Table 3: Previously identified candidate members of the $\sigma$ Orionis cluster not validated with Euclid data. Name | RA | Dec | Comment
---|---|---|---
| [hh mm ss.ss] | [deg mm ss.s] |
S Ori 69 | 05 39 18.05 |  $-$02 28 54.1 | extended
S Ori J053923$-$021235 | 05 39 23.28 |  $-$02 12 35.0 | extended
S Ori J053929$-$024636 | 05 39 29.36 |  $-$02 46 37.1 | high proper motion
S Ori 57 | 05 39 47.05 |  $-$02 25 24.5 | high proper motion
S Ori J053956$-$025315 | 05 39 56.81 |  $-$02 53 14.6 | extended
S Ori J054004$-$025332 | 05 40 04.48 |  $-$02 53 31.9 | extended
PBZ12 J054011$-$025639 | 05 40 11.62 |  $-$02 56 39.4 | high proper motion
S Ori J054014$-$025146 | 05 40 14.23 |  $-$02 51 46.3 | extended
PBZ12 J054024$-$024444 | 05 40 24.32 |  $-$02 44 44.3 | extended
PBZ12 J054025$-$024259 | 05 40 25.39 |  $-$02 42 59.7 | extended
PBZ12 J054026$-$023100 | 05 40 26.44 |  $-$02 31 00.8 | high proper motion
PBZ12 J054028$-$025116 | 05 40 27.99 |  $-$02 51 16.7 | extended
PBZ12 J054038$-$022806 | 05 40 38.42 |  $-$02 28 06.6 | extended
Table 4:  Euclid point-source selection criteria. The right ascension, RA, divides the two area into parts: the high-reddening region (${\rm RA}<85\hbox{$.\\!\\!^{\circ}$}1875$); and the low reddening region (${\rm RA}\geq 85\hbox{$.\\!\\!^{\circ}$}1875)$. |  | High-reddening region | Low-reddening region
---|---|---|---
Cut No. | Criteria | Count after cut | % of catalogue | Count after cut | % of catalogue
1 | ra_J_E Cut | 124 249 | 38.04 | 126 693 | 38.79
2 |  $-$0.011<SPREAD_MODEL_J_E<0.014 | 70 558 | 21.60 | 47 630 | 14.58
3 | 0.472<FWHM_IMAGE_J_E<2.158 | 24 174 | 7.40 | 14 932 | 4.57
4 | 0<ELLIPTICITY_J_E<0.138 | 17 423 | 5.33 | 10 742 | 3.29
5 |  $-$0.01<SPREAD_MODEL_H_E<0.016 | 14 574 | 4.81 | 7944 | 2.97
6 | 1.238<FWHM_IMAGE_H_E<2.052 | 12 262 | 3.87 | 7018 | 2.50
7 |  $-$0.005<SPREAD_MODEL_Y_E<0.017 | 11 550 | 3.62 | 6603 | 2.30
8 | 0.461<FWHM_IMAGE_Y_E<2.099 | 10 768 | 3.34 | 6208 | 2.03
9 | Drop 99 in any I_E mag | 9450 | 2.89 | 4663 | 1.43
10 |  $-$0.002<SPREAD_MODEL_I_E<0.004 | 6819 | 2.09 | 3445 | 1.05
11 | 1.127<FWHM_IMAGE_I_E<2.843 | 6614 | 2.03 | 3293 | 1.01

The contamination by background extragalactic sources, the inhomogeneous
interstellar extinction in star-forming regions, the possible presence of
colour-excesses owing to discs and accretion activity, and the low surface-
gravity and extreme youth of FFPs in Orion, together make the selection of
bona-fide substellar objects quite challenging. The Euclid passbands are not
specifically designed to distinguish FFPs from other types of objects. They
are broader than the passbands commonly used in ground-based surveys because
they include spectral regions affected by saturated telluric water absorption.
The calibrations available for this ERO study are scarce. Improved
calibrations are expected in the future when Euclid photometry and
spectroscopy of benchmark ultracool dwarfs become available. We limit the
scope of this work to present a high-purity approach to select objects using
Euclid ERO catalogue and images that is anchored to the properties of the
benchmarks described in the previous section. The selection cuts adopted in
this work are presented in Table 4. To arrive at these selection cuts, we
calculated the 1$\,\sigma$ dispersion around the mean of the values for the
benchmark sources and we added it to both extremes of the distribution.

The ERO-SOri photometric catalogue was filtered using the cuts provided in
Table 4. The number of objects left after each step and the percentage with
respect to the original sample are also given in the table. Note that the
percentage of sources detected in the $J_{\scriptscriptstyle\rm E}$ band in
the whole FoV adds up to 76.83% of the total number of sources in the ERO
catalogue. Sources not detected in the $J_{\scriptscriptstyle\rm E}$ band have
not been considered in this work because young substellar objects are expected
to be much brighter in the $J_{\scriptscriptstyle\rm E}$ band than in the
$I_{\scriptscriptstyle\rm E}$ band. The CLASS-STAR classifier was found to be
redundant with the SPREAD-MODEL parameter, and the latter was chosen because
the values for the benchmarks are more stable. The FoV was divided in two
regions separated by a constant RA value of $None$. We call the low-
reddening/dark-background part the $\sigma$ Orionis region (${\rm RA}<$$$) and
the high-reddening/bright-background part of the Horsehead region. We compared
the distribution of SPREAD-MODEL-J between these two parts of the FoV and
found that it is narrower in the $\sigma$ Orionis region than in the Horsehead
region (Fig. 4). This is likely due to the influence of a brighter background
on the Horsehead side owing to light reflected in the nebulosity. Thus, we
consider that the cuts defined in this work are valid only for regions with
low interstellar background and negligible extinction. For the regions
affected by high sky background it will be important to obtain a new sample of
substellar benchmarks using the Euclid NISP spectra.

Figure 4: Cumulative distribution of spread model values for the Euclid
$J_{\scriptscriptstyle\rm E}$ band. The distribution of values in the low-
reddening part corresponding to the $\sigma$ Orionis cluster is sharper than
in the high-reddening part.

###  4.3 Selection of new substellar member candidates in the $\sigma$ Orionis
cluster with Euclid data

Figure 5: The $I_{\scriptscriptstyle\rm E}$ versus $I_{\scriptscriptstyle\rm
E}-J_{\scriptscriptstyle\rm E}$ colour-magnitude diagram for the $\sigma$
Orionis part of the FoV. Black points are all the Euclid sources that remain
after applying all the cuts. Benchmark objects are denoted with red circles.
New objects near the cluster sequence are denoted with blue squares and
labelled with capital letters. Known sources, other than the benchmarks, in
the $\sigma$ Orionis cluster are denoted with green circles. An ATMO CEQ
isochrone (see Phillips et al. 2020) for an age of 3 Myr and a distance of
402.74 pc is shown. Theoretical masses are labelled on the isochrone.  Figure
6:  The $I_{\mathrm{E}}-Y_{\mathrm{E}}$ versus $Y_{\mathrm{E}}-H_{\mathrm{E}}$
colour-colour diagram for the same region as the previous figure ($\sigma$
Orionis). All the symbols remain the same.  Figure 7: The $I_{\mathrm{E}}$
versus $I_{\mathrm{E}}-J_{\mathrm{E}}$ colour-magnitude diagram for the
Horsehead part of the FoV (not $\sigma$ Orionis). The $\sigma$ Orionis
benchmarks are denoted with red circles. A reddening vector is shown as an
arrow.  Figure 8: The $I_{\mathrm{E}}-Y_{\mathrm{E}}$ versus
$Y_{\mathrm{E}}-H_{\mathrm{E}}$ colour-colour diagram for the Horsehead part
of the FoV (not $\sigma$ Orionis). The $\sigma$ Orionis benchmarks are denoted
with red circles. A reddening vector is shown as an arrow.

After applying all the selection cuts defined above, only 2% of the sources in
the initial catalogue remained. They are plotted in the
$I_{\scriptscriptstyle\rm E}$ versus $I_{\scriptscriptstyle\rm
E}-J_{\scriptscriptstyle\rm E}$ colour-magnitude diagram (CMD) following the
approach of previous searches for substellar objects in the $\sigma$ Orionis
region (Peña Ramírez et al. 2012), and compared with the 3-Myr isochrone
provided by the ATMO models of Phillips et al. (2020) that have been
transformed into the Euclid photometric system for this work. These models
have been tested using the dynamic lithium-boundary method for brown dwarf
binaries with dynamical masses and found to provide better fits to the
observational data than other sets of models in the literature (Martín et al.
2022). The Euclid data and the CEQ (equilibrium chemistry) ATMO 3-Myr
isochrone are shown in the CMD displayed in Fig. 5. The benchmarks clearly
define the $\sigma$ Orionis sequence, and other objects in the Euclid data
that appear to follow this cluster sequence have been previously identified in
the literature as photometric candidate members (Peña Ramírez et al. 2012).
Their Euclid coordinates and photometry are provided in Table 5. Seven new
objects were found to be located close to the cluster sequence and well
separated from the cloud of background sources, including two very faint ones
that extend the sequence to fainter magnitudes than previous surveys. The
three brighter objects were retrieved in the VHS catalogue and their
coordinates were found to agree within $100\,{\rm mas}$, so they do not have
high proper motion. The coordinates and photometry of these seven new Euclid
objects of interest identified in the $\sigma$ Orionis cluster sequence are
given in Table 6.

Table 5: Euclid photometry of previously-known non-benchmark objects in the $\sigma$ Orionis cluster sequence. RA (J2000) |  Dec (J2000) | $I_{\scriptscriptstyle\rm E}$ |  $\sigma$($I_{\scriptscriptstyle\rm E}$) | $Y_{\scriptscriptstyle\rm E}$ |  $\sigma$($Y_{\scriptscriptstyle\rm E}$) | $J_{\scriptscriptstyle\rm E}$ |  $\sigma$($J_{\scriptscriptstyle\rm E}$) | $H_{\scriptscriptstyle\rm E}$ |  $\sigma$($H_{\scriptscriptstyle\rm E}$)
---|---|---|---|---|---|---|---|---|---
$None$ |  $None$ | 20.445 | 0.002 | 17.812 | 0.002 | 17.583 | 0.001 | 17.508 | 0.001
$None$ |  $None$ | 21.207 | 0.003 | 18.451 | 0.003 | 18.196 | 0.002 | 18.043 | 0.002
$None$ |  $None$ | 24.299 | 0.027 | 20.923 | 0.016 | 20.547 | 0.009 | 20.055 | 0.006
$None$ |  $None$ | 21.158 | 0.003 | 18.269 | 0.003 | 18.127 | 0.002 | 17.920 | 0.002
$None$ |  $None$ | 23.618 | 0.016 | 20.300 | 0.011 | 20.028 | 0.007 | 19.749 | 0.006
$None$ |  $None$ | 22.725 | 0.008 | 19.478 | 0.005 | 19.124 | 0.003 | 18.861 | 0.003
$None$ |  $None$ | 23.945 | 0.022 | 20.758 | 0.017 | 20.284 | 0.009 | 19.915 | 0.007
$None$ |  $None$ | 20.358 | 0.002 | 17.994 | 0.003 | 17.216 | 0.001 | 16.513 | 0.001
$None$ |  $None$ | 24.400 | 0.039 | 21.159 | 0.017 | 20.872 | 0.011 | 20.705 | 0.010
$None$ |  $None$ | 18.348 | 0.001 | 16.570 | 0.001 | 16.416 | 0.001 | 16.196 | 0.001
$None$ |  $None$ | 18.266 | 0.001 | 15.986 | 0.001 | 15.967 | 0.001 | 15.882 | 0.001
$None$ |  $None$ | 18.387 | 0.001 | 16.209 | 0.002 | 16.075 | 0.001 | 16.024 | 0.001
$None$ |  $None$ | 18.952 | 0.001 | 16.585 | 0.001 | 16.452 | 0.001 | 16.414 | 0.001
$None$ |  $None$ | 18.877 | 0.001 | 16.491 | 0.001 | 16.351 | 0.001 | 16.613 | 0.001
$None$ |  $None$ | 19.842 | 0.002 | 17.473 | 0.002 | 17.312 | 0.001 | 17.164 | 0.001
$None$ |  $None$ | 20.055 | 0.002 | 17.779 | 0.002 | 17.424 | 0.001 | 17.179 | 0.001
$None$ |  $None$ | 19.135 | 0.001 | 16.728 | 0.002 | 16.615 | 0.002 | 16.525 | 0.002
$None$ |  $None$ | 21.907 | 0.005 | 18.837 | 0.007 | 18.606 | 0.005 | 18.353 | 0.004
Table 6:  Euclid objects of interest in the $\sigma$ Orionis region. Code | RA (J2000) |  Dec (J2000) | $I_{\scriptscriptstyle\rm E}$ |  $\sigma$($I_{\scriptscriptstyle\rm E}$) | $Y_{\scriptscriptstyle\rm E}$ |  $\sigma$($Y_{\scriptscriptstyle\rm E}$) | $J_{\scriptscriptstyle\rm E}$ |  $\sigma$($J_{\scriptscriptstyle\rm E}$) | $H_{\scriptscriptstyle\rm E}$ |  $\sigma$($H_{\scriptscriptstyle\rm E}$)
---|---|---|---|---|---|---|---|---|---|---
A | $None$ |  $None$ | 19.084 | 0.001 | 17.184 | 0.002 | 16.898 | 0.001 | 16.699 | 0.001
B | $None$ |  $None$ | 21.692 | 0.007 | 18.724 | 0.006 | 18.523 | 0.004 | 18.361 | 0.004
C | $None$ |  $None$ | 23.362 | 0.019 | 20.536 | 0.014 | 20.091 | 0.007 | 19.901 | 0.007
D | $None$ |  $None$ | 23.779 | 0.025 | 20.545 | 0.011 | 20.211 | 0.007 | 19.840 | 0.005
E | $None$ |  $None$ | 25.081 | 0.110 | 21.951 | 0.067 | 21.499 | 0.037 | 21.264 | 0.030
F | $None$ |  $None$ | 26.444 | 0.194 | 22.897 | 0.095 | 22.670 | 0.061 | 22.286 | 0.042
G | $None$ |  $None$ | 26.536 | 0.221 | 23.098 | 0.134 | 22.469 | 0.062 | 22.243 | 0.051

Further examination of the cluster sequence, its degree of agreement with the
ATMO isochrone and the location of new candidate members was made in the
colour-colour diagram shown in Fig. 6. The coolest benchmarks define a well
separated locus away from the cloud of contaminating sources. The behaviour of
the benchmarks is qualitatively fairly well reproduced by the isochrone,
although quantitatively the fit could be improved because the isochrone does
not reach as large $Y_{\scriptscriptstyle\rm E}-H_{\scriptscriptstyle\rm E}$
colour as observed. The blueing of the isochrone in the
$Y_{\scriptscriptstyle\rm E}-H_{\scriptscriptstyle\rm E}$ colour beyond
$I_{\scriptscriptstyle\rm E}-Y_{\scriptscriptstyle\rm E}\geq$3.5 is an effect
of the appearance of methane in the transition from L to T-type spectra. The
new sources with codes D, E, and G fall within the L-type benchmark locus,
making them strong FFP candidates. Source F is slightly bluer in
$Y_{\scriptscriptstyle\rm E}-H_{\scriptscriptstyle\rm E}$ than the faintest
benchmark, and is also closer to the isochrone, suggesting that it might be
the first L/T transition FFP identified in the $\sigma$ Orionis cluster.
Confirmation of these tentative assessments requires spectroscopy.

To check the effects of reddening in the selection of substellar candidates,
the same cuts that were applied to the $\sigma$ Orionis region were also
applied to the Horsehead regions. The CMD and colour-colour diagrams are shown
in Figs. 7 and 8, respectively. The separation between the cluster sequence
defined by the benchmarks and the cloud of sources is no longer well defined
in the CMD and the locus of benchmarks in the colour-colour diagram is not
well isolated. This example shows the difficulties of selecting substellar
candidates in regions with high interstellar reddening. Future work will
address this issue.

To check for the presence of binaries, we show in Fig. 9 the FWHM values (in
pixels) versus aperture magnitudes measured in the VIS images for all the
objects under study (benchmarks, confirmed candidates in the cluster sequence,
and new discoveries). Besides the two binary candidates among the benchmarks,
there is one more candidate among the confirmed objects and one more among the
new ones found with Euclid. The object labelled as G could be the first
$\sigma$ Orionis counterpart to the Jupiter-mass binary candidates reported in
the Trapezium cluster (McCaughrean & Pearson 2023), but needs confirmation
with higher spatial resolution images that could be provided by HST optical
imaging observations.

Figure 9: FWHM (in pixels) versus $I_{\scriptscriptstyle\rm E}$ apparent
magnitude (aperture photometry) for objects confirmed by Euclid to be in the
$\sigma$ Orionis cluster sequence. Both the FWHM and $I_{\scriptscriptstyle\rm
E}$ photometry values come from the ERO catalogue and were measured in the
Euclid VIS images. Four objects were found to have FWHM values larger than the
mean value of cluster members (more than 3$\,\sigma$ significance) and hence
are considered as possible binaries that deserve further scrutiny. Two of them
are benchmark objects, namely (S Ori 52 and S Ori 60), one is a known object
(S Ori 38), and the faintest one is a new discovery (Euclid object of interest
G).

##  5 The Euclid substellar IMF of the $\sigma$ Orionis cluster

The results reported in this work are useful to revise the very low-mass IMF
of the $\sigma$ Orionis cluster and try to extend it deeper into the
planetary-mass regime. The Gaia sample covers the domain of very low-mass
stars and Euclid provides a continuation into the substellar-mass regime,
reaching down to about $4\,M_{\rm J}$.

The mass-luminosity relationship from the 3-Myr ATMO CEQ models has been used
for the substellar domain. The PAdova and TRieste Stellar Evolution Code
(PARSEC) models (Bressan et al. 2012; Pastorelli et al. 2020) were used for
the stellar domain. The IMF of the $\sigma$ Orionis cluster using the Gaia-DR3
membership study by Žerjal et al. (2024), combined with the results of this
work, is displayed in Fig. 10. Our results are consistent with a multi-power-
law distribution for the IMF.

Figure 10: Combined very low-mass Euclid-Gaia IMF of the $\sigma$ Orionis
cluster with linear fits in three different mass regions.

A comprehensive study of the IMF within a distance of 20 pc from the Sun has
reported a change in the slope in the substellar domain (Kirkpatrick et al.
2024). Those authors claimed that the Solar vicinity IMF can be expressed as
${\rm d}N/{\rm d}M=C\,M^{-\alpha}$ with four different values of the power-law
exponent for different mass intervals. In particular, in this work we are
concerned with the low-mass tail of the IMF where the slope estimated by
Kirkpatrick et al. (2024) steepens from a value of $\alpha=$ 0.25 in the mass
range $0.05\,M_{\odot}<M<0.22\,M_{\odot}$ to $\alpha=$ 0.60 in the mass range
$0.01\,M_{\odot}<M<0.05\,M_{\odot}$.

In this study, we identify three different mass regimes: the very low-mass
stellar domain from 0.15 to 0.1 M⊙ with $\alpha=$ 0.26$\pm$0.10; the brown
dwarf domain from 0.1 to 0.011 M⊙ with $\alpha=$ 0.18$\pm$0.01; and the
planetary-mass domain from 0.011 to 0.003 M⊙ with $\alpha=$ 0.12$\pm$0.02.
These values have been obtained with linear fits that are shown in Fig. 10. We
excluded from the fits the mass range between 0.1 M⊙ and 0.05 M⊙ because those
objects are too faint to be complete for Gaia and too bright for Euclid. Error
bars quoted for the IMF slopes were estimated by simulations of the effects
coming from age, distance and photometric uncertainties.

Our $\sigma$ Orionis IMF results are consistent with the field in the very
low-mass stellar regime and extend deeper into the substellar regime than the
field IMF. We do not confirm a steepening of the substellar IMF at the
planetary-mass end. These comparisons are affected by low number statistics.
The census of directly imaged FFPs should be increased significantly to
investigate the possibility of substellar IMF variations in different
environments that could be an indication of specific formation pathways in the
planetary-mass domain. These results demonstrate that Euclid can play a
significant role in the detailed study of the low-mass shape of the IMF and
particularly in shedding light on the formation mechanisms of FFPs. Detailed
theoretical models developed by different groups have indicated that the shape
of the IMF is a useful indicator of the dominant mode of star formation in a
given region (Adams & Fatuzzo 1996; Chabrier 2005; Thies et al. 2015), and
that a multi-power-law IMF could arise from the interplay between the mass-
dependence and the time-dependence of exponential growth in a distribution of
accreting protostars (Essex et al. 2020).

##  6 Final remarks: The impact of Euclid on the study of FFPs in star-forming
regions

This work is a showcase of the power of the Euclid mission to provide the area
and depth required to explore the very low-mass population, including FFPs of
nearby star-forming regions and very young open clusters. In particular, for
the well-known $\sigma$ Orionis cluster, we show that the sensitivity of the
Euclid images is capable of probing down to FFPs that could have masses as low
as $4\,M_{\rm J}$ according to theoretical models (for 3 Myr ages) and at a
distance of 400 pc. This potential could be compromised by severe
contamination from numerous background extragalactic sources if we do not use
stringent selection procedures. Using the Euclid data for seven benchmark
objects in $\sigma$ Orionis, we have developed a high-purity method to filter
out the contamination. This method is valid for regions of low reddening, but
it needs additional work to be generalised to regions with any reddening. We
note that the Euclid NISP spectra will likely play an important role in this
effort. Additionally multi-epoch observations with Euclid during the lifetime
of the mission, possibly filling gaps in the cosmological surveys, can enable
the study of proper motions and photometric variability that are useful probes
for the study of the low-mass population in star-forming regions.

This is the first of a series of papers that intend to explore several star-
forming regions using Euclid observations. The observations presented here
provide a glimpse of the power of Euclid to shed light on the long-standing
question of the putative low-mass cutoff of the IMF predicted long time ago by
the theory of opacity-limited fragmentation and collapse of molecular clouds.
Our IMF for the $\sigma$ Orionis open cluster extends previous studies to
lower planetary masses and suggests that there could be a difference in slope
in the substellar regime between this young open cluster and the field,
hinting at a possible sensitivity to environmental conditions. This study
demonstrates the great potential of Euclid to tackle the study of the
substellar IMF in nearby star-forming regions and very young open clusters.

###### Acknowledgements.

This work has made use of the Early Release Observations (ERO) data from the
Euclid mission of the European Space Agency (ESA), 2024. We thank I. Baraffe
and M. Phillips for making available a digitised version of their isochrones
in the Euclid passbands. E.L.M. and M.Ž. are supported by the European
Research Council Advanced grant SUBSTELLAR, project number 101054354. This
research has made use of the Spanish Virtual Observatory
(https://svo.cab.inta-csic.es) project funded by
MCIN/AEI/10.13039/501100011033/ through grant PID2020-112949GB-I00 at Centro
de Astrobiología (CSIC-INTA). DB and NH have been supported by
PID2019-107061GB-C61 by the same agency. P.M.B. is funded by Instituto
Nacional de Técnica Aeroespacial through grant PRE-OVE. P.C. acknowledges
financial support from the Spanish Virtual Observatory project (grant
PID2020-112949GB-I00). N.P.B. is funded by Vietnam National Foundation for
Science and Technology Development (NAFOSTED) under grant number
103.99-2020.63. NL and VJSB acknowledge financial support from the Agencia
Estatal de Investigación (AEI/10.13039/501100011033) of the Ministerio de
Ciencia e Innovación and the ERDF ‘A way of making Europe’ through project
PID2022-137241NB-C1. CdB acknowledges support from a Beatriz Galindo senior
fellowship (BG22/00166) from the Spanish Ministry of Science, Innovation and
Universities. The Euclid Consortium acknowledges the European Space Agency and
a number of agencies and institutes that have supported the development of
Euclid, in particular the Agenzia Spaziale Italiana, the Austrian
Forschungsförderungsgesellschaft funded through BMK, the Belgian Science
Policy, the Canadian Euclid Consortium, the Deutsches Zentrum für Luft- und
Raumfahrt, the DTU Space and the Niels Bohr Institute in Denmark, the French
Centre National d’Etudes Spatiales, the Fundação para a Ciência e a
Tecnologia, the Hungarian Academy of Sciences, the Ministerio de Ciencia,
Innovación y Universidades, the National Aeronautics and Space Administration,
the National Astronomical Observatory of Japan, the Netherlandse
Onderzoekschool Voor Astronomie, the Norwegian Space Agency, the Research
Council of Finland, the Romanian Space Agency, the State Secretariat for
Education, Research, and Innovation (SERI) at the Swiss Space Office (SSO),
and the United Kingdom Space Agency. A complete and detailed list is available
on the Euclid web site (http://www.euclid-ec.org).

## References

  * Adams & Fatuzzo (1996) Adams, F. C. & Fatuzzo, M. 1996, ApJ, 464, 256
  * Bally et al. (2018) Bally, J., Chambers, E., Guzman, V., et al. 2018, AJ, 155, 80
  * Barrado y Navascués et al. (2001) Barrado y Navascués, D., Zapatero Osorio, M. R., Béjar, V. J. S., et al. 2001, A&A, 377, L9
  * Bayo et al. (2011) Bayo, A., Barrado, D., Stauffer, J., et al. 2011, A&A, 536, A63
  * Béjar et al. (2001) Béjar, V. J. S., Martín, E. L., Zapatero Osorio, M. R., et al. 2001, ApJ, 556, 830
  * Bodenheimer (1966) Bodenheimer, P. 1966, ApJ, 144, 103
  * Bouy et al. (2013) Bouy, H., Bertin, E., Moraux, E., et al. 2013, A&A, 554, A101
  * Bouy et al. (2022) Bouy, H., Tamura, M., Barrado, D., et al. 2022, A&A, 664, A111
  * Bressan et al. (2012) Bressan, A., Marigo, P., Girardi, L., et al. 2012, MNRAS, 427, 127
  * Chabrier (2005) Chabrier, G. 2005, in Astrophysics and Space Science Library, Vol. 327, The Initial Mass Function 50 Years Later, ed. E. Corbelli, F. Palla, & H. Zinnecker, 41
  * Chabrier et al. (2000) Chabrier, G., Baraffe, I., Allard, F., & Hauschildt, P. 2000, ApJ, 542, L119
  * Chauvin et al. (2005) Chauvin, G., Lagrange, A. M., Dumas, C., et al. 2005, A&A, 438, L25
  * Chiang & Chen (2015) Chiang, P. & Chen, W. P. 2015, ApJ, 811, L16
  * Cuillandre et al. (2024) Cuillandre, J.-C., Bertin, E., Bolzonella, M., et al. 2024, A&A, this issue
  * Damian et al. (2023) Damian, B., Jose, J., Biller, B., et al. 2023, ApJ, 951, 139
  * Depoy et al. (1990) Depoy, D. L., Lada, E. A., Gatley, I., & Probst, R. 1990, ApJ, 356, L55
  * Esplin & Luhman (2017) Esplin, T. L. & Luhman, K. L. 2017, AJ, 154, 134
  * Esplin & Luhman (2019) Esplin, T. L. & Luhman, K. L. 2019, AJ, 158, 54
  * Essex et al. (2020) Essex, C., Basu, S., Prehl, J., & Hoffmann, K. H. 2020, MNRAS, 494, 1579
  * Euclid Collaboration: Cropper et al. (2024) Euclid Collaboration: Cropper, M., Al Bahlawan, A., Amiaux, J., et al. 2024, A&A, this issue
  * Euclid Collaboration: Jahnke et al. (2024) Euclid Collaboration: Jahnke, K., Gillard, W., Schirmer, M., et al. 2024, A&A, this issue
  * Euclid Collaboration: Mellier et al. (2024) Euclid Collaboration: Mellier, Y., Abdurro’uf, Acevedo Barroso, J., Achúcarro, A., et al. 2024, A&A, this issue
  * Euclid Collaboration: Scaramella et al. (2022) Euclid Collaboration: Scaramella, R., Amiaux, J., Mellier, Y., et al. 2022, A&A, 662, A112
  * Euclid Early Release Observations (2024) Euclid Early Release Observations. 2024, https://doi.org/10.57780/esa-qmocze3
  * Gaia Collaboration et al. (2023) Gaia Collaboration, Vallenari, A., Brown, A. G. A., et al. 2023, A&A, 674, A1
  * Gauza et al. (2015) Gauza, B., Béjar, V. J. S., Pérez-Garrido, A., et al. 2015, ApJ, 804, 96
  * Green (2018) Green, G. M. 2018, The Journal of Open Source Software, 3, 695
  * Green et al. (2019) Green, G. M., Schlafly, E., Zucker, C., Speagle, J. S., & Finkbeiner, D. 2019, ApJ, 887, 93
  * Hennebelle & Chabrier (2008) Hennebelle, P. & Chabrier, G. 2008, ApJ, 684, 395
  * Hunt et al. (2024) Hunt, L., Annibali, F., Cuillandre, J.-C., et al. 2024, A&A, this issue
  * Jun-Yan Zhang et al. (2024) Jun-Yan Zhang, J., Lodieu, N., & Martín, E. 2024, arXiv e-prints, arXiv:2403.15288
  * Kirkpatrick et al. (2024) Kirkpatrick, J. D., Marocco, F., Gelino, C. R., et al. 2024, ApJS, 271, 55
  * Kluge et al. (2024) Kluge, M., Hatch, N., Montes, M., et al. 2024, A&A, this issue
  * Koshimoto et al. (2023) Koshimoto, N., Sumi, T., Bennett, D. P., et al. 2023, AJ, 166, 107
  * Kounkel et al. (2017) Kounkel, M., Hartmann, L., Mateo, M., & Bailey, John I., I. 2017, ApJ, 844, 138
  * Kounkel et al. (2016) Kounkel, M., Megeath, S. T., Poteet, C. A., Fischer, W. J., & Hartmann, L. 2016, ApJ, 821, 52
  * Langeroodi & Hjorth (2023) Langeroodi, D. & Hjorth, J. 2023, ApJ, 957, L27
  * Laureijs et al. (2011) Laureijs, R., Amiaux, J., Arduini, S., et al. 2011, ESA/SRE(2011)12, arXiv:1110.3193
  * Lodieu et al. (2021) Lodieu, N., Hambly, N. C., & Cross, N. J. G. 2021, MNRAS, 503, 2265
  * Lodieu et al. (2018) Lodieu, N., Zapatero Osorio, M. R., Béjar, V. J. S., & Peña Ramírez, K. 2018, MNRAS, 473, 2020
  * Lodieu et al. (2009) Lodieu, N., Zapatero Osorio, M. R., Rebolo, R., Martín, E. L., & Hambly, N. C. 2009, A&A, 505, 1115
  * Lucas & Roche (2000) Lucas, P. W. & Roche, P. F. 2000, MNRAS, 314, 858
  * Lucas et al. (2001) Lucas, P. W., Roche, P. F., Allard, F., & Hauschildt, P. H. 2001, MNRAS, 326, 695
  * Lucas et al. (2006) Lucas, P. W., Weights, D. J., Roche, P. F., & Riddick, F. C. 2006, MNRAS, 373, L60
  * Luhman et al. (2004) Luhman, K. L., Peterson, D. E., & Megeath, S. T. 2004, ApJ, 617, 565
  * Marleau et al. (2024) Marleau, F., Cuillandre, J.-C., Cantiello, M., et al. 2024, A&A, this issue
  * Martín et al. (2003) Martín, E. L., Barrado y Navascués, D., Baraffe, I., Bouy, H., & Dahm, S. 2003, ApJ, 594, 525
  * Martin et al. (2023) Martin, E. L., Bouy, H., Martin, D., et al. 2023, Proc., 30th Rencontres du Vietnam: Windows on the Universe
  * Martín et al. (2022) Martín, E. L., Lodieu, N., & del Burgo, C. 2022, MNRAS, 510, 2841
  * Martín et al. (2001) Martín, E. L., Zapatero Osorio, M. R., Barrado y Navascués, D., Béjar, V. J. S., & Rebolo, R. 2001, ApJ, 558, L117
  * Martín et al. (2021) Martín, E. L., Zhang, J. Y., Esparza, P., et al. 2021, A&A, 655, L3
  * Massari et al. (2024) Massari, D., Dalessandro, E., Erkal, D., et al. 2024, A&A, this issue
  * McCaughrean & Pearson (2023) McCaughrean, M. J. & Pearson, S. G. 2023, arXiv e-prints, arXiv:2310.03552
  * McMahon et al. (2021) McMahon, R. G., Banerji, M., Gonzalez, E., et al. 2021, VizieR Online Data Catalog, II/367
  * Miret-Roig (2023) Miret-Roig, N. 2023, Ap&SS, 368, 17
  * Miret-Roig et al. (2022) Miret-Roig, N., Bouy, H., Raymond, S. N., et al. 2022, Nat. Astron., 6, 89
  * Mohr et al. (2012) Mohr, J. J., Armstrong, R., Bertin, E., et al. 2012, in SPIE Conf. Ser., Vol. 8451, Software and Cyberinfrastructure for Astronomy II, ed. N. M. Radziwill & G. Chiozzi, 84510D
  * Mondal & Chattopadhyay (2019) Mondal, A. & Chattopadhyay, T. 2019, New A, 66, 45
  * Mookerjea et al. (2009) Mookerjea, B., Sandell, G., Jarrett, T. H., & McMullin, J. P. 2009, A&A, 507, 1485
  * Mróz et al. (2018) Mróz, P., Ryu, Y. H., Skowron, J., et al. 2018, AJ, 155, 121
  * Oasa et al. (1999) Oasa, Y., Tamura, M., & Sugitani, K. 1999, ApJ, 526, 336
  * Olivares et al. (2021) Olivares, J., Bouy, H., Sarro, L. M., et al. 2021, A&A, 649, A159
  * Padoan & Nordlund (2004) Padoan, P. & Nordlund, Å. 2004, ApJ, 617, 559
  * Pastorelli et al. (2020) Pastorelli, G., Marigo, P., Girardi, L., et al. 2020, MNRAS, 498, 3283
  * Peña Ramírez et al. (2012) Peña Ramírez, K., Béjar, V. J. S., Zapatero Osorio, M. R., Petr-Gotzens, M. G., & Martín, E. L. 2012, ApJ, 754, 30
  * Phillips et al. (2020) Phillips, M. W., Tremblin, P., Baraffe, I., et al. 2020, A&A, 637, A38
  * Planck Collaboration (2016) Planck Collaboration. 2016, A&A, 596, A109
  * Saifollahi et al. (2024) Saifollahi, T., Voggel, K., Lançon, A., et al. 2024, A&A, this issue
  * Salpeter (1955) Salpeter, E. E. 1955, ApJ, 121, 161
  * Scholz et al. (2023) Scholz, A., Muzic, K., Jayawardhana, R., Almendros-Abad, V., & Wilson, I. 2023, AJ, 165, 196
  * Silk (1977) Silk, J. 1977, ApJ, 214, 152
  * Solano et al. (2021) Solano, E., Gálvez-Ortiz, M. C., Martín, E. L., et al. 2021, MNRAS, 501, 281
  * Spezzi et al. (2015) Spezzi, L., Petr-Gotzens, M. G., Alcalá, J. M., et al. 2015, A&A, 581, A140
  * Stahler (1988) Stahler, S. W. 1988, ApJ, 332, 804
  * Sumi et al. (2023) Sumi, T., Koshimoto, N., Bennett, D. P., et al. 2023, AJ, 166, 108
  * Thies et al. (2015) Thies, I., Pflamm-Altenburg, J., Kroupa, P., & Marks, M. 2015, ApJ, 800, 72
  * Žerjal et al. (2024) Žerjal, M., Martín, E. L., & Pérez Garrido, A. 2024, A&A, in press
  * Walter et al. (2008) Walter, F. M., Sherry, W. H., Wolk, S. J., & Adams, N. R. 2008, in Handbook of Star Forming Regions, Volume I, ed. B. Reipurth, Vol. 4 (ASP Conf. Ser.), 732
  * Weaver et al. (2024) Weaver, J., Taamoli, S., McPartland, C., et al. 2024, A&A, this issue
  * Zapatero Osorio et al. (2000) Zapatero Osorio, M. R., Béjar, V. J. S., Martín, E. L., et al. 2000, Science, 290, 103
  * Zapatero Osorio et al. (2002) Zapatero Osorio, M. R., Béjar, V. J. S., Pavlenko, Y., et al. 2002, A&A, 384, 937
  * Zapatero Osorio et al. (2017) Zapatero Osorio, M. R., Béjar, V. J. S., & Peña Ramírez, K. 2017, ApJ, 842, 65
  * Zhang et al. (2021) Zhang, Z., Liu, M. C., Best, W. M. J., Dupuy, T. J., & Siverd, R. J. 2021, ApJ, 911, 7


[$\ast$]Corresponding and lead author;
Email address<EMAIL_ADDRESS>
Word count: 4589;
Funding information: Medical Research Council [grant number MR/N013166/1];
Commercial relationships: Jamie Burke, None; Dan Pugh, None; Tariq Farrah,
None; Charlene Hamid, None; Emily Godden, None; Tom MacGillivray, None; Neeraj
Dhaun, None; J. Kenneth Baillie, None; Stuart King, None; Ian J.C. MacCormick,
None.

# Evaluation of an automated choroid segmentation algorithm in a longitudinal
kidney donor and recipient cohort

Jamie Burke  School of Mathematics, College of Science and Engineering,
University of Edinburgh, Edinburgh, UK  Dan Pugh  British Heart Foundation
Centre for Cardiovascular Science, University of Edinburgh, Edinburgh, UK
Tariq Farrah  British Heart Foundation Centre for Cardiovascular Science,
University of Edinburgh, Edinburgh, UK  Charlene Hamid  Imaging Facility,
University of Edinburgh, The Queen’s Medical Research Institute, Edinburgh, UK
Emily Godden  Emergency Department, Royal Infirmary of Edinburgh, Edinburgh,
UK  Tom MacGillivray  Centre for Clinical Brain Sciences, University of
Edinburgh, Edinburgh, UK  Neeraj Dhaun  British Heart Foundation Centre for
Cardiovascular Science, University of Edinburgh, Edinburgh, UK  J. Kenneth
Baillie  Deanery of Clinical Sciences, College of Medicine and Veterinary
Medicine, University of Edinburgh, Edinburgh, UK  Stuart King  School of
Mathematics, College of Science and Engineering, University of Edinburgh,
Edinburgh, UK  Ian J.C. MacCormick  Centre for Inflammation Research, The
Queen’s Medical Research Institute, University of Edinburgh, Edinburgh, UK
Institute for Adaptive and Neural Computation, School of Informatics,
University of Edinburgh, Edinburgh, UK

###### Abstract

Purpose To evaluate the performance of an automated choroid segmentation
algorithm in optical coherence tomography (OCT) data using a longitudinal
kidney donor and recipient cohort.

Methods We assessed 22 donors and 23 patients requiring renal transplantation
over up to 1 year post-transplant. We measured choroidal thickness (CT) and
area and compared our automated CT measurements to manual ones at the same
locations. We estimated associations between choroidal measurements and
markers of renal function (estimated glomerular filtration rate (eGFR), serum
creatinine and urea) using correlation and linear mixed-effects (LME)
modelling.

Results There was good agreement between manual and automated CT. Automated
measures were more precise because of smaller measurement error over time.
External adjudication of major discrepancies were in favour of automated
measures. Significant differences were observed in the choroid pre- and post-
transplant in both cohorts, and LME modelling revealed significant linear
associations observed between choroidal measures and renal function in
recipients. Significant associations were mostly stronger with automated CT
(eGFR P<0.001, creatinine P=0.004, urea P=0.04) compared to manual CT (eGFR
P=0.002, creatinine P=0.01, urea P=0.03).

Conclusions Our automated approach has greater precision than human-performed
manual measurements, which may explain stronger associations with renal
function compared to manual measurements. To improve detection of meaningful
associations with clinical endpoints in longitudinal studies of OCT, reducing
measurement error should be a priority, and automated measurements help
achieve this.

Translational relevance We introduce a novel choroid segmentation algorithm
which can replace manual grading for studying the choroid in renal disease,
and other clinical conditions.

##  1 Introduction

Chronic kidney disease (CKD) is a major cause of morbidity and mortality,
affecting over 800 million people worldwide 1. CKD is a gradual loss of kidney
function, resulting in a failure to filter blood effectively and is associated
with alterations in microvascular structure and function 2. Assessment of
microvascular function is therefore helpful in the diagnosis, prognosis and
treatment of renal disease. Current clinical evaluation is based on blood and
urine testing and invasive kidney biopsy.

The eye and the kidney show a striking resemblance in anatomy, physiology and
response to disease 3, and in particular the choroidal microcirculation
reflects the renal microcirculation 4. For example, they have an analogous
vascular endothelium with similarly sized fenestrated vessel walls allowing
subretinal fluid exchange in the choroid and blood filtration in the kidneys.
Moreover, the circulatory systems in the choroid and renal cortex have similar
proportions of blood flow in contrast to their retinal and renal medullary
counterparts 5.

Choroidal thickness (CT) correlates strongly with renal dysfunction in
patients with CKD compared with sex- and age-matched healthy and hypertensive
individuals 6. This suggests that choroidal thinning may relate to systemic
microvascular injury in general and renal injury in particular. An overactive
sympathetic drive may contribute to disease progression in CKD 7, and could
explain choroidal thinning since choroidal perfusion is influenced by its
autonomic supply 6. These observations suggest the potential clinical utility
of choroidal biomarkers in renal disease. There is already a growing interest
in choroidal biomarkers derived from optical coherence tomography (OCT) in
non-ocular pathology such as sepsis 8; 9, diabetes and CKD 6; 10; 11, and
neurodegenerative disease 12; 13; 14.

chorioretinal structures with micro-meter resolution. Standard OCT imaging
focuses on imaging the retina while enhanced depth imaging OCT (EDI-OCT)
provides a deeper and stronger signal, visualising the choroid-scleral (C-S)
junction with micron resolution. Measuring the choroid manually from OCT
images is a time consuming and subjective process. Automated image analysis to
extract choroidal measures as potential biomarkers could have substantial
clinical utility if it is sufficiently reliable, robust, and reproducible.
Consequently, there have been many attempts to validate automated algorithms
for quantifying the choroid 15; 16; 17; 18. However, only a handful of these
proposed algorithms demonstrate their clinical utility in disease settings 19;
20. To the best of our knowledge, such automated algorithms have rarely been
applied to longitudinal image sets. This is important as accurate assessment
of change over time is essential for tracking disease progression.

We have previously developed an automated approach to choroid region
segmentation 21 and here we present our evaluation of its performance and
clinical utility in a longitudinal cohort of individuals with end-stage CKD
who underwent renal transplant and healthy donors who underwent unilateral
nephrectomy. Our primary objective was to compare our automated CT
measurements with the current gold standard of manual measurement of CT, as
quantitative validation across longitudinal data is an ideal approach to
evaluate novel image processing methodologies in the medical domain.

As a secondary objective, we validate our segmentation algorithm clinically
through estimating associations between the choroid and clinical biomarkers of
renal function in both cohorts. In order to limit processing time, the choroid
is typically measured manually using only thickness. Our approach permits
automatic segmentation and subsequent calculation of choroidal thickness and
area (CA), so we provide two metrics of the choroid to estimate associations
with.

##  2 Methods

###  2.1 Study Population

We prospectively analysed a longitudinal cohort of healthy kidney donors and
patients with end-stage kidney disease undergoing living donor kidney
transplantation (NCT0213274) 22. Data collection and subsequent analyses were
conducted after ethical approval from the South East Scotland Research Ethics
Committee, in accordance with the principles of the Declaration of Helsinki
and all participants gave informed consent to recruitment. Eligibility
criteria for recruitment were (1) donors must be living and healthy throughout
the period of analysis, (2) recipients with end-stage CKD have a functional
kidney transplant and (3) must be aged 18 or over. To prevent ocular issues
confounding our results, our exclusion criteria were (1) any ocular pathology
pre-transplant, (2) any previous eye surgery, (3) a refractive error exceeding
±6 dioptres or (4) a diagnosis of diabetes mellitus. We judged image quality
by the OSCAR-IB criteria 23 and excluded images with B-scan signal quality
$\leq$ 15, indistinguishable C-S junction due to speckle noise, or partial
image cropping of choroid.

Supplementary figure S1 shows a flowchart on how the population was selected
for this study. At the time of data extraction, 22 donors and 23 recipients
were eligible for analysis, after excluding a total of 75 recipients and 5
donors. The majority of exclusions were because there were no eye scans
performed for these individuals. This was because, once recruited, they were
scheduled for transplantation and then immediately returned to their referring
institution after transplant away from Edinburgh, thus making it impractical
to retain in the study and re-scan. Each participant was assessed on the day
of transplant and then attempts were made at 7 other time periods over the
following year (8 time points in total).

Donors and recipients were organised into two datasets for performance
evaluation and clinical evaluation. We used the entire analysis cohort for
performance evaluation of the automated approach against manual grading,
resulting in 483 CT measurements for comparison. After excluding 2 donors and
7 recipients due to missing clinical measurements/eye scans post-transplant,
or poor quality EDI-OCT images, we used 20 donors and 16 recipients for
clinical evaluation, i.e. association estimation with clinical variables
related to renal function. Clinical data at each time point included standard
biomarkers of renal function, including high sensitivity C-reactive protein
(hsCRP), serum urea and creatinine, estimated glomerular filtration rate
(eGFR) and urine protein to creatinine ratio. Table 1 shows the population
statistics for the entire analysis cohort.

|  Baseline |  1 Week |  2 Weeks |  4 Weeks |  8 Weeks |  18 Weeks |  28 Weeks |  52 Weeks
---|---|---|---|---|---|---|---|---
Demographic |  |  |  |  |  |  |  |
Donors |  |  |  |  |  |  |  |
Sample, n (%) |  22 (100) |  11 (50) |  2 (9) |  8 (36) |  10 (45) |  8 (36) |  10 (45) |  11 (50)
Age, years |  50 ± 11 |  - |  - |  - |  - |  - |  - |  -
Male sex, n (%) |  9 (41) |  - |  - |  - |  - |  - |  - |  -
Approx. Refractive error (D) |  0.49 ± 1.17 |  - |  - |  - |  - |  - |  - |  -
Daytime (Hr:Min) |  13:50 ± 1:41 |  13:48 ± 1:20 |  12:04 ± 1:34 |  12:48 ± 3:47 |  13:43 ± 2:12 |  13:54 ± 2:00 |  13:30 ± 2:03 |  13:48 ± 2:07
Time from baseline (weeks) |  - |  1 ± 0 |  2 ± 0 |  4 ± 1 |  8 ± 2 |  16 ± 4 |  29 ± 3 |  53 ± 6
Recipients |  |  |  |  |  |  |  |
Sample, n (%) |  23 (100) |  13 (61) |  5 (48) |  5 (48) |  10 (43) |  6 (26) |  8 (35) |  8 (35)
Age, years |  47 ± 12 |  - |  - |  - |  - |  - |  - |  -
Male sex, n (%) |  15 (65) |  - |  - |  - |  - |  - |  - |  -
Approx. Refractive error (D) |  -0.33 ± 1.73 |  - |  - |  - |  - |  - |  - |  -
Daytime (Hr:Min) |  13:59 ± 2:19 |  12:44 ± 1:42 |  11:45 ± 1:50 |  12:23 ± 2:01 |  11:31 ± 1:13 |  12:29 ± 1:55 |  11:47 ± 1:39 |  12:25 ± 1:31
Time from baseline (weeks) |  - |  1 ± 0 |  2 ± 0 |  4 ± 1 |  8 ± 2 |  17 ± 4 |  29 ± 4 |  52 ± 4
Clinical |  |  |  |  |  |  |  |
Donors |  |  |  |  |  |  |  |
BMI, kg/m2 (%) |  27 ± 3 (95) |  - |  - |  - |  - |  - |  - |  -
Systolic BP, mmHg (%) |  134 ± 14 (86) |  - |  - |  - |  - |  - |  - |  -
Diastolic BP, mmHg (%) |  86 ± 18 (86) |  - |  - |  - |  - |  - |  - |  -
MAP (%) |  102 ± 15 (86) |  - |  - |  - |  - |  - |  - |  -
hsCRP, mg/l (%) |  1 ± 2 (59) |  52 ± 30 (73) |  2 ± 1 (100) |  23 ± 34 (63) |  1 ± 1 (70) |  5 ± 9 (75) |  1 ± 1 (80) |  2 ± 4 (55)
Serum urea, mmol/l (%) |  5 ± 1 (95) |  6 ± 3 (91) |  6 ± 1 (100) |  6 ± 1 (88) |  6 ± 1 (100) |  7 ± 2 (75) |  6 ± 1 (90) |  6 ± 1 (64)
Creatinine, $\mu$mol/l (%) |  69 ± 8 (95) |  108 ± 25 (91) |  102 ± 3 (100) |  89 ± 7 (88) |  102 ± 24 (100) |  101 ± 25 (75) |  100 ± 22 (90) |  91 ± 9 (64)
eGFR, ml/min/1.73m2 (%) |  97 ± 11 (95) |  61 ± 10 (91) |  64 ± 9 (100) |  71 ± 10 (88) |  68 ± 18 (100) |  67 ± 14 (75) |  66 ± 12 (90) |  67 ± 9 (64)
Urine P:Cr, mg/mmol (%) |  3 ± 5 (41) |  185 ± 303 (55) |  1 ± 0 (50) |  3 ± 3 (38) |  1 ± 2 (60) |  1 ± 2 (63) |  1 ± 1 (60) |  1 ± 1 (27)
Recipients |  |  |  |  |  |  |  |
BMI, kg/m2 (%) |  27 ± 4 (87) |  - |  - |  - |  - |  - |  - |  -
Systolic BP, mmHg (%) |  137 ± 14 (83) |  - |  - |  - |  - |  - |  - |  -
Diastolic BP, mmHg (%) |  82 ± 8 (83) |  - |  - |  - |  - |  - |  - |  -
MAP (%) |  101 ± 9 (83) |  - |  - |  - |  - |  - |  - |  -
hsCRP, mg/l (%) |  3 ± 3 (48) |  17 ± 20 (38) |  3 ± 3 (40) |  7 ± 10 (100) |  3 ± 2 (30) |  2 ± 2 (50) |  1 ± 1 (38) |  25 ± 52 (75)
Serum urea, mmol/l (%) |  17 ± 8 (87) |  7 ± 2 (77) |  7 ± 2 (100) |  6 ± 1 (100) |  7 ± 2 (90) |  7 ± 2 (83) |  8 ± 2 (88) |  6 ± 1 (88)
Creatinine, $\mu$mol/l (%) |  581 ± 271 (87) |  117 ± 35 (77) |  92 ± 24 (100) |  104 ± 25 (100) |  116 ± 27 (90) |  110 ± 32 (100) |  115 ± 40 (88) |  109 ± 27 (88)
eGFR, ml/min/1.73m2 (%) |  19 ± 28 (87) |  61 ± 15 (77) |  79 ± 16 (100) |  71 ± 14 (100) |  67 ± 20 (90) |  70 ± 21 (100) |  64 ± 23 (88) |  69 ± 13 (88)
Urine P:Cr, mg/mmol (%) |  295 ± 360 (48) |  257 ± 28 (23) |  84 ± 72 (40) |  89 ± 57 (60) |  93 ± 126 (50) |  27 ± 14 (100) |  34 ± 20 (63) |  9 ± 13 (38)
Table 1: Population statistics for all donors and recipients, rounded to the
nearest integer. Where appropriate, values are shown as mean ± SD, and values
in parentheses represent proportion of data completeness relative to baseline
populations. SD, standard deviation; D, dioptres; Hr:min, hour:minutes; BMI,
body mass index; BP, blood pressure; MAP, mean arterial pressure, hsCRP, high
sensitivity C-reactive protein; eGFR, estimated glomerular filtration rate;
Urine P:Cr, urine protein to creatinine ratio.

###  2.2 Image Acquisition

We imaged each participant’s right eye using the Heidelberg spectral domain
OCT Spectralis Standard Module. Patients were examined between 9am and 5pm and
were endeavoured to be followed up at around the same time of day at each time
point. The average (and standard deviation) daytime which scans were taken at
each time point are listed in table 1. During each patient’s examination, a
horizontal line, EDI-OCT B-scan centred at the foveal pit was taken. Each
B-scan covered a $30^{\circ}$ (8.7mm) region and was extracted as a $768\times
768$ (pixel height$\times$width) high-resolution image for downstream image
processing.

Each scan was captured using active eye tracking with Automatic Real Time
(ART) software, averaging up to a maximum of 100 scans to generate a single
high-resolution image. EDI-OCT images include the B-scan, alongside an en face
view of the fundus with a horizontal line representing the B-scan’s location
on the macula. Although refractive error and axial length were not collected
for this population, the built-in scan focus parameter (an approximate value
for refractive error) was extracted from the acquisition metadata for each
scan and was used for downstream clinical evaluation, and is listed in table
1. Figure 1 shows an example EDI-OCT scan with results from manual and
automated assessment. At each time point, only one EDI-OCT B-scan of each
individual’s right eye was selected for analysis, and no repeated scans were
taken during the same examination.

###  2.3 Manual Measurement of Choroidal Thickness

Manual grading for measuring CT was performed by a single, trained operator
across all image sessions for each participant. Manual grading of the choroid
is described in the original study carried out by Balmforth, et al. 6 Briefly,
this was achieved using the calliper tool in HeyEx software (version 1.10.4.0,
Heidelberg Engineering, Heidelberg, Germany). Choroid thickness was measured
at 3 locations across the macula — at the fovea and 2000 microns nasal and
temporal to the fovea. The choroid region in each B-scan was defined as the
area between the lower surface of the junction between the hyperreflective
retinal pigment epithelium (RPE) layer and Bruch’s membrane complex (RPE-C
junction), and the upper surface of the junction between the choroid and
sclera (C-S junction).

Manual grading used the calliper tools on the software to mark the centre of
the fovea at the level of the photoreceptor outer segment and mark 2000
microns temporal and nasal to this point, along the RPE-C junction. Choroid
thickness was defined as the straight line distance between the RPE-C and C-S
junctions, measured locally perpendicular to the RPE-C junction. Figure 1
shows three CT measurements provided by the manual grader in green, including
the reference lines measuring approximately 2000 microns temporal and nasal to
the foveal pit along the RPE-C junction.

###  2.4 Automated Assessment of Choroidal Thickness

Our automated choroid segmentation algorithm performed individual edge tracing
to obtain the upper and lower choroid boundaries for each B-scan. The
algorithm modelled each boundary using Gaussian process regression, building a
posterior predictive function through a recursive Bayesian scheme and image
gradient scoring mechanism to detect edge pixels 21. Figure 2 presents a
schematic diagram of the image analysis pipeline of the automated approach.
Preprocessing was done using median filter denoising and contrast enhancement
using contrast limited adaptive histogram equalisation. Approximate edge maps
were then computed using discrete derivative and morphological erosion and
dilation filters.

Automated CT was measured in two different ways, yielding perpendicular CT
measurements and parallel CT measurements. Perpendicular automated CT measured
locally perpendicular to the RPE-C junction, while parallel automated CT
measured parallel to the manual measurements to mimic any potential angular
error made by the manual grader. See for example the nasal measurement in
figure 4(c), where perpendicular automated CT is shown in red, parallel
automated CT in blue, and manual CT in green. We measured CT in the same
subfoveal, temporal and nasal locations as manual grading. We measured CA by
computing the area of pixels within a 3000 micron radius centred at the foveal
pit, in accordance with the Early Treatment Diabetic Retinopathy Study area of
$6000\times 6000$ microns 24.

Figure 1: EDI-OCT scan of a donor’s right eye at baseline. (a) En face view of
the fundus with the location of the B-scan in green and markers for measuring
CT and CA in red. (b) B-scan showing chorioretinal structures with manual and
automated assessment shown. Figure 2: Schematic diagram of the automated
approach segmenting the C-S junction of the choroid on an EDI-OCT B-scan 21.
GP, Gaussian process; GPR, Gaussian process regressor; KDE, kernel density
estimate.

###  2.5 Statistical Analysis

####  2.5.1 Performance evaluation

We measured agreement between approaches by comparing (parallel) automated CT
to manual CT and performed Passing-Bablok analysis 25 to determine any
systematic or proportional differences between the two approaches. We also
investigated residuals, calculated by subtracting manual CT from automated CT
(automated - manual), using a Bland-Altman plot 26. Mean absolute error (MAE),
Pearson and intra-class correlations were also computed between both
approaches, stratified by cohort and macular location. To compare the
consistency of measurements across longitudinal data, we investigated the
angular deviation made by the manual grader. This was done by computing angles
between the calliper measurements made from manual grading against the
perpendicular automated CT measurements. Automated assessment of the choroid
and quantitative analyses comparing manual and automated measurements were
done in Python (version 3.11.3).

Rahman 27 found an unsigned residual of $32\mu$m as a threshold suggested to
exceed inter-observer variability between graders of EDI-OCT images.
Therefore, we defined major discrepancies between automated and manual CT to
be any residual greater than $32\mu$m in absolute value. These were selected
for external adjudication by a clinical ophthalmologist I.M. For each
discrepancy, I.M. was shown two CT measurements displayed on the corresponding
choroid, and was blinded to which approach was used in each case. He was asked
to rate each measurement, and the overall visibility of the C-S junction,
using an ordinal scale: “bad”, “okay” and “good”. I.M. was also asked to
select the approach which was preferred — options for both or neither
approaches were also available.

####  2.5.2 Clinical evaluation

We investigated how CT and CA measurements changed over time in donors and
recipients, and estimated linear associations with clinical variables related
to renal function using Pearson correlations — specifically eGFR, serum
creatinine and serum urea. Other clinical measures were too incomplete and
inconsistently collected to be analysed with the current sample size. CT was
averaged across macular locations, resulting in a single value of thickness
for each scan. We examined the difference in CT and CA between measurements at
baseline and 1-year post-transplant, testing for difference in their means
longitudinally via the Student’s t-test for dependent, paired samples. We
specified a P-value of 0.05 as the threshold for statistical significance.

We also looked for significant linear associations between markers of renal
function and the choroid. We assumed a nested structure to the data and used
linear mixed-effects (LME) models, setting an individual random effect to
model the variation among individuals, accounting for age, sex, approximate
refractive error (measured in dioptres) and the time of day the scan was
taken, relative to when their baseline scan was taken (measured in decimal
hours). For each clinical measure of renal function, we fitted an LME model
for each choroidal image measure in turn as one of the associated independent
variables. LME modelling was carried out using R (version 4.2.2) 28. We
identify independent variables as statistically significant predictors if
their associated 95% confidence interval excludes 0.

Metric | All | Donors | Recipients
---|---|---|---
Temporal | Subfoveal | Nasal | Temporal | Subfoveal | Nasal
Residual CT ($\mu$m) | 1.8 ± 22.0 | 5.1 ± 18.4 | -5.9 ± 17.4 | 2.1 ± 18.8 | 2.9 ± 24.3 | 3.0 ± 28.1 | 3.8 ± 21.0
MAE CT ($\mu$m) | 14.1 ± 16.9 | 13.8 ± 13.2 | 13.4 ± 12.5 | 12.9 ± 13.8 | 13.5 ± 20.4 | 17.3 ± 22.3 | 13.8 ± 16.2
Pearson, $r_{p}$ | 0.97 | 0.96 | 0.98 | 0.97 | 0.92 | 0.94 | 0.96
ICC(3,1) | 0.96 | 0.95 | 0.97 | 0.96 | 0.92 | 0.94 | 0.96
Table 2: Performance evaluation between automated and manual CT, stratified by
cohort and macular location. Where appropriate, values are shown as mean ± SD.
All Pearson and intra-class correlations were statistically significant. SD,
standard deviation; MAE, mean absolute error; CT, choroid thickness; ICC,
intra-class correlation.

##  3 Results

###  3.1 Performance Evaluation with Choroidal Thickness

Performance results between automated and manual CT measurements are shown in
table 2. There was good agreement between manual and automated measures of CT,
with an average residual of 1.8 ± 22.0$\mu$m and MAE of 14.1 ± 16.9$\mu$m
across all 483 CT measurements. Moreover, Pearson and intra-class correlation
show excellent correlations between both approaches. The largest residuals
were at the subfoveal macular location.

Passing-Bablok analysis computed a slope value of 1.02 (95% confidence
interval of 0.99 to 1.04) and an intercept of -3.64$\mu$m (95% confidence
interval of -10.78$\mu$m to 3.50$\mu$m) with an $R^{2}$ value of 0.93 (figure
3(a)). These 95% confidence intervals include 1 and 0, respectively,
suggesting that the automated and manual approaches are equivalent 29; 25. See
supplementary figures S2 and S3 for correlation plots stratified by macular
location and cohort. Bland-Altman analysis on figure 3(b) computed an average
residual of 1.84$\mu$m with limits of agreement of -44.98$\mu$m to
41.30$\mu$m. Only 10.78% of all 483 CT measurements (52 / 483) exceeded an
unsigned residual of $32\mu$m 27.

Figure 3: (a) Correlation plot of manual and (parallel) automated CT measurements. (b) Bland-Altman plot showing residual values, with 52 major discrepancies highlighted as red crosses. C-S Junction Visibility | Score
---|---
Automated | Manual
Good ($N=9$) | 8 | 2
Okay ($N=15$) | 9 | 13
Bad ($N=28$) | 24 | 15
Total ($N=52)$ | 41 | 30
Method | Discrepancy Measurement
Automated | Good: 32, Okay: 19, Bad: 1
Manual | Good: 24, Okay: 18, Bad: 10
Table 3: (Top) Numerical score of both approaches from masked adjudication of
52 major discrepancies, stratified by the visibility of the C-S junction.
(Bottom) Qualitative preference scores for both approaches.

Table 3 presents the results from the external adjudication of all 52 major
discrepancies. Overall, the automated CT measurements scored higher in terms
of preference, where 79% (41/52) of the automated thicknesses were preferred
compared to 58% (30/52) for manual thicknesses. Moreover, the automated
approach scored higher in terms of quality, with only 1 measurement judged as
“bad”, versus 10 measurements judged “bad” for the manual approach. Figure 4
shows four major discrepancies from four different choroids. Figure figure
4(a) shows the largest observed discrepancies — temporal ($97\mu$m) and
subfoveal ($114\mu$m) — with adjudicator I.M. preferring the automated
measurements.

We found that deviation in the angle of manual measurement from perpendicular
led to a disproportionate error between perpendicular automated CT and manual
CT. This is illustrated in figure 5(a) which shows the distribution (mean 0.5
and standard deviation 2.5) of angular errors made from manual grading.
Absolute differences between manual CT and perpendicular automated CT grew
quadratically as the angular error deviated from 0. We also found large
deviation in manual grading when tracking the longitudinal, within-patient
angular difference from baseline (figure 5(b)). Distributions at each time
point were estimated through empirical mean and standard deviation values.
Note that the mean fluctuation in manual grading was always above 0 in
comparison to the mean fluctuation from the automated approach which was
constant at 0.

Figure 4: A selection of major discrepancies between automated and manual CT
measurements. Red lines represent perpendicular automated CT, blue represent
parallel automated CT and green represent manual CT. The lines in red are
shown in (a,c) to demonstrate the observed angular deviation between
perpendicular automated CT and manual CT. (a) Temporal and subfoveal major
discrepancies from a donor, residuals $97\mu$m and $114\mu$m, respectively.
Nasal angular deviation (5.4∘) resulted in perpendicular and parallel
residuals as $22\mu$m and $2\mu$m, respectively. (b) Subfoveal major
discrepancy from a recipient, residual $-47\mu$m. (c) Nasal angular deviation
(8.1∘) shows perpendicular and parallel residuals as $106\mu$m and $79\mu$m,
respectively. (d) Temporal and nasal major discrepancy from a donor, residuals
$66\mu$m and $65\mu$m, respectively. Figure 5: (a) Distribution of angular
errors from manual CT measurements (blue). Average unsigned difference between
manual and perpendicular automated CT (red). (b) Unsigned, longitudinal
within-patient angular deviations, relative to baseline measurements. Coloured
lines represent distinct individuals using manual measurements.

###  3.2 Choroidal Association with Renal Function

All measures of renal function and choroidal measurements were significantly
different 1-year post-transplant compared to baseline measurements in both
cohorts (table 4). Figure 6 shows the average percentage change in choroidal
measurements from baseline measurements in both cohorts. In transplant
recipients, there was a significant increase in choroidal thickness of 12.8 ±
4.8% (median: 11.4%) from baseline after 4 weeks post-transplant using
automated CT (P=0.02). After 1 year post-transplant, we observed a significant
increase of 14.1 ± 11.4% (median: 10.7%) from baseline (P=0.01).
Interestingly, we observed a significant increase of 5.1 ± 5.6% (median: 5.4%)
1 week post-transplant in the choroid of donors (P=0.01). The average choroid
remained inflated relative to baseline measurements and at some point between
4 and 8 weeks post-transplant the choroid deflated. After 1 year post-
transplant, we observed a significant decrease of -4.9 ± 7.9% (median: -3.5%)
in automated CT (P=0.01).

| Donors | Recipients
---|---|---
Measurement | Baseline | 1 year PT |  P-value | Baseline | 1 year PT |  P-value
Automated CA (mm2) | 1.59 $\pm$ 0.41 | 1.49 $\pm$ 0.41 | 0.01 | 1.58 $\pm$ 0.41 | 1.74 $\pm$ 0.46 | 0.01
Automated CT ($\mu$m) | 278 $\pm$ 69 | 259 $\pm$ 68 | 0.01 | 271 $\pm$ 70 | 301 $\pm$ 75 | 0.01
Manual CT ($\mu$m) | 278 $\pm$ 61 | 258 $\pm$ 62 | 0.006 | 262 $\pm$ 64 | 292 $\pm$ 66 | 0.008
eGFR (ml/min/1.73m2) | 91 $\pm$ 5 | 64 $\pm$ 7 | <0.001 | 8 $\pm$ 3 | 69 $\pm$ 14 | <0.001
Creatinine ($\mu$mol/l) | 69 $\pm$ 9 | 92 $\pm$ 10 | <0.001 | 659 $\pm$ 196 | 109 $\pm$ 29 | <0.001
Urea (mmol/l) | 5.0 $\pm$ 0.8 | 6.8 $\pm$ 1.3 | 0.002 | 18.5 $\pm$ 9.7 | 6.7 $\pm$ 1.7 | 0.005
Table 4: Choroidal measurements at baseline and one year post-transplant (PT).
P-values calculated using Student’s dependent t-test for related samples.
Figure 6: Longitudinal change in the choroid, measured relative to baseline
measurements. Donors are shown as dashed lines and recipients as solid lines,
with standard errors plotted at each time point.

In the recipient cohort, all choroidal measurements linearly correlated with
eGFR, serum creatinine and serum urea with statistical significance. All
Pearson correlation coefficients with renal function were stronger in
automated choroid measurements than in manual ones (table 5). There were poor
and insignificant linear correlations found between the choroid and renal
function in the donor cohort, as seen in supplementary table S1, which also
show the corresponding P-values for all correlation analyses performed.

| Pearson, $r_{p}$
---|---
Image Measure | eGFR | Creatinine | Urea
Automated CA | 0.72 | -0.77 | -0.73
Automated CT | 0.81 | -0.76 | -0.74
Manual CT | 0.69 | -0.76 | -0.72
Table 5: Pearson correlation coefficients between choroidal measurements and
eGFR, serum creatinine and serum urea in the recipient cohort. All
correlations presented here were significant such that P<0.05 apart from eGFR
using manual CT.

Using all choroidal measurements, in transplant recipients LME modelling
showed evidence of a statistically significant, positive linear association
with eGFR, and negative associations with serum creatinine and urea levels.
Table 6 shows the model summary’s for predicting eGFR, serum creatinine and
serum urea using each choroidal measurement in turn. Models using automated
measures had greater conditional $R^{2}$ values — a measure analogous to the
$R^{2}$ value for linear models but taking into account the random and fixed
effects variables — and their respective independent variables showed stronger
association to predicting renal function. Interestingly, the time difference
between follow-up and baseline image acquisition was a statistically
significant predictor of all markers of renal functions for models using all
choroidal metrics.

There were no statistically significant associations found between any
choroidal measurement and markers of renal function in the donor cohort.
However, sex was associated with predicting serum creatinine using automated
choroidal measurements, with weak statistical significance. These LME results
can be found in supplementary table S2.

Response variable $\rightarrow$ | eGFR | Creatinine | Urea
---|---|---|---
Independent variable $\downarrow$ | $\hat{\beta}$ | 95% CI |  $P$-value | $\hat{\beta}$ | 95% CI |  $P$-value | $\hat{\beta}$ | 95% CI |  $P$-value
Intercept | -0.10 | (-1.38, 1.17) | 0.84 | 0.09 | (-1.18, 1.36) | 0.86 | 0.03 | (-0.49, 0.55) | 0.90
Age | 0.98 | (-0.47, 2.43) | 0.15 | -1.11 | (-2.54, 0.31) | 0.10 | -0.30 | (-0.95, 0.34) | 0.29
Sex (Male) | -0.24 | (-1.55, 1.07) | 0.66 | 0.27 | (-1.03, 1.57) | 0.60 | 0.22 | (-0.31, 0.76) | 0.34
Daytime from Baseline | -0.40 | (-0.59, -0.21) | <0.001 | 0.59 | (0.39, 0.80) | <0.001 | 0.57 | (0.32, 0.81) | <0.001
Approx. Refraction | -0.86 | (-2.17, 0.46) | 0.114 | 0.92 | (-0.37, 2.21) | 0.12 | 0.31 | (-0.28, 0.89) | 0.24
Automated CA | 1.54 | (0.97, 2.10) | <0.001 | -1.52 | (-2.12, -0.92) | <0.001 | -0.60 | (-1.09, -0.11) | 0.02
Patient Std. Dev. | 1.63 | Cond. $R^{2}$: 0.93 | 0.60 | Cond. $R^{2}$: 0.91 | 0.55 | Cond. $R^{2}$: 0.57
Intercept | -0.10 | (-1.19, 0.99) | 0.83 | 0.07 | (-0.91, 1.05) | 0.84 | 0.03 | (-0.48, 0.53) | 0.90
Age | 0.74 | (-0.51, 1.99) | 0.20 | -0.80 | (-1.92, 0.31) | 0.12 | -0.27 | (-0.90, 0.36) | 0.33
Sex (Male) | -0.31 | (-1.43, 0.81) | 0.49 | 0.31 | (-0.69, 1.30) | 0.44 | 0.28 | (-0.25, 0.81) | 0.24
Daytime from Baseline | -0.46 | (-0.67, -0.24) | <0.001 | 0.65 | (0.42, 0.88) | <0.001 | 0.55 | (0.30, 0.80) | <0.001
Approx. Refraction | -0.43 | (-1.55, 0.68) | 0.37 | 0.46 | (-0.54, 1.46) | 0.27 | 0.18 | (-0.35, 0.71) | 0.42
Automated CT | 1.15 | (0.51, 1.78) | <0.001 | -1.01 | (-1.62, -0.40) | 0.004 | -0.54 | (-1.06, -0.02) | 0.04
Patient Std. Dev. | 1.37 | Cond. $R^{2}$: 0.88 | 1.05 | Cond. $R^{2}$: 0.81 | 0.50 | Cond. $R^{2}$: 0.52
Intercept | -0.10 | (-1.22, 1.02) | 0.83 | 0.07 | (-0.89, 1.03) | 0.84 | 0.03 | (-0.47, 0.52) | 0.90
Age | 0.70 | (-0.59, 1.98) | 0.23 | -0.72 | (-1.82, 0.38) | 0.14 | -0.27 | (-0.89, 0.35) | 0.33
Sex (Male) | -0.29 | (-1.44, 0.86) | 0.55 | 0.27 | (-0.71, 1.24) | 0.48 | 0.28 | (-0.24, 0.80) | 0.23
Daytime from Baseline | -0.47 | (-0.68, -0.25) | <0.001 | 0.66 | (0.43, 0.90) | <0.001 | 0.56 | (0.31, 0.80) | <0.001
Approx. Refraction | -0.41 | (-1.56, 0.74) | 0.41 | 0.41 | (-0.57, 1.39) | 0.29 | 0.18 | (-0.35, 0.70) | 0.42
Manual CT | 1.11 | (0.45, 1.76) | 0.002 | -0.89 | (-1.54, -0.24) | 0.01 | -0.56 | (-1.06, -0.05) | 0.03
Patient Std. Dev. | 1.39 | Cond. $R^{2}$: 0.87 | 0.99 | Cond. $R^{2}$: 0.79 | 0.49 | Cond. $R^{2}$: 0.52
Table 6: LME summary tables for predicting eGFR, serum creatinine and serum
urea in transplant recipients using each choroidal measurement. Results for
the donor cohort are shown in supplementary table S2, but were omitted due to
a lack of significant results with the choroid. $\hat{\beta}$ represent
standardised model coefficients, with their corresponding 95% confidence
intervals and associated P-values. Statistically significant variables are
shown in bold and underlined, as well as their corresponding P-values.

##  4 Discussion

We found that automated CT measurements agreed well with manual ones in
general, but have greater precision — especially when applied to a
longitudinal series of images. Much of the superior precision from automated
CT results from eliminating inconsistent measurement angle, since the
automated method is always able to measure CT locally perpendicular at the
exact same location across all time points for each patient — this is an
important attribute for measurement protocol so that we can account for
choroidal curvature, or if the choroid does not appear predominantly
horizontal in the image. In contrast, error in the angle of manual measurement
had a disproportionate impact.

The RPE-C junction is almost never parallel to the C-S junction, making it a
challenge for humans to measure perpendicular angles by eye across repeated
measures, which is a major source of error. Furthermore, the different axial
and lateral resolutions in each B-scan can result in the slightest change in
marking a lateral position during manual grading to misrepresent the true CT.
Figures 4(a,c) represent two exemplar cases, where the residuals between
manual CT and perpendicular/parallel automated CT measurements are very
different.

Importantly, the superior precision of the automated method translated into
stronger associations with renal function, at least in the recipient cohort
where statistical significance was observed. This illustrates the necessity
for reliable and reproducible measurements in longitudinal studies and their
subsequent impact on predicting clinical outcomes.

Much of the discrepancy between manual and automated CT arose from choroidal
features that are inherently difficult to measure. For example, the C-S
junctions of larger choroids (figure 4(a, c, d)) are prone to poor quality
image acquisition due to higher incidence of poor signal penetration. However,
the external adjudicator preferred the automated measurements over the manual
grader for these major discrepancies. Furthermore, the C-S junction may be
obscured in choroids whose posterior of Haller’s layer is low contrast (figure
4(b)) — here, the external adjudicator preferred the manual grader’s
measurement. The choroid in figure 4(a) represents a source of major
disagreement between the manual grader and the automated approach. The manual
grader has defined the C-S junction as the boundary below the most visible
posterior vessels (green), while the automated approach has successfully
identified vessels with much lower visibility further below the clearer
vessels (red), of which the external adjudicator agreed with.

The choroids in figure 4 represent just over half (51.9%) of all major
discrepancies lying outside the threshold suggested to exceed inter-observer
variability between graders of EDI-OCT images 27. That is, most outliers came
from the same four choroid at different time points. Moreover, of the 28
thickness measurements from choroids described as having poor visibility, 20
of them came from the larger choroids (figure 4(a, c, d)).

From both correlation analysis and LME modelling, automated choroidal
measurements were found to correspond with markers of renal function over time
better than manual CT, probably because of reduced measurement error. All
choroidal measurements changed substantially over time for all study
participants, as did eGFR, serum creatinine and serum urea. This is consistent
with the choroid reflecting renal function during treatment of CKD. The
choroid, and indeed CT/CA, does vary naturally during the day due to diurnal
variation. Tan et al. 30 describe the average change in CT across daytime
hours to be approximately 8.5 ± 5.2%. The change in automated CT in transplant
recipients 1 year post-transplant was 14.1 ± 11.4% (14.7 ± 11.2% for CA). This
suggests that choroidal inflation in transplant recipients cannot be explained
fully through diurnal variation, but potentially through improved renal
function 31. However, the same statement for healthy kidney donors cannot be
made as confidently, where we only observed an average decrease in CT of -4.9
± 7.9% (-5.3 ± 7.7% for CA).

Although, we must note that there are big fluid shifts which occur at the time
of transplantation, and we have not been able to account for any change in
body fluid volume post-transplant and what impact that may have had on the
choroid. However, these fluid shifts would only impact the choroid in the
short term, and our follow-up data is of sufficient time course to exclude any
potential long term effect from body fluid volume on the significant changes
we see in the choroid.

In each LME model, we accounted for age, sex, approximate refractive error,
and the intra-participant relative-to-baseline daytime each scan was taken
(relative daytime). The latter two measurements were used to assess the impact
of myopia and diurnal variation in both cohorts for predicting renal function
using the choroid. Relative daytime proved to be a significant predictor
variable for markers of renal function alongside all choroidal measurements,
while approximate refractive error did not. Note however that the standardised
model coefficients are almost always larger in absolute value for the
choroidal measurements versus relative daytime.

In every model there was an opposite effect of relative daytime compared with
the choroid, suggesting that the size of the choroid is negatively offset such
that the CT and CA in a follow-up scan taken later in the day (relative to the
baseline acquisition time) is decreased in absolute value — and vice versa for
follow-up scans taken earlier than the original baseline scan. This makes
sense given we know that the choroid decreases marginally through the course
of the day 30.

This suggests that while choroidal measurements still play a significant role
in predicting markers of renal function for transplant recipients, it is
important that daytime be recorded for downstream analysis, and image
acquisition try be performed around the same time of day so as not to diminish
any longitudinal signal present in the data. Note however that removing
relative daytime still resulted in the choroid as a statistically significant
predictor variable but the overall model fit was marginally worse (data not
shown).

It may be that the immediate inflation of the choroid in the first 4 weeks
after kidney donation in donors could be a result of a prompt systemic,
cardiovascular response to the unilateral nephrectomy. While from 8 weeks
post-transplant we observed choroidal thinning from all measurements,
consistent with previous literature 32, it is within the first month in a
donor’s recovery period that compensatory renal hypertrophy takes place 33;
34. These observations align with Choi and Kim 31, who cautiously suggest that
a decrease in subfoveal CT is associated with a decline in renal function but
its increase is associated with renal hypertrophy, albeit in patients with
diabetic retinopathy.

Low signal quality, vessel shadowing, lack of signal penetration and the
potential for extravascular fluid to obscure and occlude the boundary all
contribute to the challenging task of tracing the C-S junction in OCT images.
However, the automated segmentation methodology has the ability to overcome
many of these problems due its tunable hyperparameters and model uncertainty
quantification 21. For example, the Bayesian recursive scheme allows
uncertainty in obscured or occluded regions to be quantified and correctly
interpolated. This feature is advantageous for choroid region segmentation.
Moreover, the methodology provides an analytical, functional form for the edge
which is explainable, interpretable and reproducible — features which tend to
be absent from many deep learning algorithms in medical image segmentation 35.

There were a number of limitations in this study. Firstly, our two cohorts
were limited in sample size and not all participants or clinical variables
were collected at every time point. Moreover, of the 20 donors and 16
recipients included for clinical evaluation, only 11 donors and 8 recipients
were followed up 1 year post-transplant, which potentially introduced bias
into our clinical evaluation, and contributed to a reduction of statistical
power to which we could draw our conclusions with. Furthermore, using a sub-
cohort for clinical evaluation could potentially introduce selection bias when
estimating associations between the choroid and renal function. Therefore,
further studies with a larger and more complete dataset would permit a higher
confidence regarding the significance of our analyses. However, while the
results of the clinical evaluation may suffer from a lack of complete image or
clinical data, our primary objective of comparing manual CT against automated
CT remain undiluted by these limitations.

Another limitation is that the automated approach does require some, albeit
minimal form of manual intervention to select the edge endpoint pixels before
tracing each boundary of the choroid in a single B-scan. Another limitation is
the possibility of under-approximating the C-S junction for choroids such as
the one in figure 4(b). Finally, while we have provided an analysis on
regional quantities of the choroid and their potential links to microvascular
injury and renal function, further work would aim to quantify any
relationships with the vasculature within the choroid. This could be done for
example by computing the choroid vasculature index, which has recently become
a popular and more robust way to characterise the choroid for ocular and non-
ocular pathology 11; 36; 37; 38.

##  5 Conclusion

Our automated segmentation methodology can replace human measures for studying
the choroid in renal disease, and potentially other clinical conditions. We
observed no systematic or proportional differences when comparing manual CT to
automated CT measurements. While the automated approach agreed strongly with
manual ones, automated CT eliminated angular error and therefore had greater
precision when assessing within-patient longitudinal data. The error in manual
measurement ultimately led to a lack of strength and significance in their
clinical associations. High precision and reproducibility of image measures
are critical for longitudinal studies of the choroid where repeated
measurements are made using highly sensitive retinal imaging modalities for
predicting clinical outcomes.

We observed significant choroidal thickening in recipients 1-year post-
transplant and the choroid corresponded to improved eGFR, serum creatinine and
urea levels. In donors, we observed choroidal inflation in the first 4 weeks
after the unilateral nephrectomy, followed by significant thinning 1-year
post-transplant. Initial inflation of the choroid could possibly be related to
compensatory renal hypertrophy, while long-term thinning may be linked to
long-term impairment of renal function. Future work should aim at a fuller
analysis with a larger and more complete dataset in order to increase
statistical power.

Our general purpose segmentation methodology is freely available on GitHub 39,
and we are working on producing an automated, end-to-end and open source
framework for choroidal image analysis in OCT data. Automated tools to assist
clinical prognosis and treatment will strengthen future clinical studies,
enabling the delivery of robust, reproducible and responsible research in
areas which have previously been at risk of human error.

##  6 Acknowledgements

This work was supported by the Medical Research Council [grant number
MR/N013166/1], as part of the Precision Medicine Doctoral Training Programme
with the University of Edinburgh. The authors would like to thank all
participants in the study as well as all staff at the Edinburgh Imaging
Facility who contributed to image acquisition for this study.

##  7 Conflicts of Interest

The authors declare no conflicts of interest.

## References

  * 1 Csaba P Kovesdy.  Epidemiology of chronic kidney disease: an update 2022.  Kidney International Supplements, 12(1):7–11, 2022.
  * 2 Alfons JHM Houben, Remy JH Martens, and Coen DA Stehouwer.  Assessing microvascular function in humans from a chronic disease perspective.  Journal of the American Society of Nephrology, 28(12):3461–3472, 2017.
  * 3 Chee Wai Wong, Tien Yin Wong, Ching-Yu Cheng, and Charumathi Sabanayagam.  Kidney and eye diseases: common risk factors, etiological mechanisms, and pathways.  Kidney international, 85(6):1290–1302, 2014.
  * 4 Tariq E Farrah, Baljean Dhillon, Pearse A Keane, David J Webb, and Neeraj Dhaun.  The eye, the kidney, and cardiovascular disease: old concepts, better tools, and new horizons.  Kidney international, 98(2):323–342, 2020.
  * 5 Debora L Nickla and Josh Wallman.  The multifunctional choroid.  Progress in retinal and eye research, 29(2):144–168, 2010.
  * 6 Craig Balmforth, Job JMH van Bragt, Titia Ruijs, James R Cameron, Robert Kimmitt, Rebecca Moorhouse, Alicja Czopek, May Khei Hu, Peter J Gallacher, James W Dear, et al.  Chorioretinal thinning in chronic kidney disease links to inflammation and endothelial dysfunction.  JCI insight, 1(20), 2016.
  * 7 Jasdeep Kaur, Benjamin E Young, and Paul J Fadel.  Sympathetic overactivity in chronic kidney disease: consequences and mechanisms.  International journal of molecular sciences, 18(8):1682, 2017.
  * 8 E Courtie, Tonny Veenith, A Logan, AK Denniston, and RJ Blanch.  Retinal blood flow in critical illness and systemic disease: a review.  Annals of intensive care, 10(1):1–18, 2020.
  * 9 Kristo Erikson, Janne Henrik Liisanantti, Nina Hautala, Juha Koskenkari, Remi Kamakura, Karl Heinz Herzig, Hannu Syrjälä, and Tero Ilmari Ala-Kokko.  Retinal arterial blood flow and retinal changes in patients with sepsis: preliminary study using fluorescein angiography.  Critical care, 21(1):1–8, 2017.
  * 10 Akihiro Ishibazawa, Taiji Nagaoka, Yoshiro Minami, Manabu Kitahara, Takanori Yamashita, and Akitoshi Yoshida.  Choroidal thickness evaluation before and after hemodialysis in patients with and without diabetes.  Investigative ophthalmology & visual science, 56(11):6534–6541, 2015.
  * 11 Hideyuki Nakano, Hiruma Hasebe, Kenji Murakami, Hiroyuki Cho, Daisuke Kondo, Noriaki Iino, and Takeo Fukuchi.  Choroid structure analysis following initiation of hemodialysis by using swept-source optical coherence tomography in patients with and without diabetes.  Plos one, 15(9):e0239072, 2020.
  * 12 Federico Di Staso, Marco Ciancaglini, Solmaz Abdolrahimzadeh, FABIAN D’APOLITO, and Gianluca Scuderi.  Optical coherence tomography of choroid in common neurological diseases.  in vivo, 33(5):1403–1409, 2019.
  * 13 Elena Garcia-Martin, Laura Jarauta, Luis E Pablo, Maria P Bambo, Jose R Ara, Jesus Martin, Vicente Polo, Jose M Larrosa, Elisa Vilades, Teresa Ramirez, et al.  Changes in peripapillary choroidal thickness in patients with multiple sclerosis.  Acta ophthalmologica, 97(1):e77–e83, 2019.
  * 14 Mehmet Bulut, Aylin Yaman, Muhammet Kazim Erol, Fatma Kurtuluş, Devrim Toslak, Berna Doğan, Deniz Turgut Çoban, and Ebru Kaya Başar.  Choroidal thickness in patients with mild cognitive impairment and alzheimer’s type dementia.  Journal of ophthalmology, 2016, 2016.
  * 15 Zubin Mishra, Anushika Ganegoda, Jane Selicha, Ziyuan Wang, SriniVas R Sadda, and Zhihong Hu.  Automated retinal layer segmentation using graph-based algorithm incorporating deep-learning-derived information.  Scientific Reports, 10(1):1–8, 2020.
  * 16 Li Zhang, Gabriëlle HS Buitendijk, Kyungmoo Lee, Milan Sonka, Henriët Springelkamp, Albert Hofman, Johannes R Vingerling, Robert F Mullins, Caroline CW Klaver, and Michael D Abramoff.  Validity of automated choroidal segmentation in ss-oct and sd-oct.  Investigative ophthalmology & visual science, 56(5):3202–3211, 2015.
  * 17 Saleha Masood, Ruogu Fang, Ping Li, Huating Li, Bin Sheng, Akash Mathavan, Xiangning Wang, Po Yang, Qiang Wu, Jing Qin, et al.  Automatic choroid layer segmentation from optical coherence tomography images using deep learning.  Scientific reports, 9(1):1–18, 2019.
  * 18 Ori Zahavi, Alberto Domínguez-Vicent, Rune Brautaset, and Abinaya Priya Venkataraman.  Evaluation of automated segmentation algorithm for macular volumetric measurements of eight individual retinal layer thickness.  Applied Sciences, 11(3):1250, 2021.
  * 19 Hung-Ju Chen, Yu-Len Huang, Siu-Lun Tse, Wei-Ping Hsia, Chung-Hao Hsiao, Yang Wang, and Chia-Jen Chang.  Application of artificial intelligence and deep learning for choroid segmentation in myopia.  Translational vision science & technology, 11(2):38–38, 2022.
  * 20 Rosa Dolz-Marco, María Andreu-Fenoll, Pablo Hernández-Martínez, M Dolores Pinazo-Durán, and Roberto Gallego-Pinazo.  Automated macular choroidal thickness measurement by swept-source optical coherence tomography in pseudoxanthoma elasticum.  International Journal of Retina and Vitreous, 2(1):1–6, 2016.
  * 21 Jamie Burke and Stuart King.  Edge tracing using gaussian process regression.  IEEE Transactions on Image Processing, 31:138–148, 2021.
  * 22 Neeraj Dhaun.  Optical coherence tomography and nephropathy: The octane study.  https://clinicaltrials.gov/ct2/show/NCT02132741, 2014.  ClinicalTrials.gov identifier: NCT02132741. Updated April 14, 2021. Accessed June 29, 2022.
  * 23 Prejaas Tewarie, Lisanne Balk, Fiona Costello, Ari Green, Roland Martin, Sven Schippling, and Axel Petzold.  The oscar-ib consensus criteria for retinal oct quality assessment.  PloS one, 7(4):e34823, 2012.
  * 24 Early Treatment Diabetic Retinopathy Study Research Group et al.  Early treatment diabetic retinopathy study design and baseline patient characteristics: Etdrs report number 7.  Ophthalmology, 98(5):741–756, 1991.
  * 25 H Passing and W Bablok.  A new biometrical procedure for testing the equality of measurements from two different analytical methods. application of linear regression procedures for method comparison studies in clinical chemistry, part i.  1983\.
  * 26 J Martin Bland and DouglasG Altman.  Statistical methods for assessing agreement between two methods of clinical measurement.  The lancet, 327(8476):307–310, 1986.
  * 27 Waheeda Rahman, Fred Kuanfu Chen, Jonathan Yeoh, Praveen Patel, Adnan Tufail, and Lyndon Da Cruz.  Repeatability of manual subfoveal choroidal thickness measurements in healthy subjects using the technique of enhanced depth imaging optical coherence tomography.  Investigative ophthalmology & visual science, 52(5):2267–2271, 2011.
  * 28 Douglas Bates, Martin Mächler, Ben Bolker, and Steve Walker.  Fitting linear mixed-effects models using lme4.  Journal of Statistical Software, 67(1):1–48, 2015.
  * 29 Priya Ranganathan, CS Pramesh, and Rakesh Aggarwal.  Common pitfalls in statistical analysis: Measures of agreement.  Perspectives in clinical research, 8(4):187, 2017.
  * 30 Colin S Tan, Yanling Ouyang, Humberto Ruiz, and SriniVas R Sadda.  Diurnal variation of choroidal thickness in normal, healthy subjects measured by spectral domain optical coherence tomography.  Investigative ophthalmology & visual science, 53(1):261–266, 2012\.
  * 31 Min Gyu Choi and Jee Taek Kim.  Strong correlation of renal function with choroidal thickness in patients with type 2 diabetes: retrospective cross-sectional study.  Journal of clinical medicine, 9(7):2171, 2020.
  * 32 Giuseppe Mulè, Maria Vadalà, Tiziana La Blasca, Rossella Gaetani, Giuseppe Virone, Marco Guarneri, Massimo Castellucci, Giulia Guarrasi, Micol Terrasi, and Santina Cottone.  Association between early-stage chronic kidney disease and reduced choroidal thickness in essential hypertensive patients.  Hypertension Research, 42(7):990–1000, 2019.
  * 33 Robert G Anderson, Anton J Bueschen, L Keith Lloyd, Eva V Dubovsky, and John R Burns.  Short-term and long-term changes in renal function after donor nephrectomy.  The Journal of urology, 145(1):11–13, 1991.
  * 34 Darling M Rojas-Canales, Jordan Y Li, Leek Makuei, and Jonathan M Gleadle.  Compensatory renal hypertrophy following nephrectomy: When and how?  Nephrology, 24(12):1225–1232, 2019.
  * 35 Félix Renard, Soulaimane Guedria, Noel De Palma, and Nicolas Vuillerme.  Variability and reproducibility in deep learning for medical image segmentation.  Scientific Reports, 10(1):1–16, 2020.
  * 36 Claudio Iovino, Marco Pellegrini, Federico Bernabei, Enrico Borrelli, Riccardo Sacconi, Andrea Govetto, Aldo Vagge, Antonio Di Zazzo, Matteo Forlini, Lucia Finocchio, et al.  Choroidal vascularity index: an in-depth analysis of this novel optical coherence tomography parameter.  Journal of clinical medicine, 9(2):595, 2020.
  * 37 Bjorn Kaijun Betzler, Jianbin Ding, Xin Wei, Jia Min Lee, Dilraj S Grewal, Sharon Fekrat, Srinivas R Sadda, Marco A Zarbin, Aniruddha Agarwal, Vishali Gupta, et al.  Choroidal vascularity index: a step towards software as a medical device.  British Journal of Ophthalmology, 106(2):149–155, 2022.
  * 38 Xue Han, Nan-Nan Du, Shuang Li, Zong-Li Diao, Li Fu, and Wen-Hu Liu.  Choroidal vascularity index assessment: A potential noninvasive technique for diagnosing diabetic nephropathy.  Journal of Ophthalmology, 2022, 2022.
  * 39 Jamie Burke.  Edge tracing using gaussian process regression.  https://github.com/jaburke166/gaussian_process_edge_trace, 2021\.

## Supplementary Material

Figure S1: Flow chart visualising donor and recipient cohort specification.
$N_{D}$ and $N_{R}$ represent number of donors and recipients included at each
level. $n_{D}$ and $n_{R}$ represent number of donors and recipients excluded
at each level, respectively. Figure S2: Correlation plot comparing manual and
automated choroid thickness measurements, stratified by macular location;
temporal (left), subfoveal (middle), nasal (right). Figure S3: Correlation
plot comparing manual and automated choroid thickness measurements, stratified
by cohort; donors (left), recipients (right).

Pearson, $r_{p}$ |  |  $P$-value, $P$
---|---|---
| Donors |  | Donors | Recipients
Image Measure | eGFR | Creatinine | Urea |  | eGFR | Creatinine | Urea | eGFR | Creatinine | Urea
Automated CA | -0.07 | 0.12 | -0.32 |  | 0.87 | 0.77 | 0.45 | 0.04 | 0.02 | 0.03
Automated CT | -0.09 | 0.13 | -0.27 |  | 0.82 | 0.75 | 0.51 | 0.01 | 0.03 | 0.03
Manual CT | -0.07 | 0.14 | -0.28 |  | 0.87 | 0.73 | 0.50 | 0.06 | 0.03 | 0.04
Table S1: (Left) Pearson, $r_{p}$, correlation analysis between choroidal metrics and eGFR, serum creatinine and urea for the donor cohort. Results presented in this table fail to show evidence of statistical significance. (Right) Corresponding P-values from Pearson correlation analysis in both cohorts. Bold P-values represent statistically significant correlations. Response variable $\rightarrow$ | eGFR | Creatinine | Urea
---|---|---|---
Independent variable $\downarrow$ | $\hat{\beta}$ | 95% CI |  $P$-value | $\hat{\beta}$ | 95% CI |  $P$-value | $\hat{\beta}$ | 95% CI |  $P$-value
Intercept | 0.04 | (-0.28, 0.36) | 0.78 | -0.03 | (-0.34, 0.28) | 0.83 | -0.05 | (-0.36, 0.26) | 0.72
Age | -0.34 | (-0.76, 0.08) | 0.10 | 0.07 | (-0.34, 0.47) | 0.73 | 0.08 | (-0.33, 0.48) | 0.69
Sex (Male) | 0.06 | (-0.29, 0.40) | 0.73 | 0.36 | (0.02, 0.69) | 0.04 | 0.11 | (-0.22, 0.45) | 0.48
Time from Baseline | 3.5e-3 | (-0.24, 0.25) | 0.98 | -0.02 | (-0.25, 0.21) | 0.86 | -0.06 | (0-0.31, 0.18) | 0.60
Approx. Refraction | -0.05 | (-0.47, 0.36) | 0.79 | 0.13 | (-0.27, 0.53) | 0.51 | 0.22 | (-0.18, 0.62) | 0.26
Automated CA | 6.7e-4 | (-0.33, 0.33) | 0.99 | -0.11 | (-0.42, 0.21) | 0.49 | -0.07 | (-0.39, 0.24) | 0.64
Patient Std. Dev. | 0.41 | Cond. $R^{2}$: 0.27 | 0.45 | Cond. $R^{2}$: 0.38 | 0.35 | Cond. $R^{2}$: 0.21
Intercept | 0.04 | (-0.28, 0.36) | 0.78 | -0.03 | (-0.34, 0.28) | 0.84 | -0.05 | (-0.35, 0.25) | 0.73
Age | -0.34 | (-0.76, 0.36) | 0.10 | 0.06 | (-0.35, 0.46) | 0.78 | 0.07 | (-0.33, 0.47) | 0.72
Sex (Male) | 0.05 | (-0.30, 0.40) | 0.75 | 0.36 | (0.02, 0.70) | 0.04 | 0.12 | (-0.22, 0.45) | 0.47
Time from Baseline | 3.9e-3 | (-0.24, 0.25) | 0.98 | -0.02 | (-0.25, 0.21) | 0.86 | -0.06 | (-0.31, 0.18) | 0.60
Approx. Refraction | -0.05 | (-0.47, 0.36) | 0.80 | 0.13 | (-0.27, 0.54) | 0.49 | 0.22 | (-0.17, 0.62) | 0.24
Automated CT | -0.01 | (-0.34, 0.31) | 0.95 | -0.08 | (-0.39, 0.23) | 0.60 | -0.07 | (-0.38, 0.25) | 0.66
Patient Std. Dev. | 0.41 | Cond. $R^{2}$: 0.27 | 0.45 | Cond. $R^{2}$: 0.37 | 0.34 | Cond. $R^{2}$: 0.21
Intercept | 0.02 | (-0.31, 0.35) | 0.89 | -1.2e-3 | (-0.32, 0.32) | 0.99 | -0.03 | (-0.34, 0.28) | 0.82
Age | 0.33 | (-0.76, 0.09) | 0.12 | 0.04 | (-0.37, 0.44) | 0.84 | 0.06 | (-0.34, 0.46) | 0.75
Sex (Male) | 0.07 | (-0.29, 0.43) | 0.68 | 0.33 | (-0.01, 0.68) | 0.06 | 0.06 | (-0.28, 0.40) | 0.70
Time from Baseline | 6.0e-4 | (-0.24, 0.26) | 0.96 | -0.02 | (-0.25, 0.21) | 0.88 | -0.05 | (-0.30, 0.19) | 0.66
Approx. Refraction | -0.09 | (-0.53, 0.36) | 0.68 | 0.19 | (-0.23, 0.61) | 0.34 | 0.28 | (-0.14, 0.69) | 0.17
Manual CT | -5.2e-4 | (-0.34, 0.34) | 0.99 | -0.13 | (-0.45, 0.20) | 0.42 | -0.19 | (-0.51, 0.13) | 0.23
Patient Std. Dev. | 0.43 | Cond. $R^{2}$: 0.28 | 0.44 | Cond. $R^{2}$: 0.38 | 0.34 | Cond. $R^{2}$: 0.23
Table S2: LME summary tables for predicting eGFR, serum creatinine and serum
urea in donors using each choroidal image measurement. No model produced any
statistically significant results with the choroid. $\hat{\beta}$ represent
standardised model coefficients, with their corresponding 95% confidence
intervals and associated P-values.