# Nuclear deexcitation simulator for neutrino interactions and nucleon decays
of 12C and 16O based on TALYS

Seisho Abe  0000-0002-2110-5130 Kamioka Observatory, Institute for Cosmic Ray
Research, University of Tokyo, Kamioka, Gifu 506-1205, Japan

###### Abstract

Nuclear deexcitation associated with neutrino interactions and nucleon decays
has a significant impact on a recent key observable for neutrino detectors:
neutron multiplicity. However, most existing neutrino Monte Carlo event
generators do not consider this process. For a comprehensive prediction of the
neutron multiplicity, a nuclear deexcitation simulator based on TALYS named
NucDeEx is developed. NucDeEx can be used for neutrino interactions and
nucleon decayes for 12C and 16O. The author provides the NucDeEx codes and
sample codes for applying the NucDeex to widely-used neutrino Monte Carlo
event generators, NEUT, NuWro, and GENIE.

##  I Introduction

Neutrino-nucleus interactions are frequently described by the impulse
approximation, which divides the process into three parts: Initial nucleon
state, primary interaction, and final state interactions (FSI). The initial
nucleon state is usually parameterized by the Fermi gas model or spectral
functions. The primary interaction is the process via the weak interaction of
a neutrino with a single nucleon target, treating the other nucleons as mere
spectators. The FSI is a cascade rescattering of particles in the nucleus. The
description above is adopted in most of the existing neutrino Monte Carlo
event generators. Considering actual interaction processes, a hole or holes
are created after the FSI. Then, the residual nucleus frequently remains in
the excited state and undergoes deexcitation, emitting particles such as
protons, neutrons, $\alpha$ particles, and gamma rays. However, this process
is not simulated in the major generators with few exceptions 111NEUT considers
simplified deexcitation process based on Ref. [9] only for 16O target..
Despite this fact, this description has been used for a long time in various
neutrino experiments with much success because the particles emitted by
nuclear deexcitation have low energies of a few MeV and, except for gamma
rays, are undetectable with most neutrino detectors.

Neutrino detectors can detect neutrons in two ways: Detection of recoil
protons and gamma rays emitted by neutron capture, as shown in Fig. 1. Since
the protons have a high Cherenkov threshold and short trajectories of a few
centimeters, Cherenkov and tracker detectors are forced to impose high
detection thresholds. On the other hand, gamma rays emitted by neutron capture
do not require any detection threshold for neutrons. Neutrons thermalized by
proton recoils remain in the liquid scintillator and water Cherenkov detectors
for several hundred microseconds. In these detectors, most of them are
captured by protons emitting a 2.2 MeV gamma ray. Large liquid scintillator
detectors such as KamLAND [2] and JUNO [3] are good at measuring these gamma
rays because of their large light yield. On the other hand, detecting the 2.2
MeV gamma ray is challenging due to its small light yield for water Cherenkov
detectors such as Super-Kamiokande [4]. Ongoing detector updates are
overcoming this issue by dissolving gadolinium (Gd) in water, such as Super-
Kamiokande Gadolinium [5] and ANNIE experiment [6]. Neutron capture on Gd has
a much larger cross section than protons, carbons, and oxygens. In addition,
it emits gamma rays of 8 MeV in total. Therefore, Gd-loaded water Cherekov
detectors can detect neutron capture with high efficiency.

Figure 1: Schematic view of detection of neutrino-nucleus interactions.
Neutrons recoil protons, leaving short trajectories of a few centimeters.
After thermalization, neutrons are captured mostly by protons (gadolinium)
emitting 2.2 MeV ($\sim 8$ MeV) gamma rays with a particular lifetime of about
several hundred microseconds. Neutrons are detectable and identifiable by
detecting the gamma ray without setting energy thresholds for neutrons.

These detectors are expected to improve the results of various physics
analyses by using the measured neutron multiplicity to enhance flavor
identification or signal-to-background ratio. The following three physics
targets are discussed: CP-phase measurements, diffused supernova neutrino
background (DSNB) searches, and nucleon decay searches. In the CP-phase
measurements, the charged-current quasielastic (CCQE) interaction
($\nu_{\mu}+n\rightarrow\mu^{-}+p$ and
$\bar{\nu}_{\mu}+p\rightarrow\mu^{+}+n$) is used as a signal. A comparison of
neutrino and antineutrino oscillation is achieved by using accelerator
neutrino to switch between neutrino and antineutrino dominant modes. However,
some wrong-sign neutrinos are contaminated in the beam production process. The
presence or absence of neutrons in the final state is expected to reduce this
contamination. In the DSNB searches, the inverse beta decay
($\bar{\nu}_{e}+p\rightarrow e^{+}+n$) is usually used as a signal, and the
dominant background is atmospheric neutrinos. The background can be
drastically reduced by requiring single neutron capture in the event selection
while maintaining high signal efficiency [7]. In the nucleon decay search, the
signal usually does not accompany a neutron in the final state to violate the
baryon number. If a nucleon bound in a nucleus decays, the residual nucleus is
deexcited and frequently emits neutrons in the final state. The dominant
background is again atmospheric neutrinos. Therefore, the signal-to-background
ratio can be increased by requiring the absence of neutron capture in the
event selection. These analyses entirely rely on the neutrino (or nucleon
decay) Monte Carlo event generators to predict how the particles emitted by
neutrino interactions (or nucleon decays) respond in detectors. Therefore, the
prediction accuracy of neutron multiplicity in the generators determines how
much we can improve the physics results.

Returning to residual nuclear deexcitation, the fact that this process is not
considered in most of the generators that employ the impulse approximation is
a critical problem. This process has not been simulated with few exceptions
because of the small energy of the deexcited particles. However, neutron
capture detection is susceptible to deexcitation since no detection threshold
is imposed in neutron energies. Therefore, the highest priority is
constructing a comprehensive description and simulator of neutrino-nucleus
interactions, including nuclear deexcitation. NEUT [8] considers the
deexcitation process only for 16O based on Ref. [9], mainly for gamma rays. A
more precise simulator applicable to 16O and other nuclei is necessary. Some
other simulation studies of the deexcitation process for application to
neutrino interactions and nucleon decays were conducted in Ref. [10, 11, 12,
13]. However, the simulators developed in these studies have yet to be opened.
Integration into the existing neutrino Monte Carlo event generators has yet to
be realized, leading to limited use and validation of the deexcitation
simulators in neutrino experiments.

Therefore, the author developed a dedicated software, NucDeEx, to simulate
nuclear deexcitation. Two notable features of NucDeEx are as follows: It can
be applied to ${}^{12}\text{C}$ and ${}^{16}\text{O}$ aiming for use in liquid
scintillator and water Cherenkov detectors. Moreover, NucDeEx’s code is
provided as a package applicable to existing neutrino and nucleon decay Monte
Carlo event generators. The former is because observing particles from
deexcitation becomes a problem with these detectors. The latter is essential
to be used in the running and future experiments, a crucial difference from
similar studies that are not open source. This paper is organized as follows:
Sec. II describes the overall simulation strategy; Sec. III then presents its
validation using other prediction and non-neutrino beam experiments; Sec. IV
finally shows the impacts of the deexcitation process on neutron multiplicity
associated with neutrino interactions. In this section, three widely-used
neutrino Monte Carlo event generators are discussed: NEUT [8], NuWro [14], and
GENIE [15]. The NucDeEx codes and sample codes used with the generators are
available at GitHub [16].

##  II Simulation overview

Neutrino Monte Carlo event generators are event-by-event simulators. The
deexcitation simulator NucDeEx presented in this paper is also built as an
event-by-event simulator for use with it. The basic concepts of a predecessor
deexcitation simulator to NucDeEx were explained in Refs. [17, 2]. The
predecessor was composed of two software: TALYS [18] and Geant4 [19]. TALYS,
an open-source nuclear reaction simulation package, calculates comprehensive
branching ratios based on the Hauser-Feshbach model [20]. Geant4, a widely
used particle simulation package, calculates event-by-event kinematics using
the branching ratios from TALYS. The predecessor was used with NuWro in
atmospheric neutrino analysis at KamLAND [2]. The analysis result showed
excellent agreement in neutron multiplicity between predictions and
observations. Note that the predecessor is not open-source and integrated into
NuWro.

In order to make NucDeEx readily available for other experiments, it must be
inter-operative with the existing neutrino Monte Carlo event generators. The
predecessor requires Geant4, but its large library set may introduce
complexity and compatibility issues. Aiming to minimize dependencies for
implementation to the existing generators, the author modified the code to
compute kinematics based on ROOT [21] instead of Geant4. Since the generators
already depend on ROOT, the fact that the deexcitation simulator depends on
ROOT will not be a problem. The NucDeEx code has been opened with various
other modifications, but the idea is similar to previous studies explained in
Refs. [17, 2].

###  II.1 Simulation procedure

Figure 2 shows a procedure of the deexcitation simulation. The information of
the residual nucleus after the FSI is extracted from an event sample of
neutrino interactions or nucleon decays. Particle kinematics is determined by
the kinematics simulator based on ROOT. The branching ratios and separation
energies necessary to decide the kinematics are calculated with TALYS and
tabulated in advance. Therefore, NucDeEx depends on TALYS regarding simulation
outputs but is independent regarding software codes. The branching ratios and
kinematics simulation details are described in Sec. II.3 and Sec. II.4,
respectively.

Figure 2: A procedure of the deexcitation simulation. From the event sample of
neutrino interactions or nucleon decays, information on the residual nucleus
is extracted and passed to the deexcitation simulator, NucDeEx. Using the
branching ratios calculated with TALYS [18] (denoted as the orange part),
particle kinematics is simulated (denoted as the blue part). Combining
particle information, we get a comprehensive event sample, which includes the
deexcitation process.

The key point of this design is that TALYS only calculates branching rations
for nuclei, not simulating particle kinematics event-by-event and not giving
excitation energy distribution. That is why the author prepares the particle
simulation using Geant4 or ROOT. We need to know nuclear species, hole state,
and excitation energy. These parameters are extracted from the outputs of
neutrino or nucleon decay Monte Carlo event generators.

###  II.2 Branching ratios for $p_{3/2}$-hole states

Due to its low excitation energy, the deexcitation process from $p_{3/2}$-hole
states is simple. The branching ratios for $p_{3/2}$-hole states were measured
or predicted well in Refs. [22, 10]. NucDeEx refers to these data instead of
TALYS.

In the simple shell model picture of 12C, two nucleons lie in the $s_{1/2}$
shell, and four nucleons lie in the $p_{3/2}$ shell. No nucleon exists in the
$p_{1/2}$ shell, which lies a few MeV above the $p_{3/2}$ shell. In this case,
the $p_{3/2}$-hole state always goes to the ground state (g.s.); no
deexcitation happens. However, according to more precise shell model
calculations, the $p_{1/2}$ shell is partially filled with nucleons at a
certain probability due to nucleon-nucleon correlation. As a result of this
paring effect, about $20\pm 5$% of the $p_{3/2}$-hole states are expected to
have excitation energies of a few MeV [11]. Table. 1 shows a summary of the
branching ratios for $p_{3/2}$-hole states of ${}^{11}\text{B}^{*}$ and
${}^{11}\text{C}^{*}$ used in NucDeEx. The experimental data for
${}^{11}\text{B}^{*}$ shown in this table agrees well with the predicted value
mentioned above. Since no experimental data for ${}^{11}\text{C}^{*}$ could be
found, an analogy was assumed: While the same branching ratio is used, the
excitation states are changed to ones that have the same spin-parity and
similar excitation energy.

As for 16O, all shells including $p_{1/2}$ are filled with nucleons. The
$p_{1/2}$-hole states always go to the g.s. and $p_{3/2}$-hole states go to
excited states. Table. 2 shows summaries of the branching ratios for
$p_{3/2}$-hole states of ${}^{15}\text{N}^{*}$ and ${}^{15}\text{O}^{*}$ used
in NucDeEx. It sometimes transitions to the excited states that emit a proton
or multiple gamma rays. As well as ${}^{11}\text{C}^{*}$, no data for
${}^{15}\text{O}^{*}$ could be found, so the same analogy is assumed.

From the $p_{3/2}$-hole states, neither oxygen nor carbon is accompanied by a
deexcited neutron. However, gamma rays affect the visible energy in neutrino
detectors. The contributions from the gamma ray become relatively large and
require prediction accuracy, especially in DSNB searches looking at low energy
regions below 30 MeV [23] and proton decay searches [24]. The probability of
occurrence of $p_{3/2}$-hole state is about twice larger than that of
$s_{1/2}$-hole states, which is discussed in Sec. II.3. NucDeEx precisely
considers the deexcitation from $p_{3/2}$-hole states, although they do not
affect neutron multiplicity.

Table 1: Excited states and branching ratios for $p_{3/2}$-hole states of ${}^{11}\text{B}^{*}$ and ${}^{11}\text{C}^{*}$ used in NucDeEx. The excitation energy and gamma ray energy are denoted as $E_{x}$ and $E_{\gamma}$, respectively. The brancing ratios (Br) for ${}^{11}\text{B}^{*}$ are measured by Panin et al. [22]. All gamma rays emitted from these excited states are single.  Nucleus |  $E_{x}$ (MeV) | $J^{\pi}$ | Br |  $E_{\gamma}$ (MeV)
---|---|---|---|---
${}^{11}\text{B}^{*}$ | 0 (g.s.) | $3/2^{-}$ | 0.82 | -
| 2.13 | $1/2^{-}$ | 0.10 | 2.13
| 5.02 | $3/2^{-}$ | 0.08 | 5.02
${}^{11}\text{C}^{*}$ | 0 (g.s.) | $3/2^{-}$ | 0.82 | -
| 2.00 | $1/2^{-}$ | 0.10 | 2.00
| 4.80 | $3/2^{-}$ | 0.08 | 4.80
Table 2: Excited states and branching ratios for $p_{3/2}$-hole states of ${}^{15}\text{N}^{*}$ and ${}^{15}\text{O}^{*}$ used in NucDeEx. The excitation energy and gamma ray energy are denoted as $E_{x}$ and $E_{\gamma}$, respectively. The brancing ratios (Br) for ${}^{15}\text{N}^{*}$ are from [10]. Gamma rays emitted from these excited states can be multiple. The relative branching ratios for gamma rays (RBrγ) are based on TALYS [18]. Only those with RBr${}_{\gamma}>0.01$ are listed. From excited states with high excitation energies, a proton is emited with 100%, having a energy written as $E_{p}$.  Nucleus |  $E_{x}$ (MeV) | $J^{\pi}$ | Br | RBrγ |  $E_{\gamma}$ (MeV) |  $E_{p}$ (MeV)
---|---|---|---|---|---|---
${}^{15}\text{N}^{*}$ | 6.32 | $3/2^{-}$ | 0.87 | 1.00 | 6.32 | -
| 9.93 | $3/2^{-}$ | 0.06 | 0.02 | $2.63+7.30$ | -
|  |  |  | 0.04 | $3.61+6.32$ | -
|  |  |  | 0.13 | $4.63+5.30$ | -
|  |  |  | 0.13 | $4.66+5.27$ | -
|  |  |  | 0.65 | $9.93$ | -
| 10.70 | $3/2^{-}$ | 0.06 | - | - | 0.5
${}^{15}\text{O}^{*}$ | 6.18 | $3/2^{-}$ | 0.87 | 1.00 | 6.18 | -
| 9.61 | $3/2^{-}$ | 0.06 | - | - | 2.31
| 10.48 | $3/2^{-}$ | 0.06 | - | - | 3.18

###  II.3 Calculation of branching ratios for $s_{1/2}$-hole and multi-nucleon
hole states using TALYS

In the case of high excitation energies, such as $s_{1/2}$-hole and multi-
nucleon hole states, the deexcitation process becomes complicated and various
particles are emitted. Branching ratios for $\gamma$, $\alpha$, $n$, $p$,
deuteron ($d$), triton ($t$), and 3He are calculated with TALYS version 1.96.
This calculation corresponds to the orange part in Fig. 2. A deexcitation
simulation study using SMOKER code [25] was made in Ref. [11]. SMOKER is
another nuclear simulator that uses the Hauser-Feshbach model like TALYS, but
it does not deal with deuteron, triton, and 3He emissions. One of the features
of TALYS is its ability to describe deexcitation, even for heavy ions. TALYS
provides a global optical model potential to determine the transmission
coefficients and several sophisticated level density models [26]. The author
configured TALYS to calculate the optical model for any compound nucleus. The
default level density model is a combination of the constant temperature and a
Fermi gas, which was adopted in previous studies [17, 2]. The author found
that another model, the back-shifted Fermi gas model [27] gave better
agreement with experimental data shown in Sec. III; therefore, the model is
adopted in NucDeEx.

The calculated branching ratios of $s_{1/2}$-hole states from 12C and 16O are
shown in Fig. 3. The spin parity $J^{\pi}=1/2^{+}$ is set for application to
these states. At a typical excitation energy of 23 MeV (30 MeV) for 11B∗
(15N∗), neutron emission dominates about 50%. The results indicate that the
deexcitation process has a non-negligible impact on neutron multiplicity.
Comparing the results of ${}^{11}\text{B}^{*}$ and ${}^{11}\text{C}^{*}$,
related to the 12C target, there is an approximate isospin-symmetry in the
branching ratios: For example, the brancing ratio of $n$ for
${}^{11}\text{B}^{*}$ is similar to one of $p$ for ${}^{11}\text{C}^{*}$. On
the contrary, the symmetry is almost broken for ${}^{15}\text{N}^{*}$ and
${}^{15}\text{O}^{*}$ due to their larger Coulomb potential. A general trend,
the branching ratios of $p$ for neutron-hole nuclei are larger than ones of
$n$ for proton-hole nuclei, is seen through the results.

Figure 3: Branching ratios of 11B∗, 11C∗, 15N∗, and 15O∗ as a function of
excitation energy calculated with TALYS [18]. The spin-parity
$J^{\pi}=1/2^{+}$ is set for $s_{1/2}$-hole states.

When nuclei have high excitation energy, they rarely go to the ground state by
a single-step decay but rather transition to an excited state and decay
sequentially. Thus, we have to calculate the transition probabilities of all
possible excited states of the daughter nuclei and the branching ratios from
the states. The complete sets of information are also calculated and tabulated
using TALYS. Figure 4 shows an example of the relative branching ratio of each
particle as a function of the excitation energy of the corresponding daughter
nucleus. The branching ratios for daughter nuclei (e.g., ${}^{10}\text{B}^{*}$
produced via ${}^{11}\text{B}^{*}\rightarrow n+^{10}\text{B}^{*}$) are also
calculated and tabulated in the same way. The details are omitted in this
paper due to the large data size.

Figure 4: Relative branching ratios of 11B∗ with excitation energy of 23.6 MeV
and $J^{\pi}=1/2^{+}$ calculated with TALYS [18]. The text in each panel
denotes the absolute branching ratio for each particle emission, and the
colored lines represent the relative branching ratio as a function of the
excitation energy of the corresponding daughter nucleus.

So far, we have discussed single nucleon hole states where we know the spin-
parity exactly. However, multi-nucleon holes are produced by FSI with a
probability of about 30% in GeV-order neutrino reactions. In the case of such
multi-nucleon hole states, most neutrino Monte Carlo generators cannot
determine the spin-parity of the residual nucleus because the Fermi gas model
used in FSI does not consider shell levels. Therefore, branching ratios of
multi-nucleon hole states are calculated using TALYS without specifying the
spin-parity. The spin-parity is determined according to the level density
model employed in TALYS, the back-shifted Fermi gas model.

###  II.4 Kinematics simulation

The kinematics simulation, corresponding to the blue part in Fig. 2, is based
on ROOT libraries. It considers the separation energies and the four-
dimensional momentum conservation. The deexcitation decay process could be
boosted because the residual nuclei tend to have about 200 MeV/c in momentum.
The Lorentz boost from the center-of-mass frame to the laboratory frame is
also considered in this simulation. The effect of the Lorentz boost is not so
large but introduced to accurately reproduce the detection thresholds’ effect
when compared with experimental data in Sec. III.

##  III Results of $s_{1/2}$-hole state simulation

Before showing the results of NucDeEx with neutrino interactions, its
performance is discussed in this section. In order to validate the performance
independently of neutrino interactions and generators, the deexcitation
process from specific nuclear states is compared with experimental data and
other predictions. We focus on deexcitation from $s_{1/2}$-hole states of 11B∗
and 15N∗. Two experiments are used for comparisons: Panin et al. measured
${}^{12}\text{C}(p,2p)^{11}\text{B}^{*}$ reaction and associated deexcitation
pargticles using 12C beam at an energy of about 400 MeV [22]. Single-step
decays of $n$, $d$, and $\alpha$ were measured in this experiment. Yosoi et
al. measured ${}^{12}\text{C}(p,2p)^{11}\text{B}^{*}$ and
${}^{16}\text{O}(p,2p)^{15}\text{N}^{*}$ reactions using proton beam at an
energy of 392 MeV [28, 29, 9]. They measured single-step and multistep decays
of $n$ (only for ${}^{15}\text{N}^{*}$), $p$, $d$, $t$ and $\alpha$. The
branching ratios of 3He are negligibly small for these nuclei. Since both
experiments have high incident energies, the impulse approximation is
applicable, i.e., the types of incident particles do not affect the
deexcitation process.

The excitation energy must be specified instead of the neutrino Monte Carlo
event generators in the comparisons. It is determined according to the
spectral function (SF) by Benhar et al. [30] shown in Fig. 5. The SF provides
probability distribution as a function of removal energy. The excitation
energy is obtained by subtracting the separation energy. There are two or
three peaks in the excitation energy distribution, corresponding to
$s_{1/2}$-, $p_{3/2}$-, and $p_{1/2}$-hole states. In the following
comparisons, excitation energies above 16 or 20 MeV and below 35 or 40 MeV
corresponding to the $s_{1/2}$-hole states are selected.

Figure 5: Excitation energy distribution for ${}^{11}\text{B}^{*}$ (top) and
${}^{15}\text{N}^{*}$ (bottom) based on the Benhar SF [30]. The hole states
are determined according to Table LABEL:tab:Ex_range. The blue, red, and gray
histograms denote contribution from $s_{1/2}$-, $p_{3/2}$-, and $p_{1/2}$-hole
states, respectively. The values in panels represent the probability of each
hole state.

###  III.1 Deexcitation from 11B∗

A comparison with the 12C beam experiment of relative branching ratios for
${}^{11}\text{B}^{*}$ with 16-35 MeV excitation energy range is shown in Fig.
6. All predictions shown here are based on TALYS. The differences come from
the excitation energy distribution and level density model adopted in TALYS.
The excitation energy distributions assumed in these predictions are different
and slightly change the branching ratios. The level density model is the
leading cause of the differences. As mentioned in Sec. II.3, NucDeEx uses the
back-shifted Fermi gas model, but the others use another level density model:
A combination of the constant temperature and a Fermi gas model. The result of
this work gives the best agreement with the experiment with uncertainty of
about 15%. Since this experiment used 12C beam, the center-of-mass frame was
boosted, and particles emitted by deexcitation could be measured at very low
thresholds in the laboratory frame. The agreement between the experimental
data and this work indicates that NucDeEx predicts the branching ratios to low
energies well.

Figure 6: Comparison of relative branching ratios of $n$ and $d/\alpha$ for
11B∗ with excitation energies of 16-35 MeV. The magenta histograms show the
results using NucDeEx, the green histograms show the previous study from [2],
and the orange histograms show the predicted results by Hu et al. using TALYS
[12]. The experimental data by Panin et al. [22] is shown in the blue-hatched
histograms. The branching ratios shown here account for only single-step
decays.

Another comparison with the proton beam experiment of the absolute branching
ratios with the same excitation energy range is shown in Fig. 7. We can
compare branching ratios of both single-step and multistep decays from this
data. The prediction accuracy of these decays depends not only on the
branching ratios but also on the transition probabilities to the excited
state, as shown in Fig. 4. The result of this work shows a slightly smaller
branching ratio of $n$ than other predictions, showing the same trend as Fig.
6. A large discrepancy in $t$ branching ratio is visible. The back-shifted
Fermi gas model gives better agreement but does not solve the issue entirely;
a notable difference remains. The authors of the experiment also discussed
this issue, but their simulation (the blue histograms shown in Fig. 7) did not
reproduce the data either. This discrepancy of $t$ branching ratio is still an
open question to be addressed in the feature by performing validation
experiments. The experiment applied the detection thresholds of 3.1-4.6 MeV
depending on particles [28], and these effects are considered in this
simulation. According to NucDeEx prediction, these thresholds lead to
considerable inefficiency, about 50%. To reduce this inefficiency and to
better understand deexcited particles, the ion beam experiment such as Ref.
[22] is preferable.

Figure 7: Comparison of measured and predicted branching ratios of $n$, $p$,
$d$, $t$, and $\alpha$ for 11B∗ with 16-35 MeV excitation energy. The
branching ratios of $n$ are scaled by a factor of 1/2. The magenta histograms
show the results using NucDeEx, the green histograms show the previous study
from [2], and the orange histograms show the predicted results from Hu et al.
using TALYS [12]. The black histograms denote experimental data from Yosoi et
al. with statistical errors, and the authors provide the prediction using
CASCADE code written with the blue histograms [28]. The hatched or filled
histograms represent the branching ratios for single-step decays, and the open
histograms represent those for multistep decays.

###  III.2 Deexcitation from 15N∗

A comparison with the proton beam experiment of the branching ratios for
${}^{15}\text{N}^{*}$ with 20-40 MeV excitation energy range is shown in Fig.
8. Note that this experimental data was taken using the same beamline shown in
Fig. 7, and the detection thresholds are also considered in this simulation.
Owing to the efforts of installing neutron detectors, the experimental data of
$n$ branching ratios are available. The result of this work gives good
agreement with experimental data in $n$ branching ratio both of single-step
and multistep decays. The uncertainty is estimated to be about 20%. Together
with the results of $n$ branching ratios for ${}^{11}\text{B}^{*}$, NucDeEx
predictions show reasonable agreements with the experimental data sets. As
well as ${}^{11}\text{B}^{*}$, there are large discrepancies for other
particles, especially $t$. Since all predictions do not agree with the
experimental data well and these experiments share the same beam line and
detectors, validation experiments are desired. Conducting a new experiment
using 16O beam is also useful to measure particles with low energy thresholds,
as demonstrated by Panin et al. introduced in Sec. III.1.

Kobayashi et al. made an analysis focusing on the gamma ray from
${}^{15}\text{N}^{*}$ using the same experimental data shown in Fig. 8 [9].
The branching ratios for gamma rays above 3 MeV, which are detectable in water
Cherenkov detectors, were investigated. Table 3 compares gamma ray branching
ratios between the experiment and a prediction using NucDeEx. The prediction
agrees with the experiment for low-energy gamma rays below 6 MeV, but not
above 6 MeV. The cause of this discrepancy is still under study because gamma
rays above several MeV are important in searching for DSNB and nucleon decay
using Super-Kamiokande.

Figure 8: Comparison of measured and predicted branching ratios of $n$, $p$, $d$, $t$, and $\alpha$ for 15N∗ with 20-40 MeV excitation energy. The branching ratios of $n$ are scaled by a factor of 1/2. The magenta histograms show the results using NucDeEx, The black histograms denote experimental data from Yosoi et al. with statistical errors, and the authors provide the prediction using CASCADE code written with the blue histograms [29]. The hatched or filled histograms represent the branching ratios for single-step decays, and the open histograms represent those for multistep decays.  Table 3: Comparison of branching ratios of $\gamma$ with energy of 3 MeV$<E_{\gamma}<6$ MeV and $E_{\gamma}>6$ MeV. The experimental data from Kobayashi et al. was measured using proton beams [9]. Excitation energies of 16-40 MeV are selected in this comparison.  | Branching ratio (%)
---|---
| 3 MeV$<E_{\gamma}<6$ MeV |  $E_{\gamma}>6$ MeV
Kobayashi et al. [9] | $27.9\pm 1.5^{+3.4}_{-2.6}$ | $15.6\pm 1.3^{+0.6}_{-1.0}$
This work | 30.4 | 6.6

##  IV Application to neutrino interactions

In this section, NucDeEx is evaluated with the existing neutrino Monte Carlo
event generators, and its effect on neutron multiplicity is discussed. Three
commonly-used generators are used in this paper: NEUT version 5.6.3, NuWro
version 21.09.02, and GENIE version 3.04.00 with G18_10b_02_11a model
configuration [31]. To obtain accurate excitation energy distributions to be
input to NucDeEx, the SF by Benhar et al. is adopted as the nuclear model in
NEUT and NuWro. For these two generators, the excitation energy is calculated
with the energies of incoming and outgoing particles obtained from the event
sample. GENIE provides several sets of model configurations. This paper uses
G18_10b_02_11a, which adopts the local Fermi gas and hN2018 FSI models. GENIE
also offers an effective SF model as an alternative nuclear mode. However, it
is not used because it did not show the peaks seen in Fig. 5. For GENIE, the
excitation energy is randomly determined according to the SF by Benhar et al.
(Fig. 5) irrespective of the kinematics of the event sample.

CCQE interactions of $\nu_{\mu}$ and $\bar{\nu}_{\mu}$ with monochromatic
energies of 1 GeV are investigated. The detailed treatment of excitation
energy and hole states needed to connect NucDeEx and generators are explained
in Sec. IV.1. Then, the nominal outputs of the generators are described in
Sec. IV.2. At last, the results of applying NucDeEx are shown in Sec. IV.3.

###  IV.1 Excitation energies and hole states

In the case of single nucleon holes, the generators do not clarify the hole
states while determining excitation energies. Table LABEL:tab:Ex_range shows
the excitation energy range and probability of each hole state. The hole
states are determined only from the excitation energy in this application.
This simple method is not ideal because the excitation energy distribution of
each hole state has a finite width and is superposed, as shown in Fig. 5. A
probability distribution for each hole state is needed to describe more
accurately. NEUT assumes that contributions of nucleon-nucleon correlation
with excitation energies off the peak of each shell as $s_{1/2}$-hole states.
It results in a larger probability of $s_{1/2}$-hole states shown in Table
LABEL:tab:Ex_range.

Table 4: Probability (Prob.) and excitation energy ($E_{x}$) range of each hole state for 12C and 16O. The excitation energy ranges are set to separate peaks corresponding to each hole state of Benhar SF [30] shown in Fig. 5. The probability used in NEUT’s original deexcitation process for 16O is also listed as a reference [13].  |  | NEUT | This work
---|---|---|---
Nucleus | Hole | Prob.(%) | Prob.(%) |  $E_{x}$ (MeV)
12C | $s_{1/2}$ | - | 63.9 | $E_{x}\geq 16$
| $p_{3/2}$ | - | 36.1 | $E_{x}<16$
16O | $s_{1/2}$ | 49.05 | 35.8 | $E_{x}\geq 16$
| $p_{3/2}$ | 35.15 | 44.8 | $4\leq E_{x}<16$
| $p_{1/2}$ | 15.8 | 19.4 | $E_{x}<4$

The excitation energy distribution in the multi-nucleon holes produced by FSI
is poorly understood. In most generators, FSI considers separation energy but
not excitation energy because it is based on the Fermi gas model, which does
not consider shell levels. Hence, the generators cannot predict the excitation
energy distribution in the multi-nucleon hole states. In applying NucDeEx to
the generators, the effect of FSI is neglected, only considering the
excitation energy produced by the target nucleon, even in the case of multi-
nucleon hole states.

We need a consensus on describing the excitation energies and hole states for
nucleon correlation contributions and multi-nucleon holes. Discussions with
theorists are ongoing. Note that the excitation energy and hole state are
external input parameters to NucDeEx, and any improvements in the description
will require modifications on the part of the generators.

###  IV.2 Nominal output of generators

Neutron multiplicities of the nominal output of generators are shown in Fig.
9. NEUT implements the original deexcitation process only for 16O based on
Ref. [9], but it is disabled in these comparisons. The mean neutron
multiplicities are shown in Table 5. These results show significant variations
in neutron multiplicity of about 20%, caused by different FSI implementations.
This means that the FSI models need to be carefully studied to predict neutron
multiplicity more precisely. NuWro (GENIE) predicts the smallest (largest)
mean neutron multiplicity. This trend is consistent with nucleon transparency
discussed in Ref. [32]: NuWro predicts larger transparency while GENIE gives
smaller one.

Figure 9: Neutron multiplicities associated with CCQE interactions of
$\nu_{\mu}+^{12}\text{C}$ (left top), $\bar{\nu}_{\mu}+^{12}\text{C}$ (right
top), $\nu_{\mu}+^{16}\text{O}$ (left bottom), and
$\bar{\nu}_{\mu}+^{16}\text{O}$ (right bottom). Calculations from NEUT [8],
NuWro [14], and GENIE [15, 31] are shown. Neutrino energy is monochromatic 1
GeV. Since the deexcitation process originally implemented in NEUT is
disabled, all calculations do not include the deexcitation process.

###  IV.3 After applying NucDeEx

Figure 10 shows neutron multiplicities after applying NucDeEx. The mean
neutron multiplicities are summarized in Table 5. The neutron multiplicities
are increased by 20-30% by deexcitation, which is equal to or greater than the
differences of FSI models of generators as discussed in Sec. IV.2. This result
shows that the deexcitation processes significantly impact neutron
multiplicity. It also indicates that although the uncertainty reduction of FSI
is substantial, it is even more critical to correctly treat the deexcitation
process in descriptions of neutron multiplicity associated with neutrino-
nucleus interactions.

In the results of 16O target, calculations from NEUT using its original
deexcitation process are also listed. In the interaction of
$\bar{\nu}_{\mu}+^{16}$O, the NEUT’s calculation based on Ref.[9] gives a
large discrepancy from the other calculations using NucDeEx. The difference
comes from the probability of each hole state shown in Table
LABEL:tab:Ex_range and the treatment of multiple neutron emissions. The model
implemented in NEUT does not consider multiple neutron emissions and
overestimates single neutron emission instead. However, multiple neutron
emission is not negligible in the case of high excited states with a neutron-
rich nucleus, such as ${}^{15}\text{N}^{*}$ $s_{1/2}$-hole states created by
CCQE interactions of
$\bar{\nu}_{\mu}+^{16}\text{O}\rightarrow\mu^{+}+n+^{15}\text{N}^{*}$.
According to NucDeEx, single (multiple) neutrons are estimated to be emitted
with a probability of about 55% (15%) from such states. The difference in the
treatment of multiple neutron emissions results in a large difference in the
probability of a single neutron emission. It leads to a large discrepancy in
the number of events in a bin with a neutron multiplicity of two in Fig. 10.
Since Super-Kamiokande Gadolinium has a high neutron detection efficiency of
about 70%, the data is expected to verify the difference of deexcitation
models in the future.

The increase in neutron multiplicity due to deexcitation depends on the
generators, i.e., the FSI models, because deexcitation occurs after FSI,
meaning the deexcitation depends on the residual nuclear states produced by
FSI. Even if neutrino detectors measure neutron multiplicity, separating the
deexcitation and FSI contributions would be quite difficult. The neutron
travel distance of these two contributions should differ because of the
dissimilar neutron energies: Neutrons emitted by deexcitation have only a few
MeV. However, the spread of the gamma ray and vertex resolution of detectors
smear the information. Therefore, it is challenging to determine which model
requires modification from the neutrino experimental data only. Our future
task to be addressed is conducting non-neutrino beam experiments that can
precisely measure particles around the nucleus, such as those introduced in
Sec. III, and investigating models after distinguishing between FSI and
deexcitation contributions. This task is also vital in validating the few
deexcitation experimental data so far.

Figure 10: Neutron multiplicities associated with CCQE interactions of $\nu_{\mu}+^{12}\text{C}$ (left top), $\bar{\nu}_{\mu}+^{12}\text{C}$ (right top), $\nu_{\mu}+^{16}\text{O}$ (left bottom), and $\bar{\nu}_{\mu}+^{16}\text{O}$ (right bottom). Calculations from NEUT [8], NuWro [14], and GENIE [15, 31] after applying NucDeEx are shown. The green dashed lines represent the calculations from NEUT using its original deexcitation process, which is only applicable to 16O. Neutrino energy is monochromatic 1 GeV.  Table 5: Summary of mean neutron multiplicities of CCQE interactions on 12C and 16O before and after applying NucDeEx. The numbers in parentheses shown in 16O denote results enabling NEUT’s original deexcitation process. |  | $\nu_{\mu}$ | $\bar{\nu}_{\mu}$
---|---|---|---
Nucleus |  | NEUT | NuWro | GENIE | NEUT | NuWro | GENIE
12C | Nominal | 0.39 | 0.28 | 0.42 | 1.24 | 1.24 | 1.52
| This work | 0.48 | 0.38 | 0.55 | 1.51 | 1.50 | 1.72
16O | Nominal | 0.43 (0.55) | 0.30 | 0.51 | 1.28 (1.55) | 1.24 | 1.55
| This work | 0.61 | 0.45 | 0.76 | 1.67 | 1.62 | 2.06

##  V Conclusion and prospects

This paper reports the construction of NucDeEx to describe the nuclear
deexcitation process, which is neglected in most existing neutrino Monte Carlo
event generators. The simulator comprises two components: A nuclear simulator
TALYS and a kinematics simulator based on ROOT. Notable features of NucDeEx
are that it is open-source, can simulate deexcitation of 12C and 16O, and can
be easily integrated into existing neutrino or nucleon decay Monte Carlo event
generators. The quality of the simulator is evaluated by comparisons with the
other theoretical predictions and hadron beam experiments. The most critical
parameters, branching ratios for neutron, agree within 20%. This
reproducibility is adequate for an initial implementation. The applications of
NucDeEx to neutrino interactions using NEUT, NuWro, and GENIE are also
demonstrated. For the predicted neutron multiplicity, a considerable impact
equal to or greater than that of FSI is pointed out. This result shows the
importance of considering the deexcitation process and the necessity of
modifying the existing generators.

The main future tasks for improving the accuracy are to compare NucDeEx
prediction with more experiments and use them to investigate nuclear models.
As introduced in Sec. III, only a few experiments measured the deexcitation
process. The model has room for improvement, but it is challenging to
investigate how it should be modified from the limited data. New experiments
using 12C or 16O beams are worthwhile since they can detect deexcited
particles with lower energy thresholds than proton beam experiments. In
addition, a detailed comparison between NucDeEx and other simulators is an
interesting study to be discussed in the future. Recently, a simulator that
couples an FSI model INCL with a deexcitation code ABLA has been discussed
[33]. INCL has also been used for hadronic interactions in Geant4 and has
better reproducibility than other models [34]. The discussion of the
deexcitation process based on the INCL FSI model is of interest. In order to
avoid dependence on a specific nuclear model, it is desirable to promote the
development of deexcitation simulators for both TALYS and ABLA and to compare
each other.

The author provides the NucDeEx code and sample codes for applying the NucDeEx
to the generators on Ref. [16]. The author also plans to integrate the
simulator into NEUT and nucleon decay event generators used in Super-
Kamiokande. After that, NucDeEx is expected to be used in various physics
studies performed in Super-Kamiokande and T2K experiment [35]. Integrations
for other generators have yet to be planned but could be easily done by the
generator developers. NucDeEx is expected to improve the prediction accuracy
of neutron multiplicity associated with neutrino-nucleus interactions and
nucleon decays. The author expects that NucDeEx is capable of leading to
improving various physics results using neutron multiplicity conducted in
neutrino experiments in the future: Neutrino CP-phase measurements, DSNB
searches, and nucleon decay searches.

###### Acknowledgements.

This work is supported by JSPS KAKENHI Grant No. 23KJ0319. The author
profoundly appreciates Dr. Yoshinari Hayato for his valuable discussions.

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#  Non-Contact Monitoring of Dehydration using RF Data Collected off the Chest
and the Hand

Hasan Mujtaba Buttar1, Kawish Pervez1, M. Mahboob Ur Rahman1, Kashif Riaz1,
Qammer H. Abbasi2  1 Electrical engineering department, Information Technology
University, Lahore 54000, Pakistan
2Department of Electronics and Nano Engineering, University of Glasgow,
Glasgow, G12 8QQ, UK
1{phdee21006<EMAIL_ADDRESS><EMAIL_ADDRESS>
###### Abstract

In this work, we report for the first time a novel non-contact method for
dehydration monitoring from a distance. Specifically, the proposed setup
consists of a transmit software defined radio (SDR) that impinges a wideband
radio frequency (RF) signal (of frequency 5.23 GHz) in the microwave band onto
either the chest or the hand of a subject who sits nearby. Further, another
SDR in the closed vicinity collects the RF signals reflected off the chest (or
passed through the hand) of the subject. Note that the two SDRs exchange
orthogonal frequency division multiplexing (OFDM) signal, whose individual
subcarriers get modulated once it reflects off (passes through) the chest (the
hand) of the subject. This way, the signal collected by the receive SDR
consists of channel frequency response (CFR) that captures the variation in
the blood osmolality due to dehydration. The received raw CFR data is then
passed through a handful of machine learning (ML) classifiers which once
trained, output the classification result (i.e., whether a subject is hydrated
or dehydrated). For the purpose of training our ML classifiers, we have
constructed our custom HCDDM-RF-5 dataset by collecting data from 5 Muslim
subjects (before and after sunset) who were fasting during the month of
Ramadan. Specifically, we have implemented and tested the following ML
classifiers (and their variants): K-nearest neighbour (KNN), support vector
machine (SVM), decision tree (DT), ensemble classifier, and neural network
classifier. Among all the classifiers, the neural network classifier acheived
the best classification accuracy, i.e., an accuracy of 93.8% for the proposed
chest-based method, and an accuracy of 96.15% for the proposed hand-based
method. Compared to the state-of-the-art (i.e., the contact-based dehydration
monitoring method) where the reported accuracy is 97.83%, our proposed non-
contact method is slightly inferior (as we report a maximum accuracy of
96.15%); nevertheless, the advantages of our non-contact dehydration method
speak for themselves. That is, our proposed method is non-invasive and
contact-less, has high accuracy, allows continuous and seamless monitoring, is
easy to use, and provides rapid results. The anticipated beneficiaries of the
proposed method include: sportsmen, athletes, elderly, diabetic and diarrhea
patients, and labor working outdoors.

###### Index Terms:

dehydration, non-contact methods, RF-based methods, software-defined radio,
covid19, machine learning.

##  I Introduction

A good sixty percent of the human body is composed of water, which is
essential to many of the body’s activities, including maintaining the body’s
temperature, transporting nutrients and oxygen to cells, lubricating joints,
and eliminating waste products. Consuming sufficient water on a daily basis is
necessary for preserving one’s health and warding off a variety of diseases
and adverse conditions [1]. Dehydration occurs when the body does not obtain
enough water or when the body loses water through sweating and evaporation.
When dehydration occurs, it throws off the natural equilibrium of the minerals
and electrolytes found in the body. This could result in a variety of
different health issues, ranging from quite harmless to life-threatening,
depending on how much fluid is lost and what’s causing it in the first place.
Symptoms of mild dehydration include headache, dry mouth, thirst, dizziness,
exhaustion, and dry and wrinkled skin [2],[3],[4]. In more extreme
circumstances, dehydration can result in consequences such as kidney failure,
convulsions, and even death. When the outside weather is hot and humid, then
the dehydration could lead to heat exhaustion which could induce symptoms such
as heavy perspiration, nausea, headache, and weakness. Heat exhaustion if not
addressed quickly, could escalate to heatstroke, which is a life-threatening
medical emergency that can cause damage to the brain, organ failure, and even
death. Last but not the least, dehydration could also have some long-term
adverse effects on the body, e.g., constipation, damage to the kidneys, and
infections of the urinary tract, etc. [1].

In short, dehydration could have fatal implications if left untreated, thus,
timely diagnosis of dehydration followed by imminent medical intervention is
of utmost importance. For the elderly, and for the diabetic and diarrhea
patients, it is especially important to track their hydration levels
frequently [5]. But when it comes to the existing dehydration detection
methods, they have their limitations as they are either invasive (e.g., blood
sample based), or contact-based (e.g., pulse oximeter, smart watch based).
Further, the existing methods are expensive, inconvenient and inconsistent, as
discussed below.

Existing dehydration measures and the dilemma: Some of the most common methods
for measuring hydration levels are: body mass change, total body water, serum
and urine osmolality, plasma osmolality, urine specific gravity, and urine
volume [6, 7, 8, 9, 10]. Another method that is sometimes considered as the
”gold standard” consists of a procedure whereby a subject ingests a known
quantity of an isotope, which allows one to calculate its concentration in a
bodily fluid in order to determine the body’s total water content. Now, the
dilemma. Though such ”gold standards” of hydration assessment are considered
useful for sports science, medicine, or for creating reference standards, but
since they necessitate extensive methodological control, they are not useful
for tracking one’s hydration status on daily basis during a training or
competition [11]. In other words, none of aforementioned hydration measures
has been demonstrated to be valid in all dehydration scenarios (i.e., lab and
field) [12]. Last but not the least, many of the aforementioned hydration
measures could be expensive, cumbersome, erroneous, and inconvenient (either
invasive or contact-based). This calls for the innovative and preferably non-
contact methods for dehydration monitoring, which is precisely the agenda of
this work.

Contributions. This paper proposes an RF-based dehydration monitoring method
that is non-invasive and contact-less, has high accuracy, allows continuous
and seamless monitoring, is easy to use, and provides rapid results.
Specifically, the key contributions of this work are as follows:

1) We propose a novel non-contact method called chest-based dehydration
monitoring (CBDM) method. Under this method, the subject sits nearby an RF
transceiver that impinges an OFDM signal onto the chest of the subject, while
the receiver collects the signal reflected off the chest of the subject.

2) We propose a novel non-contact method called hand-based dehydration
monitoring (HBDM) method. Under this method, the subject places his/her hand
on a table and between two antennas such that the transmitted OFDM signal
passes through the hand of the subject, and is subsequently collected by the
receiver.

The raw data collected by the receiver due to both (CBDM and HBDM) methods
consists of channel frequency response (CFR) that is fed to multiple machine
learning (ML) classifiers which eventually determine whether a person is
hydrated or dehydrated. To the best of our knowledge, this is the first work
that reports a non-contact method for dehydration monitoring.

Rationale. The proposed CBDM and HBDM methods rely upon the following to infer
dehydration related information from the data collected off the chest and the
hand of the subject: i) Dehydration results in reduced blood volume and
increased blood viscosity which in turn increases the heart rate and lessens
the force of the blood against the walls of the arteries. ii) OFDM signal,
being a wideband signal, helps in sensing for dehydration. That is, each OFDM
subcarrier captures unique signatures of dehydration due to frequency, phase
and amplitude modulation of the subcarrier reflected off the human body. Both
factors assist our ML classifiers in achieving high classification accuracy.

Outline. The rest of this paper is organized as follows. Section II discusses
the related work. Section III provides a compact discussion of the
apparatus/equipment that provides the scaffolding for our proposed non-contact
dehydration monitoring method. Section IV provides further details about the
software and hardware setup used for data collection, specifics of each of the
two proposed experiments (chest-based, and hand-based), as well as the data
acquisition protocol implemented in order to construct our custom HCDDM-RF-5
dataset. Section V talks about the training and testing of various ML
classifiers on our custom dataset, and provides a detailed performance
analysis. Section VI concludes.

##  II Related Work

The literature on dehydration monitoring is scarce, but could be broadly
classified into three categories: i) invasive methods, ii) non-invasive but
contact-based methods, iii) non-contact methods. First kind of methods (i.e.,
invasive methods) which examine blood or urine samples in order to determine
the plasma and urine osmolality (and are considered as gold standard) have
already been discussed in section I. Further, to the best of our knowledge,
there exists no work for third kind of methods (i.e., non-contact methods) for
dehydration monitoring in the open literature. Therefore, we summarize the
related work on second kind of methods (i.e., non-invasive methods) only.

###  II-A Non-invasive methods for dehydration monitoring

The non-invasive methods for dehydration monitoring typically employ wearable
sensors (e.g., oximeters, smart watch, smart wrist-bands, etc.) that capture
the photoplethysmography (PPG) and electrodermal activity (EDA) signals and
pass them through various ML algorithms in order to infer the dehydration
status of a subject.

For example, [13] collects both the EDA and the PPG data from 17 subjects and
feeds it to a range of ML algorithms in order to detect mild dehydration by
exploiting the autonomic response to cognitive stress (induced by means of
Stroop test). In [14], authors collect EDA data from 16 subjects for three
different body postures (sitting, standing, and walking), and pass it to a
hybrid Bi-LSTM neural network in order to classify the hydration level of a
subject into one of the three different states (hydrated, moderate
dehydration, extreme dehydration). Authors of [15] utilize a miniature pulse
oximeter to collect PPG data from 17 dehydrated patients admitted in emergency
of a tertiary care hospital. They then extract multiple features from the
acquired PPG data using the variable frequency complex demodulation algorithm,
feed them to a support vector machine classifier, and report an accuracy of
$67.91\%$. [16] collects the EDA data, skin temperature, heart rate and body
mass index from 16 participants while they undergo a workout/physical activity
known as circuit training. It then feeds this data to an empirically derived
formula in order to quantify fluid loss (dehydration) caused by physical
activity. In [17], authors developed a real-time Android-based tool called
”monitoring my dehydration” that utilizes the EDA data to learn the
dehydration level of a person using machine learning techniques. They did
experimental evaluation of their tool by feeding it real-world data from five
users, obtaining an accuracy of $84.5\%$. In [18], authors collect EDA data
using BITalino kit from 5 subjects for three different activities by the
subjects (sitting, standing, laying down), feed their data to various ML
classifiers to solve the binary classification problem of dehydration
detection, and report best classification accuracy of 91.3% using the random
forests ML classifer. In [19] authors collect EDA data from several subjects
under different conditions (sitting, standing), feed it to several ML
classifiers to solve the binary classification problem of dehydration
detection, and report a maximum accuracy of 87.78% using the simple k-NN
classifier. Finally, [20] takes a rather different approach, and utilizes a
leg skin microbiome data from 63 female subjects in order to accurately
predict their skin hydration levels and several other important bio-markers.

Before we conclude this section, it is imperative to have a quick discussion
about the rise of non-contact methods for remote health sensing in the post-
covid19 era.

###  II-B Non-contact methods for health sensing

The non-contact methods for monitoring of body vitals gained popularity in the
post-covid19 era when it was learned that the covid19 pathogen/virus could
stay alive on various surfaces for longer duration, and thus, could infect a
healthy individual upon contact [21]. This gave rise to non-contact methods
which can monitor a person’s vital signs from a distance, and thus, could be
used for long-term and real-time monitoring of a subject without inconvenience
[22, 23]. Such methods also have the potential to decrease the number of
visits to a hospital by a patient, thereby reducing the burden on healthcare
systems [24].

Non-contact health sensing methods could be categorized into following four
categories.

1) Camera-based sensing: These methods begin by recording the face and chest
video of a subject from a distance and calculate vital signs by using the
periodic change in skin colour to calculate the various body vitals [25, 26].

2) Radar-based sensing: These systems incorporate various kinds of radars,
e.g., ultra-wideband pulse radar, frequency modulated continuous-wave radar,
etc. that utilize the traditional radar principles of range and Doppler in
order to estimate various body vitals [27], [28].

3) Wi-Fi-based sensing: Such methods exploit the extensive existing
infrastructure of WiFi routers indoors to run cutting-edge ML and deep
learning (DL) algorithms on the data collected off the reflections from the
human subjects in order to measure body vitals [29], [28].

4) Software-defined radio (SDR)-based sensing: Such methods capitalize on the
amplitude and phase fluctuations in the signals reflected off the human body
to measure vitals [30, 31].

Note that the proposed non-contact CBDM method and HBDM method both do SDR-
based sensing for dehydration monitoring. However, to the best of authors’
knowledge, non-contact monitoring of dehydration has not been reported in the
open literature, to date.

##  III Proposed Apparatus for Non-Contact Dehydration Monitoring

The proposed non-contact system for dehydration monitoring is basically an RF
transceiver that consists of two workstations, each connected with a software-
defined radio (SDR) by means of a USB 3.0 port (see Fig. $1$). Specifically,
the SDR devices used for experiments are Universal Software Radio Peripheral
(USRP) model B210111The USRP B210 from National Instruments covers a wide
frequency range (70 MHz to 6 GHz). It can process a wideband spectrum of up to
56 MHz in real time and sample at a high rate of up to 61.44 MS/s.. Each SDR
communicates with other by means of a directional horn antenna. We use MATLAB
R2021a to program both the transmit and receive USRP SDRs. Specifically, the
transmit SDR sends an orthogonal frequency division multiplexing (OFDM) signal
with quadrature phase shift keying (QPSK) modulation on each sub-carrier,
while the receive SDR receives it and processes it.

Next, with the aim of non-contact dehydration monitoring, we design two
distinct experiments. During the first experiment, the subject’s chest is
exposed to the OFDM signals, and thus, the receive SDR collects the signal
reflected off the chest of the subject. We name this method as chest-based
dehydration monitoring (CBDM) method. During the second experiment, the
subject’s hand is exposed to the OFDM signals, and thus, the receive SDR
collects the signal that passes through the hand of the subject. We name this
method as hand-based dehydration monitoring (HBDM) method222This study was
approved by the ethical institutional review board (EIRB) of Information
Technology University, Lahore, Pakistan..

Figure 1: The proposed non-contact method for dehydration monitoring: The
apparatus consists of an SDR-based RF transceiver to collect radio data off
the chest and the hand of the subject. The collected data is subsequently
passed to various machine learning methods, which ultimately classify a
subject either as hydrated or dehydrated.

##  IV The HCDDM-RF-5 dataset

This section provides sufficient details about the hardware and software setup
used to construct the custom HCDDM-RF-5 dataset333The acronym HCDDM-RF-5
stands for Hand and Chest Data for Dehydration Monitoring via Radio Frequency
data collected from 5 subjects., our thoughtful data collection methodology
(that helped us capture dehydration related data in a very controlled manner),
as well as the intricate details of the two experiments performed in order to
collect data for the two proposed (CBDM and HBDM) methods.

###  IV-A USRP SDRs based OFDM transceiver

OFDM Transmitter: For each OFDM frame, the random bits generator block creates
pseudo-random data bits with a chunk size of 128 bits. The QPSK modulator
block maps these bits to (frequency domain) symbols which are then transformed
into a time-domain signal by means of an inverse fast Fourier transform (IFFT)
of size $N=64$ points. Further, a cyclic prefix (CP) of size 16 samples is
appended to each OFDM frame, making each OFDM frame 80 samples long. Gain of
the transmit horn antenna is set to 40 dB. Fig. 2(a) shows the Simulink
flowgraph of USRP SDR based OFDM transmitter.

OFDM Receiver: After removing the CP from each OFDM frame, fast Fourier
transform (FFT) is then used to transform the received time-domain OFDM
samples into the equivalent frequency-domain OFDM symbol. Then, keeping in
mind that the transmitted QPSK symbols on each sub-carrier are known to the
OFDM receiver, the channel coefficient $h_{i}$ for $i$-th sub-carrier could
simply be computed as: $h_{i}=\frac{y_{i}}{x_{i}}$, where $x_{i}$,$y_{i}$ are
the transmitted and received QPSK symbol on $i$-th sub-carrier, respectively.
This way, the raw CFR data $\mathbf{h}=[h_{1},\@cdots,h_{N}]^{T}$ is collected
by the OFDM transmitter, which is to be utilized later by the ML algorithms in
order to classify the status of each subject as either hydrated or dehydrated.
Fig. 2(b) shows the Simulink flowgraph of USRP SDR based OFDM transmitter.

Table I provides a quick summary of setting of various relevant parameters of
transmit and receive USRP SDRs.

(a) The transmitter flowgraph

(b) The receiver flowgraph

Figure 2: The Simulink flowcharts of the USRP-SDR based OFDM transmitter and receiver.  Parameter | Type/Value
---|---
Bits per OFDM frame | $128$
Bits per symbol | $2$
Coding scheme | Gray coding
Modulation scheme | QPSK
No. of OFDM subcarriers (N) | $64$
Data subcarriers | $52$
Pilot subcarriers | $12$
Size of FFT/IFFT |  $64$ points
Size of cyclic prefix | $16$
Sampling rate |  $20,000$ samples/sec
Antenna type | directional horn
USRP B210 frequency range |  $70$ MHz - $6$ GHz
Centre frequency |  $5.23$ GHz
Clock source & PPS source | Internal
Internal clock rate |  $200$ MHz
Interpolation factor (at Tx) | $250$
Decimation factor (at Rx) | $250$
Transmitter gain (at Tx and Rx) |  $40$ dB
Table I: Some parameters for the USRP-SDR-based OFDM transceiver used for non-
contact monitoring of dehydration.

###  IV-B Data Acquisition for the HCDDM-RF-5 dataset

The custom HCDDM-RF-5 dataset was constructed by collecting data from five
volunteers during the month of Ramadan (between March 23rd, 2023 and April
21st, 2023). Ramadan is an Islamic holy month during which devout Muslims
observe a strict fast from sunrise till sunset. That is, while they are
fasting, Muslims refrain from eating and drinking from sunrise till sunset. We
took advantage of this unique opportunity in order to collect dehydration
related data from five devout Muslims who had been fasting during this month.
Among five subjects, two were males (aged 28, 62 years), and three were
females (aged 21, 26, 61 years). For each fasting subject, we collected data
twice, once for each class label (hydrated and dehydrated) in order to
construct a balanced dataset. Specifically, first episode of data collection
took place about 30 minutes before the sunset when the subject was deemed to
be maximally dehydrated (thus, this data belongs to the first/dehydrated
class). Subsequently, the second episode of the data collection took place an
hour after the sunset, after the subject had finished eating and drinking
after breaking the fast (thus, this data belongs to the second/hydrated
class). For each subject, we conducted two kinds of experiments where we
exposed the subject’s chest and hand to the RF signals, respectively. Some
more pertinent details about data collection for our proposed CBDM and HBDM
methods are given below.

Data collection for the proposed CBDM method: During data acquisition for the
proposed CBDM method, each participant sat on a chair that was about 80 cm
away from the pair of directional horn antennas that pointed towards the chest
of the subject (see Fig. 3). As described before, the transmit horn antenna
impinged an OFDM signal onto the chest of the subject, while the receive horn
antenna gathered the signal reflected off the subject’s chest. During each
experiment session, the subject sat still in order to avoid motion-induced
artefacts in the data being gathered. Each single experiment session lasted
for 30 seconds. For each subject, we conducted five experiment sessions before
the sunset (to capture the raw CFR data for dehydrated class) and five
experiment sessions after the sunset (to capture the raw CFR data for the
hydrated class). This way, we were able to collect $30\times 5=150$ seconds
worth of data for each class (for a given subject), and thus, $150\times
2=300$ seconds worth of data per subject. Ultimately, for 5 subjects, this led
to a total dataset size of $300\times 5=1500$ seconds (or, 25 minutes) of raw
CFR data (that corresponds to a total of $5\times 5\times 2=50$ experiment
sessions).

Figure 3: Experimental setup of the proposed CBDM method.

Data collection for the proposed HBDM method: During data acquisition for the
proposed HBDM method, each participant sat on a chair that was about 60 cm
away from the pair of directional horn antennas facing each other, and placed
his/her hand on the table between the two antennas (see Fig. 4). Again, the
transmit horn antenna impinged an OFDM signal onto the hand of the subject,
while the receive horn antenna gathered the signal passed through the
subject’s hand. During each experiment session, the subject sat still in order
to avoid motion-induced artefacts in the data being gathered. The rest of the
details of data acquisition for the proposed HBDM method are the same as
before. That is, for each subject, we conducted five experiment sessions
before the sunset (to capture the raw CFR data for dehydrated class) and five
experiment sessions after the sunset (to capture the raw CFR data for the
hydrated class). This way, for 5 subjects, we acquired a dataset that
consisted of $300\times 5=1500$ seconds (or, 25 minutes) of raw CFR data (that
corresponds to a total of $5\times 5\times 2=50$ experiment sessions).

In short, combining the two smaller datasets due to CBDM method and HBDM
method together, the custom HCDDM-RF-5 dataset consists of a total of 50
minutes of raw CFR data that corresponds to a total of 100 experiment
sessions.

Figure 4: Experimental setup of the proposed HBDM method.

##  V Training and Testing of Machine Learning Classifiers

For the binary classification problem (hydrated/dehydrated) under
consideration, we train and test the following five ML classifiers and their
variants: K-nearest neighbours (KNN), support vector machine (SVM), decision
tree (DT), ensemble classifier, and neural network. Subsequently, we provide
detailed performance analysis and comparison of all the ML classifiers
implemented.

###  V-A Data Pre-processing & Training of Machine Learning Classifiers

Data Pre-processing: We utilised a low-pass filter and a Savitzky-Golay filter
to denoise the CFR extracted from the received OFDM signal, for all the
experiment sessions (for both CBDM and HBDM methods). We inspected the whole
data manually and removed artifacts where found.

Training & validation of ML classifiers:  The Matlab’s classification learner
app was used to train the following ML classifiers: K-nearest neighbour (KNN),
support vector machine (SVM), decision tree (DT), ensemble classifier, and
neural network. All the classifiers were trained on both labelled datasets
(corresponding to the CBDM method and the HBDM method). The K-fold cross-
validation strategy was used for validation in order to prevent the over-
fitting issue.

###  V-B Performance metrics

Each classifier’s performance is quantified in terms of accuracy, given as:

$\displaystyle\mathrm{Accuracy}=\frac{\mathrm{Correct\;prediction}}{\mathrm{Total\;observations}}\times
100$ (1)
$\displaystyle\mathrm{Accuracy}=\frac{T_{n}+T_{p}}{T_{n}+T_{p}+F_{n}+F_{p}}\times
100$ (2)

where $T_{n}$ represents a true negative, $T_{p}$ represents a true positive,
$F_{n}$ represents a false negative, and $F_{p}$ represents a false positive.
In addition, we also do a performance comparison of the various ML algorithms
by means of a confusion matrix.

###  V-C Performance of proposed CBDM method

We begin with performance analysis of the k-NN classifier for three distinct
values of k, i.e., k=1,k=10,k=100 (where k is the number of neighbours used to
calculate the distance to the new data point). We learn that the fine k-NN
(k=1) achieves an accuracy of 79.1$\%$, medium k-NN (k=10) achieves an
accuracy of 69.2$\%$, while the coarse K-NN (k=100) achieves a very low
accuracy of 55.3$\%$ (see Fig. 5 that displays the detailed confusion matrix).

Next, we focus on Fig. 6 and do performance comparison of the remaining four
ML classifiers (and their variants). Beginning with an SVM classifier (with
linear, quadratic, and cubic kernels), we note that the linear SVM achieves an
overall accuracy of 86.5%, quadratic SVM achieves an overall accuracy of
89.6%, while the cubic SVM achieves an overall accuracy of 90.9%. Next, we
focus on the decision tree classifier, and note that it has the lowest
accuracy of all. That is, the fine tree (despite its many leaves and despite
its ability to differentiate between classes precisely) achieved an accuracy
of 68.8% only, while the coarse tree achieved a very low accuracy of 58.0%
only. Next in line is the ensemble classifier (a mixture of many classifiers)
that is typically implemented with the aim to boost classification accuracy.
We observe the following: the ensemble boosted tree has an overall accuracy of
70.3%, the ensemble bagged tree has an accuracy of 77.9%, the ensemble
subspace KNN has an accuracy of 82.9%, while the ensemble subspace
discriminant has an accuracy of 89.6%. Finally, the neural network (NN)
classifier. Each variant of the NN classifier is a fully-connected feedforward
network. After each fully connected layer, the Relu activation function is
applied, except the last year where softmax activation function is used. We
observe that all the different variants of the NN classifier outperform the
other ML classifiers. Specifically, the narrow variant of the neural network
achieves an accuracy of 93.8%, the medium neural network achieves an accuracy
of 92.5%, the broad neural network achieves an accuracy of 92.9%, the bi-
layered variant of neural network achieves an accuracy of 93%, while the tri-
layered variant of the neural network achieves an accuracy of 93.1%.

Fig. $7$ provides an alternate way of comparing the overall accuracy of all
the five ML classifiers and their variants. We note that, for the proposed
CBDM method, the neural network classifier (with the narrow neural network)
achieves the highest accuracy, which is 93.8%.

Figure 5: Confusion matrix of k-NN algorithm for the proposed CBDM method.
Figure 6: Confusion matrix of each of SVM, DT, Ensemble classifiers, and NN
for the proposed CBDM method. Figure 7: Performance comparison of all the
classifiers for the proposed CBDM method.

###  V-D Performance of proposed HBDM method

We begin performance analysis of our proposed HBDM method from Fig. 8 which
provides confusion matrix of each of five ML classifiers (and their variants).
Beginning with an SVM classifier (with linear, quadratic, and cubic kernels),
we note that the linear SVM achieves an overall accuracy of 71.1%, quadratic
SVM achieves an overall accuracy of 89.2%, while the cubic SVM achieves an
overall accuracy of 88.2%. Next, the decision tree classifier. We observe that
once again it has the lowest accuracy of all. That is, the fine tree achieved
an accuracy of 72.2% only, while the coarse tree achieved a very low accuracy
of 61.4% only. Next, the ensemble classifier. We observe the following: the
ensemble boosted tree has an overall accuracy of 74.8%, while the ensemble
bagged tree has an accuracy of 79.7%. Finally, the neural network (NN)
classifier. Once again, all the different variants of the NN classifier
outperform the other ML classifiers. Specifically, the narrow variant of the
neural network achieves an accuracy of 94.7%, the medium neural network
achieves an accuracy of 96.15%, the broad neural network achieves an accuracy
of 95.15%, the bi-layered variant of neural network achieves an accuracy of
92.35%, while the tri-layered variant of the neural network achieves an
accuracy of 94.2%.

Fig. 9 provides an alternate way of comparing the overall accuracy of all the
five ML classifiers and their variants. We note that, for the proposed HBDM
method, the neural network classifier (with the medium neural network)
achieves the highest accuracy, which is 96.15%.

###  V-E Performance comparison with the state-of-the-art

Finally, Table II compares the accuracy of the proposed non-contact CBDM and
HBDM methods with the state-of-the-art methods which are all contact-based
methods for dehydration monitoring. Compared to the state-of-the-art where the
maximum reported accuracy is 97.83%, our proposed non-contact method is
slightly inferior (as we report a maximum accuracy of 96.15%); nevertheless,
the advantages of our non-contact dehydration method speak for themselves.
That is, our proposed method is non-invasive and contact-less, has high
accuracy, allows continuous and seamless monitoring, is easy to use, and
provides rapid results.

Figure 8: Confusion matrix of each of KNN, SVM, DT, Ensemble classifiers, and NN for the proposed HBDM method. Figure 9: Performance comparison of all the ML classifiers for the proposed HBDM method. Work | Accuracy
---|---
Liaqat et al. [14] | 97.83$\%$
Kulkarni et al. [17] | 75.96$\%$
Liaqat et al. [18] | 91.53$\%$
Rizwan et al [19] | 85.63$\%$
Carrieri et al. [20] | 73.91 $\%$
Our non-contact CBDM method | 93.8$\%$
Our non-contact HBDM method | 96.15$\%$
Table II: Accuracy comparison of our proposed non-contact CBDM and HBDM
methods with the state-of-the-art (contact-based methods).

##  VI Conclusion & Future Work

This work proposed for the first time a non-contact method to monitor the
dehydration of a subject from a distance. Specifically, we utilized a pair of
USRP SDRs whereby the transmit SDRs impinged OFDM signals onto the chest or
the hand of the subject, while the receive SDR collected the modulated signal
reflected off the body of the subject. For the purpose of training our ML
classifiers, we collected data from 5 Muslim subjects (before and after
sunset) who were fasting during the month of Ramadan. We then passed the
received raw CFR data through many ML classifiers. Among them, neural network
classifier achieved the best performance: an accuracy of 93.8% for the
proposed CBDM method, and an accuracy of 96.15% for the proposed HBDM method.
The fact that the proposed HBDM method outperforms the proposed CBDM method is
a pleasant result. This is because this allow us to promote the proposed HBDM
method as a non-contact method for dehydration monitoring (where only a hand
is exposed to RF radiation, instead of the full chest, albeit the radiation
being non-ionizing). Last but not the least, the proposed non-contact method
(with a maximum accuracy of 96.15%) performs very close to its contact-based
counterpart (with a maximum accuracy of 97.83%). Such a minor performance
degradation of our proposed non-contact method compared to its contact-based
competitor might be affordable, keeping in mind the convenience (and other
benefits) of a non-contact method.

One major advantage of the proposed approach is that it may pave the way for
the creation of a smart mobile health (m-health) solution that could be
deployed in remote areas far away from the mega cities, in order to provide
comprehensive health monitoring of the people living there.

This work opens up many exciting directions for the future work. For example,
one could construct/acquire a more challenging dataset (unlike the current
dataset that was obtained in a very controlled setting), and re-evaluate as
well as fine-tune the performance of the proposed method further, in order to
make it robust and amicable to the unseen data.

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