A Comparison of Deep Learning Techniques for Arterial Blood Pressure Prediction

Abstract

Continuous vital signal monitoring is becoming more relevant in preventing diseases that afflict a large part of the world’s population; for this reason, healthcare equipment should be easy to wear and simple to use. Non-intrusive and non-invasive detection methods are a basic requirement for wearable medical devices, especially when these are used in sports applications or by the elderly for self-monitoring. Arterial blood pressure (ABP) is an essential physiological parameter for health monitoring. Most blood pressure measurement devices determine the systolic and diastolic arterial blood pressure through the inflation and the deflation of a cuff. This technique is uncomfortable for the user and may result in anxiety, and consequently affect the blood pressure and its measurement. The purpose of this paper is the continuous measurement of the ABP through a cuffless, non-intrusive approach. The approach of this paper is based on deep learning techniques where several neural networks are used to infer ABP, starting from photoplethysmogram (PPG) and electrocardiogram (ECG) signals. The ABP was predicted first by utilizing only PPG and then by using both PPG and ECG. Convolutional neural networks (ResNet and WaveNet) and recurrent neural networks (LSTM) were compared and analyzed for the regression task. Results show that the use of the ECG has resulted in improved performance for every proposed configuration. The best performing configuration was obtained with a ResNet followed by three LSTM layers: this led to a mean absolute error (MAE) of 4.118 mmHg on and 2.228 mmHg on systolic and diastolic blood pressures, respectively. The results comply with the American National Standards of the Association for the Advancement of Medical Instrumentation. ECG, PPG, and ABP measurements were extracted from the MIMIC database, which contains clinical signal data reflecting real measurements. The results were validated on a custom dataset created at Neuronica Lab, Politecnico di Torino.

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Vol.:(0123456789)
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https://doi.org/10.1007/s12559-021-09910-0
A Comparison ofDeep Learning Techniques forArterial Blood Pressure
Prediction
AnnunziataPaviglianiti1 · VincenzoRandazzo1· StefanoVillata1· GiansalvoCirrincione2,3· ErosPasero1
Received: 2 September 2020 / Accepted: 7 July 2021
© The Author(s) 2021
Abstract
Continuous vital signal monitoring is becoming more relevant in preventing diseases that afflict a large part of the world’s
population; for this reason, healthcare equipment should be easy to wear and simple to use. Non-intrusive and non-invasive
detection methods are a basic requirement for wearable medical devices, especially when these are used in sports applica-
tions or by the elderly for self-monitoring. Arterial blood pressure (ABP) is an essential physiological parameter for health
monitoring. Most blood pressure measurement devices determine the systolic and diastolic arterial blood pressure through the
inflation and the deflation of a cuff. This technique is uncomfortable for the user and may result in anxiety, and consequently
affect the blood pressure and its measurement. The purpose of this paper is the continuous measurement of the ABP through
a cuffless, non-intrusive approach. The approach of this paper is based on deep learning techniques where several neural
networks are used to infer ABP, starting from photoplethysmogram (PPG) and electrocardiogram (ECG) signals. The ABP
was predicted first by utilizing only PPG and then by using both PPG and ECG. Convolutional neural networks (ResNet and
WaveNet) and recurrent neural networks (LSTM) were compared and analyzed for the regression task. Results show that the
use of the ECG has resulted in improved performance for every proposed configuration. The best performing configuration
was obtained with a ResNet followed by three LSTM layers: this led to a mean absolute error (MAE) of 4.118mmHg on
and 2.228mmHg on systolic and diastolic blood pressures, respectively. The results comply with the American National
Standards of the Association for the Advancement of Medical Instrumentation. ECG, PPG, and ABP measurements were
extracted from the MIMIC database, which contains clinical signal data reflecting real measurements. The results were
validated on a custom dataset created at Neuronica Lab, Politecnico di Torino.
Keywords Arterial blood pressure· Deep learning algorithms· Electrocardiogram· Machine learning·
Photoplethysmogram
Introduction
Recent studies have highlighted the clinical relevance of
continuous blood pressure (BP) monitoring [1]. Arterial
blood pressure (ABP) is an indicator of hypertension, which
is one of the most important risk factors of cardiovascular
disease (CVD). For this reason, its variability is an important
indicator associated with risky cardiovascular events.
Two clinical gold standards exist to measure arterial
blood pressure: the invasive catheter system and the cuff-
based sphygmomanometer [2]. The invasive catheter sys-
tem is performed through a catheter inserted into an artery:
it is used in intensive care units (ICU) to directly moni-
tor blood pressure in the most accurate way possible and
obtain samples for arterial blood gas analysis. However,
only physicians and specialized nurses can perform the
insertion; it is often painful and is performed by using
an anaesthetic to make it more tolerable and avoid vasos-
pasm [3]. On the other hand, cuff-based devices are the
gold standard for indirect measurements and are com-
monly recommended by physicians. These devices offer
high measurement accuracy; however, they also have sev-
eral downsides: cuff size is usually too small, leading to
errors in diagnosis [4] and the person using a cuff-based
* Annunziata Paviglianiti
annunziata.paviglianiti@polito.it
1 DET - Department ofElectronics andTelecommunications,
Politecnico Di Torino, Turin, Italy
2 Lab. LTI, Université de Picardie Jules Verne, Amiens, France
3 University ofSouth Pacific, Suva, Fiji
/ Published online: 27 August 2021
Cognitive Computation (2022) 14:1689–1710
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device has to follow a relatively strict measuring proto-
col to ensure that the measured values are correct. The
measuring procedure can be tedious and requires time and
effort; also, any physical activity (e.g. exercise) usually
does not allow for simultaneous measuring of BP with a
cuff [5]. Furthermore, the measuring event itself can cause
white coat hypertension, commonly known as white coat
syndrome: this is a condition where the patient’s blood
pressure is higher when taken in a medical setting, while
it is normal during daily activities. It is believed that the
phenomenon is due to anxiety experienced during a clini-
cal examination [4].
Continuous non-invasive arterial pressure (CNAP) meas-
urement combines the advantages of the two approaches.
CNAP systems have different requirements for general pub-
lic purposes and clinical purposes. In the public scenario, it
is sufficient to measure blood pressure changes over time,
while in the clinical case, the system must show not only
how it varies in time, but also absolute blood pressure,
physiological rhythms, and pulse waves for quality control
(Fig.1) [2].
To detect blood pressure inside an artery from the outside,
several techniques have been developed. The starting point
is usually volume and flow changes in the artery, which are
easily collectable in the periphery (e.g. in a finger); however,
these features are not linearly correlated with blood pressure,
because of the non-linearity of the elastic components of the
arterial wall and the non-elastic parts of the smooth muscles
of the finger artery [2]. Several external techniques involve
monitoring the pulse wave, which has a clear relationship
with blood pressure when vessels are more relaxed or elastic,
since the blood flows more slowly and with less pressure [1].
In this non-linear situation, artificial neural networks
(ANNs) appear to be an ideal approach. ANNs are concep-
tually simple, easy to train and use, and can approximate a
target function in an excellent way; however, their drawback
is that the model they develop is completely obscure (black-
box) and is therefore hard to analyse it [6].
The deep learning approach is gaining great popularity
due to its ability to achieve state-of-the-art performance
in different environments. In particular, deep neural net-
works have been applied to an increasing number of prob-
lems in different domains of biomedical application, such
as: protein structure classification [7] and prediction [8,9],
medical image classification [10], brain computer interface
systems [11], EEG classification [12], or genomic sequence
analysis [13].
As mentioned above, traditional ABP measurement
techniques are either invasive or cuff-based, which are
impractical, intermittent, and uncomfortable for patients.
For this reason, several methods were investigated. In
particular, PPG emerged as a potentially useful signal
(Fig.2) [14]; indeed, many studies point out a clear rela-
tionship between PPG and ABP. Since PPG and ECG
can easily be integrated into wearable devices [15−17],
they can provide the inputs of deep learning approaches
for ABP estimation, as already investigated in previous
works [18,19]. Initially, indirect approaches using fea-
tures derived from PPG and ECG were the most used:
He etal. [20] and Shriram etal. [21] showed a strong
negative correlation between ABP and pulse transit time
(PTT), but pulse wave velocity (PWV) [22] and pulse
arrival time (PAT) [23] were also studied. In addition,
Ma etal. [22] tried to show a relationship between PWV
and BP. Recently, Chua and Heneghan [23] used the
mean error as the evaluation metric between the target
BP value and the predicted one: the results have an error
of around
±
6 and
±
4mmHg for systolic blood pressure
(SBP) and diastolic blood pressure (DBP), respectively.
However, the mean error is not a suitable error metric
Fig. 1 Different blood pressure information according to time resolution
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for regression, because positive and negative differences
can compensate each other in the overall mean, show-
ing a low ME even when the individual errors are large.
In Kurylyak etal. [24] it was demonstrated that ANNs
can perform better than linear regression by extracting
a set of features from PPG recordings obtained with the
MIMIC database [25,26]: the results have an error of
around 3.80 ± 3.41mmHg on SBP and 2.21 ± 2.09mmHg
on DBP, on a very small dataset (15,000 heartbeats were
analysed, which means roughly 4h of recordings). A com-
plex recurrent neural network (RNN) was employed in
Senturk etal. [27] on 22 features extracted from MIMIC
II [28] PPG and ECG. The RMSE was 3.63 on SBP and
1.48 on DBP, i.e. a very good result.
Nowadays, thanks to the advancements in deep neural
techniques, new approaches are considered which employ
PPG raw signals. The idea to measure ABP using only PPG
signals was already investigated in Chua and Heneghan [23],
where four features were extracted from PPG signals in three
different setups: rest, exercise, and recovery. This was one
of the first studies based only on PPG, and it showed a good
correlation between BP and some features, proving that it is
possible to predict BP using only PPG based information.
The results were good, but only a few healthy people were
included in the cohort (i.e. with low ABP variability). Parati
and Valentini [1] had a huge impact on current research: the
pre-processing approach is well-suited to removing noisy
signals in MIMIC, and the validation system which was
adopted is the most robust applied to regression methods to
estimate the ABP. However, the goal was limited to measur-
ing the ABP starting from PPG and, therefore, ECG was not
considered to obtain improved performance. This was one
of the very first deep learning-based approaches: a complex
neural network was developed to automatically extract and
analyse both temporal and spectral features. This approach
employed a huge amount of data extracted from MIMIC III
and, consequently, the network was trained using a top-notch
GPU cluster.
PPG-based approaches for ABP measurement are draw-
ing ever-increasing attention in both academic and industrial
fields. The approval in 2019 of the Food and Drug Admin-
istration (FDA) first cuffless device is opening up a new and
interesting market.
In this study, blood pressure has been estimated by using
a typical regression approach with two configurations:
the first adopts the PPG signal as input, while the second
employs an ECG and PPG combination as input for the neu-
ral networks whose output is the ABP.
Methods
Data Description andPre‑processing
The MIMIC [25,26] database was exploited to evalu-
ate how PPG, ECG, and ABP are linked. It was chosen,
because it is representative of a wide range of pathophysi-
ologies that result in sudden blood pressure changes [29].
It consists of different physiological signals recorded from
121 ICU patients: data included signals and periodic meas-
urements obtained from a bedside monitor, that is from
clinical data obtained from the patient’s medical record.
Acquisitions ranged from 1 to 80h depending on patients.
Data obtained from the bedside monitors were divided into
10-min segments, which can then be assembled without
gaps to form a continuous recording. The ECG, PPG, and
ABP signals were sampled at 125Hz with 12-bit preci-
sion and negligible jitter [24]. MIMIC was extracted via
WFDB [30], a Python library supported by Physionet [31];
subsequently, each recording without the requested signals
Fig. 2 Trend of publications
on PubMed database regarding
single-site measurement PPG to
estimate BP
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was discarded. Figure3 shows the pre-processing scheme,
based on the histogram of SBP and DBP distributions. To
extract the SBP and DBP values, the algorithm developed
by Elgendi etal. [32] was applied to the raw dataset. From
the graph (see Fig.4), several problems can be identified:
first of all, there are negative BP values, some too high
values and an unusual peak at 180mmHg. Finally, both
distributions are heavily skewed towards physiological val-
ues, but SBP appears to have much larger support.
Since MIMIC was organized in 10-min recordings, in
order to maintain consistency, the following pre-processing
scheme (see Fig.3) was applied to each 10-min segment:
Fig. 3 Pre-processing scheme
Fig. 4 MIMIC SBP (purple)
and DBP (orange) distributions
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• Replacement of NaN values with the closest available
data;
• Deletion of records with “flat lines” in the ABP or PPG;
• Deletion of acquisitions where more than 5\% of the ABP
or PPG peaks were flat peaks;
• Removal of records containing abnormal ABP or PPG;
• PPG filtering using a 4th order Butterworth filter;
• PPG and ABP outlier removal through Hampel filter;
• Removal of patients’ recordings with < 3h of recording
time;
• Standardization of the PPG and ABP normalization.
NaN values were simply replaced with the closest value
because in some cases there were long time intervals
with missing values, so it was impossible to reconstruct
the missing signal. This operation did not bias the val-
ues; indeed, NaNs were associated with flat lines, which
were managed in the subsequent step of the pre-processing
scheme.
It was necessary to exclude low-quality recordings, i.e.
those containing the so-called flat lines and flat peaks, which
are recording errors mostly due to sensor problems, e.g. a
simple disconnection. Flat lines (see Fig.5a) are long peri-
ods of time where the same value is always detected, while
flat peaks (see Fig.5b) are peaks with a flattened tip.
Subsequently, anomalies in ABP signal were man-
aged: within the 10-min recording, ABP signals should
always range between a minimum of 15 and a maximum
of 300mmHg. In addition, a check on pressure and PPG
signal derivatives was introduced; in particular, the pre-
processing scheme deleted recordings that had the first
derivative always larger than zero or always less than zero
for more than 170 samples. In summary, the pre-processing
scheme eliminated all recordings in which the trend was
either increasing monotonously or decreasing monotonously
for at least 1.36s. This test was necessary because several
patients showed either negative pressure (see Fig.6a) or
strange cardiac cycles (see Fig.6b).
The remaining PPG recordings were filtered through a
band-pass 4th order Butterworth filter with a bandwidth
between 0.5 and 8Hz (see Fig.7). Afterwards, both PPG
and ABP signals were input to a Hampel filter. The But-
terworth frequencies were chosen because anything below
0.5Hz is due to baseline wandering, while beyond 8Hz,
the signal is made up of high-frequency noise. For com-
putational reasons, patients with < 190min of record-
ings were discarded, while only the first 190min were
considered from those patients with longer recordings.
Figure8 shows systolic and diastolic BP distributions;
it is apparent that they are heavily skewed toward physi-
ological values.
Finally, the PPG signal was standardized and the ABP
signal was normalized. Since the output was normalized,
predictions made by the networks had to be de-normalized
to map the output into a physiological ABP range. In this
sense, the statistics employed may not have been valid for all
the possible test sets. This assumption needs to be verified
on a real-case scenario. However, the ABP range is a very
Fig. 5 Frequent PPG anomalies: flat lines (a) and flat peaks (b)
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limited interval; therefore, new cases are most likely to have
the same dynamic as the training set which was adopted.
Target variables often need rescaling; for this reason,
a target with a large spread of values may result in large
error gradient values, which cause weight values to change
dramatically and the learning process to be unstable.
Dataset withPPG andECG
Because ABP is strictly related to ECG, several techniques
for predicting ABP were developed starting from ECG
and PPG (for instance, Pulse Transit Time). Thus, a sec-
ond dataset was created to study whether also using ECG
Fig. 6 ABP anomalies: negative BP followed by flat peaks (a) and no heartbeat for almost 2s (b)
Fig. 7 Butterworth filter: frequency response (a); original (light blue) and filtered (orange) signal comparison (b)
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could be of help with deep learning approaches. To get the
largest possible dataset, ECG lead V was used, because
it is the most frequent ECG lead recorded in the MIMIC
database.
The pre-processing scheme was the same as the one
before, extended to ECG. The ECG signal was filtered
with an 8th order passband Chebyshev type 1 filter with a
cut-off frequency of 2Hz and 59Hz to avoid motion arte-
facts and alternating current artefacts (see Fig.9). Out of
all the MIMIC dataset patients, only 51 had at least PPG,
ECG lead V, and ABP. After pre-processing, the resulting
dataset was made up of 40 patients. As shown in Fig.10,
also in this dataset, SBP and DBP distributions are skewed
towards physiological values.
Metrics
Historically, the most commonly used metric for regres-
sion task is the root-mean-squared error (RMSE), which
measures how large the difference is between the squares
of the predicted and the target values. Since it is a squared
difference, this metric gives more weight to large errors.
It is also called L2 norm and corresponds to the Euclidean
norm:
RMSE is, usually, the preferred metric; however, in some
contexts, some other functions can be employed. If there are
many outliers, the mean absolute error (MAE) could be a more
accurate performance index:
MAE (also called Manhattan norm or L1 norm) measures
the distance between two vectors, i.e. the predicted and target
value ones. However, MAE cannot be utilized as loss func-
tion for a neural network (NN) because its gradient is always
the same; thus, it will be large even for small loss values (see
Fig.11). For this reason, RMSE was chosen. In order to over-
come problems regarding robustness, the selected loss function
was the Huber loss (see Fig.12), which is also less affected by
outliers. Like the RMSE, it is differentiable in zero, but intro-
duces another hyperparameter that needs to be tuned (δ) [33]:
(1)
RMSE
(X,h)=




1
m
m

i=1
(h(x(i))−y(i))2
(2)
MAE
(X,h)=1
m
m
∑
i=1|
h
(
x(i)
)
−y(i)
|
(3)
L
𝛿(y,f(x)) =
{
1
2(y−f(x))2for
|
y−f(x)
|
≤
𝛿
𝛿
|
y−f(x)
|
−1
2𝛿2otherwise.
Fig. 8 Dataset with only PPG:
SBP (purple) and DBP (orange)
distributions
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Tested Neural Architectures
ResNet
The Residual Network (say ResNet) is an architecture inspired
by the pyramidal cells in the cerebral cortex, developed by
Kaiming He etal., and originally used for image classification
[34]. This architecture was created to overcome the difficulty
in training deep neural networks with vanishing/exploding
gradients and degradation of accuracy. The former problem
was solved by normalizing initialization and intermediate lay-
ers. The latter issue involves saturated accuracy that degrades
Fig. 9 Chebyshev filter: frequency response (a); original (light blue) and filtered (orange) signal comparison (b)
Fig. 10 Dataset with both ECG
and PPG: SBP (purple) and
DBP (orange) distributions
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rapidly; because degradation is not caused by overfitting, add-
ing more layers to a suitably deep model leads to higher train-
ing error.
In order to avoid degradation, skip connections were
introduced (see Fig.13): the signal fed to a layer was also
added to the output of the layer located a bit higher up the
stack. This new technique allowed very deep networks to be
trained like the original ResNet, which was a convolutional
neural network (CNN) composed of 152 layers. There are
many variants of this net depending on depth.
In general, a neural network is trained to make it model
a target function
h(x),
also called underlying mapping;
however, when the network is deep, it is difficult to opti-
mize it. For this reason, the input x is added to the output of
the network forcing the network to learn the residual map
f(x)=h(x)−x
. Such an approach is called residual learn-
ing. When a regular neural network is initialized, its weights
are close to zero, and therefore, the network just outputs
values close to zero. However, if there is a skip connec-
tion, the resulting network just yields a copy of its inputs;
in other words, it initially models the identity function. If
the target function is fairly close to the identity function
(as often occurs), this will speed up training time consider-
ably [35]. Moreover, if there are many skip connections,
Fig. 11 Gradient descent on MAE (left) and MSE (right)
Fig. 12 Huber loss; red dashed
line is MSE, blue dashed line is
MAE, δ = 1
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the network can start making progress even if several layers
have not started learning yet. Thanks to skip connections,
the signal can easily make its way across the whole network.
The deep residual network can be seen as a stack of residual
units, where each residual unit is a small neural network
with a skip connection [35]. Each residual unit is composed
of two convolutional layers, with Batch Normalization and
ReLU activation, using
3×3
kernels and preserving spatial
dimensions.
WaveNet
WaveNet is an architecture developed in Oord etal. [36]
and was originally designed to operate directly on raw audio
waveforms. In its simplest variant, it is just a stack of convo-
lutional layers without pooling layers and with a particular
type of padding called causal, which allows the output to
have the same time dimensionality as the input. Since this
model does not require recurrent connections, it is typically
faster to be trained than RNN, especially when applied to
very long sequences. However, one of the problems of causal
convolutions is that they require many layers, or large filters
to increase the receptive field.
In order to solve this problem, the WaveNet utilizes a dila-
tion rate (see Fig.14), which represents how spread apart each
neuron inputs are. A dilated convolution is a convolution where
the filter is applied over an area larger than its length by skip-
ping input values with a certain step. In this way, the lower lay-
ers learn short-term patterns, while the higher layers map long-
term ones. Thanks to the doubling dilation rate, the network
can process extremely large sequences very efficiently [35].
LSTM
Unlike humans, traditional neural networks restart thinking
from scratch every second; i.e. they do not have memory.
This is crucial in certain tasks, like reading, where the mean-
ing of each word is based on the previous ones. For this
reason, recurrent neural networks (RNNs) employ loops (see
Fig.15) to make information persistent over time.
As shown in Fig.15, at each time step, a RNN block
receives inputs, produces an output, and then it sends the out-
put back to itself. The network will use the last output together
with the next input to produce a new output. An RNN can be
thought as multiple copies of the same network, each pass-
ing a message to a successor. Since the output of a recurrent
neuron at time step is a function of all the inputs from previ-
ous time steps, it has a form of memory; indeed, the part of a
neural network that preserves some state across time steps is
called a memory cell. RNNs are trained using the backpropa-
gation through time; however, when the input sequence is long
the unrolled network becomes deep. As a consequence, like
every deep NN, it suffers from unstable gradients; moreover,
it may forget the first input of the sequence. For these reasons,
several types of memory cells were studied.
Figure16 shows the most famous RNN, the Long Short-
Term Memory (LSTM) cell, which is explicitly designed to
avoid the long-term dependency problem. These kinds of
cells have a long-term state, where, at every iteration, the
network learns what to store and what to read from it. The
working memory is called the hidden state
ht
.
The cell regulates its state using the gates: at first, there
is a forget gate where some memories are dropped, then the
Fig. 13 Skip connection
Fig. 14 Dilated convolution
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1 3
memories are replaced with new ones selected by the input
gate. The forget gate is rule by the following:
where
W
presents the weights vector,
b
represents the bias, σ
represents the sigmoid function, and
t
represents the current
instant.
One copy of the new state is sent to the next iteration; the
other one is passed through a tanh function and filtered by
the output gate, as follows:
This is combined with the current inputs and the previous
outputs to create the new output. The hidden state contains
information on previous inputs, and it is also used for predic-
tions. Its output is given by
The input gate recognizes important inputs and stores
them into the long-term state, the forget gate deletes input
that are no longer needed, and the output gate decides when
to extract a specific input from the long-term state.
The current input and the previous output, also called
short-term state, are fed to four different fully connected lay-
ers. The ones controlled by a sigmoid function are the layers
that control the gates; their outputs range between 0 and 1
(4)
f
t
=𝜎
(
W
f[
h
t−1
,x
t]
+b
t)
(5)
ot
=𝜎
(
W
o[
h
t−1
,x
t]
+b
o)
(6)
ht
=o
t
∗tanh
(
c
t)
and are fed to element-wise multiplication operations; in this
way, if they output is zero, they close the gate, while if the
output is one, they open it. The forget gate controls which
parts of the long-term state should be erased, the input gate
controls which new memories should be added to the long-
term state, and the output gate controls which parts of the
long-term state should be read and output at this time step.
The new memories are calculated in the layer controlled by
the tanh function.
Neural Network Implementation
In order to evaluate the best neural network architecture,
two different setups were implemented:
• Direct SBP/DBP prediction: The network analyses 5s
of recording and then directly outputs a single value for
SBP (peak) and another one for DBP (valley);
• Entire ABP signal prediction: the network predicts the
continuous blood pressure signal in real-time.
Predicting the entire signal would be better for clinical
application, while for commercial healthcare device imple-
mentation, only systolic and diastolic values are predicted.
Every neural network configuration was trained in the
two setups with both datasets and evaluated on a validation
set; then, the best performing networks were cross-validated
using the method of Leave-One-Out (LOO) since it is the
Fig. 15 RNN unrolled through
time
Fig. 16 LSTM cell
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most robust approach in terms of generalization performance
[1]. ANNs were trained by using the Adam optimizer, learn-
ing rate η = 0.001, Huber loss, and mini-batch training; they
were implemented in Tensorflow 1.15, and the training
graphs were visualized through Tensorboard (the official
Tensorflow visualization tool). Since Adam is an adaptive
learning rate algorithm, it did not require a lot of tuning;
therefore, the default learning rate was used. The Huber loss
was chosen because it is a robust metric, unaffected by outli-
ers, considering that the dataset has no bell-shaped distribu-
tion. Finally, samples of recorded PPG have different dimen-
sions between the two setups: samples in direct SBP/DBP
prediction are 5s long, while in entire BP prediction are 2s
long. This difference is due to LSTM, which has problems to
manage too long sequences, even though it performs better
than classic RNN. LSTMs are used also in the first setup;
however, in this case, it was possible to downsample the
input through convolutional layers, since it was not neces-
sary to output a value for every input.
In direct SBP/DBP prediction, recordings were divided
into 5s chunks; then, the algorithm developed in Elgendi
etal. [32] was employed to extract SBP and DBP values.
Since in 5s there are usually 4 to 6 cardiac cycles, the mean
SBP and mean DBP were taken as the target values.
Direct SBP/DBP Prediction
ResNet
The first attempt, shown in Fig.17a–b, was made by using a
ResNet18 and testing different batch sizes. Smaller batches
allowed a faster training and achieved better results, prob-
ably because they did not get stuck in some local minimum.
Fig. 17 ResNet training performance. Network trained on PPG dataset for SBP (a) and DBP (b) prediction with different batch sizes: 650
(orange), 128 (blue), and 32 (red). Network trained on PPG + ECG dataset for SBP (c) and DBP (d); batch size equal to 32
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1 3
Therefore, also for a regression task, mini-batch training is
the best way to train a neural network. In particular, three
settings were tested: in the first, 650 samples per batch were
used (i.e. maximum size permitted by Google Colab GPU),
before performing backpropagation; in the second, 128 sam-
ples, and in the third 32 samples were adopted. In every
setup, the number of training steps is always the same: this
is important because it represents the number of times the
weights are updated; therefore, the networks are comparable
only if their weights are updated the same number of times:
Classical feature selection has been automated by convo-
lutional layers and skip connections; in addition, it is pos-
sible to stack layers creating a deep neural network, which
can better analyse input data.
(7)
Trainingsteps
=epochs ∗
Numberofsamples
Batchsize
Once the best batch size was chosen (32 samples), a net-
work was trained also on the dataset composed of PPG and
ECG (see Fig.17c–d) signals.
ResNet andLSTM
The next experiment employed a ResNet, like the previous
one, followed by three LSTM layers, each one made up of
128 neurons. The first LSTM layer is bidirectional. Convo-
lutional layers are activated when they are combined with
recurrent layers: they extract features from a signal, and they
can also downsample the input sequence using the right ker-
nel size, stride, and padding. The model can learn how to
preserve the useful information dropping only the unimpor-
tant details and shortening the sequences; the convolutional
layer may help the following recurrent layers to detect longer
Fig. 18 ResNet + LSTM training performance. Network trained on PPG dataset for SBP (a) and DBP (b) prediction. Network trained on
PPG + ECG dataset for SBP (c) and DBP (d)
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1 3
patterns. This network was the best performing to directly
predict SBP/DBP values for both datasets.
Training results are shown in Fig.18: since the two data-
sets have different number of samples, the networks were
trained with a different number of training steps.
Entire ABP Signal Prediction
Fully Connected Network
It was tried to predict ABP signal through a simple fully con-
nected neural network. Different architectures were imple-
mented; however, due to the simplicity of the model, good
results were not achieved. Deeper models appear to con-
verge faster, but still give high errors, as shown in Fig.19a.
PPG + ECG datasets were used for training only on the deep-
est model; however, results did not improve significantly
(see Fig.19b).
Long Short‑Term Memory
The network is composed of three stacked LSTM layers,
each one with 128 cells. The first layer is bidirectional, while
the output layer is a fully connected neuron without any
activation function. Bidirectional Long Short-Term Memory
(BLSTM) looks for contextual features both forward and
backward, which is useful because the location of the feature
that the network wants to forget is not known. This approach
is used also by humans every day: sounds, words, and even
whole sentences that at first mean nothing are found to make
sense in the light of the future context; in practice, they are
used to increase the amount of input information available
to the network. This is the approach widely used in natural
language processing, and it was successfully used also in
ABP prediction by several researchers [27]. BLSTM usu-
ally is placed as the first layer of the network because it has
access to a much larger-scale context of the input sequence.
BLSTMs heavily increase the computational cost; thus, it is
reasonable to use only one bidirectional layer. Every sam-
ple is composed of 2s of recording; as explained earlier:
this of the value length was defined because LSTMs have
problems to manage long sequences. It is hard to remember
long-term patterns if the sequence is too long; furthermore,
long sequences imply a deep unrolled network, which makes
too hard the computation of the gradient through time. For
this reason, only the 2s before the current instant t are taken
as an input time window to predict a single output value at
the instant t. Training results are shown in Fig.20.
WaveNet
Another experiment used a simplified version of the
WaveNet, composed of two blocks each one with four con-
volutional layers. Dilation rate is the double (from 1 to 8)
in every convolutional layer inside a block. The output layer
is a fully connected neuron without any activation function.
Since the network is composed only by convolutional layers,
it converges fast and, thanks to the doubling dilation rate,
it can process extremely large sequences very efficiently.
Afterwards, a second network was built stacking three
LSTM layers, each composed by 128 neurons, where the first
layer was bidirectional. On top of this simplified WaveNet,
convolutional layers extract features that are then analysed
by LSTM layers. Training results are shown in Fig.21.
Fig. 19 Fully connected training performance. Network trained on PPG dataset with different number of neurons (a): 120–60-30 (blue), 240–
180-120 (green); network trained on PPG + ECG dataset (240–180-120) (b)
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ResNet andLSTM
Finally, since using LSTMs layers on top of convolutional
layers was proven to be a good approach, an attempt was
made to use a deeper model: a modified ResNet followed by
three LSTM layers, the first one bidirectional, whose results
are shown in Figs.22 and 23. This network is different from
the one presented in section direct SBP/DBP prediction
because max-pooling layers are not used and convolutional
layers have causal padding, like WaveNet. This is a crucial
step: in order to predict the entire signal, it was necessary to
output a sequence of the same length as the input sequence.
This network achieved the best performance in predicting
the entire signal. In this paper, every ResNet is composed
by four ResNet blocks. Convolutional layers have kernel
sizes equal to 3 and strides equal to 2, while the number of
filters increases in every block starting from 64 up to 512.
In particular, this ResNet is followed by three LSTM layers,
the first one bidirectional. Every layer is composed of 128
cells. Although by default, Keras uses Glorot initialization
Fig. 20 LSTM stack training performance: network trained on PPG dataset (a) and PPG + ECG (b)
Fig. 21 WaveNet and
WaveNet + LSTM train-
ing performance. PPG
Dataset: WaveNet (a) and
WaveNet + LSTM (b).
PPG + ECG dataset: WaveNet
(c) and WaveNet + LSTM (d)
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1 3
with a uniform distribution to reduce the risk of explod-
ing/vanishing gradients at the beginning of training; this is
not enough to solve this problem during training. For this
reason, every convolutional operation is here followed by
batch normalization, which zero-centres and normalizes
each input; afterwards, it scales and shifts the results by
using two new parameter vectors per layer: one for scal-
ing, the other for shifting. In other words, this procedure
makes the model learn the optimal scale and mean of each
of the layer inputs [35]. This network was the best perform-
ing network to predict the entire BP signal for both datasets.
The network was built ad hoc on this problem. Very simple
convolutional neural networks and recurrent neural networks
were initially trained but, as reported in “Results,” the hybrid
approach between CNN and RNN produced the best results.
The transfer learning approach has not been explored in this
case, but will be applied in future works.
Leave‑One‑Out
In order to understand the generalization performances, a
Leave-One-Out (LOO) cross-validation was conducted on
Fig. 22 ResNet + LSTM train-
ing performance: PPG dataset
(a), PPG + ECG dataset (b)
Fig. 23 BP Prediction on a
validation set sample made with
ResNet + LSTM trained with
PPG dataset: original signal
(light blue) vs network output
(orange)
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1 3
the best architecture, i.e. ResNet followed by LSTM, for
both datasets: the one built using only PPG and the one built
using both PPG and ECG. This method was chosen because
it tests every possible way to divide the original sample into
training and validation, and it has lower computational cost
compared to the alternatives [37]. The overall errors were
computed as the average of individual MAEs in each LOO
iteration. The results were worse than the ones obtained with
the same network trained and tested on the same patients,
which means that personalization boosts the predictions.
There is a correlation between mean ABP and the errors (see
Fig.24). Since the datasets have a majority of physiological
ABP, when the network is trained with a great majority of
healthy ABP and then it is used to predict an unhealthy ABP,
the error is greater than it should be. In addition, there are
some long patterns in some PPG (see Fig.25), which cannot
be recognized by the network because they are longer than
the training sample length (2s). By using the ECG signal,
the network performance is improved on the validation set
and makes the results more general; indeed, it performs bet-
ter also on LOO cross-validation and the predictions are less
dependent on mean ABP.
Fig. 24 “Entire BP prediction” LOO error for different patients depending mean ABP; a and b refer to dataset with only PPG and c and d to
dataset with PPG and ECG
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Polito Dataset
Finally, a custom dataset was created at Neuronica
Lab of Politecnico di Torino to test the proposed algo-
rithm. Nine healthy subjects (5 males, 4 females, aged
22.84 ± 1.07years) were recruited to participate in the
experiment of PPG, ECG, and BP signal acquisitions. The
recordings were gathered using a GE Healthcare B125
patient monitor, which is a certified clinical device, generally
appreciated for its intuitiveness and reliability in a variety of
acuities. The monitor delivers proven NIBP technology, uti-
lizing GE-patented “smart cuff” pressure control to improve
measurement time, patient comfort, and artefact rejection. It
meets the requirements expected by both AAMI ISO81060-2
and IEC 80,601–2-30. Time of day and ambient temperature
were not strictly controlled, although most recordings were
made in the morning. Volunteers were seated and put at ease
so that the commitments of everyday life would not affect
the recordings. PPG, ECG, and ABP were measured three
times by using the following recording protocol: first, the
PPG and ECG were recorded simultaneously; then, ABP was
measured using a sphygmomanometer. The PPG and ECG
recordings were 15s long. PPG was sampled at 300Hz,
while ECG at 100Hz; thus, both signals were resampled
both at 125Hz, with downsampling (samples were skipped)
and linear interpolation method, respectively. A sphyg-
momanometer was used because a CNAP system was not
available, while invasive methods can only be performed by
trained personnel. Only ECG lead I was recorded, because
the developed algorithm is designed to be embedded in a
wearable device, which typically only measures this lead.
In this scenario, an additional dataset was derived from
MIMIC using PPG, ECG lead I, and ABP. The previous
dataset, created by using lead V, demonstrated how the ECG
could improve the performance of a neural network that has
to predict ABP without having to deal with a small dataset.
Of course, the networks trained with lead V could not be
reused on the Polito dataset because their weights were not
trained for lead I; thus, it was necessary to create a new data-
set to train the network. The new MIMIC dataset consisted
of 12 patients to which the same pre-processing scheme was
applied as before. Then, this dataset was used for training the
previous best performing NN architecture: direct SBP/DBP
prediction ResNet + LSTM.
The scheme adopted to predict BP starting from a dataset
never met before is shown in Fig.26.
Results
Table1 summarizes the performances of SBP and DBP
prediction obtained with the two different setups and net-
works. Using both PPG and ECG improved the performance
in every configuration. In particular, the best network was
the ResNet + LSTM, which directly predicted SBP and DBP
values. The network overall MAEs on the validation set
were 4.118 and 2.228mmHg. Errors were lower on DBP,
because it had lower variability relative to SBP. As expected
direct SBP/DBP prediction seems to be the best approach
if the goal is just to output SBP and DBP values, because
the networks are tailored for this purpose. On the contrary,
when the networks have to infer the entire signal, they have
to learn pieces of information that will not be used. Another
advantage of direct SBP/DBP approach is the possibility to
analyse longer sequences, thus recognizing longer patterns.
Applying the algorithm [32] on a predicted ABP signal may
introduce further errors. Nevertheless, entire BP prediction
is an interesting approach for its clinical application and its
results are fully shown in Table2. Finally, LOO cross-val-
idation was employed on the best performing networks for
both setups. From Table1, it is clear that the best network is
the ResNet + LSTM in both cases.
As a summary, Table1 collects the results obtained
with the two approaches: in the former, the predicted
Fig. 25 NN tends to predict an ABP with similar pattern to those in PPG, while real ABP does not have them
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1 3
output value is represented by two discrete values, sys-
tolic and diastolic blood pressures; in the latter case, the
goal is to obtain the entire pressure wave; thus, after the
prediction of the signal, the peaks (systole) and the valleys
(diastole) are extracted. Subsequently, the point values of
systolic and diastolic pressures are compared. However, as
the peak and valley extraction algorithm could introduce
error, the error was calculated on the entire output pres-
sure signal (compared with the target signal), as reported
in Table2.
LOO was performed twice on the PPG trained network
because, as explained in “Leave-One-Out,” there are two dif-
ferent datasets; in particular, the dataset created using only
PPG had 50 patients, while the dataset created using PPG and
ECG had only 40 patients. During the training phase, it was
important to have access to as much data as possible; thus,
every data available was used; conversely, to compare perfor-
mance, it was useful to have the same dataset. The ECG sig-
nal improved also generalization when employed in the best
model ResNet + LSTM, as shown in Table3; however, errors
were higher than when the networks were trained and tested
on the same patients (different recordings). This phenomenon
appears in several other types of research [1,23], and it is
generally called personalization. With individual calibration,
PPG and ECG can be used to directly estimate SBP and DBP
on new data obtained from the same individual. According
to the American National Standards Institute (ANSI) for the
“Development of Medical Instrumentation”[33], in order to
validate a new device, there should be an average difference
of 5 ± 8mmHg between the standard and the new developed
device [27]. The root-mean-squared error for SBP is 5.682,
while for DBP is 2.986.
Polito Database Results
The best performing ANN (ResNet + LSTM) trained on PPG
and ECG lead I was used to predict SBP and DBP on Polito
Fig. 26 Pipeline used to process never seen data (Polito dataset)
Table 1 Errors (mmHg) on SBP and DBP prediction for different set-
ups with MIMIC database
Neural network (training dataset) SBP DBP SBP DBP
MAE RMSE
Direct SBP/DBP prediction
ResNet (PPG) 9.556 4.217 13.572 6.012
ResNet (PPG + ECG) 4.667 2.445 6.227 3.042
ResNet + LSTM (PPG) 7.122 3.534 11.214 5.029
ResNet + LSTM (PPG + ECG) 4.118 2.228 5.682 2.986
Entire BP prediction
Fully connected (PPG) 36.559 10.602 45.013 13.417
Fully connected (PPG + ECG) 29.753 12.759 39.330 15.198
LSTM (PPG) 12.118 5.018 17.875 6.890
LSTM (PPG + ECG) 7.603 3.688 11.846 5.320
WaveNet (PPG) 18.539 8.154 26.638 11.441
WaveNet(PPG + ECG) 14.501 7.224 22.922 10.477
WaveNet + LSTM (PPG) 14.353 6.311 21.323 9.150
WaveNet + LSTM (PPG + ECG) 8.812 3.471 12.967 4.864
ResNet + LSTM (PPG) 8.660 3.843 13.439 5.718
ResNet + LSTM (PPG + ECG) 4.507 2.209 6.414 3.101
Table 2 Errors (mmHg) on entire BP prediction for different setups
with MIMIC database
Tested set MAE RMSE MAE RMSE
PPG PPG + ECG
Fully connected 18.547 27.214 18.329 25.740
LSTM 8.591 13.306 5.897 9.321
WaveNet 12.292 18.297 11.338 17.518
WaveNet + LSTM 10.009 15.610 5.658 8.919
ResNet + LSTM 6.230 8.883 3.282 5.010
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1 3
volunteers: MAE was equal to 12.435mmHg on SBP and
8.567mmHg on DBP (see Table4, which shows the results
for the Polito volunteers dataset collection). The network
was trained, also, by using only the PPG. This configuration
achieved MAE equal to 9.916mmHg on SBP and 5.905 on
DBP. In this case, ECG improved the performance on data
extracted from the MIMIC database but did not affect gen-
eralization. Furthermore, it negatively influenced the results
on the Polito. The reason is probably due to the small train-
ing set; indeed, only 12 patients had ECG lead I in MIMIC
database. The unexpected results on the Polito dataset may
be due to different pressure acquisition methods. In this case,
for technical reasons, the pressure was not acquired with an
invasive method, but measured with a sphygmomanometer,
which can introduce an epistemic uncertainty. Furthermore,
this instrument has an uncertainty of 5mmHg which has,
therefore, introduced additional noise to the measurements,
the so-called “aleatoric uncertainty.”
Table5 shows the comparison of all the neural networks
employed for arterial blood pressure detection in term of
complexity. In particular, for convolutional neural networks,
the complexity affects the length of the signal, the dimension
of the input vector (1 for only PPG input and 2 for PPG and
ECG as inputs), and the kernel size, while for recurrent neu-
ral network, the complexity affects only the length and the
dimension of input vector. The ResNet + LSTM represents
the best model in terms of performance, but, at the same
time, the most expensive model in terms of computational
complexity.
Discussion
It is possible to perform accurate ABP measurements relying
only on PPG; however, the results are influenced by the inter-
person variability; to get around this problem and obtain a
greater generalization, ECG signals should be considered.
Different people show different ABP and PPG waves;
however, the results also depend on the average pressure of
the patients: the biggest mistakes were made on patients with
the highest mean ABP.
Relationship with mean ABP could be due to the dataset,
since most patients had physiological pressures and the dis-
tribution of the dataset was not Gaussian. To obtain better
results, it would be appropriate to use a larger dataset to have
a Gaussian distribution of BP. Large datasets are of utmost
importance in deep learning and the reason is clearly shown
in Polito results: although the ECG importance was proven,
it did not improve the performance, because the network was
trained on a very small dataset.
From Table4, it can be deduced that adding the ECG
signal improves the generalization error (leave-one-out) only
for DBP, but does not improve SBP errors. The reason can
be the presence of higher frequencies in the SBP signal w.r.t.
DBP, which implies a more difficult regression problem.
Working with ICU patients, even intra-person variability
is a problem; actually, within the same person, there may be
sudden changes in pressure that can bring it from physiologi-
cal to pathological values.
Finally, the LSTMs seem to play a crucial role in the
BP analysis, because they take into account the time
Table 3 LOO results on MIMIC Database with the best neural net-
work (ResNet
+
LSTM), since direct SBP/DBP prediction did not
predict the entire signal, the first two columns are empty. Errors are
expressed in mmHg. PPG refers to the configuration where only the
PPG signal is used as input, while ECG refers to the configuration
with both PPG and ECG as input signals
Tested set MAE RMSE MAE S MAE D RMSE S RMSE D
Direct SBP/DBP prediction
PPG (50 pat) 23.5976 10.7459 27.6430 12.3444
PPG (40 pat) 24.2227 11.1056 28.2470 12.6419
ECG (40 pat) 20.3667 9.5484 23.0699 10.8475
Entire BP prediction
PPG (50 pat) 15.3419 19.1549 21.4666 10.6841 25.3825 12.3489
PPG (40 pat) 15.6788 19.5598 22.4095 10.8180 26.2460 12.4111
ECG (40 pat) 14.6093 18.0184 22.0995 10.1053 24.5865 11.5292
Table 4 SBP and DBP prediction errors (mmHg) on Polito database
using the best neural network (ResNet
+
LSTM) trained on MIMIC
dataset (built using PPG and ECG lead I)
Tested set MAE SBP MAE DBP RMSE SBP RMSE DBP
PPG
Validation set 7.409 3.706 9.875 4.883
Leave-One-Out 15.706 7.251 17.792 8.171
Polito dataset 9.916 5.905 11.879 7.273
PPG + ECG
Validation set 4.546 2.515 5.766 2.982
Leave-One-Out 16.128 6.743 17.875 7.902
Polito dataset 12.435 8.567 14.082 10.211
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1 3
dependencies (the pressure at a given time cannot differ too
much from what was a moment before). For this reason, it
is natural that the addition of this layer has greatly improved
performance. However, the LSTMs should necessarily be
combined with some downsampling method because their
memory is still too short to analyse the long patterns that can
be observed on the PPG and can affect the ABP.
Conclusion
PPG-based techniques allow continuous and automated ABP
measurements; they are also well tolerated by patients and
are cheap and portable. These techniques are based on direct
detection of blood volume in the arteries under the cuff. In
this study, ECG improved PPG performance in every setup
proposed and allowed the network to generalize better: it is
therefore important to collect ECG data in deep learning
approaches. This system represents a non-invasive, easy tech-
nique for blood pressure measurements. Experiments were
carried out on a subset of patients from the MIMIC database
and a dataset of Polito volunteers. Within-subject valida-
tion was compliant with ANSI guidelines: the best perform-
ing network achieved a MAE of 4.118mmHg on SBP and
2.228mmHg on DBP. The selected network was also tested
on a different custom dataset, created at Neuronica Labs
(Politecnico di Torino), which achieved better performance
than in MIMIC LOO cross-validation. This is probably due to
the fact that this dataset was smaller and, therefore, had lower
variance. Indeed, the Polito volunteers were all young and
healthy subjects, while MIMIC is a particularly complicated
dataset, because its patients have a huge variety of patho-
physiologies that result in sudden blood pressure changes.
Furthermore, in MIMIC, ABP, PPG, and ECG were probably
collected with different measurement devices.
The proposed neural algorithm can be embedded in wearable
portable devices to perform continuous healthcare monitoring of
arterial blood pressure in order to prevent onset of irreversible
damage, like cardiovascular diseases and hypertension. Imple-
mented in a device, this algorithm may prove a powerful tool
for diagnosing the aggressive covid-19 virus at an early stage.
Future work will focus on three areas. The first will deal
with an intensive testing phase of the algorithm on larger
datasets such as MIMIC II and MIMIC III. The second will
test the algorithm on a database characterized by elderly
patients and people with cardiovascular pathologies to dem-
onstrate its validity. The third area will address the danger
related to the fact that blood pressure can change suddenly
and become dangerous. Since the variability of intra-person
arterial pressure is particularly problematic, especially in
precarious health conditions, work on detecting this danger
is the next challenge.
Funding Open access funding provided by Politecnico di Torinowithin
the CRUI-CARE Agreement. This work has been partly supported by
the “Proof of Concept” Instruments project by Link Foundation and the
PoliToBIOMed Lab—Biomedical Engineering Lab of the Politecnico
di Torino.
Declarations
Human and Animal Rights All the participants in Polito Database con-
struction gave their consent and full agreed to be part of the experimen-
tal phase. This work has not used animals in any experiments
Informed Consent All procedures performed in studies involving
human participants were in accordance with the ethical standards of
the institutional and/or national research committee. All participants
of the presented research project were informed and consented to par-
ticipate in the project.
Conflicts of Interest The authors declare no competing interests.
Open Access This article is licensed under a Creative Commons Attri-
bution 4.0 International License, which permits use, sharing, adapta-
tion, distribution and reproduction in any medium or format, as long
as you give appropriate credit to the original author(s) and the source,
provide a link to the Creative Commons licence, and indicate if changes
were made. The images or other third party material in this article are
included in the article's Creative Commons licence, unless indicated
otherwise in a credit line to the material. If material is not included in
the article's Creative Commons licence and your intended use is not
permitted by statutory regulation or exceeds the permitted use, you will
need to obtain permission directly from the copyright holder. To view a
copy of this licence, visit http:// creat iveco mmons. org/ licen ses/ by/4. 0/.
Table 5 Neural network complexity comparison
Neural network Complexity order Cost estimation (FLOPs)
PPG PPG + ECG
Fully connected
O(length ×(vectordimension)2)
∼625
∼2500
LSTM
O
(
length
×(
vectordimension
)
2)
∼625
∼2500
WaveNet
O(length ×(vectordimension)2×kernelsize)
∼1850
∼7500
WaveNet + LSTM
O(length ×(vectordimension)2×kernelsize)
∼1850
∼7500
ResNet + LSTM
O(length ×(vectordimension)2×kernelsize)
∼4375
∼17,500
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