#  A Segmented Total Energy Detector (sTED) optimized for (n,$\gamma$) cross-
section measurements at n_TOF EAR2

V. Alcayne<EMAIL_ADDRESS>D. Cano-Ott  J. Garcia  E. González-Romero
T. Martínez  A. Pérez de Rada  J. Plaza  A. Sánchez-Caballero  J. Balibrea-
Correa  C. Domingo-Pardo  J. Lerendegui-Marco  A. Casanovas  F. Calviño  O.
Aberle  S. Altieri  S. Amaducci  J. Andrzejewski  V. Babiano-Suarez  M. Bacak
C. Beltrami  S. Bennett  A. P. Bernardes  E. Berthoumieux  R. Beyer  M.
Boromiza  D. Bosnar  M. Caamaño  M. Calviani  D. M. Castelluccio  F. Cerutti
G. Cescutti  S. Chasapoglou  E. Chiaveri  P. Colombetti  N. Colonna  P.
Console Camprini  G. Cortés  M. A. Cortés-Giraldo  L. Cosentino  S. Dellmann
M. Di Castro  S. Di Maria  M. Diakaki  M. Dietz  R. Dressler  E. Dupont  I.
Durán  Z. Eleme  S. Fargier  B. Fernández  B. Fernández-Domínguez  P.
Finocchiaro  S. Fiore  V. Furman  F. García-Infantes  A. Gawlik-Ramiega  G.
Gervino  S. Gilardoni  C. Guerrero  F. Gunsing  C. Gustavino  J. Heyse  W.
Hillman  D. G. Jenkins  E. Jericha  A. Junghans  Y. Kadi  K. Kaperoni  G. Kaur
A. Kimura  I. Knapová  M. Kokkoris  Y. Kopatch  M. Krtička  N. Kyritsis  I.
Ladarescu  C. Lederer-Woods  G. Lerner  A. Manna  A. Masi  C. Massimi  P.
Mastinu  M. Mastromarco  E. A. Maugeri  A. Mazzone  E. Mendoza  A. Mengoni  V.
Michalopoulou  P. M. Milazzo  R. Mucciola  F. Murtas† E. Musacchio-Gonzalez
A. Musumarra  A. Negret  P. Pérez-Maroto  N. Patronis  J. A. Pavón-Rodríguez
M. G. Pellegriti  J. Perkowski  C. Petrone  L. Piersanti  E. Pirovano  S. Pomp
I. Porras  J. Praena  J. M. Quesada  R. Reifarth  D. Rochman  Y. Romanets  C.
Rubbia  M. Sabaté-Gilarte  P. Schillebeeckx  D. Schumann  A. Sekhar  A. G.
Smith  N. V. Sosnin  M. Spelta  M. E. Stamati  A. Sturniolo  G. Tagliente  A.
Tarifeño-Saldivia  D. Tarrío  P. Torres-Sánchez  E. Vagena  S. Valenta  V.
Variale  P. Vaz  G. Vecchio  D. Vescovi  V. Vlachoudis  R. Vlastou  A. Wallner
P. J. Woods  R. Zarrella  P. Žugec  Centro de Investigaciones Energéticas
Medioambientales y Tecnológicas (CIEMAT), Spain Instituto de Física
Corpuscular, CSIC - Universidad de Valencia, Spain  Universitat Politècnica de
Catalunya, Spain  European Organization for Nuclear Research (CERN),
Switzerland  Istituto Nazionale di Fisica Nucleare, Sezione di Pavia, Italy
Department of Physics, University of Pavia, Italy  INFN Laboratori Nazionali
del Sud, Catania, Italy  University of Lodz, Poland  University of Manchester,
United Kingdom  CEA Irfu, Université Paris-Saclay, F-91191 Gif-sur-Yvette,
France  Helmholtz-Zentrum Dresden-Rossendorf, Germany  Horia Hulubei National
Institute of Physics and Nuclear Engineering, Romania  Department of Physics,
Faculty of Science, University of Zagreb, Zagreb, Croatia  University of
Santiago de Compostela, Spain  Agenzia nazionale per le nuove tecnologie
(ENEA), Italy  Istituto Nazionale di Fisica Nucleare, Sezione di Bologna,
Italy  Istituto Nazionale di Fisica Nucleare, Sezione di Trieste, Italy
Department of Physics, University of Trieste, Italy  National Technical
University of Athens, Greece  Istituto Nazionale di Fisica Nucleare, Sezione
di Torino, Italy  Department of Physics, University of Torino, Italy  Istituto
Nazionale di Fisica Nucleare, Sezione di Bari, Italy  Universidad de Sevilla,
Spain  Goethe University Frankfurt, Germany  Instituto Superior Técnico,
Lisbon, Portugal  Physikalisch-Technische Bundesanstalt (PTB), Bundesallee
100, 38116 Braunschweig, Germany  Paul Scherrer Institut (PSI), Villigen,
Switzerland  University of Ioannina, Greece  Istituto Nazionale di Fisica
Nucleare, Sezione di Roma1, Roma, Italy  Affiliated with an institute covered
by a cooperation agreement with CERN  University of Granada, Spain  European
Commission, Joint Research Centre (JRC), Geel, Belgium  University of York,
United Kingdom  TU Wien, Atominstitut, Stadionallee 2, 1020 Wien, Austria
Japan Atomic Energy Agency (JAEA), Tokai-Mura, Japan  Charles University,
Prague, Czech Republic  School of Physics and Astronomy, University of
Edinburgh, United Kingdom  Dipartimento di Fisica e Astronomia, Università di
Bologna, Italy  INFN Laboratori Nazionali di Legnaro, Italy  Dipartimento
Interateneo di Fisica, Università degli Studi di Bari, Italy  Consiglio
Nazionale delle Ricerche, Bari, Italy  Dipartimento di Fisica e Geologia,
Università di Perugia, Italy  Istituto Nazionale di Fisica Nucleare, Sezione
di Perugia, Italy  INFN Laboratori Nazionali di Frascati, Italy  Istituto
Nazionale di Fisica Nucleare, Sezione di Catania, Italy  Department of Physics
and Astronomy, University of Catania, Italy  Istituto Nazionale di Astrofisica
- Osservatorio Astronomico di Teramo, Italy  Department of Physics and
Astronomy, Uppsala University, Box 516, 75120 Uppsala, Sweden

###### keywords:

Neutron capture , PHWT , Scintillation detectors , Monte Carlo simulation

## Abstract

The neutron time-of-ﬂight facility n_TOF at CERN is a spallation source
dedicated to measurements of neutron-induced reaction cross-sections of
interest in nuclear technologies, astrophysics, and other applications. Since
2014, Experimental ARea 2 (EAR2) is operational and delivers a neutron fluence
of $\sim$4$\cdot$107 neutrons per nominal proton pulse, which is $\sim$50
times higher than the one of Experimental ARea 1 (EAR1) of $\sim$8$\cdot$105
neutrons per pulse. The high neutron flux at EAR2 results in high counting
rates in the detectors that challenged the previously existing capture
detection systems. For this reason, a Segmented Total Energy Detector (sTED)
has been developed to overcome the limitations in the detector’s response, by
reducing the active volume per module and by using a photo-multiplier (PMT)
optimized for high counting rates. This paper presents the main
characteristics of the sTED, including energy and time resolution, response to
$\gamma$-rays, and provides as well details of the use of the Pulse Height
Weighting Technique (PHWT) with this detector. The sTED has been validated to
perform neutron-capture cross-section measurements in EAR2 in the neutron
energy range from thermal up to at least 400 keV. The detector has already
been successfully used in several measurements at n_TOF EAR2.

##  1 Introduction

The neutron time-of-flight facility n_TOF at CERN is focused on performing
measurements of neutron-induced reaction cross-sections of interest to nuclear
technologies, astrophysics, and other applications. The facility uses as a
neutron source a massive lead spallation target coupled to the CERN-PS 20
GeV/c proton beam [1] and is endowed with three experimental areas:
Experimental ARea 1 (EAR1) with $\sim$8$\cdot$105 neutrons per nominal pulse
of $\sim$7$\cdot$1012 protons, located at $\sim$185 m horizontally from the
spallation target [2], Experimental ARea 2 (EAR2) with $\sim$4$\cdot$107
neutrons per pulse, located vertically at $\sim$20 m from the spallation
target [3], and the recent NEAR station with $\sim$4$\cdot$109 neutrons per
pulse, at $\sim$3 m from the target currently under commissioning [4, 5]. EAR2
was constructed to carry out challenging cross-section measurements with low
mass samples, reactions with small cross-sections and/or highly radioactive
samples [6, 7, 8, 9, 10]. As evident from the numbers above the neutron flux
in EAR2 is $\sim$50 times higher than in EAR1 and the neutrons take $\sim$10
times less time to arrive at the experimental area. As a consequence, the
signal-to-background ratio is increased by a factor of $\sim$500 when
considering the constant room background or the radioactivity of the samples.
Accordingly, the counting rate in the detectors is also increased by
approximately the same factor, as presented in Fig. 1, which implies
considerable experimental challenges.

Figure 1: Counting rates obtained as a function of the neutron energy in the
experimental EAR1 (EAR1-Au) and EAR2 (EAR2-Au) for a BICRON detector with a
threshold of 0.15 MeV. The detectors are located at 10 cm from a 197Au sample
of 2 cm in diameter and 100 $\mu$m thickness. The counting rates of the
background obtained when measuring the dummy, hereafter a setup equal to the
one of 197Au but without the 197Au sample, are also presented for the EAR1
(EAR1-Dummy) and the EAR2 (EAR2-Dummy).

Capture cross-section measurements with C6D6 detectors have been performed
successfully at n_TOF EAR1 for about 20 years [11, 12]. In most cases, the
analysis of the C6D6 detector data was done by applying the Pulse Height
Weighting Technique (PHWT) [13, 14, 15], which allows the C6D6 to mimic the
behavior of an ideal Total Energy Detector (TED) [16]. The measurements were
mainly performed with commercial BICRON detectors (0.621 liters of C6D6) [17]
and self-made and customized detectors with carbon-fiber housing (1.0 liters
of C6D6) [18]. The photomultipliers of the two detectors were not optimized
for the high count rates of EAR2.

Two capture cross-section measurements have been carried out in EAR2 [10, 19]
with these detectors and considerable pile-up effects and gain shifts were
observed in the data due to the challenging conditions of this area [20].
These effects increased with the neutron energy (i.e. at shorter times of
flight) and required the introduction of considerable corrections in the
capture cross-section data analysis. These corrections made almost impossible
to perform capture cross section measurements above a few keV at EAR2 with
these detectors. To overcome these limitations, a Segmented Total Energy
Detector (sTED) [21] has been developed. It consists of an array of small
active volume C6D6 modules coupled to photomultipliers optimized for high
counting rates applications.

This paper discusses the performance of the large volume C6D6 detectors at
EAR2 in Section 2, the properties of the new sTED detector in Section 3 and
the performance at n_TOF EAR2 of this new detector in Section 4. The summary
and conclusions of this work are presented in Section 5.

##  2 Performance of C6D6 detectors at EAR2

As mentioned previously, the BICRON detectors and the self-made detectors with
carbon-fiber housing, have been commonly used at EAR1, but stand very high
counting rates in capture measurements at EAR2. Hence, the measured data
suffer from the effects described in the two following subsections.

###  2.1 Pile-up effects

As shown in Fig. 1 for a BICRON detector at 10 cm from a 100 $\mu$m thick and
2 cm diameter gold sample the counting rate reaches up to 10 counts per
$\mu$s. Such a high counting rate with the $\sim$10 ns Full Width at Half
Maximum (FWHM) signals of the used large volume C6D6 detectors leads to
significant pile-up effects. Pulse shape fitting can be used for
reconstructing piled up signals [22], but even with this technique $\sim$25%
of the signals are lost at a counting rate of 10 counts per $\mu$s [20]. One
possible solution for reducing the pile-up is to move the C6D6 detectors away
from the sample, thus lowering the efficiency and therefore the count rate.
However, measurements performed in EAR2 with BICRON detectors have shown that
the neutron beam-related background (i.e. counts in the detector without any
sample) is almost constant at different distances from the center of the beam
for C6D6 detectors in a wide range of neutron energies, as presented in Fig.
2. Therefore, moving the detectors further away from the sample decreases the
signal to beam-related background. Since this background of EAR2 is one of the
main limitations for performing capture measurements there [20, 23], it does
not help much to move the C6D6 detectors further away from the sample.

Figure 2: Counting rates obtained for a BICRON detector as a function of the
neutron energy with a 0.15 MeV deposited energy threshold in a beam-on
measurement without any sample in place at the nominal proton intensity. The
measurements are performed with the detector at the same distance from the
spallation target but at three different distances (5, 15 and 30 cm) from the
center of the beam.

###  2.2 Gain shift effects

At n_TOF EAR2 three different types of gain-shift effects have been observed,
which are described in the following list:

  * •

Gain shifts due to high constant counting rates appear when the counting rate
in the detector increases from one constant value to a higher constant value.
This gain shift has been observed and characterized in measurements performed
with high activity $\gamma$-ray calibration sources. Fig. 3 depicts an example
of this effect for a carbon-fiber housing detector: the pulse height spectra
in the detector recorded with strong 137Cs and 88Y sources placed together at
different distances (i.e different counting rates) is shifted. The gain
decreases with higher counting rates. As a consequence, the energy calibration
would be modified. A similar but smaller effect was also observed in the
BICRON detectors.

Figure 3: Amplitude spectra for a combination of 137Cs and 88Y calibration
sources with a total activity of $\sim$400 kBq placed at two different
distances from a carbon-fiber housing detector. A gain shift of 12% is
observed from one measurement to the other. The Counting Rates (CR) obtained
with an energy threshold of 0.15 MeV are also given in the figure.

  * •

Gain shifts due to the arrival of the particle flash of EAR2. The particle
flash formed by relativistic charged particles, high-energy neutrons, and
prompt $\gamma$-rays arriving at the experimental area at very short times
($<$1 $\mu$s) after the proton beam hits the spallation target induces a
strong saturation of the detectors. As a result, gain shifts as a function of
time of flight (i.e. neutron energy) appear during the recovery of the BICRON
and carbon-fiber housing detectors. The gain of the detectors slowly recovers
and after approximately 10 ms (corresponding to neutrons of approximately 0.02
eV) the gain is back to the same condition as before the particle flash. This
effect is illustrated in Fig. 4, where the deposited energy spectra for a
197Au sample are shown for different neutron energy ranges. The amplitude
spectra should be very similar in the energy range of the figure. Although the
visible difference (of spectra in Fig. 4) might be explained by gain change
due to different absolute count rate, we have verified from a measurement of a
radioactive 88Y source with beam that the gain change is produced by the
particle flash [20].

Figure 4: Amplitude spectra obtained from a measurement with a BICRON detector
at 5 cm from a 197Au sample of 0.5 cm diameter and 100 $\mu$m thickness. The
neutron separation energy of 197Au is 6.512 MeV. The spectra (from different
energy ranges) are normalized to the same number of detected counts.

In Fig. 5, the deposited energy spectra for three different proton intensities
in the same energy range are presented. It can be seen that the gain increases
with higher proton intensity indicating that the effects of the particle flash
increase with the beam intensities.

Figure 5: Amplitude spectra obtained for the 4.9 eV resonance of a 197Au
sample of 0.5 cm diameter and 100 $\mu$m thickness with a BICRON detector at 5
cm. Three different proton intensities are presented in the plot. The spectra
(from different proton intensities) are normalized to the same number of
detected counts.

Note that the mass of the Au sample used in the tests presented in Figs. 4 and
5 is low enough to exclude pile-up effects.

  * •

Gain shifts produced by rapid counting rate variations as a function of the
time of flight. It has been observed that the detectors show different gains
at neutron energies above and below a strong resonance inducing a high
counting rate. As shown in Fig. 6, the gain of the detector at neutron
energies 1.5-3.5 eV (below the strong 4.9 eV 197Au resonance) increases with
respect to 6-8 eV (above the Au resonance), and then recovers at the thermal
point. This effect shift goes in opposite direction than that expected due to
the particle flash. Also, this effect cannot be due to pile-up due to the fact
that the energy ranges are in the tails of the resonance in the region of
relatively low cross section and also both energy ranges have been selected to
have similar counting rates. Thus the effect is attributed to a gain shift
produced by the high counting rate ($\sim$10 counts/$\mu$s) of the strong
resonance at 4.9 eV.

Figure 6: Amplitude spectra obtained for measurements with a carbon-fiber
housing detector at 10 cm from a 197Au sample of 2 cm diameter and 100 $\mu$m
thickness. The spectra, normalized between them to the number of detected
counts, are presented for different neutron energy ranges and the nominal
proton intensity of 7$\cdot$1012 protons per pulse.

##  3 sTED description and specifications

The sTED has been specifically designed to improve the capture detection setup
at EAR2, following the simple idea of reducing the counting rate per module by
about one order of magnitude by replacing large volume C6D6 detectors with a
much larger amount of smaller modules, forming an array with a comparable
total efficiency. Each sTED module has an active volume of 0.044 liters, which
is $\sim$14 times and $\sim$23 times smaller than the active volumes of the
BICRON (0.621 liters) and the carbon-fiber housing (1.0 liters) detectors,
respectively. In addition, smaller photomultipliers optimized for high
counting rates are used to provide additional robustness. The following
subsections present the technical specifications, the detector response to
$\gamma$-rays, and the application of the PHWT to the data measured with an
sTED array consisting of three modules.

###  3.1 Detector characteristics

The sTED modules were designed via Monte Carlo (MC) simulations and one
prototype was tested in the laboratory at CIEMAT. Once validated, nine modules
were purchased from Scionix [24]. Fig. 7 shows one module and a possible
assembly of the nine modules. The C6D6 cell is coupled to the photomultiplier
with an optical quartz window. The dimensions of the module and its elements
are presented in Fig. 8.

Figure 7: Photos of one sTED module (top) and nine sTED modules grouped into a
cluster (bottom). Figure 8: Drawing of one sTED module with the different
components and their sizes in millimeters. The PMT is coupled to the optical
quartz window.

Three different 1” Hamamatsu photo-multipliers [25] coupled to an sTED module
were tested: R5611A, R2076 and R11265U-100. It was found that R5611A and R2076
also suffered from gain shifts when exposed to high counting rates of
$\sim$0.05 counts/$\mu$s, whereas the R11265U-100 showed a stable gain up to
at least 0.25 counts/$\mu$s. This photomultiplier has a borosilicate window
and Super Bialkali (SBA) photocathodes with decoupling capacitors and a
tapered voltage divider distribution ratio specially designed for high
counting rates.

In addition, we have performed a detailed study of the shape of the sTED
signals. As can be seen in Fig. 9, there are two types of signals. The ones
with a high area-to-amplitude (above the dotted line) are due to $\gamma$-rays
depositing energy in the scintillation liquid. The remaining signals have a
different origin, which was attributed to the instantaneous production of one
or a few photo-electrons in the photo-cathode of the photo-multiplier [26].
These signals are called noise in this work because they are not produced by
$\gamma$-rays interacting with the C6D6 liquid.

Figure 9: 2D plot showing the amplitude versus the area of the sTED signals
with an R11265U-100 photomultiplier when measuring an 88Y calibration source.
The black dashed line separates two different types of signals, see text for
details. The bottom figure is a zoom of the top one.

At n_TOF, the signals are digitized, stored, and then analyzed using dedicated
pulse shape analysis routines [27]. Pulse shape fitting is found to be an
optimal technique to discriminate the two types of signals [22]. To perform
the discrimination two average signal shapes (depicted in Fig. 10) have been
obtained, one for signals related to $\gamma$-rays and the other to the noise.
The use of the average signal shapes in the fitting also allows to mitigate
pile-up effects

Figure 10: Average sTED signals produced by $\gamma$-rays and noise. The
signals are normalized to the same maximum amplitude.

The time resolution of one sTED module was measured with respect to a LaBr3
detector with 354 $\pm$ 4 (statistical) $\pm$ 10 (systematic) ps time
resolution [28]. The coincident signals corresponding to the detection of the
1173 and 1332 keV $\gamma$-rays from a 60Co source in each detector were used
to determine the time resolution, assuming that both detectors have a Gaussian
time response. The distribution of the time differences between the coincident
sTED and LaBr3 events is shown in Fig. 11. The obtained time resolution of an
sTED module is 742 $\pm$ 15 ps, including both statistical and systematic
uncertainties.

Figure 11: Distribution of the time differences between signals in coincidence
between an sTED module and a LaBr3 detector, when measuring a 60Co source. The
FWHM of the distribution is 822 $\pm$ 5 ps, including the contribution of the
LaBr3 and the sTED, see text for details.

One should notice that the reduction of the active volume and thus the need of
using a thick solid housing for keeping the liquid scintillator and the use of
a PMT with a borosilicate glass window (instead of quartz) could have the
drawback of increasing the neutron sensitivity [17] compared to larger volume
detectors with similar housing thicknesses. The neutron sensitivity of the
sTED was estimated by Monte Carlo simulations for capture measurements of
various isotopes.

The sensitivity values are given in Table 1, where the magnitude of the
background due to scattered neutrons is estimated for some representative
resonance in certain nuclei. There, $E_{n}$ is the resonance energy;
$\Gamma_{n}$ and $\Gamma_{\gamma}$ are its neutron and radiative widths,
respectively; $\varepsilon_{n}$ is the probability of detecting a neutron
scattered in the sample with energy $E_{n}$; $\varepsilon_{\gamma}$ is the
efficiency of detecting the corresponding (n,$\gamma$) cascade, and
$(\varepsilon_{n}/\varepsilon_{\gamma})\cdot(\Gamma_{n}/\Gamma_{\gamma})$
estimates the size of the background due to elastically scattered neutrons
compared to the (n,$\gamma$) detected events.

Table 1: Estimation of the neutron sensitivities ($(\varepsilon_{n}/\varepsilon_{\gamma})\cdot(\Gamma_{n}/\Gamma_{\gamma})$) of one sTED module for different nuclei and resonances. For details see the text. Isotope | En (eV) | $\frac{\Gamma_{n}}{\Gamma_{\gamma}}$ | $\frac{\varepsilon_{n}}{\varepsilon_{\gamma}}$ | $(\varepsilon_{n}/\varepsilon_{\gamma})\cdot(\Gamma_{n}/\Gamma_{\gamma})$
---|---|---|---|---
197Au | 4.91 | 1.2$\cdot 10^{-1}$ | 1.6$\cdot 10^{-3}$ | 2.0$\cdot 10^{-4}$
240Pu | 5.01 | 8.4$\cdot 10^{-2}$ | 1.6$\cdot 10^{-3}$ | 1.4$\cdot 10^{-4}$
244Cm | 7.66 | 4.9 | 1.6$\cdot 10^{-3}$ | 8.0$\cdot 10^{-3}$
244Cm | 86.1 | 6.6$\cdot 10^{-1}$ | 5.5$\cdot 10^{-4}$ | 3.6$\cdot 10^{-4}$
207Bi | 12100 | 2.2$\cdot 10^{3}$ | 1.1$\cdot 10^{-4}$ | 2.4$\cdot 10^{-1}$
207Pb | 41100 | 3.7$\cdot 10^{2}$ | 2.3$\cdot 10^{-4}$ | 8.4$\cdot 10^{-2}$

The values
$(\varepsilon_{n}/\varepsilon_{\gamma})\cdot(\Gamma_{n}/\Gamma_{\gamma})$
given in Table 1 indicate that the neutron scattering background in the
resonances of 240Pu, 244Cm and 197Au are $\lesssim$ 0.1%. However, for
resonances with unfavorable $(\Gamma_{n}/\Gamma_{\gamma})$ values like the
ones in 207Pb and 209Bi, the neutron-induced background would be as large as
8.4% and 24%. In general, the increase of the ratio of
$\Gamma_{n}/\Gamma_{\gamma}$ with neutron energy will require corrections of a
few percent for almost all the nuclei at energies above 10 keV. For
measurements targeting on these cases, highly optimized C6D6 detectors such as
the ones with a carbon-fiber housing, thinner optical (or even no at all)
windows, and PMTs with quartz windows [17] could be required.

###  3.2 Detector response to $\gamma$-rays

As described in section 2, the BICRON and carbon-fiber housing detectors
exhibited gain shift when exposed to high activity $\gamma$-ray calibration
sources. The response of the sTED modules with the R11265U-100 photomultiplier
was investigated with a 20 MBq 137Cs source placed at different distances from
the detector. The comparison of the 137Cs pulse height spectra recorded at
0.25, 2$\cdot 10^{-2}$ and 1.5$\cdot 10^{-3}$ c/$\mu$s are shown in Fig. 12.
It can be concluded that for counting rates as large as 0.25 c/$\mu$s no gain
shifts are observed.

Figure 12: Deposited energy spectra for a 20 MBq 137Cs calibration source
placed at different distances from an sTED module with an R11265U-100
photomultiplier, along with the Counting Rates (CR) obtained using a deposited
energy threshold of 0.15 MeV.

The linearity and the energy resolution of the detector were characterized
with six $\gamma$-ray sources: 133Ba, 137Cs, 207Bi, 60Co, 88Y and AmBe using
the Compton edge clearly visible in the spectra. There are almost no signals
corresponding to the full-energy peak in the sTED detector with these
$\gamma$-ray sources. The procedure used consisted of:

  1. (i)

Gaussian folding of the simulated Monte Carlo spectra of deposited energies
from the $\gamma$-ray calibration source.

  2. (ii)

Energy re-calibration of the experimental data.

  3. (iii)

Repetition of points i) and ii), until the best fit of spectra near the
Compton edge is reached

  4. (iv)

In the region near the Compton edge, the relation between the amplitude of the
signals and the deposited energy in the detectors ($E$) have been determined
for each Compton edge. Also, the resolution ($\Delta E/E$) in these regions
have been determined.

  5. (v)

Least square fit of to the values obtained in the point iv) to linear and
parabolic energy calibrations for determining the energy calibration curve.

  6. (vi)

Fit of the $\Delta E/E$ values to the $\mathrm{\Delta
E/E=2.35\cdot\sqrt{\alpha/E+\beta}}$ resolution function.

In order to perform the sTED calibration with the described procedure, Monte
Carlo simulations have been performed with a detailed geometric description of
the sTED modules and the well-validated Standard Electromagnetic physics
package of Geant4 [29].

The top panel of Fig. 13 shows the least square fits of linear and parabolic
functions to the experimental Compton edges for the different $\gamma$-ray
energies. It can be seen from the coefficients of determination ($R^{2}$) that
the linear and parabolic curves reproduce with equal accuracy the data and
hence the calibration can be assumed to be linear. The fit of the detector
energy resolution is presented in the bottom panel of Fig. 13. The resolution
function obtained provides resolution values for this detector of 18% at 1 MeV
and 10% at 5 MeV. The excellent agreement between the experimental and
simulated spectra for the six $\gamma$-ray sources are shown in Fig. 14,
indicating the high quality of the energy calibration and energy resolution
determination. The differences for the AmBe spectra below 3 MeV are related to
the response to the neutrons also emitted by the source, which were not
simulated.

Figure 13: Top panel: deposited energy in the detector as a function of the
area of the signals (blue points corresponding to Compton edges). The values
have been fitted to a straight line (black dashed line) and a parabola (red
dashed line). Bottom panel: energy resolution ($\Delta E/E$) of one sTED
module as a function of the deposited energy (blue points). The experimental
points have been fitted with the function: $\mathrm{\Delta
E/E=2.35\cdot\sqrt{\alpha/E+\beta}}$. The results of the fit are
$\alpha=0.00545$ in MeV and $\beta=0.000729$. Figure 14: Experimental
deposited energy spectra obtained with an sTED module for various $\gamma$-ray
sources (133Ba, 137Cs, 207Bi, 88Y and AmBe) compared with Geant4 simulations.
The area of the experimental spectra are normalized to the simulated ones.

It is important to notice that the Monte Carlo simulations are also used in
the experimental technique applied in the analysis of (n,$\gamma$) cross-
section measurements, described in detail in Section 3.3. For this reason, the
overall quality of the simulations has been assessed with an absolute
measurement of a well-characterized 88Y source (44.3 $\pm$ 1.3 kBq) at 5.0
$\pm$ 0.1 cm from an sTED module. As it can be seen in Fig. 15, the Geant4
simulations folded with the energy resolution reproduce very accurately the
experimental response. The small difference of 2.7% between experiment and
Geant4 based simulations is compatible with the uncertainty of the activity of
the 88Y calibration source. These validated Geant4 simulations have been used
to determine the absolute efficiency to detect various $\gamma$-ray decays.
The simulated efficiencies are presented in Table 2 for the sTED, the BICRON,
and the carbon-fiber housing detectors placed at 5 cm from the $\gamma$-ray
emission point.

Figure 15: Deposited experimental energy spectra (Exp.-Back.) after subtracting the background (Back.) for an 88Y $\gamma$-ray sources of 44.3 $\pm$ 1.3 kBq compared with Monte Carlo simulations (MC). The MC simulations have been scaled by 1.0027 to normalize to the experimental results. Table 2: Detection efficiencies, expressed as percentages, for three detectors. The efficiencies are for the detection of the $\gamma$-ray decay of 137Cs and 88Y, as well as for the (n,$\gamma$) cascades of 197Au and 240Pu computed with the NuDEX code [23, 30]. The efficiencies were calculated with Monte Carlo simulations by simulating the detectors at 5 cm from the $\gamma$-ray emission point and for a deposited energy threshold of 0.15 MeV. Note that for each decay/cascade, the efficiency scales approximately with the volume of the detector. |  137Cs |  88Y |  197Au(n,$\gamma$) |  240Pu(n,$\gamma$)
---|---|---|---|---
| decay | decay | cascade | cascade
Carbon-fiber | 2.87 | 6.15 | 4.77 | 6.09
BICRON | 2.28 | 4.96 | 3.86 | 4.89
sTED module | 0.20 | 0.46 | 0.35 | 0.43

###  3.3 The pulse height weighting technique

The sTED has been designed to measure capture cross-sections using the Pulse
Height Weighting Technique (PHWT) [13, 14], in which the efficiency of the
detection system is transformed to become proportional to the total energy of
the (n,$\gamma$) cascade, and therefore independent of the de-excitation
pattern. The main conditions to be fulfilled for the applicability of this
technique are: the $\gamma$-ray detection efficiency ($\varepsilon_{\gamma}$)
is low, i.e. $\varepsilon_{\gamma}\ll 1$, and proportional to the $\gamma$-ray
energy (Eγ), i.e. $\varepsilon_{\gamma}(E_{\gamma})=k\cdot E_{\gamma}$. For
many detectors, such as the sTED, the efficiency to detect a $\gamma$-ray is
not proportional to its energy. In these cases, “a posteriori” manipulation of
the detector response function can be applied to make the detector response
proportional to the energy of the $\gamma$-rays [13, 14]. This is done by
applying a weight to each recorded count dependent on its energy (pulse
height), determined by the so-called Weighting Function (WF).

For the case of an array of many sTED modules, the total $\gamma$-ray
detection efficiency of the setup can increase considerably. However, the PHWT
can be still used to obtain the capture cross-section as presented in
reference [23], as long as the intrinsic efficiency of each module remains
small ($\varepsilon_{\gamma}\ll 1$). For the case of one sTED module, the
efficiency to detect $\gamma$-rays from the (n,$\gamma$) cascades that are
typically in the order of a few MeVs is low enough due to its small active
volume, as seen in Table 2.

In order to apply the PHWT, the WF has to be calculated for the actual
detection setup. As described in reference [14], the best known method for
determining the WF is to use accurate Monte Carlo simulations including the
detailed geometrical description of the full experimental setup. For this
reason, in Section 3.2 the Monte Carlo simulations of an sTED module have been
thoroughly validated. The WF for a setup consisting of three sTED modules has
been calculated. This particular setup was utilized to determine the capture
yield of 197Au in EAR2, as explained in Section 4. The detector response was
obtained for many $\gamma$-ray energies using the geometry depicted in Figure
16. The simulation results were then fitted to derive a WF parameterized as a
5th-degree polynomial for each sTED module, following the procedure described
in [14]. The WF for one of the modules can be seen in Fig. 17. The WFs for the
other two modules are very similar.

Figure 16: A schematic view of of the setup simulated in Geant4 with three
sTED modules and the gold sample. Figure 17: Adopted WF for one sTED module.
WF$\mathrm{(E)}$ = $\mathrm{6.5071}$ \+ $\mathrm{656.261\cdot E}$ \+
$\mathrm{113.929\cdot E^{2}}$ \+ $\mathrm{34.5488\cdot
E^{3}}$-$\mathrm{6.39125\cdot E^{4}}$ \+ $\mathrm{0.411521\cdot E^{5}}$, the
energy ($E$) is given in MeV and the coefficients correspond to $k=1$, see
3.3.

A polynomial form is used to parameterize the WF as a function of the
deposited energy. For each of 150 $\gamma$-ray energies, covering the range
from 0.1 to 10 MeV, we simulated the spectrum of deposited energies. The
detection efficiency ($\varepsilon_{\gamma\;(with\;WF)}$) for each
$\gamma$-ray energy (Eγ) was then determined from these spectra weighted with
the WF of Fig. 17 and the obtained efficiency was divided by the corresponding
$E_{\gamma}$ to determine the value $Q$. This quantity is defined in a
mathematical equation as follows:
Q=$\varepsilon_{\gamma\;(with\;WF)}$/$E_{\gamma}$. The appropriate WF should
yield $Q=k$ ($k\equiv 1$ in our case). The $Q$ values obtained for this WF are
shown in Fig. 18, the small deviations from one demonstrate the high accuracy
reached with the 5th degree polynomial WF. At energies below 0.5 MeV, the
probability of absorption of all the energy of the $\gamma$-rays increases
considerably, modifying the detector response, however, the determined WF is
still able to obtain $Q$ values at this energy with a deviation of less than
3%. These small deviations in the WFs have lead to uncertainties in the
detection efficiency of capture $\gamma$-ray cascades of the order of only
0.3% for the majority of the isotopes, similar values have been reported in
previous works [14, 20, 31].

Figure 18: $Q$ values, see Sec. 3.3 for its definition, determined for 150
$\gamma$-ray energies.

##  4 Experimental validation at n_TOF EAR2

Due to the challenging conditions for performing capture measurements at n_TOF
EAR2 described in Section 2, the most reasonable method to validate the sTED
is to perform a capture experiment and compare the results with the evaluated
cross section data. A suitable isotope for this purpose is 197Au, which can be
obtained in the form of high-purity metallic samples and has a standard
capture cross-section at thermal energy and between 0.2 and 2.5 MeV [32]. In
addition, 197Au has been measured many times at n_TOF as a reference or in
dedicated campaigns [33, 34]. In 2022, a capture measurement was carried out
with three sTED modules placed horizontally at 5 cm from the center of a 2 cm
diameter and 0.1 mm thickness 197Au sample, see Fig. 16. As presented in Fig.
19 the counting rate obtained in this measurement with a sTED module is
considerably lower than the one obtained with a BICRON detector at the same
experimental area, see Fig. 1.

Figure 19: Counting rates obtained as a function of the neutron energy in the
experimental EAR2 for a sTED module with a threshold of 0.15 MeV. The detector
is located at 5 cm from a 197Au sample of 2 cm in diameter and 100 $\mu$m
thickness. The counting rates of the background obtained when measuring a
dummy sample are also presented.

The deposited energy spectra measured for (n,$\gamma$) reactions in 197Au at
EAR2 were compared with simulations performed with Geant4 in Fig. 20. The
$\gamma$-cascades used in the simulations were obtained by fitting the Total
Absorption Calorimeter (TAC) data from a measurement performed at EAR1 [35,
36] and have been used in processing data of other experiments[20, 37, 38].
The agreement between the shape of the experiment and simulations indicates
that there are no significant gain shifts in the detector with respect to
calibrations performed with sources.

Figure 20: Experimental deposited energy spectra in one sTED module
(Exp.-Back.) with background (Back.) subtracted and simulated with Geant4 (MC)
for 197Au (n,$\gamma$) cascades.

The capture yield has been determined by applying the WF calculated in Section
3.3 to obtain the weighted counting rate as a function of the neutron energy
and dividing it by the neutron fluence of the EAR2, after subtracting the
different background components. The experimental yield was compared with the
yield obtained with the JEFF-3.3 [39] cross-section broadened with the
Resolution Function (RF) of the EAR2 [40, 41]. The comparison, normalized in
the region between 0.01 and 1 eV, is presented in Figs. 21 and 22. As can be
observed, the yields are very similar below 400 keV, which correspond to
neutrons that are at least at $\sim$2 $\mu$s from the strong EAR2 particle
flash. The small differences observed between our results and JEFF-3.3 can be
attributed to uncertainties in the preliminary fluence shape and/or in the RF
[41]. These quantities are preliminary at the moment because the spallation
target has been changed recently at n_TOF. In the valleys of the resonances in
the energy range between 10 and 100 eV, the differences are larger than 25%
due to the uncertainties in the background subtraction. At energies higher
than 400 keV, there are considerable differences, which are likely attributed
to the opening of the (n,n∣) inelastic reaction channels at $\sim$100 keV,
which have not been considered in the analysis.

The main conclusion of the analysis is that the sTED detector is capable of
measuring a capture cross section up to at least 400 keV without suffering any
degradation of its performance and thus are an excellent tool for measurements
of the capture cross section using the high intensity beam of EAR2. Also, the
detector is a very good option for any other possible facility facing high
counting rates in capture cross section measurements.

Figure 21: sTED experimental capture yield obtained with a 197Au sample
(Experimental) compared with the yield obtained from the JEFF-3.3 nuclear data
library (JEFF-3.3) in the energy region between 140 and 165 eV. In the bottom
panel of the figure, the residuals defined as the distances of the
experimental data points to the theoretical JEFF-3.3 yield divided by the
statistical uncertainties of the data points are plotted. The error bars
consider only the uncertainties due to counting statistics.

Figure 22: sTED experimental capture yield obtained with a 197Au sample
(Experimental) compared with the yield obtained from the JEFF-3.3 nuclear data
library (JEFF-3.3). The top figure has ten bins per decade and the bottom one
thirty bins per decade. The vertical blue line indicates the neutron energy of
400 keV. In the bottom panels, the ratios between the two yields are
presented. The error bars consider only the uncertainties due to counting
statistics.

The sTED detector has already been used at n_TOF EAR2 to perform capture
measurements of several isotopes (79Se, 94Nb, 160Gd and 94,95,96Mo) in various
geometric configurations, producing very promising data that are going to be
published soon [42, 43, 44, 45, 46].

##  5 Summary and conclusions

The performance of previously used C6D6 detectors at n_TOF EAR2 harsh
conditions for capture measurements has been discussed showing many
limitations. An alternative segmented Total Energy Detector (sTED), also based
on the C6D6 liquid scintillator, has been developed for improving the response
of the previously-used detectors to the high counting rates. The sTED detector
system will consist of an array of smaller active volume modules coupled to
photo-multipliers optimized for high counting rates. The main features of the
sTED to perform capture cross section measurements are:

  * •

The detector shows a linear energy response to $\gamma$-rays in the entire
energy range considered.

  * •

The experimental response of the sTED modules to $\gamma$-ray sources is well
reproduced with Monte Carlo simulations. This is important to calibrate the
detector and for the application of the PHWT.

  * •

The applicability of the PHWT is validated by Monte Carlo simulations, by
verifying that a WF is capable of producing a weighted efficiency proportional
to the $\gamma$-ray energy.

Last, but not least, an experimental campaign was carried out for validating
the sTED performance under the demanding conditions of the n_TOF EAR2. The
experimental capture yield obtained for a 197Au sample was compared to
predictions based on the JEFF-3.3 capture cross-section, showing an excellent
agreement. The data show that the detector is capable of measuring a capture
cross-section at EAR2 up to at least 400 keV, which is far above the limit
reached with large volume C6D6. The sTED has been used already in several
experimental campaigns producing very promising data.

## CRediT authorship contribution statement

This is a scientific article made by the n_TOF collaboration, where its
members have contributed to all aspects of its development.

## Declaration of competing interest

Declaration of competing interest The authors declare that they have no known
competing financial interests or personal relationships that could have
appeared to influence the work reported in this paper

## Acknowledgments

This work was supported in part by the I+D+i grant PGC2018-096717-B-C21 funded
by MCIN/AEI/10.13039/501100011033, by project PID2021-123100NB-I00 funded by
MCIN/AEI/10.13039/501100011033/FEDER, UE, by project PCI2022-135037-2 funded
by MCIN/AEI/10.13039/501100011033/ and European Union NextGenerationEU/PRTR,
by the European Commission H2020 Framework Programme project SANDA (Grant
agreement ID: 847552) and by funding agencies of the n_TOF participating
institutions.

## References

  * Esposito et al. [2021] R. Esposito, et al. (for the n_TOF Collaboration), Phys. Rev. Accel. Beams 24 (2021) 093001. doi:10.1103/PhysRevAccelBeams.24.093001.
  * Guerrero et al. [2013] C. Guerrero, et al. (The n_TOF Collaboration), Eur. Phys. J. A 49 (2013) 27. doi:10.1140/epja/i2013-13027-6.
  * Weiss et al. [2015] C. Weiss, et al. (The n_TOF Collaboration), Nucl. Instrum. Methods A 799 (2015) 90–98. doi:10.1016/j.nima.2015.07.027.
  * Ferrari et al. [2022] M. Ferrari, et al., Phys. Rev. Ac. and Be. 25 (2022). doi:10.1103/PhysRevAccelBeams.25.103001.
  * Gervino et al. [2022] Gervino, et al., Universe 8 (2022). URL: https://www.mdpi.com/2218-1997/8/5/255. doi:10.3390/universe8050255.
  * Barbagallo et al. [2016] M. Barbagallo, et al. (The n_TOF Collaboration), Phys. Rev. Lett. 117 (2016) 152701. doi:10.1103/PhysRevLett.117.152701.
  * Sabaté-Gilarte et al. [2017] Sabaté-Gilarte, et al., EPJ Web Conf. 146 (2017) 08004. doi:10.1051/epjconf/201714608004.
  * Damone et al. [2018] L. Damone, et al. (The n_TOF Collaboration), Phys. Rev. Lett. 121 (2018) 042701. doi:10.1103/PhysRevLett.121.042701.
  * Stamatopoulos et al. [2020] A. Stamatopoulos, et al. (n_TOF Collaboration), Phys. Rev. C 102 (2020) 014616. doi:10.1103/PhysRevC.102.014616.
  * Alcayne et al. [2020] V. Alcayne, et al., EPJ Web Conf. 239 (2020) 01034. doi:10.1051/epjconf/202023901034.
  * Guerrero et al. [2014] C. Guerrero, et al. (The n_TOF Collaboration), Nuclear Data Sheets 119 (2014) 5–9. doi:https://doi.org/10.1016/j.nds.2014.08.004.
  * Gunsing et al. [2017] F. Gunsing, et al. (The n_TOF Collaboration), EPJ Web Conf. 146 (2017) 11002. doi:10.1051/epjconf/201714611002.
  * Macklin and Gibbons [1967] R. L. Macklin, J. H. Gibbons, Phys. Rev. C 159 (1967) 1007\. doi:10.1103/PhysRev.159.1007.
  * Abbondanno et al. [2004] U. Abbondanno, et al. (The n_TOF Collaboration), Nucl. Instrum. Methods A 521 (2004) 454–467. doi:10.1016/j.nima.2003.09.066.
  * Borella et al. [2007] A. Borella, et al., Nucl. Instrum. Methods A 577 (2007) 626–640. doi:10.1016/j.nima.2007.03.034.
  * Moxon and Rae [1963] M. Moxon, E. Rae, Nucl. Instrum. Methods 24 (1963) 445–455. doi:10.1016/0029-554X(63)90364-1.
  * Plag et al. [2003] R. Plag, et al., Nucl. Instrum. Methods A 496 (2003) 425–436. doi:10.1016/s0168-9002(02)01749-7.
  * Mastinu et al. [2013] P. Mastinu, et al., New C6D6 detectors: reduced neutron sensitivity and improved safety, Technical Report, 2013. URL: https://cdsweb.cern.ch/record/1558147/.
  * Oprea et al. [2020] A. Oprea, et al., EPJ Web Conf. 239 (2020) 01009. doi:10.1051/epjconf/202023901009.
  * Alcayne [2022] V. Alcayne, Measurement of the 244Cm, 246Cm and 248Cm neutron-induced capture cross sections at the CERN n TOF facility, Ph.D. thesis, 2022. URL: https://cds.cern.ch/record/2811791.
  * Alcayne et al. [2023] V. Alcayne, et al., EPJ Web of Conf. 284 (2023) 01043. doi:10.1051/epjconf/202328401043.
  * Guerrero et al. [2008] C. Guerrero, et al., Nucl. Instrum. Methods A 597 (2008) 212–218. doi:10.1016/j.nima.2008.09.017.
  * Mendoza et al. [2023] E. Mendoza, et al., Nucl. Instrum. Methods A (2023) 167894. doi:10.1016/j.nima.2022.167894.
  * Sci [2022] Scionix, 2022. URL: https://scionix.nl.
  * Ham [2022] Hamamatsu, 2022. URL: https://www.hamamatsu.com/.
  * Knoll [1979] G. Knoll, Radiation Detection and Measurement, number v. 415 in Radiation Detection and Measurement, Wiley, 1979\.
  * Žugec et al. [2016] Žugec, et al. (The n_TOF Collaboration), Nucl. Instrum. Methods A 812 (2016) 134–144. doi:10.1016/j.nima.2015.12.054.
  * Gramage [2016] P. Gramage, Characterization of large-scale LaBr 3 detectors volume for gamma spectroscopy, Master’s thesis, 2016\.
  * Agostinelli et al. [2003] S. Agostinelli, et al. (the GEANT4 Collaboration), Nucl. Instrum. Methods A 506 (2003) 250–303. doi:10.1016/S0168-9002(03)01368-8.
  * Mendoza et al. [2020] E. Mendoza, et al., EPJ Web Conf. 239 (2020) 17006. doi:10.1051/epjconf/202023917006.
  * Lerendegui-Marco et al. [2018] J. Lerendegui-Marco, et al. (The n_TOF Collaboration), Phys. Rev. C 97 (2018) 024605. doi:10.1103/PhysRevC.97.024605.
  * Carlson et al. [2009] A. Carlson, et al., Nucl. Data Sheets 110 (2009) 3215–3324. doi:10.1016/j.nds.2009.11.001, special Issue on Nuclear Reaction Data.
  * Massimi et al. [2010] C. Massimi, et al. (n_TOF Collaboration), Phys. Rev. C 81 (2010) 044616. doi:10.1103/PhysRevC.81.044616.
  * Lederer et al. [2011] C. Lederer, et al. (n_TOF Collaboration), Phys. Rev. C 83 (2011) 034608. doi:10.1103/PhysRevC.83.034608.
  * Guerrero et al. [2009] C. Guerrero, et al., Nucl. Instrum. Methods A 608 (2009) 424–433. doi:10.1016/j.nima.2009.07.025.
  * Guerrero et al. [2012] C. Guerrero, et al., Nucl. Instrum. Methods A 671 (2012) 108–117. doi:10.1016/j.nima.2011.12.046.
  * Mendoza et al. [2014] E. Mendoza, et al. (n_TOF Collaboration), Phys. Rev. C 90 (2014) 034608. doi:10.1103/PhysRevC.90.034608.
  * Mendoza et al. [2018] E. Mendoza, et al. (n_TOF Collaboration), Phys. Rev. C 97 (2018) 054616. doi:10.1103/PhysRevC.97.054616.
  * Plompen et al. [2020] A. J. M. Plompen, et al., Eur. Phys. J. A 56 (2020) 181. doi:10.1140/epja/s10050-020-00141-9.
  * Vlachoudis et al. [2021] V. Vlachoudis, et al., On the resolution function of the n_TOF facility: a comprehensive study and user guide, Technical Report, 2021. URL: https://cds.cern.ch/record/2764434.
  * Pavón-Rodríguez et al. [2023] J. A. Pavón-Rodríguez, et al., EPJ Web of Conf. 284 (2023) 06006\. doi:10.1051/epjconf/202328406006.
  * Lerendegui-Marco et al. [2023] J. Lerendegui-Marco, et al., EPJ Web of Conf. 284 (2023) 01028. doi:10.1051/epjconf/202328401028.
  * Domingo-Pardo et al. [2023] C. Domingo-Pardo, et al., Eur. Phys. J. A 59 (2023) 8. doi:10.1140/epja/s10050-022-00876-7.
  * Balibrea-Correa et al. [2023] J. Balibrea-Correa, et al., EPJ Web Conf. 279 (2023) 06004. doi:10.1051/epjconf/202327906004.
  * Mastromarco et al. [2023] M. Mastromarco, et al., EPJ Web of Conf. 284 (2023) 09002. doi:10.1051/epjconf/202328409002.
  * Mucciola et al. [2023] R. Mucciola, et al., EPJ Web of Conf. 284 (2023) 01031. doi:10.1051/epjconf/202328401031.


11institutetext: University of North Carolina, Chapel Hill, NC 27514 USA
11email<EMAIL_ADDRESS>
https://grand-challenge.org/algorithms/multi-view-attention-for-ga-at-birth-
regression/

# Multi-View Attention for gestational age at birth prediction

Mathieu Leclercq 11 Martin Styner 11 Juan Carlos Prieto 11

###### Abstract

We present our method for gestational age at birth prediction for the SLCN
(surface learning for clinical neuroimaging) challenge. Our method is based on
a multi-view shape analysis technique that captures 2D renderings of a 3D
object from different viewpoints. We render the brain features on the surface
of the sphere and then the 2D images are analyzed via 2D CNNs and an attention
layer for the regression task. The regression task achieves a MAE of $1.637\pm
1.3$ on the Native space and MAE of $1.38\pm 1.14$ on the template space. The
source code for this project is available in our github
repository111https://github.com/MathieuLeclercq/SLCN_challenge_UNC.

###### Keywords:

Deep learning Regression Gestational age prediction.

##  1 Data pre-processing and augmentation

There are no pre-processing steps. The data augmentation consists of a Dropout
layer applied to the inputs and additive Gaussian noise.

##  2 Method description

###  2.1 3D shape analysis

Learning-based methods for shape analysis use the 3D models to learn
descriptors directly from them. There are mainly 3 types of learning-based
methods: multi-view, volumetric, multi-layer-perceptrons (MLP).

Multi-view approaches adapt state-of-the art 2D CNNs to work on 3D shapes. The
main impediment is the arbitrary structures of 3D models which are usually
represented by point clouds or triangular meshes, whereas the majority of deep
learning algorithms use the regular grid-like structures found in 2D/3D
images[1, 2]. By rendering 3D objects from different view points, features are
extracted using 2D CNNs[9, 3, 6]. On the other hand, volumetric approaches use
3D voxel grids to represent the shape and apply 3D convolutions to learn shape
features[13, 11, 8]. Finally, other approaches consume the point clouds
directly and implement multi-layer-perceptrons and/or transformer
architectures, or a generalization of typical CNNs [7, 5, 4, 12].

Our method falls in the multi-view category. We render the sphere with the
input features and capture 2D rendering from viewpoints following the
icosahedron subdivision level 0. Figure 1 shows the rendering of the sphere
and an icosahedron that is used to guide the location of the camera.

Figure 1: Feature rendering on the sphere’s surface with the icosahedron
subdivision. The rendered 2D images are shown in the bottom rows. These images
are used to train our neural network.

###  2.2 Rendering the 2D views

The Pytorch3D framework allows rendering and training in an end-to-end
fashion. The rendering engine provides a map that relates pixels in the images
to faces in the mesh and allows rapid extraction of point data (normals,
curvatures, labels, etc.). In this task, we extract the values for the 4 brain
features given at each vertex. The generated images have 4 components and they
are fed to the feature extraction network.

We set the resolution of the rendered images to 224px. We use ambient lights
so that the rendered images don’t have any specular components.

###  2.3 Training the neural network

Figure 2: Architecture for gestational age at birth prediction. We use
efficientnet B0 as feature extraction and weighted attention layer followed by
a linear layer to predict GA.

Our model architecture is shown in Figure 2. The model is trained in an end-
to-end fashion using 1 GPU NVIDIA TITAN RTX 24 GB, batch size 18, Adam
optimizer, learning rate $1e-4$, Dropout 0.2. We use the early stopping
criteria to track the validation loss and save the best performing model. We
use data-binning to create classes for the samples in the data set. We use 5
different age bins, i.e., 5 classes ([23 - 27], [27, 32], [32, 36], [36, 40],
[40, 44]). This binning step allows us to create weights for the under
represented classes as well as adding a new term in our loss function. The
loss function is MSE for the regression task plus a weighted classification
Cross-Entropy loss. We stop the training using the early stopping criteria
after 244 epochs and use the MSE error as validation criteria.

Our network architecture uses efficient net B0[10] to extract image features
from the 2D renderings. Then we compute a score for each image and concatenate
them to compute a weighted average of the features. The final tensor is then
fed to a linear layer that performs the regression and classification task
jointly.

We use both native and template features to train a single model for the
regression task.

##  3 Post processing

There are no post-processing steps.

##  4 Results

Space | MAE $\pm$ STDEV
---|---
Native | $1.637\pm 1.250$
Template | $1.380\pm 1.143$
Table 1: MAE and STDEV

Figure 3: Results (in weeks) on the validation set for prediction in native
space and template space.

Figure 3 show that results for native space and template space are very
similar because the network was trained using both spaces. The network is
slightly biased towards the late GA at birth because there are more sample
points in the data set.

Figure 4: Error distribution (in weeks) for prediction in native space.
Figure 5: Error distribution (in weeks) for prediction in template space.

Figures 4 and 5 show that $2/3$ of the validation samples show an absolute
error of less than 2 weeks. The model tends to under-predict in both template
and native spaces. We consider this is an indication that the model is
agnostic to the template/native features. Table 1 shows the MAE and STDEV for
the prediction task in weeks. We report the results on the validation set.

## References

  * [1] Boubolo, L., Dumont, M., Brosset, S., Bianchi, J., Ruellas, A., Gurgel, M., Massaro, C., Del Castillo, A.A., Ioshida, M., Yatabe, M.S., et al.: Flyby cnn: a 3d surface segmentation framework. In: Medical Imaging 2021: Image Processing. vol. 11596, p. 115962B. International Society for Optics and Photonics (2021)
  * [2] Deleat-Besson, R., Le, C., Zhang, W., Turkestani, N.A., Cevidanes, L., Bianchi, J., Ruellas, A., Gurgel, M., Massaro, C., Castillo, A.A.D., et al.: Merging and annotating teeth and roots from automated segmentation of multimodal images. In: International Workshop on Multimodal Learning for Clinical Decision Support. pp. 81–92. Springer (2021)
  * [3] Kanezaki, A., Matsushita, Y., Nishida, Y.: Rotationnet: Joint object categorization and pose estimation using multiviews from unsupervised viewpoints. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition. pp. 5010–5019 (2018)
  * [4] Li, Y., Bu, R., Sun, M., Wu, W., Di, X., Chen, B.: Pointcnn: Convolution on x-transformed points. Advances in neural information processing systems 31 (2018)
  * [5] Lian, C., Wang, L., Wu, T.H., Wang, F., Yap, P.T., Ko, C.C., Shen, D.: Deep multi-scale mesh feature learning for automated labeling of raw dental surfaces from 3d intraoral scanners. IEEE transactions on medical imaging 39(7), 2440–2450 (2020)
  * [6] Ma, C., Guo, Y., Yang, J., An, W.: Learning multi-view representation with lstm for 3-d shape recognition and retrieval. IEEE Transactions on Multimedia 21(5), 1169–1182 (2018)
  * [7] Qi, C.R., Su, H., Mo, K., Guibas, L.J.: Pointnet: Deep learning on point sets for 3d classification and segmentation. In: Proceedings of the IEEE conference on computer vision and pattern recognition. pp. 652–660 (2017)
  * [8] Riegler, G., Osman Ulusoy, A., Geiger, A.: Octnet: Learning deep 3d representations at high resolutions. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition. pp. 3577–3586 (2017)
  * [9] Su, H., Maji, S., Kalogerakis, E., Learned-Miller, E.: Multi-view convolutional neural networks for 3d shape recognition. In: Proceedings of the IEEE international conference on computer vision. pp. 945–953 (2015)
  * [10] Tan, M., Le, Q.: Efficientnet: Rethinking model scaling for convolutional neural networks. In: International conference on machine learning. pp. 6105–6114. PMLR (2019)
  * [11] Wang, P.S., Liu, Y., Guo, Y.X., Sun, C.Y., Tong, X.: O-cnn: Octree-based convolutional neural networks for 3d shape analysis. ACM Transactions on Graphics (TOG) 36(4), 1–11 (2017)
  * [12] Wu, W., Qi, Z., Fuxin, L.: Pointconv: Deep convolutional networks on 3d point clouds. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. pp. 9621–9630 (2019)
  * [13] Wu, Z., Song, S., Khosla, A., Yu, F., Zhang, L., Tang, X., Xiao, J.: 3d shapenets: A deep representation for volumetric shapes. In: Proceedings of the IEEE conference on computer vision and pattern recognition. pp. 1912–1920 (2015)