Linguistic Approach for Estimation of Electrocardiograms’s Subtle Changes Based on the Levenstein Distance
The purpose of the article is to develop algorithmic and software components to solve this problem and conduct experimental studies on model and real data. Methods. ECG of certain groups was automatically encoded, Levenshtein distance was calculated between ECG pairs for group and the reference codo...
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nasplib_isofts_kiev_ua-123456789-1617462025-02-23T18:33:13Z Linguistic Approach for Estimation of Electrocardiograms’s Subtle Changes Based on the Levenstein Distance Лінгвістичний підхід для оцінювання тонких змін електрокардіограми на основі відстані Левенштейна Лингвистический подход для оценивания тонких изменений электрокардиограммы на основе расстояния Левенштейна Fainzilberg, L.S. Dykach, Ju.R. Informatics and Information Technologies The purpose of the article is to develop algorithmic and software components to solve this problem and conduct experimental studies on model and real data. Methods. ECG of certain groups was automatically encoded, Levenshtein distance was calculated between ECG pairs for group and the reference codogram of the group was constructed. The evaluation of the results of experimental studies was carried out on the basis of traditional methods of statistical analysis. Results. It is shown that based on the Levenshtein distance between all pairs of codograms of the test group, the reference codogram of the group of patients with coronary artery disease (CAD) and the group of healthy volunteers can be determined. It was established that making decisions based on the comparison of the ECG codogram of the person with the reference codogram allows for the separation of representatives of the indicated groups with sensitivity SE = 72% and specificity CP = 79% even in those cases when the traditional analysis of the ECG in 12 leads is not informative. Мета статті — розробити алгоритмічні і програмні компоненти для розв’язання цього завдання і провести експериментальні дослідження за модельними і реальними даними. Методи. Забезпено автоматичне кодування ЕКГ, обчислення відстаней Левенштейна між парами ЕКГ певної групи випробовуваних і побудова референтної кодограми групи. Оцінювання результатів експериментальних досліджень проводилося на основі традиційних методів статистичного аналізу. Результати. Показано, що на основі відстаней Левенштейна між усіма парами кодограм групи випробовуваних можна визначити референтну кодограму групи хворих на ішемічну хворобу серця (ІХС) і групи здорових добровольців. Встановлено, що прийняття рішень на основі порівняння кодограми ЕКГ випробуваного з еталонною кодограмою забезпечує поділ представників зазначених груп з чутливістю SE = 72% і специфічністю CP = 79% навіть в тих випадках, коли традиційний аналіз ЕКГ у 12 відведеннях виявляється неінформативним. Цель статьи — разработать алгоритмические и программные компоненты для решения этой задачи и провести экспериментальные исследования на модельных и реальных данных. Методы. Обеспечивалось автоматическое кодирование ЭКГ, вычисление расстояний Левенштейна между парами ЭКГ определенной группы испытуемых и построение референтной кодограммы группы. Оценка результатов экспериментальных исследований проводилась на основе традиционных методов статистического анализа. Результаты. Показано, что на основе расстояний Левенштейна между всеми парами кодограмм группы испытуемых можно определить референтную кодограмму группы больных ишемической болезнью сердца (ИБС) и группы здоровых добровольцев. Установлено, что принятие решений на основе сравнения кодограммы ЭКГ испытуемого с эталонной кодограммой обеспечивает разделение представителей указанных групп с чувствительностью SE = 72% и специфичностью CP = 79% даже в тех случаях, когда традиционный анализ ЭКГ в 12 отведениях оказывается неинформативным. 2019 Article Linguistic Approach for Estimation of Electrocardiograms’s Subtle Changes Based on the Levenstein Distance / L.S. Fainzilberg, Ju.R. Dykach // Cybernetics and computer engineering. — 2019. — № 2 (196). — С. 3-26. — Бібліогр.: 30 назв. — англ. 2663-2578 DOI: https:// 10.15407/kvt196.02.003 https://nasplib.isofts.kiev.ua/handle/123456789/161746 004.021 en Кибернетика и вычислительная техника application/pdf Міжнародний науково-навчальний центр інформаційних технологій і систем НАН України та МОН України |
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Informatics and Information Technologies Informatics and Information Technologies |
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Informatics and Information Technologies Informatics and Information Technologies Fainzilberg, L.S. Dykach, Ju.R. Linguistic Approach for Estimation of Electrocardiograms’s Subtle Changes Based on the Levenstein Distance Кибернетика и вычислительная техника |
| description |
The purpose of the article is to develop algorithmic and software components to solve this problem and conduct experimental studies on model and real data. Methods. ECG of certain groups was automatically encoded, Levenshtein distance was calculated between ECG pairs for group and the reference codogram of the group was constructed. The evaluation of the results of experimental studies was carried out on the basis of traditional methods of statistical analysis. Results. It is shown that based on the Levenshtein distance between all pairs of codograms of the test group, the reference codogram of the group of patients with coronary artery disease (CAD) and the group of healthy volunteers can be determined. It was established that making decisions based on the comparison of the ECG codogram of the person with the reference codogram allows for the separation of representatives of the indicated groups with sensitivity SE = 72% and specificity CP = 79% even in those cases when the traditional analysis of the ECG in 12 leads is not informative. |
| format |
Article |
| author |
Fainzilberg, L.S. Dykach, Ju.R. |
| author_facet |
Fainzilberg, L.S. Dykach, Ju.R. |
| author_sort |
Fainzilberg, L.S. |
| title |
Linguistic Approach for Estimation of Electrocardiograms’s Subtle Changes Based on the Levenstein Distance |
| title_short |
Linguistic Approach for Estimation of Electrocardiograms’s Subtle Changes Based on the Levenstein Distance |
| title_full |
Linguistic Approach for Estimation of Electrocardiograms’s Subtle Changes Based on the Levenstein Distance |
| title_fullStr |
Linguistic Approach for Estimation of Electrocardiograms’s Subtle Changes Based on the Levenstein Distance |
| title_full_unstemmed |
Linguistic Approach for Estimation of Electrocardiograms’s Subtle Changes Based on the Levenstein Distance |
| title_sort |
linguistic approach for estimation of electrocardiograms’s subtle changes based on the levenstein distance |
| publisher |
Міжнародний науково-навчальний центр інформаційних технологій і систем НАН України та МОН України |
| publishDate |
2019 |
| topic_facet |
Informatics and Information Technologies |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/161746 |
| citation_txt |
Linguistic Approach for Estimation of Electrocardiograms’s Subtle Changes Based on the Levenstein Distance / L.S. Fainzilberg, Ju.R. Dykach // Cybernetics and computer engineering. — 2019. — № 2 (196). — С. 3-26. — Бібліогр.: 30 назв. — англ. |
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Кибернетика и вычислительная техника |
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ISSN 2663-2586 (Online), ISSN 2663-2578 (Print). Cyb. and comp. eng. 2019. № 2 (196)
Informatics
and Information Technologies
DOI: https:// 10.15407/kvt196.02.003
UDC 004.021
FAINZILBERG L.S.1, DSc. (Engineering), Professor,
Chief Researcher of the Department
of Intelligent Automatic Systems
e-mail: fainzilberg@gmail.com
DYKACH Ju.R.2, Student of Biomedical Engineering Faculty,
e-mail: jul.dykach@gmail.com
1 International Research and Training Center
for Information Technologies and Systems
of the National Academy of Sciences of Ukraine
and Ministry of Education and Science of Ukraine,
40, Acad. Glushkova av., Kyiv, 03187, Ukraine
2 The National Technical University of Ukraine
«Igor Sikorsky Kyiv Polytechnic Institute»
37, Peremohy av., Kiev, 03056, Ukraine
LINGUISTIC APPROACH FOR ESTIMATION OF ELECTROCARDIOGRAMS’S
SUBTLE CHANGES BASED ON THE LEVENSTEIN DISTANCE
Introduction. The linguistic approach, based on the transition from electrocardiogram
(ECG) to codogram, gained fame for the analysis of heart rhythm. To expand the functional-
ity of the method, it is advisable to study the possibility of simultaneously monitoring the
dynamics of changes in the duration of cardiac cycles and the indicator of simmetry T-wave
that carries information about ischemic changes in the myocardium.
The purpose of the article is to develop algorithmic and software components to solve
this problem and conduct experimental studies on model and real data.
Methods. ECG of certain groups was automatically encoded, Levenshtein distance was
calculated between ECG pairs for group and the reference codogram of the group was con-
structed. The evaluation of the results of experimental studies was carried out on the basis of
traditional methods of statistical analysis.
Results. It is shown that based on the Levenshtein distance between all pairs of codo-
grams of the test group, the reference codogram of the group of patients with coronary artery
disease (CAD) and the group of healthy volunteers can be determined. It was established that
making decisions based on the comparison of the ECG codogram of the person with the
reference codogram allows for the separation of representatives of the indicated groups with
sensitivity SE = 72% and specificity CP = 79% even in those cases when the traditional
analysis of the ECG in 12 leads is not informative.
© FAINZILBERG L.S., DYKACH Ju.R., 2019
3
Fainzilberg L.S., Dykach Ju.R.
ISSN 2663-2586 (Online), ISSN 2663-2578 (Print). Cyb. and comp. eng. 2019. № 2 (196) 4
Conclusions. The proposed approach allows to obtain additional diagnostic informa-
tion when solving actual problems of practical medicine.
Keywords: linguistic approach, diagnostic sign of ECG, Levenshtein distance.
INTRODUCTION
The physiological processes occurring in biological systems are often repetitive
in time. Such processes generate specific signals, which are commonly called
cyclical in the scientific literature [1, 2]. A typical example of a cyclical signal is
an electrocardiogram (ECG), reflecting the cyclical nature of the circulatory
system and respiratory organs of a living organism.
Despite the fact that electrocardiography for over a hundred years has been
the most common method of functional diagnostics in cardiology, the sensitivity
and specificity of traditional ECG examinations are not high enough. Thus, in
work [3] it was shown that resting ECG, assessed by generally accepted criteria,
remains normal in approximately half of patients with chronic coronary artery
disease (CAD), including during episodes of chest discomfort.
Modern digital electrocardiographs, which implement traditional ap-
proaches to the analysis and interpretation of ECG, also do not provide the re-
quired reliability of diagnostic results. Moreover, experienced clinicians still
prefer visual interpretation of ECG, not completely trusting computer algo-
rithms, which, because of the complexity of real signals, often lead to errors at
the stage of recognition of informative fragments [4].
Therefore, scientists are constantly looking for alternative approaches to
computer processing of cyclic signals, in particular, ECG. One of these ap-
proaches is based on the transformation of the original signal into a word
(sequence of characters), for the analysis of which the concepts of formal
languages are used. Such an approach in various publications is called linguistic
[5, 6], structural [7] or syntactic [8].
In cardiology practice, the linguistic approach has become famous for ana-
lyzing heart rhythm [9, 10]. It has long been known that the heart rhythm is a
universal reaction of the organism to any influence from the external and inter-
nal environment [11]. Mathematical analysis of the heart rhythm allows you to
obtain important information about the functional state of all parts of the regula-
tion of human life, both in normal conditions and in various pathologies [12].
Computer technologies of mathematical analysis of heart rate variability of the
heart rate (HRV) are still actively used to assess the state of the autonomic nerv-
ous system and adaptive reserves of the body [13].
However, only on the basis of control over the sequence of lengths of the
RR − -intervals it is impossible to judge the functional state of the heart itself as
the main system-forming organ, in particular, the ischemia of the heart muscle.
To increase the credibility of the conclusion about the functional state of the
body, it is reasonable to supplement the analysis of the dynamics of the
RR − -intervals with an analysis of the dynamics of other ECG indicators.
In [14, 15], a method for analyzing an ECG signal was proposed, which
provides for encoding ECG symbols of a given alphabet that carry information
about the increment signs of both the RR − -interval lengths and the amplitudes
of R -wave of adjacent cycles. As a result, the observed ECG generates words
Linguistic Approach for Estimation of Electrocardiograms’s Subtle Changes Based
ISSN 2663-2586 (Online), ISSN 2663-2578 (Print). Cyb. and comp. eng. 2019. № 2 (196) 5
(codograms), the processing of which by machine learning methods expands the
capabilities of the mathematical analysis of heart rhythm.
The International Scientific and Training Center for Information Technologies
and Systems of the National Academy of Sciences of Ukraine and the Ministry of
Education and Science of Ukraine has developed an innovative method for processing
electrocardiograms (ECG), which is called fasegraphy [16, 17]. A distinctive feature
of the method is the use of intelligent IT for processing the observed time signal
)(tz on the phase plane )(),( tztz & , where )(tz& is the rate of change of the electrical
activity of the heart [18]. This difference made it possible for the first time to imple-
ment a procedure for reliably determining the novel ECG feature (indicator Tβ ) char-
acterizing the symmetry of the T -wave of the cardiac cycles [19].
Large-scale clinical studies conducted with the help of the FASEGRAPH®
software and hardware complex, which implements fasegraphy method, con-
firmed that measuring the indicator Tβ and evaluating its standard deviation
RMS Tβ makes it possible to increase the accuracy of detecting the initial signs
of myocardial ischemia, even in cases where the analysis of traditional ECG
features in 12 leads is not informative [20].
It follows that, remaining within the framework of linguistic analysis, it is
advisable to study the possibility of simultaneously analysis the dynamics of
changes RR − - intervals and dynamics of changes Tβ -indicator on the se-
quence of cardiac cycles.
The purpose of the article is to develop algorithmic and software compo-
nents for solving this problem.
BASIC COMPONENTS OF LINGUISTIC ECG ANALYSIS
Recall that the general scheme of linguistic analysis of the time signal )(tz sug-
gests segmentation )(tz into a sequence of separate fragments, reflecting the
alternation of elementary events during the development of the process under
study [6]. Thus, a transition is made from the k -implementation of the signal
)(tzk observed on a limited time interval ],0[ Tt∈ to the word
KkS ααα= L21 as finite chain of characters Kjj ,...,1, =Α∈α from the al-
phabet of the “names” of the fragments. A set of all-possible words (not neces-
sarily finite) forms a formal language for which the grammar is built [21]:
00 ,,, ωΩΩ= GT PG , (1)
where 0Ω is a set of non-terminal symbols (variables); TΩ — a set of terminal
symbols (constants), Α=Ω∪Ω 0T , ∅=Ω∩Ω 0T ; GP — a set of grammatical
rules (substitution rules); 00 Ω∈ω — initial (root) non-terminal character.
In the majority of works devoted to linguistic analysis of signals, it is assumed
that the alphabet of reference fragments is known in advance [22], and the construc-
tion of grammar makers adequate to the set of observed signals is carried out by man
on the basis of informal knowledge of an expert in the subject area.
Fainzilberg L.S., Dykach Ju.R.
ISSN 2663-2586 (Online), ISSN 2663-2578 (Print). Cyb. and comp. eng. 2019. № 2 (196) 6
Despite the fact that in a number of papers, particular, in [23], the main theoretical
concepts of the general formulation of the problem of restoring grammars on a training
set of observations were revealed, it should be stated that there are still no universal
methods for practical solution of this difficult problem.
Therefore, following the works [14, 15], we will make the transition from
the k -th observed signal )(tzk to the word KkS ααα= L21 , analyzing the
sequence of sign differences in the values of ECG indices on adjacent cycles.
Let we have N ECG cycles and values of several indicators are determine-
don on each of cycles , for example, the duration of RR intervals and the index
Tβ of T wave symmetry.
Denote each of these sequences as:
Nxxx ,..., 21 . (2)
Let us determine the values of the indicator variable iV , Ni ,...,2= , by the
signs of the increments of the quantities on each cycle in relation to the previous cycle:
⎩
⎨
⎧
>−−
>−+
=
−
−
.xx,
,xx,
V
ii
ii
i 0if1
0if1
1
1 (3)
As a result, for the indicators RR and Tβ , we will get two sequences of
indicator variables )(RR
iV and )(β
iV respectively, and each ECG cycle will be
encoded with one of the four symbols of the alphabet },,,{ dcba=Α as follows
(Tabl. 1).
The sequence of characters received in accordance with Table 1 forms a
N -bit word kS (codogram) that uniquely encodes the k -th processed ECG.
For illustration, a flowchart of the codogram’s generation S , where N is
the total number of registered cardiac cycles (Fig. 1).
The proposed method of linguistic analysis and interpretation of ECG is
based on the Levenshtein distance ),( 21 SSL between two words 21, SS of
N and M symbols, respectively. Recall that the Levenshtein distance is equal to
the minimum number of editing operations such as insertion, deletion, and re-
placement of a character for converting a word 1S into a word 2S [24, 25].
The algorithm for calculating the Levenshtein distance is as follows.
Table 1. Principle of ECG cycle coding
The value of the indicator variable )( RR
iV +1 +1 -1 -1
The value of the indicator variable )( Τβ
iV +1 -1 +1 -1
Symbol а b c d
Linguistic Approach for Estimation of Electrocardiograms’s Subtle Changes Based
ISSN 2663-2586 (Online), ISSN 2663-2578 (Print). Cyb. and comp. eng. 2019. № 2 (196) 7
Begin
0 < i < N
RR(i)>RR(i-1)yes no
βТ (i)>βТ(i-1)
yes no
S(i-1)=a S(i-1)=b
βТ (i)>βТ(i-1)
yes no
S(i-1)=c S(i-1)=d
Codogram
ddabdcbadcbadca
Fig. 1. The algorithm's block diagram for the formation of codograms
We form a matrix D of dimension 1,1 ++ MN and fill the first row and
first column of the matrix D as follows:
.0,),0(
,0,)0,(
MjjjD
NiiiD
K
K
=∀=
=∀=
(4)
The remaining elements of the matrix D ( 0,0 >> ji ) is filled in accor-
dance with the rule:
{ })(),(()1,1(,1),1(,1)1,(min),( 21 jSiSmjiDjiDjiDjiD +−−+−+−= , (5)
where
⎩
⎨
⎧
≠
=
=
).j(S)i(S,
),j(S)i(S,
))j(S),i(S(m
21
21
21 if1
if0
(6)
As a result the value ),( MND determines the Levenshtein distance.
In general, there may be several optimal paths from cell )1,1(D to cell
),( MND that provide the minimum number of editing operations. Figure 2
illustrates this fact and shows the "optimal" sequence of transition from the word
=1S ddabdcbadcbadca (7)
to the word
=2S bacdaaacdadccbb. (8)
Fainzilberg L.S., Dykach Ju.R.
ISSN 2663-2586 (Online), ISSN 2663-2578 (Print). Cyb. and comp. eng. 2019. № 2 (196) 8
Fig. 2. Possible ways to ensure the optimal transition from the word S1 to the word S2
Table 2. The optimal transition from word S1 to word S2
Step
Source word Operation Result of editing
1 S1 = ddabdcbadcbadca Replacement
d → b S1 = bdabdcbadcbadca
2 S1 = bdabdcbadcbadca Deletion d S1 = babdcbadcbadca
3 S1 = babdcbadcbadca Replacement
b → c S1 = bacdcbadcbadca
4 S1 = bacdcbadcbadca Deletion с S1 = bacdbadcbadca
5 S1 = bacdbadcbadca Replacement
b → a S1 = bacdaadcbadca
6 S1 = bacdaadcbadca Replacement
d → a S1 = bacdaaacbadca
7 S1 = bacdaaacbadca Replacement
b → d S1 = bacdaaacdadca
8 S1 = bacdaaacdadca Replacement
a → c S1 = bacdaaacdadcc
9 S1 = bacdaaacdadcc Insertion b S1 = bacdaaacdadccb
10
S1 = bacdaaacdadccb
Insertion b
S1 = bacdaaacdadccbb
Linguistic Approach for Estimation of Electrocardiograms’s Subtle Changes Based
ISSN 2663-2586 (Online), ISSN 2663-2578 (Print). Cyb. and comp. eng. 2019. № 2 (196) 9
The step on i symbolizes the removal of the next symbol from the word
1S , the step on j — inserting the next word 1S symbol into the word 2S , and the
step on both indices symbolizes the replacement of the 1S symbol with the next
2S symbol or the absence of changes.
Table 2 demonstrates one of the optimal options shown in Fig. 2.
In addition to the classic Levenshtein distance, a number of its modifica-
tions are known, for example, the Damerau-Levenshtein distance, in which an
additional editing operation in the form of transposition - permutation of two
adjacent symbols, or the Levenshtein extension where different prices for ele-
mentary editing operations is introdused.
INFORMATION TECHNOLOGY OF LINGUISTIC ECG ANALYSIS
A number of important tasks can be formulated based on the calculation of the
Levenshtein distance between the ECG codograms, including:
Task 1. Study of the properties of the Levenshtein distance based on the
analysis of model signals generating an ECG of a realistic shape
Task 2. Decision making on the affiliation of the examined person one of
two groups, for example, a group of patients or a group of conditionally healthy
people, a group of trained or untrained, etc.
Task 3. Evaluation of the intra-individual characteristics of the codograms
of one person over a sufficiently large segment of observations.
Task 4. Study of the possibility of using Levenshtein distance to assess
changes in the functional state of the body under the influence of physical and
emotional stress, medication, surgery, etc.
To perform the necessary research, an information technology (IT) has been
developed, the structure of which is shown in Fig. 3.
To study the properties of the Levenshtein distances a software simulator that im-
plements a stochastic model of generating artificial electrocardiograms of a realistic
form [26] was uncluded in the IT. The generative model generates a sequence of ECG
cycles, built on the basis of the sum of asymmetric Gaussian functions.
∑ ⎥
⎦
⎤
⎢
⎣
⎡ μ−
−=
k k
k
i tb
tAtz 2
2
0 )]([2
)(exp)( (9)
with a given level of distortion of parameters that characterize the shape of the
k -th fragment },,,,,{ TSTSRQPk∈
Studies of the possibilities of the proposed approach for solving other prob-
lems were carried out on the basis of real ECGs accumulated in the database of
the FASEGRAPH® complex. The complex consists of an ECG recorder with
finger electrodes and a computer program that provides automatic ECG process-
ing and determination of traditional and original diagnostic features, in particu-
lar, the duration of RR - intervals and parameters Tβ beat to beat.
Fainzilberg L.S., Dykach Ju.R.
ISSN 2663-2586 (Online), ISSN 2663-2578 (Print). Cyb. and comp. eng. 2019. № 2 (196) 10
Sequence of values Tβ and RR
Levenshtein distance calculation module
Words (codograms) generation module
aacbadabbcbacbaabac
DATABASE OF FASEGRAPH®
The module of statistical processing and visualization
IMITATOR OF ARTIFICIAL
ELECTROCARDIOGRAMS
Fig. 3. Structure of information technology
According to the accumulated data, corresponding codograms were formed
and reference codograms of individual groups of subjects were determined, for
example, reference codograms of verified patients and conditionally healthy
volunteers, athletes and people who are not actively involved in sports, etc.
The algorithm for constructing reference ECG codograms is as follows.
Let 1Q and 2Q ECG which represent one of the two studied groups was re-
corded as a result of the experiments. Each of 1Q ECG of the first group (for
example, a group of patients) is encoded in words )1(
qS , 1,...,1 Qq = , in accor-
dance with Table 1. According to formulas (4) - (6), the Levenshtein distance
),( )1()1(
νμμν SSL between each pair )1()1( , νμ SS , 1,...,1 Q=μ , 1,...,1 M=ν encoded
ECG is determined.
Next, we form a square 11 QQ × -matrix of distances
),( )1()1(
νμμν SSL , 1,...,1 Q=μ , 1,...,1 Q=ν between all pairs of words correspond-
ing to the ECG of the first group of subjects
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⎟
⎟
⎟
⎟
⎟
⎠
⎞
⎜
⎜
⎜
⎜
⎜
⎝
⎛
=Λ
1111
1
1
,...,,
...
...,,,
..,.,,
21
22221
11211
QQQQ
Q
Q
LLL
LLL
LLL
.
The row of this matrix, the sum of the elements of which is minimal, defines
the reference word )1(
0S of the first group, i.e.
∑
=μ
μν
≤ν≤
=
1
1 11
)1(
0 minarg
Q
Q
LS . (10)
The reference word )2(
0S of the second group is determined in a similar way
by analyzing the sum of the elements of the Levenshtein distance matrix
),( )2()2(
νμμν SSL , 2,...,1 Q=μ , 2,...,1 Q=ν constructed for all pairs of codograms
of the second group, i.e.
∑
=μ
μν
≤ν≤
=
2
2 11
)2(
0 minarg
Q
Q
LS . (11)
Reference codograms (10), (11) allow solving various tasks, for example, re-
lating the analyzed ECG to the first or second groups based on a comparison of
the Levenshtein distance between the code word tS of the analyzed ECG and the
reference words )1(
0S and )2(
0S :
ECG belongs to the first group, if ),(),( )2(
0
)1(
0 SSLSSL tt ≤ , (12)
ECG belongs to the second group, if ),(),( )2(
0
)1(
0 SSLSSL tt > . (13)
A similar rule can be used to make a decision about the level of fitness of a
person on the basis of Levenshtein’s distance between his codogram tS and ref-
erence words )1(
0S and )2(
0S , constructed separately for groups of athletes and
people who are not actively involved in sports.
To assess the intraindividual features of the codograms (task 3), the data
of the concrete person was extracted from the database, which were registered
for a sufficiently large period of time. We analyzed only those persons who had
no serious organic cardiac abnormalities during the observation period.
On the basis of processing the Q codograms of a concrete person we de-
termined a reference word 0S for this person and calculated the Levenshtein
distance ),( 01 SSL ),( 02 SSL , … , ),( 0SSL Q relative to 0S . The values
),( 01 SSL ),( 02 SSL , … , ),( 0SSL Q were considered as the implementation
of a random value for which an estimate of the distribution was constructed and
its statistical characteristics were determined.
Fainzilberg L.S., Dykach Ju.R.
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For the study of changes in Levenshtein distances in the course of physical and
emotional loads, drip injections of drugs and other experimental studies (task 4), we
used the electrocardiogram accumulated in the database, recorded during the corre-
sponding observation period 0T , and plotted the changes of the distances
),( 0SSL t during the experiment relatively discrete time 0,...,2,1 Tt = .
RESULTS OF EXPERIMENTAL RESEARCHES
Let us briefly review the first practical results obtained using the developed IT.
Figure 4 shows graphs of test signals generated by an artificial ECG simula-
tor. The first signal (the signal )A is a periodic function - a sequence of ECG
cycles of a given shape without distortion. Obviously, the codogram of such a
signal contain only one letter:
=AS dddd…dddd.
The codogram AS was used as a reference for calculating the Levenshtein
distances to the codograms of two other test signals: a signal B that simulated a
sequence of reference cycles with distortions of the shape of the wave T only,
and a signal C that additionally distorted the durations RR - intervals. The stan-
dard deviation of Tβ for both signals was RMS Tβ = 0,3 units, and the standard
deviation of the RR -duration (the standard indicator of the mathematical analy-
sis of heart rate variability) was ms140=SDNN .
The codograms constructed for the distorted signals had the form:
=BS aacddccbaabdccbacabbcaaddcddadbbcaabbdaddadbabcc…
…babccdbabbdccbabcbababdcdacbabadcbadcdcbaddcd
=CS bbabcbcabccaabddcbdcabdcaaabddcabdcbabbcbccabdccabdc…
… bccbabdcbdcbcabdcbdcbdcabddcbcabcaabddca.
Table 3 summarizes the results of the comparison of distorted signals B and
C with the reference signal A .
As can be seen from Table 3, the Levenshtein distance increases as the level of
ECG cycle distortion increases. However, it was established that the statistical de-
pendence of the distance ),( 0SSL t of the analyzed codogram tS relative to the ref-
erence one 0S and index SDNN is substantially nonlinear: the coefficient of deter-
mination of the linear dependence 5,02 <R .
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Table 3. The results of the comparison with the test signal A
SIGNAL Increment of RMS Tβ , un. Increment of SDNN , ms Levenshtein distance, un.
B 0,03 0 =),( AB SSL 46
C 0,03 140 =),( AC SSL 71
RMS 0=βT , 0=SDNN
RMS 03,0=βT , 0=SDNN
RMS 03,0=βT , ms140=SDNN
A
B
C
Fig. 4. Test signals: A — without distortion, B — distortion of Tβ only, C —
both distortion Tβ and RR -intervals
Interesting results were obtained for athletes and people who are not ac-
tively involved in sports. The studies were conducted on the basis of real ECG,
obtained when testing young volunteers of both sexes aged 18–24, which were
divided into two groups:
• Group 1: 471 =Q highly qualified athletes who are engaged in boxing,
various types of wrestling and triathlon;
• Group 2: 1132 =Q people not involved in sports.
Investigations were carried out while performing the Martin test: 20 squats
in 30 seconds. We recorded ECG all person from each group before the load, at
the height of the load, and after a 3-minute rest. The values of the average heart
rate ( HR ) and the average index Tβ characterizing the symmetry of the T wave
were determined in these three states.
Following the previously obtained results [26], we will assume that an ade-
quate response of the organism to the load is that with the load both indicators
increase, and after resting they return to their original state, i.e.
Fainzilberg L.S., Dykach Ju.R.
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)()( )1()3()1()2( HRHRHRHR −>− , (14)
)()( )1()3()1()2(
TTTT β−β>β−β , (15)
where )3()2()1( ,, ηηη — the value of the corresponding indicator in the initial
state, at the height of the load and after a 3-minute rest.
We studied the differences in the body's response to exercise in athletes and
people who are not actively involved in sports, based on conditions (14), (15), and
also based on an estimate of the Levenshtein distance ),( )1()2( SSL and
),( )1()3( SSL between the codogram )2(S at load height and codogram )3(S after
resting with respect to to the original codogram )1(S .
As a working hypothesis, it was assumed that the condition
),(),( )1()3()1()2( SSLSSL > (16)
also confirms an adequate response of the organism to the load.
The results of the research are summarized in Tables 4 and 5, in the cells of
which the symbol “+” and “-” denote fulfillment or non-fulfillment of conditions
(14) – (16).
As can be seen from the data given in Tables 4 and 5, the athletes and non-
athletes observed small differences in the frequency of occurrence of events iW ,
8,...,1=i , which form a complete group. To confirm the reliability of the de-
tected differences, additional data processing was carried out on the basis of the
calculation of confidence intervals.
From probability theory it is known [29] that the frequency *P of a random event,
calculated from a sample of observations by volume Q , with reliability of inference
γ determines the confidence interval ],[ )2()1( PP=I of probability P , the
boundaries of which are determined by formulas:
Table 4. Athletes reaction to load
Indicator's recovery after the load
HR βT L (S(2), S(2))
Random
event
Condition (14) Condition (15) Condition (16)
Event
frequency, %
W1 + + + 23,40
W2 - + + 2,13
W3 + - + 2,13
W4 - - + 2,13
W5 + + - 36,17
W6 - + - 10,64
W7 + - - 14,89
W8 - - - 8,51
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Table 5. The response of non-athletes to the load
Indicator's recovery after the load
HR βT L (S(2), S(2))
Random
event
Condition (14) Condition (15) Condition (16)
Event
frequency, %
W1 + + + 26,55
W2 - + + 6,19
W3 + - + 8,85
W4 - - + 2,65
W5 + + - 34,51
W6 - + - 7,08
W7 + - - 11,50
W8 - - - 2,65
Q
t
Q
t
Q
pPt
Q
t
P
P 2
2
2**2
*
)1(
1
4
1)1(
2
1
γ
γ
γ
γ
+
+
−
−+
= (17)
Q
t
Q
t
Q
PPt
Q
t
P
P 2
2
2**2
*
)2(
1
4
1)1(
2
1
γ
γ
γ
γ
+
+
−
++
= , (18)
where 0
2
1arg * >⎟
⎠
⎞
⎜
⎝
⎛ γ+
Φ=γt , and τ
π
=Φ ∫
∞−
τ
−
dex
x
2*
2
2
1)( .
On the basis of expressions (17), (18), according to the data of Tables 4 and
5, taking into account the volumes 471 =Q and 1132 =Q of the respective sam-
ples, the confidence intervals of the probability of random events iW , 8,...,1=i
are determined. It has been established that with reliability of inference
%99=γ the reliability intervals of the probability for events 2W , 3W , 8W do
not overlap in the group of athletes and people who are not actively involved in
sports (Table 6). And this with high credibility indicates that the probabilities of
these events are different. For example, in athletes 397,0)( 2 <WP , while
498,0)( 2 >WP in people who are not actively engaged in sports.
Table 6. Significant differences in confidence intervals of probabilities
Сonfidence intervals of probabilities
Random event Athletes Non-athletes
Reliability of
inference γ
W2 ]397,0;100,0[ ]727,0;498,0[ 99 %
W3 ]397,0;100,0[ ]941,0;786,0[ 99 %
W8 ]940,0;675,0[ ]383,0;173,0[ 99 %
Fainzilberg L.S., Dykach Ju.R.
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Note that the indicators HR and Tβ represent the averaged values of the pa-
rameters of individual ECG cycles, and the condition (16) characterizes the dy-
namics of the RR -intervals and the index Tβ beat to beat. Therefore, condition
(16), to a greater extent than conditions (14), (15), characterizes transient proc-
esses when performing load tests.
The found statistically significant differences in the response of the body of ath-
letes and non-athletes to the load test may be related both to the athlete's overloads at
previous trainings and also to indicate that in the process of regular workouts the ath-
lete's body learns to more economically adapt to the load test. Both are reflected in the
features of the dynamics of change HR , Tβ and ),( )1()2( SSL . Of course, the study
of the found fact requires further deeper investigations on representative samples of
observations.
Recently, scientists have paid attention to intraindividual ECG changes of a
healthy person at rest [29], which is not a precursor of any pathology. In this regard, it
is interesting to study the intra-individual changes in the codograms of the same per-
son over a fairly long observation period.
The basis of such studies was based on the analysis of the ECG series of two
subjects, registered for six years. 261 =Q codograms of the first test subject
(male) and 252 =Q codograms of the second test subject (woman) are analyzed.
Based on the processing of the available codograms, the reference codo-
gram of the first person
=)1(
0S bccabcbadabdcadcabcabccbdcbbcabccaddcbbdaba…
…cbccbdabadadccdbcadccbaccbdcabdabbcabcabdcbacabbcadccbda
and the second person
=)2(
0S addaddacdadadcbdabcaddacbdcadabdadcadcadacd…
…adbccadcbbcadbcdadcadcdcdbcdaddacbacbcdacdadaacbabbcada
was constructed using the method described above.
Levenshtein distance between reference codograms is
52),( )2(
0
)1(
0 =SSL .
Estimates of distributions of random variables ),( )1(
0
)1( SSL t and
),( )2(
0
)2( SSL t , 2,...,1 Qt = (histograms) corresponding to ECG’s codograms
recorded during the observation period are presented in the (Fig. 5).
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P
P
L
L
),( )1(
0
)1( SSL t
),( )2(
0
)2( SSL t
Fig. 5. Histograms of distance distributions ),( )1(
0
)1( SSL t and ),( )2(
0
)2( SSL t
As can be seen from Fig. 5, Levenshtein distances
),( )1(
0
)1( SSL t ),( )2(
0
)2( SSL t varied over a fairly wide range of values for both
individuals during the observation period. For comparison, we note that during
this period there were also significant fluctuations in traditional indicators Tβ
and standard deviation of RR -intervals which amounted
079,0771,0)1( ±=βT , 125,0752,0)2( ±=βT , 1,169,37)1( ±=SDNN ,
5,105,32)2( ±=SDNN .
The study of the diagnostic capabilities of the proposed method was carried
out using a database of real ECG recorded at the Ischemic Heart Diseases De-
partment of the V.D. Strazhesko’s Research Institute of Cardiology Academy of
Medical Sciences of Ukraine (Kyiv) and four clinics in Germany — Essen Uni-
versity Hospital (Essen), Katholical Hospital "Phillpusstift" (Essen), German
Heart Center (Berlin).
The clinical material consisted of 100 ECG records of patients with chronic
ischemic heart disease (CAD), whose diagnosis was previously established by
coronary angiography (class )1V , and 100 ECG records of healthy volunteers
included in the control group (class )2V
By the formulas (10), (11) two reference codograms for the specified classes are de-
fined: the reference codogram of patients with ischemic heart disease
=)1(
0S adcbdadcadabdabcadabdadcbdab
and reference codogram of a healthy volunteers
=)2(
0S cbcdcabdcabddcaadcaa.
Fainzilberg L.S., Dykach Ju.R.
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The Levenshtein distance between these codograms was
15),( )2(
0
)1(
0 =SSL .
Based on the processing of the available data, it has been established that
decision making according to the rules (12), (13) provides sensitivity
%72=ES and specificity %.79=PC
For illustration, we present the results of the ECG evaluation for two patients —
a verified patient (male, 69 years old), whose codogram was
=)1(
tS adcabdadcadabdaddabdaadabdbdda
and a representative of the control group — a male, 54 years old, whose codo-
gram was
=)2(
tS bdcbbcdcabcdcabcdcbaa.
It is easy to verify that 13),( )1(
0
)1( =SSL t and 15),( )2(
0
)1( =SSL t , i.e.
),(),( )2(
0
)1()1(
0
)1( SSLSSL tt <
and in accordance with the rule (12), the survey must be reduced to the
CAD-group.
Similarly, for the second person we have 14),( )1(
0
)2( =SSL t and
8),( )2(
0
)2( =SSL t , i.e.
),(),( )2(
0
)2()1(
0
)2( SSLSSL tt >
and in accordance with the rule (13) the person should be reduced to a healthy
group.
It is important to note that traditional signs of myocardial ischemia (eleva-
tion or depression of the ST segment) not observed on all patient’s ECG. And
this means that conventional electrocardiography would classify all processed
ECG into healthy group.
At the same time experiments show that it is possible to classify representa-
tives of the classes even on such “complex” clinical material on the basis com-
parison of the Levenshtein distances.
Fig. 6 presents estimates of the conditional distributions )),(( )1(
0SSLP t and
)),(( )2(
0SSLP t of Levenshtein distances with respect to the reference codograms
of the sick and the healthy person.
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),( )1(
0SSL t
),( )2(
0SSL t
P,
P,
Fig. 6. Conditional distributions of Levenshtein distances to patient (top) and healthy
(bottom) standards
Testing the hypothesis of homogeneity of conditional distributions
)),(( )1(
0SSLP t and )),(( )2(
0SSLP t according to the Kolmogorov-Smirnov
criterion showed that the hypothesis of equality of distributions should be re-
jected with high statistical significance )001,0( <p . The similar fact was con-
firmed by Mann-Whitney U test.
Consequently
).|)(()|)(( 21 VLPVLP ⋅≡/⋅ (19)
If also the diagnostic sign )(⋅L is conditionally independent of indicators
SDNN and RMS, i.e.
≡β )|,,( kT VRMSSDNNLP )|,()|( kTk VRMSSDNNPVLP β ,
2,1=k ,
(20)
then, according to a theorem proved in [30], the Levenshtein distance is guaran-
teed a useful diagnostic sign in conjunction with SDNN and RMS in terms of
reducing the probability of erroneous decisions.
The analysis of the Levenshtein distances was also useful for illustrating the dy-
namics of ECG changes during the drug treatment of cardiovascular pathologies.
Fainzilberg L.S., Dykach Ju.R.
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0
10
20
30
40
50
60
70
0 20 40 60 80 100
)(⋅L
t
Fig. 7. Schedule of changes in the distance L (St, S0) in the process of
intravenous drug infusions
Fig. 7 is a graph of the change in the distance ),( 0SSL t between ECG
codograms, which were recorded during intravenous infusion of drugs to patient
R. (male, 72 years old), diagnosed with atrial fibrillation.
Patient R. was hospitalized at the Scientific and Practical Center for Preven-
tion and Clinical Medicine (Kyiv). ECGs were recorded every 5 minutes for 1
hour and 20 minutes in the process of intravenous infusion of Tivomax prepara-
tions followed by the addition of the drug Armadin.
Before the administration of the drugs, there was a pronounced extrasysitivity on
the patient's ECG, which decreased significantly to 20-th minute. With the further
administration of drugs, the heart rhythm gradually normalizes. By the end of 100
minutes, the standard deviations of the RR -interval were within the functional norm
( 30=SDNN ms). As can be seen from Fig. 7, the positive dynamics of intravenous
infusion of drugs is clearly illustrated by the graph of Levenshtein distances
),( 0SSL t changing.
The analysis of the Levenshtein distance was also used to monitor the con-
dition of patient S. (male, 61) diagnosed with atrial fibrillation combined with
arterial hypertension, who was hospitalized for 47 days in a hospital for scien-
tists of the National Academy of Sciences of Ukraine. Monitoring was carried
twice a day (Fig. 8).
The patient was treated with antiarrhythmic drugs (Digoxin et al.) and
blood pressure lowering drugs (Captopres, etc.). Periodically intravenous infu-
sions of a number of drugs were conducted.
During the entire period of treatment, the patient's condition was stable,
which was reflected only by insignificant fluctuations of the Levenshtein dis-
tance between codograms except for some moments of time
(Fig. 8). One of such measurements, marked by an arrow in Fig. 8, was associ-
ated with the treadmill study, when the heart rate was 139 beats / min, and the
T -wave symmetry index assumed an excessively high value 05,2=βT unit.
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35
40
45
50
55
60
1 11 21 31 41 51 61 71 81 91 t
)(⋅L
Fig. 8. Monitoring of state patient S
RR,s RR,s
% %
Fig. 9. Histograms RR- intervals before (left) and after (right) treatment of patient S
Daily monitoring of ECG indices using the method fasegraphy combined with
monitoring of Levenshtein distances, confirmed the effectiveness of the medical
treatment of the patient B.: the index decreased from the initial value of ms to the
value of ms. heart rate variability decreased by 73%, what clearly illustrates the com-
parison of the histograms of the durations of the RR -intervals (Fig. 9).
In conclusion we note that the considered approach of ECG coding with
subsequent analysis of the Levenshtein distance between codograms can natu-
rally be generalized to the cases when not only the intervals RR − and indicator
Tβ are used for ECG coding, but also other informative indicators, in particular,
amplitudes of R and T waves.
CONCLUSIONS
The proposed approach is based on converting sequences of parameters that
characterize the form of individual electrocardiogram cycles into a word — a
finite string of characters of a given alphabet. The words (codograms) obtained
in this way are analyzed on the basis of the Levenshtein distance, which deter-
Fainzilberg L.S., Dykach Ju.R.
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mines the minimum number of editing operations (inserting, deleting, and re-
placing a character) to convert one word into another.
The calculation of the Levenshtein distances between all pairs of codograms
of the group of subjects allows one to determine the reference codogram of this
group. Comparison of the Levenshtein distances, including the analysis of the
editorial distance between the current codogram and the reference codogram,
makes it possible to make diagnostic decisions about patient ownership of the
corresponding group.
An information technology based on the implementation of the components of
the proposed approach has been developed. Experimental studies conducted using
model and real data confirmed the potential diagnostic effectiveness of the proposed
approach for obtaining additional information in solving actual applied problems. Of
course, from the point of view of evidence-based medicine, such research should be
continued on a significantly larger amount of clinical material.
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Issue 10. P. 32–48.
Отримано 01.04.2019
Файнзільберг Л.С.1, д-р техн. наук, професор,
голов. наук. співроб. відд.
інтелектуальних автоматичних систем
e-mail: fainzilberg@gmail.com
Дикач Ю.Р.2, студент
факультет біомедичної інженерії
e-mail: jul.dykach@gmail.com
1 Міжнародний науково-навчальний центр
інформаційних технологій та систем
НАН України та МОН України,
пр.-т. Академіка Глушкова, 40, м. Київ, 03187, Україна,
2 Національний технічний університет України
«Київський політехнічний інститут імені Ігоря Сікорського»,
пр.-т. Перемоги, 37, м. Київ, 03056, Україна
ЛІНГВІСТИЧНИЙ ПІДХІД ДЛЯ ОЦІНЮВАННЯ ТОНКИХ ЗМІН
ЕЛЕКТРОКАРДІОГРАМИ НА ОСНОВІ ВІДСТАНІ ЛЕВЕНШТЕЙНА
Вступ. Лінгвістичний підхід, оснований на переході від ЕКГ до кодограми, здобув популяр-
ність для аналізу серцевого ритму. Для розширення функнальних можливостей методу доці-
льно вивчити можливості одночасного контролю динаміки тривалості серцевих циклів і
оригінального показника, який несе інформацію про ішемічні зміни міокарда.
Мета статті — розробити алгоритмічні і програмні компоненти для розв’язання цього
завдання і провести експериментальні дослідження за модельними і реальними даними.
Методи. Забезпено автоматичне кодування ЕКГ, обчислення відстаней Левенштейна
між парами ЕКГ певної групи випробовуваних і побудова референтної кодограми групи.
Оцінювання результатів експериментальних досліджень проводилося на основі традиційних
методів статистичного аналізу.
Результати. Показано, що на основі відстаней Левенштейна між усіма парами кодограм
групи випробовуваних можна визначити референтну кодограму групи хворих на ішемічну
хворобу серця (ІХС) і групи здорових добровольців. Встановлено, що прийняття рішень на
основі порівняння кодограми ЕКГ випробуваного з еталонною кодограмою забезпечує поділ
представників зазначених груп з чутливістю SE = 72% і специфічністю CP = 79% навіть в
тих випадках, коли традиційний аналіз ЕКГ у 12 відведеннях виявляється неінформативним.
Висновки. Запропонований підхід дає змогу отримати додаткову діагностичну інфор-
мацію для вирішення актуальних завдань практичної медицини.
Ключові слова: лінгвістичний підхід, діагностична ознака ЕКГ, відстань Левенштейна.
Fainzilberg L.S., Dykach Ju.R.
ISSN 2663-2586 (Online), ISSN 2663-2578 (Print). Cyb. and comp. eng. 2019. № 2 (196) 26
Файнзильберг Л.С.1, д-р техн. наук, профессор,
глав. науч. сотр. отд.
интеллектуальных автоматических систем
e-mail: fainzilberg@gmail.com
Дыкач Ю.Р.2, студент,
факультет биомедицинской инженерии
e-mail: jul.dykach@gmail.com
1 Международный научно-учебный центр
информационных технологий и систем
НАН Украины и МОН Украины,
пр-т. Академика Глушкова, 40, г. Киев, 03187, Украина
2 Национальный технический университет Украины
«Киевский политехнический институт имени Игоря Сикорского»,
пр-т. Победы, 37, г. Киев, 03056, Украина
ЛИНГВИСТИЧЕСКИЙ ПОДХОД ДЛЯ ОЦЕНИВАНИЯ ТОНКИХ ИЗМЕНЕНИЙ
ЭЛЕКТРОКАРДИОГРАММЫ НА ОСНОВЕ РАССТОЯНИЯ ЛЕВЕНШТЕЙНА
Введение. Лингвистический подход, основанный на переходе от ЭКГ к кодограмме,
получил известность для анализа сердечного ритма. Для расширения функциональных
возможностей метода целесообразно изучить возможности одновременного контроля
динамики изменения продолжительности сердечных циклов и оригинального показа-
теля, несущего информацию об ишемических изменениях миокарда.
Цель статьи — разработать алгоритмические и программные компоненты для
решения этой задачи и провести экспериментальные исследования на модельных и
реальных данных.
Методы. Обеспечивалось автоматическое кодирование ЭКГ, вычисление рассто-
яний Левенштейна между парами ЭКГ определенной группы испытуемых и построе-
ние референтной кодограммы группы. Оценка результатов экспериментальных иссле-
дований проводилась на основе традиционных методов статистического анализа.
Результаты. Показано, что на основе расстояний Левенштейна между всеми па-
рами кодограмм группы испытуемых можно определить референтную кодограмму
группы больных ишемической болезнью сердца (ИБС) и группы здоровых доброволь-
цев. Установлено, что принятие решений на основе сравнения кодограммы ЭКГ испы-
туемого с эталонной кодограммой обеспечивает разделение представителей указанных
групп с чувствительностью SE = 72% и специфичностью CP = 79% даже в тех случаях,
когда традиционный анализ ЭКГ в 12 отведениях оказывается неинформативным.
Выводы. Предложенный подход позволяет получить дополнительную диагности-
ческую информацию при решении актуальных задач практической медицины.
Ключевые слова: лингвистический подход, диагностический признак ЭКГ, расстояние
Левенштейна.
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/KOR <FEFFc7740020c124c815c7440020c0acc6a9d558c5ec0020b370c2a4d06cd0d10020d504b9b0d1300020bc0f0020ad50c815ae30c5d0c11c0020ace0d488c9c8b85c0020c778c1c4d560002000410064006f0062006500200050004400460020bb38c11cb97c0020c791c131d569b2c8b2e4002e0020c774b807ac8c0020c791c131b41c00200050004400460020bb38c11cb2940020004100630072006f0062006100740020bc0f002000410064006f00620065002000520065006100640065007200200035002e00300020c774c0c1c5d0c11c0020c5f40020c2180020c788c2b5b2c8b2e4002e>
/NLD (Gebruik deze instellingen om Adobe PDF-documenten te maken voor kwaliteitsafdrukken op desktopprinters en proofers. De gemaakte PDF-documenten kunnen worden geopend met Acrobat en Adobe Reader 5.0 en hoger.)
/NOR <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>
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/SVE <FEFF0041006e007600e4006e00640020006400650020006800e4007200200069006e0073007400e4006c006c006e0069006e006700610072006e00610020006f006d002000640075002000760069006c006c00200073006b006100700061002000410064006f006200650020005000440046002d0064006f006b0075006d0065006e00740020006600f600720020006b00760061006c00690074006500740073007500740073006b0072006900660074006500720020007000e5002000760061006e006c00690067006100200073006b0072006900760061007200650020006f006300680020006600f600720020006b006f007200720065006b007400750072002e002000200053006b006100700061006400650020005000440046002d0064006f006b0075006d0065006e00740020006b0061006e002000f600700070006e00610073002000690020004100630072006f0062006100740020006f00630068002000410064006f00620065002000520065006100640065007200200035002e00300020006f00630068002000730065006e006100720065002e>
/ENU (Use these settings to create Adobe PDF documents for quality printing on desktop printers and proofers. Created PDF documents can be opened with Acrobat and Adobe Reader 5.0 and later.)
>>
/Namespace [
(Adobe)
(Common)
(1.0)
]
/OtherNamespaces [
<<
/AsReaderSpreads false
/CropImagesToFrames true
/ErrorControl /WarnAndContinue
/FlattenerIgnoreSpreadOverrides false
/IncludeGuidesGrids false
/IncludeNonPrinting false
/IncludeSlug false
/Namespace [
(Adobe)
(InDesign)
(4.0)
]
/OmitPlacedBitmaps false
/OmitPlacedEPS false
/OmitPlacedPDF false
/SimulateOverprint /Legacy
>>
<<
/AddBleedMarks false
/AddColorBars false
/AddCropMarks false
/AddPageInfo false
/AddRegMarks false
/ConvertColors /NoConversion
/DestinationProfileName ()
/DestinationProfileSelector /NA
/Downsample16BitImages true
/FlattenerPreset <<
/PresetSelector /MediumResolution
>>
/FormElements false
/GenerateStructure true
/IncludeBookmarks false
/IncludeHyperlinks false
/IncludeInteractive false
/IncludeLayers false
/IncludeProfiles true
/MultimediaHandling /UseObjectSettings
/Namespace [
(Adobe)
(CreativeSuite)
(2.0)
]
/PDFXOutputIntentProfileSelector /NA
/PreserveEditing true
/UntaggedCMYKHandling /LeaveUntagged
/UntaggedRGBHandling /LeaveUntagged
/UseDocumentBleed false
>>
]
>> setdistillerparams
<<
/HWResolution [2400 2400]
/PageSize [612.000 792.000]
>> setpagedevice
|