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Analysis of foveal characteristics and their asymmetries in the normal
population
Patrick Scheibea,b, Maria Teresa Zocherb, Mike Franckea,c, Franziska Georgia Rauscherb
aSaxonian Incubator for Clinical Translation (SIKT), University Leipzig, Leipzig, Germany
bDepartment of Ophthalmology, Leipzig University Hospital, Leipzig, Germany
cPaul-Flechsig-Institute of Brain Research, Department of Pathophysiology of Neuroglia, University Leipzig, Leipzig,
Germany
Abstract
The advance of optical coherence tomography (OCT) enables a detailed examination of the human retina
in-vivo for clinical routine and experimental eye research. Only few investigations to date captured human
foveal morphology in a large subject group on the basis of a detailed analysis employing mathematical mod-
els. However, even for important foveal characteristics unified terminology and clear definitions were not
implemented so far. This might be a reason, why to this day the human fovea is considered to be a mostly
symmetric and round structure. Therefore, the most important finding of this work is the detailed analysis
of the asymmetric structure of the human fovea. We employed five clinically highly relevant foveal charac-
teristics, which are derived from a previously published fovea model. For each, an accurate mathematical
description is given. The presented properties include (1) mean retinal thickness inside a defined radius, (2)
foveal bowl area, (3) a new, exact definition of foveal radius, (4) maximum foveal slope, and (5) the maximum
height of the foveal rim. Furthermore, minimum retinal thickness was derived and analyzed. 220 strictly
controlled healthy Caucasian subjects of European decent with an even distribution of age and gender were
imaged with an Heidelberg Spectralis OCT. Detailed analysis demonstrated the following general results:
(1) significant gender difference regarding the central foveal subfield thickness (CFST) but no significant
differences for the minimum central retinal thickness, (2) a strong correlation between right and left eye of
the same subject, and, as essential finding, (3) strong structural differences of the fovea form in the different
anatomical directions (nasal, temporal, inferior and superior). In the analysis of the foveal asymmetry, it
will be demonstrated that the foveal radius is larger in nasal and temporal direction compared to inferior
and superior position. Furthermore, it will be shown that the circular fovea rather has an elliptic form
with the larger axis along the nasal to temporal direction. Interestingly, the foveal slope shows a divergent
behavior as the temporal direction has the smallest slope angle and both, inferior and superior angles are
clearly larger than the others. The findings in this work can be used for an exact quantification of changes
in early stages of various retinal diseases and as a marker for initial diagnosis.
Keywords: Fovea Centralis, Fovea Pit Morphology, Mathematical Model, Optical Coherence Tomography
(OCT)
1. Introduction
Optical coherence tomography (OCT) is a laser-based technique which implements laser interferometry
and is able to penetrate the retina to produce sections with a very high resolution. Light from a broad-
band laser source is divided into a sample and reference beam, and the reflection of both arms results
∗Corresponding author. Tel.: +49 341 97 39483; Fax.: +49 341 97 39609; Addr.: Saxonian Incubator for Clinical Translation
(SIKT) Leipzig, Philipp-Rosenthal-Straße 55, 04103 Leipzig
Email address: pscheibe@sikt.uni-leipzig.de (Patrick Scheibe)
Preprint submitted to Experimental Eye Research April 29, 2016
in an interference image which contains information of the sample. Based on spectrometry this signal is
captured by a camera and transferred to a computer for analysis (Drexler and Fujimoto,2008;Huang et al.,
1991). The OCT laser light is reflected differently by the layers of penetrated retinal tissue and therefore,
the scan enables histology-like examination of retinal structures in-vivo. This has multiple applications
and is used in clinical routine or experimental eye research. Only few investigations to date determine
various morphological properties of the fovea and the macula region based on accurate automated OCT
measurements.
In clinical routine, the only commonly derived measure of OCT based images is retinal thickness. Specif-
ically, the central retinal thickness (CRT) is employed for longitudinal follow-up of various retinal diseases
and it remains an important marker for initial diagnosis. Most commonly, central foveal subfield thickness
(CFST) is determined, defined as the mean thickness within a 1 mm circle centered by fixation close to
the foveal minimum (Early Treatment Diabetic Retinopathy Study Research Group,1991). A different
definition of retinal thickness is to employ the minimal thickness derived at the thinnest part of the fovea
(CRTmin).
So far, normal databases for retinal thickness suffer from different degrees of inaccuracy. OCT de-
vices from different manufacturers can produce significantly different retinal thickness measurements (Wolf-
Schnurrbusch et al.,2009). Although conversion between devices is possible (Krebs et al.,2011b,a), it
is vitally important to correctly adjust the measurement region to obtain accurate and reproducible re-
sults (Heussen et al.,2012). These might be reasons, why the full potential to use central retinal thickness
as an early indicator of developing retinal abnormalities has so far not been employed.
Previous studies have shown that men had greater retinal thickness than women. Wagner-Schuman
et al. (2011) assessed these gender differences on the same OCT device as the current study. They examined
retinal thickness in nine fields, based on circular rings with 500 m, 1500 m and 3000 m radius. Their
CFST was measured as (264.5±22.8) m for men and (253.6±19.3) m for women (p= 0.0086) and they
found significantly higher thicknesses in men for all but the superior outer and nasal outer EDTRS grid
fields (Wagner-Schuman et al.,2011). In an earlier study employing the same OCT device, mean CFST was
(270.2±22.5) m with no difference in gender which is most likely due to by to the small cohort investigated.
There, a mean CFST of (273.8±23.0) in males and (266.3±21.9) m in females (p= 0.1) was found (Grover
et al.,2009).
Some more detailed analyses of foveal pit morphology were recently carried out and various foveal char-
acteristics have been proposed. Wagner-Schuman et al. (2011) employed a difference of Gaussians (DoG)
model to determine foveal pit depth, diameter and maximum slope of 43 women and 47 men. They re-
ported a foveal pit depth of (120 ±27) m and (119 ±19) m, a foveal pit diameter of (1930 ±220) m and
(1960 ±190) m, and a maximum slope of (12.2±3.2) and (11.8±2.2) for men and women respectively.
Dubis and colleagues, who used a DoG model as well, presented the surface diameter of the foveal pit,
which they defined as the distance from rim to rim. They presented the average diameter of six scans at
30 intervals obtained with 1940 m for the Spectralis OCT (Dubis et al.,2009). Tick and colleagues (Tick
et al.,2011) have measured foveal pit diameter again derived from OCT images based on maximum rim
height and found the diameter to be larger horizontally (2210 m) compared to vertically (2450 m).
Similar to the diameter, another approach is to investigate foveal radius which is usually defined as the
distance from the foveal center to some outer boundary. Various definitions of radius and diameter regarding
the foveal zone have been examined previously that are not necessarily relying on OCT data. O’Leary
(1985) investigated foveal radius by using the commonly known kidney-shaped reflex of ophthalmoscopy in
20 myopic subjects (12 female, 8 male) and found the radius of young myopic subjects to be 1040 m to
1700 m . Delori et al. (2006) and colleagues measured the size of the reflex of the ring illumination of the
fundus camera and listed the size of the reflex in 18 subjects (8 female, 10 male) to be larger in women
than in men ((0.27 ±0.07) and (0.16 ±0.04) , respectively; p < 0.001), which they gave to equivalent to
1190 m and 744 m respectively. However, such measurement is confounded by factors such as axial length
as pointed out by Provis et al. (2013). Yuodelis and Hendrickson (1986) investigated the rod free zone of the
human fovea to be 650 m to 700 m (683 m were measured in an adult specimen). Chui et al. (2014) found
individual variations in the diameter of the foveal avascular zone (FAZ) when imaging the microvascular
structure in vivo by adaptive optics scanning laser ophthalmoscope (AOSLO). They established a horizontal
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FAZ diameter of (607 ±217) m micrometer and a vertical FAZ diameter of (574 ±155) m. Dubis et al.
(2012) listed the FAZ diameter to range from 200 m to 1080 m, again based on AOSLO measurements.
In the same work, Dubis et al. (2012) extracted foveal pit metrics from OCT derived data, and found the
diameter to be 1120 m to 2400 m. Another work by Chen et al. (2015) investigated a “floor-diameter of
the foveal pit” which they defined as the region where the retinal thickness “remained at a minimum”, based
on data obtained by the OCT device software. It was found that the average diameter of the foveal floor
was (120 ±40) m and (150 ±50) m for the right and left eye respectively. This finding, however, depends
on the resolution of the OCT since the fovea itself is a continuous pit with exactly one minimum. Therefore,
such a definition of a foveal floor will be affected by an arbitrarily chosen tolerance that is used to determine
the floor size around the foveal minimum.
Generally speaking, the size of the foveal radius, i.e. the size of the foveal pit diameter, is of great
importance, because it describes the size of an area of best resolution in the eye. However, the size of the
fovea is potentially physiologically constrained, possibly related to pupil size to achieve angular resolution
(see (Provis et al.,2013) and (Franco et al.,2000)). Even though, visual resolution is not attributable to a
single factor, it could be speculated that the size of the foveal radius may be correlated to visual performance
indicators obtained.
Beside the size of the foveal zone, the slope of the foveal pit is another characteristic that is of historical
importance as very early research connected it to visual acuity. According to Walls (1942) the optical
effect of the slope of the deep convexiclivated fovea of some birds leads to local magnification at retinal
photoreceptor level. This is supposed to be a result of the very steep fovea and a slight difference in refractive
indices of vitreous humor and retina according to Valentin (1879). Although humans do not possess such
extreme foveas, it was recently suggested, that this optical effect could be extended to primate/human
foveas (Reichenbach et al.,2012).
The development of the foveal pit in children, and the maturation of human fovea in general, is a related
interesting topic that relies on the analysis of foveal characteristics (Yanni et al.,2012;Vajzovic et al.,
2012). It has already been demonstrated that there exists a significant difference in slope as well as in
other characteristics between the foveal pits of preterm children and full-term controls (Yanni et al.,2012).
A rigorous investigation of the spectrum of foveal slopes in one subject or in different subject groups is
therefore of high interest.
Closely related to slope and radius is the foveal rim height, hrim, which is the retinal thickness at the
top of the rim. Although a prominent rim might not be visible in all foveas, it is widely accepted that there
is a point of largest retinal thickness outside the pit. Sigelman and Ozanics (1982) measured the retinal
thickness at its maximum point at the foveal rim to be 230 m based on histological preparations (shrinkage
factor). Newer data exists by Ahnelt who measured the retinal thickness at the foveal rim to be 320 m in
a light microscopy image with little shrinkage artifacts. His material was well fixed and of quality suitable
for electron microscopy without postmortem delay (Ahnelt,2016).
Tick et al. (2011) derived the maximal retinal thickness in superior (S), inferior (I), nasal (N) and
temporal (T) locations and found that (306 ±16) m was significantly lower on the temporal side, whereas
the other locations were similar (S: (332 ±16) m , I: (325 ±15) m, N: (329 ±17) m).
The current investigation aims to provide a clear definition of five intuitive foveal characteristics that are
derived from the mathematical fovea model introduced in Scheibe et al. (2014). The presented characteristics
include (1) mean retinal thickness inside a defined radius, (2) foveal bowl area, (3) a definition of foveal
radius, (4) maximum foveal slope, and (5) the maximum height of the foveal rim. While mean retinal
thickness is a characteristic of the eye as a whole, the remaining four characteristics are available in each
modeled direction. As will be shown, there are significant differences when these properties are evaluated in
different directions inside the same fovea. Therefore, an important aspect will be to highlight the asymmetric
structure of the foveal region and discuss possible explanations for varying foveal characteristics.
At first, a compact computation scheme will be presented that shows how the CFST can directly be
extracted for a modeled eye. Since the CRTmin in the center of the fovea is an intrinsic part of the modeling
procedure, this property will be analyzed as well and compared to earlier published results.
As a second fovea property, foveal bowl area, Abowl, is introduced which can be calculated as an analytic
integral equation of the model formula. This bowl area will then be used to derive a foveal radius that is
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superior to the usage of the foveal rim as boundary for the pit. These two characteristics will serve here to
show the strong correlation of right and left eye within one subject.
Finally, the foveal slope and rim height characteristics, both already introduced in (Scheibe et al.,2014),
will be investigated further. The slope will be examined for correlations to the foveal radius in different
directions. Similar, the rim height will be used to reveal directional difference between male and female
subjects.
Beside a rigorous discussion and comparison of our findings with available literature, the key point of
the current work will be the analysis of the asymmetric structure of human foveas.
2. Materials and methods
To calculate the results presented here, 220 strictly controlled normal caucasian subjects of European
descent were employed (Zocher et al.,2016). From the 220 patients both eyes were scanned, but 31 OCT
scans needed to be discarded for bad quality and therefore, a total of 409 OCT scans were analyzed. For 19
subjects only the right scan and for 12 subjects only the left scan was available, i.e. 208 right eyes and 201
left eyes were in this sample.
The data presented are based on 109 men and 111 women aged 21years to 77 years with a mean/SD
of (43 ±13) years and (44 ±14) years, respectively. The following number of men and women were within
the following age decade brackets: 20 year-decade: 25 men and 25 women, 30 year-decade: 21 men and 18
women, 40 year-decade: 29 men and 28 women, 50 year-decade: 19 men and 22 women, 60 year-decade: 12
men and 16 women, and 70 year-decade: 3 men and 2 women.
Refractive error was distributed in a range of −9D to 6 D with a mean/SD for men of (−1.04 ±2.24) D
and women of (−0.631 ±2.250) D. Women and men showed no significant differences in ametropia (p=
.108). Refraction was quantified based on the sphere obtained during best corrected subjectiv refraction.
This spherical refractive error was more hyperopic as expected with age (men: r= 0.321, p<.001,
women: r= 0.39, p<.001). Axial length was distributed between 20.8 mm to 27.6 mm with a mean/SD of
(24.30 ±1.02) mm for men and (23.40 ±1.01) mm for women. A more detailed statistic of the sampled eyes
properties can be found in table 1. The research followed the tenets of the Declaration of Helsinki for the
use of human subjects.
eye age AL BCVA SE S
right 42.6±13.6 23.8±1.12 −0.119 ±0.0862 −0.523 ±2.18 −0.823 ±2.24
left 42.7±13.6 23.8±1.13 −0.125 ±0.0774 −0.553 ±2.19 −0.824 ±2.23
Table 1: Properties of sub jects’ right and left eyes given as mean and standard-deviation. The table shows age (in years), axial
length (AL in mm), best corrected visual acuity, which is the visual acuity in logMAR achieved with the optimal refractive
correction in place (BCVA in logMar), spherical equivalent (SE in D), and sphere (S in D).
All datasets were captured with a Spectralis OCT (Heidelberg Engineering, Heidelberg, Germany) where
each volume scan consisted of 97 B-Scans (at 512 A-Scans/B-Scan) and every A-Scan consists of 496 samples.
For each OCT scan, an angle of 20 in both, x- and y-direction was used. The resulting exact metric
dimension in x- and y-direction depend on the subject’s specific eye parameters, but, approximately, each
dataset represents a scanned volume of 6mm ×6 mm ×1.92 mm.
The correct OCT image magnification was calculated, taking into account the subject’s anterior corneal
radius (mean of steep and flat meridian) and the focus obtained during measurement. These values were
used to follow the approach given in the work of Garway-Heath et al. (1998).
All calculations necessary for the modeling and all statistics were carried out with Wolfram Mathemat-
ica (Wolfram Research,2015), Version 10.3. To import the scanned volumes into Mathematica, the datasets
were saved from the Spectralis OCT using the raw data export functionality. To read the binary format into
Mathematica, an import software has been developed that is freely available from github.com/halirutan.
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2.1. Fovea Analysis
The analysis in this work uses a fovea model function Mwith four free parameters µ, σ, γ, and αthat
was introduced in Scheibe et al. (2014):
M(r;µ, σ, γ, α) = µσ2rγ·exp [−µrγ] + α(1 −exp [−µrγ]) .(1)
After importing the OCT volumes, the mode-parameters were calculated as described there using a model
fit with a maximal model radius rmax = 2 mm and with the following model parameter ranges: µ∈(0,10],
σ∈(0,2], γ∈(1,10] and α∈[−2,2]. For each eye 40 equally distributed angular directions were fitted.
bowl area
A
bowl
rim height
h
rim
95%bowl area height
foveal radius
r
fov
slope angle β
max. gradient
RPE
CRTmin
modelled fovea
Figure 1: The foveal characteristics used in this publication can be calculated automatically for each eye with the given
approach. The CRTmin represents the minimal height between the RPE and ILM which is defined as the center of the fovea.
All radially modeled fovea forms have this central point in common. The rim height hrim is the distance between RPE and the
model function at the foveal rim top. This maximum point of the rim is unique and exists in every model function. The blue
region is the area between the model function and a horizontal line that connects with the maximum rim point. It represents
the foveal bowl Abowl and its value can be calculated as shown in section 2.1.2. The point of maximal gradient that always
exist between the fovea center and the rim defines the slope angle β. The foveal radius is defined by the point, where the bowl
is filled with 95 % of its area.
The model-parameters for each subject were then employed to calculate fovea characteristics that al-
low for a detailed and intuitive analysis. Some of the used foveal characteristics were already presented
in (Scheibe et al.,2014), others will be explained below. In general, the presented foveal properties can
be divided into two groups. The first group consists of characteristics that are defined for each eye and
characterize one specific value for the fovea as an entity, while the second group are characteristics defined
for each of the 40 fitted directions per fovea.
The minimal central retinal thickness (CRTmin) and the mean retinal thickness (CFST) inside the 1 mm
circle centered on the foveal minimum are defined once per fovea and thus fall within the first group. Note
that although the CRTmin value serves as center of the fovea model, it is basically unrelated to the model fit
procedure, because its value, the distance between ILM and RPE in the foveal center, is directly extracted
from OCT.
The remaining 4 foveal characteristics used in this work are calculated for each fitted direction. Later,
either median values of the 40 directions will be analyzed or values of the anatomical directions nasal,
temporal, inferior, and superior will be compared. Characteristics that are available for each fitted direction
are the foveal bowl area (Abowl), the foveal radius (rfov), the maximal slope inside the foveal pit (slope),
and the retinal thickness of the foveal rim (hrim). All these properties are depicted in figure 1.
The definition of the foveal slope angle βand the rim height hrim was already given in Scheibe et al.
(2014) and the exact formulas are not repeated here; nevertheless, a short description will follow. Due to
the structure of the model formula, the maximum slope angle βcan easily be calculated by evaluating the
gradient of the model function m=∂rM(r) at the first inflection point. To transform the result to degree
the transformation β= 180 ·arctan(m)/π can be applied.
The foveal rim is the highest point of a fovea and is a unique maximum of the model formula. Its position
rrim can be calculated through the first derivative of the model function by solving ∂rM(r;µ, σ, γ, α)=0
5
for r. This gives
rrim =α+σ2
µσ2
1
γ
(2)
and the overall rim height hrim can be obtained by the sum of CRTmin and M(rrim).
2.1.1. Central Foveal Subfield Thickness (CFST)
Clinically it has been common to employ a nine-field grid to examine retinal thickness. These circular
rings with 500 m, 1500 m and 3000 m radius were originally defined for examination of fundus images
by the ETDRS group (Early Treatment Diabetic Retinopathy Study Research Group,1991). The grid
fields of retinal thickness generally divide the ≈20 macular region into sections where the retinal thickness
is measured and compared. Commonly, the central circle of the ETDRS grid within 1 mm diameter is the
measure investigated and it is defined as central foveal subfield thickness (CFST). If the measurement region
is centered correctly, the CFST is an important foveal characteristic with the foveola in its center.
To calculate CFST from OCT data, one has to uniformly distribute a number of sampling points inside
this 1 mm circle. The CFST is then given by the mean of all retinal thickness values at these sampling
points. In OCT data, the most direct approach for this is to use all A-scans that fall within the 1 mm circle
as sampling points.
However, in this work, a fovea is represented by a number of radial model functions centered in the
foveola and therefore, a different method is required to approximate uniform sampling. The key idea is
instead of sampling OCT data in x- and y-direction, to use a radial sampling that covers the inner 1 mm
circle by varying angles ϕand radii r. Since each fovea was modeled in 40 equally spaced directions, only
fixed sampling for ϕis available and, therefore, ϕcannot be chosen freely. Along each one of the 40 model
functions, M(r) can be evaluated for arbitrary values of r.
To achieve a uniform distribution inside the circle, every sampling point should cover the same area-
fraction. As depicted in figure 2(a), in the built-in CFST of the OCT software tool employs the following
paradigm: every sampling point covers a small rectangular area of the same size that is surrounded by gray
grid lines.
(a) (b)
Figure 2: Distribution of sampling points to calculate the CFST. Sampling points are depicted as red dots inside a gray grid,
dividing the area in equally sized partitions. In the left figure, a possible distribution is given that uses the underlying OCT
B-scans, drawn as green, dashed lines. All red sampling points are equally spaced along a B-scan and need to lie inside the
1 mm circle. In right figure, one possible distribution of sampling points is shown that can be used, when retinal thickness is
only available on radial model functions (depicted as green, dashed lines). Like in figure (b), each small partition surrounded
by gray lines has the same size.
In figure 2(b), a different partition of the 1 mm circle is depicted, which shares the property that all gray
areas containing a sampling point have the same size. Additionally, it is easily possible to construct this
partition to make all sampling points lie on the green dashed lines that represent the model-function in all
directions.
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The partition shown in 2(b) can be derived from a recurrence equation to obtain the gray circles that
are required to ensure all small sampling areas are of the same size:
Given the number of modeled directions nd, the number of different radial sampling points nrthat
can be chosen freely, and with one additional central sampling point, the overall number of red points
is n=nd·nr+ 1.
With ngiven, the area of one small partition can be calculated by dividing the area of the measurement
region, ACFST, into nequal partitions by A0=ACFST/n = 2πr2
CFST. To obtain the usual definition
of 1 mm circle CFST, rCFST =1/2mm. Therefore, the radius, r0, of the central gray circle in 2(b) is
given by r2
0=A0/π.
The area of the annulus between two adjacent radii rnand rn+1 is simply nd·A0since each ring
consists of ndsegments that have the same size A0. Additionally, taking the standard definition of an
annulus, its area can be calculated by the difference of two disk with radii rn+1 and rnwhich leads to
the recurrence equation
nd·A0=πr2
n+1 −πr2
n, r2
0=A0/π
By solving the above equation for r2
n+1 and expanding some of the recursive steps, one finds the explicit
solution for the i-th radius to be
r2
j=r2
CFST j·nd+ 1
nd·nr+ 1, j = 0, . . . , nr
Note that rnris simply rCFST and that sampling points were placed in the middle between two
neighboring radii.
Given the list of radii rj, the final approximation of the CFST using our model is given by
CFST = CRTmin +1
n
nd
X
i=1
nr−1
X
j=0
Mirj+rj+1
2,(3)
where Midenotes the model-function in the i-th direction. Readers should note that this is only one
possible approximation of CFST using radial model functions and that different sampling, interpolating and
integrating schemes can be derived as well.
2.1.2. Foveal Bowl Area
The bowl area is the blue region depicted in figure 1and it is defined as the area enclosed by the horizontal
line to the highest point on the foveal rim and the model function.
To calculate an analytic formula for this area, the point (rrim,M(rrim )) (see equation 2) is required. The
rectangular area under the horizontal upper boundary line of the foveal bowl is given by the product of rrim
and M(rrim). Using this, the foveal bowl area can be given as the difference
Abowl =rrim · M(rrim)−Zrrim
0
M(r)dr (4)
An analytic solution to equation 4is possible, but, due to its length, cannot be presented here.
2.1.3. Foveal Boundary Radius
The foveal radius was derived from the model formula to obtain a boundary for the foveal pit. While
it seems natural to use the highest point on the foveal rim, rrim, for this purpose, it would come with a
drawback, because, although most foveal shapes have a clear rim, it is possible to observe foveas where the
rim is almost even. Such foveas, although they possess a rim point, possibly have this point at a significantly
greater distance to the foveal center, compared to a fovea with similar properties alongside a more defined
7
rim structure. That would lead to a foveal radius definition with a high variance, even when the foveal
structures itself share many other characteristics.
It was found that the foveal bowl area, which includes rrim only indirectly as integration boundary, can
be used to obtain a very consistent measure for the foveal radius. For this purpose, a defined percentage
p(usually 95 %) of the foveal bowl area is used which is determined by where the foveal form is hit if the
bowl would be filled with the reduced area only. In figure 1this is exemplary shown by the red p= 95 %
line and the distance between foveal center and the red dot on the fovea shape.
Following the same argumentation as in section 2.1.2, the foveal radius rfov can be obtained by solving
the following equation
rfov · M(rfov)−Zrfov
0
M(r)dr =p·Abowl (5)
In this work, numeric solutions to equation 5were obtained by a simple bisection algorithm to find the
root. This approach is justified due to the very nature of the expression, because equation 5will have exactly
one solution in the interval 0 < r < rrim when the percentage is between 0% and 100 %.
3. Results and Discussion
The 409 available data-sets consisted of 208 right and 201 left, and 207 female and 202 male eyes
respectively. The distribution per decade (20 to 80 years of age) was chosen based on the age and gender
distribution of Leipzig, Germany (census data) and it included solely caucasian subjects. For each eye 40
equally angular distributed radial fovea fits were calculated, resulting in a total of 16360 foveal model shapes.
The overall root mean square fit error was (3.01 ±1.09) m.
Basing on the model-parameters µ, σ, γ, and α, the derivation of five useful foveal characteristics was
presented: (1) the maximum foveal slope, (2) the area inside the foveal bowl, (3) a foveal radius, (4) the
maximum hight on the foveal rim, and (5) the central foveal subfield thickness. The introduced character-
istics, that are partly known from literature with varying definitions, have now a formal definition on the
basis of the fovea model introduced in Scheibe et al. (2014). A need for such a “consensus on the terms and
methods used to define the different features of foveal morphology” was postulated previously by Provis
et al. (2013). Once a unified terminology is established, subsequent investigations into the morphology of
foveae in humans and other species will work on a common ground and results will be better comparable.
Table 3shows the mean/SD values of all obtained model parameters and foveal characteristics. For
each presented property the median value of all fitted 40 directions and the values in four the anatomical
directions nasal, temporal, inferior and superior are given. Additionally, each row is divided into right and
left eye to make a direct comparison possible. Finally, the table is divided into three large blocks presenting
all, male and female subjects separately. In addition to table 3, mean/SD values of CFST and CRTmin split
by gender and eye position are given in table 2.
Figure 3shows examples of foveas that exhibit extreme values in particular foveal characteristics. The
selected OCT images are the central scans through the fovea and show the nasal and temporal direction.
The mean value of both directions was taken to select examples that possess the largest and smallest values
in the specific characteristic. The single images show the following characteristics: 3(a) and 3(b) foveal slope
with 5.1 and 16.9 respectively, 3(c) and 3(d) foveal bowl area with 0.025 mm2and 0.098 mm2respectively,
3(e) and 3(f) foveal radius with 0.72 mm and 1.23 mm resp ectively, and 3(g) and 3(h) foveal rim height with
290.4 m and 392.8 m respectively.
In the following sections, the data presented in summarized form in table 2and 3, will be combined and
discussed in different ways to illustrate inter-relationships.
3.1. Correlation between right and left eye
One compelling topic is the correlation between a subject’s right and left eye. Regarding a specific
research question, it would theoretically be possible to double a studies sample size by using both eyes in an
analysis. For this, both eyes must be statistically independent. Merely the fact that both eyes are from the
8
(a) flat foveal slope (b) steep foveal slope
(c) small foveal bowl area (d) large foveal bowl area
(e) small foveal radius (f) large foveal radius
(g) small foveal rim height (h) large foveal rim height
Figure 3: Selected OCT scans to illustrate extreme foveal characteristics. While the left column displays minimal values,
the right column shows maximum values of the specified characteristic. From first to last row the pairs demonstrate extreme
examples for foveal slope, bowl area, radius, and rim height respectively. Each image shows the central OCT scan through the
fovea. The mean values (from nasal and temporal direction depicted) of the shown fovea are: for the foveal slope (a) 5.1 and
(b) 16.9 , for the foveal bowl area (c) 0.025mm2and (d) 0.098 mm2, for the foveal radius (e) 0.72 mm and (f) 1.23 mm, and
for the foveal rim height (g) 290.4 m and (h) 392.8 m.
9
same person disqualifies them as being as diverse as two single eyes from two independent observers. On
the other hand, there might be research questions that focus on specific problems where corresponding eyes
might indeed be regarded as uncorrelated in some sense. In general, an existing correlation between right
and left eye of the same subject is often inevitable and therefore, a usage of all eyes in e.g. a statistical test
is not allowed. A detailed discussion about this topic can be found e.g. in Armstrong (2013).
For the current work, the authors presumed that a correlation between right and left eyes most likely
appears in foveal characteristics which include information about the absolute size. Therefore, the foveal
radius rfov and the foveal bowl area Abowl were chosen to compare eyes within the same subject, where
right and left eye were available. Figure 4contains the scatter-plots of these correlations that show a
striking connection between right and left eyes. Both, the foveal radius and the foveal bowl area possess
high correlations of r= 0.924 (p<.001) and r= 0.959 (p<.001) between right and left eyes respectively.
0.7 0.8 0.9 1.0 1.1 1.2
OD [mm]
0.7
0.8
0.9
1.0
1.1
1.2
OS [mm]
(a) foveal radius (r= 0.924)
0.02 0.04 0.06 0.08 0.10
OD µm2
0.02
0.04
0.06
0.08
0.10
OS µm2
(b) foveal bowl area (r= 0.959)
Figure 4: Scatterplots for two different foveal characteristics showing the correlation between right and left eyes. The plots
clearly show that right and left eyes are highly correlated for the foveal radius (p<.001) and bowl area (p<.001). Both
characteristics are considered to be directly correlated to the overall size of the eye.
The consequence of this is that one has to be extremely cautious when mixing both, right and left eyes
into the same sample group. If in doubt, it is advised to stick to the common rule of using only one eye per
subject (e.g. right eye) as it is done in many studies. For the current work, the tables and analyses are given
for the respective eye independently and if eye position is not specified, only right eyes were compared.
Apart from showing inter-subject correlations, characteristics like the foveal bowl area and the radius
have many further application domains. Clinically, an exact description and measurement of bowl area is
useful in detection of vitreomacular interface pathology, for example macular hole development. Different
types and stages of macular holes exist, each of which will affect the bowl area parameter, beginning with
foveal detachment (stage 1), partial thickness holes (stage 2) and full thickness holes (stage three). Epiretinal
membranes which may develop pseudoholes can also be identified by the bowl area parameter. Potentially,
the bowl area parameter can only be measured in early stages, as the model used here can only successfully
deal with stage 1 holes. This has to be investigated in a subsequent study. However, as the potential key
application is early diagnosis of new cases or beginning fellow-eye involvement, the paradigm presented will
produce highly accurate results where they are needed most.
Macular holes caused by persistent adherence of the cortical vitreous to the fovea with adjacent vitreo-
retinal separation, often begin gradually and are associated with visual acuity reduction, metamorphopsia,
and a central scotoma. Fellow-eye involvement has been shown to affect 21 % of unilateral cases (Duker et al.,
1995) or was shown to newly develop in 13 % of eyes within 48 months (Benson et al.,2008). Cross-sectional
OCT images provide information on the vitreomacular interface not visible with biomicroscopy, information
is obtained on the pathogenesis, classification, and diagnosis of macular hole. In addition, the OCT has
been employed to measure the hole diameter as average of vertical and horizontal diameter, determined at
the minimal extent of the hole (Kang et al.,2003). In a different application, the OCT is used to identify
the anatomical status after macular hole surgery by an adjusted hole size parameter which is defined as the
ratio between the hole size and the fellow eye’s foveolar floor size (distance between the boundaries free of
10
ganglion cell layer) (Shin et al.,2015).
The novel assessment based on the parameters of this paper enable scientists and clinicians alike to assess
hole formation on a new level of accuracy. The hope is that by quantifying even small deviations from the
norm, a better grading and an earlier detection of hole formation is possible.
3.2. Retinal thickness differences between male and female subjects
CFST has been investigated in the past and, although, some studies generalize this to be central retinal
thickness (CRT), the current study will not employ the latter term as it can easily be confused with CRTmin,
which is a second meaningful measurement representing the deepest part of the foveal pit. Therefore, CRTmin
is the minimal retinal thickness, which is the location the ETDRS grid should be centered on.
Central foveal subfield thickness has been defined within other populations on the same OCT device.
Heussen et al. (2012) measured CFST to be 278.9 m for the device’s automatic measurement mode. Wolf-
Schnurrbusch and colleagues established 289 m (Wolf-Schnurrbusch et al.,2009) in their population, while
Grover and associates found the CFST to be (271.4±19.6) m (Grover et al.,2010). A difference in retinal
thickness between male and female subjects was already reported in different studies (Kirby et al.,2009),
however some of the research findings (Delori et al.,2006) were potentially established due to confounding
factors (e.g. axial length (Provis et al.,2013)). Previous gender related findings for CFST on the same
OCT device also found smaller thicknesses for women (men: (264.5±22.8) m and women (253.6±19.3) m
(Wagner-Schuman et al.,2011), with p= 0.0086). Grover et al. (2009) found no gender differences for CFST
measured with the Spectralis OCT (men: (273.8±23.0) m and women (266.3±21.9) m, with p= 0.1),
which can be attributed to insufficient sample sizes.
The current investigation established gender differences as depicted in Table 2and Figure 5: The CFST
is significantly larger in males than in females for both eyes (p<.001), but a significant difference in
CRTminbetween different gender could not be found (right eyes p=.139, left eyes p=.308).
all male female
CFST [ m] r 277.48 ±19.817 282.74 ±20.277 272.12 ±17.897
l 277.74 ±19.702 282.58 ±20.441 272.74 ±17.659
CRTmin [ m] r 229.67 ±18.844 232.02 ±20.402 227.27 ±16.875
l 230.00 ±18.947 231.81 ±20.305 228.14 ±17.343
Table 2: The central foveal subfield thickness (CFST) and then minimal central retinal thickness (CRTmin) both in [ m]
given as mean and standard-deviation for all subjects and divided by gender. Each row is split into right (r) and left (l)
eyes. While the CFST is significantly larger in males than in females for both eyes (p < .001 both), a significant difference in
CRTminbetween different gender could be found (right eyes p=.139, left eyes p=.308). Note that the gender differences in
CFST are still significant even if a correction for axial length was done.
With CRTmin, CFST, and hrim (see table 3), a comprehensive comparison of three retinal thickness
measures can be given. This leads to a greater insight, because as depicted in figure 5, foveal rim thickness
values can be analyzed for different anatomical directions. The box-and-whisker diagram shows that there
are clear differences between directions and that e.g. temporal rim heights are smaller than in any other
directions (p < .001 for all in men and women). Regardless of the directional differences, female subjects
show significantly smaller hrim values in all four directions (p=.002, p=.006, p=.001, and p=.03 for the
directions N, T, I and S respectively).
For the first time characteristics like hrim can be calculated for various directions like presented here for
nasal, temporal, inferior and superior directions. This sets a precedent in resolving structural variations and
since not only the four anatomical directions can be analyzed, but virtually every direction, novel findings
like shown in figure 7can easily be investigated.
The relationship of the presented hrim with data in the literature is difficult to establish. A comparison
of histology with OCT has previously been computed for a macaque fovea to aid conversion (Anger et al.,
2004), but relative shrinkage is likely depending on specific fixation and embedding protocols. Besides species
specific proportions, individual variations have to be, at least in part, attributed to preceding preparatory
influences. When manually measuring a histological fovea section of baboon tissue (Figure 6B of Krebs
11
nasal
tempor al
inferior
superio r
0.28
0.30
0.32
0.34
0.36
0.38
0.40
male
female
Figure 5: Rim height hrim [mm] of male and female subjects divided into the four anatomical directions. Male rim heights
are larger than female rim heights in each direction. The nasal, temporal, and inferior differences are significant (p=.002,
p=.006, p=.001, and p=.03 resp). Noteworthy, in superior direction, the difference is statistically not as strong as in the
other directions.
and Krebs (1991)), maximum rim height was 363 m. For a human fovea, a maximum rim height was
measured manually as 320 m (left side of image) and 333 m (right side of image), see Figure 6-91 of Fine
and Yanoff (1979). Published OCT data, for example in Figure 1 of Jonnal et al. (2014), gave 379 m nasally
and 347 m on the temporal side of the horizontal scan depicted. Although this is only an individual scan
(healthy subject “S3” of Jonnal et al. (2014), gender or age not given), this data is based on OCT, hereby
facilitating comparison to the current data. Differences of this example image to the current model data
presented in the next paragraph can be attributed to manual measurement from the published image versus
model based computation, alongside individual variation with unknown gender or age information.
In this work, nasally, hrim was 360 m and significantly larger then temporally with 342 m (p < .001).
Men presented with larger maximum rim height compared to women (right eye: nasally 364 m versus
357 m with p=.002; temporally 345 m versus 339 m with p=.001).
3.3. Asymmetry of the foveal region
As already mentioned in the discussion so far, the human fovea is not a round and symmetric structure.
When the foveal form along different (anatomical) directions is compared, the fovea presents itself as a
highly varying structure that shows clear differences in all investigated characteristics. To our knowledge, a
detailed investigation how important foveal characteristics depend on anatomical directions is not available
so far.
nasal temporal inferior superior
0.6
0.8
1.0
1.2
1.4
(a) foveal radius rfov [mm]
nasal temporal inferior superior
5
10
15
20
(b) foveal slope [ ]
Figure 6: Asymmetries of foveal characteristics when viewed for different anatomical directions. The nasal radius is larger then
all the other 3 directions (p<.001) and the temporal radius is larger than radii in inferior and superior direction (p<.001).
A difference between the foveal radius in inferior and superior direction could not be shown (p= 0.149). The foveal slope in
superior direction is larger than in nasal and temporal direction (p<.001 for both), but a significant difference to the inferior
direction cannot be shown (p=.107).
12
Figure 6reveals the dependency of foveal radius and slope angle on anatomical directions. The foveal
radius is larger in nasal and temporal direction compared to inferior and superior position. This suggests
that the fovea has an elliptic form with the larger axis along the nasal to temporal direction. Interestingly,
the foveal slope shows a different behavior as the temporal direction has the smallest slope angle and both,
inferior and superior angles are clearly larger than the others (p-values, see figure 6). This interesting finding
can be better demonstrated when taking all modeled directions into account. Figure 7shows a polar plot of
the foveal radius and slope for all right eyes. With the current data, it can be shown that the foveal radius
is inversely correlated with slope as a steeper slope will lead to a smaller radius and vice versa (r= 0.408
with p<.001). Such a demonstration of the asymmetry of the fovea has to the knowledge of the authors
not been demonstrated so far.
0
15 °
30 °
45 °
60 °
75 °
90 °
105 °
120 °
135 °
150 °
165 °
180 °
195 °
210 °
225 °
240 °
255 °270 °285 °
300 °
315 °
330 °
345 °
0.2
0.4
0.6
0.8
1.
(a) foveal radius [mm]
0
15 °
30 °
45 °
60 °
75 °
90 °
105 °
120 °
135 °
150 °
165 °
180 °
195 °
210 °
225 °
240 °
255 °270 °285 °
300 °
315 °
330 °
345 °
8.
10.
12.
14.
(b) foveal slope [ ]
Figure 7: Asymmetries of foveal radius and slope in a direct polar plot of all right eyes taking 40 modeled directions into
account. Anatomical directions N, S, T, and I are represented by 0 , 90 , 180 , and 270 resp. Subfigure (a) shows the elliptic
form of the foveal radius that has its largest extent along the N-T axis, although the ellipse appears to be slightly rotated. The
foveal slope shows similar behavior, where the largest extend is along the I-S axis.
One possible explanation for this result is the influence of the retinal nerve fiber layer (RNFL) on the
retinal thickness which in return influences the foveal slope. Nerve fibers running radially from the optic
nerve toward the fovea arrive at the nasal side. There, they split up to run around the RNFL-free zone of
the fovea until they are reunited at the temporal side. Whether this hypothesis contains some truth needs
to be further investigated and discussed with experts in the field of foveal development.
4. Conclusion
The main goal of the current study was to present a detailed and accurate analysis of various fovea
characteristics to reveal existing foveal variations and, above all, to expose the highly asymmetric form of
foveas. Another purpose was to make the current analysis comparable to existing results which is one reason
why computation schemes to commonly used characteristics like CFST were presented. In the case of CFST
it was demonstrated that some researchers found similar results (Heussen et al.,2012;Wolf-Schnurrbusch
et al.,2009;Grover et al.,2010), while others (Wagner-Schuman et al.,2011) showed larger differences
compared to the current study. In this work, previously published significant differences of CFST between
men and women were also found. On the other hand, CRTmin presented with no gender differences.
The presented results for the foveal slope showed general agreement with the results presented in Wagner-
Schuman et al. (2011); Dubis et al. (2012). The vast improvement of the current results is that now it is
possible to give a detailed analysis for various different directions. While Wagner-Schuman and colleagues
13
showed a slope of (12.2±3.2) for men, in this study a great variance of more than 2 could be demonstrated
in different anatomical directions (men right eye, N:10.8 , T:10.3 , I:12.6 , S:12.9 ).
For characteristics like hrim, a comparison to existing literature was difficult as analyses of larger subject
groups could not be found. A comparison with histological examples disclosed that such data demonstrates
hrim to be about 40 m smaller (Krebs and Krebs,1991), while manual measurement of an OCT scan
presented in a recent work (Jonnal et al.,2014) was close to the results presented here. There seems to be
a general consensus that the nasal hrim is larger than temporal. However, an analysis as detailed as given
in this work, taking all four directions into account, does not seem to exist so far.
Finally, figure 7presents a way to unleash the full potential of such a detailed multi-directional analysis as
described here. It is now not only possible to measure differences in a particular direction, with the method
at hand, completely new approaches and insights become available. For instance, figure 7raises interesting
follow-up questions, e.g. how close the presented elliptic form is to a real ellipse and how differences could
be explained. Another issue is that the ellipse-like shape seems to be slightly rotated. In the light of the
fact that the optic nerve head is towards upper right position compared to the right eye fovea, one could ask
the question whether the direction of the major axis is connected to the position of the optic nerve head.
14
model parameters foveal characteristics
µ σ γ α slope [ ] Abowl [mm2]rfov [mm] hrim [ m]
all subjects
median r 1.26 ±0.185 0.472 ±0.0378 1.68 ±0.195 0.0610 ±0.0319 11.5±2.11 0.0537 ±0.0130 0.874 ±0.0772 357 ±15.6
l 1.26 ±0.183 0.470 ±0.0344 1.68 ±0.190 0.0628 ±0.0294 11.5±2.10 0.0539 ±0.0129 0.879 ±0.0752 357 ±15.6
nasal r 1.10 ±0.302 0.469 ±0.113 1.67 ±0.235 0.0593 ±0.114 10.6±2.04 0.0628 ±0.0153 1.00 ±0.110 360 ±16.0
l 1.19 ±0.341 0.450 ±0.0839 1.68 ±0.224 0.0742 ±0.0525 10.9±2.09 0.0616 ±0.0153 0.975 ±0.108 361 ±16.2
temporal r 1.23 ±0.271 0.451 ±0.0550 1.66 ±0.212 0.0518 ±0.0361 10.1±2.13 0.0486 ±0.0127 0.894 ±0.0933 342 ±15.8
l 1.14 ±0.241 0.468 ±0.0866 1.66 ±0.223 0.0392 ±0.0837 9.81 ±2.00 0.0499 ±0.0132 0.920 ±0.0933 342 ±15.6
inferior r 1.30 ±0.249 0.512 ±0.0671 1.63 ±0.204 0.0421 ±0.0531 12.3±2.29 0.0508 ±0.0130 0.826 ±0.0803 357 ±16.3
l 1.28 ±0.240 0.516 ±0.0638 1.63 ±0.228 0.0396 ±0.0511 12.3±2.22 0.0506 ±0.0127 0.827 ±0.0784 357 ±16.2
superior r 1.43 ±0.249 0.470 ±0.0431 1.74 ±0.220 0.0721 ±0.0306 12.7±2.30 0.0549 ±0.0137 0.837 ±0.0822 362 ±16.5
l 1.43 ±0.244 0.466 ±0.0439 1.74 ±0.196 0.0747 ±0.0328 12.6±2.37 0.0554 ±0.0135 0.843 ±0.0773 363 ±16.5
male
median r 1.26 ±0.194 0.484 ±0.0410 1.62 ±0.177 0.0562 ±0.0345 11.8±2.16 0.0523 ±0.0124 0.861 ±0.0809 360 ±14.7
l 1.26 ±0.195 0.482 ±0.0328 1.62 ±0.171 0.0593 ±0.0308 11.8±2.03 0.0528 ±0.0125 0.864 ±0.0778 360 ±15.1
nasal r 1.07 ±0.312 0.494 ±0.142 1.60 ±0.220 0.0419 ±0.154 10.8±2.16 0.0613 ±0.0145 0.993 ±0.104 363 ±15.6
l 1.19 ±0.399 0.464 ±0.0927 1.62 ±0.216 0.0693 ±0.0526 11.2±2.03 0.0605 ±0.0148 0.966 ±0.106 365 ±16.3
temporal r 1.24 ±0.314 0.459 ±0.0667 1.62 ±0.210 0.0481 ±0.0387 10.3±2.16 0.0475 ±0.0127 0.884 ±0.105 345 ±15.1
l 1.14 ±0.275 0.486 ±0.102 1.60 ±0.212 0.0290 ±0.109 10.1±1.97 0.0490 ±0.0129 0.905 ±0.0998 346 ±14.8
inferior r 1.29 ±0.265 0.531 ±0.0774 1.58 ±0.200 0.0321 ±0.0640 12.6±2.39 0.0494 ±0.0124 0.813 ±0.0806 361 ±15.7
l 1.28 ±0.263 0.530 ±0.0638 1.56 ±0.211 0.0330 ±0.0559 12.6±2.16 0.0490 ±0.0124 0.813 ±0.0837 360 ±15.6
superior r 1.46 ±0.243 0.477 ±0.0437 1.70 ±0.194 0.0692 ±0.0308 12.9±2.28 0.0528 ±0.0128 0.816 ±0.0800 364 ±15.4
l 1.44 ±0.244 0.474 ±0.0431 1.70 ±0.182 0.0723 ±0.0324 12.9±2.29 0.0542 ±0.0129 0.829 ±0.0783 366 ±15.2
female
median r 1.26 ±0.176 0.460 ±0.0294 1.73 ±0.198 0.0659 ±0.0282 11.3±2.04 0.0552 ±0.0135 0.887 ±0.0712 354 ±15.9
l 1.26 ±0.171 0.457 ±0.0317 1.74 ±0.192 0.0664 ±0.0275 11.3±2.14 0.0550 ±0.0133 0.893 ±0.0699 354 ±15.7
nasal r 1.13 ±0.289 0.444 ±0.0654 1.75 ±0.228 0.0771 ±0.0413 10.5±1.90 0.0643 ±0.0159 1.01 ±0.117 357 ±15.7
l 1.19 ±0.270 0.435 ±0.0713 1.75 ±0.217 0.0793 ±0.0522 10.7±2.13 0.0626 ±0.0159 0.985 ±0.111 357 ±15.4
temporal r 1.21 ±0.220 0.443 ±0.0387 1.71 ±0.205 0.0557 ±0.0330 9.91 ±2.08 0.0497 ±0.0126 0.905 ±0.0784 339 ±15.9
l 1.13 ±0.202 0.449 ±0.0620 1.72 ±0.220 0.0498 ±0.0426 9.51 ±2.00 0.0509 ±0.0134 0.935 ±0.0840 339 ±15.7
inferior r 1.31 ±0.233 0.493 ±0.0480 1.69 ±0.192 0.0523 ±0.0367 11.9±2.14 0.0522 ±0.0135 0.838 ±0.0783 354 ±16.1
l 1.28 ±0.216 0.502 ±0.0609 1.69 ±0.227 0.0465 ±0.0449 11.9±2.23 0.0522 ±0.0130 0.842 ±0.0701 354 ±16.3
superior r 1.40 ±0.253 0.463 ±0.0416 1.78 ±0.237 0.0750 ±0.0303 12.4±2.29 0.0570 ±0.0143 0.859 ±0.0792 359 ±17.3
l 1.42 ±0.245 0.457 ±0.0433 1.78 ±0.202 0.0772 ±0.0331 12.3±2.43 0.0567 ±0.0140 0.858 ±0.0737 360 ±17.4
Table 3: Calculated model parameter and foveal characteristics grouped by gender and divided into main anatomical directions. The values in the table show the mean
and the standard deviation over all subjects in the specified group. The rows of the table are split into three main groups which are (1) all, (2) male, and (3) female
subjects. For each mentioned group, model parameters and foveal characteristics are given by a median value of the 40 fitted directions or by a value in one of the four
anatomical directions (nasal, temporal, inferior, and superior). Furthermore, each row is divided into left and right eyes. For every entry in the table, the mean and
the standard deviation is given. While the model parameters are unit-less, the used units for foveal slope, bowl area, radius, and rim height can be found in the table
heading.
15
Acknowledgment
The authors would like to thank Peter K. Ahnelt, (retired from Div. of Neurophysiology und Neurophar-
macology, Medical University Vienna, Austria) for helpful discussions regarding the histological material used
for comparsion. We further gratefully acknowledge that Professor Ahnelt provided an additional light mi-
croscopy measurement of maximum rim height. Furthermore, we would like to thank Carolin Blankenburg,
Marlen Kendziora (both Beuth University of Applied Science, Berlin, Germany) and Silvana Hermsdorf
(Ernst Abbe University of Applied Sciences, Jena, Germany) for assistance with examining study subjects.
Finally, the authors thank Ms Sylvina Eulitz, Leipzig University Hospital, Department of Opthalmology,
Leipzig, Germany for her help with data management.
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