September 2013
Volume 54, Issue 9
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Glaucoma  |   September 2013
The Influence of Intersubject Variability in Ocular Anatomical Variables on the Mapping of Retinal Locations to the Retinal Nerve Fiber Layer and Optic Nerve Head
Author Affiliations & Notes
  • Julia Lamparter
    National Institute for Health Research (NIHR) Biomedical Research Center for Ophthalmology, Moorfields Eye Hospital NHS Foundation Trust, London, United Kingdom
    Department of Ophthalmology, University Medical Center of the Johannes Gutenberg-University Mainz, Germany
  • Richard A. Russell
    National Institute for Health Research (NIHR) Biomedical Research Center for Ophthalmology, Moorfields Eye Hospital NHS Foundation Trust, London, United Kingdom
    Department of Optometry and Visual Science, City University London, United Kingdom
  • Haogang Zhu
    National Institute for Health Research (NIHR) Biomedical Research Center for Ophthalmology, Moorfields Eye Hospital NHS Foundation Trust, London, United Kingdom
    Department of Optometry and Visual Science, City University London, United Kingdom
  • Ryo Asaoka
    National Institute for Health Research (NIHR) Biomedical Research Center for Ophthalmology, Moorfields Eye Hospital NHS Foundation Trust, London, United Kingdom
  • Takehiro Yamashita
    National Institute for Health Research (NIHR) Biomedical Research Center for Ophthalmology, Moorfields Eye Hospital NHS Foundation Trust, London, United Kingdom
  • Tuan Ho
    National Institute for Health Research (NIHR) Biomedical Research Center for Ophthalmology, Moorfields Eye Hospital NHS Foundation Trust, London, United Kingdom
  • David F. Garway-Heath
    National Institute for Health Research (NIHR) Biomedical Research Center for Ophthalmology, Moorfields Eye Hospital NHS Foundation Trust, London, United Kingdom
    Department of Optometry and Visual Science, City University London, United Kingdom
  • Correspondence: David F. Garway-Heath, NIHR Biomedical Research Center for Ophthalmology, Moorfields Eye Hospital NHS Foundation Trust, City Road, London EC1V 2PD, UK; David.Garway-Heath@moorfields.nhs.uk
Investigative Ophthalmology & Visual Science September 2013, Vol.54, 6074-6082. doi:10.1167/iovs.13-11902
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      Julia Lamparter, Richard A. Russell, Haogang Zhu, Ryo Asaoka, Takehiro Yamashita, Tuan Ho, David F. Garway-Heath; The Influence of Intersubject Variability in Ocular Anatomical Variables on the Mapping of Retinal Locations to the Retinal Nerve Fiber Layer and Optic Nerve Head. Invest. Ophthalmol. Vis. Sci. 2013;54(9):6074-6082. doi: 10.1167/iovs.13-11902.

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

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Abstract

Purpose.: To investigate the influence of intersubject variation in ocular parameters on the mapping of retinal locations to the retinal nerve fiber layer and optic nerve head.

Methods.: One hundred retinal nerve fiber layer (RNFL) bundle photographs from 100 subjects were optimized digitally and single RNFL bundles manually traced back to the ONH where their entry point was noted. A 24-2 visual field (VF) grid pattern was superimposed onto the photographs in order to relate VF test points to intersecting RNFL bundles and their entry angles into the ONH. Axial length, spherical equivalent, the position of the ONH in relation to the fovea, size, orientation, tilt, and shape of the ONH were assessed. Multilevel linear models were generated for predicting the entry angle of RNFL bundles, based on ocular parameters.

Results.: A total of 6388 RNFL bundles were traced. The influence of ocular parameters could be evaluated for 33 out of 52 VF locations. The position of the ONH in relation to the fovea was the most prominent predictor for variations in the mapping of retinal locations to the ONH, followed by disc area, axial length, spherical equivalent, disc shape, disc orientation, and disc tilt.

Conclusions.: Mapping of retinal locations to the optic nerve head varies between patients according to a given patient's ocular parameters. By considering these parameters, patient-tailored, structure-function maps can be built and structural and functional measurements can be correlated more accurately. Individualized maps may assist clinicians detecting glaucoma and monitoring glaucomatous progression.

Introduction
The relationship between structure and function in glaucoma has been of great interest for more than 100 years. In 1889 and 1909, Bjerrum and Rönne described specific types of scotomata that could later be related to retinal nerve fiber layer (RNFL) bundle defects. 1,2 Since this time, investigators have developed structure-function maps in order to describe the relationship between the anatomy of the optic nerve head (ONH) and the visual field. Some of these maps are based on scotoma borders in the visual field, 3 others are based on two-dimensional planimetry data of the optic disc, 4 knowledge in primate eyes, 5 or confocal scanning laser ophthalmoscopy. 69 In 2000, Garway-Heath and colleagues developed the first complete high-resolution, structure-function map in human eyes by relating visual field test locations to the optic disc in 69 normal tension glaucoma eyes with well-defined RNFL bundle defects and/or prominent bundles (Fig. 1). 10 This map extended previous partial maps and is presently used in most studies on structure and function in glaucoma. 
Figure 1
 
Structure-function map developed by Garway-Heath et al. 10 Six sectors of the optic nerve head are correlated with sectors of the visual field. T, temporal; ST, superotemporal; SN, superonasal; N, nasal; IN, inferonasal; IT, inferotemporal.
Figure 1
 
Structure-function map developed by Garway-Heath et al. 10 Six sectors of the optic nerve head are correlated with sectors of the visual field. T, temporal; ST, superotemporal; SN, superonasal; N, nasal; IN, inferonasal; IT, inferotemporal.
To date, all structure-function maps are averaged, generalized maps that do not take into account an individual's ocular parameters. The topographic relationship between specific locations of the optic disc and their corresponding nerve fiber bundles on the retina is complex and individual variation is high. One important parameter, the position of the ONH in relation to the fovea, has already been recognized by Garway-Heath and colleagues. 10 Other parameters that may influence the structure-function relationship are axial length (AL), refraction, optic disc size, shape (ellipticity), orientation, and tilt. 1113 Denniss et al. recently developed a simulation model of the relationship between ONH sectors and visual field locations for a range of clinically plausible anatomical parameters. 14 Furthermore, Jansonius et al. recently evaluated the influence of refraction, optic disc size, and disc position on the course of retinal nerve fiber bundle trajectories in the superior-temporal and inferior-temporal regions of the human eye. 15  
The current study investigates the impact of ocular parameters (ONH position/size/shape/tilt/orientation, axial length and spherical equivalent) on the mapping of retinal locations to the retinal nerve fiber layer and optic nerve head, based on retinal nerve fiber trajectories, in a cohort of 100 eyes from 100 individuals. An understanding of the importance of these parameters is necessary in order to enhance individualized diagnosis and management of glaucoma. 
Methods
Study Participants
A total of 100 eyes from 100 subjects (56 patients with risk factors for developing glaucoma, 12 open angle glaucoma patients, and 32 healthy individuals) were included in this cross-sectional prospective study. If both eyes of a participant fulfilled the inclusion criteria, the eye with clearer ocular media or with more visible RNFL bundles was included. Patients were recruited from glaucoma clinics at Moorfields Eye Hospital London. Healthy volunteers were recruited among the staff members of the hospital, their spouses, and friends. The study was approved by the Institutional Review Board of Moorfields Eye Hospital, adhered to the tenets of the Declaration of Helsinki, and all subjects gave written informed consent prior to any intervention. 
To be included in the study, participants had to be aged 18 years or older. Patients who suffered from other (nonglaucomatous) previous or current ocular pathology, participants with a visual acuity (VA) of less than logMAR 0.3, and participants who were not able to perform the study or to fully understand the informed consent were not included. Glaucoma was defined as optic disc cupping consistent with glaucoma (diffuse or focal thinning of the neuroretinal rim) and reproducible field loss. Patients at risk had ocular hypertension (intraocular pressure [IOP] > 21 mm Hg) or pigment dispersion syndrome without structural or functional evidence of glaucomatous optic neuropathy. 
Data Acquisition
A medical history and a complete ophthalmic examination including autorefraction and keratometry (Nidek ARK-510A; Nidek Co., LTD, Aichi, Japan); slit-lamp biomicroscopy (Haag-Streit AG, Köniz, Switzerland); dilated fundus examination including red-free ophthalmoscopy to visualize the optic disc, retinal nerve fiber layer and macula; Goldmann applanation tonometry (Haag-Streit AG); and central corneal thickness (CCT) measurement (Altair ultrasonic pachymeter; Optikon 2000, Rome, Italy) were obtained from all participants. In addition, axial length measurement (IOLMaster; Carl Zeiss Meditec, Jena, Germany); scanning laser ophthalmoscopy (HRT II; Heidelberg Engineering, Heidelberg, Germany); and spectral-domain optical coherence tomography (SD-OCT, Spectralis-OCT; Heidelberg Engineering; RNFL scan pattern) were carried out in all subjects. 
Red-free fundus photography at 50° (Topcon TRC-50IX; Topcon Corporation, Tokyo, Japan), taken with a custom-made blue filter at a wavelength of 495 μm was performed in all participants. The fundus camera was calibrated with a model eye. 16,17  
Ocular Parameters
The influence of the following ocular parameters on the structure-function relationship of the eye was investigated: 
  1.  
    Spherical equivalent (SE): calculated as sphere + ½ cylinder.
  2.  
    Axial length: assessed by partial coherence interferometry.
  3.  
    Disc area: obtained with confocal scanning laser ophthalmoscopy (HRT II). Reference lines were drawn and adjusted accordingly, and the image was magnification-corrected for axial length. 18
  4.  
    Ellipticity ratio (ER; ONH shape): defined as the ratio between shortest and largest disc diameter. The clinical disc margin was assessed from the mean reflectivity image and the diameters measured with the built-in measurement tool of the Spectralis-OCT (HRA reflectance image of RNFL scan). Figure 2A shows the largest ONH diameter of a glaucoma patient (1.74 mm). Shortest diameters were measured correspondingly.
  5.  
    Orientation of the ONH: assessed by measuring the largest disc diameter and the angle between this diameter and the vertical meridian (Fig. 2A), based on the Spectralis HRA reflectance image (RNFL scan). The vertical meridian served as the reference (0°). A temporal rotation was defined positive and a nasal rotation was defined negative. A two-dimensional vector with its length being largest disc diameter and direction defined by the angle was constructed as a descriptor of the orientation of ONH.
  6.  
    Tilt of the ONH: measured with Spectralis-OCT. A line was drawn between RPE borders/Bruch's membrane opening (red points in Fig. 2B). An additional line connected two points in an arbitrary chosen distance of 2000 μm (measured with the built-in measurement tool) from RPE borders (green points). The first line was then shifted toward the additional line (blue arrows) to measure the angle of tilt (yellow angle).
  7.  
    The position of the ONH in relation to the fovea: measured as (1) the horizontal distance between the ONH center and fovea (ONH_X); and (2) the vertical distance between the ONH center and the horizontal meridian (ONH_Y). Distances were measured in degrees from the red-free fundus photo and then converted to millimeters. 16 The papillomacular position (PMP; angle between ONH center and fovea) was calculated from these measurements.
Figure 2
 
Orientation and tilt of the optic nerve head. (A) The orientation of the disc is described by the angle between the largest disc diameter and the vertical meridian. (B) The angle of tilt as measured with SD-OCT (Spectralis-OCT).
Figure 2
 
Orientation and tilt of the optic nerve head. (A) The orientation of the disc is described by the angle between the largest disc diameter and the vertical meridian. (B) The angle of tilt as measured with SD-OCT (Spectralis-OCT).
Retinal Nerve Fiber Bundle Assessment
Brightness/contrast, color balance, and sharpness of the red-free blue filter fundus photographs were optimized using digital photo editing software (Adobe Photoshop CS4; Adobe Systems, Mountain View, CA) in order to enhance visibility of RNFL bundles (Fig. 3A). Images of left eyes were vertically mirrored so that only “right-eye” images remained for further analysis. Enhanced photographs were uploaded into custom-made software (MATLAB version 7.7 [R2008b]; MathWorks, Natick, MA) where the ONH and fovea were marked manually by drawing a reference circle that was aligned to the margins of the ONH border and fovea, respectively. RNFL bundles could then be manually traced back to the ONH by setting a minimum of three marker points. The marker points were connected by cubic splines, which are a nonparametric model providing a continuous analytical function for each nerve bundle. The complexity of cubic splines is mainly controlled by the number of knot points clicked by the operator. In contrast to a parametric model, it is more versatile and flexible to quantify the morphological shape of nerve bundles. Finally, the entry angle of each bundle into the ONH was noted automatically (Fig. 3B). The temporal margin (9-o'clock position, right eye) was designated 0°, and degrees were counted in a clockwise direction. An appropriately scaled Humphrey Field Analyzer 24-2 visual field–test grid pattern (test points in a grid 6° apart) was superimposed onto the fundus image, centered on the macula. The position of the ONH in relation to the fovea was recorded by the software, and the entry point of RNFL bundles into the ONH was related to all visual field points. Each RNFL bundle had to be within 0.86° (twice the diameter of the Goldman Size III stimulus) of a visual field point. To account for the inverse relationship between retinal location and visual field location, the superior visual field locations are assigned the ONH entry position of their mirror image location in the inferior hemifield, and vice versa for inferior visual field locations. 
Figure 3
 
Preparation of retinal photographs and tracing of retinal nerve fibre bundles. (A) Blue-filter retinal photograph that was digitally enhanced in order to make single RNFL bundles more visible. (B) Visible RNFL bundles are manually drawn back to their entry into the ONH. Each entry point is assessed using custom-made software and the position of the ONH in relation to the fovea is noted.
Figure 3
 
Preparation of retinal photographs and tracing of retinal nerve fibre bundles. (A) Blue-filter retinal photograph that was digitally enhanced in order to make single RNFL bundles more visible. (B) Visible RNFL bundles are manually drawn back to their entry into the ONH. Each entry point is assessed using custom-made software and the position of the ONH in relation to the fovea is noted.
In order to evaluate inter- and intrasubject variability, eight RNFL bundle photographs were retraced. The mean difference in entry angle position differed by −1.6° between the principal investigator (JL) and an independent nonmedical coinvestigator (HZ). Mean absolute difference between the two investigators was 8.9°. In comparison, the mean difference in entry angle position for the principal investigator was reduced to 1.4° with a mean absolute difference of 5.1°. 
Data Analysis
All statistical analyses were carried out in the open-source statistical environment R. 19 The nlme package in R was used to carry out multilevel linear modeling. 20 For each visual field point with a minimum of 10 intersecting bundles, a multilevel linear model was generated where each of the above ocular parameters were used as independent variables and the entry angle into the ONH was set as dependent variable. This type of model takes into account the clustered (or nested) nature of the data (n retinal nerve fibers belonging to the same individual) and allows for different regression coefficients to be established for each level (“nesting”). The status of the eye (healthy, glaucoma subject, glaucoma) was not used as a predictor in the model but was instead used to further nest the data according to eye status. A minimum of 10 intersecting bundles was chosen to ensure there were more data points than “fixed effects” (regression coefficients) in the model. The optimal model to predict the entry angle was chosen by the Akaike information criterion (AIC) in a backward stepwise algorithm using the “stepAIC” function in R. 21 The AIC measures the quality of a model from a set of candidate models and chooses the model that minimizes the information that is lost (has a good fit to the truth) with as few parameters as possible; further details can be found in Burnham and Anderson's 21 published findings. The resultant model thereby provides information about the most important variables to predict the entry angle of an intersecting RNFL bundles into the ONH. Interaction terms between predictors were not included in the model as adding these drastically changes the interpretation of all coefficients in the model and it is therefore more difficult to interpret the main effects. 
Results
A total of 100 eyes from 100 participants (57 males, 43 females) were included in this prospective study. Demographic data of the study population are presented in Table 1. In total, 6388 RNFL bundles, based on 42,914 sampling points, were manually traced (Fig. 4). On average, 63.9 ± 22.1 (range, 24–131) bundles were drawn per participant with a mean of 6.7 sampling points per RNFL bundle (range, 3–87). 
Figure 4
 
Distribution of RNFL bundles and their corresponding visual field positions. (A) Retinal nerve fiber bundle distribution: 6388 RNFL bundles, based on 42,914 sampling points, were derived from 100 subjects; 52 VF points are superimposed on the RNFL bundle image. For reporting, the superior VF locations are assigned the ONH entry position of their mirror image location in the inferior hemifield and vice versa for inferior VF locations. (B) Between-individual RNFL bundle distribution for two individual VF locations (upper point at position 17 and lower point at position 46).
Figure 4
 
Distribution of RNFL bundles and their corresponding visual field positions. (A) Retinal nerve fiber bundle distribution: 6388 RNFL bundles, based on 42,914 sampling points, were derived from 100 subjects; 52 VF points are superimposed on the RNFL bundle image. For reporting, the superior VF locations are assigned the ONH entry position of their mirror image location in the inferior hemifield and vice versa for inferior VF locations. (B) Between-individual RNFL bundle distribution for two individual VF locations (upper point at position 17 and lower point at position 46).
Table 1
 
Demographic Data of the Study Population
Table 1
 
Demographic Data of the Study Population
Age, y logMAR VA, D Sphere, D Cyl, D SE, D IOP, mm Hg PMP, deg CCT, μm
Mean 42.5 −0.05 −2.29 −0.11 −2.35 17.1 6.7 552
SD 11.3 0.06 2.94 0.83 2.90 4.1 3.6 33
Min 22.3 −0.18 −9.25 −2.25 −9.13 10 −1.9 454
Max 70.0 0.18 3.50 2.25 3.25 32 14.1 626
Forty-six out of 52 visual field test points were assigned RNFL bundles from all subjects. A total of 33 field points were included in the statistical analysis (points with fewer than 10 intersecting bundles were excluded). The two field points located above and below the ONH center, representing the blind spot, were not investigated. Generally, central points were assigned more bundles than peripheral points due to lower image quality in the periphery or limited angular extent of the fundus photo. 
Table 2 gives an overview of all parameters that were measured for each subject. Axial lengths ranged from 21.83 to 27.73 mm, ONH disc areas ranged from 0.98 to 3.51 mm. 2 A wide variety was also present for ONH shape, orientation, and tilt. 
Table 2
 
Ocular Parameters of the Study Population
Table 2
 
Ocular Parameters of the Study Population
AL, mm Disc Area, mm2 Largest Disc Diameter, mm Shortest Disc Diameter, mm ER ONH Orientation, deg ONH Tilt, deg ONH_X, mm ONH_Y, mm
Mean 24.55 2.00 1.64 1.39 0.85 −12.6 3.65 2.72 0.32
SD 1.26 0.45 0.20 0.20 0.07 37.6 3.04 0.20 0.17
Min 21.83 0.98 1.21 0.97 0.68 −77.0 −2.2 2.25 −0.09
Max 27.73 3.51 2.16 1.90 1.11 57.0 16 3.32 0.64
Table 3 and Figure 5 present the optimal linear model for each visual field location. It is notable that parameters describing the position of the ONH in relation to the fovea were important for almost the entire visual field. Variability in disc area accounted for variation in the mapping of 19 visual field locations, while variation in axial length, spherical equivalent, and ellipticity ratio (ER) influenced the mapping of nine locations, followed by variation in orientation and tilt of the ONH (eight and six positions, respectively). Almost all ocular parameters were important for the model for field location 24 (seven out of eight parameters), which is located in proximity to the fovea. 
Figure 5
 
Presented are the relevant ocular parameters (position of the ONH, disc area, axial length, spherical equivalent, ellipticity, orientation of the ONH, and optic nerve tilt) for each of the 33 visual field locations (see Table 3). Bold symbols (e.g., X), represent statistical significance (P < 0.05), while nonbold symbols (e.g., x) indicate the individual parameter was not significant, but the overall model with this parameter was chosen as the optimum.
Figure 5
 
Presented are the relevant ocular parameters (position of the ONH, disc area, axial length, spherical equivalent, ellipticity, orientation of the ONH, and optic nerve tilt) for each of the 33 visual field locations (see Table 3). Bold symbols (e.g., X), represent statistical significance (P < 0.05), while nonbold symbols (e.g., x) indicate the individual parameter was not significant, but the overall model with this parameter was chosen as the optimum.
Table 3
 
Ocular Parameters and VF Locations That Entered the Analysis
Table 3
 
Ocular Parameters and VF Locations That Entered the Analysis
VF Location 7 8 9 12 13 14 15 16 17 21 22 23 24 25 26 29 30 31 32 33 34 36 37 38 39 40 41 42 44 45 46 47 48 Total
ONH_X X X X X X X X X X X x X X X X X X X X X X X X X X X X X X X X 31
ONH_Y X X X X X X X X X X X X X X X X X X X X X X X X x X 26
Disc Area x X X X X x X X x x x X x X X X X x x 19
AL X x x x x x x x x 9
SE x x X x x x x X x 9
ER x x X x X X x x x 9
ONH Orientation x X x x x x X X 8
ONH Tilt X x x x X x 6
Total 2 3 3 5 3 4 3 5 3 5 4 5 7 2 3 3 5 4 2 3 2 4 5 4 4 2 4 4 4 3 2 3 2
Table 4 presents mean ONH entry position and the between-individual variation. Of 33 VF locations assigned an ONH entry position in this study, the mean absolute difference in assigned position was 5° from that assigned in the previously reported map 10 and the estimated position was ≤5° different at 20 locations and ≤10° different at 32 locations. The location at which nerve fiber bundles from different individuals (intersecting a given field point) enter the optic nerve head is quite variable (12.4°; mean standard deviation of all locations). The variation explained by the model (R2 value) ranges from 14.2% for visual field location 29 to 81.8% in location 34. 
Table 4
 
Between-Individual Variation for Given VF Locations
Table 4
 
Between-Individual Variation for Given VF Locations
VF Location 7 8 9 12 13 14 15 16 17 21 22 23 24 25 26 29 30
Mean ONH entry position, ° 272 269 257 289 293 296 296 274 245 290 299 317 330 312 211 72 59
SD 16.8 14.4 10.1 20.9 10.9 11.8 10.9 13.1 11.5 16.4 13.2 11.6 10.3 12.7 10.8 16.5 12.7
Variation explained, % 72.6 52.2 33.6 77.9 69.4 71.8 74.3 73.3 59.4 39.4 65.2 68.2 56.9 75.6 66.4 14.2 43.7
VF Location 31 32 33 34 36 37 38 39 40 41 42 44 45 46 47 48
Mean ONH entry position, ° 33 11 17 165 82 74 60 57 74 104 133 88 86 87 98 111
SD 11.4 10.9 14.2 12.3 13.5 13.7 12.0 12.1 11.8 11.4 8.5 13.1 11.4 11.8 9.5 8.0
Variation explained, % 63.8 68.0 69.4 81.8 36.2 42.8 61.7 74.2 72.9 76.3 74.1 48.6 70.0 57.1 65.3 45.1
Discussion
Understanding the arrangement of RNFL bundle trajectories is of great importance for generating a topographically accurate map of structural and functional damage and, therefore, inevitably for glaucoma diagnosis and management. Several attempts have been made to describe the pattern of RNFL bundle trajectories, ranging from histologic examinations 2224 to mathematical models. 15,25 In 2000, Garway-Heath and colleagues developed a map by relating visual field test locations to the ONH entry position of retinal nerve fiber bundles. 10 As noted and discussed in the latter publication, photoreceptors and retinal ganglion cells that are stimulated at a specific point during visual field testing are not necessarily correspondent with the RNFL bundles crossing that area; these fibers can contain axons of ganglion cells from different and even remote areas of the retina. 
In accordance to the previous study, we superimposed a 24-2 visual field grid pattern on the fundus photographs. Due to the displacement of retinal ganglion cells (RGCs) subserving the cones within the human fovea, the effect of RGC displacement should be corrected when test locations in the fovea region (1.8–2.9° eccentricity) 26 are densely sampled. This is the case for the 10-2 test grid pattern and should be considered for future investigations. The 24-2 test pattern starts from 3° eccentricity and is less affected by RGC displacement. Therefore, the effect was not compensated in this study. 
Comparing the map by Garway-Heath et al. and the current map, the mean difference of entry position was less than 5° (in 32 out of 33 locations, the difference was ≤10° and in 20 locations, the difference was ≤5°). Interestingly, these 20 positions were mainly located in the central visual field, corresponding to the central fundus area between the two main vessel arcades. Weaker agreement was found in locations close to the main vessel arcades where accurate tracing is more difficult. 
There was greater between-individual variability in ONH entry position in this study (mean standard deviation 12.4°) compared with the previous report (mean standard deviation 7.2°). A possible explanation is that in this study, we aimed to recruit patients with a wide range of refractive error and axial length and this will have increased the range of values of parameters associated with axial length (such as disc area and tilt). 
This study investigated the influence of variation in ocular parameters on the mapping of retinal locations to the ONH in human eyes. For some locations, only a couple of ocular parameters were found to influence this relationship (e.g., locations 7, 25, 32, 34, 40, 46, 48), while other locations were found to be highly influenced by several different ocular parameters (up to seven parameters, principally for locations 24, 12, 16, 21, 23, 30 and 37). In general, two to four parameters were important for each model. The most prominent parameters were the position of the ONH in relation to the fovea and optic disc area. Axial length, spherical equivalent, and ellipticity ratio were the next most strongly associated, followed by the orientation of the ONH and tilt. It must be emphasized that all statements of “magnitude” regarding relative importance in this paper are based on frequency of each factor's appearance in the models and that certain biometric factors could have a large influence on just a few test points. 
The influence of ONH position as a parameter explaining between-subject variability had been previously identified by Garway-Heath et al. 10 Normalization/rotation methods for reducing this variation by bringing the centers of the ONH and fovea into line have been recently described by Jansonius et al. 25 and Hood et al. 27  
Our findings are of special interest in view of recently published data by Denniss et al. 14 and Jansonius et al. 15 Denniss et al. developed a simulation model to relate the visual field to a range of clinically plausible anatomical ocular parameters. They found ONH position in relation to the fovea, axial length, and horizontal and vertical ONH diameters heavily influencing the structure-function relationship. The agreement regarding the parameters with the strongest effect on the structure-function relationship between their computational model and our study based on human RNFL bundle trajectories and measured anatomic ONH parameters is remarkable. Jansonius et al. recently developed a mathematical model for describing RNFL bundle trajectories, and evaluated the influence of refraction (spherical equivalent), optic disc size, and disc position on the course of these trajectories in the superior-temporal and superior-nasal fundus regions. They found considerable location-specific, intersubject variability for trajectories and an asymmetry between superior and inferior locations for the effect of ocular parameters; refraction was the only significant predictor in the superior-temporal fundus region (corresponding to the inferior-nasal field) with apparently some influence of disc position. None of the parameters appeared to influence the trajectories in the temporal-inferior region (corresponding to the superior-nasal field). Our studies might not be entirely comparable since ocular parameters (except for spherical equivalent) were measured somewhat differently: Jansonius et al. calculated disc size from the macula-disc center distance in the fundus image and defined the position of the ONH by the papillomacular position, compared with magnification-corrected measurements of disc size and displacement from the fovea (in the horizontal and vertical directions, separately) in this study. Furthermore, they used a different model that is not entirely comparable with the model used in this study (parametric model compared with cubic splines). 
In recent years, many different ways of measuring ocular parameters have been described. The current study measured optic disc tilt on the basis of SD-OCT cross-sectional scans. We used HRA reflectance images (Spectralis-OCT) for measurement of disc diameters and scanning laser ophthalmoscopy for the assessment of optic disc size. A recent study by Reis et al. introduces an alternative way of measuring the optic disc margin by SD-OCT. They found Bruch's membrane opening a more consistent anatomical structure than the clinically identified disc margin. 28,29 It cannot be excluded that variation of measurement techniques will somehow influence the results of this study, which would be an interesting topic for future work. 30 A potential influence on the results may arise from cyclotorsion during imaging. 10,30 It remains uncertain whether this variability in cyclorotational alignment is due to differences in head tilt or to accommodative stimulus/response or a combination of both. 
Difficulty in the tracing of retinal nerve fiber bundles is another potential source of error in the resultant map. The identification of bundle trajectories is mainly limited by lower image quality in the periphery of the fundus or relative ocular media opacity. High resolution, sharpness, and contrast are inevitable quality parameters for accurately tracing RNFL bundles. The current study was started after a pilot study in which the authors tested several imaging and image processing techniques. The technique adopted facilitated the tracing of visible trajectories. In order to evaluate inter- and intrasubject variability, eight RNFL bundle photographs were retraced. The mean difference in entry angle position differed by −1.6° between the principal investigator (JL) and an independent, nonmedical coinvestigator (HZ). The mean absolute difference between the two investigators was 8.9°. This is comparable to the mean difference between the current study and the previously presented study by Garway-Heath et al. In comparison, the mean difference in entry angle position for the principal investigator was reduced to 1.4°, with a mean absolute difference of 5.1°. 
It is known that the position of the main blood vessels around the ONH is associated with the location of the maxima (thickest) RNFL regions around the disc. 31 It is likely that the same ocular parameters influence both of these, and so blood vessel position was not considered as an independent factor in the model. Whether blood vessel position and RNFL distribution are associated with the same ocular parameters may be considered in future investigations. 
The current study found a strong influence of ocular parameters on the structure-function relationship, which can be explained by a large intersubject variability of RNFL bundle courses and the association between the bundle course and various ocular parameters. Several studies have investigated the influence of ocular parameters on RNFL thickness. RNFL thickness and the RNFL bundle trajectories are likely to be related. Hwang et al. showed that eyes with a myopic temporal optic disc tilt and counterclockwise rotation had a thicker temporal RNFL and more temporally positioned superior peak location. 32 Tong et al. showed that ONH parameters and RNFL thickness obtained with scanning laser ophthalmoscopy are strongly influenced by the tilting of the ONH but not by refractive error or axial length. 33 ONH tilt, however, is associated with higher axial length and myopia. 12,34 The influence of axial length on peripapillary RNFL thickness has been controversial. Choi et al. reported a decreasing peripapillary RNFL thickness as the level of myopia increases and Yoo et al. reported that peripapillary RNFL thickness varies differently in different peripapillary locations as the eye gets longer. 11,35 This is in contrast with results by Hoh et al. and Wakitani et al. 36,37 who did not find any influence of axial length on the peripapillary or macular RNFL thickness. Axial length influences the lateral “magnification” in an image such that in a longer eye, a fixed angular distance of an OCT scan relates to a longer linear distance on the retina. 18 The RNFL is thinner farther from the ONH than it is closer to the ONH margin. For a scan circle centered on the ONH, the distance of the circle from the ONH center is greater in a long eye than a short eye, resulting in a thinner RNFL measurement. This effect may be offset to some extent if larger eyes have more RGCs and RGC axons. 
It was shown that RNFL profiles from the two eyes of an individual are very similar. 38 However, there is considerable intersubject variation in the RNFL profiles, especially in amplitude and profile across individuals. 39 Intersubject variability in ocular parameters may have a strong genetic influence. It was demonstrated that approximately 80% of the variability of the ONH appearance, especially its diameter (disc size) as well as its general shape forms, is heritable and that 20% of the variability is caused by nonshared environmental effects. 13,38,40  
In conclusion, this study has demonstrated a strong influence of ocular parameters on the structure-function relationship of the eye and emphasizes the need for individualized approaches when assessing agreement, or association, of structure-function measurements. Patient-tailored structure-function maps can be built by taking into account ocular parameters. These maps are important for more accurately correlating structural measurements with functional measurements and should be useful to assist clinicians detecting glaucoma as well as monitoring glaucomatous progression. 
Acknowledgments
Supported by a research grant from the German Research Foundation (Deutsche Forschungsgemeinschaft [JL]; LA 2858/1-1 and 2858/1-2 [DFG]); the Department of Health's National Institute for Health Research (NIHR) Biomedical Research Center at Moorfields Eye Hospital NHS Foundation Trust and City University London Institute of Ophthalmology (RAR, DFG-H); the International Glaucoma Association (DFG-H's chair at City University London); and a National Institute for Health Research postdoctoral fellowship (HZ). The authors alone are responsible for the content and writing of the paper. 
Disclosure: J. Lamparter, None; R.A. Russell, None; H. Zhu, None; R. Asaoka, None; T. Yamashita, None; T. Ho, None; D.F. Garway-Heath, Heidelberg Engineering (F), Carl Zeiss Meditec (F), Optovue (F), P 
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Figure 1
 
Structure-function map developed by Garway-Heath et al. 10 Six sectors of the optic nerve head are correlated with sectors of the visual field. T, temporal; ST, superotemporal; SN, superonasal; N, nasal; IN, inferonasal; IT, inferotemporal.
Figure 1
 
Structure-function map developed by Garway-Heath et al. 10 Six sectors of the optic nerve head are correlated with sectors of the visual field. T, temporal; ST, superotemporal; SN, superonasal; N, nasal; IN, inferonasal; IT, inferotemporal.
Figure 2
 
Orientation and tilt of the optic nerve head. (A) The orientation of the disc is described by the angle between the largest disc diameter and the vertical meridian. (B) The angle of tilt as measured with SD-OCT (Spectralis-OCT).
Figure 2
 
Orientation and tilt of the optic nerve head. (A) The orientation of the disc is described by the angle between the largest disc diameter and the vertical meridian. (B) The angle of tilt as measured with SD-OCT (Spectralis-OCT).
Figure 3
 
Preparation of retinal photographs and tracing of retinal nerve fibre bundles. (A) Blue-filter retinal photograph that was digitally enhanced in order to make single RNFL bundles more visible. (B) Visible RNFL bundles are manually drawn back to their entry into the ONH. Each entry point is assessed using custom-made software and the position of the ONH in relation to the fovea is noted.
Figure 3
 
Preparation of retinal photographs and tracing of retinal nerve fibre bundles. (A) Blue-filter retinal photograph that was digitally enhanced in order to make single RNFL bundles more visible. (B) Visible RNFL bundles are manually drawn back to their entry into the ONH. Each entry point is assessed using custom-made software and the position of the ONH in relation to the fovea is noted.
Figure 4
 
Distribution of RNFL bundles and their corresponding visual field positions. (A) Retinal nerve fiber bundle distribution: 6388 RNFL bundles, based on 42,914 sampling points, were derived from 100 subjects; 52 VF points are superimposed on the RNFL bundle image. For reporting, the superior VF locations are assigned the ONH entry position of their mirror image location in the inferior hemifield and vice versa for inferior VF locations. (B) Between-individual RNFL bundle distribution for two individual VF locations (upper point at position 17 and lower point at position 46).
Figure 4
 
Distribution of RNFL bundles and their corresponding visual field positions. (A) Retinal nerve fiber bundle distribution: 6388 RNFL bundles, based on 42,914 sampling points, were derived from 100 subjects; 52 VF points are superimposed on the RNFL bundle image. For reporting, the superior VF locations are assigned the ONH entry position of their mirror image location in the inferior hemifield and vice versa for inferior VF locations. (B) Between-individual RNFL bundle distribution for two individual VF locations (upper point at position 17 and lower point at position 46).
Figure 5
 
Presented are the relevant ocular parameters (position of the ONH, disc area, axial length, spherical equivalent, ellipticity, orientation of the ONH, and optic nerve tilt) for each of the 33 visual field locations (see Table 3). Bold symbols (e.g., X), represent statistical significance (P < 0.05), while nonbold symbols (e.g., x) indicate the individual parameter was not significant, but the overall model with this parameter was chosen as the optimum.
Figure 5
 
Presented are the relevant ocular parameters (position of the ONH, disc area, axial length, spherical equivalent, ellipticity, orientation of the ONH, and optic nerve tilt) for each of the 33 visual field locations (see Table 3). Bold symbols (e.g., X), represent statistical significance (P < 0.05), while nonbold symbols (e.g., x) indicate the individual parameter was not significant, but the overall model with this parameter was chosen as the optimum.
Table 1
 
Demographic Data of the Study Population
Table 1
 
Demographic Data of the Study Population
Age, y logMAR VA, D Sphere, D Cyl, D SE, D IOP, mm Hg PMP, deg CCT, μm
Mean 42.5 −0.05 −2.29 −0.11 −2.35 17.1 6.7 552
SD 11.3 0.06 2.94 0.83 2.90 4.1 3.6 33
Min 22.3 −0.18 −9.25 −2.25 −9.13 10 −1.9 454
Max 70.0 0.18 3.50 2.25 3.25 32 14.1 626
Table 2
 
Ocular Parameters of the Study Population
Table 2
 
Ocular Parameters of the Study Population
AL, mm Disc Area, mm2 Largest Disc Diameter, mm Shortest Disc Diameter, mm ER ONH Orientation, deg ONH Tilt, deg ONH_X, mm ONH_Y, mm
Mean 24.55 2.00 1.64 1.39 0.85 −12.6 3.65 2.72 0.32
SD 1.26 0.45 0.20 0.20 0.07 37.6 3.04 0.20 0.17
Min 21.83 0.98 1.21 0.97 0.68 −77.0 −2.2 2.25 −0.09
Max 27.73 3.51 2.16 1.90 1.11 57.0 16 3.32 0.64
Table 3
 
Ocular Parameters and VF Locations That Entered the Analysis
Table 3
 
Ocular Parameters and VF Locations That Entered the Analysis
VF Location 7 8 9 12 13 14 15 16 17 21 22 23 24 25 26 29 30 31 32 33 34 36 37 38 39 40 41 42 44 45 46 47 48 Total
ONH_X X X X X X X X X X X x X X X X X X X X X X X X X X X X X X X X 31
ONH_Y X X X X X X X X X X X X X X X X X X X X X X X X x X 26
Disc Area x X X X X x X X x x x X x X X X X x x 19
AL X x x x x x x x x 9
SE x x X x x x x X x 9
ER x x X x X X x x x 9
ONH Orientation x X x x x x X X 8
ONH Tilt X x x x X x 6
Total 2 3 3 5 3 4 3 5 3 5 4 5 7 2 3 3 5 4 2 3 2 4 5 4 4 2 4 4 4 3 2 3 2
Table 4
 
Between-Individual Variation for Given VF Locations
Table 4
 
Between-Individual Variation for Given VF Locations
VF Location 7 8 9 12 13 14 15 16 17 21 22 23 24 25 26 29 30
Mean ONH entry position, ° 272 269 257 289 293 296 296 274 245 290 299 317 330 312 211 72 59
SD 16.8 14.4 10.1 20.9 10.9 11.8 10.9 13.1 11.5 16.4 13.2 11.6 10.3 12.7 10.8 16.5 12.7
Variation explained, % 72.6 52.2 33.6 77.9 69.4 71.8 74.3 73.3 59.4 39.4 65.2 68.2 56.9 75.6 66.4 14.2 43.7
VF Location 31 32 33 34 36 37 38 39 40 41 42 44 45 46 47 48
Mean ONH entry position, ° 33 11 17 165 82 74 60 57 74 104 133 88 86 87 98 111
SD 11.4 10.9 14.2 12.3 13.5 13.7 12.0 12.1 11.8 11.4 8.5 13.1 11.4 11.8 9.5 8.0
Variation explained, % 63.8 68.0 69.4 81.8 36.2 42.8 61.7 74.2 72.9 76.3 74.1 48.6 70.0 57.1 65.3 45.1
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