Predictive Maintenance Approach in Ventricular Assist Devices:
Safeguarding Against Thrombus Formation
THIAGO SANTOS1, OSWALDO MARTINS1, EDUARDO BOCK1, DENNIS TOUFEN2
1Laboratory of Bioengineering and Biomaterials, Mechanical Department,
Federal Institute of Education, Science, and Technology of Sao Paulo,
Pedro Vicente Street, 625 - Caninde, Sao Paulo - SP, 01109-010,
BRAZIL
2Industrial Automation Department,
Federal Institute of Education, Science, and Technology of Sao Paulo,
Salgado Filho Avenue, 3501 – Vila Rio de Janeiro, Guarulhos - SP, 07115-000,
BRAZIL
Abstract: - Affecting millions in the world, cardiovascular diseases are a public health problem. Some patients
are not eligible for heart transplantation. Thus, a possibility is to receive a circulatory device known as a
ventricular assist device (VAD). This kind of device shows some problems, like thrombogenesis. The thrombus
formation in a VAD can cause patient death, and a previous, non-invasive diagnostic is quite complex. The
objective of this work is to develop an algorithm to reproduce time signals that indicate the presence and
absence of a thrombus, use these signals to train an artificial neural network to classify them, and use these
algorithms in a predictive algorithm for early thrombus detection. The results show that it was possible to detect
the thrombus formation in its early stages, but the noise level interferes with the accuracy of the ANN,
especially when signals in the time domain are used.
Key-Words: - Ventricular assist device, thrombus, artificial neural network, signal analysis, predictive
maintenance, artificial intelligence, machine learning.
Received: March 8, 2023. Revised: November 5, 2023. Accepted: December 7, 2023. Published: January 8, 2024.
1 Introduction
Affecting millions of people around the world,
cardiovascular diseases (CD) are responsible for the
first cause of death and hospitalization, making
them a serious public health problem, [1]. Many
patients suffering from Congestive Heart Failure
(CHF) need heart transplantation, although many of
them will die until they receive the donated heart,
[2]. To minimize this death rate, some of them
receive a circulatory device known as a ventricular
assist device (VAD), [3].
The VADs are established as a good therapy for
patients with end-stage heart failure, [2]. The
function of VAD is to replace the mechanical work
of the left or right ventricles, [4]. The VAD is a
pump with a motor, controller, outflow graft, drive
line cable, and batteries, as shown in Figure 1, [5].
Fig. 1: VAD with batteries, controller, and
peripheral systems. Adapted from, [5]
2 Thrombosis on VADs
The VADs still show some problems in
hemocompatibility, among them thrombogenesis,
which is a kind of natural coagulation when blood is
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exposed to any surface not fully covered by
endothelium, blood flow inside the pump, and
others, [6]. One of the most common therapies to
avoid thrombus formation in VAD is the
prescription of anticoagulants that will dissolve the
thrombus, [7]. However, this therapy will be
effective only if the patient starts it in the first stages
of thrombosis, [8]. Figure 2 shows a VAD with a
thrombus formation that has been removed from a
56-year-old patient. According to the authors, the
thrombus was blocking around 95% of the inlet
cannula, [9].
Fig. 2: Thrombus formation in a removed VAD.
Adapted from, [9]
The thrombus formation can result in VAD
disability or even cause the patient's death, [3],
[10]. Immediate action is necessary, but in the
current scenario is indecisive about which treatment
needs to be carried out, [11]. The thrombus
formation and its consequent release into the
patient's body is one of the main causes of death in
patients implanted with VAD, [12]. A VAD
controller that diagnoses the appearance of a
thrombus before its release can be vital to a patient’s
life, and several studies are being conducted with
this objective, [8], [13].
3 Signal Analysis
Based on data from an experimental study that
performed tests with artificial thrombus in a pump
prototype, the objective of this work is to develop a
Python language algorithm to reproduce simulated
signals obtained by that study that indicate the
disturbances caused by the presence of artificial
thrombus adhered in three different regions of the
pump, then use these signals to train an artificial
neural network (ANN) to taxonomy them, check its
robustness for noise interference, and later use this
ANN in a predictive algorithm to check the
probability of absence and presence of thrombus.
3.1 Vibration Analysis
The theoretical basis for the reconstruction and
analysis algorithms used in this work is classical
vibration theory, which we will briefly present here.
The classic model of translational forced vibration
with viscous damping is described by Equation 1,
[14].
󰇘 󰇗  󰇛󰇜 (1)
where x is the linear displacement, k is the spring
constant or stiffness, c is the damping coefficient
and 󰇛󰇜 is the excitation force.
Defining, the natural frequency as
(2)
and the fraction of critical damping as
 (3)
The acceleration is calculated by
󰇘
󰇡
󰇢󰇛󰇜 (4)
θ is the acceleration phase and Rd is a dimensionless
response factor:

󰇛󰇜 (5)
For a non-harmonic excitation force, like that
observed for the thrombus presence in VADs, [15],
Fourier analysis is used to break it down into its
harmonic components as a function of frequency.
Each of these components can have its acceleration
solution calculated by Equation 4. Assuming the
system is linear, the superposition principle allows
the summation of the solutions from multiple
components to obtain the total expected
acceleration.
3.1 Work reference
The [15], presents an in vitro study where the
vibrational signal analysis, obtained with
Microelectromechanical Systems (MEMS)
accelerometers, was used to identify disturbances or
stimulations that indicate dynamic changes on the
pump's rotor when the thrombi adhere or if there is
wear on the rotating elements. The Fast Fourier
Transform (FFT) is used to characterize signal
components in the frequency domain. Figure 3
shows the experimental set-up used by the authors
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for their study, and Figure 4 shows the areas where
the thrombosis was simulated. The material used to
simulate the thrombus had a density of 0.97 g/cm2,
and the liquid used to simulate the circulatory
system was water, [15].
Fig. 3: Experimental set-up. Adapted from, [15]
Fig. 4: Areas where the thrombus was simulated
According to the results shown by the authors,
the MEMS could detect disturbances caused by
thrombus formation. In that work, it is informed that
the presence or absence of a thrombus is
characterized by the occurrence of peaks at
determinate frequencies. The red arrow in the graph
of the Figure 5 spectrum indicates an imbalance
caused by thrombus presence. For example, the
peak next to the 145 Hz frequency indicates an
unbalance on the rotor caused by the thrombus
presence at the rotor's base.
Fig. 5: Frequency spectrum patterns for thrombus
absence and presence at rotor’s base. Adapted from,
[15]
4 Methodology
This work was divided into four main
methodologies: 1 - creation of a synthetic dataset
that reproduces the time signals obtained by, [15]; 2
- creation of an algorithm to simulate the evolution
of thrombus formation and evaluate it by the
wavelet analysis; 3 - creation of ANN algorithm to
classify the signals in the synthetic dataset; 4 -
creation of a predictive algorithm, using the ANN to
check the probability of thrombus absence and
presence.
4.1 Time Signals Reconstruction
The results from [15], were used to create the
Signals Reconstruction Algorithm (SRA), which
was used to create a synthetic dataset in Python
language of voltage in the time and frequency
domain. The graphs shown in that work provide
data such as the maximum voltage amplitude for
each frequency peak, noise, and sampling rate. With
these data, cosine signals were used to create a clean
signal with the same amplitudes. After modeling the
“clean signal," background noise was added with a
Gaussian distribution, represented by Equation 6, to
get a more realistic synthetic dataset simulated
signal like the real one,
󰇛󰇜󰇛󰇜󰇛󰇜 (6)
where s(t) is the signal as a function of time, A is
the amplitude of the signal, is the frequency of the
signal, t is time, is the phase of the signal and n(t)
is the Gaussian noise component.
The Fourier transform, computed using the fast
Fourier transform (FFT) in combination with a
window function, was applied to each one of those
created signals, then the results were squared to get
the power spectrum value, and these results were
plotted.
This methodology was applied to all the results
of the work referenced in this section. The algorithm
sequence is presented below.
1. Parameters Definition: The process starts
by defining crucial parameters such as the
sampling rate, data acquisition time, and
background noise amplitude, along with
creating a time vector.
2. Noise Generation: A vector of Gaussian
noise is generated, representing the noise
component to be added later to the signals.
3. Signal Generation Without Thrombus: A
correction factor is defined, and a signal
vector without thrombus is created by
adding sine waves of different frequencies
based on defined amplitudes.
4. Calculation of Power Spectrum Without
Thrombus: The signal.welch function is
used to calculate the power spectrum of the
signal without thrombus.
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5. Signal Generation with Thrombus at the
base, vanes, and spiral: The process from
step 3 is repeated to generate signals with
thrombus at different parts of the VAD,
adjusting amplitudes and specific correction
factors.
6. Graph Creation: Graphs are plotted to
visualize the signals and power spectra,
organized into multiple subplots for each
signal type.
4.2 Wavelet Analysis
This work step involves developing the Changing
State Algorithm (CSA) to simulate the signal's state
transition, reflecting thrombus formation evolution.
Leveraging data from the SRA and wavelet analysis,
[16], the algorithm sequence is outlined. Figure 6
visually represents the transition between two
different signals.
1. Importation of Signals: Signals generated
by the SRA are initially imported.
2. Simulation of State Transition: The code
enters a loop simulating a state transition
over a period ti. The loop increments or
decrements the amplitudes of specific
frequencies, simulating a transition from the
initial state to the final state.
3. Creation of the Complete Signal: The
signal is constructed by summing the
sinusoidal components of specified
frequencies over time and adding previously
generated noise.
4. Analysis and Visualization of Power
Spectrum: The code creates a spectrogram
using the pcolormesh function to plot the
magnitude of the Continuous Wavelet
Transform against time and frequency.
Default settings were used for both
commands [16].
5. Display of Results: The graphical results
are plotted.
In the sequence above, the period ti can be
interpreted as a time value, representing days,
weeks, months, etc. The higher the value of ti, the
smoother the curve representing the state change.
The value used for ti was 1000. In plotting the
results, the argument cmap=jet was used,
representing a color palette with smooth transitions
from blue to red. Thus, the higher the amplitude, the
redder the coloration presented.
Fig. 6: Transition from a thrombus-free state to the
presence of a thrombus at the base of the rotor.
4.3 Artificial Neural Network
The ANN is a computational model of Machine
Learning inspired by the complex functionality of
the human brain, where billions of neurons process
information in parallel, [17]. An ANN is made up of
three main layers: the input layer, the hidden layer,
and the output layer. These layers are interconnected
by non-linear nodes, forming a neural network of
interconnections. In an ANN, each input is
multiplied by a synaptic weight (a weighting factor),
and each neuron has its synaptic weight to be added,
[18]. The activation potential is calculated by
adding the bias to the product of the inputs and their
corresponding synaptic weights. This activation
potential is then applied to an activation function,
resulting in the neuron's output, [17]. In summary,
the output of a neuron can be represented by
Equation 7, where y represents the neuron output, σ
is the activation function, n is the number of inputs,
wi are the synaptic weights associated with the
inputs, xi are the input values, and θ is the neuron
bias
󰇛
 󰇜 (7)
4.3.1 Implemented Artificial Neural Network
This algorithm takes the data and classifies it based
on its characteristics. Figure 7 shows an example of
how the ANN algorithm works.
Fig. 7: ANN classifying the synthetic signals
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The dataset obtained by the SRA was processed
by a fully connected Feed Forward ANN
architecture. Four classes and four labels for data
classification (Table 1) were chosen. To train and
test the ANN, the dataset was divided as follows:
70% for training and 30% for validation. This
procedure was applied to both types of obtained
signals time and frequency domains. The created
has 3 layers, and its characteristics are as follows:
Layer 1 Type dense, number of neurons =
26, activation function = “relu”.
Layer 2 Type dense, number of neurons =
128, activation function – “relu”.
Layer 3 Type dense, number of neurons =
4, activation function – “SoftMax”.
The number of epochs was 4000 and the optimizer
used to reduce overall loss was, [19]. The metric
used to check performance was accuracy. To assess
the noise sensitivity of the ANN, it was tested and
trained with signals from both the time and
frequency domains, with the background noise
being gradually increased. The best-performing
ANNs in terms of accuracy sensitivity will be used
in the predictive algorithm.
Table 1. Dataset created to classify different VAD
working scenarios
Label
Class
0
Thrombus absence
1
Thrombus at rotor’s base
2
Thrombus at rotor’s vanes
3
Thrombus at rotor’s spiral
4.4 Predictive Algorithm
This model utilizes the best ANNs with the dataset
generated by the SRA to predict the probability of
thrombus absence or presence in a specific
timeframe. The objective is to merge signals
representing the absence of a thrombus with signals
indicating the presence of a thrombus, simulating
the transition of signals from "without thrombus" to
"with thrombus" over time. This model provides a
comprehensive analysis of the temporal variations in
the probabilities of thrombus presence or absence
and was designed to better simulate real-life
applications.
The code initiates a loop that varies the starting
point of the region, indicating the absence of a
thrombus, adjacent to the region indicating
thrombus presence. In each iteration, the thrombus
probability is calculated for this evolving data range,
and the calculated probabilities are stored. At the
end of the iterations, they are visually represented in
a line graph, illustrating how the probabilities
evolve. This allows for a detailed analysis of
changes as the data range varies. The algorithm
sequence is presented below.
1. Loading the pre-trained ANN: The
algorithm loads the ANN from the file
where it was saved using the “TensorFlow”
library.
2. Calculation Loop: The code enters a loop
that calculates tracks of the dataset with
different starting points for region 1
(without thrombus) and varies the start of
region 2 (with thrombus). At the loop's
initiation, the track contains only data from
region 1. As the iterations progress, region 1
decreases at the same rate as region 2
increases. The total number of iterations is
defined by the size of the matrix previously
pre-processed by the ANN algorithm.
3. Average Calculation: The code calculates
the average of all rows in the data range.
4. Reshape the Data for the ANN: The
average data is reshaped to have the
appropriate format to be used as input for
the ANN.
5. ANN predictions: Predictions are obtained
by applying the implemented ANN to the
simple average data. This algorithm
calculates the probability of thrombus
presence or absence based on the
information in the data track.
6. Probability Calculation: The probabilities
computed by the ANN are converted into
percentage values representing the
likelihood of thrombus presence or absence.
7. Probability Storage: The calculated
probabilities are stored in two separate lists:
one for thrombus absence probability and
the other for thrombus presence probability,
for recording and analysis purposes.
8. Chart Plotting: Finally, the code generates
a line chart using the matplotlib library to
display the evolution of probabilities over
iterations. The chart shows the probabilities
of "Prob. Without Thrombus" and "Prob.
With Thrombus" on the vertical axis in
percentage and the iterations on the
horizontal axis.
5 Results
In this section, we will present the results obtained
by the SRA, the CSA, the results obtained by the
ANNs in classifying the reproduced signals, and
their performance with increased background noise.
Finally, we will present the results of the predictive
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algorithms. To facilitate comprehension, these
results have been divided into the following four
subsections.
5.1 Signal Reconstruction Algorithm
The spectrum pattern representing the absence of
thrombi is characterized by peaks at the
fundamental frequency of 30 Hz and its respective
harmonics (60, 90, and 120 Hz). The presence of a
thrombus at the base is identified by a peak near the
frequency of 140 Hz. In the case of thrombus
presence at the vanes, an increase in amplitudes at
frequencies of 90 and 120 Hz and the appearance of
peaks at frequencies of 150 and 180 Hz indicate this
anomaly. The elevation in amplitudes at frequencies
of 90 and 120 Hz indicates the presence of a
thrombus in the rotor spiral.
5.2 Changing State Algorithm
Figure 8 shows the spectrograms from CSA for the
three thrombus positions studied. Figure 8 (a)
displays the time series changing from the absence
to the presence of a thrombus at the rotor's base.
From a certain point onward, it was possible to
observe that the region associated with the
frequency of 140 Hz became visible on the scale.
This gradual change in coloration indicates a
progressive increase in the amplitude of this
frequency, directly related to the appearance of the
thrombus at the rotor's base. At a certain moment,
the areas corresponding to the frequencies of 90 and
120 Hz began to become less visible. The
spectrograms of the other two thrombus positions,
the rotor’s vanes and the rotor’s spiral are presented
in Figure 8 (b) and (c), respectively. In both cases,
we observe an intense peak at 90Hz growing with
time. For the thrombus in the rotor’s vane, Figure 8
(b), we observe a growing doublet at 125 and 150
Hz and for the thrombus in the rotor’s spiral, Figure
8 (c), just a peak in 125 Hz is observed. The
behavior of these two signals follows what is
expected, showing a smooth transition between the
peak of thrombus absence and presence.
Fig. 8: Plotted results from the CSA for all working
states
5.3 Implemented Artificial Neural Network
With very low noise (A = 1e-6), the ANN obtained
an average accuracy of around 100% for classifying
each of the signals. It was observed that, in all
scenarios, as the background noise level increases,
the mean accuracy decreases. A trendline was
adjusted to quantify the decrease in accuracy with
noise amplitude. It was noticed that the angular
coefficient (α) of the trendline in frequency domain
signals (αf = -0.019) is smaller than in time domain
signals (αf = -0.061). Figure 9 shows the influence
of noise on ANN accuracy analysis for both time
and frequency domains.
Fig. 9: ANNs performance for each kind of signal
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5.4 Predictive Algorithm
To demonstrate the capability of the ANN to predict
thrombus formation with a small frequency
signature, the output probabilities are presented in
Figure 10 for three thrombus positions. In all
scenarios, illustrated throughout the iterations,
where the iterations represent the degree of mixing
of signals with the absence and presence of
thrombus, the probabilities of thrombus absence and
presence vary. As expected, the probabilities always
start with 100% for thrombus absence. With the
increase in mixing, they converge to around 50%
when approximately half of each signal type is
being analyzed. After reaching this equilibrium
point, the curves begin to diverge, reaching values
of 0% for thrombus absence and 100% for thrombus
presence when about 30% of the signals correspond
to thrombus absence, and the remaining 70% are
signals of thrombus presence.
Fig. 10: Predictive analysis over the time
6 Conclusion
This study investigated the application of signal
processing and machine learning algorithms for the
detection of thrombi in VADs under different
operating conditions. The analysis covered signal
reconstruction techniques, signal analysis,
classification by ANNs, and their application in a
predictive algorithm. Frequency analysis
highlighted specific characteristics for each
scenario, with some frequencies indicating
normality and the absence of a thrombus, while
others indicated the presence of a thrombus,
signaling anomalies and imbalances in the rotor.
A signal made by mixing signals with and without a
thrombus was verified using wavelet analysis to
represent how thrombus formation might develop
over time, indicating that at a certain point, the signs
indicating the presence of a thrombus become
measurable. Classification analyses were carried out
using ANNs, considering data in the time domain
and the frequency domain.
Overall, frequency domain signals demonstrated
superiority to time domain signals in terms of
sensitivity to disturbances caused by noise, although
the frequency domain requires greater
computational effort to pre-process the measured
signals. The frequency domain signals were used to
carry out predictive analyses to calculate the
probabilities of the presence or absence of thrombi
in various VAD operating scenarios, including
situations of total absence or presence of thrombi, as
well as the variable combination of these signals
over time. It was found that the probabilities varied
significantly as the proportions of thrombus
presence and absence data changed.
Therefore, the results of this study, especially
those obtained by the predictive algorithm,
contribute to the further development of a smart
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pump, where more effective monitoring and control
systems can be incorporated into VADs, making
them more efficient, as well as suggesting the
feasibility of implementing prescriptive
maintenance strategies. By analyzing the data, the
device itself can indicate to the patient or physician
when and what should be done. It is important to
note that the results of this study were obtained
using only one VAD model and cannot yet be
generalized.
Acknowledgement:
Special thanks to the Laboratory of
Bioengineering and Biomaterials crew and the
Federal Institute of Education, Science and
Technology of São Paulo for their support
throughout the research process.
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DOI: 10.37394/23208.2024.21.1
Thiago Santos, Oswaldo Martins,
Eduardo Bock, Dennis Toufen
E-ISSN: 2224-2902
8
Volume 21, 2024
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Contribution of Individual Authors to the
Creation of a Scientific Article (Ghostwriting
Policy)
- Thiago Santos was responsible for the research
and algorithm creation and implementation.
- Oswaldo Martins was responsible for double-
checking the results and paper review.
- Dennis Toufen and Eduardo Bock were
responsible for supporting the algorithm's creation
and paper review.
Sources of Funding for Research Presented in a
Scientific Article or Scientific Article Itself
No funding was received for conducting this study.
Conflict of Interest
The authors have no conflicts of interest to declare.
Creative Commons Attribution License 4.0
(Attribution 4.0 International, CC BY 4.0)
This article is published under the terms of the
Creative Commons Attribution License 4.0
https://creativecommons.org/licenses/by/4.0/deed.en
_US
WSEAS TRANSACTIONS on BIOLOGY and BIOMEDICINE
DOI: 10.37394/23208.2024.21.1
Thiago Santos, Oswaldo Martins,
Eduardo Bock, Dennis Toufen
E-ISSN: 2224-2902
9
Volume 21, 2024