Analysis of instantaneous cardiac rhythm in a model of multifractal dynamics based on Holter monitoring

详细信息    查看全文

• 作者：A. P. Ivanov ; A. N. Kudinov ; D. Yu. Lebedev…
• 关键词：instant cardiac rhythm ; multifractal dynamics ; piecewise linear trend ; fractal dimension ; self ; similarity
• 刊名：Mathematical Models and Computer Simulations
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：8
• 期：1
• 页码：7-18
• 全文大小：548 KB
• 参考文献：1.A. N. Kudinov, D. Yu. Lebedev, V. P. Tsvetkov, and I. V. Tsvetkov, “Mathematical model of the multifractal dynamics and analysis of heart rates,” Math. Models Comput. Simul. 7, 214–221 (2015).CrossRef MathSciNet
  2.A. N. Kudinov, V. P. Tsvetkov, and I. V. Tsvetkov, “Catastrophes in the multi-fractal dynamics of social-economic systems,” Russ. J. Math. Phys. 18, 149–155 (2011).CrossRef MathSciNet MATH
  3.L. V. Shpak, Cardiointervalography and its Clinical Significance: A Teaching Aid (Faktor, Tver, 2002) [in Russian].
  4.R. M. Baevskii, Prediction of States on the Verge of Norm and Pathology (Meditsina, Moscow, 1979) [in Russian].
  5.G. V. Ryabykina and A. V. Sobolev, ECG Monitoring with the Analysis of Heart Rate Variability (Medpraktika-M, Moscow, 2005) [in Russian].
  6.R. M. Bayevsky, G. G. Ivanov, L. V. Chireyin, et al., “HRV Analysis under the usage of different electrocardiography systems (methodical recommendations),” Vestn. Aritmol. 24, 65–87 (2001).
  7.O. S. Gulyaeva and I. V. Tsvetkov, “Determination of fractal dimension by measuring the time series chart lengths in various time scales,” Vestn. Tver. Univ., Ser. Prikl. Mat., No. 17 (45), 155–160 (2007).
  8.O. I. Krylova and I. V. Tsvetkov, “Complex of the programs and algorithm of calculation of the fractal dimensions and a linear trend of the time series,” Program. Produkty Sist., No. 4, 87–90 (2012).
  9.I. V. Tsvetkov, “Catastrophe theory and fractal model for crisis socio-economic processes,” Vestn. Tver. Univ., Ser. Prikl. Mat., No. 12, 55–59 (2010).
  10.M. Ryan, B. Lown, and H. Horn, “Comparison of ventricular ectopic activity during 24-hour monitoring and exercise testing in patients with coronary heart disease,” New England J. Med. 292, 224–229 (1975).CrossRef
  
• 作者单位：A. P. Ivanov (1)
  A. N. Kudinov (2)
  D. Yu. Lebedev (2)
  V. P. Tsvetkov (2)
  I. V. Tsvetkov (2)
  
  1. Tver Regional Cardiology Centre, Tver, Russia
  2. Tver State University, Tver, Russia
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematical Modeling and IndustrialMathematics
  Simulation and Modeling
  Russian Library of Science
  
• 出版者：MAIK Nauka/Interperiodica distributed exclusively by Springer Science+Business Media LLC.
• ISSN：2070-0490

文摘

For the specific analysis of the variability of RR intervals of the cardiac rhythm, a method for measuring the instantaneous cardiac rhythm (ICR) represented by a multifractal dynamical model (MDM) has been developed. The advantages of this method, compared to the statistical methods of analysis of the RR intervals used, have been demonstrated. The method allows possible catastrophes of the cardiovascular system to be predicted. Using the data of Holter monitoring and the program system developed, we have plotted ICR curves, an ICR piecewise linear trend, and variability charts for three randomly chosen time intervals. The self-similarity (fractality) of the ICR up to an accuracy of 5% has been shown based on the explicit data. The MDM parameters have been calculated based on the ICR data. The analysis of the dynamics of these parameters has been conducted and their compliance with the status of the patient examined has been studied. The relevance of the ICR examination within MDM is closely related to the necessity of recognizing new markers of adverse cardiovascular episodes. The research performed shows that the results obtained could be taken as a basis for developing a new mathematical method of ICR examination based on Holter monitoring. Keywords instant cardiac rhythm multifractal dynamics piecewise linear trend fractal dimension self-similarity