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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.

4

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.

6

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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