Open Access
Add to BibSonomy
Abstract
We acquired 1325 nm OCT images of the sclera and ciliary muscle of human subjects. The attenuation coefficients of the sclera and ciliary muscle were determined from a curve fit of the average intensity profile of about 100 A-lines in a region of interest after correction for the effect of beam geometry, using a single scattering model. The average scleral attenuation coefficient was 4.13 ± 1.42 mm-1 with an age-related decrease that was near the threshold for statistical significance (p = 0.053). The average ciliary muscle attenuation coefficient was 1.72 ± 0.88 mm-1, but this value may be an underestimation due to contributions from multiple scattering. Overall, the results suggest that inter-individual variations in scleral attenuation contribute to variability in the quality of transscleral OCT images of the ciliary muscle and the outcome of transscleral laser therapies.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
During accommodation in the human eye, contraction of the ciliary muscle produces changes in the lens shape that allow the eye to change focus. The ability of the eye to accommodate progressively decreases with age, eventually leading to presbyopia, the loss of near visual function. There is evidence that changes in ciliary muscle morphology may be a factor in presbyopia [1–3]. Despite its critical role in both accommodation and presbyopia, there have been few studies characterizing the response of the ciliary muscle in vivo. Images of the ciliary muscle have been acquired using ultrasound [4–6], MRI [7–9] and more recently OCT [10–16]. Compared to ultrasound and MRI, OCT has the advantage of providing both high speed and high-resolution images without requiring contact with the eye. A limitation of OCT imaging is that optical attenuation by the sclera and ciliary body reduces image contrast and limits the imaging depth. In many subjects, it is difficult to detect the inner boundary of the ciliary structures in the region of the ciliary body apex [11,17,18]. Yet, this region is of particular interest since the displacement of the ciliary body apex is directly correlated to the forces that produce the change in lens shape.
The ciliary body cannot be imaged using the standard OCT beam delivery because of its peripheral location posterior to the iris. Instead, images of the ciliary body must be acquired through the sclera (transscleral imaging). OCT images of the ciliary muscle are generally acquired at 1300 nm due to the increased penetration in the sclera and the ciliary muscle compared to shorter wavelengths [12,16,19]. At shorter wavelengths there is an increase in scattering and absorption. Before reaching the apex of the ciliary body the OCT beam is transmitted through the entire thickness of the sclera and ciliary body. As the beam is transmitted through the sclera and the ciliary body it is attenuated primarily due to scattering by the tissue matrix but also due to absorption by water, blood and pigments. Attenuation causes a loss of signal which reduces image contrast and in turn increases the uncertainty of thickness measurements which are used to quantify the response of the ciliary muscle accommodation. In addition, there is a large variability in image quality of OCT images of the ciliary body across individuals [11,18], which may be due to differences in thickness, pigmentation, vascularity and structure of the sclera and ciliary muscle. Knowledge of the scleral and ciliary muscle attenuation coefficients and their variability across subjects will help better understand the factors that contribute to signal loss during ciliary body imaging with OCT and may inform beam delivery design to optimize image quality. This knowledge is also critical to understand potential inter-individual variations in treatment outcomes of both transscleral and transpupillary laser therapies of ciliary structures such as transscleral cyclophotocoagulation [20,21].
To the best of our knowledge, the only published data regarding the attenuation coefficient of the ciliary body has been acquired on excised tissue from rabbit eyes [22]. There have been a number of studies that have quantified the optical properties of the sclera in vitro on dissected scleral tissue samples [22–28]. However, measurements on scleral tissue samples dissected from cadaver eyes may not be representative of the native physiological state. Changes in hydration, blood flow, temperature and mechanical stresses for instance can have significant effects on the measured optical properties [24,29]. A prior study on four subjects using polarization sensitive OCT (PS-OCT) shows the feasibility of using OCT intensity profiles to quantify the depth-dependent attenuation in the sclera [30]. However, this prior study did not isolate the contribution of the tissue to the measured attenuation. Accurate computation of tissue attenuation coefficients from OCT images requires correction for the contribution of sensitivity fall-off and the effects of beam geometry to the depth-dependence of the OCT signal [31–33].
The goal of the present study was to acquire measurements of the attenuation coefficient of the sclera and ciliary body in vivo at 1325 nm from transscleral OCT images, and to investigate their interindividual variability.
2. Methods
2.1 Study design
Following an Institutional Review Board approved protocol, 45 subjects, ranging in age from 16 to 79 years old, were enrolled in the study. All subjects provided written informed consent. The imaging sessions were part of a larger study that also involved imaging of the anterior segment and the retina. For these reasons, the exclusion criteria were a history of prior ocular surgery, macular degeneration or macular edema, previous corneal surgery including PRK/LASIK, amblyopia, corneal edema, or strabismus, corneal endothelial disease, glaucoma, and previous retinal detachment. OCT images of the sclera and ciliary muscle were acquired in the unaccommodated state in the temporal region of the left eye of each participant. The boundaries of the sclera and ciliary muscle in each OCT image were identified by visual inspection and a rectangular region of interest (ROI) was defined in the sclera and in the ciliary body. The average depth-dependent intensity profile in each region of interest was calculated. The attenuation coefficients of the sclera and ciliary muscle were calculated from a curve fit of these average intensity profiles after removal of outliers and correction for beam geometry, assuming a single-scattering model [31,32].
2.2 OCT imaging system
Images of the sclera and ciliary body were acquired using a commercial research-grade Spectral-Domain OCT system (Thorlabs Telesto, Newton, NJ) operating at a central wavelength of 1325 nm (Fig. 1). The system has a lateral resolution of about 15 μm, an axial resolution of about 7.5 µm (in air) over an axial range of 2.5 mm, with a depth of focus (twice the Rayleigh range) of 0.21 mm in air (0.29 mm in tissue) and is operated at a fixed imaging rate of 28,000 A-lines/s. The system has a sensitivity roll-off of 4 dB from 10 to 90% of the imaging range. The beam focus in air was measured to be located at a distance of 0.65 mm from the zero-delay position. That is, the boundary of a sample imaged in air at the position of the beam focus will be located at an image depth zf-air=0.65 mm. The power incident on the sclera was approximately 3mW. Each image was a B-scan with a lateral scan length of 10.5 mm consisting of 897 A-lines. The system is integrated into a platform for accommodation biometry that enables simultaneous synchronized imaging of the lens and ciliary muscle in real-time during accommodation, using two separate OCT systems. A detailed description of the accommodation biometry design has been published previously [10]. In short, the beam delivery unit of the transscleral OCT system was mounted on a custom-built mechanical platform that enables precise positioning and alignment while the subject fixates on a custom-built fixation target. The platform is mounted on an adjustable slit-lamp table with a head and chin rest.
Fig. 1. Optical Coherence Tomography imaging system used to acquire images of the ciliary muscle. The system operated at 1325 nm with a speed of 28,000 A-lines/s and contains an axial resolution of approximately 7.5 µm in air and a scan depth of 2.5 mm in air.
2.3 Imaging protocol
The imaging sessions start by having the subject sit in front of the slit-lamp table and place his or her head on the headrest. The subject is asked to maintain fixation on the target while the target is manually adjusted to the subject’s far point. The system is aligned so that the optical axis of the eye is aligned with the fixation target. This alignment is achieved by visualizing real-time images of the anterior segment. The alignment of the system is adjusted manually until the corneal reflex is approximately centered in the pupil and the iris plane and lens appear horizontal on the images. The position of the ciliary muscle OCT system was then adjusted until the apex of the ciliary body was seen in real-time images. Once the system was aligned, the subject was asked to keep their eyes still and fixated on the distant target. The recording was then started. A time sequence of two-dimensional images was acquired for each subject at 31 frames per second, with a total image recording time of 5.1s. Even though a total of 160 images was recorded, only the first image of the time sequence was used in this study, except for the evaluation of repeatability.
2.4 Image post-processing and data analysis
2.4.1 Identification of ROIs
A computer program was developed in-house using MATLAB (The Mathworks, Inc. R2020a, Version 9.8.0.1396136) to process the transscleral OCT images from raw data and calculate the attenuation coefficient. The program enabled a user to manually select a rectangular region of interest (ROI). First, the first image of the 160 images set is loaded, and the user is asked to manually click on the ciliary body apex, creating a line. The A-line passing through the apex defines the vertical boundary of the ROI on the right side of the image (Fig. 2). The program automatically selects the vertical boundary on the temporal side to create ROIs with 100 A-lines (width of 0.35 mm). Once the vertical boundaries are defined, the user clicks on four points along the air-tissue boundary that are contained within the lateral bounds of the ROIs. The depth of the air-tissue boundary is taken to be the average depth coordinate of these four points. In one image, the air-tissue boundary was outside the image range within the lateral bounds of the ROI. In this subject we estimated the position of the boundary by extrapolation from the regions located temporally from the ROI, producing value of -0.12 mm. The average depth of the air-tissue boundary was 0.23 +/- 0.11 mm. For measurements of the scleral attenuation coefficient, the user is then instructed to click on the boundary between the sclera and episclera. The depth coordinate of this point represents the upper horizontal boundary of the scleral ROI. Next, the user is asked to click on the boundary between the ciliary muscle and the sclera near the A-line passing through the ciliary muscle apex. Due to the curved shape of the boundaries, to produce a rectangular region of interest, the user is instructed to click slightly above the boundary when measuring the scleral attenuation coefficient. When measuring the ciliary muscle, the user is instructed to click slightly below the boundary. The depth coordinate of this point defines the inner horizontal boundary of the ROI when measuring the sclera and the outer horizontal boundary of the ROI when measuring the ciliary muscle. The user is then instructed to click a point of the ciliary body in the vicinity of the right-hand boundary of the ROI at a depth close to the depth of the iris root. The depth coordinate of this point represents the inner horizontal boundary of the ciliary muscle ROI. The program then automatically caps the depth of inner boundary of the ciliary muscle ROI to 1.8 mm to minimize potential effects of multiple scattering (see section D4). The depth coordinates of the ROIs for each subject are shown in Fig. 3. The ROI covered an average axial depth range of 0.44 ± 0.08 mm for the sclera and 0.34 ± 0.08 mm for the ciliary muscle, in optical depth units.
Fig. 2. Image analysis steps to select the ROI. A) Selection of vertical boundary passing through ciliary muscle apex and automatic generated boundary 100 a-lines from first selection. B) Air-tissue boundary selection. C-D) Selection of the sclera ROI. E-F) Selection of the ciliary muscle ROI. The shaded squares show ROI of respective regions. The vertical and horizontal line appear after the user clicks. The depth of the inner boundary of the ciliary muscle ROI is capped at 1.8mm.
Fig. 3. Axial position in optical depth units of the air tissue boundary, ROI boundaries and beam focus. The solid horizonal line correspond to the average values: air-tissue: mean = 0.23 mm, min = -0.12 mm, max = 0.40 mm; episclera-sclera: mean = 0.71 mm, min = 0.45 mm, max = 0.90 mm; beam focus: mean = 1.06 mm, min = 0.89 mm, max = 1.34 mm; sclera-ciliary muscle: mean = 1.14 mm, min = 0.91 mm, max = 1.30 mm; ciliary muscle- sclera: mean = 1.32 mm, min = 1.06 mm, max = 1.55 mm; end of the ciliary muscle: mean = 1.66 mm, min = 1.42 mm, max = 1.80 mm. The air-tissue boundary was outside the image range (negative value) for one subject. For this subject the boundary position was estimated by extrapolation.
2.4.2 Calculation of the focus position
For all subjects, the depth of the air-tissue boundary was less than the focus position in air (zf-air = 0.65 mm). Therefore, in all subjects, the OCT beam focus was located within the tissue. Taking into account the focus shift due to refraction at the air-tissue boundary, the depth coordinate of the beam focus in the image calculated in paraxial approximation is:
where z0 is the position of the air tissue boundary and 1.40 is the estimated group refractive index of the sclera at 1325 nm. Since the sclera and cornea have approximately the same composition, the scleral group refractive index was estimated using the value of the corneal group refractive index at 800nm [34] and the dispersion of water [35,36]. An error analysis shows that within our range of values of zf-air- z0, an error of 0.01 in the group refractive index produces an error of less than 0.01 mm in the estimate of the focus depth. The depth coordinates of the air-tissue boundary for each subject relative to the position of the ROIs is shown in Fig. 3, in optical depth units. With zf-air = 0.65mm, the optical depth of the beam focus in the image, z0 + 1.40 × 1.40 × (zf-air-z0), was 1.06 ± 0.01 mm, with a range from 0.89 mm to 1.34 mm. On average, these depths are slightly anterior to the position of the sclera-ciliary muscle boundary (See also Fig. 3).2.4.3 Correction for the effect of beam geometry and sensitivity roll-off
The raw depth-dependent intensity profile includes the contribution of the sensitivity roll-off and beam geometry [33,37]. These contributions must be taken into account in the analysis to produce accurate estimate of the attenuation coefficient. Assuming a single scattering model, the recorded signal can be written [31,33]:
The specified sensitivity roll-off in our system is 4 dB from 10-90% of the 2.5 mm imaging range. The 4 dB value is close to the value predicted obtained assuming that the fall-off is due primarily to the decrease in sampling rate of the interference fringes with depth. We therefore modeled the sensitivity fall off using the equation [39,40]:
where z is the imaging depth and zmax=2.5 mm is the maximum image depth.To isolate the effects of attenuation, we first subtracted from the signal (in dB units) the contribution of the sensitivity roll-off over the entire imaging depth. We then subtracted contribution of the confocal point spread-function for depth ranging from the air-tissue boundary to the end of the imaging range. For this correction, we used the individual value of zf obtained for each subject and the specified value of the Rayleigh range in air: zr=0.105 mm. (Fig. 3).
2.4.4 Evaluation of the correction method
To confirm experimentally the validity of the correction method we imaged solutions of Intralipid 20% (Millipore Sigma, I141-100ML) diluted with distilled water at concentrations of 1%, 2%, 4%, 8%, 16%, 32% and 64%. The solutions were poured in a circular glass Petri dish with diameter 10 cm. The Petri dish was filled with approximately 50 ml of solution and was left uncovered. The OCT delivery probe was mounted above the dish on a linear translation stage with 0.001” (0.0254 mm) resolution. To avoid saturation due to the strong reflection at the air-Intralipid boundary, the probe was tilted slightly in the direction perpendicular to the scan, by 4.7°, corresponding to an inclination of 3.5° of the beam in the solution. Images were acquired for 6 positions of the probe corresponding to 6 different positions of the beam focus. For the first image, the position of the probe was adjusted until the air-Intralipid boundary was located near the top of the image (at approximately 0.05 mm depth). The distance between the probe and Intralipid solution was then increased in 0.01” (0.254 mm) increments between successive images. The focus position was calculated using Eq. (1) assuming a group refractive index of 1.35 for intralipid at 1325nm [41] . Two of the measurements were found to produce a focus position (zf = 0.94 mm and zf = 1.14 mm in optical depth units) that approximately corresponds to the range of the focus positions in our human imaging experiments (0.89 to 1.34 mm, Fig. 3). Data obtained for these two positions were analyzed.
Results of these validation experiments are shown in Fig. 4, for concentrations of 1%, 4%, 8%, 16%, 32% and 64%. As a first step, to verify the values of zf and zr, the intensity profiles were fit with Eq. (2) using MATLAB curve fitting tool. The noise (N(z)) was assumed to be independent of depth and the roll-off (h(z), Eq. (3)) was subtracted from the intensity profiles before performing the fit. The values of zf and, zr obtained from the fit were compared with the value of zf predicted from Eq. (1) and the nominal value of the Rayleigh range in air (Fig. 5). The focus position determined from the fit was in very close agreement (within ± 0.05 mm) of the values determined using Eq. (1), except for the 64% solution. This finding confirms the validity of Eq. (1) for the estimation of the focus position in the sample. The Rayleigh range predicted from the fit was also in close agreement with the nominal value (within ± 0.008 mm), except for the 32% and 64% solutions. The larger error at the two higher concentrations is expected, since the peak caused by the beam focus becomes less pronounced as the attenuation increases and the effective Rayleigh range is expected to increase as the scattering coefficient increases [33,38]. In turn, this increases the uncertainty of the fitting parameters corresponding to the beam geometry.
Fig. 4. Focus position and Rayleigh range obtained from the fit compared to the nominal values (zr = 0.105 mm, zf = 1.14 mm at z0 = 0.05 mm, zf = 0.94 mm at z0 = 0.3 mm). The prediction error is higher for the 32% and 64% concentrations, where the relative effect of the focused beam geometry becomes less pronounced and the fit uncertainty increases. For clarity, the value of zr at 64% for z0=0.05 mm (zr=20.5 mm) is not shown.
Fig. 5. Intensity profiles recorded in a 1%, 4%, 8% 16%, 32% and 64% solution Intralipid 20% at two different focus positions approximately covering the range of focus in the transscleral imaging experiments. The profiles start at the air-IL boundary. The noise floor is 34dB. The solid lines are the curve fits of the intensity profiles using Eq. (2), assuming a single scattering model. For concentrations up to 32%, the fits closely match the experimental profiles for depths up to approximately 1.8mm.
The Intralipid experiments also show that the intensity profiles recorded in Intralipid taper off at a given depth that decreases as the Intralipid concentration increases. This transition corresponds to the transition from single to multiple scattering regime and/or limits of validity of the Gaussian beam model. The implications for the measurements of the scleral and ciliary muscle attenuation coefficients are discussed below.
As a final validation step, we calculated the attenuation coefficient of the Intralipid solutions using the same method as for the transscleral images (Fig. 6). The intensity profiles were corrected for sensitivity roll-off and beam geometry using a fixed value of zr=0.105 mm and a fixed value of the focus position calculated from Eq. (1). The corrected profiles were then fit with an exponential model corresponding to single scattering conditions. The curve fit was limited to the depth range equivalent to the averaged ROI of the sclera and ciliary muscle (Fig. 6). The scattering coefficient was calculated by subtracting the absorption coefficient of water (0.154 mm-1) from the total attenuation coefficient. The measured scattering coefficient was compared to the dependent scattering coefficient calculated for 1325 nm using the formulas of Aernouts et al. [42]. Figure 7 shows that there was excellent agreement between our experimental results and the values predicted using the formulas in the depth range of the sclera ROIs. On the other hand, in the depth range of the ciliary muscle ROIs, accurate values of the attenuation coefficient are obtained only for concentrations up to 16%. At the higher concentrations, the single scattering model no longer provides reliable values of the attenuation coefficient. At 32% and 64% concentrations, the depth range of the ciliary muscle ROI overlaps with the depth range where multiple scattering becomes a factor (see also Fig. 5). These results show that the intensity profiles recorded in the ciliary muscle ROIs must be carefully evaluated to ensure that they fall within the single scattering model. In our analysis we capped the depth of the inner boundary of the ciliary muscle ROI to 1.8 mm and we confirmed the validity of the single scattering model by verifying that the intensity profiles in the ciliary muscle ROIs are linear (in dB units).
Fig. 6. Intensity profile of Intralipid corrected for sensitivity roll-off and confocal point spread function using the method described in Section D.4. The linear region of the corrected intensity profile corresponds to the domain validity of the single scattering regime which includes the scleral ROI for all concentrations and the ciliary body ROIs for concentrations up to 16%. A small residual artifact due to the beam geometry is visible in lower concentrations probably due to a small residual error in the focus position and Rayleigh range assumed for the fit (See Fig. 5).
Fig. 7. Comparison of measured and calculated attenuation coefficient for 4%, 8%, 16%, 32% and 64% concentrations of Intralipid 20%. The measured attenuation coefficient was obtained from curve fits of the corrected intensity profiles at depths corresponding to the locations of the scleral and ciliary muscle ROIs using a single scattering model (See Fig. 6). The calculated attenuation coefficient was obtained by adding the scattering coefficient calculated using the formulas from Aernouts et al [41,42] and the absorption coefficient of water [35]. Multiple scattering effects produce measurement errors in the ciliary muscle ROIs at 32% and 64% concentrations.
2.4.5 Calculation of the scleral and ciliary muscle attenuation coefficient
The attenuation coefficient was calculated from the corrected intensity profiles in several steps to enable an assessment of the variability across the ROI and the exclusion of outliers. First, the corrected depth-dependent profile of each of the 100 A-lines was fit with a linear function to provide the attenuation coefficient along each A-line [31]. After confirming normality of the distribution, the mean and standard deviation of the attenuation coefficients corresponding to the 100 A-lines were calculated. To reduce the effect of local variability due to pigments or blood vessels, A-lines with an attenuation coefficient that were outside 2 standard deviations from the mean were discarded. The truncated average and standard deviation, with outlier A-lines removed, were calculated and A-lines with attenuation coefficients outside of 2 standard deviations from the mean of the truncated set were discarded again. The average intensity profile of the of the remaining A-lines in the ROI was calculated and a final linear regression was performed to obtain the estimated scleral or ciliary body attenuation coefficient. A visual inspection of the goodness of the fits was performed. In 7 eyes, the ROI was re-adjusted manually to avoid tissue heterogeneities, such as blood vessels or cysts, or image artefacts, and a new fit was performed on the modified ROI. The attenuation coefficient obtained from the fit was multiplied by the group refractive indexes to account for the fact that distances in OCT images correspond to the optical path length [10]. For the group refractive index, we assumed a value of 1.40 for the sclera and ciliary body.
2.4.6 Reproducibility and age-dependence of the attenuation coefficient
The attenuation coefficient for all subjects was analyzed as a function of age using a linear regression to determine if there was an age dependence. Repeatability across images was investigated by repeating the analysis five times in five consecutive frames of the same subject acquired during the same imaging sequence. The variability across measurements was investigated by repeating the measurement 5 times on the same image. Both analyses were performed for five subjects.
3. Results
The image quality was acceptable in 39 out of 45 eyes. The other 6 eyes were excluded from the analysis: One eye was excluded because of excessive tilt, one eye was flagged as an outlier (attenuation coefficient outside of 3 standard deviations from the mean) and 4 eyes were excluded because poor image quality prevented a reliable analysis. These 4 eyes were all from subjects older than 60 years (Fig. 8). In these images, there is visible elevation and flattening of the conjunctiva that could be associated with conditions such as pinguecula and pterygium. These conditions result in images with increased shadowing due to increased vasculature, specular reflection artefacts and/or poor overall signal strength which prevented reliable measurement of the attenuation coefficient.
Fig. 8. Transscleral OCT images of the 4 subjects that were excluded from the analysis due to poor image quality. All four subjects were above 60 years of age: 71-year-old (A) 79-year-old (B) 70-year-old (C) 60-year-old (D) subject. The additional anatomical structures and increased vasculature produce shadowing, specular reflection artefacts and/or poor overall signal strength which prevented reliable measurement of the attenuation coefficient.
An example of an OCT image with the average intensity profile in the ROI of the sclera and ciliary muscle before and after correction and the corresponding curve fits is shown in Fig. 9. As expected, the correction increases the signal relative to the uncorrected signal in regions located anterior or posterior to the beam focus. The variations of the sclera and ciliary muscle attenuation coefficients within the regions of interest are shown in Fig. 10. The rectangles represent the ROIs that were defined for measurement of the attenuation coefficient using the analysis software.
Fig. 9. Typical image analysis for one subject. A) Transscleral OCT image showing the ciliary muscle and the sclera. Blue and red lines show the ROI containing 100 A-lines. The black shaded regions represent the ROI of sclera and ciliary muscle. B) Intensity profiles corrected and uncorrected. C) Fitted intensity profile, the vertical red line represents the position of the air-tissue boundary, and the red lines within the intensity profile are the linear fits for the ROI of the sclera and the ROI of the ciliary muscle, respectively. The scleral attenuation coefficient for this subject was 2.55 mm-1. The ciliary muscle attenuation coefficient for this subject was 2.53 mm-1.
Fig. 10. Example of data analysis of the sclera for a 17 y/o (A-C) and a 53 y/o (D-F) subject. A and D) Transscleral OCT images showing the sclera and ciliary muscle ROI (black shaded regions). B, C, E and D) Scatter plots of the measured attenuation coefficient of all 100 A-lines within the ROI. The blue lines show the mean and 2 times the standard deviation of the 100 A-lines. The red lines show the mean and 2 times the standard deviation of the points that fall within the blue lines. Values outside of the red lines were excluded from the final measurement. The attenuation coefficients for the 17 y/o were 5.35 mm-1 for the sclera and 1.17 mm-1 for the ciliary muscle, and the attenuation coefficients for the 53 y/o were 3.43 mm-1 for the sclera and 2.52 mm-1 for the ciliary muscle.
The repeatability of measurements was quantified in 5 subjects. For the sclera, the standard deviation of 5 measurements acquired on 5 consecutive frames was 0.20 mm-1 on average (range: 0.04 mm-1 to 0.33 mm-1) with a coefficient of variation of 7.0% (range: 1.4% to 14%). For the ciliary muscle, the standard deviation was 0.31 mm-1 on average (range: 0.13 mm-1 to 0.40 mm-1), and the coefficient of variation was 13% (range: 11% to 18%). The standard deviation of 5 measurements acquired on the same image was 0.16 mm-1 for the sclera (range: 0.04 mm-1 to 0.22 mm-1) with a coefficient of variation of 4.6% (range: 1.4% to 7.0%). For the ciliary muscle the standard deviation was 0.14 mm-1 on average (range: 0.05 mm-1 to 0.33 mm-1) and the coefficient of variation was 5.7% on average (range: 1.9% to 12%).
Figure 10 shows an example of the variation of the attenuation coefficients in a 17-year-old and a 53-year-old subject before removal of outliers. The images illustrate the variability of the attenuation coefficient across individual A-lines within the ROI due to noise and structural heterogeneity. The presence of blood vessels, pigmented structures, and other local variations in anatomical structure produce large local fluctuations in the attenuation coefficient. The number of A-lines that were discarded as outliers in the 39 images that were included in the final analysis ranged from 4 to 13 for the sclera and 3 to 15 for the ciliary muscle out of 100 A-lines.
To determine if there exist any correlation between the average ciliary muscle and sclera attenuation coefficients for each subject, both variables were plotted as a function of each other, and a linear regression was performed (Fig. 11). A statistically-significant correlation was found between the ciliary muscle and scleral attenuation coefficients. The dependency of the two variables could be an artefact caused by limits of validity of the single scattering model or confocal point-spread function in deeper regions of the tissue, which would produce an underestimation of the ciliary muscle attenuation coefficient as the scleral attenuation coefficient increases. Also, the standard deviation of the 100 measurements of the attenuation coefficients of the sclera and the ciliary muscle of each subject were tested following the same steps and no correlation was found.
Fig. 11. Within-subject analysis of the attenuation coefficient. Left, ciliary muscle attenuation coefficient versus scleral attenuation coefficient. A statistical correlation was found (correlation coefficient = -0.44, p-value = 0.005). Right, standard deviation of the ciliary muscle attenuation coefficient measured from the 100 A-lines for each subject versus that of the sclera. No significant correlation was found (correlation coefficient = -0.12, p-value = 0.46).
The average attenuation coefficient of the sclera was 4.13 ± 1.42 mm-1 (range: 1.56 mm-1 to 6.92 mm-1) and the average attenuation coefficient of the ciliary muscle was 1.72 ± 0.88 mm-1 (range: 0.06 mm-1 to 3.72 mm-1) for all subjects. The attenuation coefficient of the sclera was found to be near the threshold for statistical significance with age (p = 0.053, Fig. 12). On the other hand, within our data set, there was no statistically significant dependence of the ciliary muscle attenuation coefficient on the age (p = 0.42, Fig. 12).
Fig. 12. Left, scleral attenuation coefficient as a function of age for all subjects (correlation coefficient = -0.31, p-value = 0.053). Right, ciliary muscle attenuation coefficient as a function of age for all subjects (correlation coefficient = 0.13, p-value = 0.46). The attenuation coefficient of the sclera and ciliary muscle range from 1.56 to 6.92 and from 0.06 to 3.72 mm-1, respectively.
Figure 13 shows the scleral and ciliary muscle attenuation coefficient as a function of thickness. There was no correlation between thickness and attenuation coefficient. The thickness of the sclera and ciliary muscle across individuals in our study is contained in a relatively small range (0.41 mm to 0.75 mm and 0.51 mm to 0.76 mm, respectively). We therefore do not expect to find a dependence on thickness of the attenuation coefficient.
Fig. 13. Attenuation coefficient as a function of thickness for all subjects. Left, scleral thickness and (correlation coefficient = 0.06, p-value = 0.70). Right, ciliary muscle thickness (correlation coefficient = 0.03, p-value = 0.87).
4. Discussion
Optical attenuation coefficients of the sclera and ciliary muscle were determined from in vivo OCT images. To the best of our knowledge, the study represents the first measurement of scleral attenuation coefficients in vivo and the first measurement of ciliary muscle attenuation coefficients both ex vivo and in vivo. The study revealed that there is a significant variability across individuals in both scleral and ciliary body attenuation coefficient. This variability most likely reflects differences in scleral and ciliary body ultrastructure, vasculature, and pigmentation. The study also found that there are significant local variations in attenuation coefficient within individuals, due to the presence of blood vessels and other structural heterogeneities that are visible in the OCT images. The results also suggest that the scleral attenuation coefficient may decrease with age, but additional data is needed to confirm this finding.
Our calculations assumed a simple exponential depth-dependence of the OCT signal, corresponding to a single-scattering model [31–33,37,43]. We selected the single-scattering model since linear regression of the intensity profile (in dBs) in the sclera and ciliary muscle ROIs provided good fits of the data after correction for sensitivity roll-off and beam geometry. Our experiments on Intralipid solutions show that the single scattering model gives accurate values of the attenuation coefficient in the depth range corresponding to the sclera, but that multiple scattering effects may cause an underestimation of the attenuation coefficient in the depth range corresponding to the ciliary muscle ROIs. The intensity profiles in the 32% and 64% Intralipid solutions become non-linear in this depth range, reflecting the contribution of multiple scattering or broadening of the beam beyond the predictions of the Gaussian model. To minimize the potential impact of these effects, we capped the depth of the ciliary muscle ROIs to 1.8 mm and inspected each fitted ROI to ensure that it falls within the linear region. Nevertheless, the finding that the ciliary muscle attenuation coefficient is negatively correlated with the scleral attenuation coefficient may be caused by increased effects of multiple scattering as the scleral attenuation coefficient increases (Fig. 11).
Another effect that must be taken into account in the computation of attenuation coefficient from OCT intensity profiles is the contribution of the sensitivity fall-off and focused beam geometry to the depth-dependence of the signal [33,37]. To correct for these effects, we used the approach of Faber et al [33], where the effect of the focused beam geometry is modeled with a confocal axial point spread function that assumes a Gaussian beam with an effective Rayleigh range equal to twice the Rayleigh range in tissue. Our experiments in Intralipid demonstrate that this model very closely fits our experimental data, but that the goodness of fit is reduced beyond a depth of approximately 1.8 mm to 2 mm depending on the Intralipid concentration (Fig. 4). Beyond this depth, the intensity profile in Intralipid starts to plateau, while the curve fit using the single scattering model predicts a linear decrease in intensity (in dB units). A similar behavior is observed in the transscleral images, at depths of approximately 2 mm (see Fig. 9). As discussed above, this difference is most likely due to limits of validity of the single-scattering or Gaussian beam models in deeper regions of the tissue.
In principle, polarization effects could also affect our measurements. The OCT system used in this study delivers an elliptical beam to the sample and reference arms. Increased polarization mismatch of the backscattered light as the OCT beam propagates through the tissue could contribute to signal decay. However, a prior study using PS-OCT to image the sclera shows that the conjunctiva and episclera have high extinction coefficients, significantly higher than expected from the tissue composition and structure (on the order of 75 dB/mm for the conjunctiva), suggesting that these tissues are highly depolarizing [30]. We therefore expect that the beam will be highly depolarized by the time it reaches the depths corresponding to our scleral and ciliary muscle ROIs. The architecture and polarization properties of the sclera and ciliary muscle will therefore not have a major impact on the calculation of the attenuation coefficient.
The large interindividual variability of the sclera and ciliary muscle optical attenuation has implications for both optical imaging and laser therapy. Combined with variations in thickness, it is probably one of the primary causes for the large difference in image quality observed in studies using OCT to image the ciliary muscle [11,18]. The ability to image the ciliary muscle is a critical aspect of studies of the mechanism of accommodation and to understand the potential role of the ciliary muscle in presbyopia [44,45]. The difficulty in detecting the inner boundary of the ciliary muscle near the apex and the interindividual variability has been reported previously [10,11,18]. The difficulty in detecting the boundary increases the measurement uncertainty.
Our findings also have implications for transscleral laser therapies. The difference between individuals suggests that laser treatments should ideally be tailored to each patient to produce the desired treatment outcomes while preventing damage to the sclera and ciliary body. The large interindividual and local variations in scleral and ciliary muscle attenuation may explain the variability in outcomes that is observed clinically [21]. We found an attenuation coefficient ranging approximately from 1.6 mm-1 to 6.9 mm-1 (6.9 dB/mm to 30 dB/mm) for the sclera and 0.1 mm-1 to 3.7 mm-1 (0.4 dB/mm to 16 dB/mm) for the ciliary muscle. Assuming a scleral thickness of 0.6 mm and a ciliary muscle thickness at the apex of 0.5 mm, the transmission through the sclera ranges from 1.6% to 38% and the transmission through the ciliary muscle ranges from 16% to 95%. These calculations show that, for any given scleral thickness, the interindividual variations in attenuation result in large differences in irradiation within the ciliary body. Variations in both thickness and optical properties combine to produce significant interindividual variations in scleral transmission.
Using the same values of thickness, the round-trip attenuation for reflection coming from the ciliary muscle apex ranges from approximately 8.8 to 52 dB (8.3 dB to 36 dB in the sclera, 0.4 dB to 16 dB in the ciliary muscle), which represents a significant variation that may explain the variability in image quality between individuals. The dynamic range of the images can be improved by increasing the laser power incident on the sclera, and knowledge of the total attenuation and of the attenuation coefficient can be used to calculate the required increase in power. For instance, if the inner 0.2 mm of the ciliary body is found to be at or below the noise level and the attenuation coefficient of the ciliary muscle is 22dB/mm, then the signal to noise ratio must be increased by 16 dB/mm x 0.4 mm = 6.7 dB (round trip). This increase in signal to noise ratio can be achieved by increasing the power in the sample arm by a factor of 2.2 (106.7/20). We used an incident power of 3 mW. A careful analysis needs to be performed with the specific beam geometry and scan pattern to determine how much the power can be increased. The power must remain with the exposure limits defined by the relevant safety standards [46]. In addition, the values of the attenuation coefficient can be used in light propagation models to evaluate the effect of beam and tissue geometry on the backscattered signal for imaging. The values of the attenuation coefficient can also be used in optical-thermal models of laser therapies to evaluate how variations in the scleral attenuation coefficient affect the light and temperature distribution in the ciliary body during treatments such as transscleral cyclophotocagulation [22,23,26].
Our in vivo measurement of the attenuation coefficient of the sclera are comparable to previously published measurements obtained in vitro in the sclera [47]. The average values for the attenuation coefficient in our study was 4.1 ± 1.4 mm-1 for the sclera. Rol [28] found values of 16% 10% and 6% for the axial transmission of scleral samples of thickness 0.7, 0.8 and 0.9 mm at 1.3 μm, corresponding to attenuation coefficients of 2.6, 2.9 and 3.1 mm-1. Despite difference in methodology and reliance on ex vivo tissue, these values are in good agreement with our measurements. Results from other studies cannot be directly compared because they were either collected using different wavelengths [22,25], or other optical properties of the human sclera were measured such as optical density [27,28] and reduced scattering coefficient or absorption coefficient [26]. All previous studies were conducted on scleral patches excised from cadaver eyes. In vivo measurements provide more physiologically relevant values, that take into account vasculature.
One limitation of the in vivo technique is that it provides only a measurement of the total attenuation coefficient, which is the sum of the absorption coefficient and scattering coefficient. The method employed in our study does not enable us to separate contributions from absorption and scattering. However, we expect that the absorption coefficient of the sclera in the infrared will be on the order of the absorption coefficient of water or blood. At 1325nm, the absorption coefficient is 0.15 mm-1 for water [35] and 0.35 mm−1, for blood [48,49]. which is well below the attenuation coefficient that we measured. We can therefore conclude that the attenuation is due primarily to scattering.
The rectangular scleral regions of interests closely follow the contours of the episclera-sclera and sclera-ciliary muscle boundaries. The inner boundary of the ciliary muscle has a more complex shape that is not captured by the rectangular ROI. Following the curvature of the inner boundary of the ciliary muscle would increase the depth of the region of interest, but the signal in these regions is too low to produce reliable data. For this reason, we chose a rectangular region of interest that delimits the regions of the ciliary muscle with sufficient signal to provide reliable measurements of the attenuation coefficient.
The ROI was chosen with variable depths to take into account variations in the geometry of the sclera and ciliary muscle across individuals. The depth of the ROI ranged from 0.33 to 0.69 mm for the sclera and from 0.02 from 0.47 mm for the ciliary muscle. We found no correlation between ROI depth and attenuation coefficient in our study. In principle, using variable ROI depth may introduce a variability in the reliability of the curve fit. However, an observation of the images in our data set shows that inter-individual variability of the goodness of fit is due primarily to differences in noise and to structural heterogeneity with depth in the sclera or ciliary muscle. Taking a uniform ROI across all subjects will therefore probably not reduce the variability of the goodness of fit. For this reason, we decided to use the maximal possible depth for each subject of minimize the effect of these heterogeneities.
Initially, we attempted to quantify the attenuation coefficient from the single A-line passing through the ciliary muscle apex. As in previous studies [31,32], we found that speckle and other sources of noise, as well as tissue heterogeneities resulted in significant variations between neighboring A-lines. The use of the region of interest with 100 A-lines reduces the variability and noise and produces a more reliable regional estimate of the scleral properties. Some of the variability of the attenuation coefficient, and particularly the fluctuations between neighboring A-lines may be due to the presence of noise which reduces the reliability of the curve fits. However, there are also structural heterogeneities visible within the sclera and ciliary muscle that contribute to some of the lateral variations of the attenuation coefficient observed in some subjects. In the region near the apex of the ciliary body, there is evidence of regional variations in scleral properties, including both thickness and mechanical properties [21]. These variations may also apply to optical properties. In addition, measurements acquired in more posterior regions of the globe may produce different values due to differences in the structure between the anterior and posterior of the sclera [50,51].
We found a decrease of the scleral attenuation coefficient with age that is near the threshold of statistical significance. While more data is needed to confirm this finding, it suggests that there may be changes in the structure of the sclera with age that alter the scattering properties [52]. We also found that there is a much higher variability in the structure in older subjects which significantly affect the image quality. This factor prevented us from calculating reliable values of the attenuation coefficient in older eyes [50]. We may speculate on the influence of certain ocular conditions, such as myopia, on the attenuation coefficient. Myopia is characterized by thinning of the sclera which has implications on the sclera rigidity [53]. Mechanical properties of the sclera such as rigidity and density can affect light penetration therefore affecting the attenuation coefficient. Even though within our data, scleral thickness does not change with age, decrease of scleral attenuation coefficient may be indicative of changes in the mechanical properties of the tissue with age.
In conclusion, we calculated the attenuation coefficient of the human sclera and the ciliary muscle in vivo from OCT images. The reliance on a single scattering model and Gaussian beam assumption may produce an underestimation of ciliary muscle attenuation coefficient. Nevertheless, the scleral and ciliary muscle attenuation coefficient were found to vary significantly between individuals reflecting difference in tissue structure, vasculature and pigmentation. These findings suggest that interindividual variability in optical attenuation have a significant effect on the quality of images acquired transsclerally and on the outcome of transscleral laser therapies.
Funding
Florida Lions Eye Bank; National Eye Institute (1F30EY027162, 2R01EY14225, P30EY14801); Henri and Flore Lesieur Foundation; Drs. Raksha Urs and Aaron Furtado; Karl R. Olsen, MD and Martha E. Hildebrandt, PhD; Research to Prevent Blindness.
Acknowledgements
The authors thank Leana Rohman for assistance with the calibration experiments using scattering media and Prof. Omer Kocaoglu for helpful discussions during revisions of the manuscript
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. P. L. Kaufman, E. Lütjen-Drecoll, and M. A. Croft, “Presbyopia and glaucoma: Two diseases, one pathophysiology? The 2017 Friedenwald lecture,” Invest. Ophthalmol. Vis. Sci. 60(5), 1801–1812 (2019). [CrossRef]
2. J. B. Eskridge, “Review of ciliary muscle effort in presbyopia,” Optometry and Vision Science 61(2), 133–138 (1984). [CrossRef]
3. M. A. Croft, J. P. McDonald, A. Katz, T.-L. Lin, E. Lütjen-Drecoll, and P. L. Kaufman, “Extralenticular and lenticular aspects of accommodation and presbyopia in human versus monkey eyes,” Invest. Ophthalmol. Vis. Sci. 54(7), 5035 (2013). [CrossRef]
4. O. Stachs, H. Martin, A. Kirchhoff, J. Stave, T. Terwee, and R. Guthoff, “Monitoring accommodative ciliary muscle function using three-dimensional ultrasound,” Graefe’s Arch. Clin. Exp. Ophthalmol. 240(11), 906–912 (2002). [CrossRef]
5. Z. Wang, J. Huang, J. Lin, X. Liang, X. Cai, and J. Ge, “Quantitative measurements of the ciliary body in eyes with malignant glaucoma after trabeculectomy using ultrasound biomicroscopy,” Ophthalmology 121(4), 862–869 (2014). [CrossRef]
6. R. H. Silverman, F. L. Lizzi, B. G. Ursea, M. J. Rondeau, N. B. Eldeen, A. Kaliscz, H. O. Lloyd, and D. J. Coleman, “High-resolution ultrasonic imaging and characterization of the ciliary body,” Investig. Ophthalmol. Vis. Sci. 42, 885 (2001).
7. S. A. Strenk, L. M. Strenk, and J. L. Semmlow, “MRI study of the effect of age and accommodation on ciliary muscle location,” Invest. Ophthalmol. Vis. Sci. 45, 2395 (2004).
8. S. A. Strenk, L. M. Strenk, and S. Guo, “Magnetic resonance imaging of aging, accommodating, phakic, and pseudophakic ciliary muscle diameters,” J. Cataract Refract. Surg. 32(11), 1792–1798 (2006). [CrossRef]
9. S. A. Strenk, J. L. Semmlow, L. M. Strenk, P. Munoz, J. Gronlund-Jacob, and J. K. DeMarco, “Age-related changes in human ciliary muscle and lens: A magnetic resonance imaging study,” Optometry and Vision Science 40, 1162–1169 (1999). [CrossRef]
10. M. Ruggeri, C. de Freitas, S. Williams, V. M. Hernandez, F. Cabot, N. Yesilirmak, K. Alawa, Y.-C. Chang, S. H. Yoo, G. Gregori, J.-M. Parel, and F. Manns, “Quantification of the ciliary muscle and crystalline lens interaction during accommodation with synchronous OCT imaging,” Biomed. Opt. Express 7(4), 1351 (2016). [CrossRef]
11. S. Wagner, E. Zrenner, and T. Strasser, “Ciliary muscle thickness profiles derived from optical coherence tomography images,” Biomed. Opt. Express 9(10), 5100 (2018). [CrossRef]
12. M. Ruggeri, V. Hernandez, C. de Freitas, F. Manns, and J.-M. Parel, “Biometry of the ciliary muscle during dynamic accommodation assessed with OCT,” in Ophthalmic Technologies XXIV (2014).
13. L. A. Lossing, L. T. Sinnott, C.-Y. Kao, K. Richdale, and M. D. Bailey, “Measuring changes in ciliary muscle thickness with accommodation in young adults,” Optom. Vis. Sci. 89(5), 719 (2012). [CrossRef]
14. M. D. Bailey, “How should we measure the ciliary muscle?” Invest. Ophthalmol. Vis. Sci. 52(3), 1817 (2011). [CrossRef]
15. K. Richdale, L. T. Sinnott, M. A. Bullimore, P. A. Wassenaar, P. Schmalbrock, C.-Y. Kao, S. Patz, D. O. Mutti, A. Glasser, and K. Zadnik, “Quantification of age-related and per diopter accommodative changes of the lens and ciliary muscle in the emmetropic human eye,” Invest. Ophthalmol. Vis. Sci. 54(2), 1095 (2013). [CrossRef]
16. A. L. Sheppard and L. N. Davies, “In vivo analysis of ciliary muscle morphologic changes with accommodation and axial ametropia,” Invest. Ophthalmol. Vis. Sci. 51(12), 6882 (2010). [CrossRef]
17. Y.-C. Chang, K. Liu, F. Cabot, S. H. Yoo, M. Ruggeri, A. Ho, J.-M. Parel, and F. Manns, “Variability of manual ciliary muscle segmentation in optical coherence tomography images,” Biomed. Opt. Express 9(2), 791 (2018). [CrossRef]
18. D. S. Laughton, B. J. Coldrick, A. L. Sheppard, and L. N. Davies, “A program to analyse optical coherence tomography images of the ciliary muscle,” Contact Lens and Anterior Eye 38(6), 402–408 (2015). [CrossRef]
19. M. Ruggeri, C. de Freitas, S. Williams, V. M. Hernandez, F. Cabot, N. Yesilirmak, K. Alawa, Y.-C. Chang, S. H. Yoo, G. Gregori, J.-M. Parel, and F. Manns, “Quantification of the ciliary muscle and crystalline lens interaction during accommodation with synchronous OCT imaging,” Biomed. Opt. Express (2016).
20. P. Rol, W. Barth, M. Schwager, N. Zuber, F. Fankhauser, S. Fankhauser, and P. Niederer, “Devices for the control of laser transmission across the sclera during transscleral photocoagulation,” Ophthalmic Surg Lasers Imaging 23(7), 459 (1992). [CrossRef]
21. A. V Yuzhakov, A. P. Sviridov, O. I. Baum, E. M. Shcherbakov, and E. N. Sobol, “Optical characteristics of the cornea and sclera and their alterations under the effect of nondestructive 1.56-μm laser radiation,” J. Biomed. Opt. 18(5), 058003 (2013). [CrossRef]
22. B. Nemati, H. G. Rylander, and A. J. Welch, “Optical properties of conjunctiva, sclera, and the ciliary body and their consequences for transscleral cyclophotocoagulation,” Appl. Opt. 35(19), 3321 (1996). [CrossRef]
23. A. N. Bashkatov, E. A. Genina, V. I. Kochubey, and V. V. Tuchin, “Optical properties of human sclera in spectral range 370–2500 nm,” Opt. Spectrosc. 109(2), 197–204 (2010). [CrossRef]
24. E. K. Chan, B. Sorg, D. Protsenko, M. O’Neil, M. Motamedi, and A. J. Welch, “Effects of compression on soft tissue optical properties,” IEEE J. Sel. Top. Quantum Electron. 2(4), 943–950 (1996). [CrossRef]
25. M. Hammer, A. Roggan, D. Schweitzer, and G. Muller, “Optical properties of ocular fundus tissues-an in vitro study using the double-integrating-sphere technique and inverse Monte Carlo simulation,” Phys. Med. Biol. 40(6), 963–978 (1995). [CrossRef]
26. A. Vogel, C. Dlugos, R. Nuffer, and R. Birngruber, “Optical properties of human sclera, and their consequences for transscleral laser applications,” Lasers Surg. Med. 11(4), 331–340 (1991). [CrossRef]
27. I. Fine, E. Lowinger, A. Weinreb, and D. Weinberger, “Optical properties of the sclera,” Phys. Med. Biol. 30(6), 565–571 (1985). [CrossRef]
28. P. Rol, P. Niederer, U. Durr, P. D. Henchoz, and F. Fankhauser, “Experimental investigations on the light scattering properties of the human sclera,” Lasers Light Ophthalmol. (1990).
29. P. Rol, S. Kwasniewska, E. van der Zypen, and F. Fankhauser, “Transscleral iridotomy using a neodymium: YAG laser operated both with standard equipment and an optical fiber system–a preliminary report: Part I–Optical system and biomicroscopic results,” Ophthalmic Surg. 18, 176 (1987).
30. A. Miyazawa, M. Yamanari, S. Makita, M. Miura, K. Kawana, K. Iwaya, H. Goto, and Y. Yasuno, “Tissue discrimination in anterior eye using three optical parameters obtained by polarization sensitive optical coherence tomography,” Opt. Express 17(20), 17426 (2009). [CrossRef]
31. P. Gong, M. Almasian, G. van Soest, D. M. de Bruin, T. G. van Leeuwen, D. D. Sampson, and D. J. Faber, “Parametric imaging of attenuation by optical coherence tomography: review of models, methods, and clinical translation,” J. Biomed. Opt. 25(04), 1 (2020). [CrossRef]
32. S. Chang and A. K. Bowden, “Review of methods and applications of attenuation coefficient measurements with optical coherence tomography,” J. Biomed. Opt. 24(09), 1 (2019). [CrossRef]
33. D. Faber, F. van der Meer, M. Aalders, and T. van Leeuwen, “Quantitative measurement of attenuation coefficients of weakly scattering media using optical coherence tomography,” Opt. Express 12(19), 4353 (2004). [CrossRef]
34. W. Drexler, C. K. Hitzenberger, A. Baumgartner, O. Findl, H. Sattmann, A. F. and, and Fercher, “Investigation of dispersion effects in ocular media by multiple wavelength partial coherence interferometry,” Exp. Eye Res. 66(1), 25–33 (1998). [CrossRef]
35. G. M. Hale and M. R. Querry, “Optical constants of water in the 200-nm to 200-μm wavelength region,” Appl. Opt. 12(3), 555 (1973). [CrossRef]
36. D. A. Atchison and G. Smith, “Chromatic dispersions of the ocular media of human eyes,” J. Opt. Soc. Am. A 22(1), 29 (2005). [CrossRef]
37. B. Ghafaryasl, K. A. Vermeer, J. Kalkman, T. Callewaert, J. F. de Boer, and L. J. Van Vliet, “Analysis of attenuation coefficient estimation in Fourier-domain OCT of semi-infinite media,” Biomed. Opt. Express 11(11), 6093 (2020). [CrossRef]
38. T. G. Van Leeuwen, D. J. Faber, and M. C. Aalders, “Measurement of the axial point spread function in scattering media using single-mode fiber-based optical coherence tomography,” IEEE J. Sel. Top. Quantum Electron. 9(2), 227–233 (2003). [CrossRef]
39. M. Almasian, N. Bosschaart, T. G. van Leeuwen, and D. J. Faber, “Validation of quantitative attenuation and backscattering coefficient measurements by optical coherence tomography in the concentration-dependent and multiple scattering regime,” J. Biomed. Opt. 20(12), 121314 (2015). [CrossRef]
40. J. Yang, I. A. Chen, S. Chang, J. Tang, B. Lee, K. Kılıç, S. Sunil, H. Wang, D. Varadarajan, C. Magnain, S.-C. Chen, I. Costantini, F. Pavone, B. Fischl, and D. A. Boas, “Improving the characterization of ex vivo human brain optical properties using high numerical aperture optical coherence tomography by spatially constraining the confocal parameters,” Neurophotonics 7(04), 1–16 (2020). [CrossRef]
41. B. Aernouts, E. Zamora-Rojas, R. Van Beers, R. Watté, L. Wang, M. Tsuta, J. Lammertyn, and W. Saeys, “Supercontinuum laser based optical characterization of Intralipid® phantoms in the 500-2250 nm range,” Opt. Express 21(26), 32450 (2013). [CrossRef]
42. B. Aernouts, R. Van Beers, R. Watté, J. Lammertyn, and W. Saeys, “Dependent scattering in Intralipid® phantoms in the 600-1850nm range,” Opt. Express 22(5), 6086 (2014). [CrossRef]
43. B. Ghafaryasl, K. A. Vermeer, J. F. de Boer, M. E. J. van Velthoven, and L. J. van Vliet, “Noise-adaptive attenuation coefficient estimation in spectral domain optical coherence tomography data,” in 2016 IEEE 13th International Symposium on Biomedical Imaging (ISBI) (IEEE, 2016), pp. 706–709.
44. W. N. Charman, “Developments in the correction of presbyopia I: spectacle and contact lenses,” Ophthalmic Physiol Opt 34(1), 8–29 (2014). [CrossRef]
45. W. N. Charman, “Developments in the correction of presbyopia II: surgical approaches,” Ophthalmic Physiol Opt 34(4), 397–426 (2014). [CrossRef]
46. The Accredited Committee Z80 for Ophthalmic Standard, “Ophthalmics-Light Hazard Protection For Ophthalmic Instruments,” Am. Natl. Stand. Inst. ANSI Z.80.36 (2016).
47. P. O. Rol, “Optics for Transscleral Laser Applications,” Swiss Federal Institute of Technology (1992).
48. A. Roggan, M. Friebel, K. Dörschel, A. Hahn, and G. Müller, “Optical properties of circulating human blood in the wavelength range 400–2500 nm,” J. Biomed. Opt. 4(1), 36 (1999). [CrossRef]
49. N. Bosschaart, G. J. Edelman, M. C. G. Aalders, T. G. van Leeuwen, and D. J. Faber, “A literature review and novel theoretical approach on the optical properties of whole blood,” Lasers Med. Sci. 29(2), 453–479 (2014). [CrossRef]
50. B. Geraghty, S. W. Jones, P. Rama, R. Akhtar, and A. Elsheikh, “Age-related variations in the biomechanical properties of human sclera,” J. Mech. Behav. Biomed. Mater. 16, 181–191 (2012). [CrossRef]
51. M. A. Fazio, R. Grytz, J. S. Morris, L. Bruno, C. A. Girkin, and J. C. Downs, “Human scleral structural stiffness increases more rapidly with age in donors of african descent compared to donors of European descent,” Invest. Ophthalmol. Vis. Sci. 55(11), 7189 (2014). [CrossRef]
52. B. Coudrillier, J. Pijanka, J. Jefferys, T. Sorensen, H. A. Quigley, C. Boote, and T. D. Nguyen, “Collagen structure and mechanical properties of the human sclera: analysis for the effects of age,” J. Biomech. Eng. 137, 041006 (2015). [CrossRef]
53. J. A. Summers Rada, S. Shelton, and T. T. Norton, “The sclera and myopia,” Exp. Eye Res. 82(2), 185–200 (2006). [CrossRef]
