Application of probabilistic-time graphs for evaluating the effectiveness of the electrocardiological study process

Abstract

This work is devoted to the development of a structural model of the patient’s electrocardiological study process
based on graph theory, probability theory and the method of generating functions. The developed structural model is presented in the
form of a probabilistic-time graph, in which nine main states and an uncertainty state (a set of states that do not lead to the goal) are
identified, as well as the probabilistic-time characteristics of the arcs of transitions from one graph state to another. The following
are identified as the main states characterizing the process to complete an electrocardiological study: the beginning of the study;
indications were defined; morphological analysis of biomedical signals with locally concentrated features was performed;
pathological changes were identified; comparison with previous electrocardiological studies was performed; dynamics evaluation
was completed; evaluation of treatment effectiveness was completed; diagnostic decision was made; recommendations were issued
(the end of the electrocardiological study). For the proposed model of the electrocardiological study process by the Mason method,
there are obtained analytical expressions for the generating functions of the entire graph, as well as the part of the graph that
characterizes the successful completion of the electrocardiological study. Using the indicated generating functions, analytical
expressions were obtained to calculate the average transit time of an electrocardiological study and the probability of successful
completion of this process. To get all analytic expressions, a program was written in the Matlab language. The developed structural
model of an electrocardiological study in the form of a probabilistic-time graph made it possible to identify the main states and
determine the criteria for the effectiveness of the process in terms of average time and the probability of a successful study.