=Paper=
{{Paper
|id=Vol-3041/450-454-paper-83
|storemode=property
|title=NARX Neuromorphic Software for ECG Wave Prediction
|pdfUrl=https://ceur-ws.org/Vol-3041/450-454-paper-83.pdf
|volume=Vol-3041
|authors=Mihai-Tiberiu Dima,Svetlana Pitina
}}
==NARX Neuromorphic Software for ECG Wave Prediction==
https://ceur-ws.org/Vol-3041/450-454-paper-83.pdf
Proceedings of the 9th International Conference "Distributed Computing and Grid Technologies in Science and
Education" (GRID'2021), Dubna, Russia, July 5-9, 2021
NARX NEUROMORPHIC SOFTWARE FOR ECG WAVE
PREDICTION
T. Dima1,a, S. Pitina2
1
Univ. of Bucharest, Bucharest, Romania
2
Privolzhsky Research Medical Univ., Nizhny-Novgorod, Russia
E-mail: a ttdragonel@yahoo.com
ECG wave prediction with non-linear autoregressive exogenous neuromorphic (NARX) software is a
novel method aimed at Holter monitoring and early warning. Such predictions are important in
comparing the underlying QRS complex of the ECG-wave with the slowly deteriorating waves (or
arrythmia) in cardiac patients. A deep Q-wave for instance (such as 1/4 of the R-wave) is a typical
sign of (inferior wall) myocardial necrosis - associated in most cases with vascular dysfunction. It is
important to have a rolling predictor - slow ECG wave degradation being normal. A real-time
predictor takes into account a suite of influencing parameters (body temperature, effort, current
medication, sugar levels, stress, etc), being much better suited in making a call for "normal" vs.
"anomalous" ECG waves, rather than some outdated reference waves. Although this research is in its
begining, it shows encouraging results, which clinical studies can conclude as to how effective
the approach may be.
Keywords: ECG, NARX neuromorphic software
Mihai-Tiberiu Dima, Svetlana Pitina
Copyright © 2021 for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
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Proceedings of the 9th International Conference "Distributed Computing and Grid Technologies in Science and
Education" (GRID'2021), Dubna, Russia, July 5-9, 2021
1. Introduction
Increasingly, over the past two decades, new electronics [1] and neuromorphic data processing
solutions [2] have become part of standard ECG signal processing. This was made possible by the
portation of ECG wave databases – such as [3, 4], in digital format.
The introduction of artificial intelligence in clinical practice makes it possible to automate
analysis and reveal, hidden or non-obvious patterns [5].
Whereas cardiologists can only build up experience on waveform printout, neural networks
can make correlations in high dimensionality spaces and can measure features that are beyond the
resolution of the human eye.
Currently, methods are being developed using artificial intelligence for the diagnosis of
arrhythmias (using Holter monitoring data), myocardial infarction and left ventricular systolic
dysfunction [6, 7, 8].
As a result of fast and accurate diagnosis and choice of therapy, treatment will become in the
years to come more effective, convenient and personalized.
Neuromorphic software is a learning algorithm inspired from biological neurons, consisting of
a set of connected S-threshold units, or artificial neurons. A neuron receives a set of signals from
previous neurons, takes the sum and enters it into a threshold function (such as arctan). This is
essentially the McCulloch-Pitts neuron [9] of 1943. Versions thereof fine tune the slope of the
threshold function and the offset. The biggest improvements thereafter were two fold: on one hand
higher computational speeds owing to hardware progress and on the other more performant optimiser
algorithms which determine the weights of the inter-neuron links - a well performing example thereof
being the Nelder-Mead optimiser [10].
Present day neural software, with layered neuron design, was first investigated by Ivakhnenko
and Grigorevich [11] at CCM Information Corporation. A good review on the subject is by
Schmidhuber [12] and developments on the training of neural software is given in [13].
Nonlinear autoregressive exogenous [14] models are a class of artificial neural networks
graphed along a temporal sequence, allowing them to exhibit temporal dynamic behavior. They derive
from feed-forward neural networks and use internal buffers to predict the outcome desired.
The networks come as finite impulse recurrent networks (as directed acyclic graphs unfoldable
into a traditional feed-forward neural network) and infinite impulse networks (in which the graph
cannot be unfolded).
The weights of the network increase or decrease during the training of the network and
neurons have a threshold such that a signal is sent only if the sum of signals crosses the threshold.
Typically, neurons are aggregated into layers, with different layers performing different
classes of transformations on the inputs. Signals travel from the first layer (the input layer), to the final
layer (the output layer).
Figure 1. Exemplificative schematic of a NARX cell’s unfolding into a time sequence
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Proceedings of the 9th International Conference "Distributed Computing and Grid Technologies in Science and
Education" (GRID'2021), Dubna, Russia, July 5-9, 2021
A schematic example of a NARX cell is shown in figure 1, the network trained to learn a
repetitive sequence (such as the Fibonacci numbers for instance), but also to learn to respond to non-
endogenous stimuli, that change in time (such as the case of ECG waveforms).
2. Savitzky-Golay filter
To overcome unwanted artefacts in the ECG waveform, we need first a smooth, analytical
version of the waveform – impossible in general, but achievable locally, piece-wise connected with
smooth boundary conditions.
Further more, we can relax to a small extent the smooth boundary conditions and replace this
with an almost-smooth function that we obtain from a Savitzky-Golay filter on k bins around the
current bin. For this we used a OIII spline function with coefficients C, A, D, Y to optimise the position
of the current bin:
where xi are the time bins and yi the ECG waveform amplitude at bin-i. We take the derivatives with
respect to the 4 parameters and find the solution.
The coefficient Y will give the position of the current bin. The number of bins we
determined such as to keep waveform flexibility, while at the same time eliminate noise – k = 5. The
result of the filter on a section of ECG wave is shown in figure 2.
Figure 2. Performance of our Savitzky-Golay spline filter (with k = 5) for a section of the ECG-
waveform. The value k = 5 was determined such as to keep waveform flexibility, while at the same
time eliminate noise
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Proceedings of the 9th International Conference "Distributed Computing and Grid Technologies in Science and
Education" (GRID'2021), Dubna, Russia, July 5-9, 2021
3. Performance of the NARX software
We used the NARXsim package [16] from them Facultat d’Informàtica de Barcelona -
Universitat Polytecnica de Catalunya.
The learning patterns were offseted a time elapse t = -5 s, the amount of time in advance that
we want to predict the ECG-waveform.
The exogenous parameters are the 4 coefficients of the Savitzky-Golay filter, plus the residual
noise difference Y-yi.
We trained the network on a wave 300 s long from CARDIODAT [5].
Figure 3 shows the t = -5 s predicting ability of our NARX-network. Our excellent
preliminary result is encouraging from a cardiological point of view, as this software can be
incorporated in Holter devices.
Figure 3. NARX-software predicted (t = -5 s) ECG wave. Notice that the software has a latency in
the prediction upon encountering a rise in signal a matter we are currently investigating. The QRS
complex of the ECG-wave is for the rest well recovered, which is marked interest for Q-wave
parameter-integrity, an important aspect in cardiology.
It can be noticed still that the software has a latency in the prediction upon encountering a rise
in signal. We are currently investigating to what cause this is due, and how to address this issue. The
QRS complex of the ECG-wave is for the rest well recovered, which is marked interest for Q-wave
parameter-integrity. The reconstruction of the Q-wave is very important, because the appearance of a
deep Q-wave (such as 1/4 of the R-wave) is a typical sign of myocardial necrosis – associated in most
cases with vascular dysfunction.
Our ability to predict “steady-state” ECG wave can be compared by the Holter with actual
measurement and signal “unexpected wave degradation”. This is valuable in classifying myocardial
infarction and early warning. Clear signal expression, in the case of multi-lead ECG recordings, allows
the localization [15] of the necrosis focus.
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Proceedings of the 9th International Conference "Distributed Computing and Grid Technologies in Science and
Education" (GRID'2021), Dubna, Russia, July 5-9, 2021
Concluding, our NARX-software shows very promising prospects in variable aforetime
prediction of ECG waves. This is particularly valuable for Holter devices, in comparing “steady state”
predicted rhythm to actual measurement and signaling “unexpected wave degradation”. This impacts
patient management tactics, offering precious advance warning. In this respect our NARX-software
performance - and subsequent improvements expected, is an important contribution.
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