain (blue) are plotted against the relative distance into the lens (r/a), where 0 and 1 represent the lens center and periphery, respectively. Arrows in (B) show that changes to the GRIN induced by inhibiting lens physiology are more apparent on the anterior side (blue arrow) of the lens rather than the posterior surface (purple arrow). (D, E) Comparison of regional differences in the average RI from the outer cortex (OC), inner cortex (IC), and nucleus (N) obtained from for the anterior (AP) and posterior (PP) poles (B) or equatorial (C) axes of lenses cultured in AAH (green), AAH-High K+ (red), or AAH + ouabain (blue). Brackets indicate the regions where a statistically significant difference (P < 0.01) between the RI of control lenses (AAH) and the two experimental groups (AAH-High K+ or AAH + ouabain) were obtained.
Figure 3
 
Inhibition of lens physiology alters the GRIN in organ-cultured bovine lenses. (A) The T2 constant maps obtained for lens organ cultured in either AAH, AAH-High K+, and AAH + ouabain shown in Figure 2C have been converted using Equation 4 into color coded maps of refractive index (n) to visualize the GRIN. (B, C) Line profiles of refractive index extracted through the anterior (AP) and posterior (PP) poles (B) or equatorial (C) axis of lenses cultured in AAH (green), AAH-High K+ (red), or AAH + ouabain (blue) are plotted against the relative distance into the lens (r/a), where 0 and 1 represent the lens center and periphery, respectively. Arrows in (B) show that changes to the GRIN induced by inhibiting lens physiology are more apparent on the anterior side (blue arrow) of the lens rather than the posterior surface (purple arrow). (D, E) Comparison of regional differences in the average RI from the outer cortex (OC), inner cortex (IC), and nucleus (N) obtained from for the anterior (AP) and posterior (PP) poles (B) or equatorial (C) axes of lenses cultured in AAH (green), AAH-High K+ (red), or AAH + ouabain (blue). Brackets indicate the regions where a statistically significant difference (P < 0.01) between the RI of control lenses (AAH) and the two experimental groups (AAH-High K+ or AAH + ouabain) were obtained.
Figure 4
 
Effect of ouabain on the water content of bovine lenses. Color maps of calculated T1 constants that are directly proportional to free water content, obtained from bovine lenses organ cultured in either AAH (A) or AAH + ouabain (B). (C) Line profiles of T1 values extracted through the equatorial axis of lenses cultured in AAH (green), AAH-High K+ (red), or AAH + ouabain (blue) plotted against the relative distance into the lens (r/a), where 0 and 1 represent the lens center and periphery, respectively. (D) Comparison of regional differences in the average T1 values from the outer cortex (OC), inner cortex (IC), and nucleus (N) extracted from the equatorial (C) axis of lenses cultured in either AAH, AAH-High K+, and AAH + ouabain. Brackets indicate the regions where a statistically significant difference (P < 0.01) between the average T1 values of control lenses (AAH) and the two experimental groups (AAH-High K+ or AAH + ouabain) were obtained.
Figure 4
 
Effect of ouabain on the water content of bovine lenses. Color maps of calculated T1 constants that are directly proportional to free water content, obtained from bovine lenses organ cultured in either AAH (A) or AAH + ouabain (B). (C) Line profiles of T1 values extracted through the equatorial axis of lenses cultured in AAH (green), AAH-High K+ (red), or AAH + ouabain (blue) plotted against the relative distance into the lens (r/a), where 0 and 1 represent the lens center and periphery, respectively. (D) Comparison of regional differences in the average T1 values from the outer cortex (OC), inner cortex (IC), and nucleus (N) extracted from the equatorial (C) axis of lenses cultured in either AAH, AAH-High K+, and AAH + ouabain. Brackets indicate the regions where a statistically significant difference (P < 0.01) between the average T1 values of control lenses (AAH) and the two experimental groups (AAH-High K+ or AAH + ouabain) were obtained.
Figure 5
 
Inhibition of lens physiology alters the optical properties of organ-cultured bovine lenses. The average geometric parameters (Fig. 2B) and the GRIN (Fig. 4) obtained from T2 imaging of bovine lenses cultured in either AAH, AAH-High K+, or AAH + ouabain we used by ZEMAX to calculate the optical power (A) and spherical aberration (B) of lenses in each condition. The relative contribution of the GRIN (light gray) to overall optical power and spherical aberration in lenses incubated under the different conditions was determined by re-solving the model in absence of a gradient in refractive index using a constant value for refractive index. *P < 0.01.
Figure 5
 
Inhibition of lens physiology alters the optical properties of organ-cultured bovine lenses. The average geometric parameters (Fig. 2B) and the GRIN (Fig. 4) obtained from T2 imaging of bovine lenses cultured in either AAH, AAH-High K+, or AAH + ouabain we used by ZEMAX to calculate the optical power (A) and spherical aberration (B) of lenses in each condition. The relative contribution of the GRIN (light gray) to overall optical power and spherical aberration in lenses incubated under the different conditions was determined by re-solving the model in absence of a gradient in refractive index using a constant value for refractive index. *P < 0.01.
Figure 6
 
Extraction of anatomical measures of the bovine eye for optical modeling. (A) A single T1-weighted MRI image splice from a 3D data set of the bovine eye showing the cornea (C) vitreous, (V), lens (L) and retina (R). (B) Same T1-weighted MRI dataset processed using MATLAB to allow accurate measurement of the 3D surfaces of the cornea, lens, and retina that shows the corneal thickness, (CT), corneal radius of curvature (CR), aqueous chamber thickness (AT), vitreous chamber thickness (VT), and retinal radius of curvature (RR). (C) Table showing the average values of the parameters defined above extracted from 10 bovine eyes. The values for the refractive index of the cornea, aqueous, and vitreous were obtained from the literature.66,67
Figure 6
 
Extraction of anatomical measures of the bovine eye for optical modeling. (A) A single T1-weighted MRI image splice from a 3D data set of the bovine eye showing the cornea (C) vitreous, (V), lens (L) and retina (R). (B) Same T1-weighted MRI dataset processed using MATLAB to allow accurate measurement of the 3D surfaces of the cornea, lens, and retina that shows the corneal thickness, (CT), corneal radius of curvature (CR), aqueous chamber thickness (AT), vitreous chamber thickness (VT), and retinal radius of curvature (RR). (C) Table showing the average values of the parameters defined above extracted from 10 bovine eyes. The values for the refractive index of the cornea, aqueous, and vitreous were obtained from the literature.66,67
Figure 7
 
Inhibition of lens physiology alters the optical properties of a model bovine eye. The average optical properties obtained for bovine lenses cultured in either AAH, AAH-High K+, or AAH + ouabain (Fig. 5) were implemented in a ZEMAX model of the bovine eye that used the geometrical parameters and refractive indices defined in Figure 6C to calculate the optimal focal length (A), and spherical aberration (B) of the bovine eye for each condition. (A) The optimal focal length is calculated using the “best focus” feature of the ZEMAX modeling platform which calculates for each lens dataset the ideal focal length of the model bovine eye. The dotted line represents the vitreous chamber thickness (VT), which acts as a reference for comparison of the in situ of focal length of the bovine eye to focal lengths calculated by the model eye. (B) Contribution of the cornea (positive) and lens (negative) to total spherical aberration of the bovine model eye. While the contribution of the cornea to total spherical aberration is constant, the negative contribution of the lens decreases in AAH-High K+ and AAH + ouabain, resulting in an overall increase in total positive spherical aberration. *P < 0.01.
Figure 7
 
Inhibition of lens physiology alters the optical properties of a model bovine eye. The average optical properties obtained for bovine lenses cultured in either AAH, AAH-High K+, or AAH + ouabain (Fig. 5) were implemented in a ZEMAX model of the bovine eye that used the geometrical parameters and refractive indices defined in Figure 6C to calculate the optimal focal length (A), and spherical aberration (B) of the bovine eye for each condition. (A) The optimal focal length is calculated using the “best focus” feature of the ZEMAX modeling platform which calculates for each lens dataset the ideal focal length of the model bovine eye. The dotted line represents the vitreous chamber thickness (VT), which acts as a reference for comparison of the in situ of focal length of the bovine eye to focal lengths calculated by the model eye. (B) Contribution of the cornea (positive) and lens (negative) to total spherical aberration of the bovine model eye. While the contribution of the cornea to total spherical aberration is constant, the negative contribution of the lens decreases in AAH-High K+ and AAH + ouabain, resulting in an overall increase in total positive spherical aberration. *P < 0.01.
Figure 8
 
Inhibition of lens physiology alters image quality of a model bovine eye. The ability of the model bovine eye to reproduce an input image of a young child was tested using the image simulation capability of ZEMAX. This analysis was performed using either the calculated optimal focal length for the model eye (A, C, E) or a fixed-focal length given by the vitreous chamber depth (B, D, F), which more closely represents the situation in the bovine eye. Images at the optimal and fixed focal lengths are shown for models in which the optical properties of the lens were extracted from lenses organ cultured in either AAH (A, B), AAH-High K+ (C, D), or AAH + ouabain (E, F). Used with permission from Singapore Laser Pte LTD.
Figure 8
 
Inhibition of lens physiology alters image quality of a model bovine eye. The ability of the model bovine eye to reproduce an input image of a young child was tested using the image simulation capability of ZEMAX. This analysis was performed using either the calculated optimal focal length for the model eye (A, C, E) or a fixed-focal length given by the vitreous chamber depth (B, D, F), which more closely represents the situation in the bovine eye. Images at the optimal and fixed focal lengths are shown for models in which the optical properties of the lens were extracted from lenses organ cultured in either AAH (A, B), AAH-High K+ (C, D), or AAH + ouabain (E, F). Used with permission from Singapore Laser Pte LTD.
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