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Physiology and Pharmacology  |   August 2012
Differential Effects of Trabecular Meshwork Stiffness on Outflow Facility in Normal Human and Porcine Eyes
Author Affiliations & Notes
  • Lucinda J. Camras
    From the Department of Biomedical Engineering, Duke University, Durham, North Carolina; and the
  • W. Daniel Stamer
    Department of Ophthalmology, Duke University Medical Center, Durham, North Carolina.
  • David Epstein
    Department of Ophthalmology, Duke University Medical Center, Durham, North Carolina.
  • Pedro Gonzalez
    Department of Ophthalmology, Duke University Medical Center, Durham, North Carolina.
  • Fan Yuan
    From the Department of Biomedical Engineering, Duke University, Durham, North Carolina; and the
    Department of Ophthalmology, Duke University Medical Center, Durham, North Carolina.
  • Corresponding author: Fan Yuan, Department of Biomedical Engineering, 136 Hudson Hall, Duke University, Durham, NC 27708; fyuan@duke.edu
Investigative Ophthalmology & Visual Science August 2012, Vol.53, 5242-5250. doi:10.1167/iovs.12-9825
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      Lucinda J. Camras, W. Daniel Stamer, David Epstein, Pedro Gonzalez, Fan Yuan; Differential Effects of Trabecular Meshwork Stiffness on Outflow Facility in Normal Human and Porcine Eyes. Invest. Ophthalmol. Vis. Sci. 2012;53(9):5242-5250. doi: 10.1167/iovs.12-9825.

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

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Abstract

Purpose.: The study was designed to determine trabecular meshwork (TM) stiffness and its relationship to outflow facility (C) in perfused normal human and porcine eyes.

Methods.: Human and porcine eyes were perfused at pressures of 10, 20, 30, and 40 mm Hg to determine C and how outflow resistance (R = 1/C) varied with the pressure. Following perfusions, TM tissue segments were dissected and stretched uniaxially to determine the circumferential bulk Young's modulus (E). The statistical significance of difference between different groups was evaluated using a two-tailed Student's t-test or Mann-Whitney U test.

Results.: A larger E correlated with a higher C measured at 10 and 20 mm Hg (P < 0.05), and a similar trend was observed at 30 and 40 mm Hg in human eyes (n = 7). Additionally, a higher C correlated to a lower variance of R, and a stiffer TM correlated to a lower variance of R in human eyes (P < 0.05). For porcine TM, E was inversely correlated to a cross-sectional area (P < 0.003, n = 11), and its value (24.9 and 1.5 kPa; geometric mean and geometric SE) was lower than E of human TM (515 ± 136 kPa; mean ± SE) (P < 0.01). C and variance of R were not significantly different between the species.

Conclusions.: A higher circumferential stiffness of the TM correlated with a higher outflow facility and less IOP elevation-induced variation in outflow resistance in normal human eyes, but not in porcine eyes. For future studies, these correlations need to be evaluated in glaucomatous eyes to better understand normal and abnormal TM functions.

Introduction
The main risk factor for developing glaucoma is elevated intraocular pressure (IOP). 1,2 In most cases, the pressure elevation in glaucomatous eyes is the result of increased resistance to aqueous humor outflow in the conventional outflow pathway. 3,4 The greatest resistance to aqueous outflow is in the juxtacanalicular (JCT) region of the trabecular meshwork (TM) and the inner wall of Schlemm's canal (SC). 510 However, mechanisms responsible for the generation and (dys)regulation of resistance remain unclear. 
Natural fluctuations of IOP occur throughout the day due to eye movements, blinking, circadian variations in aqueous production, ciliary muscle contraction, and ocular pulsations. 1114 These normal IOP changes alter mechanical stresses that induce deformation in ocular tissues, particularly the pressure-responsive TM. Consequently, the deformation may significantly affect tissue permeability to fluid flow or the hydraulic conductivity as reported in other tissues. 1517 Additionally, IOP fluctuation–induced TM deformation in extreme or chronic circumstances may lead to the collapse of SC that increases resistance to aqueous humor outflow, 6,1823 which in turn causes an increase in IOP. The magnitude of the TM deformation is influenced by the bulk Young's modulus, or “stiffness,” of the tissue. The stiffness may change with aging or due to pathological processes. Recent evidence has demonstrated the association between the higher Young's modulus of the JCT and glaucoma. 24,25 The local modulus in glaucomatous eyes is observed to be significantly higher and more variable than that in normal, age-matched eyes. However, the local modulus is only a measure of surface stiffness rather than a bulk tissue property that would have a greater influence on tissue deformation. 6  
Outflow resistance has been shown to increase with IOP elevation in perfused human eyes ex vivo. 2630 The resistance increase is believed to be caused by IOP elevation-induced ocular tissue deformation that obstructs outflow pathways. For example, TM deformation in the outflow direction will reduce the cross-sectional area of SC, which leads to an increase in the resistance to fluid flow in the SC. 18 Therefore, it is expected that the outflow resistance depends on not only the local stiffness of JCT/inner wall of SC, but also the bulk Young's modulus of TM, which depends mainly on structures of uveal and corneoscleral meshworks. 
The bulk Young's moduli of other ocular tissues, such as the sclera, lamina, cribrosa and cornea, have been investigated experimentally. 3134 However, despite its relevance to ocular hypertension in glaucoma, only the local Young's modulus of TM has been measured experimentally. 25 The bulk moduli of TM have only been estimated theoretically. 21,35,36 Furthermore, no study has tested whether TM stiffness correlates with outflow facility. To this end, we designed the study to measure the stress-strain curves of TM in normal human and porcine eyes and to correlate their bulk Young's moduli to outflow facilities. To our knowledge, this study marks the first experimental documentation of the bulk Young's modulus of TM in human and porcine eyes. Results from the study may lead to a better understanding of the relationship between mechanical properties of the outflow pathway and fluid dynamics in the eye. 
Methods
Eye Preparation
Both human and porcine eyes were prepared for whole globe perfusion as described previously. 3,26,28,37 Human eyes were obtained from Lions Eye Institute of Tampa, FL, and had no reported history of ocular diseases and/or surgeries. They were kept in saline-wetted gauze, placed in moist chambers, and shipped on ice. The left donor eyes were perfused within 48 hours post-mortem. Porcine eyes were obtained within 3 hours post-mortem from a local slaughterhouse and shipped on ice. Porcine eyes were refrigerated upon arrival and perfused within 7 hours post-mortem. All animals were treated in accordance with the ARVO Statement for the Use of Animals in Ophthalmic and Vision Research. All subjects were treated in accordance with the Declaration of Helsinki. 
Perfusion System
An isotonic solution was prepared with 5.5 mM of glucose in Dulbecco's PBS (276 ± 12 mOsm; Sigma Chemical Co., St. Louis, MO) to imitate aqueous humor. 38 The perfusion system design was a modified version of the system described by Camras et al. 39 to measure outflow facility. A syringe filled with solution was connected to a three-way stopcock that was linked to pressure tubing. One of the tubes was connected to a pressure transducer (Honeywell model 140 PC; Honeywell Sensing and Control, Freeport, IL). The other tube was attached to a second three-way stopcock linked to a fluid column, which acted as a manometer to set the perfusion pressure through control of the height of fluid column. The pressure transducer was connected using an analogue cable to a computer and calibrated by varying the height of fluid column. The calibration was also checked prior to each experiment by referencing a fluid column height to pressure detected by the transducer. The system pressure was referenced to zero corresponding to a zero flow rate. A 25-gauge needle was attached to the second stopcock and placed in the posterior chamber of the eye. A small moist wipe (Kimwipe; Kimberly-Clark, Neenah, WI) was placed over the cornea to prevent dehydration. Eyes were set in a water bath maintained at 34°C. Integrated data recording software (PowerLab; ADInstruments, Inc., Colorado Springs, CO) was used to record the pressure for the duration of the experiment at a sampling rate of 10 Hz. At the end of the experiment, the needle was rezeroed to verify that no obstructions in the perfusion system had occurred. 
Outflow Facility Calculation
Outflow facilities were calculated from the stabilized flow rates measured at set perfusion pressures of 10, 20, 30, and 40 mm Hg. As described in our previous study, 39 the fluid exiting the perfusion system was proportional to the decline in height of the column or decline in pressure over time. The volume of the fluid column was calibrated to be equivalent to 170.75 μL/mm Hg based on its 4-mm diameter. We assessed a steady state of perfusion by monitoring the pressure decline rate (mm Hg/s) in 3-minute intervals. Additionally, we made sure that the pressure in the eye matched the pressure in the fluid column by briefly valving off the column so the transducer referenced the pressure in the eye. When the pressure decline rate changed less than 10% between two adjacent intervals and the pressure in the eye matched the pressure set by the fluid column, we assumed that the perfusion had reached a steady state. Steady state occurred typically in a 10-minute recording period, after which the eyes were perfused for an additional 6 to 10 minutes. The average pressure and pressure decline rate were assessed over 6 minutes of the steady-state recording. For all experiments, the pressure drop was less than 1 mm Hg at a steady state; therefore, we assumed that the steady state eye perfusion was performed under a constant pressure condition. The average pressure decline rate was then converted to a flow rate (μL/min). The perfusion measurement described above was repeated for the four pressure levels set in the system in ascending order (10, 20, 30, and 40 mm Hg). The total perfusion time was less than 1.5 hours for porcine eyes to minimize the effects of washout. 37  
For enucleated eyes, there is no aqueous production, the episcleral venous pressure can be assumed to be zero, and the uveoscleral outflow is considered negligible. 3,40 Therefore, the inflow rate of fluid from the perfusion system F equals the outflow rate of fluid through the trabecular meshwork; and the IOP equals the perfusion pressure set in the system (Pc ). Based on these assumptions, the outflow facility for each level of Pc was calculated by 39 : The inverse of outflow facility is defined as the outflow resistance (R). The values of R at the four different levels of Pc were used to determine the statistical variance (i.e., the square of standard deviation) of R for each eye. 
Trabecular Meshwork Dissection
Each eye was removed from the perfusion system and cut along its equator. The choroid, iris, and lens were removed from the anterior segment. The TM was isolated by using a small surgical blade to cut along the pigmented line of the scleral spur below the TM. Forceps were used to grab the TM and pull it free along Schwalbe's line (see Fig. 1). Once the TM was isolated, it was placed in PBS and kept at 4°C until mechanical assessment. Post-TM removal, one porcine anterior segment was embedded in paraffin, cut into 0.5-μm thick sections, and stained with toluidine blue to visually examine the quality of the dissection. 
Figure 1. 
 
TM dissection method. Human and porcine eyes were dissected in a similar manner. Thus, only porcine TM dissection procedures are shown here. (A) Portion of TM that was removed from a porcine anterior segment. When TM was completely removed, remnants of pigment and scleral spur were removed to further isolate the TM for mechanical measurement. Images of the final sample are shown in two panels: (B) Low magnification. (C) High magnification. (D) Histology of 0.5-μm thick section of the AS of the porcine eye after TM removal. OW, outer wall of aqueous plexus. Scale bar indicates 100 μm.
Figure 1. 
 
TM dissection method. Human and porcine eyes were dissected in a similar manner. Thus, only porcine TM dissection procedures are shown here. (A) Portion of TM that was removed from a porcine anterior segment. When TM was completely removed, remnants of pigment and scleral spur were removed to further isolate the TM for mechanical measurement. Images of the final sample are shown in two panels: (B) Low magnification. (C) High magnification. (D) Histology of 0.5-μm thick section of the AS of the porcine eye after TM removal. OW, outer wall of aqueous plexus. Scale bar indicates 100 μm.
Trabecular Meshwork Preparation and Mechanical Test
The TM was cut into approximately 1-cm long segments and secured onto a bracket cut from cardstock paper (Fig. 2A). The ends of the TM segment were glued to the top and bottom of the bracket. The bracket was labeled and placed in a petri dish. Drops of PBS were applied to the TM to assure that it remained hydrated. All TM segments secured on the brackets were then imaged with an optical coherence tomography (OCT) instrument to assess the width and thickness, to determine the cross-sectional area for the later mechanical assessments. Fifty B-scans or cross-sectional views were acquired along a 5-mm length of each TM segment. Volume reconstruction was performed to determine uniformity of its width (Fig. 2B). Cross-sectional areas (Fig. 2C) were averaged over 3 regions approximately 1–2 mm apart using a custom designed computer code (courtesy of Hansford Hendargo) with a computing software (MATLAB; MathWorks, Natick, MA). 
Figure 2. 
 
Cross-sectional area calculation. (A) Diagram showing the ends of TM segments to be adhered to the top and bottom of a cardboard bracket. (B) OCT was used to make a volume scan of the TM segment. Areas at three cross-sections were evaluated along the TM segment (white dashed lines). The average of three areas was used to determine the normal stress in TM based on the force measurement. (C) In each cross-section, the thickness (T, solid arrow) and width (W, dashed arrow) were measured in terms of the number of pixels. Each pixel was equivalent to 2.07 μm. The area was estimated to be thickness times width.
Figure 2. 
 
Cross-sectional area calculation. (A) Diagram showing the ends of TM segments to be adhered to the top and bottom of a cardboard bracket. (B) OCT was used to make a volume scan of the TM segment. Areas at three cross-sections were evaluated along the TM segment (white dashed lines). The average of three areas was used to determine the normal stress in TM based on the force measurement. (C) In each cross-section, the thickness (T, solid arrow) and width (W, dashed arrow) were measured in terms of the number of pixels. Each pixel was equivalent to 2.07 μm. The area was estimated to be thickness times width.
The TM underwent a quasistatic uniaxial tensile mechanical test at room temperature within 6 hours after whole eye perfusion to determine its bulk Young's modulus. Prior to being loaded into the testing machine, TM segments secured to brackets were submerged in PBS. The TM was loaded into a micro-strain analyzer (MSA) by clamping the top and bottom of the bracket into the upper and lower fiber/film holders, respectively (Fig. 3A). Once loaded, the spine of the bracket was cut, leaving the two ends of TM secured to fiber/film holders. The TM was stretched continuously at 0.1% strain per second until mechanical failure. The percent strain (ε) and force were recorded by using data analysis software (TA Orchestrator; TA Instruments, New Castle, DE) and exported to spreadsheet software (Excel; Microsoft, Redmond, WA) for offline analysis.To minimize tissue dehydration during the mechanical test, the experimental procedures from loading of the TM to completion of the mechanical test were finished in less than 5 minutes. 
Figure 3. 
 
Mechanical test of TM. (A) Bracket with the TM (see Fig. 2A) was first secured to the upper and lower holders of an MSA. Afterwards, the spine of the bracket was removed. (B) A typical stress-strain curve of human TM. The stress was determined by dividing the force measured by MSA by the average cross-sectional area calculated from the OCT images. (C) Curve-fitting of data points at the strain range between 0 and 2%. The symbol represents experimental data and the solid curve is the nonlinear fitting of the data, using equation 2. The curve fitting provided the values of A and B for each TM segment. The bulk Young's modulus at 0% strain was determined using the equation: E = Ae = A.
Figure 3. 
 
Mechanical test of TM. (A) Bracket with the TM (see Fig. 2A) was first secured to the upper and lower holders of an MSA. Afterwards, the spine of the bracket was removed. (B) A typical stress-strain curve of human TM. The stress was determined by dividing the force measured by MSA by the average cross-sectional area calculated from the OCT images. (C) Curve-fitting of data points at the strain range between 0 and 2%. The symbol represents experimental data and the solid curve is the nonlinear fitting of the data, using equation 2. The curve fitting provided the values of A and B for each TM segment. The bulk Young's modulus at 0% strain was determined using the equation: E = Ae = A.
The tensile stress (σ) was calculated by dividing the force by the average cross-sectional area determined from the OCT images. A typical stress-strain curve is shown in Figure 3B; and its small deformation portion was fitted with an exponential function (equation 2),34,41,42 using a custom designed computer code with software (MATLAB; MathWorks; see Fig. 3C).  where A and B are constants. The apparent Young's modulus (E) was defined by Equation 3: which depends on the strain. Only the modulus at its relaxed state (i.e., 0% strain) was analyzed in this study, which is equal to the constant A
Statistics
All data were evaluated to determine their distributions using box and whisker plots. If a plot was significantly positively skewed and bounded by zero, a logarithmic transformation was used for normalization of the distribution. Comparisons between different experimental groups were evaluated with unpaired, two-tailed Student's t-tests for approximately normally distributed data, and two-tailed Mann-Whitney U tests for abnormally distributed data. Linear regression analysis was performed to evaluate the correlation between variables or logarithmically transformed variables. Statistical significance was defined when the P value was less than 0.05. 
Results
Human donors (n = 7) were primarily Caucasian and between the ages of 53 and 72 years (Table 1). The left eyes were perfused less than 48 hours post-mortem and outflow facilities were measured at pressures of 10, 20, 30, and 40 mm Hg, respectively (Table 2). To determine stiffness of the TM in two species, the stress-strain curves of human (n = 7) and porcine (n = 11) TM tissues are shown in Figure 4. Based on the curves, the bulk Young's modulus was determined for each sample at zero strain. The data are summarized in Tables 3 and 4. Box plots revealed that the Young's modulus of porcine TM (PTM) segments were positively skewed (Fig. 5A).Therefore, the porcine moduli were logarithmically transformed to normalize the data distribution for statistical analysis (Fig. 5A). The geometric mean and SE of the porcine moduli are reported in Table 4. The distribution of human TM (HTM) modulus data was approximately symmetric about the mean (data not shown), so no transformation was made. The PTM and HTM data were compared using the Mann-Whitney U test since the distribution of data in these two groups differed. The average modulus of HTM segments was significantly higher than that of PTM segments (P < 0.01; Table 4). 
Figure 4. 
 
Stress-strain curves of all TM samples. The curves were generated using the equation: σ(ε)=A/B(eB ε −1), where values of A and B were determined for each TM based on curve-fitting of experimental data. If two segments from the same TM were measured in the study, the arithmetic average of the two stress-strain curves is plotted here. (A) Stress-strain curves of seven human TM samples (dashed lines) and the arithmetic average of these curves (solid line). (B) Stress-strain curves of 11 porcine TM samples (dashed lines) and the geometric average of these curves (solid line).
Figure 4. 
 
Stress-strain curves of all TM samples. The curves were generated using the equation: σ(ε)=A/B(eB ε −1), where values of A and B were determined for each TM based on curve-fitting of experimental data. If two segments from the same TM were measured in the study, the arithmetic average of the two stress-strain curves is plotted here. (A) Stress-strain curves of seven human TM samples (dashed lines) and the arithmetic average of these curves (solid line). (B) Stress-strain curves of 11 porcine TM samples (dashed lines) and the geometric average of these curves (solid line).
Figure 5. 
 
Box plots of the bulk Young's modulus and variance of outflow resistance. (A) Porcine TM modulus and its logarithmic transformation (n = 11). (B) Variances of outflow resistance (VAR of R) and their logarithmic transformations for porcine TM. (C) Same plots as those in (B) for human TM. The VAR of R in porcine (n = 11) and human (n = 7) eyes were positively skewed, but their logarithmic transformations were approximately symmetric to the geometric means.
Figure 5. 
 
Box plots of the bulk Young's modulus and variance of outflow resistance. (A) Porcine TM modulus and its logarithmic transformation (n = 11). (B) Variances of outflow resistance (VAR of R) and their logarithmic transformations for porcine TM. (C) Same plots as those in (B) for human TM. The VAR of R in porcine (n = 11) and human (n = 7) eyes were positively skewed, but their logarithmic transformations were approximately symmetric to the geometric means.
Table 1. 
 
Human Donor Eye Information
Table 1. 
 
Human Donor Eye Information
Donor Sex Ethnicity Cause of Death Age (y) PMT (h)
1 Male White Prostate cancer with metastasis 70 46
2 Female Pacific Brain aneurysm, gallbladder cancer, sepsis 53 45
3 Male White Cardiac arrest, acute cardiac crisis, sepsis 53 42
4 Male White Respiratory failure, sepsis 56 44
5 Male White Lung cancer, respiratory failure, sepsis 68 36.5
6 Male White Lymphoma 72 24.5
7 Female White Bladder cancer 55 33.5
Average 61.0 38.8
Table 2. 
 
Outflow Facility of Human Donors
Table 2. 
 
Outflow Facility of Human Donors
Donor (OS) C at 10 mm Hg* C at 20 mm Hg C at 30 mm Hg C at 40 mm Hg VAR of R
1 0.250 0.248 0.341 0.361 0.455
2 0.180 0.224 0.211 0.240 0.352
3 0.361 0.358 0.347 0.355 0.002
4 0.137 0.154 0.120 0.080 6.996
5 0.273 0.207 0.162 0.165 1.387
6 0.334 0.366 0.363 0.384 0.026
7 0.179 0.212 0.226 0.211 0.268
Average 0.245 0.254 0.253 0.257 0.220‡
Table 3. 
 
E and Morphology of Human Donor TM
Table 3. 
 
E and Morphology of Human Donor TM
Donor (OS) E (kPa) Width (μm) Thickness (μm) Area (mm2)
1 228 306 124 0.038
2 622* 230† 127† 0.029†
3 1085 102 79 0.008
4 13 145 106 0.015
5 410 149 47 0.007
6 819* 244† 190† 0.044†
7 426* 259† 183† 0.048†
Average 515 205 123 0.027
Table 4. 
 
Comparison of Human vs. Porcine Data
Table 4. 
 
Comparison of Human vs. Porcine Data
Parameter Human Sample (mean ± SE, n = 7) Porcine Sample (mean ± SE, n = 11) P Value
PMT (h) 38.8 ± 2.9 4.6 ± 0.4 <0.001
Area (mm2) 0.027 ± 0.006 0.052 ± 0.005 <0.005
Thickness (μm) 123 ± 20 152 ± 9.0 0.09
Width (μm) 205 ± 28 339 ± 23 <0.005
E (kPa) 515 ± 136 24.9 & 1.5* <0.01†
C at 10 mm Hg‡ 0.245 ± 0.032 0.305 ± 0.032 0.23
C at 20 mm Hg 0.254 ± 0.030 0.311 ± 0.030 0.22
C at 30 mm Hg 0.253 ± 0.037 0.267 ± 0.025 0.75
C at 40 mm Hg 0.257 ± 0.043 0.260 ± 0.022 0.94
VAR of R§ 0.220 & 2.71* 0.130 & 1.50* 0.58
The outflow resistance varied with increasing IOP levels; and the distribution of its variance at different IOP levels were positively skewed for both porcine TM (Fig. 5B) and human TM (Fig. 5C). Thus, they were logarithmically transformed, and the geometric means and SEs are reported in Table 4. The distribution of other data (i.e., outflow facilities and TM thickness) examined for porcine and human eyes were approximately symmetric about their means and thus were evaluated for statistically significant differences between PTM and HTM data using unpaired, two-tailed Student's t-tests. No significant differences were observed for these data between porcine and human eyes. 
Linear regression analysis showed significant correlations between three parameters in human eyes. First, the outflow facility correlated with the Young's modulus; however, this correlation was only statistically significant for outflow facilities measured at 10 and 20 mm Hg (P < 0.05; R 2 = 0.61 and 0.76, respectively; Fig. 6A). A similar trend was observed at pressures of 30 and 40 mm Hg, but they were statistically insignificant. Second, the bulk modulus was inversely correlated to the variance of outflow resistance (P < 0.05; R 2 = 0.88; Fig. 6B). Lastly, the variance of outflow resistance decreased with increasing outflow facility measured at 10, 20, 30, and 40 mm Hg (P < 0.05; R 2 = 0.66, 0.87, 0.66, and 0.63, respectively; Fig. 6C). The age of the donor, dimensions of the TM (i.e., thickness and cross-sectional area), and the post-mortem time (PMT) did not significantly correlate with any parameters measured in human eyes. 
Figure 6. 
 
Correlations between E, C, and VAR of R in human eyes. (A) C, measured at perfusion pressure of 10 mm Hg (C 10) and 20 mm Hg (C 20), increased with an increase of the bulk modulus (P < 0.05, n = 7). Although not statistically significant, C measured at 30 and 40 mm Hg followed the same trend with an increase in the bulk modulus. (B) Logarithmically transformed VAR of R inversely correlated with E (P < 0.05, n = 7, R 2 = 0.88). (C) Logarithmically transformed VAR of R inversely correlated with C at all pressure levels (P < 0.05, n = 7; R 2 = 0.66, 0.88, 0.66, 0.63 for pressures of 10, 20, 30, 40 mm Hg, respectively). The unit of VAR of R is (mm Hg/μL/min)2.
Figure 6. 
 
Correlations between E, C, and VAR of R in human eyes. (A) C, measured at perfusion pressure of 10 mm Hg (C 10) and 20 mm Hg (C 20), increased with an increase of the bulk modulus (P < 0.05, n = 7). Although not statistically significant, C measured at 30 and 40 mm Hg followed the same trend with an increase in the bulk modulus. (B) Logarithmically transformed VAR of R inversely correlated with E (P < 0.05, n = 7, R 2 = 0.88). (C) Logarithmically transformed VAR of R inversely correlated with C at all pressure levels (P < 0.05, n = 7; R 2 = 0.66, 0.88, 0.66, 0.63 for pressures of 10, 20, 30, 40 mm Hg, respectively). The unit of VAR of R is (mm Hg/μL/min)2.
For porcine eyes, the only significant correlation observed was between the cross-sectional area and bulk Young's modulus (P < 0.005, R 2 = 0.645, n = 11; Fig. 7), suggesting that the modulus measured depended on the width of dissected TM. This variability in dissection may partly explain the lack of significant correlations between the bulk Young's modulus and other parameters. 
Figure 7. 
 
Cross-sectional area and E of PTM. E decreased with an increase in the cross-sectional area for porcine TM (P < 0.005, n = 11, R 2 = 0.645). The unit of E is kPa. The symbol represents experimental data and the solid line is the linear curve fitting.
Figure 7. 
 
Cross-sectional area and E of PTM. E decreased with an increase in the cross-sectional area for porcine TM (P < 0.005, n = 11, R 2 = 0.645). The unit of E is kPa. The symbol represents experimental data and the solid line is the linear curve fitting.
To understand mechanisms of the difference between human and porcine eyes, structures of extracellular matrix (ECM) in the TM were examined based on tissue autofluorescence. The images shown in Figure 8 were obtained when TM tissues were epi-illuminated. They indicated that orientations of fibers in the ECM were random in PTMs, but approximately aligned in the circumferential direction in HTMs. 
Figure 8. 
 
Autofluorescence images of TM. Autofluorescence from TM tissues was imaged with a green fluorescence protein filter set (Zeiss). The fluorescence images show ECM fibers. (A) PTM (B) HTM. The black arrows highlight the orientation of the fibers in the TM. ECM fibers in the HTM appeared to be aligned more parallel to each other in the circumferential direction in comparison with those in the PTM. Scale bars indicate 50 μm.
Figure 8. 
 
Autofluorescence images of TM. Autofluorescence from TM tissues was imaged with a green fluorescence protein filter set (Zeiss). The fluorescence images show ECM fibers. (A) PTM (B) HTM. The black arrows highlight the orientation of the fibers in the TM. ECM fibers in the HTM appeared to be aligned more parallel to each other in the circumferential direction in comparison with those in the PTM. Scale bars indicate 50 μm.
Circumferentially along the TM, the bulk Young's modulus was nonuniform since variations were observed between the moduli of two TM segments from the same eye. The difference in the moduli between two HTM segments (ΔE) from the same eye was 488 ± 192 kPa (mean ± SE, n = 3), indicating that the mean of ΔE was large since it was comparable to the arithmetic mean of E of all human TM samples (515 kPa, n = 7). For HTM samples whose stiffness was measured using two different segments, Table 3 shows the TM modulus of the donor eye determined by the mean of the two fitted stress-strain curves. For PTM, it was observed that the geometric mean and SE of ΔE were 3.1 and 2.5 kPa (n = 4), respectively, suggesting that ΔE between two PTM segments from the same eye was small because the geometric mean of ΔE was only 12% of the geometric mean of E of all PTM samples (24.9 kPa, n = 11). Taken together, the data described above suggested that circumferential distribution of E in PTM was less heterogeneous compared with that in HTM. 
Discussion
This study marks the first time that the circumferential stiffness of the TM is measured and correlated with C and IOP-induced variation in R. Human eyes demonstrated significant correlations between the circumferential E of the TM, C, and the variance of R. Specifically, a larger E (or stiffer TM) significantly correlated to a higher C measured at 10 and 20 mm Hg, respectively, and to a lower variance of R. Additionally, a higher C correlated with a lower variance of R at every given pressure. In contrast, the only statistically significant relationship found in porcine eyes was that a smaller E correlated with a larger cross-sectional area. Comparing human with porcine eyes, it was observed that HTM was ∼20 times stiffer than PTM, while C and variance of R were statistically the same between the two species. 
Bulk Young's Modulus of TM
The stress-strain curve of TM was nonlinear, indicating that the apparent tissue stiffness increased with increasing strain. In this study, only E at zero strain was analyzed, representing the TM stiffness at a relaxed state. The experimental data of E in humans were close to those predicted by mathematical models. 35,36 However, these values were much higher than the local Young's modulus of TM determined by using atomic force microscope (AFM) for both normal and glaucoma eyes. 25 This difference between local and bulk stiffness was consistent with the findings regarding E in other soft tissue studies, 43 suggesting that the measurements with different techniques reflect different structural properties of tissues. We previously measured porcine TM stiffness (Yuan F, et al., IOVS 2011:ARVO E-Abstract 6693) with AFM. The average local modulus of porcine TM (n = 9) was 1.38 kPa, which was one order of magnitude lower than the bulk modulus of the same tissue reported in this study. This discrepancy suggests that the moduli of TM measured with different techniques reflect different structural properties of the tissue. 43 It is likely that local Young's modulus measured with AFM reflects the stiffness of individual cells or bending stiffness of fibers in ECM, whereas the bulk Young's modulus reveals tensile strength of ECM fibers. In future studies, mathematical models need to be developed that can integrate local properties of cells and ECM at microscopic scales for predicting bulk properties of tissues. Experimentally, mechanical tests will be needed to determine anisotropic properties of the TM since the Young's modulus may depend on the direction of tissue deformation. TM stiffness measured under uniaxial tension in the circumferential direction may be different from those when TM is stretched in other directions. The information on anisotropic properties of TM is critical for determination of strain distribution in the TM caused by IOP elevation. 
Cell viability was not measured in this study. Although performed with different experimental conditions, evidence in the literature indicates that the majority of TM cells are still alive if the PMT is less than 36 hours. 44 In this study, outflow facility measurements in human eyes began within 24.5 to 48 hours PMT and the mechanical tests were performed in less than 6 hours afterwards, indicating that cell viability may be a concern for some of the samples used in this study. However, all outflow facility measurements were within the normal physiologic range and stable during the course of the experiments. Furthermore, regression analysis revealed no correlation between PMT and C, E, or variance of R. These observations suggest that changes in cell viability were insignificant, compared to other factors, for determining the trends in E, C, and variance of R in the seven human samples used in this study. These trends were more likely to be caused by intrinsic differences in tissue structures. In TM stiffness analysis, we assumed that the bulk modulus in the circumferential direction was minimally dependent on the viability and contraction/relaxation of TM cells as the corneoscleral and uveal beams provided the major resistance to tissue deformation in this direction (JCT and inner wall of SC were minor components in dissected TM tissues). In future studies, it is important to quantitatively investigate if TM cells have any influence on E and C through direct manipulation of cell viability in experiments. It is also important to investigate changes in C in response to treatments that cause TM cell contraction or relaxation in human eyes with wide ranges of PMT and donor ages. 
Mechanical properties of soft tissues are affected by hydration. 45 Prior to the mechanical testing, the TM used in this study remained submerged in PBS. The tissue hydration levels might change when the TM was removed from the PBS for measurement of E. However, the measurement took less than 5 minutes; and only the data with <3% strain in the stress-strain curves were used for determination of E, which were collected in less than 3 minutes after TM was removed from the PBS. Within this short period, we did not consider effects of tissue dehydration on E being important. In future studies, the hydration level should be controlled during mechanical stretching of TM. 
Porcine TM with a lower modulus had a larger cross-sectional area. This phenomenon might be attributed to a more disorganized ECM in PTM (see Fig. 8A). This fiber matrix could not provide significant resistance to tissue stretching since the axes of some fibers were perpendicular to the direction of deformation. In the HTM, ECM fibers were aligned mainly in the direction of mechanical deformation (see Fig. 8B). They together provided a higher resistance to tissue stretching under the applied forces. This difference in fiber orientation may partly explain the inverse dependence of the TM modulus on the cross-section area of PTM and the difference in tissue stiffness between HTM and PTM. The same observation may also indicate that the cells themselves provide minimal contributions to the modulus, and the organization of the ECM has a greater effect on its bulk modulus. Ultimately, to determine the validity of this hypothesis, future studies need to be performed quantitatively to separate contributions of ECM and cells to the bulk modulus. 
There were some variations in the modulus of TM in different segments within the same eye. The variation in E was larger in HTM than in PTM. These data were consistent with the notion that the modulus may be segmental in the TM, similar to the aqueous humor outflow 4649 and microscopic TM stiffness 22 reported previously. Future studies may elucidate these findings when regional changes in modulus and preferential flow patterns in TM are investigated simultaneously. 
Effects of TM Bulk Young's Modulus on C and Variance of R
Compared with data in the literature, the outflow facility measurements in this study were consistent with those reported for human 2630 and porcine 29,30,37 eyes. A lower variance of outflow resistance was statistically correlated to larger outflow facility and stiffer TM in human eyes. 12  
Outflow facility measured at 10 and 20 mm Hg was statistically significantly correlated to the bulk Young's modulus of TM in human eyes (see Fig. 6A). The bulk moduli of TM measured in this study represents the circumferential stiffness of the entire meshwork, presumably contributed mostly by corneoscleral and uveal beam network. A stiffer uveal and corneoscleral meshwork would provide structural support to the highly resistant JCT and inner wall of SC and facilitate more expansion of these tissues in the direction of aqueous outflow, which increased tissue porosity and thus reduced outflow resistance. Outflow facility measured at 30 and 40 mm Hg showed a supportive trend, but the relationship was not statistically significant. This may be explained largely by the fact that outflow facility did not always decrease with IOP elevation; in fact in over half of the cases in this study, the outflow facilities were increased. It is well known that IOP elevation increases outflow rate and drag forces on the trabecular beams, which compress TM and reduce the cross-sectional area of SC. 18,20,23 Both structural changes will lead to an increase in outflow resistance. However, the IOP elevation will also increase the pressure in SC, which may lead to a decrease in the downstream resistance, potentially through inducing dilation of collector channels to facilitate outflow. The IOP elevation may also alter giant vacuole structures in the inner wall of SC, thereby increasing its hydraulic conductivity. 50 Taken together, the changes in structures of outflow pathway or driving forces for aqueous outflow, induced by IOP elevation, may either increase or decrease the outflow facility, depending upon conditions of the tissues. In all cases, the IOP elevation should cause less change in the outflow facility if the ocular tissues are stiffer. That may explain why the variance of outflow resistance decreased with increasing TM stiffness observed in this study. 
However, the correlations between outflow facility, TM stiffness, and variance of outflow resistance, were insignificant in porcine eyes. The discrepancy between human and porcine eyes might be explained by differences in tissue structures. The outflow pathway in porcine eyes is anatomically different from that in humans. After passing through the TM, aqueous humor enters a series of discontinuous collector vessels or the angular plexus in porcine eyes rather than a continuous vascular ring (i.e., SC) in human eyes. 51 The segmental structures of the outflow pathway in porcine eyes may provide the main support to the JCT and inner wall region, making them less reliant on mechanical support provided by the uveal and corneoscleral meshwork. As a result, there was a minimal variability in porcine outflow facility measured in this study, making it difficult to find correlations between variance of outflow resistance and bulk Young's modulus of TM. Overall, porcine eyes did not appear to be a good model for predicting the effects of TM stiffness on outflow resistance in human eyes. 
A recent study reported that the local modulus of TM was higher in glaucomatous eyes than in normal human eyes. 25 Glaucomatous eyes are also known to have lower outflow facility than normal eyes. 3 Thus, a stiffer TM has been presumed to lead to lower outflow facility. 25 However, we observed that a stiffer TM was correlated with a higher outflow facility in human eyes. This apparent contradiction with observations in the literature can be explained as follows. The local modulus as measured by Last 25 is fundamentally a different mechanical property of tissues compared with the bulk modulus measured in the circumferential direction in the present study. Most soft tissues are anisotropic; therefore, differences in the type (compression, bending, tensile, etc.); direction; rate; and frequency of the applied forces, as well as locations in tissues selected for a mechanical test, can result in variable mechanical stiffness. The local modulus may be stiffer in glaucomatous eyes, which influences outflow resistance in JCT and inner wall of SC regions through changes in gene expressions, cell behavior, and ECM structures, whereas the bulk modulus 43 measured in this study may influence the resistance to aqueous outflow mainly through affecting the height of SC and compression of the TM in the outflow direction. Further analysis is needed to determine how different moduli influence the outflow facility in glaucomatous eyes and compare these moduli and the influence with those in normal human eyes. 
Conclusions
The circumferential bulk Young's modulus of the TM was evaluated in this study. The results showed that in normal human eyes, larger circumferential bulk modulus of TM correlated to increased outflow facility and decreased variance of outflow resistance. Stiffer TM may, macroscopically, reduce tissue deformation under mechanical loading, thereby making TM structures more stable during IOP fluctuations. Porcine eyes did not show the same correlation, indicating that this species was not a good model for investigation of the effects of TM stiffness on outflow facility. Additional studies are needed to evaluate the bulk modulus of TM, outflow facility, and the variance of outflow resistance in glaucomatous eyes with different donor ages, and compare the observations with those in normal human eyes. 
Acknowledgments
The authors thank I-Chien Liao for training on the MSA system, Hansford Hendargo for guidance with OCT measurements and analysis, and Joseph Izatt for use of OCT. 
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Footnotes
 Disclosure: L.J. Camras, Ivantis, Inc. (F); W.D. Stamer, None; D. Epstein, None; P. Gonzalez, None; F. Yuan, None
Figure 1. 
 
TM dissection method. Human and porcine eyes were dissected in a similar manner. Thus, only porcine TM dissection procedures are shown here. (A) Portion of TM that was removed from a porcine anterior segment. When TM was completely removed, remnants of pigment and scleral spur were removed to further isolate the TM for mechanical measurement. Images of the final sample are shown in two panels: (B) Low magnification. (C) High magnification. (D) Histology of 0.5-μm thick section of the AS of the porcine eye after TM removal. OW, outer wall of aqueous plexus. Scale bar indicates 100 μm.
Figure 1. 
 
TM dissection method. Human and porcine eyes were dissected in a similar manner. Thus, only porcine TM dissection procedures are shown here. (A) Portion of TM that was removed from a porcine anterior segment. When TM was completely removed, remnants of pigment and scleral spur were removed to further isolate the TM for mechanical measurement. Images of the final sample are shown in two panels: (B) Low magnification. (C) High magnification. (D) Histology of 0.5-μm thick section of the AS of the porcine eye after TM removal. OW, outer wall of aqueous plexus. Scale bar indicates 100 μm.
Figure 2. 
 
Cross-sectional area calculation. (A) Diagram showing the ends of TM segments to be adhered to the top and bottom of a cardboard bracket. (B) OCT was used to make a volume scan of the TM segment. Areas at three cross-sections were evaluated along the TM segment (white dashed lines). The average of three areas was used to determine the normal stress in TM based on the force measurement. (C) In each cross-section, the thickness (T, solid arrow) and width (W, dashed arrow) were measured in terms of the number of pixels. Each pixel was equivalent to 2.07 μm. The area was estimated to be thickness times width.
Figure 2. 
 
Cross-sectional area calculation. (A) Diagram showing the ends of TM segments to be adhered to the top and bottom of a cardboard bracket. (B) OCT was used to make a volume scan of the TM segment. Areas at three cross-sections were evaluated along the TM segment (white dashed lines). The average of three areas was used to determine the normal stress in TM based on the force measurement. (C) In each cross-section, the thickness (T, solid arrow) and width (W, dashed arrow) were measured in terms of the number of pixels. Each pixel was equivalent to 2.07 μm. The area was estimated to be thickness times width.
Figure 3. 
 
Mechanical test of TM. (A) Bracket with the TM (see Fig. 2A) was first secured to the upper and lower holders of an MSA. Afterwards, the spine of the bracket was removed. (B) A typical stress-strain curve of human TM. The stress was determined by dividing the force measured by MSA by the average cross-sectional area calculated from the OCT images. (C) Curve-fitting of data points at the strain range between 0 and 2%. The symbol represents experimental data and the solid curve is the nonlinear fitting of the data, using equation 2. The curve fitting provided the values of A and B for each TM segment. The bulk Young's modulus at 0% strain was determined using the equation: E = Ae = A.
Figure 3. 
 
Mechanical test of TM. (A) Bracket with the TM (see Fig. 2A) was first secured to the upper and lower holders of an MSA. Afterwards, the spine of the bracket was removed. (B) A typical stress-strain curve of human TM. The stress was determined by dividing the force measured by MSA by the average cross-sectional area calculated from the OCT images. (C) Curve-fitting of data points at the strain range between 0 and 2%. The symbol represents experimental data and the solid curve is the nonlinear fitting of the data, using equation 2. The curve fitting provided the values of A and B for each TM segment. The bulk Young's modulus at 0% strain was determined using the equation: E = Ae = A.
Figure 4. 
 
Stress-strain curves of all TM samples. The curves were generated using the equation: σ(ε)=A/B(eB ε −1), where values of A and B were determined for each TM based on curve-fitting of experimental data. If two segments from the same TM were measured in the study, the arithmetic average of the two stress-strain curves is plotted here. (A) Stress-strain curves of seven human TM samples (dashed lines) and the arithmetic average of these curves (solid line). (B) Stress-strain curves of 11 porcine TM samples (dashed lines) and the geometric average of these curves (solid line).
Figure 4. 
 
Stress-strain curves of all TM samples. The curves were generated using the equation: σ(ε)=A/B(eB ε −1), where values of A and B were determined for each TM based on curve-fitting of experimental data. If two segments from the same TM were measured in the study, the arithmetic average of the two stress-strain curves is plotted here. (A) Stress-strain curves of seven human TM samples (dashed lines) and the arithmetic average of these curves (solid line). (B) Stress-strain curves of 11 porcine TM samples (dashed lines) and the geometric average of these curves (solid line).
Figure 5. 
 
Box plots of the bulk Young's modulus and variance of outflow resistance. (A) Porcine TM modulus and its logarithmic transformation (n = 11). (B) Variances of outflow resistance (VAR of R) and their logarithmic transformations for porcine TM. (C) Same plots as those in (B) for human TM. The VAR of R in porcine (n = 11) and human (n = 7) eyes were positively skewed, but their logarithmic transformations were approximately symmetric to the geometric means.
Figure 5. 
 
Box plots of the bulk Young's modulus and variance of outflow resistance. (A) Porcine TM modulus and its logarithmic transformation (n = 11). (B) Variances of outflow resistance (VAR of R) and their logarithmic transformations for porcine TM. (C) Same plots as those in (B) for human TM. The VAR of R in porcine (n = 11) and human (n = 7) eyes were positively skewed, but their logarithmic transformations were approximately symmetric to the geometric means.
Figure 6. 
 
Correlations between E, C, and VAR of R in human eyes. (A) C, measured at perfusion pressure of 10 mm Hg (C 10) and 20 mm Hg (C 20), increased with an increase of the bulk modulus (P < 0.05, n = 7). Although not statistically significant, C measured at 30 and 40 mm Hg followed the same trend with an increase in the bulk modulus. (B) Logarithmically transformed VAR of R inversely correlated with E (P < 0.05, n = 7, R 2 = 0.88). (C) Logarithmically transformed VAR of R inversely correlated with C at all pressure levels (P < 0.05, n = 7; R 2 = 0.66, 0.88, 0.66, 0.63 for pressures of 10, 20, 30, 40 mm Hg, respectively). The unit of VAR of R is (mm Hg/μL/min)2.
Figure 6. 
 
Correlations between E, C, and VAR of R in human eyes. (A) C, measured at perfusion pressure of 10 mm Hg (C 10) and 20 mm Hg (C 20), increased with an increase of the bulk modulus (P < 0.05, n = 7). Although not statistically significant, C measured at 30 and 40 mm Hg followed the same trend with an increase in the bulk modulus. (B) Logarithmically transformed VAR of R inversely correlated with E (P < 0.05, n = 7, R 2 = 0.88). (C) Logarithmically transformed VAR of R inversely correlated with C at all pressure levels (P < 0.05, n = 7; R 2 = 0.66, 0.88, 0.66, 0.63 for pressures of 10, 20, 30, 40 mm Hg, respectively). The unit of VAR of R is (mm Hg/μL/min)2.
Figure 7. 
 
Cross-sectional area and E of PTM. E decreased with an increase in the cross-sectional area for porcine TM (P < 0.005, n = 11, R 2 = 0.645). The unit of E is kPa. The symbol represents experimental data and the solid line is the linear curve fitting.
Figure 7. 
 
Cross-sectional area and E of PTM. E decreased with an increase in the cross-sectional area for porcine TM (P < 0.005, n = 11, R 2 = 0.645). The unit of E is kPa. The symbol represents experimental data and the solid line is the linear curve fitting.
Figure 8. 
 
Autofluorescence images of TM. Autofluorescence from TM tissues was imaged with a green fluorescence protein filter set (Zeiss). The fluorescence images show ECM fibers. (A) PTM (B) HTM. The black arrows highlight the orientation of the fibers in the TM. ECM fibers in the HTM appeared to be aligned more parallel to each other in the circumferential direction in comparison with those in the PTM. Scale bars indicate 50 μm.
Figure 8. 
 
Autofluorescence images of TM. Autofluorescence from TM tissues was imaged with a green fluorescence protein filter set (Zeiss). The fluorescence images show ECM fibers. (A) PTM (B) HTM. The black arrows highlight the orientation of the fibers in the TM. ECM fibers in the HTM appeared to be aligned more parallel to each other in the circumferential direction in comparison with those in the PTM. Scale bars indicate 50 μm.
Table 1. 
 
Human Donor Eye Information
Table 1. 
 
Human Donor Eye Information
Donor Sex Ethnicity Cause of Death Age (y) PMT (h)
1 Male White Prostate cancer with metastasis 70 46
2 Female Pacific Brain aneurysm, gallbladder cancer, sepsis 53 45
3 Male White Cardiac arrest, acute cardiac crisis, sepsis 53 42
4 Male White Respiratory failure, sepsis 56 44
5 Male White Lung cancer, respiratory failure, sepsis 68 36.5
6 Male White Lymphoma 72 24.5
7 Female White Bladder cancer 55 33.5
Average 61.0 38.8
Table 2. 
 
Outflow Facility of Human Donors
Table 2. 
 
Outflow Facility of Human Donors
Donor (OS) C at 10 mm Hg* C at 20 mm Hg C at 30 mm Hg C at 40 mm Hg VAR of R
1 0.250 0.248 0.341 0.361 0.455
2 0.180 0.224 0.211 0.240 0.352
3 0.361 0.358 0.347 0.355 0.002
4 0.137 0.154 0.120 0.080 6.996
5 0.273 0.207 0.162 0.165 1.387
6 0.334 0.366 0.363 0.384 0.026
7 0.179 0.212 0.226 0.211 0.268
Average 0.245 0.254 0.253 0.257 0.220‡
Table 3. 
 
E and Morphology of Human Donor TM
Table 3. 
 
E and Morphology of Human Donor TM
Donor (OS) E (kPa) Width (μm) Thickness (μm) Area (mm2)
1 228 306 124 0.038
2 622* 230† 127† 0.029†
3 1085 102 79 0.008
4 13 145 106 0.015
5 410 149 47 0.007
6 819* 244† 190† 0.044†
7 426* 259† 183† 0.048†
Average 515 205 123 0.027
Table 4. 
 
Comparison of Human vs. Porcine Data
Table 4. 
 
Comparison of Human vs. Porcine Data
Parameter Human Sample (mean ± SE, n = 7) Porcine Sample (mean ± SE, n = 11) P Value
PMT (h) 38.8 ± 2.9 4.6 ± 0.4 <0.001
Area (mm2) 0.027 ± 0.006 0.052 ± 0.005 <0.005
Thickness (μm) 123 ± 20 152 ± 9.0 0.09
Width (μm) 205 ± 28 339 ± 23 <0.005
E (kPa) 515 ± 136 24.9 & 1.5* <0.01†
C at 10 mm Hg‡ 0.245 ± 0.032 0.305 ± 0.032 0.23
C at 20 mm Hg 0.254 ± 0.030 0.311 ± 0.030 0.22
C at 30 mm Hg 0.253 ± 0.037 0.267 ± 0.025 0.75
C at 40 mm Hg 0.257 ± 0.043 0.260 ± 0.022 0.94
VAR of R§ 0.220 & 2.71* 0.130 & 1.50* 0.58
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