This work is devoted to evaluating the effectiveness of the electrocardiological study process without using and using cardiological decision support systems. To assess the effectiveness, analytical expressions of the probabilistic-time characteristics of the developed structural model of the electrocardiological study process are used. An analysis of the time characteristics of the model is performed when different initial conditions are set for three different types of electrocardiological studies: the study is conducted for the first time, the study is repeated as a result of screening, the study is repeated after treatment. The work shows that the use of cardiological decision support systems based on the developed methods for analyzing biomedical signals with locally concentrated features reduced the average time required for the electrocardiological study of each of the considered types.
Currently, a sharp increase in the amount of information processed in solving traditional medical problems has led to the introduction of various medical information systems (MIS) into modern medicine, from simple electronic medical records to complex decision support systems (DSS) [1-3]. The electrocardiological (ECG) study process is based on the analysis of biomedical signals (BMS) with locally concentrated features (LCF) associated with the cyclic work of the heart and cardiovascular system [4]. Various computerized cardiological systems, including cardiological DSS, are used to automate the collection and processing of such information. The authors developed the structural model of the ECG study process in the form of a probabilistic-time graph, which made it possible to obtain analytical expressions for the analysis of this process given initial conditions (the presence or absence of previous examinations and treatment), as well as determine the criteria for the effectiveness of ECG studies [5]. 2
A review of the literature showed that most often attention is paid to the analysis of individual stages of the ECG study process, among which the following: • detection of indications for examination; • recording and digitization of BMS with LCF; • preprocessing of BMS with LCF; • morphological analysis of BMS with LCF; • detection of diagnostic indicators; • diagnostics and issuing a diagnostic report.
The quality and effectiveness of the ECG study depend on the quality of the recording BMS with LCF.
As a result of preprocessing of BMS with LCF, there are most often performed removing artifacts from the signal by methods based on the use of various types of filters [6, 7] and of wavelet transform [8-10], compensation of the isoline drift by methods based on interpolation of the ECG isoelectric line [11, 12].
One of the difficult and critical stages is the stage of the morphological analysis of BMS with LCF for which various methods are used: ─ analysis of BMS with LCF in the time domain using modern classification methods such as cluster analysis and pattern recognition [13, 14], probabilistic classification [15], neural networks [16], fuzzy clustering [17, 18]; ─ analysis of BMS with LCF in the time-frequency domain, for example, local (window) Fourier transform (spectral-time mapping) and wavelet transform [19, 20], as well as in the phase plane [4]; ─ morphological filtration of BMS with LCF using the multichannel matched morphological filter proposed by the authors [21].
Diagnostic features are formed in the form of parameters of the found structural elements based on the morphological analysis of BMS with LCF [22, 23]. Thus, errors at the stage of the morphological analysis of BMS with LCF can lead to the incorrect diagnostic solutions.
Therefore, the quality of the ECG study directly depends on the quality of the morphological analysis of BMS with LCF.
Different MISs are used with varying degrees of effectiveness at each of the listed stages. However, a systematic analysis of the ECG study process without using and using cardiological DSS is not found in literary sources.
The aim of the work is to analyze the effectiveness of the ECG study process without using and using cardiological DSS based on the morphological analysis of BMS with LCF.
To achieve this goal, the following tasks are solved: ─ to determine the average examination time under various initial conditions by the developed structural model; ─ to evaluate the effectiveness of ECG studies without using and using cardiological
DSS by the developed criterion. 4
Let us consider the structural model developed in [5] for the process of ECG study, shown in Fig. 1.
S9
1
S8
1
(
S1 that when finding the products of the arc functions, the probabilities pij are multiplied and the times tij are summed:
fij (z) = pij z tij , where z – a parameter of the arc function, the degree of which characterizes the time of transition from one state to another ( z 1 ).
The following states are identified in the structural model MS : S0 – the beginning
of the study; S1 – indications were defined; S2 – morphological analysis of BMS
with LCF was performed; S3 – pathological changes were identified; S4 –
comparison with previous ECG studies was performed; S5 – dynamics evaluation was
completed; S6 – evaluation of treatment effectiveness was completed; S7 – the diagnostic
decision was made; S8 – recommendations were issued (the end of the ECG study);
S9 – a set of states that do not lead to the goal (the state of uncertainty); fij(z) ,
i, j = 0;9 – arc function by (
In [5], it is indicated that the structural model MS is no state associated with the direct recording of the ECG signal because the duration of the ECG signal recording is strictly regulated by the protocol of the type of the ECG study and can vary from several minutes to several hours and days. That is, this time cannot be optimized, and the duration of the recording process does not affect the effectiveness of the ECG study.
The generating function of the graph shown in Fig. 1 has the following form:
F(z) = F08(z) + F09(z) ,
(
F09(z) = p01((1− p12)zt19 + p12((1− p21 − p22 − p23)zt29 + + p23((1− p31 − p32 − p34 − p37)zt39 +p34((1− p45 − p46)zt49 +
+ p45((1− p57)zt59 + p57(1− p77 − p78)zt57+t79 )zt45 + + p46((1− p67)zt69 + p67(1− p77 − p78)zt67+t79 )zt46 )zt34 + + p37(1− p77 − p78)zt37+t79 )zt23 )zt12 )zt01 (1− p77zt77 ) (1− p12(p21(1+ p23p32zt23+t32 )zt21 + p23p31zt23+t31 )zt12 − p23p32zt23+t32 − p22zt22 ).
Using the generating function (
PECG = F(z) z=1; TECG = dF(z) .
dz z=1
Since the analytical expressions for the probability PECG and the average time TECG of an ECG study are too cumbersome, in [5] the authors developed a program in the Matlab language for getting these analytical expressions as well as an analytical ex+ pression of the probability PECG of a successful ECG study which has the following form taking into account restrictions: PE+CG = p34 p37 = 0; p34 + p37 (0;1; p45 p46 = 0; p45 + p46 (0;1.
Also in [5], there were proposed the following criteria for the effectiveness of the ECG study process by the average time taken to complete the study and the probability of its successful completion: TECG → min; p34 p37 = 0; p34 + p37 (0;1; p45 p46 = 0; p45 + p46 (0;1; PE+CG → max; p34 p37 = 0; p34 + p37 (0;1; p45 p46 = 0; p45 + p46 (0;1.
Let us use the obtained analytical expressions that describe the probabilistic-time characteristics of the ECG study process under given initial conditions (the presence or absence of previous examinations and treatment), as well as use the proposed criteria of the effectiveness for analysis and optimization of the entire process and its individual stages. 5
To analyze the probabilistic-time characteristics of the ECG study process, it is necessary to set the initial conditions.
According to the structural model M S of the ECG study (Fig. 1), there are three alternative ways of transition from the initial state S0 to the final state S8 which correspond to three different types of ECG studies [5]: • the study is conducted for the first time; • the study is repeated as a result of screening; • the study is repeated after treatment.
In this case, let us consider a simplified version of the model when the ECG study process does not go into a state of uncertainty S9 , that is p19 = p29 = p39 = p49 = p59 = p69 = p79 = 0 and t19 = t29 = t39 = t49 = t59 = t69 = t79 = 0 . Since all transitions from the current state Si form a complete group of events, the following expressions can be written: p01 = p12 = p57 = p67 = 1;
p23 + p21 + p22 = 1 ;
p34 + p37 + p31 + p32 = 1 ;
p45 + p46 = 1 ;
p78 + p77 = 1 .
(
Let us denote PECG – probability of transition to a state of uncertainty S9 , then,
taking into account the simplified model ( p19 = p29 = p39 = p49 = p59 = p69 = p79 = 0 )
− +
PECG = 0 , which means PECG = 1 for any admissible probability values in the
expression (
In this case, the analytical expression for the average time Tsimp of the ECG study,
calculated according to the simplified model, is too cumbersome, but it is easy to
obtain using the program in the Matlab language, if, taking into account (
Let us analyze the average time of conducting an ECG study using a simplified model M S separately for each of the cases under different initial conditions. Moreover, in each of the cases we will consider the average execution time of each stage for three options: ─ using cardiological DSS with the module of morphological analysis of BMS with
LCF (DSS1) developed by the authors [21]; ─ using cardiological DSS in which the morphological analysis of BMS with LCF is performed in a semi-automatic mode (DSS2); ─ without using any MIS (without MIS).
In all experiments, we take p21 = p31 = 0 . Then according to (5) p22 = 1 − p23 . 5.1
If an ECG study is conducted for the first time, then p34 = 0 , and then a simplified structural model of an ECG study has the form shown in Fig. 2.
The analytical expression for the average time T1 of the ECG study, which is conducted for the first time, was obtained from the Matlab, performing the following substitution at the end of the program given in [5]: T1 = simplify(subs(Tsimpl, p34, 0));
Let us consider the dependence T1 ( p23 ) under the following initial conditions: p37 = p78 = 1 . The initial conditions for the average execution time of each stage are given in Table 1. It should be noted here that only the time t12 differs when conducting an ECG study with DSS1 and DSS2 (Table 1).
Table 2 shows the minimum and maximum values of the average time T1 of the ECG study without using and using cardiological DSS in experiments at different values p32 .
From an analysis of the data presented (Table 2 and Fig. 3), we can conclude that in each of the experiments the following trend is observed: ─ max T1DSS1 min T1DSS2 (for p32 = 0 and p32 = 0.1 ); ─ max T1DSS1 min T1DSS2 (for p32 = 0.3 ); ─ max T1DSS1 min T1without MIS and max T1DSS2 min T1without MIS (for all values p32 ). 5.2
If the ECG study is repeated as a result of screening, then p37 = 0 and p46 = 0 , and then the simplified structural model of the ECG study has the form shown in Fig. 4.
Let us consider the dependence T2 ( p23 ) under the following initial conditions: p34 = p45 = p57 = p78 = 1 . The initial conditions for the average execution time of each stage are given in Table 3. As in the first case, only the time t12 differs when conducting an ECG study with DSS1 and DSS2 (Table 3). ECG study without using and using DSS in experiments at different values p32 . study without using and using cardiological DSS at various initial values p32 .
If the ECG study is repeated after treatment, then p37 = 0 and p45 = 0 , and then the simplified structural model of the ECG study has the form shown in Fig. 6. The analytical expression for the average time T3 of the ECG study that is repeated as a result of screening was obtained from the Matlab, performing the following substitution at the end of the program given in [5]: T3 = simplify(subs(Tsimpl,[p37, p45, p46],[0, 0, 1]));
Let us consider the dependence T3 ( p23 ) under the following initial conditions: p34 = p46 = p67 = p78 = 1 . The initial conditions for the average execution time of each stage are given in Table 5. As in the first two cases, only the time t12 differs when conducting an ECG study with DSS1 and DSS2 (Table 5).
without using and using cardiological DSS: a) p32 = 0 ; b) p32 = 0.1 ; c) p32 = 0.3 ; d) p32 = 0.5 ─ ─ ─ 6
From an analysis of the data presented (Table 6 and Fig. 7), we can conclude that in each of the experiments, the trend described for the first two cases remains: max T3DSS1 min T3DSS2 (for p32 = 0 and p32 = 0.1 ); max T3DSS1 min T3DSS2 (for p32 = 0.3 ); max T3DSS1 min T3without MIS and max T3DSS2 min T3without MIS (for all values p32 ).
In this work, using the simplified structural model of an ECG study, analytical expressions were obtained to calculate the average execution time of this process for three different types of studies: the study is conducted for the first time, the study is repeated as a result of screening, the study is repeated after treatment.
Using the obtained analytical expressions, an analysis of the time characteristics of the ECG study was performed without using and using cardiological DSS separately for each of the considered study types. The above data show that the use of any cardiological DSS significantly reduces the time for the ECG study of each of the considered types, even if the worst option of the ECG study using any cardiological DSS was being compared with the best option of the ECG study without using any MIS. Moreover, if cardiological DSS is used with an improved module for the morphological analysis of BMS with LCF (DSS1) then even the best option for conducting the ECG study using DSS2 in almost all cases is inferior in time to the worst option for conducting the ECG study using DSS1.
Further studies are aimed at experimental verification of the effectiveness of ECG
studies both in time and in the probability of successful completion of the considered
process under various initial conditions using the proposed full structural model.
entific and Technical Journal “Problems of control and informatics”, 2, pp 58–71 (in
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