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Glaucoma  |   February 2007
The Relationship between Nerve Fiber Layer and Perimetry Measurements
Author Affiliations
  • Ronald S. Harwerth
    From the College of Optometry, University of Houston, Houston, Texas.
  • Abhiram S. Vilupuru
    From the College of Optometry, University of Houston, Houston, Texas.
  • Nalini V. Rangaswamy
    From the College of Optometry, University of Houston, Houston, Texas.
  • Earl L. Smith, III
    From the College of Optometry, University of Houston, Houston, Texas.
Investigative Ophthalmology & Visual Science February 2007, Vol.48, 763-773. doi:10.1167/iovs.06-0688
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      Ronald S. Harwerth, Abhiram S. Vilupuru, Nalini V. Rangaswamy, Earl L. Smith, III; The Relationship between Nerve Fiber Layer and Perimetry Measurements. Invest. Ophthalmol. Vis. Sci. 2007;48(2):763-773. doi: 10.1167/iovs.06-0688.

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      © 2016 Association for Research in Vision and Ophthalmology.

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Abstract

purpose. Losses of retinal ganglion cells (RGCs) in glaucoma are the cause of visual field defects and thinning of the retinal nerve fiber layer (RNFL), but methods of correlating these events have not been developed. The present study was conducted to investigate the relationship between standard automated perimetry (SAP) measures of RGCs and optical coherence tomography (OCT) measures of the ganglion cell axons entering the optic nerve from corresponding visual field locations.

methods. SAP and OCT data from normal monkeys were used to develop methods for estimating neuron counts and mapping SAP visual field locations onto the optic nerve head (ONH). The procedures developed for normal eyes were applied to monkeys with experimental glaucoma.

results. The number of neurons derived from SAP and OCT data for normal eyes were in close agreement. The estimates of the number of RGCs in retinal areas of the Humphrey Field Analyzer 24-2 (Carl Zeiss Meditec, Inc., Dublin, CA) visual field and the axons entering the ONH were both approximately 1.5 million. The neural losses derived from subjective and objective measurements in monkeys with early experimental glaucoma correlated highly, with a mean ± SD difference of 0.6% ± 22% between the two estimates in control eyes and 3% ± 24% in laser-treated eyes.

conclusions. SAP measures of visual field defects and OCT measures of RNFL defects are correlated measures of glaucomatous neuropathy. The normal intersubject variability and the dynamic ranges of the measurements suggest that RNFL thickness may be a more sensitive measurement for early stages and perimetry a better measure for moderate to advanced stages of glaucoma.

The deterioration of a patient’s vision caused by glaucoma is a result of the progressive, pathologic loss of the retinal ganglion cells (RGCs) and their axons that form the optic nerve. 1 2 The cause of glaucoma is unknown and, therefore, its diagnosis and an assessment of the stage of disease require ophthalmic examination to identify and quantify the clinical characteristics of the neuropathy. 3 4 Traditionally, the standard ophthalmic examination has been perimetric measures of visual sensitivity, 3 4 5 6 7 but more recently, high-resolution imaging of anatomic structures has also become a standard examination procedure. 8 9 With either type of examination (i.e., visual function or retinal structure), abnormal findings may be sufficient to identify RGC losses, but to optimize clinical applications for early diagnosis and evaluation of progression, it is important also to understand the quantitative relationships between the functional and structural measurements. 
On the face of it, there must be an essential relationship between subjective measurements by perimetry and certain objective measurements, such as optical coherence tomography (OCT) measurements of the thickness of the retinal nerve fiber layer (RNFL). 10 11 Logically, the degree of reduced visual sensitivity in an area of the visual field must be proportional to the amount of loss of ganglion cells in the corresponding area of the retina. 12 13 14 15 Similarly, the number of axons entering the optic nerve from an area of the retina must be equal to the number of RGCs and therefore also proportional to the degree of reduced visual sensitivity. However, recent clinical studies have suggested less straightforward interpretations of mechanistic relationships between standard automated perimetry (SAP) and OCT. For example, OCT has been reported to be a highly reproducible measurement with very high sensitivity and specificity in discriminating between control and patient populations. 16 17 18 19 20 21 Without exception, RNFL thickness measurements that are outside the 95% normal confidence limits identify patients with glaucoma who have moderate glaucomatous field defects 17 and, thus, in stages where there is an established relationship between visual and neural losses, both procedures detect the neuropathy. 14 15 Other studies, however, have suggested a “disconnect” between the structural and functional measurements. 22 23 24 In a longitudinal study of persons with suspected glaucoma and patients with known disease, a larger percentage of patients were classified as having progressive disease by OCT than by SAP measurements, and it was suggested that structural changes may precede functional changes in early stages of the disease (preperimetric glaucoma), or lag behind functional changes in the late stages, because of a curvilinear relationship between functional and structural defects caused by glaucoma. 24 In support of preperimetric neural loss, several other investigations have found evidence of an earlier detection of neuropathy by measurement of the nerve fiber layer compared with perimetry. 25 26 27 28 In addition, although RNFL thickness parameters have relatively high sensitivity for identifying glaucoma, there may be less agreement between perimetry and nerve fiber layer instruments for classifying eyes with glaucoma, which suggests that different techniques may identify different characteristics of glaucomatous damage. 29  
These prior clinical studies of morphologic imaging have failed to produce a consensus about the causal relationship between nerve fiber layer and perimetry measurements and, it is also important to note, none has suggested a quantitative structure–function relationship between these clinical measurements. It is likely that the absence of accord between measurements by SAP and OCT stems from the difficulty in comparing two very different measurements without a common scale—that is, visual sensitivity in decibels and nerve fiber layer thickness in micrometers. However, as mentioned, there should be a very close relationship between SAP thresholds in a given location, which is determined by the number of RGCs in the corresponding retinal area, and the RNFL thickness, which represents the number of RGC axons from a given location in the retina. Thus, the number of RGCs provides a common denominator underlying the two clinical procedures that should define a quantitative relationship (Knighton RW et al. IOVS 2005;46:ARVO E-Abstract 3744). To explore this approach, we undertook the present investigations to study the relationship between SAP measures of the number of RGCs and OCT measures of the number of RGC axons. The investigations were conducted in two phases, with macaque monkeys used for subjects in both. The first phase was the development of methods and procedures for relating visual sensitivity and RNFL thickness, which were based on an analysis of SAP and OCT measurements from normal control eyes. The second phase was an application of the methods and procedures developed in phase 1 to study the relation between behavioral SAP and clinical OCT measurements of the neuropathy caused by experimental glaucoma. Some of the results of these studies have been presented in abstract form (Harwerth RS et al. IOVS 2006;47:ARVO E-Abstract 1235). 
Materials and Methods
Subjects
The subjects for the investigations were adult rhesus monkeys (Macaca mulatta). All the experimental and animal care procedures were reviewed and approved by the Institutional Animal Care and Use Committee of the University of Houston. The use of animals for these experiments adhered to the ARVO Statement for the Use of Animals in Ophthalmic and Vision Research. 
For the first phase, two separate groups of subjects were used to obtain normative data for SAP and OCT data. The SAP normative data were the baseline data obtained from 35 monkeys before laser treatment to induce experimental glaucoma. These monkeys had all been subjects in previous studies, 30 31 32 33 34 35 and none of them were also subjects for the OCT measurements of the first phase or any part of the second phase of the current investigation. The normative OCT data were obtained from 20 monkeys that were in the same age range as the subjects for SAP (6–9 years of age). Most of these monkeys were in the colony for other investigations that did not involve procedures that might affect the retina or optic nerve, but three of the subjects for normative OCT measurements were subsequently treated to induce experimental glaucoma for the second phase experiments. A total of seven monkeys with experimental glaucoma and behavioral training for SAP were subjects for the second phase, in which the relationship between nerve fiber layer and perimetry measurements was studied. 
Experimental Glaucoma
The experimental model of glaucoma was unilateral, laser-induced ocular hypertension. 36 37 The intraocular pressures of the monkeys’ right eyes were elevated by scarification of their trabecular meshwork by argon laser treatment, using energy levels that destroy the trabecular meshwork and obliterate Schlemm’s canal in the vicinity of the burn. In preparation for the laser procedure, the monkeys were anesthetized with ketamine (20 mg/kg) and acepromazine (0.2 mg/kg) and a topical corneal anesthetic (0.5% proparacaine) instilled in the eye to be treated. The animals’ heads were stabilized on the chin rest of a standard clinical laser slit lamp system, and the laser treatments were performed by using a gonio laser lens designed for monkey eyes. The laser energy (nominal laser parameters: blue-green mode, 1.0-W power, 50-μm spot size, and 0.5-second exposure duration) were equivalent to those used in previous investigations of experimental glaucoma in macaques. 36 37 38 39 40 41 42 43 The burns were spaced to produce contiguous tissue blanching. The treatment protocol involved an initial laser procedure over 270° of the drainage angle and subsequent treatments covering 180°, retreating as necessary to elevate the IOP, with an interval of at least 3 weeks between procedures. Relatively high argon laser energy was needed to produce ocular hypertension, and the resultant pressures were generally quite high compared with the IOPs of patients with chronic ocular hypertension, but a systematic relationship between total laser energy and either the maximum IOP or the rate of elevation of IOP has not been found. 37  
Behavioral Perimetry
The visual field defects caused by experimental glaucoma were assessed by static threshold perimetry using standard clinical instrumentation. The visual field data were acquired with a Humphrey Field Analyzer (HFA; Carl Zeiss Meditec, Inc., Dublin, CA) that was attached to a primate-testing cubicle. The visual thresholds were determined by the behavioral responses of monkeys that were trained to fixate and perform a psychophysical detection task that is essentially the same as that used for clinical patients. The general scheme of the testing procedure, which has been described in detail, 30 is as follows: The monkeys were seated in a custom-made primate chair that allowed adjustments for alignment of their eyes at the correct viewing location and the placement of their mouths on a juice spout used to deliver behavioral rewards. While in the chair, they were able to grasp the response switch used for behavioral responses. Thresholds for fixation and perimetry stimuli were obtained by a psychophysical method, a criterion response-time paradigm for monkeys, which retains the essential requirements of the test procedure used for patients. The monkeys were required to press and hold down the response switch to initiate a trial and, subsequently, to release the switch in the presence of a visual stimulus. The occurrence of a stimulus presentation was random (within a 5.5 seconds interval) and, if the monkey’s switch release correlated closely with the visual stimulus presentation (within a 900-ms response interval), then the response was operationally defined as a true-positive response (a hit), and it was rewarded. Alternatively, if the switch release was beyond the response interval, it was considered as a false-negative response (a miss) and the monkey was neither rewarded nor punished. The test stimulus in any trial could be a central fixation stimulus or one of the peripheral perimetry stimuli. The locations and intensities of the peripheral test stimuli are determined by the Humphrey Field Analyzer’s C24-2 full-threshold program. 
Optical Coherence Tomography
For OCT measurements, the animals were anesthetized with an intramuscular injection of ketamine (20–25 mg/kg per hour) and xylazine (0.8–0.9 mg/kg per hour) and were treated with subcutaneous atropine sulfate (0.04 mg/kg). The pupils were dilated to approximately 8.5 mm in diameter with topical tropicamide (1%) and phenylephrine (2.5%), and a plano-power contact lens was placed on the eye to maintain optical clarity during the measurements. During the measurements, the monkey’s body temperature was maintained between 36.5°C and 38°C with a thermostatically controlled blanket and the heart rate and blood oxygen were monitored using a pulse oximeter. A padded mouth bar and an occipital bar were used to stabilize and position the head. The head support device was attached to a rotational mount that allowed the head to be aligned appropriately for the series of OCT measurements. 
All the RNFL images were acquired by one of the authors (ASV) using a StratusOCT running version 4.0.4 software (Carl Zeiss Meditec, Inc.). The monkeys’ clear optics and dilated pupils, along with a stable eye position during the procedure, provided high-quality images, and essentially all the scans had a signal strength of 10. The standard RNFL thickness protocol was used to obtain measures at 512 points in the nominal 10.87-mm scan length (circumference) of a circle of 3.4-mm diameter that is centered on the optic nerve head (ONH). Three standard scans were collected for each eye and subsequently exported to a computer using proprietary software provided by the manufacturer. The data-acquisition protocol for humans was used without modification for the measurements on monkey eyes, because the variability between monkeys and humans should not be larger than the variability between humans with different sizes of optic nerves. The variability in RNFL thickness between large and small nerves has been attributed to differences in the distance from the edge of the optic nerve to the location of the scan line, as a result of using a fixed diameter scan circle for OCT measurements. 44 45 46 The shorter axial lengths of monkeys’ eyes, approximately 19 mm compared with 25 mm for humans’ eyes, could make the scan circle smaller and closer to the edge of the ONH. However, measurements estimated from the OCT fundus photographs of the relationship between the scan circle and ONH indicated that the scan line and disc edge are separated by at least 600 μm, which is a distance where OCT and histologic measures of nerve fiber layer have been shown to be in agreement. 46 In addition, with appropriate age compensation, the data from the normal, control eyes of monkeys fall within the expected normal range of human eyes. Thus, although the standard circle scan for RNFL thickness may have been designed for human eyes, compensation for differences in axial lengths between the two species was not necessary. However, it should also be noted that the specific parameters used to design the instrument should have had little effect in the present studies, because the detection of change and the analysis of axon density were based on comparisons to normative data from monkeys of similar age or to each monkey’s own control eye. 
Results
SAP and OCT Relationships for Normal Eyes.
Quantification of the relationships between visual field defects and RNFL thinning caused by glaucoma requires methods of estimating the RGC populations underlying each of the measurements. The procedures for estimating RGC populations involved three steps that were initially developed from SAP and OCT normative data from monkeys’ eyes. The first step was to estimate the number of RGCs in an area of the retina from the corresponding SAP measurements of visual sensitivity. The second step required an estimation of RGC axons in a sector of the ONH from the corresponding OCT measurements of RNFL thickness. The final step was to correlate RGCs and axons for local regions of the visual field and nerve fiber layer through a mapping of SAP test locations onto the ONH. 
The methods of estimating the number of ganglion cell from perimetry measurements were developed from data obtained by behavioral perimetry and retinal histology in experimental glaucoma 14 and subsequently verified for histology and clinical perimetry in patients with glaucoma. 15 Briefly, these studies demonstrated nonlinear pooling of ganglion cell responses during the detection of visual stimuli in perimetry, but for purposes of predicting RGC density from visual sensitivity, the relationships became linear when both variables were expressed in logarithmic units. Thus, the empiric relationship between visual sensitivity, in decibels (the threshold value from a given test location for the 24-2 program of the HFA), as a function of ganglion cell density, in dB (10 times the logarithm of the histologic count of ganglion cells at the corresponding retinal location), was linear for each retinal eccentricity (arcdeg radius from the fixation point). However, the parameters of the linear function varied with eccentricity and, thus, the model required two equations to determine the slope and y-intercept as a function of eccentricity, which in turn provided the parameters for the third function for predicting ganglion cell density from visual sensitivity. The three equations are the slope of the function (m) at eccentricity (e):  
\[m{=}(0.054e){+}0.95,\]
the intercept of the function (b) at eccentricity (e):  
\[b{=}({-}1.5e){-}14.8,\]
and the predicted ganglion cell density (gc) for a sensitivity (s):  
\[gc{=}(s{-}b)/m.\]
 
To obtain the total number of ganglion cells in an area of the retina, we considered the cell density derived from each perimetry measurement to be uniform over an area of retina corresponding to a 6° × 6° area of visual space that separates test locations in SAP. Thus, to determine the total number of RGCs in a specific area of the visual field, the ganglion cell density from equation 3 was unlogged and multiplied by 2.25 (based on a conversion factor of 1 mm retinal distance per 4° visual angle for the monkey eye). Finally, to determine the number of axons entering a region of the optic nerve, the ganglion cell densities were summed across the visual field locations that were mapped onto a given ONH sector. 
Using these procedures for a normal eye, the total number of RGCs in the area of the visual field that is sampled by the 24-2 HFA test pattern was estimated from the normative visual field data from the 140 visual fields of 35 monkey eyes. The normative thresholds and standard deviations are presented in Figure 1A , with the data arranged to match the locations of the 24-2 test grid for a right eye. The two perimetry test locations near the ONH were omitted from the calculations of RGCs. In addition, the test locations in the temporal visual field, adjacent to the blind spot, were also excluded from the calculation because there are too few test locations in that area to compare with the number of axons entering the nasal ONH from these regions of the retina. With these locations excluded, the total number of RGCs of the normal monkey eye was 1,537,621, which is at the higher end of the range of published estimates of axons in the optic nerves of monkeys 48 49 50 or humans. 50 51 52  
For the second step in relating SAP and OCT measurements, the number of RGC axons represented by RNFL thickness measures were estimated from the area defined by the RNFL thickness profile and the normal density of axons in the RNFL. The OCT scan length for the standard scan (10.87 mm) was sampled in 512 pixels, and each pixel thus represented a retinal distance of 21.2 μm. The scan height across pixels provided the total area occupied by RNFL axons in the ONH. The axon density in the RNFL has not been determined, but several histologic studies have assessed axon diameters. 49 52 53 In one study in which axon diameters were compared across the regions of the nerve fiber bundles, it was found that the median diameter (0.4–0.8 μm) varied with bundle location, but in each location, the distribution of axon diameters was skewed toward diameters larger than the median. 53 Other studies have reported larger mean diameters 49 54 or have shown variations in diameter along the length of an axon. 55 For purposes of the present study, a small range of axon densities that were compatible with published data were evaluated to obtain the best match between axon and RGC numbers for the normative data. Based on these calculations, a density of 1.71 axons/μm2 (∼0.75-μm diameter) was set as the coefficient of proportionality for the number of axons per unit area of the OCT scan. Although the empiric constant is reasonable, small variations would not introduce large errors, typically about a 5% change in total axon number per 0.1 change in axon density. 
The number of axons entering the normal ONH was estimated from the OCT data from 40 scans in 20 monkeys. The double-hump scan profile for the mean RNFL thickness and 95% confidence limits (Fig. 1B)is remarkably similar to measurements of normal human eyes—that is, the scan generally follows an “ISNT” rule, with the greatest thickness at the inferior pole, followed by the superior, nasal, and temporal regions of the ONH. In addition, the RNFL average thickness of 94 μm is similar to that expected for the eyes of 25- to 30-year-old humans, which is the approximate human-equivalent age of the monkeys. Using the axon density of 1.71 axons/μm2, the total area under the monkeys’ RNFL thickness profile represented 1,507,216 axons, which is within 2% agreement with the number of RGCs derived from SAP measurements. 
The agreement in the number of ganglion cells in the retina and their axons in the nerve fiber layer provided evidence that these measures of structure and function reflect a common neural basis, at least in normal eyes. However, for the diagnosis and assessment of glaucoma, the structure-function relationship must also demonstrate a spatial agreement between the SAP and RNFL defects. Therefore, the final step for determining the relationship between nerve fiber and perimetry measurements was to develop an appropriate topographical mapping of the visual field onto the ONH. Although several mapping relationships have been proposed, 56 57 58 59 none produced a tenable relationship between the RGC and RNFL data, and therefore a modified scheme was developed for the SAP-OCT relationship that is illustrated in Figure 2 . With this scheme, the ONH was divided into 10 equal sectors of 36° (Fig. 2A) , each representing 51 pixels of the OCT scan (Fig. 2B) . The number of visual field locations assigned to a sector varied from one SAP location near the fovea entering the ONH in sector 1 or 10, to 13 SAP locations for the arcuate locations of the visual field entering the ONH in sector 4 or 7 (Fig. 2C) . The final RGC to RNFL relationship was derived by the sum of ganglion cells inputting to an ONH sector, as estimated from the perimetry sensitivities at each test field location, and the total number of RGC axons at the ONH that was estimated from the area of the nerve fiber layer for each sector multiplied by the density of RNFL axons. 
The results of using these methods for deriving the number of cells and axons are presented in Figure 2D . The total number of ganglion cells (squares) or neuron axons (circles) in each ONH sector is plotted at the center of the pixel range representing that sector. The agreement between the two estimates of neural elements is generally excellent. For example, the function indicates that the axons of nearly 150,000 ganglion cells from SAP test location 1 enter ONH sector 1 and, similarly, the OCT scan height across sector 1 converts to approximately 150,000 axons entering ONH sector 1. The agreement between the two estimates is consistent for all the sectors except for sectors 5 and 6. The obvious SAP underestimation of RGC axons entering these sectors is irresolvable because perimetry does not sample a sufficient amount of retina to determine the axon count into the nasal ONH, and consequently these sectors were omitted from subsequent analyses of visual field and nerve fiber layer defects. For the other sectors, the estimates of the normal populations of RGCs and axons were essentially equal, which suggests that the procedures for deriving topographically related RGC populations from SAP and OCT measures can be applied to study the progressive neuropathy caused by experimental glaucoma. 
SAP and OCT Relationships in Experimental Glaucoma
The investigations of structural and functional relationships in experimental glaucoma were based on SAP and OCT measurements that followed the final laser treatment in the series of treatments that were necessary to initiate visual and neural changes. The general results of the study are illustrated by examples for one monkey, using data that were collected over the time course of progression from normal visual fields to a stage of moderate visual field defects (Fig. 3 , Table 1 ). The subject (OHT-48) had three laser treatments of the right eye over an 8-month period that did not cause measurable neuropathy (Fig. 3A) 3and then a fourth laser treatment that led to the progressive changes illustrated (Figs. 3B-D ). The first set of data, labeled preglaucoma are representative of normal visual fields and normal RNFL thicknesses, as indicated by the symmetric and equal data for the SAP and OCT measurements in the laser-treated and control eyes and by the similarity in estimated RGCs and neurons for both measurements and across the two eyes. Further, as a standard clinical metric of visual fields, the global indices for these functions (Table 1)demonstrate that the SAP fields are within the ranges of normal data for monkeys’ eyes. The perimetric indices mean deviation (MD) and pattern standard deviation (PSD) were based on the standard StatPac (Carl Zeiss Meditec, Inc.) methods of statistical analyses, 60 but used SAP visual fields from normal monkeys. In addition to the derived MD and PSD in decibels, the deviations from the expected norm are given in z-score units, to provide an indication of the significance of the effects of experimental glaucoma. At this stage, the indices for both eyes were well within the 95% confidence limits (1.96 z-score units) for normal fields. 
Similar analyses of global indices, though nonconventional for OCT measurements, were conducted on the data for RNFL thicknesses and are also presented in Table 1 . This approach was taken because MD and PSD are very familiar clinical indices, and the z-score transformation provides a straightforward comparison of statistical significance of OCT and SAP results. Thus, for the RNFL measurements, the OCT (MD) represents the weighted average deviation from the expected normal RNFL thickness in monkeys and the OCT (PSD) provides an index that reflects more localized alterations, with respect to the normal scan profile. As with the SAP indices, the OCT indices, presented in the units of the measurements (μm) and in z-score units, demonstrate that the RNFL functions in Figure 3Aare at a preglaucoma stage, with only nonsignificant variations from normal monkeys. As well, the estimates of the numbers of RGCs derived from SAP data and the number of ONH axons based on OCT data are also consistent in showing similarities across procedures for estimating neural cells or axons for each eye and across the two eyes. 
Examples of the early alterations of SAP and OCT measurements from the monkey’s experimental glaucoma are presented in Figure 3B . By 1 month after the final laser treatment of the trabecular meshwork, the monkey had developed mild visual field defects that are apparent in the gray scale plots and by a relative RNFL thinning around the inferior pole of the ONH. The clinical significances of these changes are indicated by the statistical indices (Table 1) , which show that the measurements by SAP are outside of the 95% confidence limits of normal values, whereas the OCT data are not significant. The z-score transformation also demonstrates that the changes in the visual fields and nerve fiber layer are similar when the deviations are expressed as SD units, based on the distribution of normative data for the respective measure. The agreements between the SAP and OCT measures of early neuropathy are also shown by the estimates of RGCs and ONH axons that were derived from the measures (Fig. 3B , Table 1 ). It is an important note that these data demonstrate that the procedures developed for normative data from a large number of eyes were equally successful for an individual eye, and that comparisons of the data for the unlasered left eye across time demonstrate the reproducibility of the methods and measures that were used in the study. 
As illustrated by the data presented in Figure 3C , the monkey’s visual field and nerve fiber layer defects progressed rapidly over the next month. At that time, the visual field sensitivity of the laser-treated eye was generally depressed, but with somewhat deeper scotomas in the arcuate region of the lower hemifield. In concordance with the visual fields, the RNFL thickness profile also was generally thinner across the scan, but with a relatively greater thinning in the superior than inferior region of the ONH. Thus, the defects are more severe in the visual field area and the region of the RNFL scan that are represented by sector 4 of the SAP to OCT map, compared with ONH sector 7 that represents the superior arcuate region of the visual field and the inferior region of the RNFL. The same agreement between the alterations in structure and function is evident in the statistical indices derived for the data from the laser-treated eye. All the measurements reveal significant variations from expected normal values, with similar levels of significance (a z-score of approximately 7) across the MD and PSD indices for both SAP and OCT measurements. The reduced populations of RGCs and ONH axons estimated from the SAP and OCT measurements provide additional evidence of the close relationship between visual and neural defects from glaucoma. 
The final examples to illustrate the relationships between visual sensitivity and nerve fiber layer thickness in experimental glaucoma (Fig. 3D)are from data collected 6 months after the final laser treatment. Compared with the data from 5 months earlier, there was only a small incremental deepening of visual field defects and, although there was a decrease in the RNFL thickness at the inferior pole, the mean RNFL thickness was essentially unchanged. The slowing of visual defects is not unusual for this model 37 43 and, most important, the relationships between measures were completely consistent with the prior examples. Thus, the examples demonstrate concordance between the structural and functional measures in normal eyes and their alterations caused by glaucomatous neuropathy over the time course from normal to moderate stages of neuropathy for this animal, which was also found for the other subjects with experimental glaucoma. 
The results from all the monkeys in the study are presented in Figure 4by an assessment of agreement between the estimates of RGCs by SAP and their axons by OCT, that is, the agreement between functions like the examples for the right and left eyes of subject OHT-48 that are presented in the bottom graphs in Figure 3 . The sign convention adopted for the analysis was to assign negative values to differences when the estimate of RGCs by SAP was less than the estimate of axons by OCT, or positive values if the SAP estimate of neurons was larger than the OCT estimate. The percentage of data with a given magnitude of disagreement was determined for each sector of the RNFL, allowing repeated measures from single animals if the measurements were separated by 3 weeks, or more. Histograms of the percentage of data as a function of the magnitude of differences between SAP and OCT estimates demonstrate substantive agreement for both the control (Fig. 4A)and laser-treated (Fig. 4B)eyes, with approximately 60% of the estimates within ±25% of agreement for each eye. The smaller differences (<55%) are normally distributed around the null point, as is illustrated by the curves superimposed on the histograms. These solid lines represent Gaussian distributions with means and standard deviations based on statistics shown in the insets. In each case, the normal distribution is an adequate description of the data, except that the laser-treated eyes have a substantial percentage of data with differences greater than 55% between the SAP and OCT estimates. These negative-signed values represent disagreements in which SAP estimates of RGCs are less than the OCT estimates of axons, that is, the functional defects are larger, or preceding, the structural defects. This type of disagreement between estimates was observed in two situations. First, during the time course of experimental glaucoma, there were episodes in which the visual field defects progressed more rapidly than neural defects, with the RNFL thinning “catching up” at a later time. The second situation involved more advanced neuropathy, in which the RNFL seemed to stop thinning while visual field defects continued to progress. 
Although these large differences are interesting, they represent a relatively small portion of the data and, most often, the independent measures of structure and function were well correlated. The correlations of neural losses are demonstrated by the data in Figure 5 , which compare the neural losses derived by the two methods of estimation. For this analysis, the neural loss by SAP measurements was the percentage difference between a subject’s control and laser-treated eyes in the number of RGCs estimated for each sector of the RNFL. Similarly, the corresponding OCT neural loss represents the percentage difference between the same subject’s eyes in the number of axons estimated from measures of RNFL thickness in each sector. For reference, the solid line superimposed on the data is the one-to-one line representing perfect agreement and the dashed lines represent the 95% confidence limits of agreement for neural losses by SAP and OCT. It is apparent that the relationship is linear (r = 0.67), but the differences are not evenly distributed around the line of unity correlation. The mean difference between SAP and OCT estimates is 5.5% ± 20%, with the measure of visual function, on average, producing estimations of greater losses of neurons than the objective measurement of structure. It is not clear, however, whether the direction and magnitude of disagreement for these data, as well as the largest negative-signed values in Figure 4B , represent a true loss of function before structure, or whether there are compensating changes in the supportive tissue 44 61 62 of the RNFL that occur with axonal loss and alters the transformation of RNFL thickness to the number of axons, when a constant value for axonal density is used. These aspects of RNFL thinning must be addressed in subsequent histologic studies of the retinas of these monkeys. 
Discussion
The glaucomas are a group of diseases with the common manifestation of progressive death of RGCs and their axons that form the optic nerve. 1 2 It is therefore axiomatic that valid clinical procedures for diagnosis and assessment of glaucoma must reflect the state of RGC populations, but there are many clinical tests, based on many diverse properties of neural function, 63 64 65 66 67 68 69 and it is difficult to relate the stage of glaucoma across tests. The present study was an investigation of a potential method of relating the results of different tests by estimating the number of RGCs from subjective or objective measurements and then using the RGC estimates as an assessment of the state of glaucomatous neuropathy. In the first phase of the study (Figs. 1 2) , normative data from SAP and OCT data from the control eyes of rhesus monkeys were used to develop procedures to (1) translate visual sensitivity to a corresponding number of RGCs, (2) to derive the number of RGC axons from RNFL thickness measures and, (3) to map the visual field onto the ONH. The second phase of the study tested the procedures for relating the neural basis of standard clinical measurements and demonstrated that SAP measures of visual field defects and OCT measures of RNFL defects reflect a common progressive RGC pathophysiology over the time course of experimental glaucoma in macaque monkeys (Fig. 3)
The results with experimental glaucoma are in agreement with many prior clinical studies showing that SAP and OCT measures have a high degree of agreement in discriminating between normal and glaucomatous eyes. 9 17 18 19 20 21 Even though the two measurements are completely different—that is, a loss of visual sensitivity on a logarithmic scale versus the RNFL thinning on a linear scale—defects by either measure reflect a loss of retinal neurons with respect to normal values for age-matched patients and identified glaucoma. Thus, based on an analysis of specific events, such as a reduced average or inferior RNFL thickness by OCT or a criterion number of abnormal test locations by SAP, both procedures have high diagnostic sensitivity and specificity, 9 17 18 24 25 28 but an event analysis does not determine whether the two procedures define the same stage of disease. In contrast, the translation of the clinical data to a common neural count produces the same high degree of diagnostic agreement between procedures and provides methods for quantifying the severity of disease and using trend analyses for progression that are similar to perimetry. 69 70 It should be mentioned that, although the comparison of the results of objective and subjective measurements through underlying neural mechanisms provides a causal relationship, an empiric comparison of results based on the normal intersubject variance of the procedure—that is, z-score units—also produces a continuous, graded measure of the stage of glaucoma that is comparable for the two measures (Table 1)
Over much of the range from normal vision to deep perimetric defects, the neural losses estimated from SAP and OCT measurements were highly correlated, and thus it might be assumed that RNFL thickness measurement is simply an objective form of perimetry. However, there are differences in both the precision for detection of early neural loss and the dynamic range of measurement that distinguishes between the procedures. For example, many clinical studies have suggested that, in early stages of glaucoma, significant RNFL thinning can occur before significant perimetric defects; a condition classified as preperimetric glaucoma. 25 26 27 28 29 On the contrary, the present investigation has shown the opposite circumstance—that is, instances of visual field defects preceding RNFL thinning (Fig. 3B) —and it seems sensible that, although neural dysfunction could cause functional defects that precede structural defects, visual function can never be better than the limit set by the number of neurons processing visual information. Therefore, it is likely that preperimetric glaucoma does not represent a decorrelation of the structure–function relationship, but rather, perimetry is less sensitive to small neural losses than nerve fiber layer measurements. The differences in sensitivity to early neural losses are a result of two factors. First, the underlying mechanisms are different. Visual sensitivity represents a nonlinear pooling of detector outputs that are best described by a logarithmic relationship between visual sensitivity and the number of neural detectors, 47 48 whereas RNFL thickness is a linear function of the number of axons over the dynamic range of measurement. The linear relationship produces a higher sensitivity for the detection of small changes, although the resolution will be less near the upper limit of measurement. 35  
The second reason that SAP is less likely to reveal early functional defects is because intersubject variance is greater for SAP than OCT measurements. The differences in intersubject variance are illustrated by the coefficient of variation (CV) as a function of the ONH sector (Table 2)derived from the normative data of monkeys (Figs. 1 2) . The CV for OCT for each sector represents the SD as a percentage of the mean thickness for the 51 pixels in that sector averaged across the 40 normal monkeys’ eyes. For SAP, the CV was based on the SD and mean of the 140 normal visual fields. In this case, the visual sensitivities (in decibel units) were converted to light intensity at threshold (apostilb units), and the data for the SAP test locations inputting to a given ONH sector were averaged. A comparison of CV for the two procedures shows that the CV for OCT is at least 50% lower than for SAP in every ONH sector. Thus, the lower intersubject variance allows smaller changes to be identified as statistically significant by OCT compared with SAP and, taken with logarithmic versus linear differences in the two procedures, it is logical that measures of nerve fiber thickness would identify glaucoma at an earlier stage than would SAP. 
At the other end of the range of measurement, with more advanced stages of the disease, SAP should provide better clinical quantification of defects and progression than OCT. The dynamic range for SAP measures of visual sensitivity is nearly three orders of magnitude and, for example, near the fovea the functional range corresponds to a range of RGC densities of approximately 50,000 cells/mm2 for normal vision to 100 cells/mm2 at the lower limit of the SAP measurement. 47 In comparison, the typical, normal average RNFL thickness is approximately 100 μm and decreases with the stage of disease to a minimum of approximately 45 μm for eyes with moderate field defects (Fig. 3D)or eyes that are blind from glaucoma. 21 72 This analysis of the dynamic range of measurement and the sensitivity to early losses of RGCs, illustrate that SAP provides a better clinical measure for moderate to advanced stages of glaucoma, while OCT provides better clinical information for the early diagnosis of glaucoma. In between, for most patients with glaucoma, the results of the subjective and objective measures should be in substantive agreement and provide intertest confirmation of the stage of neuropathy. 
Several schemes of mapping the visual field onto the optic nerve have been presented, 56 57 58 59 but the published mappings did not provide groupings of test locations that produced a strong correlation between the SAP and OCT data. Therefore, a system of mapping the visual field onto the ONH was developed that more satisfactorily correlated structure and function data in localized regions of the visual field. With this mapping, the number of SAP test locations represented in a sector of the ONH varied from 1 to 13, with at least five test locations for each sector except 1 and 10. The test field locations that defined a sector were based on a general knowledge of the anatomy of retinal nerve fibber bundles and refined by empiric comparison of the estimates of neurons and axons derived from the SAP and OCT data. The variation in the test locations in each cluster is reasonable with respect to the large variation in RGC densities with eccentricity, but it was also of benefit in reducing the intrasubject variability, in a similar way as the Glaucoma Hemifield Test. 73 The system of relating clusters of visual field locations to specific sectors of the RNFL profile provided reasonable agreement between the estimates of neurons and axons across all sectors (Fig. 5) , except for the two sectors with input from the nasal retina. However, the analysis of local regions of the visual field was not stringent, because visual field defects and nerve fiber layer thinning caused by experimental glaucoma are diffuse, compared with most cases of glaucoma in clinical patients. Thus, it is important to extend the studies to clinical glaucoma, which also requires consideration of normal aging effects 74 75 76 77 that were not necessary for the monkey subjects of the present investigation. 
In total, the study demonstrated that SAP measurements of visual sensitivity and OCT measurements of RNFL thickness are correlated measures of the underlying populations of RGCs. Employing procedures to derive RGCs from corresponding visual field locations and RNFL sectors produced agreement between these two methods of assessing retinal neurology, both for retinas with normal populations of RGCs and for retinas with progressively decreased populations of RGCs from the neuropathy of experimental glaucoma. Thus, the results establish that when the measurements are translated to their common parameter of RGCs there is concordance between the structure and function of normal and defective vision from glaucoma. 
 
Figure 1.
 
Normative data for SAP and OCT. (A) The SAP data represent the mean and SD of 140 visual fields from 35 normal monkeys. The data for each visual field location of the C24-2 full-threshold program are presented. (B) The OCT data represent the mean ± 95% confidence intervals for standard scans (512 pixels) by OCT from 40 normal eyes of 20 monkeys.
Figure 1.
 
Normative data for SAP and OCT. (A) The SAP data represent the mean and SD of 140 visual fields from 35 normal monkeys. The data for each visual field location of the C24-2 full-threshold program are presented. (B) The OCT data represent the mean ± 95% confidence intervals for standard scans (512 pixels) by OCT from 40 normal eyes of 20 monkeys.
Figure 2.
 
Mapping the visual field onto the ONH to correlate RNFL thickness and visual sensitivity across the visual field. (A) The ONH was divided into 10 equal sectors, and the portion of the RNFL thickness and the C24-2 perimetry test locations corresponding to each sector are shown in (B) and (C), respectively. (D) The number of retinal ganglion cells derived from the perimetry measurements (□) and the number of ganglion cell axons derived from OCT nerve fiber layer thickness measurements (○) for each of the 10 sectors of the ONH.
Figure 2.
 
Mapping the visual field onto the ONH to correlate RNFL thickness and visual sensitivity across the visual field. (A) The ONH was divided into 10 equal sectors, and the portion of the RNFL thickness and the C24-2 perimetry test locations corresponding to each sector are shown in (B) and (C), respectively. (D) The number of retinal ganglion cells derived from the perimetry measurements (□) and the number of ganglion cell axons derived from OCT nerve fiber layer thickness measurements (○) for each of the 10 sectors of the ONH.
Table 1.
 
Subject OHT-48: Magnitudes and z-Score Estimates of Deviations from Expected Normal Values
Table 1.
 
Subject OHT-48: Magnitudes and z-Score Estimates of Deviations from Expected Normal Values
Months after Glaucoma Induction
Preglaucoma One Two Six
OS OD OS OD OS OD OS OD
SAP (MD) 0.54. dB z = 0.52 −0.47 dB z = 0.78 0.68 dB z = 0.70 −2.14 dB z = 2.92 0.27 dB z = 0.17 −5.89 dB z = 7.72 0.35 dB z = 0.28 −6.81 dB z = 8.90
SAP (PSD) 2.07 dB z = 0.28 1.26 dB z = 1.97 1.71 dB z = 0.72 2.73 dB z = 2.11 1.84 dB z = 0.36 5.38 dB z = 9.47 2.52 dB z = 1.53 4.09 dB z = 5.89
OCT (MD) 0.40 μm z = 0.18 −1.12 μm z = 0.14 1.92 μm z = 0.51 −9.31 μm z = 1.88 −0.58 μm z = 0.03 −33.00 μm z = 6.92 −1.50 μm z = 0.22 −38.20 μm z = 8.03
OCT (PSD) 10.11 μm z = 0.17 7.00 μm z = 1.39 10.61 μm z = 0.02 13.83 μm z = 1.29 10.63 μm z = 0.03 28.61 μm z = 7.08 10.51 μm z = 0.02 32.57 μm z = 8.64
SAP (RGCs) 1,572,912 1,419,969 1,671.950 1,302,716 1,611,170 792,061 1,601,108 703,805
OCT (axons) 1,517,889 1,500,216 1,529,234 1,353,952 1,542,388 771,308 1,482,450 649,249
Figure 3.
 
Progressive visual field defects and RNFL thinning caused by experimental glaucoma in a monkey. Each of the four sets of data show the grayscale plots for visual fields, the RNFL thickness profile for the right (solid line) and left (dashed line) eyes, and the lower plots present the number of ganglion cells (□) and axons (○) derived from the SAP and OCT data, respectively, for each eye (A) before and (B) 1, (C) 2, and (D) 6 months after induced glaucoma. The time that the data were collected is with respect to the time of the laser treatment that initiated the progressive neuropathy.
Figure 3.
 
Progressive visual field defects and RNFL thinning caused by experimental glaucoma in a monkey. Each of the four sets of data show the grayscale plots for visual fields, the RNFL thickness profile for the right (solid line) and left (dashed line) eyes, and the lower plots present the number of ganglion cells (□) and axons (○) derived from the SAP and OCT data, respectively, for each eye (A) before and (B) 1, (C) 2, and (D) 6 months after induced glaucoma. The time that the data were collected is with respect to the time of the laser treatment that initiated the progressive neuropathy.
Figure 4.
 
The degree of agreement between estimates of ganglion cells and axons for the control (A) and laser-treated (B) eyes of seven monkeys. The histograms represent the percentage of measurements that differed by the amounts shown on the abscissa. The sign convention for the plot was to assign negative values if the estimates of ganglion cells from SAP measurements were less than the estimates of axons from OCT measurements or to assign positive values when SAP estimates were larger than estimates from OCT data. The solid curves superimposed on the data are Gaussian distributions, with means and SDs equal to the mean and SD of data for unsigned differences of less than 55% between the measures.
Figure 4.
 
The degree of agreement between estimates of ganglion cells and axons for the control (A) and laser-treated (B) eyes of seven monkeys. The histograms represent the percentage of measurements that differed by the amounts shown on the abscissa. The sign convention for the plot was to assign negative values if the estimates of ganglion cells from SAP measurements were less than the estimates of axons from OCT measurements or to assign positive values when SAP estimates were larger than estimates from OCT data. The solid curves superimposed on the data are Gaussian distributions, with means and SDs equal to the mean and SD of data for unsigned differences of less than 55% between the measures.
Figure 5.
 
Comparison of the neural losses that were estimated by SAP and OCT. The data represent the percentage loss of neurons or axons for the laser-treated eye, with respect to the control eye, from SAP estimates versus OCT estimates. Solid line: unity correlation; dashed lines: 95% confidence limits from linear regression.
Figure 5.
 
Comparison of the neural losses that were estimated by SAP and OCT. The data represent the percentage loss of neurons or axons for the laser-treated eye, with respect to the control eye, from SAP estimates versus OCT estimates. Solid line: unity correlation; dashed lines: 95% confidence limits from linear regression.
Table 2.
 
Coefficient of Variation for OCT and SAP Measurements
Table 2.
 
Coefficient of Variation for OCT and SAP Measurements
ONH Sector 1 2 3 4 5 6 7 8 9 10
OCT 13 12 9 14 16 15 11 8 12 14
SAP 52 28 29 30 41 53 49 24 26 36
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Figure 1.
 
Normative data for SAP and OCT. (A) The SAP data represent the mean and SD of 140 visual fields from 35 normal monkeys. The data for each visual field location of the C24-2 full-threshold program are presented. (B) The OCT data represent the mean ± 95% confidence intervals for standard scans (512 pixels) by OCT from 40 normal eyes of 20 monkeys.
Figure 1.
 
Normative data for SAP and OCT. (A) The SAP data represent the mean and SD of 140 visual fields from 35 normal monkeys. The data for each visual field location of the C24-2 full-threshold program are presented. (B) The OCT data represent the mean ± 95% confidence intervals for standard scans (512 pixels) by OCT from 40 normal eyes of 20 monkeys.
Figure 2.
 
Mapping the visual field onto the ONH to correlate RNFL thickness and visual sensitivity across the visual field. (A) The ONH was divided into 10 equal sectors, and the portion of the RNFL thickness and the C24-2 perimetry test locations corresponding to each sector are shown in (B) and (C), respectively. (D) The number of retinal ganglion cells derived from the perimetry measurements (□) and the number of ganglion cell axons derived from OCT nerve fiber layer thickness measurements (○) for each of the 10 sectors of the ONH.
Figure 2.
 
Mapping the visual field onto the ONH to correlate RNFL thickness and visual sensitivity across the visual field. (A) The ONH was divided into 10 equal sectors, and the portion of the RNFL thickness and the C24-2 perimetry test locations corresponding to each sector are shown in (B) and (C), respectively. (D) The number of retinal ganglion cells derived from the perimetry measurements (□) and the number of ganglion cell axons derived from OCT nerve fiber layer thickness measurements (○) for each of the 10 sectors of the ONH.
Figure 3.
 
Progressive visual field defects and RNFL thinning caused by experimental glaucoma in a monkey. Each of the four sets of data show the grayscale plots for visual fields, the RNFL thickness profile for the right (solid line) and left (dashed line) eyes, and the lower plots present the number of ganglion cells (□) and axons (○) derived from the SAP and OCT data, respectively, for each eye (A) before and (B) 1, (C) 2, and (D) 6 months after induced glaucoma. The time that the data were collected is with respect to the time of the laser treatment that initiated the progressive neuropathy.
Figure 3.
 
Progressive visual field defects and RNFL thinning caused by experimental glaucoma in a monkey. Each of the four sets of data show the grayscale plots for visual fields, the RNFL thickness profile for the right (solid line) and left (dashed line) eyes, and the lower plots present the number of ganglion cells (□) and axons (○) derived from the SAP and OCT data, respectively, for each eye (A) before and (B) 1, (C) 2, and (D) 6 months after induced glaucoma. The time that the data were collected is with respect to the time of the laser treatment that initiated the progressive neuropathy.
Figure 4.
 
The degree of agreement between estimates of ganglion cells and axons for the control (A) and laser-treated (B) eyes of seven monkeys. The histograms represent the percentage of measurements that differed by the amounts shown on the abscissa. The sign convention for the plot was to assign negative values if the estimates of ganglion cells from SAP measurements were less than the estimates of axons from OCT measurements or to assign positive values when SAP estimates were larger than estimates from OCT data. The solid curves superimposed on the data are Gaussian distributions, with means and SDs equal to the mean and SD of data for unsigned differences of less than 55% between the measures.
Figure 4.
 
The degree of agreement between estimates of ganglion cells and axons for the control (A) and laser-treated (B) eyes of seven monkeys. The histograms represent the percentage of measurements that differed by the amounts shown on the abscissa. The sign convention for the plot was to assign negative values if the estimates of ganglion cells from SAP measurements were less than the estimates of axons from OCT measurements or to assign positive values when SAP estimates were larger than estimates from OCT data. The solid curves superimposed on the data are Gaussian distributions, with means and SDs equal to the mean and SD of data for unsigned differences of less than 55% between the measures.
Figure 5.
 
Comparison of the neural losses that were estimated by SAP and OCT. The data represent the percentage loss of neurons or axons for the laser-treated eye, with respect to the control eye, from SAP estimates versus OCT estimates. Solid line: unity correlation; dashed lines: 95% confidence limits from linear regression.
Figure 5.
 
Comparison of the neural losses that were estimated by SAP and OCT. The data represent the percentage loss of neurons or axons for the laser-treated eye, with respect to the control eye, from SAP estimates versus OCT estimates. Solid line: unity correlation; dashed lines: 95% confidence limits from linear regression.
Table 1.
 
Subject OHT-48: Magnitudes and z-Score Estimates of Deviations from Expected Normal Values
Table 1.
 
Subject OHT-48: Magnitudes and z-Score Estimates of Deviations from Expected Normal Values
Months after Glaucoma Induction
Preglaucoma One Two Six
OS OD OS OD OS OD OS OD
SAP (MD) 0.54. dB z = 0.52 −0.47 dB z = 0.78 0.68 dB z = 0.70 −2.14 dB z = 2.92 0.27 dB z = 0.17 −5.89 dB z = 7.72 0.35 dB z = 0.28 −6.81 dB z = 8.90
SAP (PSD) 2.07 dB z = 0.28 1.26 dB z = 1.97 1.71 dB z = 0.72 2.73 dB z = 2.11 1.84 dB z = 0.36 5.38 dB z = 9.47 2.52 dB z = 1.53 4.09 dB z = 5.89
OCT (MD) 0.40 μm z = 0.18 −1.12 μm z = 0.14 1.92 μm z = 0.51 −9.31 μm z = 1.88 −0.58 μm z = 0.03 −33.00 μm z = 6.92 −1.50 μm z = 0.22 −38.20 μm z = 8.03
OCT (PSD) 10.11 μm z = 0.17 7.00 μm z = 1.39 10.61 μm z = 0.02 13.83 μm z = 1.29 10.63 μm z = 0.03 28.61 μm z = 7.08 10.51 μm z = 0.02 32.57 μm z = 8.64
SAP (RGCs) 1,572,912 1,419,969 1,671.950 1,302,716 1,611,170 792,061 1,601,108 703,805
OCT (axons) 1,517,889 1,500,216 1,529,234 1,353,952 1,542,388 771,308 1,482,450 649,249
Table 2.
 
Coefficient of Variation for OCT and SAP Measurements
Table 2.
 
Coefficient of Variation for OCT and SAP Measurements
ONH Sector 1 2 3 4 5 6 7 8 9 10
OCT 13 12 9 14 16 15 11 8 12 14
SAP 52 28 29 30 41 53 49 24 26 36
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