# MetricGAN+/-: Increasing Robustness of
Noise Reduction on Unseen Data ††thanks: This work was supported by the Centre
for Doctoral Training in Speech and Language Technologies (SLT) and their
Applications funded by UK Research and Innovation [grant number EP/S023062/1].
This work was also funded in part by TOSHIBA Cambridge Research Laboratory.

George Close, Thomas Hain, and Stefan Goetze
Dept. of Computer Science, The University of Sheffield, Sheffield, United
Kingdom
{glclose1, t.hain<EMAIL_ADDRESS>
###### Abstract

Training of speech enhancement systems often does not incorporate knowledge of
human perception and thus can lead to unnatural sounding results.
Incorporating psychoacoustically motivated speech perception metrics as part
of model training via a predictor network has recently gained interest.
However, the performance of such predictors is limited by the distribution of
metric scores that appear in the training data.
In this work, we propose MetricGAN+/- (an extension of MetricGAN+, one such
metric-motivated system) which introduces an additional network - a “de-
generator” to improve the robustness of the prediction network (and by
extension of the generator) by ensuring observation of a wider range of metric
scores in training. Experimental results on the VoiceBank-DEMAND dataset show
relative improvement in PESQ score of $3.8\%$ ($3.05$ vs. $3.22$ PESQ score),
as well as better generalisation to unseen noise and speech signals.

###### Index Terms:

speech enhancement, noise reduction, speech quality metrics, neural networks,
GAN, metric prediction

##  I Introduction

SE has been an active research topic for decades now, given its myriad
applications in human-to-human (h2h) communication in video or voice calls as
well as in human-to-machine (h2m) communication in home, industry and mobile
device assistant products [1, 2]. Use of neural network (NN) systems to
perform speech enhancement has shown great success in recent years [3, 4, 5,
6, 7]. Training of NNs for speech enhancement requires selection of an
objective function appropriate for the task. Direct comparison between ‘clean’
audio and the output of a neural network given an artificially corrupted
version of that audio has been found to be only weakly correlated with
objective measures (metrics) of intelligibility, quality and performance for
both forms of speech communication [8, 9, 10]. A recent publication [11]
proposed a loss function that corresponds to one of these psychoacoustically
motivated metrics. However, such objective functions must be carefully
designed as many objective measures contain calculations that are non-
differentiable. Several systems circumvent this limitation via use of an
additional model that mimics the behaviour of the metric [12, 13, 14], with
this network being used as a surrogate of the metric used as an objective
function in training of the speech enhancement model. The baseline system that
this work builds upon is one such system, MetricGAN+ [15] (itself an extension
of previous work MetricGAN [16]). Two popular objective measures the
Perceptual Evaluation of Speech Quality (PESQ) [17] and the Short-Time
Objective Intelligibility (STOI) [18] for speech quality and intelligibility
respectively are used. Both measures account for human perception and are
often highly correlated with Mean Option Score (MOS) of human evaluators [11,
8, 19]. The computation of STOI is relatively simple, and a version of it
suitable for use as an objective function is detailed in [11]. Calculation of
PESQ is more complex, and thus cannot be formulated in a differentiable way to
be used as objective functions. To handle this problem, a secondary
”discriminator” network is introduced that, given a representation of the
reference and the degraded signal, predicts the metric score corresponding to
those two signals. Such a metric prediction network is sometimes referred to
as a QualityNet [12]. The output of this discriminator network is then used to
train the speech enhancement (generator) network. The two networks are trained
in a Generative Adversarial Network (GAN) style strategy. In this work we
introduce a further network, a ’de-generator’ which attempts to produce
outputs with a set lower metric score, aiming to improve the ability of the
discriminator to predict the metric on a more complete range of metric scores.
The remainder of this paper is structured as follows: Section II presents the
baseline system, its model structure and training setup. The proposed
extension is introduced in Section III, followed by a comparison to the
baseline in Section IV and a brief conclusion in Section V.

##  II Baseline System - MetricGAN+

The MetricGAN+ framework [15] consists of two networks: a speech enhancement
model $\mathcal{G}$, which aims to remove the undesired signal parts, i.e the
noise $v[n]$ from a noisy signal

$x[n]=s[n]+v[n]$ (1)

to produce an estimate of a clean signal $s[n]$, denoted in the following by
$\hat{s}[n]$ and a metric discriminator (more correctly an evaluator)
$\mathcal{D}$, which predicts the possibly psychoacoustically motivated
performance metrics(s) providing a target to optimise the signal enhancement.

####  II-1 Input Features

STFT
---
log$(|\mathbf{P}|+1)$
---
Feature Computation (FC)
---
$|\mathbf{P}|$
---
$\mathbf{P}_{f}$
---
$p[n]$
---
$x[n]$
---
$s[n]$
---
$\hat{s}[n]$
---
$\angle\,\mathbf{P}$
---

Figure 1: Illustration of feature computation (FC), $p[n]$ can be any signal
$x[n],\hat{s}[n],s[n]$

Features are calculated from different time domain signals denoted here by
$p[n]$ and which is a placeholder for the signals ${x[n],s[n],\hat{s}[n]}$ for
the time index $n$ which we will omit in the following. First a spectral
magnitude $P_{k,\ell}$ for frequency $k$ and frame $\ell$ is calculated of the
time domain audio signal $p$ using the Short Time Fourier Transform (STFT),
followed by transformation to the feature space by adding $1$ to and taking
the logarithm of each element to give the feature representation
$\mathbf{P}_{f}$ as shown in Fig. 1. The phase of the spectral bins $\angle
p_{k,\ell}$ will be used later to resythesize the time domain signal using the
Overlap-Add (OLA) method.

####  II-2 Generator Network for Signal Enhancement

Fig. 2 shows the training of $\mathcal{G}$. The dotted blue arrows and
processes show the objective function and loss calculation back-propagated to
the model. In order to obtain the enhanced signal $\hat{s}$ from the noisy
features $\mathbf{X}_{f}$ in the generator $\mathcal{G}$’s training and
inference, the transform is reversed by subtracting $1$ from each element and
taking the exponential of each element in the feature representation.

MSE
---
$\mathcal{G}$
---
$|\mathbf{X}|$
---
$\mathbf{X}_{f}$
---
$\angle\mathbf{X}$
---
exp$(\mathbf{X}_{f}-1)$
---
$s$
---
$1$
---
$\cdot$
---
$\mathbf{S}_{f}$
---
$\mathcal{D}$
---
FC
---
FC
---
Re-Synth
---
(OLA)
$\hat{s}$
---
$\hat{\mathbf{S}}_{f}$
---
$\mathcal{D}(\hat{\mathbf{S}}_{f},{\mathbf{S}}_{f})$
---
$\mathbf{M}_{\mathcal{G}}$
---
Clamp
---
($\xi=0.5$)

Figure 2: Training and inference of MetricGAN+ Generator.

The output of $\mathcal{G}$ is a time-frequency (T-F) mask matrix
$\mathbf{M}_{\mathcal{G}}$ , which is then multiplied with the noisy magnitude
spectogram $|\mathbf{X}|$ to result in the enhanced signal matrix
$|\mathbf{\hat{S}}|$. The enhanced time domain audio signal $\hat{s}[n]$ is
calculated using OLA resythesis. Note that each element in
$\mathbf{M}_{\mathcal{G}}$ is ‘clamped’ in order to reduce residual musical
tones caused by the mask, i.e. it is limited to element wise values
$\xi\leq\mathbf{M}_{\mathcal{G}}\leq 1$. The objective function of the speech
enhancement network $\mathcal{G}$ is dependent entirely on the metric score of
its output $\hat{s}$ (in its feature space representation
$\mathbf{\hat{S}}_{f}$) as predicted by discriminator $\mathcal{D}$

$L_{\mathcal{G},\mathrm{MG+}}=\mathbb{E}[(\mathcal{D}(\mathbf{\hat{S}}_{f},\mathbf{S}_{f})-1)^{2}]$
(2)

where $1$ represents a ‘perfect’ score in the normalised metric
$Q^{\prime}(\cdot)$.

####  II-3 Discriminator Network for Metric Prediction

The discriminator $\mathcal{D}$ is trained to reproduce the normalised target
metric $Q^{\prime}(\cdot)$ minimising the distance from its output and the
‘true’ normalised metric score used as its objective function, as visualised
in Fig. 3. Arrows and processes marked blue denote those which occur only
during training.

Metric
---
FC
---
FC
---
$\mathcal{D}$
---
$p$
---
$x$
---
$s$
---
$\hat{s}$
---
$Q(p,s)$
---
$\mathbf{P}_{f}$
---
$\mathbf{S}_{f}$
---
Normalization
---
$\mathcal{D}(\mathbf{P}_{f},\mathbf{S}_{f})$
---
$Q^{\prime}(p,s)$
---
MSE
---

Figure 3: Training and inference of MetricGAN+ Discriminator.

The loss of the discriminator comprises three mean squared error (MSE) terms
depending on the clean reference signal $s$, or $\mathbf{S}_{f}$, the degraded
noisy signal $x$, or $\mathbf{X}_{f}$, and the enhanced signal $\hat{s}$, or
$\mathbf{\hat{S}}_{f}$. More specifically, its objective function is given as:

$L_{D,MG+}=\mathbb{E}[(\mathcal{D}(\mathbf{S}_{f},\mathbf{S}_{f})-1)^{2}+(\mathcal{D}(\mathbf{\hat{S}_{f}},\mathbf{S}_{f})-Q^{\prime}(\hat{s},s))^{2}+\\\
(\mathcal{D}(\mathbf{X}_{f},\mathbf{S}_{f})-Q^{\prime}(x,s))^{2}]$ (3)

The $1$ in the first term of (3) represents the fact that $Q^{\prime}(s,s)=1$.
In the second term, the scores of signals enhanced by $\mathcal{G}$, $\hat{s}$
are considered and compared to the ground truth score for the enhanced signal.
In the final term, the scores of noisy signals $x$ are considered and compared
to the true score for the noisy signal. Note that in the case of the metrics
investigated in this work the input to the function that defines the metric
are the time domain signals $x$, $\hat{s}$ and $s$, but this may not always be
the case.

####  II-4 MetricGAN+ Training

Each epoch of training consists of four steps, the first three representing
the training of $\mathcal{D}$ and the final step the training of
$\mathcal{G}$. At the start of each epoch, $I$ audio segments are randomly
picked out from the training set. Firstly $\mathcal{D}$ is trained as given in
(3) on these $I$ random audio segments. The audio segments are time domain
signals of varying length. Then, in the second step, $\mathcal{D}$ is trained
using a ’replay buffer’ where saved enhanced outputs of the generator
$\mathcal{G}$ from past epochs are used to train $\mathcal{D}$. The size of
this replay buffer is decided by a ‘history_portion’ $H$ hyper-parameter,
which corresponds to the replay buffer growing by a set percentage of the
audio segments observed each epoch. This is done to prevent $\mathcal{D}$ from
‘forgetting’ too much about the behaviour of $Q^{\prime}(\cdot)$ on previously
enhanced speech.
Then the first step is repeated with $\mathcal{D}$ again being trained using
the $t$ random samples. Finally, $\mathcal{G}$ is trained also using these $t$
samples as in (2). During training of $\mathcal{D}$, $\mathcal{G}$ is ‘frozen’
and its parameters are not updated; the opposite is true during
$\mathcal{G}$’s training. Note that samples are added to the replay buffer
during the first step of $\mathcal{D}$’s training, meaning that 20% of the
‘current’ epoch data are always present in the replay buffer. As $\mathcal{D}$
is trained before $\mathcal{G}$, the $\hat{s}$ in (3) actually represents the
output of the previous epoch’s $\mathcal{G}$.

####  II-5 Discriminator Model Structure

The discriminator $\mathcal{D}$’s structure is a Convolutional Neural Network
(CNN) with four 2D convolutional layers with 15 filters of a kernel size of
$(5,5)$. To account for the variable length of input data, a global 2-D
average pooling layer is placed immediately after the input, fixing the
feature representation at $15$ dimensions. After the convolutional layers, a
mean is taken over the $2$nd and $3$rd dimensions, and this representation is
fed into three sequential linear layers, with $50$, $10$ and $1$ output
neurons, respectively. The first two of these layers have a LeakyReLU
activation while the final layer has no activation.

The generator $\mathcal{G}$’s network structure consists of a Bidirectional
Long Short-Term Memory (BLSTM) [20] with two LSTM layers with 200 neurons
each. This is followed by two fully connected layers, the first with 300
output neurons and a LeakyReLU [21] activation and the second 257 output
neurons with a ’Learnable’ Sigmoid activation function. This Learnable Sigmoid
is given as:

$y_{\mathrm{learnable-sigmoid}}=\frac{\beta}{1+e^{-\alpha x}}$ (4)

where $\beta$ is a hyper-parameter (default to $1.2$) and $\alpha$ is a
learnable parameter. In the original work the authors found that allowing
$\beta$ to be learnable did not increase performance.

##  III Proposed System - MetricGAN+/-

###  III-A MetricGAN+/- Framework

The framework proposed in this work, MetricGAN+/-, expands on MetricGAN+ in
one major way - we introduce an additional network, a ‘de-generator’
$\mathcal{N}$ which, given an input signal $x$, will attempt to output a
signal with a non-perfect score of metric $Q^{\prime}$. The key idea of this
extension is to allow $\mathcal{D}$ to observe a wider range of metrics scores
outside of those present in the training data. The output audio of
$\mathcal{N}$’s mask $\mathbf{M}_{\mathcal{N}}$ applied to noisy magnitude
spectogram $|\mathbf{X}|$ is defined as $y$ and its feature space
representation as $\mathbf{Y}_{f}$. An extra term is appended to the objective
function of $\mathcal{D}$ that accounts for the prediction of the $Q^{\prime}$
scores of these ‘de-enhanced’ signals:

$L_{D,\mathrm{MG+/-}}=\mathbb{E}[(\mathcal{D}(\mathbf{S}_{f},\mathbf{S}_{f})-1)^{2}+(\mathcal{D}(\mathbf{\hat{S}}_{f},\mathbf{S}_{f})-Q^{\prime}(\hat{s},s))^{2}\\\
+(\mathcal{D}(\mathbf{X}_{f},\mathbf{S}_{f})-Q^{\prime}(x,s))^{2}+(\mathcal{D}(\mathbf{Y}_{f},\mathbf{S}_{f})-Q^{\prime}(y,s))^{2}]$
(5)

where $y$ represents the output of the de-generator network on the noisy
signal $x$. The objective function of $\mathcal{N}$ is given as

$L_{\mathcal{N},\mathrm{MG+/-}}=\mathbb{E}[(\mathcal{D}(\mathbf{Y}_{f},\mathbf{S}_{f})-w)^{2}],\,\,\,\mathrm{for}\,0<w<1,$
(6)

where $w$ is a hyper-parameter corresponding to the value of $Q^{\prime}$ we
train $\mathcal{N}$ to output signals with. The objective function of
$\mathcal{G}$ is the same as for MetricGAN+, as given in (2). The training of
$\mathcal{N}$ is the same as the training of $\mathcal{G}$ depicted in Fig. 2
except that $\mathcal{G}$ is replaced by $\mathcal{N}$, $\hat{s}$,
$\mathbf{\hat{S}}_{f}$ by $y$, $\mathbf{Y}_{f}$ and the $1$ in the MSE by $w$.
This means that the training of $\mathcal{N}$ is influenced entirely by its
performance as assessed by $\mathcal{D}$, in the same manner as $\mathcal{G}$.
We use an identical network structure to $\mathcal{G}$ for $\mathcal{N}$ \- We
leave to future work to change this structure, as well as related hyper-
parameters such as the clamp threshold.

The training of MetricGAN+/- is similar to that that of MetricGAN+ given above
with slight differences. Firstly $\mathcal{D}$ is trained using (5); as a
result the replay buffer now contains both enhanced and de-enhanced data,
effectively doubling its size. After $\mathcal{D}$’s training, $\mathcal{N}$
is trained using (6). Then $\mathcal{G}$ is trained as usual.

##  IV Experiments

###  IV-A Dataset

The dataset used in the following experiments is VoiceBank-DEMAND [22]. This
is a popular and commonly used dataset for single channel speech enhancement.
Its training set consists of $11572$ clean $s[n]$ and noisy $x[n]$ speech
audio file pairs, mixed at 4 Signal to Noise Ratios $0$, $5$, $10$, $15$ dB.
Eight noise files are sourced from the DEMAND [23] noise dataset - a
cafeteria, a car interior, a kitchen, a meeting, a metro station, a
restaurant, a train station and heavy traffic, and two others a babble noise
and a speech-shaped noise. The utterances in the set vary in length from
around $10$ seconds to $1$. The training set contains speech from 28 different
speakers ($14$ male, $14$ female), English or Scottish accents. The testset
containing $824$ utterances is mixed at SNRs of $2.5$, $7.5$, $12.5$ and
$17.5$ dB, with five different noises which do not appear in the training set
from the DEMAND corpus (bus, cafe, office, public square and living room) and
contains speech from two (one male, one female) speakers who do not appear in
the training set.

In order to better assess the system’s ability to generalise to unseen noise
types and recording scenarios as well as real recordings, we also assess
performance of the models trained on VoiceBank-DEMAND training set on the test
set of the CHiME3 [3] challenge dataset. This test set consists of $1320$ real
and $1320$ simulated noisy clean/speech pairs. For the real recordings the
clean ‘reference’ is a close-talk headset microphone which may also capture
some of the background noise from the recording environment. There are $6$
channels of noisy recordings; we select the $5$th channel as input to the
single channel systems as it has the most direct energy to the speaker and is
the one used in the baseline system of the CHiME3 challenge. The recording
environments of the real data and background noise of the simulated are a bus,
a cafe, a pedestrian area and a street junction. The simulated data is not
mixed at any fixed SNR, instead an ideal mixing SNR is calculated from
analysis of the clean reference and the background recording.

###  IV-B Experiment Setup

The aim of the following experiments is to compare the performance of the
baseline system MetricGAN+ which is available as part of the SpeechBrain [24]
toolkit with our extension, MetricGAN+/-. The Adam optimiser [25] with a
learning rate of $0.0005$ is used. The STFT is used with a DFT length of
$L_{\mathrm{DFT}}=$$512$, a window length of $512$ ($32$ ms) at sampling
frequency of $f_{s}=16$ kHz and a hop (overlap) length $256$ ($16$ ms),
resulting in a $50\%$ overlap between frames. The minimum value in the time
frequency masks $\mathbf{M}_{\mathcal{G}}$ and $\mathbf{M}_{\mathcal{N}}$ is
set to $\xi=0.05$.

We experiment with both PESQ and STOI as objective $Q$ and different values of
$w$. The values of $w$ are selected such that they correspond to sparely
populated values of $Q^{\prime}$ in the dataset. We also performed one
experiment (denoted by * in Table I) where the value of $\beta$ in
$\mathcal{N}$’s Learnable Sigmoid activation as given in (4) to also learned
(in addition to $\alpha$). Additionally, we experiment with reducing the size
of the replay buffer training step for $\mathcal{D}$, via modifying $H$. In
order to ensure that our performance gain does not come entirely from the
larger $H$ in MetricGAN+/-, we report also the baseline MetricGAN+ performance
with $H$ set to $0.4$.

###  IV-C Experiment Results

Table I shows the performance of MetricGAN+/- relative to the MetricGAN+
baseline and the unprocessed noisy audio on the VoiceBank-DEMAND testset. We
also compare performance with a second baseline system SEGAN [26], a state-of-
the-art speech enhancement system. For more comparison baseline performances
the interested reader is referred to Table 3 in [15], which shows that
MetricGAN+ with a PESQ objective outperforms all systems listed terms of PESQ
score. We assess this performance using PESQ and STOI and also using the
Composite [27] Measure, where Csig, Cbak and Covl are intrusive measures of
speech signal quality, background noise reduction quality, and overall quality
respectively.

TABLE I: Performance of MetricGAN+ (MG+) and MetricGAN+/- (MG+/-) on
VoiceBank-DEMAND test set for objective PESQ (P) or STOI (S), * denotes the
simulation where $\beta$ is made learnable

Model Name | Obj. | w | H | P | S | Csig | Cbak | Covl
---|---|---|---|---|---|---|---|---
Noisy | - | - | - | 1.97 | 92 | 3.35 | 2.44 | 2.63
MG+ (P) [15] | P | - | 0.2 | 3.05 | 93 | 4.03 | 2.87 | 3.52
MG+ (S) | S | - | 0.2 | 2.42 | 93.4 | 3.56 | 2.58 | 2.97
SEGAN [26] | - | - | - | 2.42 | 92.5 | 3.61 | 2.61 | 3.01
MG+ | P | - | 0.4 | 3.17 | 92.3 | 4.05 | 2.91 | 3.59
MG+/- | P | 1.0 | 0.2 | 3.20 | 93.0 | 4.08 | 2.94 | 3.62
MG+/- | P | 0.50 | 0.2 | 3.22 | 91.3 | 4.05 | 2.94 | 3.62
MG+/- | P | 0.45 | 0.2 | 3.21 | 91.9 | 4.09 | 2.95 | 3.64
MG+/-* | P | 0.45 | 0.2 | 3.17 | 93.0 | 4.16 | 2.93 | 3.65
MG+/- | P | 0.45 | 0.1 | 3.13 | 92.1 | 4.05 | 2.91 | 3.58
MG+/- | P | 0.30 | 0.2 | 3.04 | 93.0 | 4.07 | 2.88 | 3.55
MG+/- | S | 0.45 | 0.1 | 2.13 | 93.2 | 3.04 | 2.42 | 2.56
MG+/- | S | 0.30 | 0.2 | 2.31 | 93.3 | 3.19 | 2.49 | 2.72

The first four rows in Table I present the results the un-enhanced noisy data
and of different baselines. The results for the baseline MetricGAN+ models
shown here are obtained using the implementation in SpeechBrain [24]. Further
simulations are conducted for various values of hyperparameter $w$ used in the
training of $\mathcal{N}$. Table I shows a clear improvement in PESQ score for
PESQ objective MetricGAN+/- models over the baseline MetricGAN+ ($3.05$ vs
$3.22$ PESQ), and also versus the PESQ value reported in [15] of $3.15$. We
also observe increase in the composite measure scores. Interestingly, there is
an improvement even when $w=1$, which is the case where $\mathcal{N}$ and
$\mathcal{G}$ have the same objective, and thus $\mathcal{N}$ also learns to
enhance. We hypothesise that this is due to slight variations in the outputs
of $\mathcal{N}$ and $\mathcal{G}$ during training, as well as the increased
replay buffer size compared to the baseline. Highest performance in terms of
PESQ score is obtained with a $w$ value set to 0.5, which means that
$\mathcal{N}$ attempts to produce signals with a PESQ score of 3. We speculate
that this performance increase is due to there being few clean/noisy pairs in
the training set with a PESQ score around this value.

By making the $\beta$ parameter in $\mathcal{N}$’s activation function
learnable, we observe a slight improvement against the baseline, as well as
increased Csig and Covl scores versus all other simulations. We find also that
increasing $H$ in the baseline MetricGAN+ from $0.2$ to $0.4$ such that its
size is comparable to MetricGAN+/-’s does slightly improve PESQ score. This is
contrary to the findings in [15] where they report no improvement for values
larger than $0.2$. Larger values of $H$ will drastically increase the training
time requirement of the system. We speculate that a better understanding of
what $\mathcal{D}$ leans from the replay buffer training and better curation
of its contents is the key to further performance gains, as well as reduced
training time required.

###  IV-D Spectogram Analysis

Fig. 4 shows the spectrograms of the clean reference $|\mathbf{S}|$, noisy
input $|\mathbf{X}|$, generator output mask $\mathbf{M}_{\mathcal{G}}$ and
this mask applied $|\mathbf{\hat{S}}|$ for baseline MetricGAN+, MetricGAN+/-
($w=0.45$) PESQ objective models. The mask in Fig. 4 (e) attempts to remove
low frequency signal content while boosting the area corresponding to the
frequency curve of the fundamental speech frequencies. Futhermore, the
baseline MetricGAN+ PESQ model in Fig. 4 (c, d) attenuates the signal in the
initial non speech region, while the MetricGAN+/- model in Fig. 4 (e, f)
suppresses less energy around $400$ Hz over the whole utterance.

(e)
---
(f)
---
(MG+/-) $\mathbf{\hat{S}}_{f}$
---
(MG+/-) $\mathbf{M_{G}}$
---
$\mathbf{S}_{f}$
---
(a)
---
(b)
---
$\mathbf{X}_{f}$
---
(c)
---
(MG+) $\mathbf{M_{G}}$
---
(d)
---
(MG+) $\mathbf{\hat{S}}_{f}$
---

Figure 4: Spectograms of: (a) clean reference features $\mathbf{S}_{f}$, (b)
noisy features $\mathbf{X}_{f}$, (c) Mask $\mathbf{M}_{\mathcal{G}}$ and (d)
enhanced output $\hat{S}_{f}$ for MetricGAN+ baseline PESQ objective model,
(e) Mask $\mathbf{M}_{\mathcal{G}}$ and (f) enhanced output $\hat{S}_{f}$ for
MetricGAN+/- PESQ objective model. Source audio file is p232_014.wav of
VoiceBank-DEMAND testset.

This artefact can already be observed in the baseline MetricGAN+ but is more
prominent for the proposed method, which could explains the relatively low
Cbak score for this method. We hypothesise that this is a results of
$\mathcal{D}$ not learning to properly penalise errors in this region, perhaps
due to the additional influence of $\mathcal{N}$’s outputs on it’s training.
Further experimentation is required to fully understand this artefact.

###  IV-E Generalisation To Unseen Data

TABLE II: Performance on real component of CHiME3 test set

Model Type | PESQ | STOI | Csig | Cbak | Covl
---|---|---|---|---|---
Noisy | 1.37 | 44.0 | 2.96 | 1.42 | 2.09
MG+ PESQ | 1.54 | 45.8 | 2.67 | 2.09 | 2.00
MG+ STOI | 1.24 | 44.7 | 2.45 | 1.84 | 1.76
MG+/- PESQ | 1.76 | 44.3 | 2.86 | 2.03 | 2.20
MG+/- STOI | 1.22 | 45.3 | 2.31 | 1.81 | 1.67

TABLE III: Performance on simulated component of CHiME3 test set

Model Type | PESQ | STOI | Csig | Cbak | Covl
---|---|---|---|---|---
Noisy | 1.27 | 87.0 | 2.61 | 1.39 | 1.88
MG+ PESQ | 2.14 | 87.4 | 3.05 | 2.31 | 2.53
MG+ STOI | 1.52 | 88.9 | 2.75 | 2.07 | 2.08
MG+/- PESQ | 2.38 | 86.1 | 3.17 | 2.41 | 2.70
MG+/- STOI | 1.47 | 88.5 | 2.62 | 2.02 | 1.99

Tables II and III shows the performance of the baseline MetricGAN+ and the
best performing proposed MetricGAN+/- systems on this test set. We observe an
increased performance in terms of PESQ, Csig, Cbak and Covl between PESQ
objective MetricGAN+/- and the baseline, as well as a slight improvement in
STOI score for STOI objective MetricGAN+/-. This suggests that $\mathcal{D}$’s
access to the de-generated signals produced by $\mathcal{N}$ allows
$\mathcal{G}$ in MetricGAN+/- systems to generalise better to unseen
environments.

##  V Conclusion

In this work, we present an extension to the MetricGAN+ baseline framework,
which improves its performance in terms of PESQ score and related measures, as
well as improving its generalisation to unseen data. We find that training the
discriminator network on a wider range of metric scores and with a larger
replay buffer achieves greater performance that the baseline system.

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  *[h2h]: human-to-human
  *[h2m]: human-to-machine
  *[NN]: neural network
  *[NNs]: neural network
  *[PESQ]: Perceptual Evaluation of Speech Quality
  *[STOI]: Short-Time Objective Intelligibility
  *[MOS]: Mean Option Score
  *[GAN]: Generative Adversarial Network
  *[STFT]: Short Time Fourier Transform
  *[OLA]: Overlap-Add
  *[MSE]: mean squared error
  *[SNR]: Signal to Noise Ratio


# Analysis of bio-electro-chemical signals from passive sweat-based wearable
electro-impedance spectroscopy (EIS) towards assessing blood glucose
modulations

Devangsingh Sankhala  Department of Electrical Engineering, The University of
Texas at Dallas, 800 W Campbell Rd, Dallas 75080 TX, USA  Madhavi Pali
Department of Bioengineering, The University of Texas at Dallas, 800 W
Campbell Rd, Dallas 75080 TX, USA  Kai-Chun Lin  Department of Bioengineering,
The University of Texas at Dallas, 800 W Campbell Rd, Dallas 75080 TX, USA
Badrinath Jagannath  Department of Bioengineering, The University of Texas at
Dallas, 800 W Campbell Rd, Dallas 75080 TX, USA  Sriram Muthukumar  EnLiSense
LLC, 1813 Audubon Pond Way, Allen 75013 TX, USA  Shalini Prasad  Department of
Bioengineering, The University of Texas at Dallas, 800 W Campbell Rd, Dallas
75080 TX, USA

###### Abstract

There has been a recent tremendous interest in label-free detection of
biomarkers which is a critical enabler of point-of-need diagnostics.A low-
power, small form factor, multiplexed wearable system is proposed for
continuous detection of glucose in passively expressed sweat using
electrochemical impedance spectroscopy (EIS) measurement. The wearable EIS
system consists of a sensing analog front end integrated with a low-volume
(1-5 $\mathrm{\mu}$L) ultra-sensitive flexible biosensors. A passive sweat
sensor was designed integrating glucose oxidase electrochemical system on an
active semiconducting material. The non-faradaic EIS response of the biosensor
was used to calibrate the analog front end’s response using ratiometric
Discrete Fourier Transform (DFT) for a shorter measurement time. In this work,
a stringent assessment of a continuous glucose sensing platform is performed
in a bottom-up approach, going from the biosensor to the system system to the
interaction with a human subject. The active semiconductor-based biosensors
are dosed with glucose concentrations ranging from 5-200 mg/dL and detection
is performed using the analog front end. In addition, detailed analysis of
battery life and performance of a wearable EIS system is discussed to define a
figure of merit for an optimally integrated design. Moreover, a continuous
glucose detection test is performed on a healthy human subject cohort to
investigate the stability of sensor-system mechanism for an 8-hour period and
a time-series based, auto-regressive (AR) model was created for the system.

###### keywords:

Glucose biosensing, electrochemical impedance spectroscopy, discrete Fourier
transform, time division multiplexing, figure of merit, time series analysis,
auto-regression

## Introduction

There is a significant interest in wearable biosensing platforms in the recent
times. Constant improvements are being made in developing accurate and robust
sensing mechanisms for various biomolecules of interest that demonstrate
temporal dynamics. Wearable biosensors are enablers for point of need tracking
of chronic conditions and can be beneficial both to the user as well as the
healthcare professional in guided therapy [1]. Glucose is a key biochemical
marker with temporal dynamics in context to monitoring chronic health
condition of diabetic patients. Current technologies to monitor blood glucose
in small and/or wearable form factors still require frequent finger pricks or
needle based interstitial blood glucose monitoring methods such as the Abbott
Freestyle Libre or the Dexcom G6 to be integrated with pedometers and other
lifestyle management tools towards achieving patient actionable glycemic
control. Glucose biosensors, found commercially as well as in literature,
implement a microneedle-based, chronoamperometry [2, 3, 4, 5] and square-wave
voltammetry [6] biosensor compatible for wearable devices, due to ease of
electrical circuit implementation. These sensors may provide good sensitivity
at the cost of larger sample volumes of interstitial fluid or sweat to adhere
to acceptable CGM standards [7]. Moreover, due to larger settling time of
current, density gradients cause undesirable convective disruption of the
diffusion layer [8]. In addition, large settling time of an amperometric
sensing scheme results in relatively higher current consumption.

There is an immense opportunity in designing a wearable electronic system
towards supporting such point-of-need sensing applications with low-volume,
true no-needle insertion mechanisms. A case study of such a system is
performed here by coupling a low-volume passive sweat biosensor [9] with a
rapid response electrochemical impedance spectroscopy (EIS)-based system [10].
The proposed glucose reporting mechanism utilizes passively expressed system
sweat towards achieving quantitative decision making; therefore low sample
volume makes it prone to erroneous measurement in a real-world scenario. Error
can be defined as a property of the system which introduces a deterministic
undesirable offset in the measured outcome of the device. In this context,
deterministic offset would mean an offset that can be mathematically
represented using a polynomial. On the other hand, noise is a probabilistic
property of the system which introduces a random offset in the measured
outcome of the system and is modeled as a probability distribution function.
The presence of relatively higher noise and error affects the battery
performance of a device as it would require more samples to average or filter
out the undesirable signal counterpart. In this work, the sensor’s impedance
change is reported and correlated to the conventional statistical methods to
establish good sensitivity. Continuous sensing of glucose dose concentration
and differentiation of normal and hyperglycemic rate of change of glucose is
demonstrated in a healthy cohort of 20 subjects, using an auto-regressive
model, in comparison to an interpolated sweat glucose time series.

## Results

### Calibration of the system using lumped elements

The proposed system was tested for individual channel offset on the
calibration channel of a universal dummy cell (Gamry Instruments). Fig. 2
shows the variation of measured impedance of the universal dummy cell using n
= 3 replicates of that same system. It is seen that the measured impedance.
The accuracy of the device is demonstrated in Fig.2a over n = 3 devices over a
single channel. The expected calibration impedance at $100Hz$ was $4k\Omega$.
However, a systematic negative offset of $50\Omega$ is observed with a
variability of $50\Omega$ on the measured impedance. This accounts for a
$1.25\%$ inter-device variation along with a $-1.25\%$ error. The precision of
a single device replicate is observed by taking n = 100 measurements for all
four channels using the universal dummy cell. The peak inter-channel
variability of $\leavevmode\nobreak\ 150\Omega$ is observed.

### Calibration dose response of the system

Glucose dose concentrations ranging from 5-200 mg/dL were made in synthetic
sweat buffer with pH values 4, 6 and 8 were introduced on a functionalized
sensor and the impedance at $100Hz$ was recorded to demonstrate proof of
binding interaction on the sensor surface. Fig. 3a shows the response of the
system as standard error of mean of the percentage change function of
impedance impedance to varying pH and dose concentrations with a linear fit.
Eqn. 1 shows the mathematical percentage change of the measured impedance used
to plot dose response. The system response shows $\leavevmode\nobreak\ 3\%$
standard error on most of the dose concentrations thus demonstrating precision
of measurement.

$\text{Percentage change in Z}=\%\Delta
Z=\dfrac{Z-Z_{baseline}}{Z_{baseline}}$ (1)

Box-whisker plots were created as shown in Fig 3b to investigate the
variability of the system response for a given dose concentration irrespective
of buffer pH. The true variability of the sensor response was observed to be
$\leavevmode\nobreak\ 10\%$ inter-sample variation in the form of inter-
quartile region height of each of the glucose dose concentrations. It can be
observed that even with a larger variability, the median divides the inter-
quartile region symmetrically, demonstrating a Gaussian distribution. However,
there is a need to model this variation as a mathematical relationship to
allow accurate detection as well as differentiation of glucose dose
concentrations across the dynamic range.

### Identification of sources of noise and error

Noise is an undesirable measured quantity that accompanies a true measured
quantity. This introduces an amount of uncertainty in the accuracy and
repeatability of the measurement device. Sources of noise have been well
characterized for CMOS devices in the past [11, 12]. Primarily, the two major
sources of noise discussed in academic as well as industrial design are
thermal noise and flicker noise for complementary metal-oxide-semiconductor
(CMOS) transistors. Thermal noise is a result of electrical fluctuations
caused by thermal energy [12]. This electron motion is popularly known as
Brownian motion. The RMS noise voltage is expressed as in Eqn. 2 where $k$ is
the Boltzmann constant, $T$ is the absolute temperature in kelvin and $R$ is
the resistance of the device under test. Thus, thermal noise will increase
with rise in temperature. In CMOS transistors, this noise is a summation of
the noise generated by the gate and channel resistance. In case a capacitor is
connected in parallel with the resistive noise source, the RMS thermal noise
is denoted as in Eqn. 3. Thus, thermal noise can be controlled using a shunt
capacitor [13].

$\bar{v}_{n,thermal}=\sqrt{4kTR}$ (2)
$\bar{v}_{n,thermal,RC}=\sqrt[]{\dfrac{kT}{C}}$ (3)

Flicker noise or popularly known as 1/f noise is the resultant of attractive
forces at the silicon-oxide interface in a CMOS transistor giving rise to
several energy states [13, 11]. The RMS flicker noise is expressed as in Eqn.
4 where $K$ is a statistically calculated, process dependent parameter, $W$
and $L$ are the dimensions of the transistor, $C_{ox}$ is the capacitance of
oxide film per square and $f$ is the frequency of interest. Thus, 1/f noise is
a function of frequency, and is a source of error for low frequency circuits.

$\bar{v}_{n,1/f}=\sqrt[]{\dfrac{K}{WLC_{ox}}.\dfrac{1}{f}}$ (4)

A noise model proposed by Hassibi and others [14] is used to provide a noise
treatment for the biosensors mentioned in this work. For a non-faradaic
electrode-electrolyte interface, the valence of the electrolyte is $z$. In
addition, the measurement is performed for a single frequency, thus the
bandwidth of the system is 1 Hz. Fig 1c shows the incremental circuit model
established using impedance measurements in Munje et. al. [9] and this work.
Three noise sources due to $R_{s}$, $R_{ASA}$ and $R_{ct}$ can be identified
using previously mentioned noise equations. Moreover, the measurement device’s
response time of 13 ms is smaller than the biosensor’s response time of 5
minutes. Based on these assumptions [14], a noise model was proposed for the
biosensor used in this work as shown in Fig. 1d, which was derived from Fig.
1c [9] by dividing the cross-section of the sensor in three parts.

Since an active semiconducting film is a partially conductive film with some
resistance based on its doping levels, it is prone to a noise voltage similar
to a resistor and can be modeled as a thermal noise source. However,
considering semi-conducting properties of the film in mind [15], it can be
assumed that there is a presence of $1/f$ noise due to this film, which is a
result of charge carrier generation as well as recombination. However, since a
capacitance $C_{ASA}$ exists in parallel with the noise sources, this noise
can be modeled as a $kT/C$ noise of the active semiconducting film.
Considering the biosensing electrical double layer and charge transfer
resistance, these are modeled to be circuit components for an ideal polarized
electrode (IPE), however, they are imperfect in a real scenario. Thus, the
noise of this region can be assumed to be a variation in the current density
of the charge carriers depending upon the strength of the electrical
potential, which in turn depends on the location of the slip plane. However,
since the ion motion is slower than an electron’s motion, a function
$M(\omega)$ is used to model the frequency dependent effect of this current
noise source. The solution resistance is a bulk effect and can be assumed to
be a resistor, thus the thermal noise effect. The final expression of the
noise voltage would be a summation of all these noise sources as given in Eqn.
5.

$\bar{v}^{2}={4kT(R_{s}+R_{electrode})+2zqI.M(\omega).(R_{ct}||\dfrac{1}{j\omega
C_{dl}})+\dfrac{kT}{C_{ASA}}+\dfrac{K}{WLC_{ox}}.\dfrac{1}{f}}$ (5)

The veracity of this model is confirmed using a noise test for 30 minutes on a
non-functionalized sensor surface wet with 1X phosphate saline buffer(PBS)
using a high-speed potentiostat (Zurich Instruments, Switzerland). Fig. 2c
shows the variation of noise spectra at an interval of 5 minutes. The noise
voltage follows a trend inversely proportional the the frequency and is
maximum at t=5 minutes, whereas it decreases with time and is at a minimum at
t=30 minutes at 100 Hz excitation frequency. Thus, as the introduction of PBS
reaches an equilibrium, the noise amplitude of the system start decreasing
with respect to 100 Hz excitation frequency. The RMS noise voltage is shown in
Fig. 2b.

Mean absolute relative difference (MARD) [16] was used to emphasizes that
noisy measurements are a function of the true measurement and a summation of
systematic bias and coefficient of variation, to establish reliability of the
wearable biosensor. This expression is given as in Eqn. 6 where $\hat{G}$ is
the noisy measurement, $G$ is the true measurement, $\%b$ is the systematic
bias obtained from the measurement system’s properties, $\%cv$ is the
coefficient of variation among each sample for the given dose step and
$\epsilon_{n}$ is a standard random variable. Thus, the systematic bias will
be a constant offset correction where as the standard variable which accounts
for variation from external environmental effects in a band limited by $\%cv$.

$\hat{G}=G(1+\%b+\%cv\times\epsilon_{n})$ (6)

This approach can be used to characterize sources of variability in system
performance. Systematic offset can be observed as a result of device accuracy
and precision, offset of the measurement device and specific signal threshold
of the biosensor. Coefficient of variation arises from sample-to-sample
variation and is calculated as a ratio of standard deviation to mean for a
given dose concentration. In addition, environmental factors such as
temperature, relative humidity, variation in volume dispensed, etc. play an
important part in the system’s response. However, it would be an extensive
effort to characterize for each of them separately and superimpose. A standard
normal variable can be used to account for all these variations. Thus,
variation is accounted for statistically, whereas systematic offsets are
accounted for by observation and nullified by software when using Eqn. 6.

Variable |  Source of error |  Value |  Comments
---|---|---|---
%b |  Non-functionalized biosensor electrical noise ($thermal+1/f$) |  0.35% to 2% |  Variation of RMS noise of the sensor with respect to excitation voltage = 10 mV RMS
Instrumentation loop offset |  -1.25% |  Offset in impedance mesaurement for $Z_{cal}=3990\Omega$ at $f=100Hz$
|  Biosensor specific signal threshold |  11% |  Y-intercept=11% for sensor output impedance response from Fig. 3a at buffer pH = 4.
%cv |  Biosensor-dependent sample-to-sample variation |  8% to 10% |  Variation @ $f_{s}=100Hz$ observed in Fig. 3b.
Instrumentation loop variability |  -0.4% to -1.5% |  Sample-to-sample variation of impedance mesaurement for $Z_{cal}=3990\Omega$ at $f=100Hz$
Table 1: A simplified MARD model for the proposed wearable platform was
created using sources of error as a percentage component of the device under
test in a real world environment in the presence of noise.

### Performance metrics for wearable devices

There is a need to encompass all important specifications as one numerical
expression to represent the performance of an electrical design in question
relative to other alternative designs. This numerical expression is called the
figure of merit (FOM). Such a design comparison is very popular among data
conversion designs [17] and is defined as the energy required for one data
conversion. For deciding an expression for the figure of merit of a design,
the system was split into the measurement device and the biosensor and their
inherent properties were observed.

For the measurement device, the ultimate objective to be achieved would be
very similar to a data conversion system, i.e. achieving a low power
consumption per every measurement performed. Similarly, the capability of the
device to measure with minimal power will be observed by varying operating
conditions. A battery operated device is generally operated at a very low,
sleep-mode supply current. However, the device requires a comparatively larger
amount of current to operate in an active state. Thus, for such an uneven
distribution of current, an average over the time taken by the device to
execute the program from start to end. Thus, the battery selection for a fixed
average current is performed as follows. Let the sleep current of the device
in question is $I_{sleep}$ for time $t_{sleep}$ and the active current of the
device is $I_{active}$ for time $t_{active}$. Since the device completes one
program cycle, the total time for one program cycle $t_{total}$ is the
summation of $t_{sleep}$ and $t_{active}$.

$t_{total}=t_{sleep}+t_{active}$ (7)
$I_{avg}=I_{sleep}\times\dfrac{t_{sleep}}{t_{total}}+I_{active}\times\dfrac{t_{active}}{t_{total}}$
(8)

The figure of merit (FOM) of an electrical device can be defined as the energy
spent to convert a physical sensor signal at an instant of time. However, to
demonstrate the increased throughput capacity of the device against power
consumption, parameters $n$ and $p$ were included, where $n$ as number of
sensors channels available by design and $p$ is the number of points per one
measurement cycle. Here, one measurement cycle implies measuring all points
until settling for amperometric designs, or one sweep from lowest to highest
frequency in impedance spectroscopy designs. For the proposed design, the
figure of merit is calculated for $n=4$, $p=10$, $NBITS=16$,
$f_{s}=\dfrac{1}{13ms}$ as one conversion period. The voltage is assumed to be
$3.7V$ as of a standard lithium polymer battery. Thus, an FOM of $19nJ/point$,
or $190nJ/sweep$ was obtained.

$\text{FOM}_{\text{device}}=\dfrac{npV_{batt}I_{avg}}{f_{s}\times 2^{NBITS}}$
(9)

A biosensor is expected to demonstrate a large dynamic range with a low order
curve fit equation for lesser computation requirement and low power
consumption. Moreover, it is expected that the biosensor is sensitive to the
very low concentrations of biomarkers of interest. Thus, the figure of merit
(FOM) of a biosensor can be defined as in Eqn. 10, where a relative percentage
value of the specific signal threshold and linear dynamic range are
considered. thus, higher the FOM, higher the ease of integration irrespective
of dissimilar sensor, measurement device or electrochemical technique used or
any combination of the former.

$\text{FOM}_{\text{sensor}}=\dfrac{\%LDR}{\%SST}$ (10)

The above mentioned figures of merit of individual system sub-blocks define
the efficiency of the device to perform under trade-offs under the designer’s
control. However, if these are inconsistent between two sub-blocks of a
system, the integrated system may function inaccurately due to a cumulative
effect of errors generated by individual sub-blocks. To ensure maximum
integrability of the measurement device and the biosensor, an attempt was made
to mathematically define a statistical relationship between sub-block
accuracy. Accuracy $A$ of a quantity is defined as the difference between the
actual value $x$ of the quantity and the ideal or true value $X$ of the
quantity as shown in Eqn. 11. Similarly, mismatch between two quantities
$x_{1}$ and $x_{2}$ is the difference between the actual ratio of the
quantities and the desired ratio of the two quantities as shown in Eqn. 12.
For the proposed biosensor, the FOM of 11.87 if obtained for $\%LDR=95\%$ and
$\%SST=8\%$.

$A=\dfrac{x-X}{X}=\dfrac{\Delta x}{X}$ (11)
$\delta=\dfrac{\dfrac{x_{2}}{x_{1}}-\dfrac{X_{2}}{X_{1}}}{\dfrac{X_{2}}{X_{1}}}$
(12)

Both the accuracy and mismatch numbers should be zero for a perfectly non-
erroneous measurement, which is a highly unlikely in the presence of sources
of variation and noise. Thus, this specification helps a system integrator to
analyze the quality of sub-blocks available and investigate methods of error
compensation, either by hardware or software. For the proposed system system,
for simplicity it is assumed that the since the measurement device and the
biosensor are made of different materials, the offsets are uncorrelated, thus
additive. The accuracy of the measurement device is 1.25% as per Fig. 2a
whereas the accuracy of the biosensor is $10\%$ as per the Fig. 3b. Thus, the
mutual mismatch as a resultant of coupling both would be $\delta=-0.875\%$ as
per Eqn. 12. For an optimal system level design, $\delta\rightarrow 0$ thus
demonstrating the robustness of integration.

### Continuous measurement testing

The dose calibration response of the sensor describes the accuracy of the
system at a given steady state. In contrast, real-world applications demand
the need for providing a steady sensor output irrespective of change in
environmental conditions. A method of conversion of impedance measurements to
real-time glucose measurements would bridge the gap between the sensor output
and the much-needed user information to be generated. Such a multi-variable
problem can be solved using predictive methods for time-series based analysis.
Various models such as auto-regression[18, 19] and neural network based
approach[20, 21, 22, 23, 24] have been used, as they consider the previous
input, the previous output and the current input of the system. Also, these
models have been created using interstitial fluid (ISF) based continues
glucose monitoring systems (CGM), hence these are not based on non-invasively
sampled data sets.

A more simplistic approach is the application of time-series analysis to
measurements provided by the proposed system. The system was put on N=20 human
subjects for a period of 8 hours, wherein their glucose sensor output, skin
temperature, skin humidity was measured continuously while 4 sweat samples
were collected per subject. The sweat sample was used to measure sweat glucose
levels using a reference method. Since only 4 reference points were available
considering the limitations of the IRB, an interpolation curve was created
using the 4 reference points to match the length of output of the system.

$y=X_{1}\beta_{1}+...+X_{10}\beta_{10}+\mu_{t}$ (13)
$(1-\phi_{1}L-...-\phi_{10}L^{10})\mu_{t}=(1+\theta_{1}L+\theta_{2}L^{2}+\theta_{3}L^{3})\epsilon_{t}$
(14)

ARIMA(p,d,q) is one of the most commonly used curve fit functions used for
time-series analysis, where $p$ is the order of auto-regressive (AR) terms,
$d$ is the number of integrating terms and $q$ is the number of moving
-average (MA) terms. For the above data set, $p$ was determined using the
number of significant peaks in the auto-correlation plot of the primary
predictors impedance magnitude (Zmod) and first differential of impedance
magnitude (dZmod), which shows a change in sensor response with change in
glucose concentration as per dose calibration. Figs. 4a,4d show 2 extreme
cases among the 20 data set, wherein the auto-correlation plot shows 5 initial
lag peaks for subject 1 and 10 initial lag peaks for subject 2, which exceed
the $3\sigma$ confidence interval. Hence, the maximum peaks defined $p=10$.
The ARIMA(10,0,3) regression curve fit used for the above data sets is given
in Eqn. 13 and Eqn. 14, where $y$ is the output, $X$ are the input values for
the predictors, $\beta$ are the coefficients obtained from regression ARIMA
fit, $\mu_{t}$ is the variance, $L$ is the lag operator, $\theta$ are the
moving average coefficients and $\epsilon_{t}$ is Gaussian white noise.

The coefficients of the ARIMA(10,0,3) curve fit are shown in Table 2. The
p-value for a given predictor defines its significance in predicting the
output time series, which is the interpolated sweat glucose value. If
$p<0.05$, then the predictor is assumed to be significant as it rejects the
null hypothesis, else the predictor can be assumed to be non-significant,
hence can be removed from the curve fit expression. In this case, predictors
$AR4$ can be safely assumed to be not contributing to the prediction. The AIC
of this curve fit was $-3131.438$, ensuring good curve fit and low prediction
error. This is corroborated by the ARIMA outputs plotted against the
interpolated glucose values in Figs. 5a, 5b. The error histogram is shown in
Fig. 5c, demonstrating a low predicted sweat glucose error with respect to the
interpolated sweat glucose measurements.

Predictor |  Value |  Std. Error |  t-stat |  p-value
---|---|---|---|---
Intercept |  2.2236 |  0.0011792 |  1885.6396 |  0
AR1 |  1.1696 |  0.016376 |  71.4217 |  0
AR2 |  -0.79248 |  0.015316 |  -51.7426 |  0
AR3 |  0.71839 |  0.044644 |  16.0916 |  2.9197e-58
AR4 |  0.10234 |  0.044076 |  2.322 |  0.020235
AR5 |  -0.22962 |  0.032213 |  -7.1282 |  1.0166e-12
AR6 |  0.1 |  0.034417 |  2.9055 |  0.0036662
AR7 |  -0.20436 |  0.034488 |  -5.9257 |  3.109e-09
AR8 |  0.11278 |  0.03253 |  3.4668 |  0.00052668
AR9 |  -0.075336 |  0.032725 |  -2.3021 |  0.021328
AR10 |  0.085203 |  0.026248 |  3.246 |  0.0011702
MA1 |  -0.60583 |  0.017528 |  -34.5629 |  9.1092e-262
MA2 |  0.7133 |  0.024382 |  29.255 |  3.8771e-188
MA3 |  -0.40103 |  0.050977 |  -7.8668 |  3.6377e-15
Beta(Zimag) |  -0.00025308 |  4.887e-06 |  -51.7866 |  0
Beta(Zmod) |  0.00054978 |  1.1027e-05 |  49.8589 |  0
Beta(Zphase) |  -0.023363 |  0.0014868 |  -15.7133 |  1.2261e-55
Beta(Zreal) |  -0.00047466 |  9.8819e-06 |  -48.033 |  0
Beta(dZimag) |  -5.2582e-06 |  6.8561e-07 |  -7.6694 |  1.7285e-14
Beta(dZmod) |  -7.0023e-06 |  1.5741e-07 |  -44.4853 |  0
Beta(dZphase) |  -0.0045203 |  0.0022546 |  -2.0049 |  0.044974
Beta(dZreal) |  1.1458e-05 |  6.5176e-07 |  17.5794 |  3.5439e-69
Beta(rh) |  -0.022069 |  0.00070336 |  -31.3763 |  4.2615e-216
Variance |  0.0075866 |  0.00025797 |  29.4091 |  4.2045e-190
Table 2: Values of ARIMA regression coefficients along with standard error, t-statistic and p-value as obtained from fitting on test data sets. Specification |  Jalal et. al. [3] |  Lee et. al. [2] |  This work
---|---|---|---
Sensing mechanism |  chronoamperometry |  chronoamperometry with potential pre-stabilization |  EIS
Front end |  LMP91000 + reference generator + DAC + passive 2nd order filter |  MAX4617 (analog mux) + MAX7405 (8th order filter) + AFE4490 (amperometric front end) |  ADuCM350
Sensor + electronic response time |  200 s (OCP) + 200 s (chronoamp) |  60 s (pre stabilization) + 180 s |  180 s + 13 ms
Processor |  TI MSP430F5229 |  ATMEGA328 |  ADuCM350
Sensing algorithm |  hysteresis (hard thresholds) on OCP + chronoamperometry |  temperature and PPS based normalization (guarantees accuracy ) |  auto-regression
Battery size |  1000 mAh |  N/A |  300 mAh
Peripherals |  Bluetooth, BMS, EEPROM |  Bluetooth, BMS, SpO2, PPG, temperature |  BLE, BMS, temperature, RH
Table 3: Electrical comparison of specifications of system level designs
reported in literature.

## Discussion

Various electrochemical techniques such as cyclic voltammetry,
chronoamperometry and impedance spectroscopy techniques exist for the
characterization of electrochemical cells and have been successfully employed
for biosensing applications. However, there has been less interest in design
impedance spectroscopy device due to increased complexity required for phase
as well as magnitude detection on the hardware aspect. Moreover, added
hardware increases the size and power consumption on a system level scale for
most designs. Thus, the first wearable, electrochemical impedance spectroscopy
system is proposed for glucose detection in sweat with a battery lifetime of
215 hours. Moreover, a small form factor of the device is demonstrated by
implementing a monolithic SoC with an EIS dedicated front-end with four
channel sensing. Table 3 compares the electrical specifications and system
level mechanism in general to highlight the advantages of using an impedance
based spectroscopy design over an amperometric design.

The proposed biosensor is capable of sensing glucose concentrations in sweat
from 10 mg/dL to 200 mg/dL in various synthetic sweat buffers of various pH
values. Moreover, the stability of the sensor response is established not only
from a conventional statistical approach, but also using sample-to-sample
variation observations and demonstrates a 20% variability similar to safe
limits on a Clarke Error Grid. In addition, for the first time, a semi-
quantitative method of detecting rate of change of glucose is proposed for
aiding real-time diagnostic efforts using a slope feature extraction algorithm
on the impedance response of the sensor. This algorithm also demonstrates a
rate-of-change occurrence probability-based reduction in time complexity,
leading to low power operation on a wearable platform.

From a system level perspective, this work is a first attempt to dive into the
specifics of interdisciplinary system integration for biosensing applications.
A simplistic noise model for the biosensor is demonstrated along with noise
measurements to correlate with change of noise behavior in time based on
conventional electrical circuit noise analyses. The analysis is tested against
noise measurements made on a high-speed potentiostat and mathematically
verified. In addition, the accuracy of the measurement device is identified
and coupled to a source of error which corroborates the MARD based analysis of
sample-to-sample variability. Finally, a mismatch expression is proposed to
demonstrate low mismatch due to coupling of the biosensor and the measurement
device with a mismatch coefficient of -0.875%.

## Methods

### Sensor fabrication

Fig. 1a shows the cross-sectional view of the chemi-impedance biosensor and
the formation of the immunoassay on the functionalized surface. The biosensor
substrate is a 100 $\mu$m thick,flexible nanoporous polyamide substrate (GE
Lifesciences, NJ). Gold electrodes were patterned using shadow mask and
deposited using e-beam cryo-evaporator. ZnO thin films were sputtered onto
patterned in the area between the two gold electrodes to get maximum overlap
using an AJA Orion RF magnetron with a 99.999% ZnO target (Kurt J. Lesker) at
room temperature [9].

### Materials for implementing glucose assay

Poly-amide substrates with 0.2 $\mu$m pore size were obtained from GE
Healthcare Life Sciences (Piscataway, NJ, USA). The linker molecule dithiobis
[succinimidyl propionate] (DSP) and its solvent dimethyl sulfoxide (DMSO) were
ordered from Thermo Fisher Scientific Inc. (Waltham, MA, USA). The monoclonal
glucose oxidase antibody was obtained from Thermo Fisher Scientific Inc.
(Waltham, MA, USA). Glucose oxidase from Aspergillus niger and D(+)-glucose
was obtained from Sigma-Aldrich (St. Louis, MO, USA). The glucose antibody was
diluted in 1X phosphate buffered saline (PBS, Thermo Fisher Scientific Inc.,
Waltham, MA, USA). Synthetic sweat was prepared as per the recipe stated in
M.T. Mathew et al. The pH range is varied by varying the concentration of the
components. Human sweat was purchased from Lee Biosolutions Inc. (St. Louis,
MO, USA), where it was collected from single human donor with pH $\approx$
4–5. No preservatives have been added to this product and it was stored
unfiltered at below - 20 °C [9].

### Wearable EIS device disassembly

The wearable EIS device used for experiments in this work is shown in Fig. 1f.
The design is primarily divided into two parts: a mother board and a daughter
board. The motherboard houses the integrated circuits required for measurement
and communication. The daughter board houses four flexible biosensors using
slide-in connectors. The daughter board connects to the motherboard using a
slide-in connector as well. The motherboard is further divided into four
subsections. The first subsection is the ADuCM350 system-on-chip (SoC) (Analog
Devices Inc.) which is the heart of the wearable platform. It is equipped with
an impedance analyzer block which gives the real and imaginary part of an
unknown impedance using a ratiometric discrete Fourier transform (DFT)
accelerator. The second subsection is the nRF8001 (Nordic Semiconductor ASA)
Bluetooth Low Energy (BLE) chip-set which communicates with a mobile
application. The third subsection is the temperature and RH sensing which was
implemented using HDC1080 (Texas Instruments Inc.). The fourth subsection is
the power management system implemented using BQ24040 (Texas Instruments
Inc.). This subsections supplies power to the other subsection either using a
lithium battery or USB and manages the charge-discharge cycle of the lithium
battery.

### Glucose sensor experimental protocol

Gold surface was functionalized with 3 $\mu$L of 10 mmol DSP linker after
incubation for 2 hours. The PBS wash was carried out followed by 15 min
incubation of 3 $\mu$L of 10 $\mu$g/mL glucose oxidase antibody. Thereafter, 3
$\mu$L of 1 mg/mL glucose oxidase enzyme obtained from Aspergillus Niger is
dispensed. Serial dilutions of glucose in synthetic sweat were prepared to
range from 5 mg/dL to 200 mg/dL, which were dispensed after antibody
incubation. Each glucose concentration was incubated for 5 minutes on the
sensor surface prior to measurement. Sensor calibration response was obtained
in human sweat with increased glucose concentration doses from 5 mg/dL to 200
mg/dL with n=4 replicates of chips. Two test sample chips with 5 mg/mL and 200
mg/mL glucose concentration doses on each were also measured. The average
readings were then compared with the values obtained from calibration dose
response in human sweat. These EIS measurements were performed by recording
current flow using ADuCM350 after applying 10 mV AC voltage with a frequency
of 100 Hz.

### Human subject enrollment

Human subjects for sweat sample collection and on-body continuous measurement
in compliance with the protocol approved by Institutional Review Board (IRB)
at the University of Texas at Dallas (IRB number 19-146). A written and
informed consent was obtained from all participants of this study. A study was
performed on 20 subjects to collect sedentary sweat glucose, skin temperature
and RH over a period of 8 hours in compliance with the (IRB number 19-146)
approved at the University of Texas at Dallas. All subjects belonged to the
age range of 18-40 years with no prior diagnosis of diabetes mellitus. Each
subject was made to follow the following schedule: The subject will come in at
T0 and has breakfast at T0.5 and blood glucose measures are taken at T0 and
T1, where n is the number of hours for a time instant Tn. The subject will
have lunch at T3, and the blood glucose will be observed at T4. A final blood
glucose measure will be taken at T8 to capture the fall in blood glucose over
the duration of experiment. The output of the proposed device and prediction
system was validated against the interpolated sweat glucose sample collected
separately using a MacroDuct®sweat collector at above mentioned time points.

### On-body measurement of human subjects

A written and informed consent was taken from all participants prior to sample
collection. All enrolled subjects wore the devices during the duration of the
testing and continuous measurements were recorded in compliance with the
protocol approved by the IRB committee. The wearable sweat sensor device was
placed on the antebrachial region (lower forearm) of the subject. The human
subjects were neither allowed to exert themselves physically nor their skin
was excited using a sweat induction method such as iontophoresis. This ensured
a full passive generation of sweat to be sampled by AWARE. Continuous on-body
measurements sampled every minute for the duration of the testing and
depending on the availability of the subject. The concentration profile of the
biomarker was reported over the entire time period of recording.

## Acknowledgements

The authors acknowledge David Kinnamon and Paul Rice for technical support on
sensor fabrication and mechanical design.

## Author contributions statement

S.P. and S.M. conceived the experiments, K.C.L. and J.B. performed glucose
sensor dose calibration, M.P. conducted the human subject data collection and
validation, D.S. conducted the electrical characterization test experiments,
curated all human subject data and created the AR model, all authors analyzed
the results and reviewed the manuscript.

## Additional information

Drs. Shalini Prasad and Sriram Muthukumar have a significant interest in
Enlisense LLC, a company that may have a commercial interest in the results of
this research and technology. The potential individual conflict of interest
has been reviewed and managed by The University of Texas at Dallas, and played
no role in the study design; in the collection, analysis, and interpretation
of data; in the writing of the report, or in the decision to send the report
for publication. Authors D.S, M.P., K.C.L. and J.B. declare no competing
financial interests.

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(a)

(b)

(c)

(d)

(e)

(f)

(g)

Figure 1:  1a Detection mechanism of the glucose immunoassay on the sensor
surface is created using glucose oxidase antibody-antigen interaction in the
presence of glucose oxidase enzyme. 1b Cross section of the sensor surface. 1c
Equivalent incremental circuit modeling arising from sensing mechanism. 1d
Equivalent circuit model with respective sources of noise added to the sensing
mechanism. Disassembly of the wearable EIS device. 1e Block diagram of the
proposed EIS device. 1f The motherboard used for EIS experiments is equipped
with an ADuCM350 SoC and nRF8001 Bluetooth Low Energy (BLE) chip-set. The
slide-in connector on the bottom allows for connecting sensors. 1g Wearable
EIS device worn as a band.

(a)

(b)

(c)

(d)

Figure 2: Impedance of a universal test cell was measured using n = 3
replicates of the wearable EIS device. 2a Spread of measured impedance across
all device replicates at frequencies ranging from 80 Hz to 1 kHz demonstrate
reasonable accuracy with respect to the PSPICE simulated impedance. 2d Current
consumption was measured for the proposed EIS device using the Agilent N6705B
power analyzer. Various operating modes of the device are shown with their
characteristic current consumptions. 2c Noise spectrum of a biosensor measured
using a high speed potentiostat while introducing PBS on the non-
functionalized sensor surface. 2b Measured RMS noise amplitude of the sensor
surface at 100 Hz shows a decrease in cumulative sensor noise with time.

(a)

(b)

Figure 3:  3a Calibration dose response of the system using synthetic sweat
buffer of various pH. 3b A box-whisker plot is used to observe the true
variability of a given dose concentration as a composite of all buffers used
in the work.

(a)

(b)

(c)

(d)

(e)  (f)

3

Figure 4:  4a Autocorrelation plot for Zmod for subject 1. 4b Autocorrelation
plot for Zmod for subject 2. 4c Autocorrelation plot for dZmod for subject 1.
4d Autocorrelation plot for dZmod for subject 2. 4e Skin temperature and
relative humidity for subject 1. 4f Skin temperature and relative humidity for
subject 2.

(a)

(b)

(c)

Figure 5:  5a Comparison of interpolated vs. RegARIMA sweat glucose
concentrations for subject 1. 5b Comparison of interpolated vs. RegARIMA sweat
glucose concentrations for subject 2. 5c Histogram of residuals for
ARIMA(10,0,3) model.


11institutetext:  Instituto de Física Corpuscular (centro mixto CSIC-UV),
46980 Paterna, Valencia, Spain22institutetext: Institute of Space Sciences
(ICE, CSIC), Campus UAB, 08193 Barcelona, Spain33institutetext: Institut
d’Estudis Espacials de Catalunya (IEEC), 08034 Barcelona,
Spain44institutetext: Frankfurt Institute for Advanced Studies, 60438
Frankfurt am Main, Germany

# Properties of the $T_{cc}(3875)^{+}$ and the $T_{\bar{c}\bar{c}}(3875)^{-}$
states in nuclear matter

Víctor Montesinos 11<EMAIL_ADDRESS>Miguel Albaladejo 11 Juan Nieves 11
Laura Tolos 223344

###### Abstract

Since its first detection, the interesting properties of the
$T_{cc}(3875)^{+}$ have made it to be one of the most prominent tetraquark-
like states up to date. In this work we present a joint analysis of the
$T_{cc}^{+}$ and its charge-conjugated partner in a dense nuclear medium. We
start by considering both states as purely isoscalar $D^{\ast}D$ and
$\overline{D}{}^{\ast}\overline{D}$ $S$-wave bound states, respectively. We
use previous results for the in-medium $D$, $\overline{D}$, $D^{\ast}$ and
$\overline{D}{}^{\ast}$ spectral functions to determine the modified two-meson
amplitudes. We find important changes in the in-medium mass and width of both
tetraquark-like resonances, which become more visible when increasing the
nuclear density and molecular probabilities. The experimental confirmation of
the found distinctive patterns will support the existence of molecular
components in the $T_{cc}^{+}$ and $T_{\bar{c}\bar{c}}^{-}$ wave functions.

##  1 Introduction

In the past years the field of hadron spectroscopy has seen a new “golden age”
with the discovery of many exotic states which do not fit the conventional
quark models. This new revolution, which started with the $X(3872)$
Belle:2003nnu , continues to see more new and interesting states to this day.
One such state is the doubly-charmed $T_{cc}(3875)^{+}$ LHCb:2021vvq ;
LHCb:2021auc , observed in the $D^{0}D^{0}\pi^{+}$ mass distribution with a
mass of $m_{\rm{thr}}+\delta m_{\rm{exp}}$, being
$m_{\text{thr}}=3875.09\,\text{MeV}$ the $D^{*+}D^{0}$ threshold and $\delta
m_{\rm{exp}}=-360\pm 40^{+4}_{-0}\,\text{keV}$, and a width $\Gamma=48\pm
2^{+0}_{-14}\,\text{keV}$ LHCb:2021auc . Among the possible models, the
molecular interpretation is being supported due to its closeness to the
$D^{0}D^{*+}$ and $D^{+}D^{*0}$ thresholds.

More experimental input on this state is thus very welcome in order to
determine its internal structure. Recent works have studied the femtoscopic
correlation functions of the $D^{0}D^{*+}$ and $D^{+}D^{*0}$ channels in
heavy-ion collisions (HICs) Kamiya:2022thy ; Vidana:2023olz . Another possible
way to gain some insight into the nature of the $T_{cc}^{+}$ is to study its
behavior under extreme temperature or density conditions, as has already been
performed for the $X(3872)$ Albaladejo:2021cxj . In this work we have followed
the previous work of Ref. Albaladejo:2021cxj  in order to study the behavior
of the $T_{cc}^{+}$ and its charge conjugated partner the
$T_{\bar{c}\bar{c}}^{-}$ in a dense nuclear environment, with the objective of
analyzing the finite-density regime of HICs in experiments such as CBM at
FAIR.

##  2 Formalism

In this section we briefly summarize the formalism of Ref. Montesinos:2023qbx
where this exotic state is generated as a result of $D^{\ast}D$ interaction.
The $T_{cc}^{+}$ state is seen in the $D^{0}D^{0}\pi^{+}$ spectrum, right
below the $D^{\ast+}D^{0}$ threshold, and has most probably quantum numbers
$I(J^{P})=0(1^{+})$. Therefore, we start by considering $D^{\ast}D$ scattering
in vacuum in this channel. We work in the exact isospin limit for the
$D^{(\ast)}$ masses. In this limit, both isospin channels decouple and we are
left with a single-channel Bethe-Salpeter equation, which in the on-shell
approximation has as solution the unitary $T$ matrix

$T^{-1}(s)=V^{-1}(s)-\Sigma(s).$ (1)

In the previous expression $V$ is a contact potential, and $\Sigma(s)$ is the
$D^{\ast}D$ loop function. We consider two energy-dependent potential
families:

$V_{A}(s)=a+bs,\quad V_{B}(s)=\frac{1}{c+ds},$ (2)

with $a$, $b$, $c$ and $d$ parameters that can be fixed through Eq. (1) by
imposing that the mass of the $T_{cc}^{+}$ in vacuum is $m_{0}$ and that the
coupling of the $T_{cc}^{+}$ to the $D^{\ast}D$ channel is $g_{0}$:

$T^{-1}(m_{0}^{2})=0,\quad\frac{dT^{-1}(s)}{ds}\Big{|}_{s=m^{2}_{0}}=\frac{1}{g^{2}_{0}},\quad
P_{0}=-g_{0}^{2}\Sigma^{\prime}(m_{0}^{2}).$ (3)

We also take into account Weinberg compositeness condition Weinberg:1965zz
(last equality in Eq. (3)), re-discussed in Gamermann:2009uq , in order to
analyze our results in terms of the molecular probability $P_{0}$ instead of
the vacuum coupling $g_{0}$. Given that we are working in the exact isospin
limit, the physical $T_{cc}^{+}$ mass cannot be used, and instead we take
$\delta m=-800$ keV with respect to the $D^{*}D$ threshold Albaladejo:2021vln
. We do not fix $g_{0}$ or $P_{0}$ to any given value. This allows us to
discuss our results in terms of these parameters.

At leading order, the effects of the nuclear medium on the scattering
amplitude enter only through the meson loop function in Eq. (1) (the potential
is left unchanged):

$\Sigma(s;\,\rho)=i\int\frac{d^{4}q}{(2\pi)^{4}}\Delta_{D^{\ast}}(P-q;\,\rho)\Delta_{D}(q;\,\rho),$
(4)

where the in-medium mesonic propagator can be written as

$\Delta_{U}(q\,;\rho)=\frac{1}{(q^{0})^{2}-\omega_{U}^{2}(\vec{q}^{2})-\Pi_{U}(q^{0},\,\vec{q};\,\rho)}=\int_{0}^{\infty}d\omega\left(\frac{S_{\\!U}(\omega,\,\lvert\vec{q}\rvert;\,\rho)}{q^{0}-\omega+i\varepsilon}-\frac{S_{\\!\bar{U}}(\omega,\lvert\vec{q}\rvert;\,\rho)}{q^{0}+\omega-i\varepsilon}\right),$
(5)

being $\Pi_{U}(q^{0},\,\vec{q};\,\rho)$ the meson self energy and
$S_{\\!U}(\omega,\,\lvert\vec{q}\rvert)$ its spectral function. We use the
model developed in Refs. Tolos:2009nn ; Garcia-Recio:2010fiq ; Garcia-
Recio:2011jcj  for computing the meson self energies. In order to regularize
the loop integral of Eq. (4) we use a sharp cutoff over three momentum of
$\Lambda=700$ MeV. Further details on the computation of Eq. (4) can be found
in Refs. Albaladejo:2021cxj ; Montesinos:2023qbx .

The discussion for the $T_{\bar{c}\bar{c}}^{-}$ runs parallel to that for the
$T_{cc}^{+}$, but considering the meson pair
$\overline{D}{}^{\ast}\overline{D}$ instead of the $D^{\ast}D$ one. The
distinction arises from the anti-meson self energies, which divert
significantly from those of mesons due to the quite different
$\overline{D}{}^{(\ast)}N$ and $D^{(\ast)}N$ interactions Tolos:2009nn ;
Garcia-Recio:2010fiq ; Garcia-Recio:2011jcj .

##  3 Results

Here we compare the results obtained in the $D^{*}D$ and
$\overline{D}{}^{\ast}\overline{D}$ channels, where the $T_{cc}^{+}$ and
$T_{\bar{c}\bar{c}}^{-}$ poles are respectively found, for densities up to
$\rho_{0}=0.17$ fm-3 (normal nuclear density).

Figure 1: Left column: real (top) and imaginary (bottom) parts of the
$\overline{D}{}^{\ast}\overline{D}$ (solid lines) and $D^{*}D$ (dashed lines)
loop functions for different values of the nuclear medium density as a
function of the center-of-mass energy $E$ of the meson pair. Right column: in-
medium $\overline{D}{}^{*}\overline{D}$ (solid lines) and $D^{*}D$ (dashed
lines) modulus square amplitudes obtained by solving Eq. (1) using the
$V_{A}(s)$ potential, for molecular probabilities $P_{0}=0.2$ (orange) and
$P_{0}=0.8$ (blue), and for different nuclear densities.

In the left column of Fig. 1 we plot the real and imaginary parts of the
$\overline{D}{}^{\ast}\overline{D}$ and $D^{*}D$ loop functions. The in-medium
loop functions are smooth at threshold, and they develop an imaginary part
below threshold. This accounts for the opening of new decay channels for the
charmed mesons due to their interaction with the nucleons of the medium.
Comparing both loop functions we see that they exactly coincide in vacuum,
owing to charge conjugation symmetry, but when increasing density they stray
apart. This different behavior is due to the very different $D^{(\ast)}N$ and
$\overline{D}{}^{(\ast)}N$ interactions. Focusing now on the real part of the
loop functions we find that it is more negative for
$\overline{D}{}^{\ast}\overline{D}$ than for $D^{*}D$ scattering. This can be
naively interpreted as the medium generating more repulsion in the $D^{*}D$
interaction than in the $\overline{D}{}^{\ast}\overline{D}$ one, but there is
no clear answer as the imaginary part is not negligible Albaladejo:2021cxj ;
Montesinos:2023qbx .

On the right column of Fig. 1 we plot the modulus squared of the in-medium
$\overline{D}{}^{\ast}\overline{D}$ and $D^{\ast}D$ amplitudes for different
densities and molecular probabilities, using the $V_{A}$ potential family
presented in Eq. (2). Results using the $V_{B}$ potential are very similar to
those stemming from $V_{A}$, specially for high molecular components
Albaladejo:2021cxj ; Montesinos:2023qbx . We find that the $T_{cc}^{+}$ and
$T_{\bar{c}\bar{c}}^{-}$, which were bound states in vacuum, develop some
width when embedded in the nuclear medium. Both states can be easily told
apart in the high $P_{0}$ scenarios, and become more difficult to
differentiate for small $\rho$ and $P_{0}$. Lastly, in the $P_{0}=0.8$ case we
can clearly see that the $T_{cc}^{+}$ peak sits to the right of the
$T_{\bar{c}\bar{c}}^{-}$ one, pointing to a more repulsive interaction in the
$D^{\ast}D$ channel than in the $\bar{D}{}^{\ast}\bar{D}$ one, as we already
mentioned when discussing the loop functions.

##  4 Conclusions

We have studied the behavior of the $T_{cc}(3875)^{+}$ and the
$T_{\bar{c}\bar{c}}(3875)^{-}$ in a dense nuclear environment and have found
that the medium effects are sizable when considering large values of the
molecular probability, as opposed to the scenario where the molecular
component is small. More specifically, we have observed an important increase
in the width of the states and a noticeable shift in their masses.
Furthermore, and due to the different $D^{(\ast)}N$ and
$\overline{D}{}^{(\ast)}N$ interactions, we have seen that the $T_{cc}^{+}$
and the $T_{\bar{c}\bar{c}}^{-}$ states behave distinctly in the medium, the
former shifting towards higher masses than the latter and becoming broader. If
the $T_{cc}^{+}$ and $T_{\bar{c}\bar{c}}^{-}$ were to be predominantly compact
objects, their density behavior, although distinct from one another, would
likely be very different from the one found in the present work. All in all,
we conclude that an interesting way to discern the molecular nature of the
tetraquark-like $T_{cc}(3875)^{+}$ and $T_{\bar{c}\bar{c}}(3875)^{-}$ is to
experimentally determine its density pattern in a dense nuclear environment.
This could be tested at experiments such as PANDA (FAIR) with fixed nuclear
targets like $\bar{p}$-nuclei, or in HICs at the CBM (FAIR).

## Acknowledgements

This work was supported by the Spanish Ministerio de Ciencia e Innovación
(MICINN) under contracts No. PID2019-110165GB-I00 and No.
PID2020-112777GB-I00, by Generalitat Valenciana under contract
PROMETEO/2020/023, and from the project CEX2020-001058-M Unidad de Excelencia
“María de Maeztu"). This project has received funding from the European Union
Horizon 2020 research and innovation programme under the program
H2020-INFRAIA-2018-1, grant agreement No. 824093 of the STRONG-2020 project.
M. A. and V. M. are supported through Generalitat Valenciana (GVA) Grants No.
CIDEGENT/2020/002 and ACIF/2021/290, respectively. L. T. also acknowledges
support from the CRC-TR 211 ‘Strong-interaction matter under extreme
conditions’- project Nr. 315477589 - TRR 211 and from the Generalitat de
Catalunya under contract 2021 SGR 171.

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