# Machine Learning-based Signal Quality Assessment for Cardiac Volume
Monitoring in Electrical Impedance Tomography

Chang Min Hyun1, Tae Jun Jang1, Jeongchan Nam2, Hyeuknam Kwon3, Kiwan Jeon4,
and Kyunghun Lee5555To whom correspondence should be addressed
<EMAIL_ADDRESS>1School of Mathematics and Computing (Computational
Science and Engineering), Yonsei University, Seoul, Republic of Korea.
2BiLab, Pangyo, Republic of Korea.  3Division of Software, Yonsei University,
Wonju, Republic of Korea.  4National Institute for Mathematical Sciences,
Daejeon, Republic of Korea.  5Kyung Hee University, Seoul, Republic of Korea.

###### Abstract

Owing to recent advances in thoracic electrical impedance tomography, a
patient’s hemodynamic function can be noninvasively and continuously estimated
in real-time by surveilling a cardiac volume signal associated with stroke
volume and cardiac output. In clinical applications, however, a cardiac volume
signal is often of low quality, mainly because of the patient’s deliberate
movements or inevitable motions during clinical interventions. This study aims
to develop a signal quality indexing method that assesses the influence of
motion artifacts on transient cardiac volume signals. The assessment is
performed on each cardiac cycle to take advantage of the periodicity and
regularity in cardiac volume changes. Time intervals are identified using the
synchronized electrocardiography system. We apply divergent machine-learning
methods, which can be sorted into discriminative-model and manifold-learning
approaches. The use of machine-learning could be suitable for our real-time
monitoring application that requires fast inference and automation as well as
high accuracy. In the clinical environment, the proposed method can be
utilized to provide immediate warnings so that clinicians can minimize
confusion regarding patients’ conditions, reduce clinical resource
utilization, and improve the confidence level of the monitoring system.
Numerous experiments using actual EIT data validate the capability of cardiac
volume signals degraded by motion artifacts to be accurately and automatically
assessed in real-time by machine learning. The best model achieved an accuracy
of 0.95, positive and negative predictive values of 0.96 and 0.86, sensitivity
of 0.98, specificity of 0.77, and AUC of 0.96.

##  1 Introduction

Over several decades, continued advances in electrical impedance tomography
(EIT) have expanded the clinical capability of real-time cardiopulmonary
monitoring systems by overcoming the limitations of traditional methods, such
as cardiac catheterization through blood vessels [3, 8, 18, 19, 28, 29, 37,
41, 57]. Recently, based on thoracic EIT, a patient’s hemodynamic function can
be noninvasively and continuously estimated in real-time by surveilling a
signal extracted using EIT, the so-called cardiac volume signal (CVS), which
has a strong relationship with key hemodynamic factors such as stroke volume
and cardiac output [27, 4, 51]. In clinical applications, however, a cardiac
volume signal is often of low quality, mainly because of the patient’s
deliberate movements or inevitable motions during clinical interventions such
as medical treatment and nursing. Because postural change causes movement of
the chest boundary to which existing EIT solvers are highly sensitive owing to
time-difference-reconstruction characteristics [1, 7, 32, 36, 44], motion-
induced artifacts are generated in the CVS, as shown in Figure 1.

Figure 1: Motion-induced artifacts in cardiac volume monitoring using
electrical impedance tomography. Patient’s deliberate movements or inevitable
motions during clinical intervention cause severe artifacts in a cardiac
volume signal.

CVS extraction is to separate a cardiogenic component from the EIT voltage
data, resulting from current injections at electrodes attached across a human
chest. In recent studies [27, 39], effective CVS extraction was successful in
motion-free measurements where voltage data are mainly influenced by air and
blood volume changes in the lungs, heart, and blood vessels comprehensively,
but not by motions. In contrast, achieving the cardiogenic component
separation in motion-influenced measurements is still a long-term challenge.
Postural changes in EIT measurements cause strong distortion of the voltage
data [1, 56] and easily disturb the extraction of relatively weak cardiogenic
signals [6, 40, 33].

Handling motion interference has been a huge challenge in most EIT-based
techniques for enhancing clinical capability, but not researched much yet
[54]. Adler et al. [1] and Zhang et al. [56] investigated the negative motion
effect in the EIT. Soleimani et al. [43] and Dai et al. [17] proposed a
motion-induced artifact reduction method by reconstructing electrode movements
along with conductivity changes. Lee et al. [36] analyzed motion artifacts in
EIT measurements and proposed a subspace-based artifact rejection method. Yang
et al. [54] suggested the discrete wavelet transform-based approach that
reduces motion artifacts of three specific types. However, clinical motion
artifacts are still not effectively addressed because of practical motion’s
immense diversity and complexity. Accordingly, for the time being, the EIT-
based hemodynamic monitoring system attempts to be preferentially developed
toward filtering motion-influenced CVSs rather than recovering them. In the
clinical environment, this filtration can provide immediate warnings so that
clinicians can minimize confusion regarding the patient’s condition, reduce
clinical resource utilization, and improve the confidence level of the
monitoring system [16].

This study aims to develop a signal quality indexing (SQI) method that
assesses whether motion artifacts influence transient CVSs. To take advantage
of the periodicity and regularity in cardiac volume changes, the assessment is
performed on each cardiac cycle, whose time intervals are identified using the
synchronized electrocardiography (ECG) system. We leverage machine learning
(ML), which has provided effective solutions for various biosignal-related
tasks through feature disentanglement of complicated signals [5, 9, 14, 25,
34, 47, 48, 52]. The use of ML could be suitable for our real-time monitoring
application that requires fast inference and automation as well as high
accuracy.

We apply divergent ML methods, which can be sorted into discriminative-model
and manifold-learning approaches. The discriminative-model approach is first
considered, where an SQI map is directly trained using a paired dataset of CVS
and its label [12, 22, 45]. Although this approach provides a high performance
on a fixed dataset, owing to the class imbalance problem, there is a risk of
overfitting on motion-influenced CVS data in the scope of generalization or
stability [10, 15, 23, 49]. Motion artifacts can vary considerably in real
circumstances, whereas collecting CVS data in numerous motion-influenced cases
is practically limited because of the high cost, intensive labor, security,
and ambiguity in clinical data acquisition and annotation [13, 46, 50, 58]. To
handle this conceivable difficulty, the manifold-learning approach [26, 30, 2,
24] is examined as an alternative. It does not learn irregular and capricious
patterns of motion-influenced CVSs and only takes advantage of the learned
features from motion-free CVSs.

Numerous experiments have been conducted using actual EIT data. Empirical
results demonstrate that discriminative and manifold-learning models provide
accurate and automatic detection of motion-influenced CVS in real-time. The
best discriminative model achieved an accuracy of 0.95, positive and negative
predictive values of 0.96 and 0.86, sensitivity of 0.98, specificity of 0.77,
and AUC of 0.96. The best manifold-learning model achieved accuracy of 0.93,
positive and negative predictive values of 0.97 and 0.71, sensitivity of 0.95,
specificity of 0.80, and AUC of 0.95. The discriminative models yielded a more
powerful SQI performance; in contrast, the manifold-learning models provided
stable outcomes between the training and test sets. Regarding to practical
applications, the choice of two models relies on what should be emphasized in
the monitoring system in terms of performance and stability.

##  2 Methods

Figure 2: 16-channel system of thoracic EIT and CVS extraction. The EIT
machine measures voltage differences by injecting currents via electrodes
attached along human chest. A cardiac volume signal
$\boldsymbol{x}_{\boldsymbol{t}}$ is extracted by taking suitable weighting
$\boldsymbol{w}$ to the time-difference transconductance
$\dot{\boldsymbol{g}}_{t}$, which is defined by measured voltage data. Here,
$\boldsymbol{w}$ is called as a leadforming vector, which is designed to
separate a cardiogenic trans-conductance change from superposed data
$\dot{\boldsymbol{g}}_{t}$ [39].

This study considers the 16-channel system of the thoracic EIT, where 16
electrodes are attached along the human chest (see Figure 2). The EIT system
is assumed to be synchronized with the ECG system, which provides the time
interval for each cardiac cycle. The EIT device measures a set of voltage
differences by injecting an alternative current of $I$ (mA) through pairs of
adjacent electrodes while keeping all other electrodes insulated. At sampling
time $t$, the following voltages are acquired:

$\\{V^{j,k}_{t}~{}:~{}V^{j,k}_{t}=U_{t}^{j,k}-U_{t}^{j,k+1},j\in\mathcal{I},k\in\mathcal{I}\backslash\\{j,j+1\\}\\}$
(1)

where $\mathcal{I}$ is an index set defined by
$\mathcal{I}=\\{1,2,\cdots,16\\}$, $\mathcal{E}_{k}$ is the $k$-th electrode,
and $U_{t}^{j,k}$ is the electrical potential on $\mathcal{E}_{k}$ subject to
the current injection from $\mathcal{E}_{j}$ to $\mathcal{E}_{j+1}$. For
notational convenience, $\mathcal{E}^{0}$ and $\mathcal{E}^{17}$ can be
understood as $\mathcal{E}^{16}$ and $\mathcal{E}^{1}$, respectively. Once the
current is injected from $\mathcal{E}^{j}$ to $\mathcal{E}^{j+1}$ for some
$j\in\mathcal{I}$, the voltage is measured at each of the 16 adjacent
electrode pairs $(\mathcal{E}^{k},\mathcal{E}^{k+1})_{k\in\mathcal{I}}$. Among
the 16 voltages, $V_{t}^{j,j-1}$, $V_{t}^{j,j}$, and $V_{t}^{j,j+1}$ are
discarded to reduce the influence of the skin-electrode contact impedance
[44]. Because we perform 16 independent current injections, in total, $208$
$(=16\times 13)$ voltages are obtained and used to produce the CVS.

###  2.1 CVS Extraction Using EIT and Influence of Motion

A transconductance (column) vector $\boldsymbol{g}_{t}\in\mathbb{R}^{208}$ can
be defined using the voltage data (1) as follows:

${\footnotesize\boldsymbol{g}_{t}=\begin{bmatrix}\dfrac{I}{\mathfrak{R}(V^{1,3}_{t})},\cdots,\dfrac{I}{\mathfrak{R}(V^{1,15}_{t})},\cdots,\dfrac{I}{\mathfrak{R}(V^{16,2}_{t})},\cdots\dfrac{I}{\mathfrak{R}(V^{16,14}_{t})}\end{bmatrix}^{T}}$
(2)

where $T$ represents the vector transpose and $\mathfrak{R}$ is an operation
for extracting the real part of a complex number. Here, $\boldsymbol{g}_{t}$
is updated every 10ms.

A CVS, denoted by $\boldsymbol{x}_{t}\in\mathbb{R}$, is obtained by

$\boldsymbol{x}_{t}=\boldsymbol{w}^{T}\dot{\boldsymbol{g}_{t}}$ (3)

where $\boldsymbol{w}\in\mathbb{R}^{208}$ is a weighting (so-called
leadforming) vector and $\dot{\boldsymbol{g}_{t}}$ is time difference of
$\boldsymbol{g}_{t}$ given by

$\dot{\boldsymbol{g}}_{t}=\boldsymbol{g}_{t}-\boldsymbol{g}_{t_{0}}\mbox{ for
reference time }t_{0}$ (4)

In the absence of motion, the transconductance $\dot{\boldsymbol{g}}_{t}$ can
be expressed by

$\dot{\boldsymbol{g}}_{t}=\dot{\boldsymbol{g}}^{\mbox{\scriptsize
air}}_{t}+\dot{\boldsymbol{g}}^{\mbox{\scriptsize blood}}_{t}$ (5)

where ${\boldsymbol{g}}^{\mbox{\scriptsize air}}_{t}$ and
${\boldsymbol{g}}^{\mbox{\scriptsize blood}}_{t}$ are transconductance vectors
related to air and blood volume changes in the lungs and heart, respectively.
The weighting vector $\boldsymbol{w}$ is designed to provide

$\boldsymbol{w}^{T}\dot{\boldsymbol{g}}_{t}=\boldsymbol{w}^{T}(\dot{\boldsymbol{g}}^{\mbox{\scriptsize
air}}_{t}+\dot{\boldsymbol{g}}^{\mbox{\scriptsize
blood}}_{t})=\boldsymbol{w}^{T}\dot{\boldsymbol{g}}^{\mbox{\scriptsize
blood}}_{t}$ (6)

See Figure 2. Kindly refer to [39] for details on determining
$\boldsymbol{w}$. Even though the cardiogenic signal
${\boldsymbol{g}}^{\mbox{\scriptsize blood}}_{t}$ is weak, it can be
accurately decomposed from the data $\boldsymbol{g}_{t}$.

In light of the previous analysis in [36], the following explains why the
quality of the CVS is degraded by motion, as shown in the middle part of
Figure 1. In the presence of motion, the transconductance
$\dot{\boldsymbol{g}}_{t}$ can be approximated by

$\dot{\boldsymbol{g}}_{t}\approx\dot{\boldsymbol{g}}_{t}^{\mbox{\scriptsize
normal}}+\dot{\boldsymbol{g}}^{\mbox{\scriptsize motion}}_{t}$ (7)

where $\dot{\boldsymbol{g}}^{\mbox{\scriptsize
normal}}_{t}=\dot{\boldsymbol{g}}^{\mbox{\scriptsize
air}}_{t}+\dot{\boldsymbol{g}}^{\mbox{\scriptsize blood}}_{t}$ and
$\dot{\boldsymbol{g}}^{\mbox{\scriptsize motion}}_{t}$ is the motion-induced
effect. Appendix A presents details of (7). Determining the vector
$\boldsymbol{w}$ itself can be considerably affected by motion artifacts [39].
Moreover, even if $\boldsymbol{w}$ satisfies (6), we have

$\boldsymbol{x}_{t}=\boldsymbol{w}^{T}\dot{\boldsymbol{g}}_{t}\approx\boldsymbol{x}_{t}^{\mbox{\scriptsize
normal}}+\boldsymbol{x}_{t}^{\mbox{\scriptsize motion}}$ (8)

where $\boldsymbol{x}_{t}^{\mbox{\scriptsize
normal}}=\boldsymbol{w}^{T}\dot{\boldsymbol{g}}_{t}^{\mbox{\scriptsize
blood}}$ and $\boldsymbol{x}_{t}^{\mbox{\scriptsize
motion}}=\boldsymbol{w}^{T}\dot{\boldsymbol{g}}_{t}^{\mbox{\scriptsize
motion}}$. The last term $\boldsymbol{x}_{t}^{\mbox{\scriptsize motion}}$
describes motion artifacts in the CVS.

Figure 3: Schematic description of machine learning-based signal quality
assessment for cardiac volume monitoring in electrical impedance tomography.

###  2.2 CVS Quality Assessment and Data Preprocessing

This study aims to assess the CVS ($\boldsymbol{x}_{t}$) for detecting motion-
induced signal quality degradation. See Figure 3. This can be accomplished by
developing an SQI map
$\boldsymbol{f}:\boldsymbol{x}_{t}\mapsto\boldsymbol{y}_{t}$ such that

$\boldsymbol{f}(\boldsymbol{x}_{t})=\boldsymbol{y}_{t}=\left\\{\begin{array}[]{cl}1&\mbox{if
}~{}\boldsymbol{x}_{t}^{\mbox{\scriptsize motion}}\approx 0\\\ 0&\mbox{if
}~{}\boldsymbol{x}_{t}^{\mbox{\scriptsize motion}}\not\approx 0\\\
\end{array}\right.$ (9)

However, it is arduous to achieve (9), where the assessment is conducted on an
individual CVS at every sampling time. Instead, we take advantage of the
periodicity and regularity of cardiac volume changes according to the
heartbeat. The time interval of each cardiac cycle is identified using a
synchronized ECG system.

Our quality assessment is conducted on every cardiac cycle of CVS, where a
cardiac cycle is defined by the time interval consisting of two consecutive
ECG R-wave peaks as the end points. For a given time $t_{\mbox{\scriptsize
cyc}}$, let the interval $[t_{\mbox{\scriptsize cyc}},t_{\mbox{\scriptsize
cyc}}+\Delta t_{\mbox{\scriptsize cyc}}]$ be the corresponding cardiac cycle,
where $\Delta t_{\mbox{\scriptsize cyc}}$ is assumed to be $\Delta
t_{\mbox{\scriptsize cycle}}=10\mbox{ms}\times(\boldsymbol{v}-1)$ for some
$\boldsymbol{v}\in\mathbb{N}\backslash\\{1\\}$. Here, $\mathbb{N}$ denotes the
set of positive integers. A vector gathering all CVSs during the cycle,
denoted by $\boldsymbol{X}_{t_{\mbox{\scriptsize
cyc}}}\in\mathbb{R}^{\boldsymbol{v}}$, is defined as

$\boldsymbol{X}_{t_{\mbox{\scriptsize
cyc}}}=\begin{bmatrix}\boldsymbol{x}_{t_{\mbox{\scriptsize
cyc}}},\boldsymbol{x}_{t_{\mbox{\scriptsize cyc}}+10\mbox{\scriptsize
ms}},\cdots,\boldsymbol{x}_{t_{\mbox{\scriptsize cyc}}+10\mbox{\scriptsize
ms}\times(\boldsymbol{v}-1)}\end{bmatrix}^{T}$ (10)

The map $f$ in (9) can be modified into

$\boldsymbol{f}(\boldsymbol{X}_{t_{\mbox{\scriptsize
cyc}}})=\boldsymbol{y}_{t}=\left\\{\begin{array}[]{cl}1&\mbox{for normal
}\boldsymbol{X}_{t_{\mbox{\scriptsize cyc}}}\\\ 0&\mbox{for motion-influenced
}\boldsymbol{X}_{t_{\mbox{\scriptsize cyc}}}\\\ \end{array}\right.$ (11)

To find $\boldsymbol{f}$ in (11), we leverage ML, which can learn the domain
knowledge of normal and motion-influenced CVSs from a training dataset of $N$
data pairs $\\{\boldsymbol{X}^{(i)},\boldsymbol{y}^{(i)}\\}_{i=1}^{N}$. Prior
to ML applications, the following issues need to be addressed in the CVS data.
First, CVSs have significant inter-subject and intra-subject variability. This
is because cardiac volume varies depending on various factors, including sex,
age, condition, time, and body temperature. Therefore, scale normalization is
required to enhance the stability and performance of ML while mitigating the
high learning complexity associated with scale-invariant feature extraction
[20, 53]. Second, the dimensions of the input CVS data in (11) do not match
each other (i.e., $\boldsymbol{v}$ is not constant) owing to heart rate
variability [11]. Because most existing ML methods are based on an input with
consistent dimensions, size normalization is required. Figure 4 schematically
illustrates the overall process.

Figure 4: From the monitoring system, electrocadiography and cardiac volume
signals are obtained. By identifying a cardiac cycle through
electrocadiography data (R-wave peak detection), we extract cardiac volume
signals at the corresponding cycle and then lastly apply normalization in
terms of scale and size.

####  2.2.1 Scale normalization

A simple method of normalizing the scale is to rescale the CVS data for
individual cardiac cycles. Specifically, for a given CVS vector
$\boldsymbol{X}_{t_{\mbox{\scriptsize cyc}}}\in\mathbb{R}^{\boldsymbol{v}}$,
the scaling factor $\mathcal{S}$ is obtained using

$\mathcal{S}=\underset{i\in\mathcal{V}}{\mbox{max}}~{}|\boldsymbol{x}_{t_{\mbox{\tiny
cyc}}+10\times i\mbox{\tiny(ms)}}|$ (12)

where the index set $\mathcal{V}$ is given by
$\mathcal{V}=\\{0,1,\cdots,\boldsymbol{v}-1\\}$. Normalized CVS data, denoted
by $\underline{\boldsymbol{X}}_{t_{\mbox{\tiny cyc}}}$, are obtained by

$\underline{\boldsymbol{X}}_{t_{\mbox{\tiny
cyc}}}=\dfrac{\boldsymbol{X}_{t_{\mbox{\tiny cyc}}}}{\mathcal{S}}$ (13)

However, this scaling may not be appropriate to our application for the
following reason. Abnormalities in CVS data include sudden increases or
decreases in signal amplitude as well as irregular deformations of the shape
profile. The normalization in (13) can contribute to ignoring rapid amplitude
changes.

This study uses the following subject-specific scale normalization strategy.
When the EIT device is used to monitor a certain subject, it is supposed that
during the initial 20s calibration process, the device measures the normal CVS
data available for scale normalization. Let $\mathcal{X}^{\mbox{\scriptsize
subject}}$ be a set of corresponding CVSs given by

$\mathcal{X}^{\mbox{\scriptsize subject}}=\\{\boldsymbol{x}_{10\times
i\mbox{\tiny(ms)}}:i=-1999,-1998,\cdots,-1\\}$ (14)

Using the set $\mathcal{X}^{\mbox{\scriptsize subject}}$, a subject-specific
scaling factor $\mathcal{S}^{\mbox{\scriptsize subject}}$ is obtained by

$\mathcal{S}^{\mbox{\scriptsize
subject}}=\underset{\boldsymbol{x}\in\mathcal{X}^{\mbox{\scriptsize
subject}}}{\mbox{max}}|\boldsymbol{x}|$ (15)

This scale factor $\mathcal{S}^{\mbox{\scriptsize subject}}$ is used for the
normalization in (13) instead of the naive factor $\mathcal{S}$ in (12).

####  2.2.2 Size normalization

To make the dimensions of the CVS data consistent, a CVS vector
$\underline{\boldsymbol{X}}_{t_{\mbox{\scriptsize cyc}}}$ is embedded into
$\mathbb{R}^{\nu}$ for a fixed constant $\boldsymbol{\nu}$. In the empirical
experiment, the embedding space dimension was to be larger than any dimension
of the CVS data in our dataset ($\boldsymbol{\nu}=150$).

Two normalization methods are considered. The first approach is to resample
$\boldsymbol{\nu}$ points using linear interpolation with $\boldsymbol{v}$
data points in $\underline{\boldsymbol{X}}_{t}$. For the stationary interval
$[0,1]$, the following linear interpolation function $\mathcal{L}$ is
constructed:

$\mathcal{L}(\dfrac{i}{\boldsymbol{v}-1})=\underline{\boldsymbol{x}}_{t_{\mbox{\tiny
cyc}}+10\mbox{\tiny(ms)}\times(i-1)}\mbox{ for }i=0,\cdots,\boldsymbol{v}-1$
(16)

Subsequently, we obtain the normalized vector
$\overline{\boldsymbol{X}}_{t_{\mbox{\tiny
cyc}}}\in\mathbb{R}^{\boldsymbol{\nu}}$ using

$\overline{\boldsymbol{X}}_{t_{\mbox{\tiny
cyc}}}=\left[~{}\mathcal{L}(0),\mathcal{L}(\dfrac{1}{\boldsymbol{\nu}-1}),\mathcal{L}(\dfrac{2}{\boldsymbol{\nu}-1}),\cdots,\mathcal{L}(1)~{}\right]^{T}$
(17)

This method normalizes the signal profile of CVS data into the desired length
($\boldsymbol{\nu}$) with no significant loss, but loses sampling time
information. Second, the last value in
$\underline{\boldsymbol{X}}_{t_{\mbox{\scriptsize cyc}}}$ (i.e.,
$\boldsymbol{x}_{t_{\mbox{\scriptsize
cyc}}+10\mbox{\scriptsize(ms)}\times(\boldsymbol{v}-1)}$) is padded up to the
desired length. This constant padding provides a vector
$\overline{\boldsymbol{X}}_{t_{\mbox{\scriptsize
cyc}}}\in\mathbb{R}^{\boldsymbol{\nu}}$, expressed by

$\displaystyle\overline{\boldsymbol{X}}_{t_{\mbox{\tiny cyc}}}=$
$\displaystyle[~{}\underline{\boldsymbol{x}}_{t_{\mbox{\tiny
cyc}}},\cdots,\underline{\boldsymbol{x}}_{t_{\mbox{\tiny
cyc}}+10\mbox{\tiny(ms)}\times(\boldsymbol{v}-2)},\underline{\boldsymbol{x}}_{t_{\mbox{\tiny
cyc}}+10\mbox{\tiny(ms)}\times(\boldsymbol{v}-1)},$ (18)
$\displaystyle~{}~{}\underline{\boldsymbol{x}}_{t_{\mbox{\tiny
cyc}}+10\mbox{\tiny(ms)}\times(\boldsymbol{v}-1)},\cdots,\underline{\boldsymbol{x}}_{t_{\mbox{\tiny
cyc}}+10\mbox{\tiny(ms)}\times(\boldsymbol{v}-1)}~{}]^{T}$ (19)

where the part (19) corresponds to the padding. In contrast to the first
method, this normalization can preserve time information regarding sampling
frequency, whereas the core profile of the CVS is supported at different time
intervals.

###  2.3 Machine Learning Application

At this point, we are ready to apply ML for determining the SQI function (11).
Collected from various subjects and cardiac cycles, the following dataset is
used:

$\\{\overline{\boldsymbol{X}}^{(i)},\boldsymbol{y}^{(i)}\\}_{i=1}^{N}$ (20)

where $\boldsymbol{y}^{(i)}$ is the SQI label corresponding to
$\overline{\boldsymbol{X}}^{(i)}$. We note that $\overline{\boldsymbol{X}}$ is
the CVS data for a cardiac cycle of some subjects and is normalized for both
scale and size. In practice, the available training dataset (20) was highly
imbalanced, where there were relatively few negative samples (motion-
influenced CVSs).

Figure 5: (a) Discriminative-model approach learns a signal quality indexing
map $f$ by using CVS and label data. (b) Manifold-learning approach first
learns common features of normal CVS data by finding a low dimensional
manifold $\mathcal{M}^{\mbox{\scriptsize normal}}$. Signal quality assessment
is based on computing the residual between original CVS data and projected one
onto or near the learned manifold.

####  2.3.1 Discriminative-model approach

The discriminative-model approach trains the SQI map
$\boldsymbol{f}:\overline{\boldsymbol{X}}\mapsto\boldsymbol{y}$ in the
following sense:

$\boldsymbol{f}=\underset{\boldsymbol{f}\in\mathbb{F}}{\mbox{argmin}}~{}\dfrac{1}{N}\sum_{i=1}^{N}\mbox{dist}(\boldsymbol{f}(\overline{\boldsymbol{X}}^{(i)}),\boldsymbol{y}^{(i)})$
(21)

where $\mathbb{F}$ is a set of learnable functions for a given ML model and
dist is a metric that measures the difference between the ML output
$f(\overline{\boldsymbol{X}})$ and label $\boldsymbol{y}$. See Figure 5 (a).
In our application with high class-imbalance, the following weighted cross-
entropy can be used:

$\mbox{dist}(\boldsymbol{f}(\overline{\boldsymbol{X}}),\boldsymbol{y})=-\boldsymbol{\zeta}_{\mbox{\scriptsize
pos}}\boldsymbol{y}\mbox{log}(\boldsymbol{f}(\overline{\boldsymbol{X}}))-\boldsymbol{\zeta}_{\mbox{\scriptsize
neg}}(1-\boldsymbol{y})\mbox{log}(1-\boldsymbol{f}(\overline{\boldsymbol{X}}))$
(22)

where $\boldsymbol{\zeta}_{\mbox{\scriptsize pos}}$ and
$\boldsymbol{\zeta}_{\mbox{\scriptsize neg}}$ are the relative ratios of the
positive and negative samples, respectively. Various classification models can
be used, such as the logistic regression model (LR) [12], multi-layer
perceptron (MLP) [22], and convolutional neural networks (CNN) [45]. Detailed
models used in this study are explained in Appendix B.1.

The discriminative model approach is a powerful method to guarantee high
performance in a fixed dataset. However, it might suffer from providing stable
SQI results in clinical practice because of highly variable negative samples.
This is because these methods take advantage of learned information using only
a few negative samples [10, 15, 23, 49]. To achieve stable prediction, the
manifold-learning approach can be alternatively used [13, 50, 58].

####  2.3.2 Manifold-learning approach

The manifold-learning approach learns common features from positive samples
(i.e., normal CVS) and uses them to develop an SQI map. The remaining negative
samples are utilized as auxiliary means for selecting a hyperparameter. Figure
5 (b) shows a schematic description of this process.

A set of positive samples is denoted by
$\\{\overline{\boldsymbol{X}}_{\mbox{\scriptsize
pos}}^{(i)}\\}_{i=1}^{N_{\mbox{\scriptsize pos}}}$, where
$N_{\mbox{\scriptsize pos}}$ denotes the number of positive samples. In the
first step, we learn a low-dimensional representation of
$\overline{\boldsymbol{X}}_{\mbox{\scriptsize pos}}$ by training an encoder
$\mathcal{E}:\overline{\boldsymbol{X}}_{\mbox{\scriptsize
pos}}\mapsto\boldsymbol{z}$ and decoder
$\mathcal{D}:\boldsymbol{z}\mapsto\overline{\boldsymbol{X}}_{\mbox{\scriptsize
pos}}$ in the following sense [26, 21]:

$(\mathcal{D},\mathcal{E})=\underset{(\mathcal{D},\mathcal{E})}{\mbox{argmin}}~{}\dfrac{1}{N_{\mbox{\scriptsize
pos}}}\sum_{i=1}^{N_{\mbox{\scriptsize
pos}}}\|\mathcal{D}\circ\mathcal{E}(\overline{\boldsymbol{X}}_{\mbox{\scriptsize
pos}}^{(i)})-\overline{\boldsymbol{X}}_{\mbox{\scriptsize
pos}}^{(i)}\|_{2}^{2}$ (23)

where $\boldsymbol{z}$ is a low dimensional latent vector and $\|\cdot\|_{2}$
is the standard Euclidean norm. The architectures $\mathcal{D}$ and
$\mathcal{E}$ can be used in PCA [26], VAE [30], and $\beta$-VAE [24]. See
more details in Appendix B.2.

Borrowing the idea from [2], an SQI map $f$ is constructed as follows: For a
given CVS data $\overline{\boldsymbol{X}}$ in any class, a residual
$\boldsymbol{r}$ is computed by

$\boldsymbol{r}=\|\overline{\boldsymbol{X}}-\mathcal{D}\circ\mathcal{E}(\overline{\boldsymbol{X}})\|_{2}$
(24)

The decoder $\mathcal{D}$ is trained to generate normal CVS-like output. In
other words, operation $\mathcal{D}\circ\mathcal{E}$ transforms
$\overline{\boldsymbol{X}}$ to lie in or near the learned manifold using
normal CVS data [44, 55]. Therefore, the residual $\boldsymbol{r}$ can be
viewed as an anomaly score, where $\boldsymbol{r}$ is small if
$\overline{\boldsymbol{X}}$ is normal CVS data, and large if
$\overline{\boldsymbol{X}}$ is motion-influenced CVS data. For some non-
negative constant $d$, an SQI map $\boldsymbol{f}$ can be constructed using

$\boldsymbol{f}(\overline{\boldsymbol{X}}_{t})=\left\\{\begin{array}[]{cl}1&\mbox{if
}\boldsymbol{r}\leq\boldsymbol{d}\\\ 0&\mbox{if
}\boldsymbol{r}>\boldsymbol{d}\end{array}\right.$ (25)

The remainder of this subsection explains how the thresholding value
$\boldsymbol{d}$ is determined by utilizing negative samples as well as
positive. By varying $\boldsymbol{d}$ from 0 to $\infty$, a receiver operating
characteristic (ROC) curve is calculated, where a point in the ROC curve is
obtained using a fixed $\boldsymbol{d}$. We choose $\boldsymbol{d}$ such that
maximizing Youden’s $\boldsymbol{J}$ statistics, which is known as an unbiased
metric in the class imbalance case [42]. The value $\boldsymbol{J}$ is given
by

$\boldsymbol{J}^{\boldsymbol{d}}=\mbox{Sensitivity}^{\boldsymbol{d}}+\mbox{Specificity}^{\boldsymbol{d}}-1$
(26)

where

$\mbox{Sensitivity}^{\boldsymbol{d}}=\dfrac{N_{\mbox{\scriptsize
TP}}^{\boldsymbol{d}}}{N_{\mbox{\scriptsize
TP}}^{\boldsymbol{d}}+N_{\mbox{\scriptsize FN}}^{\boldsymbol{d}}}\mbox{ and
}\mbox{Specificity}^{\boldsymbol{d}}=\dfrac{N_{\mbox{\scriptsize
TN}}^{\boldsymbol{d}}}{N_{\mbox{\scriptsize TN}}^{d}+N_{\mbox{\scriptsize
FP}}^{\boldsymbol{d}}}$ (27)

Here, $N_{\mbox{\scriptsize TP}}^{\boldsymbol{d}}$, $N_{\mbox{\scriptsize
TN}}^{\boldsymbol{d}}$, $N_{\mbox{\scriptsize FP}}^{\boldsymbol{d}}$, and
$N_{\mbox{\scriptsize FN}}^{\boldsymbol{d}}$ respectively represent the number
of true positives, true negatives, false positives, and false negatives for
predictions depending on a selected threshold value $\boldsymbol{d}$.

##  3 Results

###  3.1 Data Acquisition and Experimental Setting

Our dataset was obtained from healthy volunteers using an EIT-based
hemodynamic monitoring device (HemoVista, BiLab, South Korea). Synchronized
ECG data were obtained with EIT and used to identify the cardiac cycles. While
lying in a hospital bed, each subject was requested to make intentional
motions mimicking postural changes in the clinical ward. A total of 16140 CVS
data were obtained regarding the cardiac cycle.

Manual labeling was individually performed by two- and ten- years bio-signal
experts (Nam and Lee). Subsequently, they reviewed the results and made the
final decision about CVS abnormality through an agreement between them. The
final labels were annotated into three classes: normal, ambiguous, and motion-
influenced. When classified as normal or abnormal by both experts with an
agreement, CVS data were annotated as normal or motion-influenced classes. The
ambiguous class stands for CVS data in which motion artifacts were included
with high possibility, but the experts did not reach an explicit agreement
about motion influence. The assigned label is $\boldsymbol{y}=1$ for the
normal class and $\boldsymbol{y}=0$ for the other classes. As a result, 12928
(80.09$\%$), 1526 (9.45$\%$), and 1686 (10.45$\%$) samples were labeled as
normal, ambiguous, and motion-influenced classes, respectively.

For ML applications, a total of 16372 CVS data were divided into 13100
(80$\%$), 1520 (10$\%$), and 1520 (10$\%$), which were used for training,
validation, and testing, respectively. The data split was performed such that
CVS data obtained from a common subject did not exist between the three sets.
For the training dataset, labels for the ambiguous class were reassigned to
$\boldsymbol{y}=0.25$. This was done to prevent the over-classification of
ambiguous classes.

ML experiments were conducted in a computer system with GeForce RTX 3080 Ti,
Intel® Core™ X-series Processors i9-10900X, and 128GB DDR4 RAM. Python with
scikit-learn and Pytorch packages were used for the ML implementation. When
training the ML models, the Adam optimizer was consistently employed, which is
an effective adaptive stochastic gradient descent method [31]. Hyperparameters
such as epoch and learning rate were heuristically chosen based on the
validation results.

###  3.2 Results of CVS Quality Assessment

We compared the performance of the ML-based CVS quality assessment results by
using six metrics: accuracy, positive and negative predictive values (PPV and
NPV), sensitivity, specificity, and AUC. Accuracy, PPV, and NPV were defined
by

$\mbox{Accuracy}=\dfrac{N_{\mbox{\scriptsize TP}}+N_{\mbox{\scriptsize
TN}}}{N_{\mbox{\scriptsize TP}}+N_{\mbox{\scriptsize TN}}+N_{\mbox{\scriptsize
FP}}+N_{\mbox{\scriptsize FN}}},\mbox{PPV}=\dfrac{N_{\mbox{\scriptsize
TP}}}{N_{\mbox{\scriptsize TP}}+N_{\mbox{\scriptsize FP}}},\mbox{ and
}\mbox{NPV}=\dfrac{N_{\mbox{\scriptsize TN}}}{N_{\mbox{\scriptsize
TN}}+N_{\mbox{\scriptsize FN}}}$ (28)

and AUC was the area under the ROC curve. NPV, specificity, and AUC should be
emphasized in our evaluation owing to the high-class imbalance (small negative
samples).

(a) SQI with scale and size normalization using linear interpolation.
Discriminative Model LR MLP1 MLP2 VGG16-3 VGG16-4 VGG16-5 Test Accuracy 0.8665
0.9323 0.9348 0.9468 0.9468 0.9437 PPV 1.0000 0.9790 0.9747 0.9525 0.9605
0.9679 NPV 0.1097 0.7241 0.7445 0.9047 0.8591 0.8083 Sensitivity 0.8643 0.9404
0.9479 0.9866 0.9776 0.9657 Specificity 1.0000 0.8860 0.8607 0.7215 0.7721
0.8185 AUC 0.6615 0.9506 0.9558 0.9709 0.9645 0.9653 Manifold-learning Model
PCA VAE $\boldsymbol{\beta}$-VAE CVAE $\boldsymbol{\beta}$-CVAE - Test
Accuracy 0.8468 0.9066 0.9221 0.9292 0.9298 PPV 0.9510 0.9687 0.9672 0.9688
0.9739 NPV 0.4573 0.6181 0.6900 0.7100 0.7011 Sensitivity 0.8675 0.9218 0.9439
0.9486 0.9441 - Specificity 0.7142 0.8095 0.7952 0.8047 0.8380 AUC 0.8735
0.9513 0.9489 0.9528 0.9603

(b) SQI with scale and size normalization using constant padding.
Discriminative Model LR MLP1 MLP2 VGG16-3 VGG16-4 VGG16-5 Test Accuracy 0.8664
0.9487 0.9518 0.9455 0.9487 0.9500 PPV 1.0000 0.9745 0.9767 0.9533 0.9655
0.9731 NPV 0.0826 0.7851 0.8065 0.8870 0.8433 0.8185 Sensitivity 0.8648 0.9651
0.9666 0.9844 0.9748 0.9681 Specificity 1.0000 0.8521 0.8652 0.7173 0.7956
0.8434 AUC 0.6628 0.9725 0.9669 0.9782 0.9683 0.9757 Manifold-learning Model
PCA VAE $\boldsymbol{\beta}$-VAE CVAE $\boldsymbol{\beta}$-CVAE - Test
Accuracy 0.8809 0.8918 0.9214 0.9015 0.8861 PPV 0.9590 0.9660 0.9679 0.9731
0.9636 NPV 0.5333 0.5629 0.6694 0.5882 0.5467 Sensitivity 0.9014 0.9074 0.9407
0.9118 0.9029 - Specificity 0.7450 0.7892 0.7941 0.8333 0.7745 AUC 0.9150
0.9206 0.9412 0.9170 0.9041

Table 1: Machine learning-based CVS quality assessment results

####  3.2.1 Discriminative Models

The first and second rows of Tables 1 (a) and (b) show the quantitative
evaluations of CVS quality assessment using various discriminative models: LR,
MLPs, and CNNs. The results in Tables 1 (a) and (b) differ in size
normalization: (a) linear interpolation and (b) constant padding.

MLPs and CNNs performed better than LR, which provided miserable NPV and AUC.
MLPs and CNNs outperformed each other in specificity and NVP respectively,
while achieving comparable levels for the other metrics. There was no
significant performance gap depending on the size normalization.

One interesting observation was as follows: In our experiments, there seems to
be a compensation between specificity and NPV, depending on the emphasis on
locality and globality. Enriching global information on CVS data positively
affected specificity; in contrast, local information helped improve NPV. As
the receptive field size in VGG16 increased (see Appendix B.1), specificity
tended to increase and NPV decrease. In MLP, which is more flexible for
catching global information than CNNs, specificity was highest, and NPV
lowest. In other words, the local information of CVS data is likely to play a
crucial role in reducing false negatives rather than false positives. From a
practical point of view, reducing false negatives is more desirable;
therefore, using VGG16-3 or VGG16-4, which have the powerful ability to take
advantage of locality, can be an excellent option.

####  3.2.2 Manifold-learning Models

Figure 6: Test samples and VAE-based projection results for (a) normal and (b)
motion-influenced CVS data, where the red line is original CVS data and the
blue line is the correspondent CVS data projected by VAE. By the way, ROC
curves for (c) VGG 16-4 and (d) $\beta$-VAE are provided, where the blue and
red lines correspond to the curves calculated using training and test sets,
respectively.

Positive samples in the validation set were used for hyperparameter selection
in training the encoder and decoder. A threshold value was determined by using
data from all the training and validation sets.

Figure 6 shows manifold projection results of test samples in normal and
motion-influenced classes. An input CVS is projected onto or near a manifold
learned by positive samples. As desired, the residual (24) tends to be small
for normal samples and high for motion-influenced samples.

The third and fourth rows of Tables 1 (a) and (b) show the final assessment
results using manifold-learning models. The performance was comparable to that
of discriminative models. We note that the manifold-learning models never
learned negative samples for classifier development. As shown in Figure 6 (d),
the manifold-learning model’s performance gap between training and test sets
was very small.

There was a slight difference in performance for the manifold-learning models
depending on the size normalization. Linear interpolation promised a slightly
better assessment of accuracy, NPV, and AUC than the other. For the case of
constant padding, because core profiles of CVS data are supported at different
intervals, the learning complexity can be increased, which is associated with
invariant feature extraction to the intervals. This may cause a slight drop in
performance.

In our dataset, both discriminative and manifold learning models provided
accurate detection of motion-influenced CVS. The discriminative model yielded
a more powerful SQI performance; in contrast, the manifold-learning model
provided stable outcomes between the training and test sets. Regarding
practical applications, the choice of two models relies on what should be
emphasized in the monitoring system in terms of performance and stability.
Their ensemble is also worth considering.

####  3.2.3 Impact of Scale Normalization

| With Scaling | Without Scaling
---|---|---
Model |  VGG16-3 |  VAE |  VGG16-3 |  VAE
Accuracy |  0.9468 |  0.9066 |  0.7862 |  0.7509
PPV |  0.9525 |  0.9687 |  0.9763 |  0.9668
NPV |  0.9047 |  0.6181 |  0.4038 |  0.3327
Sensitivity |  0.9886 |  0.9218 |  0.7671 |  0.7373
Specificity |  0.7215 |  0.8095 |  0.8945 |  0.8380
AUC |  0.9709 |  0.9513 |  0.9067 |  0.8906
Table 2: Results of machine learning-based CVS quality assessment with and
without scale normalization.

Table 2 shows the worst case when scale normalization was not applied. In
CNNs, network training was very unstable, and assessment performance was
considerably degraded, especially regarding accuracy, NPV, sensitivity, and
AUC. In VAEs, large-scale variability of CVS data highly affected the loss of
accuracy in manifold projection; therefore, the performance significantly
deteriorated in terms of accuracy, NPV, sensitivity, and AUC. This verifies
the impact of scale normalization.

####  3.2.4 Inference Time

Model |  LR |  MLP1 |  MLP2 |  VGG16-3 |  VGG16-4
---|---|---|---|---|---
Time |  0.633$\mu$s |  1.265$\mu$s |  0.700$\mu$s |  1.897$\mu$s |  3.162$\mu$s
Model |  VGG16-5 |  PCA |  VAE |  CVAE |  -
Time |  3.562$\mu$s |  48.412$\mu$s |  3.703$\mu$s |  15.192$\mu$s |  -
Table 3: Test inference time of machine learning-based CVS quality assessment
methods.

In real-time monitoring, assessment should be performed quickly. The input for
the proposed method was updated for every heartbeat in the EIT system.
Assuming a subject with a constant 80bpm, the CVS input is updated every
0.75s. Roughly, the assessment should be faster than approximately $10^{-2}$s.
Table 3 shows the inference time for the test data, calculated by taking the
average over the entire test data. The ML models provided a test outcome with
inference times between 100$\mu$s ($10^{-4}$s) and 0.1$\mu$s ($10^{-7}$s).
This confirms that the proposed method meets the speed requirements for real-
time monitoring.

##  4 Conclusion and Discussion

We developed a novel automated SQI method using two machine learning
techniques, the discriminative model and manifold learning, to detect abnormal
CVS caused by motion-induced artifacts. We discussed how body movement
influences the transconductance data and how the resulting CVS is degraded by
movement. Numerous experiments support the idea that the proposed method can
successfuly filter motion-induced unrealistic variations in CVS data.

To the best of our knowledge, this is the first attempt to assess CVS quality
to enhance the clinical capability of an EIT-based cardiopulmonary monitoring
system. From a practical point of view, the proposed method can alert
clinicians about CVS corruption to minimize misinformation about patient
safety and facilitate adequate management of patients and medical resources.
The proposed method can be combined with a software system for existing EIT
devices.

The use of only healthy subject data in the training process did not fully
consider possible influence of the subject’s illness on CVS. SQI performance
might be degraded in patients with illnesses such as arrhythmias, in which
irregular deformation may occur in CVS due to premature ventricular
contraction and lead to be classified as low signal quality. However, when ill
patient data are available and appended in the training process, a slightly
modified SQI can detect the illness and motion by adding another label class.
Meanwhile, arrhythmia can be easily detected using ECG signals.

A further collection of CVS data could be a strategy for enhancing model
generalization or stability toward being equipped with an actual monitoring
system. In discriminative models, even with additional data collection,
generalization or stability might not be meaningfully improved because the
class imbalance problem remains or increases. In contrast, the manifold-
learning models can accurately infer common features (i.e., data manifolds) as
the total number of normal CVS data grows regardless of class imbalance. In
addition, it can be extended into a semi-supervised or unsupervised learning
framework [2, 46], which reduces the requirement for labeled datasets. Thus,
manifold-learning models might be favorable.

## Data Availability

The data that support the findings of this study are available from the
corresponding author, K. Lee, upon reasonable request.

## Acknowledgements

This work was supported by the Ministry of Trade, Industry and Energy (MOTIE)
in Korea through the Industrial Strategic Technology Development Program under
Grant 20006024. Hyun was supported by Samsung Science & Technology Foundation
(No. SRFC-IT1902-09). We are deeply grateful to BiLab (Pangyo, South Korea)
for their help and collaboration.

## Conflict of Interest

The authors have no conflicts to disclose.

##  Appendix A Motion-induced Effect on Trans-conductance

In the 16 channel EIT system, the voltage data $\\{V^{j,k}_{t}\\}_{j,k}$ in
(1) are governed by the following complete electrode model [44]: At time $t$,
the electric potential distribution ($u_{t}^{j}$) and electric potential on an
electrode ($U_{t}^{j,k}$) satisfy

$\left\\{\begin{array}[]{rl}\displaystyle\nabla\cdot(\gamma_{t}\nabla
u^{j}_{t})&=0~{}~{}~{}~{}\mbox{ in }\Omega\subset\mathbb{R}^{3}\\\
\gamma_{t}\nabla u_{t}^{j}\cdot n&=0~{}~{}~{}~{}\mbox{ on
}\partial\Omega\backslash\bigcup_{i}^{16}\mathcal{E}^{k}\\\
\displaystyle\int_{\mathcal{E}^{k}}\gamma_{t}\nabla u_{t}^{j}\cdot
n&=0~{}~{}~{}~{}\mbox{ for }k\in\mathcal{I}\backslash\\{j,j+1\\}\\\
\displaystyle u_{t}^{j}+z_{k}(\gamma_{t}\nabla u_{t}^{j}\cdot
n)&=U_{t}^{j,k}\mbox{ on }\mathcal{E}^{k}\mbox{ for }k\in\mathcal{I}\\\
\displaystyle\int_{\mathcal{E}^{j}}\gamma_{t}\nabla u_{t}^{j}\cdot
nds&=-\displaystyle\int_{\mathcal{E}^{j+1}}\gamma_{t}\nabla u_{t}^{j}\cdot
nds=I\end{array}\right.$ (29)

where $\gamma_{t}$ is a conductivity distribution in a human chest $\Omega$ at
$t$, $n$ is an unit normal vector outward $\partial\Omega$, $ds$ is a surface
element, and $z_{k}$ is a skin-electrode contact impedance on
$\mathcal{E}^{k}$. The amount of electric current $I$, which is injected to
the domain $\Omega$, can be scaled and, thus, assumed to be $I=1$.

In the case that the human chest $\Omega$ is time-varying owing to motions,
Reynolds transport theorem yields the following approximation [39]:

$\dot{V}^{j,k}_{t}\approx\dot{V}^{j,k,\mbox{\scriptsize
normal}}_{t}+\dot{V}^{j,k,\mbox{\scriptsize motion}}_{t}$ (30)

where

$\displaystyle\dot{V}^{j,k,\mbox{\scriptsize normal}}_{t}$
$\displaystyle=-\int_{\Omega}\dot{\gamma}_{t}(\boldsymbol{r})\nabla
u^{j}_{t}(\boldsymbol{r})\cdot\nabla u_{t}^{k}(\boldsymbol{r})d\boldsymbol{r}$
(31) $\displaystyle\dot{V}^{j,k,\mbox{\scriptsize motion}}_{t}$
$\displaystyle=-\int_{\partial\Omega}\boldsymbol{v}_{n}(\boldsymbol{r},t)\gamma_{t}(\boldsymbol{r})\nabla
u^{j}_{t}(\boldsymbol{r})\cdot\nabla u^{k}_{t}(\boldsymbol{r})ds$ (32)

Here, $\boldsymbol{v}_{n}$ is an outward-normal directional velocity of
$\partial\Omega$ and $\boldsymbol{r}\in\Omega$ is a position vector in
$\Omega$. The term $\dot{V}^{j,k,\mbox{\scriptsize normal}}_{t}$ and
$\dot{V}^{j,k,\mbox{\scriptsize motion}}_{t}$ can be viewed as voltage data
acquirable in normal EIT measurement and motion-induced inference,
respectively.

A similar relation to (30) for trans-conductance can be derived as follows:
Let us define a trans-conductance-related value $g_{t}^{j,k}$ by

$g_{t}^{j,k}=\dfrac{I}{\mathfrak{R}(V_{t}^{j,k})}$ (33)

By differentiating $g_{t}^{j,k}$ with respect to $t$, we obtain

${\scriptsize\dot{g}_{t}^{j,k}=\dfrac{-I\mathfrak{R}(\dot{V}_{t}^{j,k})}{\left(\mathfrak{R}(V_{t}^{j,k})\right)^{2}}\approx\dfrac{-I(\mathfrak{R}(\dot{V}_{t}^{j,k,\mbox{\scriptsize
normal}})+\mathfrak{R}(\dot{V}_{t}^{j,k,\mbox{\scriptsize
motion}}))}{\left(\mathfrak{R}(V_{t}^{j,k})\right)^{2}}}$ (34)

The approximation (34) can be expressed as

$\dot{g}_{t}^{j,k}\approx\dot{g}_{t}^{j,k,\mbox{\scriptsize
normal}}+\dot{g}_{t}^{j,k,\mbox{\scriptsize motion}}$ (35)

where

$\dot{g}_{t}^{j,k,\mbox{\scriptsize
normal}}=\dfrac{-I\mathfrak{R}(\dot{V}_{t}^{j,k,\mbox{\scriptsize
normal}})}{(\mathfrak{R}(V_{t}^{j,k}))^{2}}\mbox{ and
}\dot{g}_{t}^{j,k,\mbox{\scriptsize
motion}}=\dfrac{-I\mathfrak{R}(\dot{V}_{t}^{j,k,\mbox{\scriptsize
motion}})}{(\mathfrak{R}(V_{t}^{j,k}))^{2}}$ (36)

We note that, in the case of $\boldsymbol{v}_{n}=\boldsymbol{0}$ in (32)
(i.e., EIT measurement is not affected by motions), the relation (34) becomes
$\dot{g}_{t}^{j,k}=\dot{g}_{t}^{j,k,\mbox{\scriptsize normal}}$ by the reason
of $V_{t}^{j,k,{\mbox{\scriptsize motion}}}=0$. In the form of trans-
conductance vector, the following approximation holds:

$\dot{\boldsymbol{g}}_{t}\approx\dot{\boldsymbol{g}}_{t}^{\mbox{\scriptsize
normal}}+\dot{\boldsymbol{g}}_{t}^{\mbox{\scriptsize motion}}$ (37)

where

$\dot{\boldsymbol{g}}_{t}^{\mbox{\scriptsize
normal}}=\begin{bmatrix}\dot{g}^{1,3,\mbox{\scriptsize
normal}}_{t},\cdots,\dot{g}^{16,14,\mbox{\scriptsize
normal}}_{t}\end{bmatrix}\mbox{ and
}\dot{\boldsymbol{g}}_{t}^{\mbox{\scriptsize
motion}}=\begin{bmatrix}\dot{g}^{1,3,\mbox{\scriptsize
motion}}_{t},\cdots,\dot{g}^{16,14,\mbox{\scriptsize
motion}}_{t}\end{bmatrix}$ (38)

If $\dot{\boldsymbol{g}}_{t}^{\mbox{\scriptsize normal}}$ satisfies the
relation (5), we consequently obtain

$\dot{\boldsymbol{g}}_{t}\approx\dot{\boldsymbol{g}}_{t}^{\mbox{\scriptsize
air}}+\dot{\boldsymbol{g}}_{t}^{\mbox{\scriptsize
blood}}+\dot{\boldsymbol{g}}_{t}^{\mbox{\scriptsize motion}}$ (39)

Here, we note that $\dot{\boldsymbol{g}}_{t}^{\mbox{\scriptsize motion}}$
becomes more significant as motion (i.e., $|\boldsymbol{v}_{n}|$ in (32)) is
large.

##  Appendix B Machine Learning Models

###  B.1 Discriminative Models

#### Logistic Regression (LR)

A LR model $f_{\mbox{\scriptsize LR}}$ consists of linear transformation and
sigmoid as follows:

$f_{\mbox{\scriptsize
LR}}(\overline{\boldsymbol{X}})=\sigma(\mathbf{w}^{T}\overline{\boldsymbol{X}}+b)$
(40)

where $\mathbf{w}\in\mathbb{R}^{150}$ and $b\in\mathbb{R}$ are learnable
weight and bias, and $\sigma$ is a sigmoid function given by
$\sigma(x)=(1+\exp(x))^{-1}$.

#### Multilayer Perceptron (MLP)

A MLP model $f_{\mbox{\scriptsize MLP}}$ has a hierarchical structure with
nonlinearity compared to LR. Each layer consists of linear transformation and
nonlinear activation. In our MLP models, ReLU is used in all layers except the
last to avoid gradient vanishing [20]. Table 4 shows the architectures of the
MLPs used in this study.

#### Convolutional Neural Network (CNN)

A CNN model $f_{\mbox{\scriptsize CNN}}$ consists of two paths; 1) feature
extraction and 2) classification paths. In this study, the feature extraction
path is based on VGG16 [45], as shown in Table 4. The resultant feature map is
flattened and then forwarded to the classification path, which is a MLP.

The feature extraction path is a series of two convolutional and maxpooling
(or flatten) layers, whose depth is associated with receptive field (RF) size
of a unit in the last convolutional layer [35]. According to the length of
this series, VGG16-3, -4, and -5 are defined, where 3, 4, and 5 represent the
iteration number of the layers in the series. Here, RFs are given by 32, 68,
and 140, respectively.

(a) MLP1 (MLP2)
Layer Input Dim Output Dim Activation Linear 150 (150) 150 (150) ReLU Linear
150 (150) 300 (150) ReLU Linear 300 (150) 300 (100) ReLU Linear 300 (100) 150
(50) ReLU Linear 150 (50) 150 (25) ReLU Linear 150 (25) 150 (10) ReLU Linear
150 (10) 1 (1) Sigmoid
(b) VGG16-5; [1] Feature extraction and [2] Classification networks
Layer Input Dim Output Dim Kernel Activation RF [1] Conv1D 150$\times$1
150$\times$4 3$\times$4 ReLU 3 Conv1D 150$\times$4 150$\times$4 3$\times$4
ReLU 5 MaxPool1D 150$\times$4 75$\times$4 2 ReLU 6 Conv1D 75$\times$4
75$\times$8 3$\times$8 ReLU 10 Conv1D 75$\times$8 75$\times$8 3$\times$8 ReLU
14 MaxPool1D 75$\times$8 37$\times$8 2 ReLU 16 Conv1D 37$\times$8 37$\times$16
3$\times$16 ReLU 24 Conv1D 37$\times$16 37$\times$16 3$\times$16 ReLU 32
MaxPool1D 37$\times$16 18$\times$16 2 ReLU 36 Conv1D 18$\times$16 18$\times$32
3$\times$32 ReLU 52 Conv1D 18$\times$32 18$\times$32 3$\times$32 ReLU 68
MaxPool1D 18$\times$32 9$\times$32 2 ReLU 76 Conv1D 9$\times$32 9$\times$64
3$\times$64 ReLU 108 Conv1D 9$\times$64 9$\times$64 3$\times$64 ReLU 140
Flatten 9$\times$64 576$\times$1 - - - [2] Linear 576$\times$1 576$\times$1 -
ReLU - Linear 576$\times$1 1$\times$1 - Sigmoid -

Table 4: Network architectures; MLP and VGG16-6.

###  B.2 Manifold-learning Models

This subsection explains structures of an encoder $\mathcal{E}$ and a decoder
$\mathcal{D}$ in (23), which were used for the manifold-learning approach
described in Section 2.3.2. The dimension of the latent vector
$\boldsymbol{z}$ was constantly set as 10 in our experiments.

#### Principal Component Analysis (PCA)

PCA learns principal vectors
$\\{\boldsymbol{v}_{i}\in\mathbb{R}^{150}\\}_{i=1}^{10}$ in the following
sense: For $i=1,\cdots,10$,

$\boldsymbol{v}_{i}=\underset{\|\boldsymbol{v}\|=1}{\mbox{argmax}}~{}\|\mathfrak{X}_{i}\boldsymbol{v}\|_{2}^{2}\mbox{
and
}\mathfrak{X}_{i}=\mathfrak{X}_{i-1}-\boldsymbol{v}_{i-1}\boldsymbol{v}_{i-1}^{T}$
(41)

where $\mathfrak{X}_{1}:=[\overline{\boldsymbol{X}}_{\mbox{\scriptsize
pos}}^{(1)},\overline{\boldsymbol{X}}_{\mbox{\scriptsize
pos}}^{(2)},\cdots,\overline{\boldsymbol{X}}_{\mbox{\scriptsize
pos}}^{(N_{\mbox{\scriptsize pos}})}]^{T}$. For ease of explanation,
$\mathfrak{X}_{1}$ is assumed to be zero-mean. An encoder
$\mathcal{E}_{\mbox{\scriptsize pca}}$ and a decoder
$\mathcal{D}_{\mbox{\scriptsize pca}}$ are given by

$\mathcal{E}_{\mbox{\scriptsize
pca}}(\overline{\boldsymbol{X}})=\boldsymbol{z}:=\begin{bmatrix}\langle\overline{\boldsymbol{X}},\boldsymbol{v}_{1}\rangle,\cdots,\langle\overline{\boldsymbol{X}},\boldsymbol{v}_{10}\rangle\end{bmatrix}\mbox{
and }\mathcal{D}_{\mbox{\scriptsize
pca}}(\boldsymbol{z})=\sum_{j=1}^{10}\boldsymbol{z}_{i}\boldsymbol{v}_{i}$
(42)

where $\boldsymbol{z}_{i}$ is $i$-th component of $\boldsymbol{z}$.

(a) VAE
Encoder Layer Input Dim Output Dim Activation Linear 150 125 ReLU Linear 125
75 ReLU Linear 75 50 ReLU Linear 50 10$\times 2$ - Sampling 10$\times 2$ 10 -
Decoder Linear 10 50 ReLU Linear 50 75 ReLU Linear 75 125 ReLU Linear 125 150
-
(b) Convolutional VAE
Encoder Layer Input Dim Output Dim Kernel Activation Conv1D 150$\times$1
75$\times$8 3$\times$8 ReLU Conv1D 75$\times$8 38$\times$16 3$\times$16 ReLU
Conv1D 38$\times$16 19$\times$24 3$\times$24 ReLU Conv1D 19$\times$24
10$\times$32 3$\times$32 ReLU Flattening 10$\times$32 320$\times$1 - - Linear
320$\times$1 10$\times$2 - - Sampling 10$\times$2 10$\times$1 - - Decoder
Linear 10$\times$1 320$\times$1 - - Reshaping 320$\times$1 10$\times$32 - -
DeConv1D 10$\times$32 19$\times$24 3$\times$24 ReLU DeConv1D 19$\times$24
38$\times$16 3$\times$16 ReLU DeConv1D 38$\times$16 75$\times$8 3$\times$8
ReLU DeConv1D 75$\times$8 150$\times$8 3$\times$8 ReLU Conv1D 150$\times$8
150$\times$1 1$\times$1 ReLU Linear 150$\times$1 150$\times$1 -

Table 5: VAE network architectures.

#### Variational Auto-encoder (VAE)

Table 5 shows encoder-decoder models for VAE, whose network architecture is
based on either MLP or CNN. In VAE, $\boldsymbol{z}$ is given by the following
sampling procedure:
$\boldsymbol{z}=\boldsymbol{\mu}+\boldsymbol{\sigma}\odot\boldsymbol{z}_{\mbox{\scriptsize
noise}}$ and $\boldsymbol{z}_{\mbox{\scriptsize
noise}}\sim\mathcal{N}(\boldsymbol{0},\boldsymbol{I})$, where
$\boldsymbol{\mu}$ and $\boldsymbol{\sigma}$ are substantial outputs generated
by a neural network, $\odot$ is the element-wise product, and
$\mathcal{N}(\boldsymbol{0},\boldsymbol{I})$ is the normal distribution of
mean $\boldsymbol{0}$ and covariance $\boldsymbol{I}$. Here, $\boldsymbol{0}$
is the zero vector and $\boldsymbol{I}$ is the identity matrix of $10\times
10$.

For VAE training, the following term is added to the loss function (23):

$\mbox{KL}(\mathcal{N}(\boldsymbol{\mu},\boldsymbol{\Sigma})\|\mathcal{N}(\boldsymbol{0},\boldsymbol{I}))=\dfrac{1}{2}\sum_{i=1}^{10}(\boldsymbol{\mu}_{i}^{2}+\boldsymbol{\sigma}_{i}^{2}-\log\boldsymbol{\sigma}_{i}-1)$
(43)

where KL is Kullback-Leibler divergence and $\boldsymbol{\Sigma}$ is a
$10\times 10$ diagonal matrix whose $(i,i)$ entry is
$\boldsymbol{\sigma}_{i}$. This term enables VAE to learn dense and smooth
latent space embedding in or near $\mathcal{N}(\boldsymbol{0},\boldsymbol{I})$
[30, 47, 55].

####  $\beta$-Variational Auto-encoder ($\beta$-VAE)

$\beta$-VAE differs with VAE in terms of loss function while sharing a model
architecture. For some $\beta\in\mathbb{R}$, $\beta\times\mbox{KL}$ is added
to the loss (23) instead of (43) (i.e., VAE is the case of $\beta=1$). This
simple weighting is known to be advantageous on disentangled representation
learning of underlying factors [24]. We determined an optimal $\beta$ as the
empirical best. Table 6 showed SQI performance variation about $\beta$ in the
dataset where the scale and size normalization using linear interpolation were
applied.

|  $\boldsymbol{\beta}$-VAE |  $\boldsymbol{\beta}$-CVAE
---|---|---
|  $\boldsymbol{\beta}=\frac{1}{3}$ |  $\boldsymbol{\beta}=\frac{1}{2}$ |  $\boldsymbol{\beta}=1$ |  $\boldsymbol{\beta}=2$ |  $\boldsymbol{\beta}=3$ |  $\boldsymbol{\beta}=\frac{1}{3}$ |  $\boldsymbol{\beta}=\frac{1}{2}$ |  $\boldsymbol{\beta}=1$ |  $\boldsymbol{\beta}=2$ |  $\boldsymbol{\beta}=3$
Test |  Accuracy |  0.9060 |  0.9092 |  0.9066 |  0.8951 |  0.9221 |  0.9208 |  0.9298 |  0.9292 |  0.9195 |  0.9189
PPV |  0.9694 |  0.9680 |  0.9687 |  0.9682 |  0.9672 |  0.9750 |  0.9739 |  0.9688 |  0.9663 |  0.9663
NPV |  0.6151 |  0.6282 |  0.6181 |  0.5802 |  0.6900 |  0.6617 |  0.7011 |  0.7100 |  0.6720 |  0.6693
Sensitivity |  0.9203 |  0.9255 |  0.9218 |  0.9084 |  0.9441 |  0.9322 |  0.9441 |  0.9486 |  0.9397 |  0.9389
Specificity |  0.8142 |  0.8047 |  0.8095 |  0.8095 |  0.7952 |  0.8476 |  0.8380 |  0.8047 |  0.7904 |  0.7904
AUC |  0.9503 |  0.9439 |  0.9513 |  0.9426 |  0.9489 |  0.9531 |  0.9603 |  0.9528 |  0.9528 |  0.9471
Table 6: $\boldsymbol{\beta}$-VAE performance comparison about varying
$\boldsymbol{\beta}$.

## References

  * [1] A. Adler, R. Guardo, Y. Berthiaume, “Impedance imaging of lung ventilation: Do we need to account for chest expansion?” _IEEE Trans. Biomed. Eng_ , 43, 414-20, 1996.
  * [2] J. An, and S. Cho, “Variational autoencoder based anomaly detection using reconstruction probability,” _Special Lecture on IE_ , 2(1), 1-18, 2015.
  * [3] A. Adler and A. Boyle “Electrical impedance tomography: Tissue properties to image measures,” _IEEE Transactions on Biomedical Engineering_ , 64(11), 2494-2504, 2017.
  * [4] A. T. Askari and A. W. Messerli, “Cardiovascular Hemodynamics”, 2nd ed., Cham, _Switzerland: Humana Press_ , 2019.
  * [5] M. Alfaras, M. C. Soriano, and S. Ortin, “A fast machine learning model for ECG-based heartbeat classification and arrhythmia detection,” _Frontiers in Physics_ , 7, 103, 2019.
  * [6] B. H. Brown et al., “Blood flow imaging using electrical impedance tomography,” _Clin. Phys. Physiol. Meas._ , vol. 13, pp. 175–179, 1992.
  * [7] A. Boyle and A. Adler, “Electrode models under shape deformation in electrical impedance tomography,” _Journal of Physics: Conference Series_ , Vol. 224, No. 1, 2010.
  * [8] J. B. Borges et al., “Regional lung perfusion estimated by electrical impedance tomography in a piglet model of lung collapse,” _J. Appl. Physiol._ , vol. 112, pp. 225-236, 2012.
  * [9] D. Belo, J. Rodrigues, J. R. Vaz, P. Pezarat-Correia, and H. Gamboa, “Biosignals learning and synthesis using deep neural networks,” _Biomedical engineering online_ , 16(1), 1-17, 2017.
  * [10] M. Buda, A. Maki, and M. A. Mazurowski, “A systematic study of the class imbalance problem in convolutional neural networks,” _Neural networks_ , 106, 249-259, 2018.
  * [11] Van Ravenswaaij-Arts, Conny MA, et al., “Heart rate variability”, _Annals of internal medicine_ , 118(6), 436-447, 1993.
  * [12] J. S. Cramer, “The origins of logistic regression,” _Tinbergen Institute Working_ , 4, 2002.
  * [13] O. Chapelle, B. Scholkopf, and A. Zien, “Semi-supervised learning,” (chapelle, o. et al., eds.; 2006)[book reviews]. _IEEE Transactions on Neural Networks_ , 20(3), 542-542, 2009.
  * [14] S. Celin, and K. Vasanth, “ECG signal classification using various machine learning techniques,” _Journal of medical systems_ , 42(12), 1-11, 2018.
  * [15] K. Cao, C. Wei, A. Gaidon, N. Arechiga, and T. Ma, “Learning imbalanced datasets with label-distribution-aware margin loss,” _Advances in neural information processing systems_ , 2, 2019.
  * [16] P. H. Charlton et al., “An impedance pneumography signal quality index: Design, assessment and application to respiratory rate monitoring,” Biomed. Sig. Proc. Cont., vol. 65, 2021, Art. no. 102339.
  * [17] T. Dai, C. Gómez-Laberge, and A. Adler, “Reconstruction of conductivity changes and electrode movements based on EIT temporal sequences”, _Physiol. Meas._ , 29(6), S77-S88, 2008.
  * [18] J. M. Deibele, H. Luepschen, and S. L. Leonhardt, “Dynamic separation of pulmonary and cardiac changes in electrical impedance tomography,” _Physiol. Meas._ , vol. 29, pp. S1-S14, 2008.
  * [19] I. Frerichs, T. Becher, and N. Weiler, “Electrical impedance tomography imaging of the cardiopulmonary system,” _Curr. Opin. Crit. Care_ , vol. 20, pp. 323-332, 2014.
  * [20] I. Goodfellow, Y. Bengio, and A. Courville, “Deep Learning,” MIT Press, 2016.
  * [21] G. E. Hinton, and R. R. Salakhutdinov, “Reducing the dimensionality of data with neural networks,” _science_ , 313(5786), 504-507, 2006.
  * [22] G. E. Hinton, “Learning multiple layers of representation,” _Trends in cognitive sciences_ , 11(10), 428-434, 2007.
  * [23] H. He, and E. A. Garcia, “Learning from imbalanced data,” _IEEE Transactions on knowledge and data engineering_ , 21(9), 1263-1284, 2009.
  * [24] I. Higgins, L. Matthey, A. Pal, C. Burgess, X. Glorot, M. Botvinick et al., “beta-vae: Learning basic visual concepts with a constrained variational framework,” 2016.
  * [25] C. M. Hyun, S. H. Baek, M. Lee, S. M. Lee, and J. K. Seo, “Deep learning-based solvability of underdetermined inverse problems in medical imaging,” _Medical Image Analysis_ , 69, 101967, 2021.
  * [26] I. T. Jolliffe, and J. Cadima, “Principal component analysis: a review and recent developments,” _Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences_ , 374(2065), 20150202, 2016.
  * [27] G. Y. Jang et al., “Noninvasive, simultaneous, and continuous measurements of stroke volume and tidal volume using EIT: Feasibility study of animal experiments,” _Sci. Rep._ , vol. 10, 2020.
  * [28] W. G. Kubicek, R. P. Patterson, and D. A. Witsoe, “Impedance cardiography as a noninvasive method of monitoring cardiac function and other parameters of the cardiovascular system,” _Ann. New York Acad. Sci._ , vol. 170, pp. 724-732, 1970.
  * [29] N. Kerrouche, C. N. McLeod, and W. R. B. Lionheart, “Time series of EIT chest images using singular value decomposition and fourier transform,” _Physiol. Meas._ , vol. 22, pp. 147-157, 2001.
  * [30] D. P. Kingma, and M. Welling, “Auto-encoding variational bayes,” _arXiv preprint arXiv:1312.6114_ , 2013.
  * [31] D. P. Kingma, and J. Ba, “Adam: A method for stochastic optimization,” _arXiv:1412.6980_. 2014.
  * [32] WRB Lionheart, “Boundary Shape and Electrical Impedance Tomography,” _Inverse Problems_ , 14 139-47, 1998.
  * [33] S. Leonhardt and B. Lachmann, “Electrical impedance tomography: The holy grail of ventilation and perfusion monitoring,” _Intensive Care Med._ , vol. 38, pp. 1917–1929, 2012.
  * [34] Y. LeCun, Y. Bengio, and G. Hinton, “Deep learning,” _nature_ , 521(7553), 436-444, 2015.
  * [35] W. Luo, Y. Li, R. Urtasun, R. Zemel, “Understanding the Effective Receptive Field in Deep Convolutional Neural Networks,” _arXiv:170.04128_ , 2017.
  * [36] K. Lee, E. J. Woo, and J. K. Seo, “A fidelity-embedded regularization method for robust electrical impedance tomography,” _IEEE transactions on medical imaging_ , 37(9), 1970-1977, 2017.
  * [37] J. H. Lee, Y. R. Park, S. Kweon, S. Kim, W. Ji, and C. M Choi, “A Cardiopulmonary Monitoring System for Patient Transport Within Hospitals Using Mobile Internet of Things Technology: Observational Validation Study,” _JMIR mHealth and uHealth_ , 6(11), 2018.
  * [38] M. H. Lee, G. Y. Jang, Y. E. Kim, P. J. Yoo, H. Wi, T. I. Oh, and E. J. Woo, “Portable multi-parameter electrical impedance tomography for sleep apnea and hypoventilation monitoring: feasibility study,” _Physiological Measurement_ , 2018.
  * [39] K. Lee, G. Y. Jang, Y. Kim, and E. J. Woo, “Multi-Channel Trans-Impedance Leadforming for Cardiopulmonary Monitoring: Algorithm Development and Feasibility Assessment Using In Vivo Animal Data,” _IEEE Transactions on Biomedical Engineering_ , 69(6), 1964-1974, 2021.
  * [40] R. Pikkemaat et al., “Recent advances in and limitations of cardiac output monitoring by means of electrical impedance tomography,” _Anesth.Analg._ , vol. 119, pp. 76–83, 2014.
  * [41] C. Putensen et al., “Electrical impedance tomography for cardiopulmonary monitoring,” _J. Clin. Med._ , vol. 8, 2019.
  * [42] M. D. Ruopp, N. J. Perkins, B. W. Whitcomb, and E. F. Schisterman, “Youden Index and optimal cut‐point estimated from observations affected by a lower limit of detection,” _Biometrical Journal: Journal of Mathematical Methods in Biosciences_ , 50(3), 419-430, 2008.
  * [43] M. Soleimani, C. Gómez-Laberge, and A. Adler, “Imaging of conductivity changes and electrode movement in EIT”, _Physiol. Meas._ , 27(5), S103-S113, 2006.
  * [44] J. K. Seo and E. J. Woo, _Nonlinear Inverse Problems in Imaging_ , Chichester, U.K.:Wiley, 2013.
  * [45] K. Simonyan, and A. Zisserman, “Very deep convolutional networks for large-scale image recognition,” _arXiv preprint arXiv:1409.1556_ , 2014.
  * [46] T. Schlegl, P. Seeböck, S. M. Waldstein, U. Schmidt-Erfurth, and G. Langs, “Unsupervised anomaly detection with generative adversarial networks to guide marker discovery,” _In International conference on information processing in medical imaging_ , pp. 146-157, Springer, Cham, 2017.
  * [47] J. K. Seo, K. C. Kim, A. Jargal, K. Lee, and B. Harrach, “A learning-based method for solving ill-posed nonlinear inverse problems: a simulation study of lung EIT,” _SIAM journal on Imaging Sciences_ , 12(3), 1275-1295, 2019.
  * [48] S. Sahoo, M. Dash, S. Behera, and S. Sabut, “Machine learning approach to detect cardiac arrhythmias in ECG signals: a survey,” _Irbm_ , 41(4), 185-194, 2020
  * [49] G. Van Horn, and P. Perona, “The devil is in the tails: Fine-grained classification in the wild,” _arXiv preprint arXiv:1709.01450_ , 2017.
  * [50] J. E. Van Engelen, and H. H. Hoos, “A survey on semi-supervised learning,” _Machine Learning_ , 109(2), 373-440, 2020.
  * [51] N. Westterhof et al., “Snapshots of Hemodynamics”, 3rd ed., Cham, _Switzerland: Springer_ , 2019.
  * [52] M. Wasimuddin, K. Elleithy, A. S. Abuzneid, M. Faezipour, and O. Abuzaghleh, “Stages-based ECG signal analysis from traditional signal processing to machine learning approaches: A survey,” _IEEE Access_ , 8, 177782-177803, 2020.
  * [53] Y. Xu, T. Xiao, J. Zhang, K. Yang, and Z. Zhang, “Scale-invariant convolutional neural networks,” _arXiv preprint arXiv:1411.6369_ , 2014.
  * [54] L. Yang et al, “Removing Clinical Motion Artifacts During Ventilation Monitoring With Electrical Impedance Tomography: Introduction of Methodology and Validation With Simulation and Patient Data,” _Frontiers in medicine_ , 2022.
  * [55] H. S. Yun, C. M. Hyun, S. H. Baek, S.-H. Lee, J. K. Seo, “A semi-supervised learning approach for automated 3D cephalometric landmark identification using computed tomography,” _PLoS ONE_ , 17(9), e0275114, 2022.
  * [56] J. Zhang and R. P. Patterson, “EIT images of ventilation: What contributes to the resistivity changes?”, _Physiol. Meas._ , 26(2), S81-S92, 2005
  * [57] S. Zlochiver et al., “Parametric EIT for monitoring cardiac stroke volume,” _Physiol. Meas._ , vol. 27, pp. S139-S146, 2006.
  * [58] X. Zhu and A. B. Goldberg, “Introduction to semi-supervised learning,” _Synthesis lectures on artificial intelligence and machine learning_ , 3(1), 1-130, 2009.