Modal content of living human cone photoreceptors - OSA Publishing

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Y. Yang, J. Lee, K. Reichard, P. Ruffin, F. Liang, D. Ditto, and S. Z. Yin, ...... experimental 0.6° and 3° results (gray bars) with the predicted LP01 modes (solid ..... Electronic/machining support were provided by William Monette and Thomas.
Modal content of living human cone photoreceptors Zhuolin Liu,1,2,* Omer P. Kocaoglu,2 Timothy L. Turner,2 and Donald T. Miller1,2 1

Graduate Program in Vision Science, Indiana University, 800 East Atwater Avenue, Bloomington, IN 47405, USA 2 School of Optometry, Indiana University, 800 East Atwater Avenue, Bloomington, IN 47405, USA *[email protected]

Abstract Decades of experimental and theoretical investigations have established that photoreceptors capture light based on the principles of optical waveguiding. Yet considerable uncertainty remains, even for the most basic prediction as to whether photoreceptors support more than a single waveguide mode. To test for modal behavior in human cone photoreceptors in the near infrared, we took advantage of adaptive-optics optical coherence tomography (AO-OCT, λc = 785 nm) to noninvasively image in three dimensions the reflectance profile of cones. Modal content of reflections generated at the cone inner segment and outer segment junction (IS/OS) and cone outer segment tip (COST) was examined over a range of cone diameters in 1,802 cones from 0.6° to 10° retinal eccentricity. Second moment analysis in conjunction with theoretical predictions indicate cone IS and OS have optical properties consistent of waveguides, which depend on segment diameter and refractive index. Cone IS was found to support a single mode near the fovea (≤3°) and multiple modes further away (>4°). In contrast, no evidence of multiple modes was found in the cone OSs. The IS/OS and COST reflections share a common optical aperture, are most circular near the fovea, show no orientation preference, and are temporally stable. We tested mode predictions of a conventional step-index fiber model and found that in order to fit our AO-OCT results required a lower estimate of the IS refractive index and introduction of an IS focusing/tapering effect. © 2015 Optical Society of America OCIS codes: (010.1080) Active or adaptive optics; (110.4500) Optical coherence tomography; (330.5310) Vision - photoreceptors; (330.4300) Vision system - noninvasive assessment; (330.7331) Visual optics, receptor optics.

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Received 4 Dec 2014; revised 7 Aug 2015; accepted 12 Aug 2015; published 17 Aug 2015 1 Sep 2015 | Vol. 6, No. 9 | DOI:10.1364/BOE.6.003378 | BIOMEDICAL OPTICS EXPRESS 3378

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Received 4 Dec 2014; revised 7 Aug 2015; accepted 12 Aug 2015; published 17 Aug 2015 1 Sep 2015 | Vol. 6, No. 9 | DOI:10.1364/BOE.6.003378 | BIOMEDICAL OPTICS EXPRESS 3379

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1. Introduction Photoreceptor inner and outer segments (IS, OS) are highly evolved for capturing and guiding light. First discovered by Stiles and Crawford [1], this biological specialization is highly sensitive to the direction of the rays entering and exiting the photoreceptor. The process has been extensively studied experimentally both psychophysically and in reflection, the former coined the Stiles‐Crawford effect (SCE) and the latter the optical SCE [2–11]. As normal photoreceptor directionality requires normal morphology, the SCE and optical SCE are of significant clinical interest. The directional properties have been used in preliminary studies to indicate the stage and degree of various retinal abnormalities as listed in Gao, et al. [7]. Parallel to these experimental measures of photoreceptor directionality, extensive theory has been developed for modeling light propagation in photoreceptors based on the principles of optical waveguides, i.e., tiny optical fibers or light pipes [12–18]. These elegant models predict not only the directional sensitivity, but also the existence of so‐called optical modes, which represent the spatial distribution of the light energy as it propagates through the photoreceptor. This modal representation provides a more fundamental descriptor of the photoreceptor’s ability to capture light than directionality with the number of modes depending crucially on the physical properties of the photoreceptor IS and OS. The modes exquisite sensitivity to the photoreceptor properties has led to considerable interest in their use to define visual performance at the photoreceptor level and to detect perturbations in the photoreceptor properties associated with pathology. Unfortunately, theoretical models have remained largely abstractions, owing in part to the lack of experimental tests of their predictions [8] and their exquisite sensitivity to refractive index [12]. Even though multimode behavior was reported many decades ago in animal models in postmortem [19], only recent evidence has suggested similar behavior might also occur in human photoreceptors [20–23]. Human evidence was obtained using adaptive optics (AO) ophthalmic methods that provide

#229071 (C) 2015 OSA

Received 4 Dec 2014; revised 7 Aug 2015; accepted 12 Aug 2015; published 17 Aug 2015 1 Sep 2015 | Vol. 6, No. 9 | DOI:10.1364/BOE.6.003378 | BIOMEDICAL OPTICS EXPRESS 3380

sub-cellular imaging of the retina. Even with these latest findings, however, uncertainty surrounds even the most basic question as to whether cone photoreceptor segments support just one mode (single mode behavior) or more than one mode (multimode behavior). In this paper, we take advantage of the micron-level 3D resolution afforded by AO and optical coherence tomography (OCT) to probe the waveguide properties of cone photoreceptors in the living human eye. To do this, we illuminate cones through a large pupil at the eye (6.7 mm) and collect the reflected cone signal through the same large pupil. In this way the cone numerical aperture (NA), which is narrower than the Stiles-Crawford effect [3], is overfilled thereby increasing the likelihood to excite waveguided modes, and to detect modes owing to the increased lateral resolution. Note that this approach is limited to measuring the mode profile only after exiting the cone segments in reflection, a process that is influenced by both forward and backward propagation of the modes and optical properties of the reflective site in the segments. This constraint is not unique to this study, however, as photoreceptors are most commonly studied in reflection, and commercial optical fibers are sometimes assessed in a similar manner. Our AO-OCT experiment was designed to test two hypotheses. One, cone IS and OS have optical properties consistent of waveguides, which depend on segment diameter and refractive index. Two, cone IS and OS support different optical modes. We tested both by taking advantage of the monotonic increase in cone diameter with retinal eccentricity and by imaging at the focal plane that gave best cone image quality. We compared these experimental findings to theoretical predictions of cone modes using a step-index optical fiber model of the cone. Discrepancies between prediction and measurement motivated us to improve the model, and this involved the test of two additional hypotheses in the Discussion section. Note that an early derivation of this work has been published in a conference proceeding [24]. 2. Methods Methods is divided in five sections. Section 2.1 describes the Indiana AO-OCT system used in this study to image cone photoreceptors. Section 2.2 presents the experimental protocol for acquiring cone images over a range of retinal eccentricities in two normal subjects. Data processing of the cone images and second moment analysis of modal content are described in section 2.3 and 2.4, respectively. Section 2.5 presents a theoretical model to predict waveguide modes of cones and to which the second moment analysis was applied. 2.1. AO-OCT imaging system A detailed description of the AO-OCT system can be found in Liu, et al. [22]. Important to this study was the superluminescent diode (SLD) (BLM-S-785, Superlum, Ireland) with central wavelength at λc = 785 nm and bandwidth of Δλ = 47 nm that was used for both OCT imaging and wavefront sensing. The source provided a nominal axial resolution in retinal tissue (n = 1.38) of 4.2 μm. The detection channel of the SD-OCT system was designed around a Basler Sprint camera (SPL4096-140km, Exton, PA, USA) whose line rate was maximized for the source spectral bandwidth, in this case achieving an A-line rate of 250 KHz using the central 832 pixels. Empirically we found this speed a reasonable compromise for cone imaging. The axial resolution and signal-to-noise were sufficient for individuating and detecting the three primary reflections of cone photoreceptors (external limiting membrane (ELM), inner segment and outer segment junction (IS/OS), and cone outer segment tip (COST)), which was a key requirement of the study. The high acquisition speed (250 KHz) reduced eye motion artifacts, minimizing motion-induced degradation of cone spatial content. New to this study, accuracy and speed of centroiding the Shack-Hartmann wavefront sensor (SHWS) spots were improved. To do this, we developed an adaptive algorithm with windowing based on that of Yin, et al. [25]. Our method accounted for spot brightness and

#229071 (C) 2015 OSA

Received 4 Dec 2014; revised 7 Aug 2015; accepted 12 Aug 2015; published 17 Aug 2015 1 Sep 2015 | Vol. 6, No. 9 | DOI:10.1364/BOE.6.003378 | BIOMEDICAL OPTICS EXPRESS 3381

operated on a reduced search box centered on the brightest pixel. For faster execution, the C + + code was converted to MATLAB Executable file (MEX) and called directly by Matlab. 2.2 Experiment Two normal subjects free of ocular disease were recruited for the study. All procedures on the subjects adhered to the tenets of Helsinki declaration and approved by the Institutional Review Board of Indiana University. Written informed consent was obtained after the nature and possible risks of the study were explained. Both subjects had best corrected visual acuity of 20/20 or better. Age, spherical-equivalent refractive error, and axial length were 36 and 47 years; −3 and −2.5 D; and 26.07 and 25.4 mm. Eye length was measured with the IOLMaster® (Zeiss, Oberkochen, Germany). Maximum power delivered to the eye was 350 µW, measured at the cornea and within safe limits established by ANSI [26]. The right eye was cyclopleged and dilated with one drop of Tropicamide 0.5% for imaging and maintained with an additional drop every hour thereafter. The eye and head were aligned and stabilized using a bite bar mounted to a motorized XYZ translation stage. Because cone image quality is sensitive to system focus, it was critical to find the focal plane that provided best cone quality at each retinal location imaged. To achieve this, we systematically focused the AO-OCT system over a narrow range, from approximately −0.15 diopters (D) to + 0.2 D relative to the zero focus reported by SHWS after the AO converged to a stable correction. Step size was 0.025 D, equivalent to just 9 µm (using conversion of 1 D = 370 µm) in retinal depth and realized by adding desired amount of defocus to SHWS reference. The 0.35 D (~130 µm in retinal depth) range was large enough to traverse the plane of best cone quality, defined as the plane that maximized power at the cone fundamental frequency, i.e., produced maximum cone contrast. Optimizing cone image quality in this way avoided potential subjective biases and facilitated consistent comparison across retinal locations. At each focus step, ten 0.5° × 0.5° volumes were acquired in 2.3 seconds. Dense Ascan sampling (0.6 μm/pix in both lateral dimensions across the retina) assured spatial mode detail in the cone image was not sampling limited by the AO-OCT. A fast B-scan rate of 1,042 Hz reduced eye motion artifacts. Volumes were acquired at 4.3 Hz and at eight retinal locations (0.6°, 2°, 3°, 4°, 5.5°, 7°, 8.5°, and 10°) temporal to the fovea, a range over which the cone IS and OS diameters increase monotonically with retinal eccentricity (see Fig. 1(b)). As a further step to minimize image quality variations that might mask mode appearance, volumes were excluded whose AO correction as reported by the SHWS was not diffraction limited (>0.07 waves RMS). Important for the analysis of cone images, we confirmed the image aspect ratio was unity for the lateral (XY) dimensions of the AO-OCT volumes. This was realized using a model eye and a calibrated grid target as retina. 2.3 Image preparation and Fourier analysis Software tools for image processing and analysis of the AO-OCT volumes were developed in MATLAB and ImageJ (Java plugins) [27]. To start, axial eye motion was removed from each AO-OCT volume by axially registering fast B-scans using a custom ImageJ plugin based on dynamic programming [28] in which fast OCT B-scans were shifted axially in order to align IS/OS in the slow B-scan projection view. Next the bright reflectance bands corresponding to IS/OS and COST layers were segmented and projected in en face to create 2D areal images of the cone mosaic at both depths [28]. Power spectra of the IS/OS and COST en face images were computed by Fourier transformation from which circumferential averages were determined and DC normalized. Averaging of power spectra from different AO-OCT volumes (typically ~5) acquired at the same focus and retinal location improved signal to noise. Best focus for cone imaging was determined by finding the circumferential-averaged power spectrum with maximum energy at the cone fundamental frequency. Noise was

#229071 (C) 2015 OSA

Received 4 Dec 2014; revised 7 Aug 2015; accepted 12 Aug 2015; published 17 Aug 2015 1 Sep 2015 | Vol. 6, No. 9 | DOI:10.1364/BOE.6.003378 | BIOMEDICAL OPTICS EXPRESS 3382

reduced by averaging the five pixels that covered the cone spectral peak. All further analysis of the AO-OCT images were limited to those acquired at this plane of best focus. For each cone mosaic image, 50 to 100 cones were selected manually. Selection criteria was clear visibility of the cone at both IS/OS and COST layers, absence of vasculature shadows and motion artifacts, and a spatial distribution of cones that roughly covered the full AO-OCT image. Selected cones were extracted from the IS/OS and COST layers by cropping a square region centered on the cone, large enough to encompass the cone reflection, but small enough to avoid adjacent cones. For retinal eccentricities where cones are densely packed (0.6° and 2°), we found an additional circular binary mask, of same diameter as the selected square region, was necessary to remove adjacent cones that sometimes appeared in the corners of the square. Note that the XY coordinate of the selected region for a given cone was the same for both the cone’s IS/OS and COST reflections as these two reflections share the same set of AO-OCT A-lines. Selected region size was fixed for all cones at the same retinal eccentricity, but adjusted over eccentricities to account for varying cone diameter. Finally, selected regions were visually examined to assure only one cone per region. The number of cones selected (50 to 100) depended on retinal eccentricity. Close to the fovea, it was easy to find more than 100 cones that met our criteria, owing to the high cone density and limited retinal vasculature there. Here we were less concerned about cone selection as the cones were uniform in appearance. In contrast in the peripheral retina, for example 10° from fovea, number of cones selected approached 50. Reduced cone density accompanied with increased retinal vasculature were primary contributing factors. Note that to avoid possible cone distortion created by the flyback of the fast-axis scanner, cones were selected from a narrower 0.3° × 0.5° image section. 2.4 Second moment analysis for quantifying modal content Moment theory has been extensively used to describe quantitatively the features of images [29]. Here we apply the second moment to characterize the lateral spatial distribution of the cone intensity pattern, i.e., mode profile. The distinguishing features of this method compared to others already in the literature are discussed in Section 4.2. In general form, the second moment is expressed as

μ pq

  (x − x) ( y − y) =   I (x , y ) n

m

i =1

j =1

p

i

q

j

n

i =1

I ( xi , y j )

m

j =1

i

(1)

,

j

where p and q are integers and constrained by the condition p + q = 2. xi and yj are the pixel coordinates in the cone image, I(xi,yj) is the corresponding pixel intensity, and n and m are the pixel dimensions in x and y directions. x and y are the centroids of cone image and given by

  x=   n

m

i =1 n

j =1 i m

i =1

x I ( xi , y j ) I ( xi , y j )

j =1

  , and y =   n

m

i =1 n

j =1 i m

i =1

y I ( xi , y j ) I ( xi , y j )

.

(2)

j =1

The covariance matrix of I(x,y) contains the three second moment terms and is given as

μ C = cov ( I ( x, y ) ) =  20  μ11

μ11  , μ02 

(3)

where the central moments µ20 and µ02 give the variance about the cone centroid, and the covariance µ11 characterizes the orientation of the cone image. Next eigenvectors (V) and eigenvalues (Λ) were computed for the covariance matrix,

#229071 (C) 2015 OSA

Received 4 Dec 2014; revised 7 Aug 2015; accepted 12 Aug 2015; published 17 Aug 2015 1 Sep 2015 | Vol. 6, No. 9 | DOI:10.1364/BOE.6.003378 | BIOMEDICAL OPTICS EXPRESS 3383

[V , Λ ] = eigen[C ],

(4)

and from which were derived minor (a) and major (b) principal axes: a = 2 × Λ1 , b = 2 × Λ 2 (Λ1 < Λ 2 )

(5)

and the orientation of the equivalent ellipse:

θ = angle(b, x).

(0° < q ≤ 180°)

(6)

where θ is defined as the angle between b and a reference axis (x), which we chose here as the horizontal meridian of the eye (x-axis of image). Of importance here is that the two principal axes correspond to the minimum and maximum second moments of an equivalent ellipse that is of uniform intensity and has the same centroid and total energy as I(x,y) [29]. Thus in this way, the complicated reflectance distribution of a cone is simplified to three parameters that define an ellipse: size (s), circularity (c), and orientation (θ). The size, s = a 2 + b 2 , represents the second moment value of the equivalent ellipse and corresponds to the overall cone spatial extent. For cones that are circular or nearly circular, the effective diameter of the cone mode is approximately equal to 2 times the second moment value, a relation we take advantage of in the Discussion section to compare results. Circularity (c) differentiates cones based on mode shape and is defined as the ratio of the minor to major principal axes, a/b, of the equivalent ellipse. It reflects the overall roundness of the cone shape, 1 being perfectly circular and 0 perfectly flat (extreme ellipse). Orientation (θ) differentiates non-circular cone modes based on mode angular orientation. Prior to computing the second moment of cones in the AO-OCT en face images, we found it necessary to remove the noise floor that surrounded each cone. This was realized with an adaptive threshold in which pixels with an intensity value below 30% of the cone peak were removed. 30% was found empirically a good compromise between removing the noise floor and preserving the cone signal, but other comparable proportions were equally effective and yielded similar second moments. As additional analysis to quantify cone modal behavior, we computed average and variance cone maps at each retinal eccentricity. This was accomplished by normalizing the peak reflectance of the selected 50 to 100 cones, rotating the major axes of the cones around their centroids ( x and y ) so that they co-align (i.e., made θ zero), registering the cones to each other, and finally taking the average and variance of the cones. Second moment analysis was then re-applied to the averaged cone, but limited to the second moment, s, and circularity, c. 2.5 Evaluation of second moment analysis using cone optical model To evaluate our second moment analysis for distinguishing cone mode behavior, we modeled the waveguide properties of cones and then applied the second moment analysis to the predicted mode pattern. Here we chose a simplistic cone model consisting of cylindrical IS and OS of diameters di and do, and homogeneous refractive indices ni and no as shown in Fig. 1(a). The surrounding medium has a refractive index, ns. While more complex models are possible, simple models such as the one chosen here are widely used and believed to capture the waveguide properties of cones. Furthermore, uncertainties in the cone physical parameters that all models require irrespective of their complexity remain a major point of debate, one that is addressed in the Discussion section by taking account of our AO-OCT findings. For the three refractive indices in our cone model, we used ni = 1.353 [12, 14], no = 1.419, and ns = 1.347 [13]. We would have liked to use no (1.430) and ns (1.340) from [12, 14], but these yielded model predictions further from our AO-OCT measurements. Despite this, it is important to note these indices from the literature were obtained for visible wavelengths and

#229071 (C) 2015 OSA

Received 4 Dec 2014; revised 7 Aug 2015; accepted 12 Aug 2015; published 17 Aug 2015 1 Sep 2015 | Vol. 6, No. 9 | DOI:10.1364/BOE.6.003378 | BIOMEDICAL OPTICS EXPRESS 3384

in postmortem animal tissue, sometimes in conjunction with optical theory to extrapolate to human. Thus the effect of dispersion at the longer wavelength of our AO-OCT system (785 nm) and imaging in living human tissue are important factors that could outweigh differences between the reported numbers themselves. From 0.6° to 10° retinal eccentricity, IS diameter increased monotonically from 3.2 to 7.5 µm as measured by Curcio, et al. at the ELM [30]. OS diameter also increased monotonically, but noticeably less so, increasing from 1.5 to 2.2 µm as reported in Banks, et al. [31], which are consistent with Hoang, et al. [32]. We chose the former owing to their denser sampling of measurements across the macula. Figure 1(b) shows the IS and OS diameters as a function of retinal eccentricity along with the corresponding mode cutoff frequency (V number). The intensity profile of LP modes for the cone IS and OS was computed by simulating wave propagation in the cone model. This was realized using commercial software COMSOL Multiphysics with the Wave Optics Module add-on (COMSOL, Burlington, MA) that is widely used for electromagnetic simulation in linear and nonlinear optical media, such as optical fiber. To simplify the optical waveguide model, we considered only the waveguide property of a single cone and thus no waveguide interaction with adjacent cones was considered. The predicted complex field distribution across the cone diameter was then exported from COMSOL, convolved with the diffraction-limited coherent point spread function of the human eye for a 6.7 mm pupil, converted to intensity by taking the modulus squared, and finally resampled to that of the AO-OCT data (0.6 μm/px). The convolution and resampling steps were added to more accurately emulate cone imaging with the AO-OCT system and to facilitate comparison with the experiment results. Finally, second moment analysis was applied to the cone intensity distribution predicted for cones between 0.6° to 10° retinal eccentricity. Note that for both experiment and theory, we did not consider the polarization state of the imaging light nor the effect cones may have on it. While such knowledge is necessary to differentiate polarization degenerate states of the LP mode indices (e.g., degenerate states within each LP11, LP21, etc.), it is unnecessary to differentiate between the LP mode indices themselves and for that matter between single mode and multiple modes, a main objective of our study. Cone

10

Diameter: di,o (μm)

di

IS/OS

8

IS OS

8

V number

ELM

6

3.832 (LP21,02)

4

2.405 (LP11)

2 0 COST (a)

2

4 6 8 Ret. Ecc. (deg) (b)

10

0 0 (LP ) 01

Fig. 1. Cone model. (a) Simplistic cone model composed of two cylinders, IS and OS, of homogeneous refractive index and surrounded by interphotoreceptor matrix. (b) Cone segment diameters (solid curves) [30, 31] and theoretical V numbers (dashed curves) increase monotonically as function of retinal eccentricity for IS (red) and OS (blue). V number was calculated from V =

π d i ,o λ

ni , o − n s , where di,o is the cone IS or OS diameter, ni,o is the 2

2

refractive index of IS or OS, ns is the refractive index of interphotoreceptor matrix, and λ is the wavelength, 785 nm for this study. V number predicts the mode cutoff frequencies of the cone model, as for example when V