A system of differential equations was found that describes the dynamics of the cardiac cycle. The dependence of the probability of finding the heart in the states of systole (systole) and diastole (diastole) on time and diagnostic parameters of the cardiac cycle is determined. Considered examples that illustrate the broad possibilities of applying the method of differential equations for the used dynamics of the cardiac cycle “normally” and in the presence of diseases. The initial data for solving the Cauchy problem are \(R \to R\) the duration \(T_{0}\) of the cardiac cycle and the systolic index of electromechanical activity of the heart \(K\) , determined by the electrocardiogram and Buzzet's formula.The obtained results can be useful to specialists who are professionally engaged in diagnosing cardiovascular systems and processing electrocardiograms. When evaluating the daily parameters of Holter heart rhythm monitoring, the automated analysis of electrocardiograms allows you to verify heart rhythm parameters under the condition of ensuring the minimum full probability of a diagnostic error. In this case, the minimum full probability of a correct diagnosis is ensured with limited resources spent on studying and processing the electrocardiogram. To solve the problem of verifying the parameters of the heart, an approach to solving the problem of mathematical modeling of the dynamics of the cardiac cycle is proposed by using the method of comparisons and solving differential equations, which are a formal description of the change in the state of the heart during the cardiac cycle, and the detection of integral diagnostic parameters.

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Mathematical Modeling of Cardiac Cycle Dynamics

  • Viktor Semko,
  • Oleksiy Semko

摘要

A system of differential equations was found that describes the dynamics of the cardiac cycle. The dependence of the probability of finding the heart in the states of systole (systole) and diastole (diastole) on time and diagnostic parameters of the cardiac cycle is determined. Considered examples that illustrate the broad possibilities of applying the method of differential equations for the used dynamics of the cardiac cycle “normally” and in the presence of diseases. The initial data for solving the Cauchy problem are \(R \to R\) the duration \(T_{0}\) of the cardiac cycle and the systolic index of electromechanical activity of the heart \(K\) , determined by the electrocardiogram and Buzzet's formula.The obtained results can be useful to specialists who are professionally engaged in diagnosing cardiovascular systems and processing electrocardiograms. When evaluating the daily parameters of Holter heart rhythm monitoring, the automated analysis of electrocardiograms allows you to verify heart rhythm parameters under the condition of ensuring the minimum full probability of a diagnostic error. In this case, the minimum full probability of a correct diagnosis is ensured with limited resources spent on studying and processing the electrocardiogram. To solve the problem of verifying the parameters of the heart, an approach to solving the problem of mathematical modeling of the dynamics of the cardiac cycle is proposed by using the method of comparisons and solving differential equations, which are a formal description of the change in the state of the heart during the cardiac cycle, and the detection of integral diagnostic parameters.