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Diagnostics 2020, 10, 322; doi:10.3390/diagnostics10050322 www.mdpi.com/journal/diagnostics
Article
Cardio-Diagnostic Assisting Computer System
Galya Georgieva-Tsaneva *, Evgeniya Gospodinova, Mitko Gospodinov and
Krasimir Cheshmedzhiev
Institute of Robotics, Bulgarian Academy of Science, 1113 Sofia, Bulgaria; jenigospodinova@abv.bg (E.G.);
mitgo@abv.bg (M.G.); cheshmedzhiev@gmail.com (K.C.)
* Correspondence: galicaneva@abv.bg
Received: 4 April 2020; Accepted: 13 May 2020; Published: 19 May 2020
Abstract: The mathematical analysis and the assessment of heart rate variability (HRV) based on
computer systems can assist the diagnostic process with determining the cardiac status of patients.
The new cardio-diagnostic assisting computer system created uses the classic Time-Domain,
Frequency-Domain, and Time-Frequency analysis indices, as well as the nonlinear methods
(Poincaré plot, Recurrence plot, Hurst R/S method, Detrended Fluctuation Analysis (DFA), Multi-
Fractal DFA, Approximate Entropy and Sample Entropy). To test the feasibility of the software
developed, 24-hour Holter recordings of four groups of people were analysed: healthy subjects and
patients with arrhythmia, heart failure and syncope. Time-Domain (SDNN < 50 ms, SDANN < 100
ms, RMSSD < 17 ms) and Frequency-Domain (the spectrum of HRV in the LF < 550 ms2, and HF <
540 ms2) parameter values decreased in the cardiovascular disease groups compared to the control
group as a result of lower HRV due to decreased parasympathetic and increased sympathetic
activity. The results of the nonlinear analysis showed low values of (SD1 < 56 ms, SD2 < 110 ms) at
Poincaré plot (Alpha < 90 ms) at DFA in patients with diseases.Significantly reducing these
parameters are markers of cardiac dysfunction. The examined groups of patients showed an
increase in the parameters (DET% > 95, REC% > 38, ENTR > 3.2) at the Recurrence plot. This is
evidence of a pathological change in the regulation of heart rhythm. The system created can be
useful in making the diagnosis by the cardiologist and in bringing greater accuracy and objectivity
to the treatment.
Keywords: computer system; heart rate variability; cardiovascular diseases; Holter records;
arrhythmia; heart failure; syncope; mathematical analysis
1. Introduction
Diseases of the heart and blood vessels are one of the major problems of medicine today. The
mathematical analysis of cardiac examination data can be used in diagnostics to clarify the diagnosis,
to predict future diseases and to carry out effective treatment. One of the methods of diagnosing
cardiovascular disorders about the tasks of preventive medicine is the analysis of HRV information,
which is based on a mathematical analysis of the dynamics of changes in heart rate [1,2]. HRV is
currently one of the popular methods in non-invasive cardiology, sports medicine, and physiology.
The term "heart rate variability" refers to natural fluctuations in the number of intervals between
successive heartbeats. The method is based on the recognition and measurement of time intervals
between the R peaks (RR intervals) of electrocardiogram (ECG) signals (or P peaks of
photoplethysmogram (PPG) signals—PP intervals) and the subsequent analysis of the obtained
numerical values-of the studied parameters or graphical images, using various mathematical
methods [3]. Heart rate reflects not only the state of the cardiovascular system but also the whole
organism, as it is a major biomarker for the functioning of the autonomic nervous system and reflects
the balance between the two compartments—the sympathetic and the parasympathetic. Increased
Diagnostics 2020, 10, 322 2 of 26
activity of the sympathetic nervous system leads to a decrease in HRV, and the inverse activity of the
parasympathetic division of the nervous system leads to an increase in HRV [4].
In recent years, the proportion of medical software products has grown rapidly because
healthcare is an important part of many people's lives and their use has the potential to improve the
quality and effectiveness of medical services for the ongoing monitoring of patients' health. The
benefits of using software products in medicine are: providing remote medical consultation (which
is particularly useful for people living in small, non-hospital towns), functional, database-based
diagnostics processed automatically without the participation of a doctor, and to notify the user of
any deviations in the values of the investigated parameters [5]. Because of such software products,
diagnosis becomes more accurate and faster, and the prescribed treatment is more effective.
Research that is currently of interest to health professionals is largely related to the use of
methods for mathematical analysis of HRV, as one of the most accessible and fairly informative ways
to analyse and evaluate the general condition of the human body. The combination of simple, non-
invasive information-gathering technology obtained from ECG and PPG devices [6] with full
automation of the calculations and the ability to physiologically interpret the results obtained
through the application of software products is the basis for the widespread clinical use of HRV
technology in the diagnostic process, medical screening and treatment.
1.1. Background
HRV is widely used as a biomarker for the diagnosis and prognosis of several cardiovascular
diseases. Reynders et al. [7] investigate changes in HRV (of ECG data) parameters in Multiple
Sclerosis Disease. The studies done include the parameters in the time domain.
Kim et al. [8] include HRV obtained via an ECG (five minutes, Lead II channel) in the creation
of a predictive model useful in the diagnosis of cardiovascular disease. The methods used are:
determining parameters in Time and Frequency Domain, Poincaré plot indicators, Approximat e
Entropy, Hurst exponent, and exponent α of the 1/f spectrum.
Park et al. [9] examine the impact of six activities (sitting, standing, walking, ascending, resting,
and running) using HRV (ECG data obtained in a controlled laboratory environment) to evaluate the
impact of human activity on a person's health.
Investigation of the differences between several cardiac diseases using mathematical methods is
researched in [10]. The following methods are used: Approximate Entropy, Bi-Spectral Entropies,
Recurrence Entropy, and Sample Entropy. Based on the methods studied, the authors present a
Composed Integrated Index to help distinguish between normal and abnormal classes more
accurately.
Several authors have been working to accurately identify atypical heart contractions. Inan et al.
[11] use a wavelet-based method to detect premature ventricular contractions that are characteristic
of some types of arrhythmias. The method is applied to public databases.
In their study, the authors of [12] point out the benefits of using computer systems for analysis
and diagnosis in medicine: reducing time and improving accuracy in diagnosis. A review of scientific
publications concerning computer-aided cardiac data analysis has been made and the differences
between an offline and an online system are outlined.
HRV is also suitable for analysis in patients with other conditions (such as diabetes) [13].
Computer tools for processing diagnostic information are increasingly being used and preferred in
the study of biomedical information obtained from patients with cardiovascular disease [14]. In
clinical cardiology, computerized diagnostic procedures are being used today to aid diagnosis and
treatment. Early diagnosis is crucial for a good prognosis of any disease [15], this also applies to the
early diagnosis of heart disease, which has a high prevalence rate.
Software systems for the analysis of the HRV, developed in recent years, mainly offer the
classical analysis in the time domain and the frequency domain. Of the nonlinear methods, the
Poincaré plot is predominantly proposed, other software systems only offer DFA, and a small number
of systems offer both analyses. Some of these software systems offer a graphical user interface,
allowing them to be used by a wider range of users. Most systems are desktop applications and are
Diagnostics 2020, 10, 322 3 of 26
created in MATLAB (Kubios [16], CODESNA_HRV [17], KARDIA [18], SinusCor [19], POLYAN [20]
etc.), and gHRV [21] was created in the Python programming language, rHRV [22] was developed in
the "R" programming language. These software systems use the following methods:
• Kubios: Time and Frequency analysis, Poincaré plot, DFA; ApEn, Recurrence plot, Entropy;
• CODESNA_HRV: Time and Frequency analysis, Entropy;
• KARDIA: Time and Frequency analysis, DFA;
• SinusCor: Time and Frequency analysis, Time-Frequency analysis (Fast Fourier Transform
and AutoRegressive method);
• POLYAN: Time and Frequency analysis, Nonlinear methods;
• gHRV: Time and Frequency analysis, Poincaré plot, Entropy, Fractal Dimension;
• rHRV: Time and Frequency analysis, Poincaré plot.
Many mathematical methods for analysing and evaluating HRV can be successfully used to
assist diagnosis in determining the cardiac status of patients. Graphic representation of the results of
the application of such methods is a synthesized assessment of the current state of patients for the
studied period. Application of mathematical methods through modern high-performance portable
computer systems enables rapid, inexpensive assessment of cardiac activity in all conditions. They
are at the basis of modern cardiology telemedicine and the ability to consult specialists in real time,
regardless of the patient's location.
The review of existing software for analysis and evaluation of HRV shows that there is currently
no uniform format for the presentation of input data (RR interval series). In many cases, available
software products do not allow the use of data obtained from different ECG and PPG devices.
The creating of a computer system to support the diagnostic process, integrating all proven
methods of HRV analysis time domain (statistical and geometrical methods), frequency domain, and
nonlinear means (Poincaré plot, DFA, Multi-Fractal DFA, Hurst R/S, entropy) is a task that would
help improve the efficiency of using mathematically based tools for cardiac data analysis.
1.2. The Purpose of This Article
The purpose of this article is to present a computerized system for assisting cardio diagnosis,
consisting of developed algorithms, software for mathematical analysis of HRV and a database
consisting of patients' Holter records, and numerical and graphical results for different disease
groups to support the diagnosis. The development is based on established mathematical methods for
the processing and analysis of diagnostic cardiac information for patients to evaluate the condition
of the cardiovascular system and determine the current or predict future cardiac disease.
For validation of the developed cardio-diagnostic assisting system, named by the authors
HeartAnalyzer, four groups of subjects were examined: healthy and patients with different
cardiovascular diseases (arrhythmia, heart failure, and syncope) by applying linear and nonlinear
mathematical methods. The system allows autonomous computer processing and analysis of patient
data to monitor their cardiac status in real time. In case of deviation in the results, they can seek
professional advice, help, and treatment from a cardiologist.
2. Materials and Methods
2.1. A Computer System for Analysis and Evaluation of HRV
The motivation for creating a new computer system is determined by the need to increase the
efficiency in the development of automated systems to support the activity of diagnosing the
functionality of the human body, which is achieved through the development of a set of algorithms
and software for analysis and evaluation of HRV. The HeartAnalyzer offers, in addition to the ability
to analyze and evaluate HRV and study the dynamics of changes in cardiovascular activity, creating
an archive for each patient that allows the treating physician to view the patient's data and monitor
his or her condition. In addition to the results of the patient's analysis, the database will also store
graphic information specific to the various diseases to assist the physician in diagnosing the disease.
Diagnostics 2020, 10, 322 4 of 26
The presented software system is in the process of testing. It is a computerized system that is created
solely for the purpose of research and has no commercial purpose.
Figure 1 shows the block diagram of the created diagnostic HeartAnalyzer, which operates in
the following three main modes:
• Cardiology registration via ECG, PPG and Holter devices and receipt of PP/RR time series;
• Mathematical analysis of the recorded data by applying linear and nonlinear methods. The
results of the analysis are presented in tabular and graphical form;
• Creating a Report based on the results obtained, which can be stored in the patient database
for later review and/or printing. In addition to the patient data, the database contains
graphical information obtained through the graphical methods of analysis of HRV
characteristics of various cardiovascular diseases.
The software checks that the RR/PP time series are normalized and, if not, normalizes them. The
normalization is the following: it removes any RR/PP intervals that are shorter than 330 ms or longer
than 1.2 s, and those that are 25% shorter or 25% longer than the median of the previous five RR/PP
intervals.
Mathematical analysis is performed on the normalized RR/PP time series by applying the
following linear and nonlinear methods:
• Linear methods: Time-Domain, Frequency-Domain, and Time-Frequency analysis;
• Nonlinear methods: Poincaré plot, Recurrence plot, Hurst R/S method, DFA, Multi-Fractal
DFA, AppEn and SampEn.
Figure 1. Block diagram of the cardio-diagnostic HeartAnalyzer.
Figure 2 shows the home page of the HeartAnalyzer diagnostic system. It allows you to select
an input file and then begins analysing the data. The results of the analysis and evaluation are
displayed by selecting the appropriate button (Time-Domain, Frequency-Domain, Time-Frequency
and Nonlinear analysis), by default the results of Time-Domain analysis are displayed. The results
are presented in two ways: tabular and graphical.
Diagnostics 2020, 10, 322 5 of 26
In addition to the values of the investigated parameters, in the table shows and the reference
values from the Time-Domain and Frequency-Domain analysis. These methods are standardized by
the European Society of Cardiology and the North American Society of Pacing and Electrophysiology
[23], with the limits of norm-pathology known. When the value of the parameter under study is
within the limits of the reference values, in the Status field indicates N, and when the value is below
the lower limit—L and above the upper limit—H. The graphical results are displayed in the right of
the table by selecting the appropriate radio button.
2.2. Linear Methods for HRV Analysis
2.2.1. Time-Domain Analysis
HRV time-domain analysis is based on the statistical analysis of changes in the duration of
consecutive normal NN (RR) intervals obtained from ECG signals. This type of analysis is performed
for long records (24 hours) through statistical and graphical measurements. The statistical analysis
calculates the following parameters [24]:
• SDNN (ms)—this parameter calculates the standard deviation from the average duration of
RR intervals over the entire study period. It is used to evaluate total HRV and especially its
parasympathetic component. The longer the study lasts, the more total HRV accumulates, so
it is necessary that the compared signals have the same duration;
• SDANN (ms)—it defines the standard deviation from the average length of RR intervals by
calculating the 5-minute segments. The registration period is split when a 24-hour ECG
recording is used. This parameter is used to evaluate the low frequency components of HRV;
• SDNN index—determines the average of standard deviations from the average duration of
RR intervals for all 5-minute periods divided by the observation period;
• RMSSD (ms)—determines the root mean square difference between the duration of adjacent
RR intervals. This parameter reflects the fast, high frequency variability changes;
• NN50—the number of the pairs of consecutive NN intervals differing by more than 50 ms
obtained over the entire recording period;
• pNN50—the percentage of consecutive intervals that differ by more than 50 ms. Because this
parameter is determined by adjacent intervals, it reflects fast, high frequency variability
changes.
Diagnostics 2020, 10, 322 6 of 26
Figure 2. The home page of the proposed diagnostic HeartAnalyzer.
The Time-Domain analysis parameters are integral to the sample and describe the average
statistical characteristics of the digital performance of the entire signal or fragments thereof. The
values of the statistical parameters depend on the duration of the data surveyed and on what hours
of the day and under what conditions the ECG records were made.
Time-Domain heart rate analysis not only allows you to determine the values of HRV statistics
but can also present them graphically.
Histograms construction refers to geometric methods. They allow graphical representation of
the distribution of RR interval series. Geometric methods are less affected by the quality of the
recorded data and can be considered as an alternative to statistical measurements. However, the
recorded ECG signals should be at least 20 minutes in length, therefore short-term records cannot be
estimated using the geometric methods. The geometric methods calculate the following parameters:
• TINN—the distribution of RR intervals is approximated to a triangle and its base is measured
in milliseconds. The essence of the algorithm is the following: the histogram is conventionally
represented as a triangle, the base of the triangle is calculated by the formula: b = 2A/h, where
h is the largest number of RR intervals, and A is the area of the whole histogram, i.e., the total
number of all RR intervals analysed. This parameter avoids taking into account the RR
intervals associated with artifacts and extrasystoles that form additional peaks and domes of
the histogram;
• HRV triangular index—this parameter plot a histogram of RR intervals at 7.8125 ms (1/128
sec). The total number of RR intervals is divided by the peak height of the histogram. This
index reflects total HRV and is directly proportional to parasympathetic activity.
Using the histogram, the relationship between the total number of identified RR intervals and
their variation is calculated. For the HRV triangular index, the highest peak of the histogram is taken
as the triangle point, the basis of which corresponds to the quantitative value of the variability of the
RR intervals. The height of the triangle corresponds to the most frequently observed duration of the
Diagnostics 2020, 10, 322 7 of 26
RR intervals, and its face corresponds to the total number of all RR intervals involved in its
construction. The HRV triangular index parameter provides an estimate of the overall HRV.
2.2.2. Frequency-Domain Analysis
Spectral analysis of cardiac data (showing the mode of action of the heart and the entire
cardiovascular system) presents the distribution of frequencies present in the NN interval series as a
mathematical sum of regular sinusoids of different amplitudes.
The evaluation of HRV in frequency analysis is performed by determining the power spectral
density (PSD) characteristic, which is investigated in different frequency ranges. Cardiac recordings
lasting from 5 to 30 minutes are obtained under steady-state conditions using an electrocardiograph
and are defined as short-term data records. Long-term Holter monitoring of cardiac activity records
in real non-stationary conditions (having a duration of 24 to 72 hours and even up to 2 weeks) is
defined as long-term data records. There are some differences in the way long-term and long-term
data records are analysed, which were defined in the Common European American Standard in 1996
(recommendations have been made for studies to use certain frequency bands) [23].
Following physiological reasons, the spectral parameters in the frequency range are determined
and distributed in the following frequency ranges [23]:
• Very low frequency—VLF: from 0.003 Hz to 0.04 Hz;
• Low frequency—LF: from 0.04 Hz to 0.15 Hz;
• High frequency—HF: from 0.15 Hz to 0.4 Hz.
This article uses the Welch mathematical method to determine the spectral parameters, which is
a modification of the traditional periodogram and is proven to be an effective spectral analysis
method. The investigated cardiac series that have undergone preprocessing and consisting of normal
intervals are divided into overlapping segments to reduce the high dispersion of the periodogram.
With the Welch method, the data located at the end of the time series studied are processed to
obtain a smaller weighting factor than the data located in the center. Assuming that each segment
has M elements, then a modified periodogram for one of the overlapping segments is calculated by
the formula [25]:
,()=
.(
)() , (1)
where:
= 0 1,
= 0 1,
M – length of the blocks;
()=(+) —i-th block;
f—frequency;
w—window function;
iD—offset of i-th block;
U is the normalizing factor [25]: =
.
().
The modified Welch periodogram is applied sequentially to all segments, after which the
average PSD of the studied segments is determined [25]:
() =
,()
, (2)
L—Number of segments.
Diagnostics 2020, 10, 322 8 of 26
2.2.3. Time-Frequency Analysis
Time-Frequency Analysis, Wavelet-Based Method
Using the time-frequency method of analysis, graphical representations of ordinary and
logarithmic spectrograms of spectral density can be constructed using three popular and efficient
methods: the Burg method, the LombScargle method, and the Wavelet based method. Spectrograms
are color graphs that show the frequency distribution (vertical axis) versus time (horizontal).
The spectrograms give a visual idea of signal strength by using a pre-selected color palette. The
dark blue color is an indication of the absence of a frequency in the frequency spectrum. Light blue
to yellow to red indicates an increase in the power of the corresponding frequency in the energy
spectrum. The highest frequency power is indicated by a dark red. Dense horizontal lines mark the
boundaries of the frequency ranges.
Methods for constructing spectrograms:
• Burg method—this method uses an autoregressive model of a different order, spline
interpolation, Heming window, and window overlap apply;
• LombScargle method—the method calculates a non-normalized Lomb–Scargle periodogram;
• Wavelet method—based on the application of wavelet theory methods; applies wavelet
interpolation of the investigated data, uses different wavelet bases (Morlet, Dobeshi, bi-
orthogonal wavelets, and other wavelet bases) and calculates a continuous wavelet spectrum.
The results in the frequency domain are assumed to be calculated according to the variability
standard for a selected five-minute segment of the input data. Cubic spline wavelet interpolation is
used in the present work.
The numerical results give information about the values of the spectrum of data in absolute
units—, in percentages and normal units for the three frequency bands VLF, LF, and HF.
Frequency peaks for each frequency range are determined. The sympathetic balance index LF/HF is
also calculated. Investigations are conducted based on the removed trend data during preprocessing.
The results of the wavelet spectral analysis and the determined frequency characteristics in this work
are calculated for real cardiac recordings.
2.3. Nonlinear Methods for HRV Analysis
Traditional techniques for HRV analysis in time and frequency domains are often not sufficient
to characterize the complex dynamics of cardiac rhythm since the mechanisms involved in
cardiovascular regulation are likely to interact in a nonlinear manner [26]. It has been shown that the
heart of a healthy person can act very randomly, and the reduction of HRV and the appearance of a
pronounced periodicity can be associated with several diseases [27]. Guided by this concept, the use
of nonlinear mathematical methods in the analysis of HRV may provide additional, useful
information to evaluate the functional state of the organism, but also monitor its dynamics and the
occurrence of pathological conditions with a sharp decrease in HRV and high likelihood of sudden
death [28]. According to the recommendations of the European Society of Cardiology and the North
American Society of Pacing and Electrophysiology [23], the study of the applicability of nonlinear
HRV methods is currently one of the most important research areas.
2.3.1. Geometric Nonlinear Methods
The correlation rhythmogram (spectrogram) obtained by the Poincaré plot allows a compact
representation of the entire series of cardio intervals, no matter how long the study lasted—several
minutes or many hours [28]. In the rectangular coordinate system, each pair of RR intervals (previous
and next) has coordinates (x, y), where x is the value of the RRn interval and y is the value of RRn + 1.
The formation of the graph yields a segment of points whose center is located on the line of identity.
The identity line is a graph of the function x = y (RRn = RRn+1). On the identity line of the correlation,
rhythmograms are those cardio intervals whose duration is approximately equal to the duration of
the previous interval. If the point corresponding to a cardio interval is located above the line of
Diagnostics 2020, 10, 322 9 of 26
identity, this indicates how much longer the heart interval is than the previous one, i.e., x < y (RRn <
RRn+1). Accordingly, if the point is below the identity line, this indicates that the RRn+1 interval is
shorter than the RRn interval (RRn > RRn+1). Therefore, the shape of the point segment (RRn; RRn+1 ) on
the graph reflects the change in the duration of the RR intervals, i.e., the variance. If an ellipse with a
longitudinal and a transverse axis is placed on the graph constructed by Poincaré plot, the following
parameters can be determined [29]:
• Ellipse length (SD2 [ms] parameter)—corresponds to long-term variability of RR intervals
and reflects total HRV;
• Ellipse Width (SD1 [ms] parameter)—represents the scattering of the dots perpendicular to
the identity line and is associated with rapid variations between heart beats;
• The SD1/SD2 ratio reflects the relationship between short- and long-term HRV.
The main features that are used for visual analysis of HRV using the Poincaré method are: the
shape, size of the main segment of points, and the symmetry of points concerning the identity line.
The shape of the segment of points is categorized for the different functional states of the person
[28,29]:
• The healthy subject's graph has one major segment of points, which has the shape of a comet
with a narrow bottom and gradually expanding to the top;
• The chart of the sick subject has the form of a torpedo, a fan or a complex form (consisting of
several segments) depending on the type of disease.
Graphics constructed using Poincaré plot can be quantified by placing an ellipse on the graphical
form. The size of the segment of points is characterized by the parameters: length and width of the
ellipse.
The length of the ellipse reflects the involvement of the non-respiratory components in the
formation of the common HRV and is determined by the parameter SD2 [29].
The width of the ellipse takes into account the long-term variations and demonstrates the
contribution of respiratory arrhythmias to the total HRV and is determined by the parameter SD1
[29].
The symmetry of the segment of points defined concerning the line of identity is the next factor to
be considered in the visual analysis of the resulting graph. Symmetry shows the equilibrium state of
the HRV and the absence of rhythmic disturbance, and asymmetry is the opposite—for the presence
of such.
The size of the segment of points and the symmetry of the points in the graph are categorized
for the different functional states of the person [29]:
• The graphic of a healthy subject has a clear ellipse;
• If the graph looks like a compressed segment of dots, then the narrow "compressed" ellipse
means low HRV and is an indicator of a disease state;
• If the length and width of the ellipse are approximately equal and it approaches a circle, in
this case, the HRV is low, which is an indicator of the disease state;
• If the points in the graph are symmetrical relative to the identity line, then there is no rhythm
disturbance;
• If the points in the graph are asymmetric relative to the identity line, then the patient has
rhythmic disturbances.
Another promising method for studying the physiological fluctuations of non-stationary
processes is the Recurrence plot, which allows visualizing certain regularities in the models of the
complex non-stationary fluctuations [30–32]. The basis of the method is the construction and analysis
of a recurrence diagram. The algorithm for construction and analysis by the Recurrence plot consists
of the reconstruction of the phase space. There are two major factors that play an important role in
the reconstruction of the phase space of a dynamic system: embedding dimension m and time delay
τ. The parameter m is determined by the False Nearest Neighbours (FNN) method [33,34] and τ is
determined by the Mutual information function [35]. Based on these two parameters, the phase space
is constructed and Euclidean distances between vectors (system states) are analysed. If the distances
between the points i and j are below the threshold value ε, i.e., =SDNNm, where SDNN is the
Diagnostics 2020, 10, 322 10 of 26
standard deviation of the normal RR intervals, then a point with the coordinates i and j is placed in
the recurrence diagram. In this way, a pattern of points forming vertical and diagonal lines appears
on the recurrence diagram. The diagonal lines reflect the reappearance of a sequence of system states
and are manifestations of the coincidence of system behaviour in two different time sequences.
Vertical lines arise because of the stability of a condition over some time. The analysis of the topology
of the recurrence diagram allows us to classify the following processes:
• Homogeneous processes with independent random values;
• Processes with slowly changing parameters;
• Periodic or oscillating processes, etc.
The numerical analysis of the recurrence diagrams consists of determining the following
parameters:
• Recurrence rate (REC%)—this parameter reflects the level of recurrence, indicating the
probability of finding a recurring point in the RR series, that is, determining the probability
of a recurrence of the condition. This variable ranges from 0% to 100%.
• Determinism (DET%)—this parameter is a characteristic of the predictability of the system.
It is defined as the ratio between the number of recurrent points located on diagonal lines
and the total number of recurrent points.
• Lmax, Lmean indicators reflect the maximum and average length of the diagonal lines,
assuming that Lmin = 2. The Lmax parameter is associated with the largest Lyapunov
exponent (LLE) [36,37].
• ENTR—this parameter is related to Shannon entropy.
The advantage of the Recurrence plot is that it allows the properties of the studied processes to
be represented as a geometric figure. This method is a tool for detecting hidden dependencies in the
observed RR interval series.
2.3.2. Fractal Methods
It is common knowledge that RR intervals are nonlinear and non-stationary time series, with
much of the information encoded in the dynamics of their fluctuations. These fluctuations have an
internal structure with fractal (self-similar) properties that can be observed at different time intervals.
Therefore, fluctuations can be measured by fractal and multifractal indicators. One of the main
properties of fractal processes is: self-similarity. The degree of self-similarity can only be determined
by one parameter known as the Hurst parameter (H) [38,39]. The value of this parameter is in the
range between 0 and 1. When 0 < H < 0.5, the process is antipersistence, which means that the upward
trend in the past means a decline in the future and vice versa. If H > 0.5, the process is persistence
and it has stable behaviour, i.e., the upward trend in the past remains in the future. The higher the
value of this parameter, the stronger the trend. In the case of H = 0.5, no process trend is observed
and it has Brown motion behaviour. Therefore, based on the value of the Hurst exponent, it is possible
to predict and predict the future behaviour of the investigated RR signal. The following methods are
used in this software to determine the Hurst parameter: Hurst R/S method, Detrended Fluctuation
Analysis and Multi-Fractal Detrended Fluctuation Analysis (MFDFA).
Hurst R/S method is a process that requires processing a large amount of data. In this method,
the RR interval series is divided into non-overlapping blocks, and for each block, the range R (n) and
standard deviation S (n) are determined, where n is the number of points [40,41]. A linear regression
model is constructed between the dependent variable Log10(R(n)/S(n)) and the independent variable
Log10(block size). The method of least squares determines the regression coefficients:
• β0—the point at which the regression line intersects the ordinate;
• β1 —the slope of the regression line.
The value of the Hurst parameter is equal to the slope of the regression line: H = β1. If the value
of H is in the range (0.5, 1.0), then the process under study is fractal.
Detrended Fluctuation Analysis is suitable for studying both stationary and non-stationary
processes in terms of statistical self-similarity [42,43]. The DFA determines the signal fluctuation
coefficient that is related to the Hurst exponent. To determine the "profile" of the study signal with a
Diagnostics 2020, 10, 322 11 of 26
length of N, it is divided into no overlapping blocks of length s. The local trend for each segment s is
calculated, using the least squares method and determination of the sums for the segments. For
different values of the parameter, s is calculated the fluctuation function: ()~. The graphical
dependence of Log10(Fs) vs Log10(s) is plotted and the value of the fluctuation index α is determined
from the slope of the line. The DFA exponent α and the Hurst parameter H are related by:
• H = α if 0< α <1;
• H = α-1 if α ≥ 1.
If the value of parameter α is less than one, then its value is equal to the Hurst exponent. The
value of the α parameter in the case of fractal signals is greater than 0.5 and less than 1. The greater
the value of the H parameter, the more regular the process with a high degree of self-similarity.
The DFA method shows typically two ranges of scale invariance, which are quantified by two
separate scaling exponents, α1 and α2, reflecting the short-term and long-term correlation. The short-
term fluctuation is characterized by the slope α1 obtained from the (log10(s), log10(Fs)) graph within
range [4,16] and long-range fluctuation is characterized by the slope α2 obtained from the range [17].
Multi-Fractal Detrended Fluctuation Analysis is a method to examine the self-similarity of a
nonlinear, chaotic, and noisy time series [44–47]. Fractal processes are of two main classes:
monofractal and multifractal. The monofractal process is homogeneous in the sense that it has the
same scale properties locally as well as globally. These processes can be described with only one value
of the Hurst exponent or with one value of the fractal dimension. In contrast to these signals,
multifractal signals can be decomposed into a large number of homogeneous, fractal subsets that are
characterized by a spectrum of local Hurst exponents. The multifractal approach us allows to describe
a broad class of structurally more complex signals than those that are completely characterized by a
single fractal dimension. This approach makes it possible to obtain new estimates that give an idea
of the intrinsic, nonlinear, dynamic processes in the studied signals. MFDFA quantifies the presence
or absence of fractal, correlation properties in the non-stationary signals studied.
2.3.3. Entropies Methods
Approximate Entropy (AppEn) and Sample Entropy (SampEN) as nonlinear methods for
analysing HRV. These methods determine the degree of irregularity of the RR time series. The low
entropy values are characteristic of regular time series, while higher values are inherent in stochastic
data [45].
2.4. Data Collection
The cardiology data used to conduct the study in this article were recorded using a Holter
monitoring device at the Medical University of Varna, Bulgaria. The Holter device has been on the
patients for about 10 hours in the morning under the supervision of a cardiologist, after which the
patients were free to perform their daily routine. Registration of data under the conditions in which
the individual usually lives is of particular importance, given a realistic picture of the conditions in
which his or her heart problems occur. The Holter data are transferred to the server the next day after
the Holter device has been removed. This study was approved by the Research Ethics Committee at
Medical University—Varna, Bulgaria., Protocol/Decision No. 82, 28 March 2019. All participants were
informed in advance of the research that would be done to them. The participants are from Varna,
Bulgaria and are aged 49 to 68 years, men and women. Holter records have been made between April
2019 and March 2020. In addition, 229 Holter records were investigated, 14 of which were excluded
due to concomitant diseases, and 3 records were excluded due to the assumption that the records
were not correct (records contain corrupted data). The records are approximately 24 hours in length
and have been reviewed for the correctness of data.
The 212 records studied were divided into groups according to their major cardiac disease, as
determined by a cardiologist: Group 1—healthy controls (48 number volunteers who were not
diagnosed with cardiac disease), Group 2—patients with arrhythmia (56 number), Group 3—patients
with heart failure (59 number), and Group 4—patients with syncope (49 number).
Diagnostics 2020, 10, 322 12 of 26
2.5. Statistical Analysis
Continuous variables are reported as mean and standard deviation (SD). Results were expressed
as mean ± SD unless indicated otherwise. Statistical significance. In the field of research, from the
statistical point of view, it is important to choose the cut-off point below which, if the p-value falls,
the parameter under study is considered statistically significant. In our study, if the p-value tested
was less than or equal to 0.05 (5%), the result was considered statistically significant. All statistical
analyses (performed between each heart disease group and the healthy control group) were
performed using the t-test.
3. Results
3.1. Linear Methods for HRV Analysis
Table 1 shows the values of the studied parameters in Time-Domain analysis for the four studied
groups. The statistical parameters SDNN, SDANN, and SDNN index reflect the analysis of
consecutive RR intervals. The values of these parameters decreased in the cardiovascular disease
groups compared to the control group. This approach eliminates random fluctuations in RR intervals,
often associated with artefacts or the occurrence of arrhythmias and another cardiovascular disease.
The standard [23] provides for the use of graphical methods for the evaluation of histograms and the
calculation of parameter values: TINN and HRV triangular index. The value of the HRV triangular
index parameter decreases in groups with cardiovascular disease compared with healthy controls.
Table 1. Time-Domain HRV analysis results for studied groups.
Parameter
Group 1
(mean ± SD)
n = 48
Group 2
(mean ± SD)
n = 56
Group 3
(mean ± SD)
n = 59
Group 4
(mean ± SD)
n = 49
Statistical p-Value
Gr1,2 Gr1,3 Gr1,4
Statistical measurement
MeanRR [ms]
849 ± 28
679 ± 18
880 ± 20
855 ± 35
0.0001
0.0005
0.0001
SDNN [ms]
121.8 ± 21
62 ± 15
72 ± 18
60 ± 15
0.0001
0.0001
0.0001
SDANN [ms]
140 ± 15
64 ± 10
70 ± 12
28 ± 4
0.0001
0.0001
0.0001
pNN50 [%]
14.8 ± 3
13 ± 5
9.1 ± 2
6.7 ± 1
0.03
0.0001
0.0001
RMSSD [ms]
25.8 ± 9
17 ± 2
16 ± 3
12 ± 5
0.0001
0.0001
0.0001
Geometrical measurement
HRVti [numb]
21.8 ± 10
6.2 ± 2.7
1.5 ± 1.2
3.1 ± 1.6
0.0001
0.0001
0.0001
TINN [ms]
493 ± 80
542 ± 70
381 ± 60
52 ± 11
0.002
0.0001
0.0001
Figure 3 (A, B, C, D) shows the histograms of a healthy subject, a patient with arrhythmia, heart
failure, and syncope. The graphs clearly show that there is a difference in the shape of the histograms
in patients with cardiovascular disease and healthy subjects. The healthy controls are characterized
by the central arrangement of the pillars in the diagram of the RR intervals with the localization of
the highest pillars (fashion) in the range 0.7–1.0 sec. Normal cardiac activity is characterized by
asymmetrical, dome-shaped and dense histogram, the shape is similar in appearance to the Gaussian
curve (Figure 3A). The asymmetric shape of the histogram shows the arrhythmic nature of the ECG.
An example of such a histogram is shown in Figure 3B. In Figure 3C shows a histogram of a patient
with heart failure. This histogram has a very narrow base and a pointed tip. Figure 3D shows the
histogram of a patient with syncope. This chart is multifaceted and there are two pronounced peaks.
The considered parameters for Time-Domain analysis are highly correlated with each other,
which is why the standard [23] proposes to use clinically the following five parameters: SDNN,
SDANN, pNN50%, RMSSD and HRV triangular index, for which reference values are entered, i.e.
the boundaries of norm-pathology are known.
Diagnostics 2020, 10, 322 13 of 26
Figure 3. Histograms for healthy subject and patients with arrhythmia, heart failure, and syncope. (А)
Healthy subject. (B) Patient with arrhythmia. (C) Patient with heart failure. (D) Patient with syncope.
The results of the studies performed in the Frequency domain on three patient groups and the
healthy control group are summarized in Table 2. In the healthy control group (Figure 4 A), high
values of the spectral parameters can be established in the three tested frequency bands, with the LF
Power/HF Power ratio reflecting the mean value for the studied group 1.52, which is within the range
of values indicating good health status according to the variability standard.
Table 2. Frequency-Domain HRV analysis results for studied groups.
Parameter
Group 1
(mean ± SD)
n = 48
Group 2
(mean ± SD)
n = 56
Group 3
(mean ± SD)
n = 59
Group 4
(mean ± SD)
n = 49
Statistical p-Value
Gr1,2 Gr1,3 Gr1,4
VLF Power [ms
2
]
13226.42 ± 674.12
12602.93 ±984.17
11939.57 ± 489.73
17846.84 ± 692.41
0.0004
0.0001
0.0001
LF Power [ms
2
]
1198.88 ± 562.93
549.98 ± 181.42
411.82 ± 247.79
486.26 ± 164.33
0.0001
0.0007
0.0001
HF Power [ms
2
]
791.03 ±243.18
675.71 ± 269.14
301.93 ± 354.81
534.35 ± 388.96
0.0234
0.002
0.0002
LF Power nu
0.602 ± 0.23
0.449 ± 0.11
0,577 ± 0.19
0.476 ± 0.21
0.0001
(0.5393)
0.0059
HF Power nu
0.398 ± 0.19
0.551 ± 0.13
0.423 ± 0.08
0.524 ± 0.195
0.0001
(0.3615)
0.0018
LF/HF
1.52 ± 0.57
0.81 ± 0.22
1.36 ± 0.07
0.91 ± 0.68
0.0001
0.0475
0.0001
* NS—Not Significant
Patients with arrhythmia (Figure 4 B) have low LF and HF spectral components properties and
the lowest LF/HF Power ratio (0.81 versus 1.52 for health group, p-value = 0.0001). These values
indicate that arrhythmia as a disease significantly impairs the spectral characteristics of the heart rate
signal, indicating that this disease impairs the body's restorative powers and is an indicator of the
severity of this common heart disease.
Diagnostics 2020, 10, 322 14 of 26
A significant decrease in VLF Power values was observed in patients with heart failure (Figure
4 C) (11939.57 versus 13226.42 ms2 for health group, p-value = 0.0001). Reduced VLF Power in
combination with other variables may indicate patients with heart failure who are at increased risk
of future cardiovascular events. The values of the spectral components in the LF and HF area show a
2 to 3-fold decrease in heart failure patients compared to the healthy control group. This is most
characteristic of conducted studies of patients with heart failure: slightly lowered VLF Power values,
but several times lowered LF Power values (411.82 versus 1198.88 ms2 for health group) and HF
Power (301.93 versus 791.03 ms2 for health group) areas. Studies on daily parts of the Holter record
show even greater reductions in LF and HF Power values, up to five times lower than healthy (in
some patients even greater). It can be concluded that the overall activity of the sympathetic nervous
system is increasing.
Figure 4. Frequency domain, PSD. (А) Healthy subject. (B) Patient with arrhythmia. (C) Patient with
heart failure. (D) Patient with syncope.
Cardiac patients who have developed syncope (Figure 4D) have a marked increase in spectrum
in VLF (17846.86 versus 13226.42 ms2 for health group). Syncope is a sudden loss of consciousness
caused by a sharp decrease in heart rate and/or blood pressure. Assessment by gender, age, obesity,
diabetes, and other physiological parameters showed no significant differences. This is most
Diagnostics 2020, 10, 322 15 of 26
characteristic of patients undergoing syncope: have high VLF Power values (significantly higher than
healthy) at the expense of rather low values in LF Power (486.26 versus 1198.88 ms2 for health group)
and HF Power (534.35 versus 791.03 ms2 for health group) areas. VLF Power values reflect the activity
of the sympathetic nervous system, parasympathetic rhythms, mechanisms of thermoregulation and
the renin-angiotensin-aldosterone system. The LF/HF = 0.91 ratio indicates a disease according to the
variability standard. A possible option is: high VLF Power reflects the sympathetic balance at rest in
subjects who will receive syncope and so that prediction can be made of the occurrence of this event
(based on high VLF Power above normal value). In normal units, the spectral components in LF and
HF areas are determined (relative to the total power in these two areas).
Relative to the healthy control group, all LFnu and HFnu have segmental differences except for
heart failure values. In heart failure, LFnu and HFnu (p-value > 0.05) cannot be considered as defining
indicators for this group relative to healthy controls.
The results in the time-frequency domain are presented as spectrograms obtained by applying
a wavelet-based method. In healthy subjects, the power of the investigated signal is high in the three
frequency bands depicted in Figure 5A through vast areas of red and orange fields. The spectrogram
of Figure 5B is characteristic of patients in the study group diagnosed with arrhythmia. Moments of
high variability (mainly in the LF region) are observed, followed by longer intervals of low variability
(fields in blue).
The results of Figure 5C present a spectrogram of a patient with heart failure. The study group
of patients showed high signal power values only in the VLF range. The other two frequency bands
are characterized by low signal power values, which is indicative of HRV in HF and LH areas.
The power of the investigated signal is very low in all frequency ranges, in patients diagnosed
with syncope (Figure 5D) across vast areas of blue. The spectrogram shows graphically low heart rate
variability across all frequency ranges.
Diagnostics 2020, 10, 322 16 of 26
Figure 5. Time-Frequency spectrograms. (А) Healthy subject. (B) Patient with arrhythmia. (C) Patient
with heart failure. (D) Patient with syncope.
3.2. Nonlinear Methods for HRV Analysis
Poincaré plot. The quantitative characteristics of the SD1, SD2 parameters and the relationship
between them for the study groups are shown in Table 3. The value of the SD1 parameter decreased
in the three groups of patients compared to the healthy controls. This decrease was statistically
significant (p < 0.0001). The value of SD2 decreased almost twice in patients with diseases compared
to healthy controls (p < 0.0001). Based on the examined 24-hour Holter ECG records, Figure 6 shows
the graphs constructed using the Poincaré method for a healthy subject and patients with arrhythmia,
heart failure, and syncope. The healthy subject's graph (Figure 6A) is shaped like a comet with a
pointed bottom and gradually expanding to the top. The arrhythmia patient chart (Figure 6B) is in
the form of a ventilator and the cardiac failure chart is strongly compressed (Figure 6B), while the
syncope patient chart is a torpedo (Figure 6C). An ellipse is constructed for each diagram. In a healthy
subject, the ellipse is clearly pronounced, whereas in patients with arrhythmia and syncope, the
Diagnostics 2020, 10, 322 17 of 26
length and width of the ellipse are approximately equal and the ellipse approaches a circle. For the
four graphs, the locations of the points in the segments relative to the identity line are symmetrical.
Figure 6. Poincaré plot for healthy subject and patients with arrhythmia, heart failure, and syncope.
(А) Healthy subject. (B) Patient with arrhythmia. (C) Patient with heart failure. (D) Patient with
syncope.
Recurrence plot. The results of the Recurrence Quantification Analysis (DET%, REC%, Lmax,
ShanEn) are reported in Table 3. The values of the studied parameters are increased in the patients
with arrhythmia, heart failure and syncope compared with healthy subjects with their statistical
significance being p < 0.0001. Figure 7 shows the graphs obtained using the Recurrence plot for the
first 10 minutes of the 24-hour Holter records for the four groups studied. For a healthy subject, the
graph has fewer squares compared to patients with cardiovascular disease. This is evidence of a
higher HRV. Anomalies such as arrhythmia and syncope have more squares in the graph showing
the frequency of the signal being tested. In this case, HRV decreases. Similar results have been
reported in [32]. The visual evaluation of the repetitive diagrams provides quick information on the
behavior of the studied process. Reducing the complexity of the process (heart rhythm) and switching
to periodicity is indicative of a pathological change in the regulation of heart rhythm. The
cardiovascular disease significantly affects the dynamics of RR intervals, with HRV decreasing. The
advantage of this method is that it can clearly illustrate the properties of the studied processes.
Diagnostics 2020, 10, 322 18 of 26
Figure 7. Recurrence plot for healthy subject and patients with arrhythmia, heart failure, and syncope.
(А) Healthy subject. (B) Patient with arrhythmia. (C) Patient with heart failure. (D) Patient with
syncope.
Hurst R/S method. Table 3 shows the values obtained for the Hurst exponent of the study
groups. Hurst exponent is a marker for predictability of time series. The value of this parameter in
the four groups studied has a high degree of self-similarity, with a statistical significance greater than
0.05. Therefore, this method cannot distinguish healthy subjects from patients with cardiovascular
disease.
DFA method. The values of α, α1, and α2 parameters for the signals studied are shown in Table
3. The values of thеsе parameterе decrease in patients with cardiovascular disease (arrhythmia, heart
failure, and syncope), as the statistical significance of less than 0.0001. Therefore, this method can
distinguish healthy subjects from those with diseases. Figure 8 shows the graphical dependencies of
the four studied groups. The graphs are linear, which is evidence of the fractal behavior of the signals.
MFDFA method. The Hurst parameter determines the degree of regularity and the large-scale
invariance of the study process.
The range of values of the Hurst parameter varies from 1.5 to 0.9 in the case of different values
of the q parameter for a healthy subject (Figure 9), therefore these RR intervals have multifractal
behavior. In the case of a patient with arrhythmia (Figure 9), the Hurst parameter is almost constant
at different values of the q parameter, so this signal has a monofractal behavior. RR interval series of
patients with heart failure and syncope (Figure 9) have multifractal behavior concerning the Hurst
parameter, but less pronounced compared with the behavior of the healthy subject. Figure 10 shows
the multifractal signal spectrum of the studied groups. The healthy subject's RR signal exhibits a
broad spectrum of scaling, indicating that it has multifractal behavior. The signals of patients with
arrhythmia, heart failure, and syncope show a narrower range of the multifractal spectrum than that
Diagnostics 2020, 10, 322 19 of 26
of the healthy subject. The multifractal spectrum of a patient with arrhythmia is almost four times
smaller than that of a healthy subject.
Figure 8. DFA for healthy subject and patients with arrhythmia, heart failure, and syncope.
Figure 9. Generalized Hurst exponent for healthy subject and patients with arrhythmia, heart failure,
and syncope.
Diagnostics 2020, 10, 322 20 of 26
Figure 10. Multifractal analysis for healthy subject and patients with arrhythmia, heart failure, and
syncope.
Table 3. Nonlinear HRV analysis results for studied groups.
Parameter
Group 1
(mean ± SD)
n = 48
Group 2
(mean ± SD)
n = 56
Group 3
(mean ± SD)
n = 59
Group 4
(mean ± SD)
n = 49
Statistical p-Value
Gr1,2 Gr1,3 Gr1,4
Poincaré plot
SD1 [ms]
61.2 ± 10.3
55.5 ± 12.8
49.8 ± 9.9
45.1 ± 11.0
0.014
0.0001
0.0001
SD2 [ms]
218.1 ± 26.2
73.3 ± 10.5
106.2 ± 11.9
96.1 ± 9.2
0.0001
0.0001
0.0001
SD1/SD2
0.31 ± 0.7
0.87 ± 0.11
0.54 ± 0.2
0.52 ± 0.12
0.0001
0.0001
0.0001
Recurrence plot
DET [%]
90.8 ± 0.11
97.9 ± 0.13
99.06 ± 0.09
98.8 ± 0.1
0.0001
0.0001
0.0001
REC [%]
36.3 ± 0.2
43.4 ± 0.5
41.1 ± 0.3
39.5 ± 0.3
0.0001
0.0001
0.0001
L
max
[beats]
58 ± 12
136 ± 22
305 ± 31
104 ± 11
0.0001
0.0001
0.0001
ENTR
3.20 ± 0.3
3.48 ± 0.4
4.12 ± 0.1
3.80 ± 0.3
0.0001
0.0001
0.0001
R/S method
Hurst
0.98 ± 0.07
0.95 ± 0.04
0.96 ± 0.05
0.94 ± 0.13
0.06
0.09
0.06
Detrended Fluctuation Analysis
α
0.98 ± 0.03
0.77 ± 0.05
0.86 ± 0.06
0.81 ± 0.07
0.0001
0.0001
0.0001
α
1
1.16 ± 0.04
0.79 ± 0.04
0.89 ± 0.05
0.82 ± 0.06
0.0001
0.0001
0.0001
α2
0.91 ± 0.03
0.68 ± 0.03
0.75 ± 0.04
0.72 ± 0.04
0.0001
0.0001
0.0001
Multi-Fractal Detrended Fluctuation Analysis
Δα=α
max
−α
min
0.956 ± 0.05
0.281 ± 0.01
0.773 ± 0.03
0.494 ± 0.04
0.0001
0.0001
0.0001
Entropies
AppEn
1.57 ± 0.19
1.29 ± 0.25
1.08
1.32
0.0001
0.0001
0.0001
SampEn
1.53 ± 0.22
1.14 ± 0.21
1.17
1.25
0.0001
0.0001
0.0001
4. Discussion
4.1. Linear Analysis
All Time-Domain analysis parameters examined are within the normal range for healthy
subjects. In patients, there is a decrease in RR intervals and in HRV, which is due to a decrease in
parasympathetic and increased sympathetic activity.
Diagnostics 2020, 10, 322 21 of 26
The SDNN and SDANN parameters reflect the overall effect of autonomic regulation of the
heart, therefore their reduction in patients with cardiovascular disease (arrhythmia, heart failure, and
syncope) indicates a weakening of the autonomic regulation of the cardiovascular system as a whole
(both sympathetic and sympathetic and sympathetic) and reducing the adaptive capacity of the
cardiovascular system, which is an adverse factor. The decrease in the values of these two parameters
is a very specific sign for the prediction of serious cardiovascular disease, which can endanger the
life of the patient [48]. There was a significant decrease in the SDANN parameter (p < 0.0001), which
was less than 100 ms in all three patient groups (arrhythmia, heart failure, and syncope), indicating
a decrease in HRV.
The RMSSD parameter estimates the degree of the difference between two adjacent RR intervals.
In the absence of fluctuations in adjacent RR intervals, this parameter tends to zero. The greater the
difference between the adjacent intervals (i.e., more pronounced sinus arrhythmia), the higher the
RMSSD values are, therefore the more active the relationship of parasympathetic regulation.
According to our results, the decrease in the rMSSD quantitative values in the three groups of patients
with cardiovascular disease compared with the group of healthy subjects showed a decrease in the
parasympathetic nervous system tone and an increase in sympathetic activity. The determined values
of this parameter have a statistical significance of p-value < 0.0001. Similar information can also be
obtained from the pNN50 index, which expresses in % the number of difference values greater than
50 ms. The NN50 parameter also reflects the difference between the adjacent RR intervals, but the
main evaluation criteria, in this case, is the difference between two adjacent intervals of more than 50
ms. This situation occurs when there are sudden pauses or faster rhythms. The main reason for the
sudden pauses is the dominance of the parasympathetic effects on heart rate. Of the methods based
on the analysis of the difference between adjacent NN intervals, the calculation of RMSSD is
preferable since it has better statistical properties than NN50 and pNN50.
Geometric methods allow a visual representation of the distribution of RR intervals. It is
generally accepted to use a histogram of the distribution of RR intervals, the width of which indicates
the values of the RR intervals and the height the frequency of occurrence of these cardio intervals.
The shape of the histogram depends on the specific physiological condition of the subject. The healthy
people have a histogram similar in appearance to the symmetric Gaussian curve (Figure 3A). The
asymmetric shape of the histogram (Figure 3B) shows a violation of the stationary process of
regulating the heart rhythm and is observed in transition and pathological conditions in the
cardiovascular system, such as arrhythmia. The histogram with a very narrow base and a pointed tip
is registered under severe stress and pathological conditions, such as heart failure (Figure 3C). A two-
tip histogram (Figure 3D) may be due to the presence of a non-sinus rhythm (atrial fibrillation,
extrasystole), as well as to artefacts that appear during electrocardiogram registration. To describe
the deviation of the histogram shape from the normal distribution law, geometric estimates are used:
HRVti and TINN. The main advantage of geometric methods is that they are poorly influenced by
extrasystoles—if for some reason they do not recognize and remove extrasystoles, this will not lead
to any significant changes in the result.
Frequency-Domain Analysis. The healthy control group studied has high values of spectral
components in all tested frequency bands and a sympathetic balance value corresponding to good
health (according to HRV standard).
Higher diagnostic and prognostic value compared to short records is achieved when performing
research on 24-hour Holter records.
Studies of patients with arrhythmia show low values of spectral parameters, which can conclude
the severity of this widespread heart disease. This is the group with the lowest LF vs. HF ratio (0.81),
which shows significantly lower LF values that reflect the sympathetic and parasympathetic activity
of the nervous system.
Reduced VLF in combination with multiple reduced spectral components in the LF and HF area
indicates patients with heart failure who are at increased risk of future cardiovascular events.
Diagnostics 2020, 10, 322 22 of 26
Measured high VLF values in patients (significantly higher than in healthy subjects) with heart
disease may be a good predictor of subsequent syncope in the subject; the value of VLF can be used
to evaluate patients admitted after a loss of consciousness.
The studies and the results obtained show that realistic diagnostic and prognostic conclusions
can be drawn by evaluating the spectral components of HRV.
Time-Frequency Analysis. Time-Frequency spectrograms clearly illustrate HRV values in the
three tested frequency bands and can be an effective tool for creating a rapid diagnostic and
prognostic picture for the development of a patient's heart disease. Healthy individuals are
characterized by high variability in the three frequency bands represented by a warm-color
spectrogram. Arrhythmia recording spectrograms show decreasing trends and then increasing
variability. Heart failure records are characterized by average HRV levels in VLF and LF areas and
very low HF areas in the spectrogram. Syncope recordings are characterized by high variability in
the VLF area and low in the other two regions (represented by blue fields in the spectrogram).
4.2. Nonlinear Analysis
The great methodological difficulty in assessing HRV is related to the unstable nature of cardio
intervals. Heart rate fluctuations have a self-similarity (fractal characteristics), which is why it is
necessary to use mainly long-term ECG records provided by Holter monitoring.
Poincaré's nonlinear method is a useful tool when rare and sudden abnormalities occur in the
background of a monotonous heart rate. This method is suitable for the study of certain
cardiovascular diseases, such as arrhythmias, where the methods of statistical and spectral analysis
of HRV are uninformative and, in these cases, it is appropriate to use the Poincaré plot estimate.
Through this method, the activity of the sympathetic autonomic nervous system in relation to the
heart can be evaluated. The scatherogram of a healthy subject has a well-defined ellipse, which means
that a certain amount of non-respiratory arrhythmia is added to the respiratory arrhythmia. If the
ellipse is in the form of a circle, it means the absence of non-respiratory components of arrhythmia.
The lower values of the SD1 and SD2 parameters in patients with arrhythmia, heart failure, and
syncope lead to a decrease in HRV, which is a prognostic marker for the presence of cardiovascular
disease. This visual method enables doctors to view the entire 24-hour ECG record at a glance and
quickly detect cardiovascular disorders if any.
Another promising method for HRV research is the Recurrence plot, which allows the
visualization of certain regularities in the complex non-stationary fluctuations of the RR interval
series. The method is based on the design and analysis of recurrence diagrams. The point model of
the Recurrence plot (Figure 7) in patients with diseases is significantly different from that of healthy
subjects. First of all, there is an increase in the number of points, which also increases the number of
conditions, the distances between which are smaller than the threshold value, i.e., the value of REC%
increases. At the same time, an increase in the length of the diagonal lines is observed, with
significantly increased values of Lmax, Lmin, and ENTR. Increasing the length of the diagonal lines
leads to a decrease in the chaotic component of the HRV, since the maximum and average length are
characterized by an inverse correlation concerning the indicator of the chaotic properties of the
studied process—the largest Lyapunov index. An increase in the DET% ratio also indicates a decrease
in the signal complexity level. The DET% value is maximum (100%) for a periodic process and
minimum (0%) for a stochastic process. The results of the study indicate that Recurrence plots can be
good tools for analysing and evaluating HRV time series.
The results obtained by applying the R/S method show that the Hurst exponents tend to be 1.0,
therefore the studied groups have fractal behaviour with a high degree of self-similarity. These values
of the Hurst parameter indicate that the investigated signals have less variability and less roughness.
The results obtained show that this method cannot distinguish healthy subjects from those with the
cardiovascular disease since they have no statistical significance (p > 0.05). The probable reasons for
this result can be the following: the investigated signals are long (24 hours), containing a large
number of intervals (about 100,000); the investigated signals are characterized by nonlinear
behaviour, and the method is designed for the study of stationary signals. In such cases, the R/S
Diagnostics 2020, 10, 322 23 of 26
method is only appropriate to check that the signals under study have fractal behaviour, but where
a more accurate determination of the Hurst parameter is required, a more accurate statistical method
should be applied.
The results of the nonlinear analysis obtained by applying the DFA method show a higher value
of the Alpha parameter in healthy subjects compared to patients with cardiovascular disease.
Therefore, the level of complexity and the chaotic component decrease and the degree of self-
similarity at RR intervals increases in healthy subjects.
The multifractal spectrum of the patients with arrhythmia, heart failure, and syncope is
narrower than healthy controls, indicating a significant decrease in nonlinear heart rate measured by
HRV. A significant reduction in the width of the multifractal spectrum is a marker of cardiac
dysfunction. Patients with cardiovascular disease in terms of spectrum width are examples of
monofractal behaviour. The multifractal spectrum of the studied groups is statistically significant (p
< 0.0001); therefore, healthy subjects may be distinguished from patients with arrhythmia, heart
failure, and syncope in terms of multifractal width parameter.
AppEn and SampEn are higher for healthy subjects than patients with arrhythmia, heart failure,
and syncope. Higher values of these parameters are evidence that RR interval series for healthy
people have stochastic behaviour.
5. Limitations
This study has a few limitations. The established HeartAnalyzer was tested with a limited
number of Holter data for the individual patient groups and the control group of healthy individuals
(total number of analysed 212) provided to us by the Medical University, Varna, Bulgaria. At the
moment, the authors are working on the creation of a real cardiology database consisting of Holter
recordings obtained from monitoring patients with various cardiac diseases. In their future studies,
the authors will provide data from studies conducted on a larger number of Holter records (including
from various medical institutions), which will guarantee high reliability of the developed computer
system.
6. Conclusions
Overall assessment of HRV is aimed at diagnosing the patient's functional status, the analysis is
a non-specific diagnostic method. The evaluation of the totality of its indicators and their dynamics
during multiple examinations of the patient allows the diagnostic search to be directed in the right
direction and helps to clarify the functional and prognostic components of the clinical diagnosis.
In the current stage of the practical application of the methods of HRV analysis in applied
physiology and clinical medicine, the above approaches to the physiological and clinical
interpretation of the data allow for solving many problems from the diagnostic and prognostic profile
more effectively, to evaluate the functional states, to evaluate monitors for the effectiveness of
therapeutic and prophylactic effects, etc. However, the possibilities of this methodology are far from
being exhausted and its development continues.
The computer system presented in this article can be used to provide a mathematical
interpretation of cardiac patient studies. Through the obtained analyses and results, the
HeartAnalyzer can improve the accuracy of diagnosis, assist the treating cardiologist in the right
choice of appropriate drugs and thus shorten the time for decision-making by the physician, speed
up the healing process and reduce the costs of treating patients. The HeartAnalyzer created is an
opportunity to overcome the presence of the subjective factor in making the diagnosis and to bring
greater accuracy and objectivity in the conduct of treatment.
The presented HeartAnalyzer can be used for prevention as the parameters of the HRV begin to
change before the risk event itself occurs. In this way, the HeartAnalyzer can assist with the early
detection of diseases and their prompt treatment. The system can also serve as a predictor of a life-
threatening event and enable the patient and physician to overcome the oncoming health crisis.
Diagnostics 2020, 10, 322 24 of 26
One of the main advantages of this work is the research on real Holter data, which makes it
possible to test the performance of the HeartAnalyzer through cardiac data obtained from patients
examined at a medical establishment in Bulgaria.
As a result, it can be expected that having a non-commercial computerized system in place can
help improve people's health and be a prerequisite for improving health.
Author Contributions: Conceptualization and design: E. G. and G.G.-T; Data curation and Holter records
reviews for the correctness: M.G. and. К.C. Investigation and Methodology: G.G.-T. and E.G.; E.G. and G.G.-T.
created a HeartAnalyzer for mathematical analysis of Holter data, performed the experiments and wrote the
manuscript. Data analysis: G.G.-T. and E.G. Finally, M.G. reviewed the manuscript and contributed to the final
version. All authors have read and agreed to the published version of the manuscript.
Funding: This research was funded by the National Science Fund of Bulgaria (scientific project “Investigation of
the application of new mathematical methods for the analysis of cardiac data”), Grant Number КP-06-N22/5,
07.12.2018.
Conflicts of Interest: The authors declare no conflict of interest.
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