Deepa Ghosh Research Foundation, West Bengal, India

- *Corresponding Author:
- Dipak Ghosh

Deepa Ghosh Research Foundation

60/7/1, Maharaja Tagore Road

Kolkata 700031

West Bengal, India

**Tel:**+91 8697035971/+91 33 4065 8334

**E-mail:**[email protected]

**Received date:** June 23, 2016;** Accepted date:**July 07, 2016;** Published date:** July 11, 2016

**Citation:** Nilanjana P, Anirban B, Susmita B, et al. Non-Invasive Alarm Generation for Sudden Cardiac Arrest: A Pilot Study with Visibility Graph Technique. Transl Biomed. 2016, 7:3.

**Objective: **The objective of this work is to formulate biomarkers based on visibility graph technique for early detection of sudden cardiac arrests.

**Background: **Sudden cardiac arrest is a serious medical condition claiming numerous lives across the globe. The fact that in most cases the victim succumbs to death within an hour of the onset of symptoms itself indicates the dreadful nature of the disease. This very fact has prompted us to analyze an ECG waveform using a chaos based non-linear technique viz. visibility graph technique.

**Method: **The visibility graph algorithm has been used to convert the ECG time series data into visibility graphs and then calculate power of scale-freeness in visibility graph (PSVG) values at an interval of one minute across the time series. Subsequently, comparative analysis of PSVG values has been carried out between diseased and normal subjects.

**Results:** The comparative study of PSVG values of diseased and normal subjects clearly shows that for diseased subjects mean PSVG is always less and this difference is statistically significant. Decrease in PSVG values is an indicator of dysfunction of the heart and the extent of deviation is an indicator of the degree of dysfunction.

**Conclusion:** The analysis leads to formulation of biomarkers which may be used to detect abnormalities of the human heart sufficiently ahead of the time before it turns out to be fatal.

Sudden cardiac arrest; Biomarker; Visibility graph; PSVG

Sudden Cardiac Arrest (SCA) is a medical condition which
occurs due to **arrhythmia** of the heart causing it to stop
effectively pumping blood to the brain and body. The fallout is
almost immediate as the victim succumbs to death often
within an hour of the onset of the symptoms [1]. What makes
SCA further dangerous is the fact that it can affect a person
who appears to be healthy and is not suffering from a cardiac
ailment [2]. However, people with some sort of coronary
disorder are at a higher risk of SCA.

An implantable cardioverter defibrillator (ICD) is useful to
restore normal **heart beat** in patients who have suffered
ventricular tachycardia or fibrillation. Though ventricular
fibrillation is the major cause of **sudden cardiac arrests**, there
are other causes of SCA as well. Moreover, protection against
sudden cardiac death by ICD implantation is invasive and
expensive, and therefore target patients must be selected with
very high predictive accuracy [1].

An entirely different approach towards early diagnosis of
**cardiac dysfunction** has gained sufficient momentum which
involves studying ECG signals of the heart using fractal analysis
[3,4]. In the realm of SCA, fractal analysis of heart rate
variability has been used to predict cardiac **mortality** [5]. In
earlier works [6], using detrended fluctuation analysis
technique, scaling exponents have been calculated to predict
both arrhythmic mortality and the spontaneous onset of lifethreatening
arrhythmias.

In this paper, we have applied the visibility graph technique [7,8] for a quantitative assessment of cardiac dysfunction in the event of SCA, and analysis of the observed results has led to some interesting finding, which might lead to a clinical tool for risk management. The paper is organized in the following manner. In section 2 the methods describing the analysis techniques in the context of chaos theory are summarized. Section 3 provides the description and source of the data as well as the analysis done on them and the summary of the results. The paper wraps up with a discussion and conclusion in section 4.

**Fractals and non-linear methods**

Mandlebrot [9] introduced the concept of fractals. A fractal
is a never ending pattern that repeats itself at different scales
and exhibits a property called “self-similarity”. Fractals are
observed all around us, with different scaling factors; from the
tiny branching of our **blood vessels** and neurons to the
branching of trees, lightning bolts, and river networks.
Regardless of scale, these patterns are all formed by repeating
a simple branching process. Any particular region of a fractal
looks very similar to the entire region though not necessarily
identical. The calculation of fractal dimension for measuring
self-similarity is a significant area in the study of chaos.
Following are the various methods proposed for measuring
fractal dimension (FD):

• Spectral analysis

• Rescaled range analysis

• Fluctuation analysis (FA)

• Detrended fluctuation analysis (DFA)

• Wavelet transform modulus maxima (WTMM)

• Detrended moving average (DMA)

• Multi-fractal detrended fluctuation analysis (MF-DFA)

• The latest addition being PSVG or power of scale-freeness of a visibility graph.

**Visibility graph**

Lacasa et al. [8] formulated the visibility algorithm to
convert a time series data into a graph called the visibility
graph. The work further stated that fractal series convert into
scale-free networks and its structure is related to the fractal
nature (self-similarity) and complexity of the time series [8,10].
This methodology has been used for simulation of both
artificial fractal series and real (small) series concerning **Gait
disease** [7]. In this technique each node of the visibility graph
represents a time sample of the time series, and an edge
between two nodes shows the corresponding time samples
that can view each other. The visibility graph algorithm maps
time series X to its Visibility Graph. Let X_{i} be the i_{th} point of the
time series. X_{m} and X_{n}, the two vertices (nodes) of the graph,
are connected via a bidirectional edge if and only if the below
equation is valid.

As shown in **Figure 1**, X_{m} and X_{n} can see each other, if the
above condition is satisfied. With this logic two sequential
points of the time series can always see each other hence all
sequential nodes are connected together. The time series
should be mapped to positive planes as the above algorithm is
valid for positive values in the time series. The degree of a
node in a graph is defined as the number of edges with the
other nodes of the graph. P(k) or the degree distribution of the
overall network formed from the time series is thereby the
fraction of nodes with degree k in the network. Thus, if there
are a total of n nodes in the network and n_{k} of them have
degree k, then P(k) = n_{k}/n. Two quantities satisfy the power
law when one quantity varies as a power of another. The scalefreeness
property of a Visibility graph states that the degree
distribution of its nodes satisfies the power law i.e. P(k) = k^{-λ},
where λ is a constant and it is known as PSVG. PSVG, denoted
by λ here, which is calculated as the gradient of log_{2}P(k) vs
log_{21}/k, corresponds to the amount of complexity and fractal
nature of the time series indicating Fractal Dimension FD of
the signal [7,8]. Ahmadlou et al. applied the visibility graph
algorithm to convert time series to graphs, while preserving
the dynamic characteristics such as complexity [11]. It is also
proved that there exists a linear relationship between the
PSVG λ and the Hurst exponent H of the associated time series
[7]. The visibility algorithm therefore provides an alternative
method of computing the Hurst exponent. Also it has been
shown, for example, that gait cycle (the stride interval in
human walking rhythm) is a physiological signal that displays
fractal dynamics and long-range correlations in healthy young
adults. The algorithm of visibility graph predicts gait dynamics
in slow pace, in perfect agreement with previous results based
on the usual method of de-trended fluctuation analysis [7]. As
the visibility graph is an algorithm that maps a time series into
a graph, the methods of complex network analysis can also be
applied to characterize a time series from a brand new
viewpoint. Graph theory techniques can also provide an
alternative method of quantifying long-range dependence and
fractal nature in time series. Each pattern and behavior in a
fractal time series is repeated frequently, in different scales,
which has been proved by Ahmadlou et al. for a visibility
graph, by calculating the PSVGs of a time series in multiple
scales [12].

Using visibility graph algorithm we have converted the **ECG** time series data into visibility graphs at an interval of one
minute across the time series. The present work is devoted to
the calculation of PSVG values for each of the visibility graphs
followed by a comparative analysis of PSVG values between
diseased and normal subjects.

**Data**

Data from two Physionet databases [13,14] have been used for analysis. The detailed description of the data is available on the website. The former database contains 23 complete Holter recordings for subjects experiencing sudden cardiac arrests while the latter contains 18 long-term ECG recordings of subjects having no significant arrhythmias. The naming conventions for the data followed in the subsequent texts of this paper are as per the website.

**Analysis**

The ECG data from diseased and normal subjects have been split in a manner such that each split spans approximately one minute of the ECG time series and consists of 10,000 data points being sampled across the span of a split.

With 10,000 data points the visibility graph of a split is constructed.

For each Visibility Graph, the value of P(k) is calculated for
each of the values of k as described in Section 2. The variation
of P(k) against k is found to satisfy the power law as shown in
the **Figure 2 **(for a particular subject).

The plot of log_{2}P(k) vs log_{21}/k is a straight line and, the
gradient of the graph is the PSVG (**Figure 3**).

The mean PSVG <PSVG>_{i-th half-hour, j-th subject} and standard
deviation <PSVG>_{i-th half-hour, j-th subject} are calculated for 30
consecutive splits (approximately 30 minutes) till the entire
signal duration of the ECG is exhausted for each of the normal
and affected subjects for each electrode. Thus, if the signal
duration of a subject is T minutes, then the mean PSVG and SD
are calculated for approximately T/30 splits for each of the
normal and affected subjects for each electrode.

Once mean PSVG and SD calculation is done for all affected
subjects for a particular electrode for each half an hour time
interval of the entire signal duration of the ECG, the diseased
mean PSVG <PSVG>_{i-th half-hour diseased} is calculated across all
affected subjects for each similar half hour interval for each
electrode.

Similarly normal mean PSVG <PSVG>_{i-th half-hour normal} and
normal SD PSVG <PSVG>_{i-th half-hour normal} are calculated across
all normal subjects for each similar half hour interval for each
electrode.

A plot of normal mean PSVG <PSVG>_{i-th half-hour normal} and
normal SD PSVG <PSVG>_{i-th half-hour normal} is depicted in **Figure 4** to show the trend of deviation of PSVG from the mean for the
first 24 half hour intervals or first 12 hours.

This is followed by a plot of PSVG _{i-th half-hour j-th diseased subject}
for a randomly selected diseased subject C42 for the first 24
half hour intervals or first 12 hours (**Figure 5**).

Next normal mean PSVG <PSVG>_{i-th half-hour normal} and PSVG ith
half-hour j-th diseased subject (for a randomly selected diseased
subject C42) are plotted for the first 24 half hour intervals or
first 12 hours as depicted in **Figure 6**.

Finally diseased mean PSVG <PSVG>_{i-th half-hour diseased} and
normal mean PSVG <PSVG>_{i-th half-hour normal} are plotted for the
first 24 half hour intervals or first 12 hours (**Figure 7**).

A number of interesting observations are obtained after the analysis as described below.

The plot of normal mean PSVG <PSVG>_{i-th half-hour normal} and
normal SD PSVG <PSVG>_{i-th half-hour normal} in **Figure 4** shows that
deviations in PSVG values from the mean PSVG are
significantly small in normal subjects. Hence it can be
concluded that PSVG values of normal subjects hover around
the mean. Also the mean PSVG of normal subjects remains
steady over a span of 12 hours.

The plot of PSVG _{i-th half-hour j-th diseased subject} for a randomly
selected diseased subject C42 shows considerable fluctuations
over a span of 12 hours as in **Figure 5**. Also the PSVG values of
the diseased subject remain outside the range of normal mean
PSVG <PSVG>_{i-th half-hour normal} ± normal SD PSVG <PSVG>i-th halfhour
normal as evident in **Figure 6**.

The comparative plot of values of mean PSVG for normal
subjects and that of diseased subjects for 12 hours at an
interval of ½ hour (**Figure 7**) reveals lower PSVG values for a
diseased heart than that for a normal heart. The deviation of
PSVG values of the affected patients from normal PSVG values
remains within the range of 0.1 to 0.2 for the first 8 hours and
henceforth becomes sharp with the PSVG shift going as high as
0.35 at a later point of time.

The higher values of PSVG indicate a better and stable functioning of the human heart [15]

Following parameters are obtained from the Visibility Network Graph analysis:

diseased mean PSVG <PSVG>_{i-th half-hour diseased}

normal mean PSVG <PSVG>_{i-th half-hour normal}

normal SD PSVG <PSVG>_{i-th half-hour normal}

The plot (**Figure 7**) clearly shows that for diseased subjects
mean PSVG <PSVG> is always less and this difference is
statistically significant. Decrease in PSVG values is an indicator
of dysfunction of the heart and the extent of deviation is an
indicator of the degree of dysfunction.

The 3^{rd} 1/2-hour probe gives an indication of a major
dysfunction, which can be used to trigger an initial alarm. This
gets pronounced at the 6^{th}, 9^{th} and 11^{th} hours. There is a huge
spike at the 11^{th} hour indicating a serious medical condition.

This principle may be put to use for early detection of
**cardiac disorder** in patients suffering from sudden cardiac
arrest.

The fact that heart beat is chaotic enables us to analyze it
using non-linear techniques e.g. visibility graph method. This
analysis leads to formulation of certain parameters or
**biomarkers** which may be used to detect abnormalities of the
**human heart** sufficiently ahead of the time before it turns out
to be fatal.

Initially, the software to compute and compare PSVG values may be used to detect onset of sudden cardiac arrest in hospitalized patients who are under ECG surveillance. As PSVG values start falling indicating a possible cardiac arrest, remedial action can be taken well before the dysfunction takes a fatal turn.

Eventually mobile apps may be prepared to compute the bio markers on a real time basis. The app will read data from an implanted loop recorder [16], compute PSVG and compare it with a benchmark PSVG preloaded for a healthy heart. Whenever the computed PSVG overshoots/ falls below the preloaded healthy PSVG by a pre-defined tolerance value, some audio visual markers will alert the individual of the impending cardiac disorder.

We thank the Department of Higher Education, Govt. of West Bengal, India for providing us the computational facilities to carry on this work.

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